Hssc i objective workbook

Mathematics

Objective

MathematicsMATHEMATICS

DEPARTMENT

PAKTURK INTERNATIONAL SCHOOLS AND COLLEGES

Intermediate Part I

By Engin Baştürk

PAKTURK

PAKTURKMATHEMATICS

DEPARTMENT

Copyright PAKTURK MATHS DEPARTMENT, 2015

All rights reserved. No part of this publication may be reproduced,translated, stored in a retrieval system of transmitted, in any form or by any means, without the prior permission of PAKTURK MATHS DEPARTMENT.

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For any question mail us at [email protected]

Composed by Engin Baştürk FEDERAL BOARD

TYPE Objective Number System No 1

Q1: a bi can be written also as:

A) a bi B) ,a b

C) a bi D) ,b a


A) a bi B) a bi

C) ,a b D) ,a b


A) a bi B) a bi

C) ,a b D) a bi

Q4: What is the value of 2

i ?

A) 0 B) -1

C) 1 D) i

Q5: i can be written as:

A) 1,0 B) 0,1

C) 1,0 D) 0, 1

Q6: 2

i can be written as ............

A) 1,0 B) 0,1

C) 1,0 D) 0, 1

Q7: What is the value of 40

i ?

A) 0 B) -1

C) 1 D) i

Q8: The real part of a complex number a bi is .......

A) b B) 0,1

C) a D) 0, 1

Q9: The imaginary part of a complex number a bi is:

A) b B) 0,1

C) a D) 0, 1

Q10: Any real number a can be written as: (as order pair of

complex numbers)

A) ai B) 0,a

C) ,1a D) ,0a


Q11: , , ?a b c d

A) ,ac bd ad bc B) .ad bc ac bd

C) ,bd ac ad bc D) ,ac bd ad bc

Q12: ?a bi c di

A) ac bd ad bc i

B) bd ac ad bc i

C) ad bc ac bd i

D) ac bd ad bc i

Q13: , , ?a b c d

A) ,a d b c B) ,a c b d

C) 2 ,2a d D) ,b d a c

Q14: ?a bi c di

A) a d b c i B) a c b d i

C) a c b d i D) b d a c i

Q15: , , ?r R r a b

A) ,a b B) ,ra b

C) ,a rb D) ,ra rb

Q16: If 1, .........z a bi z

A) a bi B) a bi

C) 2 2 2 2

a bi

a b a b

D)

2 2 2 2

a bi

a b a b

Q17: If 1, , .........z a b z

A) ,a b B) ,a b

C) 2 2 2 2

,a b

a b a b

D) 2 2 2 2

,a b

a b a b

Q18: If 11,2 , .........z z

A) 1

1,2

B) 1 1

,2 5

C) 1 2

,5 5

D) 1 2

,5 5

Q19: If 15 3 , .........z i z

A) 5 3

34 34i B)

5 3

34 34i

C) 5 3

34 34i D)

5 3

34 34i

Q20: Simplify 4

2 2i

A) 1 i B) 1 i

C) 2i D) i

Answer Key

1 2 3 4 5 6 7 8 9 10

B D A B B C C C A D

11 12 13 14 15 16 17 18 19 20

D A B C D C D D A B



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Q1: Every real number is also a .............

A) Natural Number B) Complex Number

C) Rational Number D) Whole Number

Q2: If z a bi then z is:

A) a ib B) a ib

C) a ib D) 2 2

a b

Q3: If z a ib , then z a ib is called …...... of z

A) Root B) Inverse

C) Conjugate D) Identity

Q4: The complex number "a "i is called purely:

A) Real B) Complex

C) imaginary D) None

Q5: z is same with ……………

A) z B) z

C) z D) z

Q6: If a+ bz i , then z ________

A)2 2

a b B) 2 2

a b

C) a b D) None of these

Q7: If z a bi then z

A) 2 2

a b B) 2 2

a b

C) 2 2

a b D) 2 2

a b

Q8: Find the modulus of 3 4i

A) 5 B) 5

C) 5 D) 5

Q9: If 7 2z i then z

A) 53 B) 53

C) 53 D) 45

Q10: If 1 5 4z i and 2 5 2z i then 1 2 ...........z z

A) 4i B) 10

C) 10 D) 2i


Q11: Which of the following is equal to 2

z

A) 2

z B) .z z

C) 2

z D) z

Q12: 81 16 is equal to ………

A) 5i B) 5i

C) 13i D) 12i

Q13: 64 100 is equal to ………

A) 2i B) 2i

C) 18i D) 18i

Q14: 12 144 is equal to ………

A) 12 2 3i B) 12 2 3i

C) 12 2 3i D) 12 4 3i

Q15: The polar form of a complex number is ….

A) tan cotr i B) sin cosr i

C) sec cscr i D) sec cscr i

Q16: 1 3

........2 2

i

A) 3 B) 1

C) 2 D) 0

Q17: 2

............1 i

A) 1 i B) 1 i

C) 2 1 i D) 2 1 i

Q18: 7

5

is ……..

A) 7

5

i

i B)

7

5

C) 7

5i D) None of these

Q19: The additive identity in Complex numbers is:

A) 0,0 B) 1,1

C) 1,0 D) 0,1

Q20: In terms of i , 3 ______.

A) 3i B) 3 i

C) 3 i D) 3i

Answer Key

1 2 3 4 5 6 7 8 9 10

B A C C C B B A A D

11 12 13 14 15 16 17 18 19 20

B A B A B B A C C B



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Q1: 0 is ................

A) Positive Integer B) Irrational Number

C) Negative Number D) Complex Number

Q2: If z a bi then z z

A) 2a B) 2a bi

C) 2 2a bi D) 2bi

Q3: If z a bi then z

A) a bi B) a bi

C) a bi D) a bi

Q4: If 2 3z i then z

A) 2 3i B) 2 3i

C) 2 3i D) 3 2i

Q5: A complex Number is called zero complex number if ............x y

A) B) 0

C) Non-zero D) Equal

Q6: 22,z C z z

A) Imaginary B) Real

C) Zero D) Negative

Q7: , cos sin ......n

n Z i

A) sin cosn i n B) tan cotn i n

C) cos sinn i n D) cos sinn i n

Q8: The numerical value of 2

i is ________

A) 1 B) 1 C) i D) 1

Q9: The product of two imaginary no is always:

A) Imaginary B) Real

C) Negative D) None of these

Q10: The quotient of two imaginary numbers in simplest

form is always ….

A) Real number B) Imaginary number

C) Positive D) negative


Q11: The value of 56

i is ………..

A) i B) -1 C) 1 D) i

Q12: Simplify 3

2 2i

A) 1 i B) 1 i C) 2i D) 3 3

4

i

Q13: Simplify 4 1 1i i

A) 8 B) 8i C) 4i D) 8

Q14: Simplify 4 4

1

i

i

A) 8 B) 8i C) 4i D) 4i

Q15: Simplify 31 i

A) 1 i B) 2 1 i

C) 1 i D) 2 1 i

Q16: 31 ?i

A) 3 3i B) 2 2i

C) 2 2i D) 2 2i

Q17: Simplify 21 i

A) 2 B) 1 C) 2i D) 2i

Q18: Simplify 21 i

A) 0 B) 1 C) 2i D) 4i

Q19: Simplify 21 2i i

A) 0 B) 2i C) 4i D) 2i

Q20: 112 ?i

A) 1 B) 0 C) 1 D) 2

Answer Key

1 2 3 4 5 6 7 8 9 10

D A C A B B D B B A

11 12 13 14 15 16 17 18 19 20

B D A C B D D C B C



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Q1: 7 is ........

A) an irrational number B) a prime number

C) a rational number D) a whole number

Q2: Golden rule of fraction is that for 0, ...........a

kb

A) ab

k B)

k

ab

C) kb

ka D)

ka

kb

Q3: Whicf of the following sets has closure property with

respect to addition?

A) 1,1 B) 1

C) 1 D) 0

Q4: Whicf of the following sets has closure property with

respect to multiplication?

A) 1,1 B) 1

C) 1,0 D) 0,2

Q5: For , , , , 0, 0a b c d R b d then a c

b d

A) ac bd

bd

B)

ab cd

bd

C) ad bc

bd

D) abcd

Q6: Rational Numbers expressed in the form of ……..

A) a

b B)

a

b

C)

2

2

a

b D) ab

Q7: For any two real No’s , 0x y x y the x and y

are …………. of each other.

A) Identity B) Inverse

C) Reciprocal D) None of these

Q8: For any two real numbers , . 1x y x y , this property

is called as …………..

A) Multiplicative Identity B) Multiplicative inverse

C) additive inverse D) none of these

Q9: The property used in 11 11 0 is said to be:

A) Additive Inverse B) Additive identity

C) Inverse D) None of These

Q10: For , ,a b c a c b c a b , this

property is called _________ property w.r.t to addition.

A) Additive B) Multiplicative

C) Cancelation D) None of these


Q11: Which of the following sets has closure property w.r.t

multiplication ________?

A) 0 B) 0,1

C) 1,1

D) 0, 1

Q12: The value of 2 is …………

A) Rational Number B) Irrational number

C) Natural number D) None of these

Q13: Which of the following sets has closure property w.r.t

multiplication ________?

A) 2, 1,0 B) 2,0,1

C) 0, 1,1

D) 0, 1

Q14: The additive identity of real numbers is always ….

A) Two B) Three

C) One D) Zero

Q15: The property used in

, ,x y z x y z x z y z is ……… property.

A) Distributive B) Commutative

C) Associative D) None

Q16: The sum of Real and Imaginary numbers is known as

….

A) Real Number B) Complex Number

C) Rational Number D) Irrational Number

Q17: Which of the following is associative property of real

numbers?

A) A B B A

B) A B C A B C

C) A B B A

D) A B C A B A C

Q18: Which of the following is commutative property of real

numbers?

A) A B B A

B) 3 4 5 3 4 5

C) 2 2 0

D) 4 1 4

Q19: Which of the following is additive property of real

numbers?

A) 4 4a b a b B) 4 4a b a b

C) 0a a D) 1

1aa

Q20: The sum of multiplicative identity and its multiplicative

inverse is:

A) 1 B) 0

C) 1 D) 2

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: , , 0, 0, .......a b R a b a b

A) a b B) a b

C) 1 1

a b D)

1 1

a b

Q2: 1 1

, , 0, 0, .......a b R a ba b

A) a b B) a b

C) 1 1

a b D) a b

Q3: , , 0, 0, .......a b R a b a b

A) a b B) a b

C) a b D) a b

Q4: If 0a then ..............

A) 0a B) 0a

C) 1

0a D)

10

a

Q5: If 0a then ..............

A) 0a B) 0 a

C) 1

0a D)

10

a

Q6: If a b b c c d then .................

A) a d B) a d

C) a d D) c a

Q7: If1 1

,a b

then ………….

A) a b B) a b

C)1 1

a b D) a b

Q8: If a b ,then …………..

A) a b B) a b

C)1 1

a b D) a b

Q9: What is the name of property used in

4 3 1 0

A) Multiplicative B) Additive

C) Identity D) None

Q10: , ,a b c R either a b and b c then a c . The

given property is called:

A) Trichotomy B) Transitive

C) Reflexive D) Symmetric


Q11: ,a b R either a b or a b or a b . The given

property is called:



Q12: What is the property used in 3 2 0 1

A) Additive property B) Multiplicative property

C) Transitive property D) Multiplicative Identity



C) Multiplicative Identity D) Transitive property




Q15: What is the property used in 0 0a a



Q16: What is the property used in 1 1

a ba b



Q17: What is the property used in a b a b









Q20: What is the property used in a b b a



Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: , , 0, 0, .......a b R a b a b

A) a b B) a b

C) 1 1

a b D)

1 1

a b

Q2: 1 1

, , 0, 0, .......a b R a ba b

A) a b B) a b

C) 1 1

a b D) a b

Q3: , , 0, 0, .......a b R a b a b

A) a b B) a b

C) a b D) a b

Q4: If 0a then ..............

A) 0a B) 0a

C) 1

0a D)

10

a

Q5: If 0a then ..............

A) 0a B) 0 a

C) 1

0a D)

10

a

Q6: If a b b c c d then .................

A) a d B) a d

C) a d D) c a

Q7: If1 1

,a b

then ………….

A) a b B) a b

C)1 1

a b D) a b

Q8: If a b ,then …………..

A) a b B) a b

C)1 1

a b D) a b

Q9: What is the name of property used in

4 3 1 0

A) Multiplicative B) Additive

C) Identity D) None

Q10: , ,a b c R either a b and b c then a c . The

given property is called:




Q11: ,a b R either a b or a b or a b . The given

property is called:












Q15: What is the property used in 0 0a a



Q16: What is the property used in 1 1

a ba b



Q17: What is the property used in a b a b









Q20: What is the property used in a b b a



Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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TYPE Objective Sets, Functions and Groups No 1

Q1: If A B , then the complement of B is ..........

A) A B B) U B C) A B D) A B

Q2: A set contaning only one element is called ........

A)Null set B) Empty Set

C) Singleton set D) Inverse set

Q3: 0 is ...........

A)Empty Set B) Singleton Set

C) Null Set D) Solution Set

Q4: If n A k , then ..........nP A

A) 2k B)

22 k C) 2k D)

2k

Q5: The set of students of PAKTURK is ..............

A) Infinite Set B) Finite Set

C) Empty Set D) Null Set

Q6: The set 1,2,3 is:

A) Infinite Set B) Singleton set

C) Empty Set D) Three point Set

Q7: If A , then ...........P A

A)Empty Set B) 0 C) D) None

Q8: The number of subsets of a set of 5 elements is ...........

A)32 B) 16 C) 4 D) 25

Q9: The set 1,2,3 , 1,2 has ............

A) Two elements B) Five element

C) Infinite elements D) One element

Q10: The union of two sets A and B is ..............

A) A B B) B A C) A B D) A B


Q11: The intersection of two sets A and B is ..............

A) A B B) B A C) A B D) A B

Q12: If A and B are disjoint sets, then ............

A) A B B) B A A

C) A B D) A B

Q13: If A and B are overlapping sets, then ...........

A) A B B) B A A

C) A B D) A B

Q14: ..........A B

A) B A B) B A C) A B D) B A

Q15: ..........A B

A) B A B) B A C) A B D) B A

Q16: ..........A B C

A) A B C B) A B C

C) A B C D) B A B

Q17: ..........A B C

A) A B C B) A B C

C) A B C A D) A B C

Q18: ..........A B C

A) A B A C B) A B A C

C) A B A C D) A B A C

Q19: ..........A B C

A) A B A C B) A B A C

C) A B A C D) A B A C

Q20: ..........A A B

A) B B) A B C) A B D) A

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: ..........A A B

A) B B) A B C) A B D) A

Q2: For a set A and the universal set U , C

A A

A) A B) C

A C) D) U

Q3: For a set A and the universal set U , CC

A

A) A B) C

A C) D) U

Q4: For a set A and the universal set U ,C

A A

A) A B) C

A C) D) U

Q5: For any subsets A and B of U , CA B

A) A B B) C C

A B C) C C

A B D)

Q6: For any subsets A and B of U , CA B

A) A B B) C C

A B C) C C

A B D)

Q7: ..........C

C CA B

A) A B B) C C

A B C) A B D) C C

A B

Q8: ..........C

C CA B

A) A B B) C C

A B C) A B D) C C

A B

Q9: If B A , then the shaded region represents ……

A) A B B) C C

A B C) A B D) C C

A B

Q10: The number of subsets of a set having three elements is

……………

A)4 B) 6 C) 8 D) 10


Q11: If B A , then the shaded region represents ……

A) A B B) C C

A B C) A B D) C C

A B

Q12: A subset of A A is called a ……..

A) Relation from A to B B) Relation from B to A

C) Relation in A D) Relation in B

Q13: A subset of B B is called a ……..



Q14: The range of , ,1 , 0,3f m y n is ……..

A) ,1,3y B) , ,m n o

C) , ,3, ,1,3m n o

D) m

Q15: The domain of ,1 ,2f a b is ……..

A) ,a b B) 1,2,3 C) , ,1,2a b D) a

Q16: The cancellation laws hold in ………….

A) Sets B) Numbers

C) Group D) Abelian Group

Q17: If p is any proposition its negation is denoted by

………

A) p B) p C) p D) p

Q18: If p is true, then p is ………………….

A) True B) has no information

C) False D) equivalent to p

Q19: If p is true, then p is ………………….

A) True B) has no information

C) False D) equivalent to p

Q20: The conjunction of two statements p and q is denoted

by ………………….

A) p q B) p q C) p q D) p q

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: p q represents ……………

A) Disjunction B) Conjunction

C) Conditional D) Quantifier

Q2: A conjunction of two statements p and q is true only

if ..

A) p is true B) Both p and q are true

C) q is true D) Both p and q are false

Q3: p: Islamabad is a capital of Pakistan and q: Lohore is

not a city of Pakistan, the conjunction p q is ………..

A) True B) not valid C) False D) unknown

Q4: p: Islamabad is a capital of Pakistan and q: Multan is a

city of Pakistan, the conjunction p q is ………..


Q5: : 4 7, : 7 11p q , then the conjunction p q is

………..


Q6: :3 5, : 7 4p q , then the conjunction p q is

………..


Q7: : 4 7, : 7 11p q , then the conjunction p q is

……


Q8: p: Islamabad is a capital of Pakistan and q: Lahore is

not a city of Pakistan, the conjunction p q is ………..


Q9: The disjunction of two statements p and q is denoted

by ………………….


Q10: A disjunction of two statements p and q is false only

if ……………

A) p is true B) Both p and q are true

C) q is true D) Both p and q are false


Q11: A compound statement of the form “ if p then q ” is called an ………..

A)Implication B) Hypothesis C) Conclusion D) Unknown

Q12: An implication or conditional “ if p then q ” is denoted by ……………..

A) p q B) . p q . C) p q D) p q

Q13: An implication or conditional “ if q then p ” is denoted by ……………..

A) p q B) q p C) q p D) p q

Q14: In a statement “ if q then p ” p is ……………….

A) Implication B) Hypothesis

C) Conclusion D) Unknown

Q15: In a statement “ if q then p ” q is ……………….

A) Implication B) Hypothesis

C) Conclusion D) Unknown

Q16: A conditional is regarded as false only when the

antecedent is true and consequent is …………

A) True B) Known

C) False D) Unknown

Q17: A subset of A B is called a ……..



Q18: A subset of B A is called a ……..



Q19: If A then A is called ………………… set.

A) Sub B) Empty C) Singleton D) Null

Q20: The set of real numbers between 1 and 2 is …………..

A) Finite B) Empty

C) Infinite D)Non-Empty

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: For , ,a A b B then r a b is ………



Q2: For , ,a A b B then r b a is ………A)

Relation from A to B B) Relation from B to A


Q3: The set of the first elements of the ordered pairs

forming a relation is called its ……………….

A) Relation in A B) Relation in B

C) Range D) Domain

Q4: The set of the second elements of the ordered pairs

forming a relation is called its ……………….

A) Relation in A B) Relation in B

C) Range D) Domain

Q5: The domain of ,1 , 2 , ,3f a a a is ……..

A) a B) 1,2,3 C) ,2,3a D) 2

Q6: The inverse of a relation ,1 , , 2 , ,3x y z is

…………..

A) ,1 , , 2 , ,3x y z B) 1, , 2, , 3,x y z

C) 1 1 1

,1 , ,2 , ,3x y z

D) , , , , ,x x y y z z

Q7: The inverse of an identity relation is ……….

A) Not an identity relation B) Not a relation

C) an identity relation D) An empty set

Q8: A subset f of A B is said to be a function from A

to B if domain of f is A and first elements of order pairs of f

………….

A) Do not repeat B) Do not exist

C) The members of B D) Repeat

Q9: Which one is a function from A to B if , ,A a b c

and 1,2,3B

A) ,1 , ,1 , , 2a b c B) ,1 , ,1 , ,3a b b

C) ,1 , ,1 , , 2a b a D) ,1 , ,1 , , 2a b b

Q10: A function in which the second elements of the order

pairs are distinct is called ………..

A) Onto function B) One-one function

C) Identity function D) Inverse function


Q11: A function from A to B is called the onto function if its

range is ………

A) A B) B

C) Neither A nor B D) Both A and B

Q12: A function whose range consists of just one element is

called ………..

A) One-one function B) Constant function

C) Onto function D) Identity function

Q13: If , ,A a b c , 1,2,3B and

,1 ,1 , ,1f a b c is ………………

A) One-one function B) Constant function

C) Onto function D) Identity function

Q14: The range of ,1 ,1 , ,1f a b c is ……..

A) , ,a b c B) 1

C) , , ,1a b c

D) a

Q15: The domain of ,1 , 2 , ,3f a b c is ……..

A) , ,a b c B) 1,2,3 C) ,2,3a D) a

Q16: The function ,f x y y mx c is ……..

A) Quadratic function B) Constant function

C) Cubic function D) Linear function

Q17: The graph of a linear function represents ………..

A) Triangle B) Straight Line

C) Circle D) Parabola

Q18: The function 2,f x y y ax bx c is ……..



Q19: The function 2, 3 5f x y y x x is ……..



Q20: The function , 11f x y y is ……..

A) Onto function B) Constant function

C) One-one function D) None of these

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: If A B then A B ……………….

A) A B) B C) U D)

Q2: A bijective function is ……..

A) Onto but not one-one B) One-one but not onto

C) One-one and onto D) Only onto

Q3: A set which has no element is called ……..

A) Power set B) Empty set

C) Non-empty set D) Subset

Q4: Every set is ……………. of itself.

A) an empty B) an improper set

C) proper Subset D) None of these

Q5: If A B and A B , then A is ………….. of B .

A) Proper Subset B) Improper subset

C) Super set D) Power set

Q6: The two sets and A B are said to be …………… if they have equal number of elements.

A) Equal B) Finite Set

C) Equivalent set D) Singleton set

Q7: A set consisting of only one element is called

………………

A) Equal B) Finite Set

C) Equivalent set D) Singleton set

Q8: Power set is a set which consists of all the possible

…………….. of a given set.

A) Subsets B) Super sets

C) Elements D) None of these

Q9: The power set of an empty set i.e. P is ……….

A) Singleton Set B) Empty Set

C) Non-empty Set D) Infinite set

Q10: If A B then A B ……………….

A) A B) B C) U D) c

A


Q11: If A B then A B …………………

A) A B) B C) U D) c

A

Q12: A set whose last element is known and which is a

containable set is called ………………

A) Singleton set B) Infinite set

C) Finite set D) Non-empty

Q13: If A B then …………………

A) c c

A B B) c c

B A C) c

A B D) c

B A

Q14: If , cA A then

cA A …………..

A) A B) C) U C) c

A

Q15: If and , then c cA A A A …………..

A) A B) U C) B D) c

A

Q16: If A and B are two sets then A B =………………..

A) /x x A x B B) /x x A x B

C) /x x A x B D) /x x A x B

Q17: The two sets A and B are said to be …………. if they have the same elements.

A) Equivalent B) Equal

C) Empty D) None of these

Q18: The set of all the members under consideration is called

………………

A) Subset B) Power set

C) Universal set D) None of these

Q19: If A U then c

A =…………….

A) A U B) U A

C) U A D) None of these

Q20: If B A , then c

B A ………………

A) U B) B C) A D)

Answer Key

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Q1: The statement " "p q is called ………..

A) Conditional B) Implication

C) Bi-conditional D) Conjunction

Q2: p q q p is equal to …………..

A) p q B) q p

C) p q D) p q

Q3: p q is equal to ………..


Q4: For any two sets, A B B A if ………..

A) A

B) B

C) A B D) A B

Q5: The Cartesian product of A B is defined as …..

A) ,x y x A y B B) ,x y y A x B

C) ,x y x A y B D) ,x y x B y A

Q6: For any three sets; A , B andC , A B C

………..

A) A B C B) A B C

C) A B C D) None of these

Q7: c c cA B A B is called ________ law.

A) Commutative B) Associative

C) De Morgan’s D) Complementation

Q8: A ________.

A) A B) c

A C) U D)

Q9: The Tabular form of set 2 16 0x x x R is__________.

A) 4 B) 4 C) D) 1

Q10: The presentation of sets through the diagrams is called

________

A) Argand Diagram B) Venn Diagram

C) Circular Diagram D) None of these


Q11: If c

A B A then A B _______

A) A B B) c

A C) D) None

Q12: ?c cA B

A) U A B B) U A B

C) U A B D) None of these

Q13: The number of elements of a set is …… if it has 31 subsets.

A) 3 B) 4

C) 5 D) All of these

Q14: The set of first co-ordinates of A B is called:

A) Range B) Function

C) Domain D) Binary function

Q15: A function of the type f : x 2x is called:

A) Quadratic B) Linear

B) Trigonometric C) None of these

Q16: If as Set A has m elements and set B has n elements

then A B has _______ elements.

A) 2 2

m n B) 2

m C) 2

n D) n m

Q17: The function which is both one-to-one and onto is

called _______

A) Onto function B) Onto one function

C) Bijective function D) Into function

Q18: The number of subsets of set having 9 elements is:

A) 128 B) 256 C) 420 D) 512

Q19: If " "p is false then p is:

A) True B) False C) Both D) None

Q20: The number of elements of a set having 128 subsets is:

A) 4 B) 5 C) 7 D)8

Answer Key

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TYPE Objective Matrices and Determinants No 1

Q1: The list of numbers within a square bracket is

called ………..

A) Determinant B) Set

C) Matrix D) Equation

Q2: m n represent ……….. of a Matrix

A) Row B) Columns

C) Order D) None

Q3: A matrix of the form

4

1

4

A

is called ….Matrix

A) Column B) Row

C) Square D) Zero

Q4: A matrix of the form B a b c is called … matrix

A) Column B) Row

C) Square D) None

Q5: A matrix is said to be rectangular matrix if its order

is …………

A) m n B) m n

C) 2m D) 3n

Q6: What is the additive identity of matrices (2x2)

A) 0 0

0 0

B) 1 0

0 1

C) 1 0

0 0

D) None of these

Q7: A,B and C are three matrices then If AB C what

is A?

A) 1CB

B) CB

C) C

A D) none

Q8: Which of the following is false

A) 1.A A I B) 1.B B I

C) .A I A D) .0A I

Q9: If

1

3

7

A

then A is

A) 1 2 B) 2 3 C) 3 1 D) 1 3

Q10: If 3 9

1 3A

then which of the following is true

A) 18A B) A is a singular matrix

C) A is non singular matrix D) A is a scalar matrix


Q11: A matrix of the form 1 2

3 4A

is called …….

matrix

A) Rectangular B) Square

C) Identity D) Row

Q12: The order of matrix aij is ……….. If 1,2i and

1,2,3j

A) 2x2 B) 3x2

C) 2x3 D) 3x3

Q13: A matrix “A” will be a square matrix if ………

A) m n B) 2 2m n

C) m n D) m n

Q14: A matrix of the form

5 0 0

0 7 0

0 0 8

is called …….

A) Identity B) Scalar

C) Rectangular D) Diagonal

Q15: If 1 0

0 1A

then A is not called ………. Matrix

A) Scalar B) Identity

C) Rectangular D) Diagonal

Q16: If a b

Ac d

and 1 5 4B then .......

A) A B B) TA B C) B I D) A B

Q17: The two matrices are said to be conformable for

addition. If ………..

A) Both are square matrices B) Both are row matrices

C) Both are column matrices D) Both are in same order

Q18: A matrix

0 0 0

0 0 0

0 0 0

A

is called ….. matrix

A) Rectangular B) Identity

C) Null D) Rectangular

Q19: The identity matrix in the matrix addition is ……

A) Column matrix B) Square matrix

C) Null matrix D) None of them

Q20: If A nad B are two matrices of the same order such

that 0A B B A , then ..........B

A) –B B) Zero matrix

C) –A D) A

Answer Key

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Q1: The two matrices A and B are said to be additive

inverse of each other if ………

A) A B I B) 0A B C) AB I D) 0AB

Q2: The two matrices A and B are said to be

multiplicative inverse of each other if ………

A) AB BA B) BA A C) AB BA I D) 0AB

Q3: If “A” is a matrix of order mxn and “B” is a matrix of order pxq, their product AB is defined if ……..

A) m=q B) n=p C) n=q D) m=p

Q4: If 2 5

2 0A

and 1 0

1 2A

then, .....AB

A) 2 0

2 0

B) 7 10

2 0

C) 10 0

0 2

D) 7 2

10 0

Q5: 1 0

0 9

is a …………….

A) Diagonal B) Identity C) Scalar D) Zero

Q6: If m n

Ak l

then, AdjA is …..

A) l k

n n

B) l k

n m

C) l n

k m

D) m k

n l

Q7: 3 5 4 9 ... ...

A) 1 14 B) 1 14 C) 7 14 D) 7 14

Q8: If A and B are the two matrices of the same order

then AB BA if …………

A) A B B) A B C) A B I D) B A

Q9: If “B” is diagonal matrix and 11 22 33...... nn

a a a a k then “B” is called …… matrix of order “n” where 0,1k

A) Identity B) Rectangular

C) Square D) Scalar

Q10: If “B” is diagonal matrix and 11 22 33...... 1

nna a a a then “B” is not called …… matrix.

A) Scalar B) Rectangular

C) Unit D) Square


Q11: If A aij then aji is called …… matrix

A) Symmetric B) Transpose

C) Identity D) Scalar

Q12: If A is any square matrix, then the matrix obtained

by the interchange of rows and columns of A is called

…….. of A

A) Scalar B) Symmetric

C) Transpose D) None of these

Q13: If tA A then A is known as ……… matrix

A) Transpose B) Scalar

C) Symmetric D) Identity

Q14: If tA A , then A is known as ………… matrix

A) Symmetric B) Skew symmetric

C) Transpose D) Zero matrix

Q15: Transpose of identity matrix tI is ……

A) Scalar B) Symmetric

C) Identity D) Zero matrix

Q16:

0 0

0 0

0 0

a

a

a

is a ………… if 0,1a

A) Scalar matrix B) Unit Matrix

C) Zero Matrix D) Diagonal matrix

Q17: If A is order of m n , then the order of tA is

…….

A) m n B) n m C) m m D) n n

Q18:

4 5 6

5 3 2

6 2 8

is ………………………………

A) Rectangular Matrix B) Diagonal Matrix

C) Square Matrix D) Scalar Matrix

Q19: If A A , then A is called ………

A) Real Matrix B) Symmetric Matrix

C) Hermitian Matrix D) Skew Hermitian Matrix

Q20: If t

A A , then A is called ………

A) Transpose B) Symmetric Matrix


Answer Key

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Q1: Which of the following is conjugate matrix?

A) 1 5

5 6

B) 2 6

9 4

C) 3 5

6 7

i i

i i

D) 0 0

0 0

Q2: Transpose of a square matrix is ……………

A) Rectangular Matrix B) Scalar Matrix

C) Square Matrix D) Identity matrix

Q3: If t

A A , then A is called ………

A) Transpose B) Symmetric Matrix


Q4: The additive inverse of cos sin

tan cot

is

………..

A) sin cos

cot tan

B) cos sin

tan cot

C) cos sin

tan cot

D) sin cos

cot tan

Q5: If two rows or two columns of a square matrix A

are identical then ...........A

A) 1 B) -1

C) 0 D) Non-zero

Q6: Find adjoint matrix of 2 3

3 2

A) 2 3

3 2

B) 2 3

3 2

C) 2 3

3 2

D) 2 3

3 2

Q7: The determinant of

2 1 3

1 1 0

2 3 4

is ………

A) 11 B) 10 C) -10 D) -11

Q8: If ij

A a is any square matrix, then co-factor of

an element ij

a is ………….

A) 1i j

ijM

B) 1i j

ijM

C) 1i j

jiM

D) 1i j

jiM

Q9: Which of the following is a not scalar matrix?

A)

5 0 0

0 5 0

0 0 5

B)

1 0 0

0 1 0

0 0 1

C)

4 0 0

0 4 0

0 0 16

D)

0 0 0

0 0 0

0 0 0


Q10: If A and B are of the same order then which one is

always true

A) AB BA B) A B B A

C) AB BA D) None of these

Q11: What is determinant of zero matrix

A) 1 B) 0

C) -1 D) Not possible

Q12: 1...........AB

A) 1 1A B B) AB

C) BA D) 1 1B A

Q13: ...........t

AB

A) t tA B B) AB

C) BA D) t tB A

Q14: If AB BA then which of the following is correct?

A) A I or B I B) ,A I B I

C) 2 2A B D) None of these

Q15: A and B are of the same order and AB BA I

then ……………

A) A B B) B I

C) A I D) 1A B

Q16: If A is non-singular matrix then …………….

A) 0A B) 0A

C) 1A D) A is zero matrix

Q17: A is a square matrix then 11

A is equal to

………….

A) 1A B) A C) t

A D) I

Q18: Determinant of

3 4 2

1 7 3

0 0 0

is equal to …………

A) 12 B) 0 C) 15 D) 1

Q19: Determinant of

1 2 9

3 7 8

1 2 9

is equal to …………

A) 9 B) -3 C) 13 D) 0

Q20: Inverse of a square matrix “A” exists if ………….

A) 0A B) 0A

C) 1A D) A is zero matrix

Answer Key

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Q1: Determinant of A is possible only when A is

………….

A) Symmetric Matrix B) Rectangular Matrix

C) Square matrix D) None of these

Q2: A is a square matrix, then tA is equal to ………..

A) tA B) A C) t

A D) A

Q3: The value of

cos 0 sin

1 1 0

sin 0 cos

is equal to ….

A) 0 B) 1 C) -1 D)

Q4: A is a non-singular matrix then 1t

A is equal to

….

A) 1A B) 1

tA

C) t

A D) None

Q5: The matrix

0 1 2 4

0 0 1 3

0 0 0 4

0 0 0 0

is ……………..

A) In reduced form B) In echelon form

C) In rank form D) In Identity form

Q6: The number of non-zero rows in the Echelon form

is called …………… of the matrix

A) Transpose B) Determinant

C) Rank D) Adjoint

Q7: The rank of

1 4 2

0 1 3

0 0 0

is equal to …….

A)1 B) 2 C) 3 D) 0

Q8: For what value of the matrix

2 6 5

4 4 6

0 1

A

is

a singular matrix

A) 0 B) 1 C) -2 D) -1

Q9: The order of A is 4 4 then what will be the order

of 1A

A) 5 5 B) 6 6 C) 4 4 D) None

Q10: If any two rows or columns of a square matrix A

interchanged then determinant will be equal to …………

A) A B) A C) 2

A D) A


Q11: The product of ac d

b

is equal to …..

A) ab cd B) ac ad

bc bd

C) ac bd D) None of these

Q12: The solution set 0,0,0 is called ……….. for homogeneous system of linear equations

A) Non-trivial B) Trivial

C) Unique D) Infinite

Q13: If a system , 0AX B B is called ……. If it has unique or infinite many solutions

A) Trivial B) Non-trivial

C) Consistent D) Inconsistent

Q14: The system of linear equations is said to be ….. if it has no solution

A) Trivial B) Non-trivial

C) Consistent D) Inconsistent

Q15: Those equations whose solution is common are

called …………..

A) Quadratic Equations B) Linear Equations

C) Simultaneous Equations D) Homogeneous Equations

Q16: A system 0AX has non-trivial solution if

…………

A) 0A B) 0A

C) A A D) A A

Q17: C and D are two non singular matrices then

11 1

C D is equal to …………

A) 1 1D C

B) CD C) DC D) 1 1C D

Q18: The ratio of the adjoint and determinant of non

singular matrix is ……………. of the matrix

A) Inverse B) Transpose

C) Co-factor D) None of these

Q19: Cramer’s Rules is applicable on AX B if ….

A) 0A B) 0A C) 0A D) 0A

Q20: The value of

1

1

1

y z x

z x y

x y z

is equal to ……

A) 1 B) 0 C) x y z D) xyz

Answer Key

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Q1: The square of a scalar matrix is a …………..

A) Identity Matrix B) Rectangular Matrix

C) Scalar Matrix D) Identity Matrix

Q2: A is a unit matrix , then A is equal to …………

A) 0 B) 1 C) -1 D) 2

Q3: Order of 3 5 is ……….

A) 1x1 B) 1x2 C) 2x1 D) 2x2

Q4: 1 0

0 1

is a …………….. matrix

A) Singular B) Zero C) Unit D) None

Q5: If 1AA I

, then 1A is ……….. of matrix A

A) Adjoint B) Multiplicative inverse

C) Additive inverse D) Transpose of A

Q6: If matrix 4 16

8n

is singular, then ...n

A) -2 B) 2 C) 4 D) -4

Q7: If A,B and C are three matrices which are

conformable for multiplication, then ...........A BC

A) AC B B) BC A C) AB C D) CA B

Q8: 31 4 .............

5

A) 2 3

4 5

B) 3 12

5 20

C) 2 12

4 25

D) 12 3

16 8

Q9: 2...........

3x y

A) 3x y B) 3x y C) 2 3x y D) 3x y

Q10: 5 0

0 5

is a …………. Matrix

A) Zero B) Identity C) Unit D) Scalar


Q11: If4 2 92

6 5 12 2 25

m

, then ...........m

A) 3 B) 5 C) 7 D) 9

Q12: The matrix of co-efficient for the equations

3 12x y and 3 2 8x y is ………………..

A) 1 3

3 2

B) 1 12

3 8

C) 3 12

2 8

D) 3 1

3 2

Q13: If 2 3

2 1A

then A is …….

A) -4 B) 4 C) -5 D) 5

Q14: If 1 0

0 1A

then, 1 ..........A

A) 1 0

0 1

B) 1 0

0 1

C) 1 0

0 1

D) None

Q15: If the number of rows and columns in a matrix are

not equal, then the matrix is called....

A) Square matrix B) Zero matrix

C) Unit matrix D) Rectangular matrix

Q16: If 5 3

12 2 5A

then A is …….

A) -4 B) 4 C) -5 D) 5

Q17: Matrix 0 0

0 0

is a ………. matrix

A) Zero B) Unit

C) Column D) Row


A) 1AA I

B) tI I C) t

tA A D) 1t

A A

Q19: If 1 0

0 1A

then, which of the following is false

A) A is scalar matrix B) A is unit matrix

C) A is zero matrix D) A is diagonal matrix

Q20: What is the multiplicative identity of matrices

(2x2)?

A) 0 0

0 0

B) 1 0

0 1

C) 1 0

0 0

D) none

Answer Key

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Q1: 1 0

0 1

is ……………………..

A) not unit matrix B) additive identity

C) zero matrix D) multiplicative identity

Q2: 3

5A

and 2

7B

then A+B=?

A) 1

12

B) 5

12

C) 1

2

D) 1

12

Q3: 10

5A

and 2

6B

then A-B=?

A) 8

11

B) 8

11

C) 12

1

D) 12

11

Q4: Which of the following is a zero matrix

A) 0 0

0 1

B) 21 1 2 4

2 2 0

C) 2 2 0

0 3 1

D) 0 0

0 11

Q5: Which of the following is a scalar matrix

A) 2 0

0 2

B) 7 0

0 17

C) 5 0

0 25

D) 1 0

0 1

Q6: Which of the following is a unit matrix

A) 5 4 0

0 1

B) 0 0

0 0

C) 0 0

0 1

D) 0 1

1 0

Q7: Which of the following is row matrix

A) 3 4 B) 3 0

2 1

C) 0 0

0 1

D) None of these

Q8: 3 9 is a ……….

A) Row matrix B) Column matrix

C) Scalar matrix D) Zero matrix

Q9:

0

0

0

is a ………………

A) unit matrix B) zero matrix

C) scalar matrix D) diagonal matrix

Q10: 1 0

0 1

is a …………….

A) unit matrix B) row matrix

C) zero matrix D) None of these


Q11: If 2 4

1 8A

then ?A

A) 10 B) -12 C) 12 D) 0

Q12: If 2 4

4 8A


A) A is a non singular matrix B) A is a singular matrix

C) A is scalar matrix D) A is unit matrix

Q13: If 2 4

1 8A

then ?A

A) 2 B) -2 C) 4 D) -4

Q14: Which of the following is diagonal matrix

A) 1 0

0 1

B) 1 9

0 1

C) 1 1.2

0.8 1

D) 1 5

5 1

Q15: If 1 0

0 1A

then which of the following is false

A) A is a unit matrix B) A is a scalar matrix

C) A is a diagonal matrix D) A is a zero matrix

Q16: If 4

12

x y

x y


A) 1 1 12

1 1 4

x

y

B)

1 1 12

1 0 4

x

y

C) 1 1 4

1 1 12

x

y

D)

1 1 4

1 1 12

x

y


A) If A is a singular matrix then 0A

B) If B is a zero matrix then all terms are o

C) If A is unit matrix then 1A

D) Unit matrix is a zero matrix

Q18: What is the additive inverse of 2 9

5 4

A) 2 5

9 4

B) 2 9

5 4

C) 0 0

0 0

D) None of these

Q19: If 1 2

3 4A

then ...........tA

A) 4 2

3 1

B) 1 3

2 4

C) 4 3

2 1

D)4 3

2 1

Q20: If 4

2 2

xA

is a singuler matrix then

.............x

A) 4 B) -2 C) 2 D) -4

Answer Key

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Q1: Which of the following matrix is symmetric matrix?

A) 3 4

4 3

B) 1 0

0 1

C) 3 3

0 3

D) 0 4

4 0

Q2: If

2 1 2

0 3 3

1 2 4

, then what is 23A ?

A) 3 B) 5 C) 3 D) 5

Q3: If

2 1 2

0 2 1

1 3 4

, then what is 33M ?

A) 3 B) 4 C) 3 D) 4

Q4: 21 22 23

21 22 23

4, 3, 7?

2, 1, 3

a a aA

A A A

A) 18 B) 12 C) 16 D) 21

Q5: 31 32 33

31 32 33

2, 3, 5?

2, 1, 4

a a aA

M M M

A) 13 B) 21 C) 14 D) 19

Q6: Find x if

1 4 7

0 1 8

2 30 0

4

x

has unique solution.

A) 3

8 B)

3

2 C)

2

3 D)

8

3

Q7: If 1 2

334 3

x

x

, then what is x ?

A) 3 B) 2 C) 3 D) 1

Q8:

5 0 0

3 2 1 ?

1 2 3

A) 15 B) 20 C) 10 D) 15

Q9: If 4

94

x

x , then what is x ?

A) 5,5 B) 5,5 C) 5,5 D) 5,5

Q10:

5 15 20

7 14 21 ?

4 8 12

A) 140 B) 75 C) 1 D) 0


Q11: Find x and y if 3 1 2 1

3 2 3 2

x

A) 2 B) 3 C) 1 D) 0

Q12: Find .x y if 3 1 7 1

3 3 4 3 11

x

y

A) 12 B) 9 C) 15 D) 21

Q13: If 1 2 3

1 0 2A

and 0 3 2

1 1 2B

, then find

4 3A B

A) 4 5 6

1 3 2

B) 4 5 6

1 3 2

C) 4 5 6

1 3 2

D) 4 3 6

1 4 2

Q14: Find 2

A if 1 2

3 0A

A) 7 2

3 6

B) 7 2

0 6

C) 7 2

0 6

D) 7 2

3 6

Q15: If 1 1 2

0 3 1A

and 2 3 0

1 2 1B

, then find

tA B

A)

3 1

3 4

1 0

B)

3 1

2 3

2 1

C)

3 1

2 5

2 0

D)

4 1

2 3

2 0

Q16: Find the multiplicative inverse of 2 1

1 1

A) 1 1

1 2

B) 1 1

1 2

C) 1 1

1 2

D) 1 1

1 2

Q17: 2 7

..........3 5

A) 2 7

3 5

B) 5

2

C) 9

8

D) 9

8

Q18: 2 2 0 3

....3 3 1 2

A) 2 5

2 1

B) 2 1

2 1

C) 2 5

2 1

D) 0

Q19: What is the value of A B if 1A B

A) 0 B) A C) I D) B

Q20: Determinant of unit matrix is ...............

A) Unit Matrix B) Scalar matrix

C) Diagonal matrix D) Zero matrix

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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TYPE Objective Quadratic Equations No 1

Q1: 21 ............

A) 1 B) 0 C) 1 D)

Q2: 1 ............

A) 1 B) 2 C)

2 D) 0

Q3: 21 ............

A) 1 B) C) D) 0

Q4: 50 ............

A) 1 B) 2 C) D) 1

Q5: 3 ............

A) 1 B) 2 C)

2 D) 0

Q6: 1 ............

A) 1 B) 3 C)

2 D) 2

Q7: Solve 2 5 4 0x x

A) 1, 4 B) 1,4 C) 1,3 D) 2,4

Q8: Solve 2 36 0x

A) 6 B) 6 C) 6i D)

Q9: Solve 2 4 0x

A) 4 B) 2 C) 4i D) 2i

Q10: Solve 2 3 0x x

A) 2, 3 B) 3, 2 C) 2 D) 3


Q11: If 2 1 3

2

i , then what is the value of

A) 1 3

2

i B)

1 3

4

i C)

1 3

2

i D)

1 3

2

i

Q12: If 1 3

2

i , then what is the value of

2

A) 1 3

2

i B)

1 3

2

C)

1 3

2

i D)

1 3

2

i

Q13: Find the cube root unity of 3 125x

A) 25,5 ,5 B)

25, 5 , 5

C) 25, 5 ,5 D)

2 35,5 ,5

Q14: 46 47 48 ...........

A) B) 3 C)

2 D) 0

Q15: Find the product of roots of 23 7 12 0x x

A) 12

3 B)

12

3 C)

7

3 D)

7

3

Q16: Find the sum of roots of 22 5 3 0x x

A) 5

2 B)

5

2 C)

3

2 D)

3

2

Q17: Solve 4 16 0x

A) 2, 2,2 , 2i i B) 4, 4,4 , 4i i

C) 8, 8,8 , 8i i D) 16, 16,16 16i i

Q18: What is the sum of roots of 4 81 0m

A) 12i B) 12i C) 12 D) 0

Q19: What is the product of roots of 4 256 0x

A) 64 B) 256 C) 16 D) 128

Q20: 4 4

1 3 1 3 ...............

A) 16 B) 16 C) 8 D) 8

Answer Key

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11 12 13 14 15 16 17 18 19 20



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Q1: 1, 1, ,i i is called.......................

A) The cube roots of unity B) The fourth roots of unity

C) The fifth roots of unity D) None of these

Q2: Which of the following is false?

A) The complex fourth roots of unity are conjugate of each

other

B) The real fourth roots of unity are inverse of each other

C) Sum of all the four fourth roots of unity is zero

D) Product of all the fourth roots of unity is 1

Q3: Product of all the fourth roots of unity is equal to

.............

A) 1 B) i C) 1 D) i

Q4: Find the solution set of 2 1 0x

A) 1, 1 B) 0, 1 C) 1,0 D) ,i i

Q5: Find the solution set of 2 1 0x

A) 1, 1 B) 0, 1 C) 1,0 D) ,i i

Q6: Evaluate 821

A) 256 B) 128 C) 256 D) 128

Q7: Evaluate 28 29 1

A) 1 B) 0 C) D) 2

Q8: Evaluate 2 21 1

A) 4 B) 4 C) 4 D) 4

Q9: Evaluate

7 7

1 3 1 3

2 2

A) B) C) 1 D) 1

Q10: Evaluate 5 5

1 3 1 3

A) 32 B) 32 C) 32 D) 32


Q11: The highest power of a polynomial function is called

.....

A) Degree B) Power C) Monomial D) Binomial

Q12: What is the sum of roots of 4 1 0x

A) 1 B) 2 2i C) 0 D) 2

Q13: What is the sum of roots of 3 1 0x

A) 1 B) 2 C) 0 D) 2 3

Q14: What is the product of roots of 3 1 0x

A) 1 B) 2 C) 0 D) 2 3

Q15: What is the sum of real roots of 4 16 0x

A) 1 B) 1 C) 0 D) 2 3

Q16: 2 .............

A) 0 B) 1 C) 1 D)

Q17: Find the remainder when 3 2 2 4 0x x x is

divided by 1x

A) 1 B) 2 C) 2 D) 0

Q18: Find the numerical value of k if 3 2 2 6 0x x kx

has a remainder of12 , when divided by 1x

A) 1 B) 2 C) 4 D) 0

Q19: If 2 0ax bx c and

2 4 0b ac then the roots

will be....................

A) real and equal B) complex and equal

C) real and unequal D) complex and unequal

Q20: If 2 0ax bx c and

2 4 0b ac and not a perfect

number, then the roots will be....................

A) real and equal B) complex and equal

C) real and unequal D) complex and unequal

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: Find the solutions set of 2 7 12 0x x

A) 3,4 B) 4,1

C) 4, 3 D) 4,3

Q2: Find the solutions set of 2 2x x

A) 1, 2 B) 1,2

C) 3, 4 D) 1,2

Q3: Which of the following is a radical equation?

A) 2 4 0x B) 3 1x

C) 2x D) 2 1 12x

Q4: Find the solutions set of 2 1 0x

A) 1x B) 1

2x

C) 2x D) 2x

Q5: Find the three cube roots of 8 if 1 3

2 .

A) 22, 2 , 2 B)

22, ,

C) 2 D) 22,2 ,2

Q6: Find the three cube roots of -8 if 1 3

2 .

A) 22, 2 , 2 B)

22, ,

C) 2 D) 22,2 ,2

Q7: Find the three cube roots of 27 if 1 3

2 .

A) 23,3 ,3 B)

23,3 ,3

C) 3,3 D) 21,3 ,6

Q8: 3 3 ...............a b

A) 2 2a b a ab b B) 2 2

a b a ab b

C) 2 22a b a ab b D) 2 2a b a ab b

Q9: 3 3 ...............a b

A) 2 2a b a ab b B) 2 2

a b a ab b

C) 2 22a b a ab b D) 2 2a b a ab b

Q10: 2 2 ...............a b

A) a b a b B) a b a b

C) a b a b D) 2 2

a ab b


Q11: 2

2

1.............x

x

A)

21

2xx

B)

21

4xx

C)

21

2xx

D)

21

2xx

Q12: 2

2

1.............x

x

A)

21

2xx

B)

21

4xx

C)

21

4xx

D)

21

2xx

Q13: 100 200 300 ?

A) 2 B)

C) 1 D) 0

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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TYPE Objective Partial Fractions No 1

Q1:

3

2 3x x can be written in the form of partial

fractions as ...............

A) 2 3

A B

x x

B)

232

A B

xx

C) 2

2 3

A B

x x

D)

2 3

A B

x x

Q2: If the degree of the polynomial P x is less than the

degree of the polynomial Q x in a rational fraction

P x

Q x,

then the fraction is called ..................

A) Improper Rational Fraction B) Proper Rational Fraction

C) Improper Rational Equation D) Proper Rational Equation

Q3: If the degree of the polynomial P x is equal to or

greater than the degree of the polynomial Q x in a rational

fraction

P x

Q x, then the fraction is called ........

A) Improper Rational Fraction B) Proper Rational Fraction

C) Improper Rational Equation D) Proper Rational Equation

Q4: Which of the following is quadratic factor?

A) 2 4x B)

2 1x

C) 2 2 1x x D)

2 5 4x x

Q5: Which of the following is not quadratic factor?

A) 2 4x B)

2 1x

C) 2 1x x D)

2 2x x

Q6: Which of the following is a linear factor

A) 2

x ax B) 2

x bx C) ax b D) 3 1x

Q7: Which of the following is a proper fraction?

A)

2 2 3

2 .2

x x

x x

B)

3 2 8

9

x x

x

C)

1 1 3

1 1 4

x x x

x x x

D) 1

x

Q8: Which of the following is an improper fraction?

A)

2 2 3

2 . 1 . 1

x x

x x x

B)

3

4

2 8

9

x x

x

C) x a x b x c

x a x b x c

D)

2

3

1

1

x

x

Q9: The partial fraction of 2

1

1x is ............

A)

1 1

2 1 2 1x x

B)

1 1

2 1 2 1x x

C)

1 1

2 1 2 1x x

D)

1 1

2 1 2 1x x

Q10: To resolve a combined fraction into its pars is

called………….

A) Partial Fractions B) Proper Fraction

D) Improper Fraction D) Combined Fraction

Q11: The form of partial fractions of

2

1

1 4x x is:

A) 21 4

A B

x x

B)

21 4

A Bx C

x x

C) 1 2 2

A B C

x x x

D)

2

1

1 4

A

x x


Q12: The form of partial fractions of 2

4

3 4

x

x x is:

A) 2

4

1 4

x

x x

B)

21 4

A B

x x

C) 3 2 2

A B C

x x x

D)

23 4

A Bx C

x x

Q13: The form of partial fractions of 2 2

1

1 4

x

x x

is:

A) 2 21 4

A B

x x

B)

2 21 4

Ax B Cx D

x x

C)

2

2 21 4

Ax B Cx Dx

x x

D)

2 21 4

Ax B Cx D

x x


2

2 2

1

1 3

x

x x

is:

A) 2 21 31

A Bx C Dx E

x xx

B) 2 21 31

A B C

x xx

C) 2 21 31

A B Cx D

x xx

D) 2 2

1 31 3

A B C D

x xx x


1

1

x

x x

is:

A) 1

A B

x x

B)

1

A Bx C

x x

C) 1 1

1x x

D)

1

A B

x x

Q16: Resolve 3

2

1x

A) 2

2

1 1

x

x x x

B)

2

2 2

1 1

x

x x x

C) 2

2 2

1 1

x

x x x

D)

2

1 2

1 1

x

x x x

Q17: Resolve 3

11

1x

A) 2

11 11 22

3 1 3 1

x

x x x

B)

2

11 11 22

1 1

x

x x x

C) 2

11 11 22

3 1 3 1

x

x x x

D)

2

11 22 11

3 1 3 1

x

x x x

Q18: Partial fractions of 2

1

1x are equivalent to:

A)

1 1

2 1 2 1x x

B)

1 1

2 1 2 1x x

C)

1 1

4 1 4 1x x

D)

1 1

2 1 2 1x x


1

4x are equivalent to:

A)

1 1

4 1 4 1x x

B)

1 1

2 1 2 1x x

C)

1 1

4 2 4 2x x

D)

1 1

4 2 4 2x x


1

9x are equivalent to

……………

A)

1 1

9 3 9 3x x

B)

1 1

3 3 3 3x x

C)

1 1

6 3 6 3x x

D)

1 1

4 1 4 1x x

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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TYPE Objective Sequences and Series No 1

Q1: An arrangement of number formed according to some

definite rule is called:

A) Series B) Polynomial

C) Sequence D) Equation

Q2: A sequence is a function whose domain is the set of:

A) Integers B) Real No.

C) Natural no. D) Even No.

Q3: The sequence whose difference between every two

consecutive terms is a same is called:

A) G.P B) H.P C) Binomial D) A.P

Q4: The general term of .A P is:

A) 1

1

n

na a r

B) 1 1n

a a n d

C) 1 1n

a a n d D) 1

2n

n na

Q5: The general term of the sequence 1,1, 1,1,..... is:

A) 1n

na B) n

a n

C) 11

n

na

D) 11

n

na

Q6: The sequence whose general term is

1 2n

n

na

n

is:

A) 1 1

1,0, ,3 2

B)

1 11,0, ,

3 2

C) 1 1

1,0, ,3 2

D)

1 11,0, , ,...

3 2

Q7: The sequence whose general term is

1 1n

na n is:

A) 2,3, 4,5 B) 2,3, 4,5

C) 2, 3,4,5 D) 2,3,4, 5

Q8: If 1 5a and 3d ,then 10 ?a

A) 30 B) -32 C) 31 D) 32

Q9: If , ,a A b are in A.P , then ?A

A) Geometric Mean B) Arithmetic Mean

C) Harmonic Mean D) None of these

Q10: The .A M between 4 5 & 2 5 is:

A) 2 5 B) 5

3 C) 3 5 D)

6 5

7


Q11: The10thterm of the sequence

52, ,3,....

2is:

A) 13

2 B)

13

2

C)

11

2 D)

2

13

Q12: The A.M between 2 3x y and8 5x y is:

A) 5x y B) 3x y C) 5x y D) 3x y

Q13: Which term of the .A P3 13

,2, ,...4 4

is98

4?

A) 21st B) 19th

C) 20th D) 18th

Q14: The 8th term of A.P

3 13,2, ,...

4 4 is:

A) 39

4 B)

38

4 C)

37

4 D)

43

4

Q15: The A.M between the two numbers 5 4 and

5 4 is:

A) 5 B) 2 5 C) 4 5 D) 5

Q16: How many terms are in A.P if 30,n

a 25,d

5a ?

A) 1 B) 2 C) 3 D) 4

Q17: The A.M between a and b is:

A) 2

a b B)

2ab

a b C)

2

a b D) ab

Q18: The H.M between a and b is:

A) 2

a b B)

2

a b C)

2

a b

ab

D)

2ab

a b

Q19: The G.M between a and b is:

A) a b B) ab C) a b D) 2

a b

Q20: The Sum of the terms of a sequence is called:

A) Sequence B) Series C) Function D) Fraction

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: The sum for 1 2 3 4 ..... n is:

A) 1 1a n d B) 1

2

n n

C) 1

2

n n D) NONE

Q2: 1 1 1 12 ... 1 ?a a d a d a n d

A) 1 12

na n d B) 12 1n a n d

C) 12 12

na n d D) 12 1

2

na n d

Q3: Which formula is used for arithmetic series?

A) 1 12

n

nS a n d B) 1

2n n

nS a a

C)

1

1

1

n

n

rS a

r

D) NONE

Q4: The sum of 1st 100 positive even integers is:

A) 10000 B) 10111 C) 10101 D) 10100

Q5: The sum of the series 5 9 13 ... 41 is:

A) 220 B) 230 C) 240 D) 280

Q6: The sum of the series 8 6 4 ... up to 10 terms is:

A) -8 B) 8 C) 10 D) -10

Q7: How many terms of the series

11 7 3 ... will sum up 304?

A) 19

2n

B) 15n C) 16n D) 17n

Q8: The sequence 1 2 3

1 1 1 1 1, , , ,..., na a r a r a r a r is called …

A) A sequence B) H.P

C) G.P D) A.P

Q9: The H.M between 9 and 11is:

A) 9

10 B)

7

10

C) 99

10 D) None of these

Q10: The positive G.M between 4 and 64 is:

A) 4 B) 16 C) 32 D) 64


Q11: In G.P 1

1

n

na a r

where r is:

A) Common difference B) Common Ratio

C) Common Factor D) NONE

Q12: If the 1st three terms of G.P are 1,

3,

4

9

16 then the 6th

term is:

A) 242

257 B)

241

1024 C)

243

1024 D) None

Q13: The 7th term of the G.P 5,15,.... is:

A) 3544 B) 3645 C) 3646 D) 3640

Q14: The general term of a G.P is:

A)1

n

na a r B)

1

1

n

na a r

C) 1

1

n

na a r

D) 1na a r

Q15: If 1r then the G.S is called as:

A) Convergent B) Divergent C) Finite D) Constant

Q16: If 1r then the infinite G.S is called as:

A) Divergent B) Convergent C) Finite D) Constant

Q17: If , ,a G b are in G.P then G is called:

A) Geometric Progression B) Geometric mean

C) A.M D) Harmonic Mean

Q18: If 1 44, 256,a a then r is:

A) 2 B) 3 C) 4 D) 1

2

Q19: The geometric mean between 1

22

and 1

122

is:

A) 5 5

3 B)

5

2 C)

5 2

2 D)

5 5

2

Q20: The sum of the series 1 2 3 1

1 1 1 1 1, , , ,..., na a r a r a r a r

if 1r

is:

A)

1 1

1

na r

r

B)

1

1

a

r

C)

1 1

1

na r

r

D)

1

1

nr

r

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: If 1r then, the sum of the finite Geometric Series is:

A)

1 1

1

na r

r

B)

1 1

1

na r

r

C) 1

2

n n D) 1

2n

na a

Q2: For finite geometric series which statement is not true?

A) 1r B) 1r C) 2r D) 1r

Q3: If 1 3a , 2r then 6 .............S

A) -93 B) -102 C) -190 D) -189

Q4: How many terms are in G.P: 1 1 1

1, , ,...,2 4 1024

A) 10 B) 11 C) 12 D) None

Q5: Find the last term of 1 3 2 7 3 11 .....

A) . 1n n B) . 1n n C) . 4 1n n D) . 4 1n n

Q6: The sum of the 1st 16 terms of the Geometric Series

1 1 1 1 1 1 1.... is:

A) 1 B) -1 C) 0 D) 2

Q7: The sum of the infinite geometric series is:

A) 1

1

a

r B) 12

1

a

r C) 1

1

a

r D)

1 1

1

na r

r

Q8: The sum of the series 1 1 1

1 ....3 9 27

is:

A) 2

3 B)

2

3 C)

3

2 D)

3

2

Q9: Is the series 2 8 32 128 ... convergent?

A) Yes B) No C) Neither D) None

Q10: The series 1 1 1 1 1 ... is:

A) Convergent B) Divergent

C) Finite D) Does not converge


Q11: 2.410 in the common fraction is:

A) 410

999 B)

2308

999 C)

2408

999 D) None

Q12: If the first three terms of G.P are 4 3,8 3,16 3,...

then 4a is:

A) 15 3 B) 3 16 C) 16 3 D) 32 3

Q13: The reciprocal of A.P is called:

A) G.P B) G.M C) A.M D) H.P

Q14: If 1 1 1

, , ,...3 8 13

is H.P, then 12a is:

A) 1

54 B)

1

55 C)

1

59 D)

1

58

Q15: If 1 1 1 1 1 1 1 ... is a sequence to n terms

then , what is n

S if n is even.

A) 1 B) -1 C) 0 D) 2

Q16: If 1

125 2, , 8,

8 5a r n then 8 _____a

A) 16

625 B)

625

16 C)

17

125 D) NONE

Q17: The series 3 3

6 3 ...2 4

is _____

A) Divergent B) Convergent C) G.P. D) Constant

Q18: The series 1 2

1 1 1 .....a a r a r has a sum 1

1

a

r if:

A) 1r B) 1r C) 1r D) 2

3r

Q19: The sum of 2 1 1 2 1 .... is____

A) 2 B) 1

2 2

C) Possible D) Impossible

Q20: The common difference fraction of 1.321 is:

A) 44

33 B)

440

333 C)

40

33 D)

441

331

Answer Key

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20



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Q1: If 2 3

2 3

1 1 1.....

3 3 3y x x x then x is:

A) 2

1

y

y B)

1

y

y C)

3

1

y

y D) NONE

Q2: If

1 1 1

8 16 3216 16 16 .....y then y is:

A) 4 B) 2 C) 3 D) 2

Q3: If A,G & H are the . , . . A M G M and H M between a

& b , then which one of the following is true:

A) A G H B) A G H

C) H A G D) G A H

Q4: The sum of the series 3 3 3 31 2 3 ......n is:

A) 22 1

4

n n B)

22 1

2

n n C)

23 1

4

n n D) NONE

Q5: The general term of the sequence 2 4 6 8, , ,.....x x x x

is:

A) 21n n

na x B) 1

1n n

na x

C) 31n n

na x D) 2n

na x

Q6: If 1 1 1

, ,a b c

are in a H.P, then b is:

A) 2ab

a b B)

2ac

a c C)

2

a c D)

2

a b

ac

Q7: If 1 1 1

,2 1 4 1

andk k k

are in H.P, then k is:

A) 1 B) 3 C) 2 D) 5

Q8: The 7th term of H.P

1 1 1, , ,.....

3 5 7 is:

A) 15 B) 1

14 C)

1

15 D)

1

10

Q9: If .G G M , .A A M and .H H M then:

A) 2 2 2.G A H B) .G A H

C) 2 .G A H D)

2.G A H

Q10: Which one is H.P?

A) 3,6,9,... B) 1 1 1

, , ,...2 5 11

C) 1 1 1

, , ,...3 6 9

D) NONE


Q11: If ,2 2,3 3,...y y y is a G.P, then y is:

A) 1,4 B) 1,4 C) 1, 4 D) 1, 4

Q12: 1 2 3 .............. ?n

A) 1n n B) 1

2

n n C)

1

2

n n D)

2 1

2

n n

Q13: 2 2 2 21 2 3 .............. ?n

A) 1 2 1

3

n n n B)

1 2 1

2

n n n

C) 1 2

3

n n n D)

1 2 1

6

n n n

Q14: 3 3 3 31 2 3 .............. ?n

A) 2

1

2

n n

B) 2

1

2

n n

C) 3

1

2

n n

D) 2

1

3

n n

Q15: 0

1 ?n

n

k

S

A) 1 B) n C) 1n D) 2

n

Q16: 0

?n

n

k

S k

A) 1n n B) 1

2

n n C)

1

2

n n D)

2 1

2

n n

Q17: 2

0

?n

n

k

S k

A) 1 2 1

3

n n n B)

1 2 1

6

n n n

C) 1 2

3

n n n D)

1 2

6

n n n

Q18: 3

0

?n

n

k

S k

A) 2

1

2

n n

B) 2

1

2

n n

C) 3

1

2

n n

D) 2

1

3

n n

Q19: The difference of two consecutive terms of an A.P is

called its:

A) A.M B) G.M

D) Common Difference D) Common Ratio

Q20: 5,15,20,25 ... is:

A) A.M B) G.M D) H.M D) NONE

Answer Key

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Q1: 2,8,32,...............is ..........................

A) A.M B) G.M D) H.M D) None

Q2: (n-1) th term of an A.P is ..................

A) 1 1a n d B) 12 1a n d

C) 1 2a n d D) 12 2a n d

Q3: The common difference of the sequence

3,15,27,.............. is ...........

A) 2 B) 12 D) 6 D) None

Q4: Find the common ratio of the sequence 0.5, 0.25,

0,125,............

A) 10 B) 5 D) 0.5 D) 1.5

Answer Key

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TYPE Objective Permutation, Combination and Probability No 1

Q1: The product of all positive integers equal to or less

than ‘ n ’ is called ……………….. of n.

A) Factor B) Factorial

C) Sequence D) Series

Q2: If ‘ n ’ is a positive integer then !n is:

A) 2 3 ....2.1n n n B) 4 5n n n

C) 1 2 ....3.2.1n n n D) .5.4.3.2.1n

Q3: 0! ?

A) 0 B) 2 C) 1 D) -1

Q4: The arrangement of finite No of objects taken

some or all at a time in certain order is called:

A) Probability B) Factorial

C) Permutation D) Combination

Q5: 5! ?

A) 24 B) 120 C) 720 D) -120

Q6: ?n

rP

A) !

!

n

r B)

!

! !

n

r n r

C)

1 !

! !

n

r n r

D)

!

!

n

n r

Q7: ?n

nP

A) 0 B) 1 C) n D) !n

Q8: 0 ?nP

A) 0 B) 1 C) n D) !n

Q9: 10

3 ?P

A) 10!

3! B) 5040 C) 720 D)

10!

7!3!

Q10: If 3 4

n nP P , then n is:

A) 5 B) 0 C) 1 D) 4


Q11: Total number of words formed from the letter

“TRIANGLE” using all the letters is:

A) 41320 B) 4320

C) 40320 D) None of these

Q12: If 11 990n

P , then n is:

A) 11 B) 4 C) 19 D) 3

Q13: The numbers of signals that can be given by six

flags of different colors using three flags at a time are:

A) 6 B) 120 C) 24 D) 18

Q14: If 1 30n

P , then n is:

A) 24 B) 15 C) 30 D) 120

Q15: 16

2 ?P

A) 250 B) 240 C) 120 D) 230

Q16: 7!

?2!3!

A) 120 B) 400 C) 420 D) 24

Q17: How many words can be formed from the letter

ARTICLE using all the letters ………………..

A) 5040 B) 5050 C) 5000 D) 720

Q18: If 1

4 3: 9 :1n nP P

, then n is:

A) 8 B) 9 C) 10 D) 5

Q19: If 4 36n n

P P then n is:

A) 11 B) 10 C) 9 D) 15

Q20: The number of words can be formed from the letter

“MISSISSIPPI” using all the letters is:

A) 34650 B) 34600 C) 35650 D) None

Answer Key

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Q1: Total number of words can be formed from the letters

of the word ‘mathematics’ using all letters is:

A) 4889600 B) 4889660

C) 48899600 D) 4899660

Q2: In how many different ways can seven female be seated

at around table?

A) 750 B) 120 C) 24 D) 720

Q3: How many 7-digit numbers can be formed from

2,2,3,3,3,4,4 ?

A) 200 B) 220 C) 210 D) 720

Q4: How many different numbers greater than 3 million can

be formed from the digits 1,1,1,1,2,2,3?

A) 16 B) 15 C) 20 D) 24

Q5: How many different ways are possible of the letter

‘SOME’ ?

A) 2! B) 3! C) 4! D) 5!

Q6: ?n

rC

A)

!

!

n

n r B)

!

!

n

r

C)

!

1 !

n

r D)

!

! !

n

n r r

Q7: 1 ?n

nC

A) !n B) 1n C) n D) !n

Q8: 0 ?n

C

A) 1 B) 0 C) n D) !n

Q9: 1 ?nC

A) 1 B) !n C) 0 D) n

Q10: ?n

nC

A) 0 B) n C) 1 D) !n


Q11: ?n

n rC

A) n

nC B)

!

! !

n

n r r C)

!

!

n

n r D)

!

1 !

n

r

Q12: If 5

nC =

7

nC than .............n

A) 7 B) 5


Q13: Which one of the following is true?

A) n

rP = ! n

rr C B)

n

rC = !n

rP r

C) n

rC =

n

rP D) !n n

r rC r P

Q14: 1 1

1 ?n n

r rC C

A) 1n

rC

B)

1

n

rC C)

n

rC D)

n

rP

Q15: If 1

3 23 7n nC C

then ?n

A) 5n B) 4n C) 6n D) 10n

Q16: If 4

nC = 5

nC then ...........n

A) 10n B) 9n C) 6n D) 8n

Q17: If 6. 4

nC =

3

nP , then ?n

A) 6 B) 7 C) 8 D) 5

Q18: If 220n

rC and 1320n

rP , then the values of n

and r are:

A) 12n , 2r B) 11, 3n r

C) 12, 3n r D) None

Q19: The total No of the diagonals in a ten sided figure is:

A) 40 B) 30 C) 35 D) 20

Q20: 16 16

10 11 ?C C

A) 16

12C B) 16

10C C) 16

15C D) 17

11C

Answer Key

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Q1: In how many ways can ‘6’ questions be selected out of 10 questions?

A) 220 B) 120 C) 250 D) 210

Q2: If2 2

8 4: 7 :6n nC P

, then ?n

A) 50 B) 10


Q3: Number of different committees of 3 men and 4 woman

out of 8 men and 6 woman are:

A) 800 B) 720

C) 840 C) None of these

Q4: The prediction of the chances that an event will occur is

called:

A) Combination B) Permutation

C) Probability D) Event

Q5: The set of all possible outcomes of an experiment is:

A) Sample space B) Permutation

C) Probability D) Event

Q6: Any subset of a sample space “S” called:

A) Event B) Element

C) Probability D) Experiment

Q7: What is the probability of selecting a prime number

from first 10 whole numbers?

A) 2

5 B)

3

10 C)

1

2 D)

3

4

Q8: An event “A”is called sure or absolute certain event if ?P A

A) 200 B) 20 C) 0 D) 1

Q9: If “S” is sample space, then ?P S

A) 0 B) 1 C) 2 D) 1/2

Q10: The two events A and B are said to be mutually

exclusive or disjoint if ?A B

A) A B) A B C) B D)


Q11: If B S then ?P B

A)

n B

n S B)

n S

n B

C) n B n S D) n S n B

Q12: If 0P A , then event “A” is called:

A) absolute impossible event B) favorable event

C) possible event D) sure event

Q13: The two events A and B are said to be mutually

exclusive or disjoint if A B is:

A) P A B B) P A P B

C) .P A P B D) 1

Q14: If for two events A and B,

P A B P A P B P A B , then the events A

and B are called:

A) Mutually exclusive B) Disjoint

C) Not mutually exclusive D) Sure

Q15: A dice is rolled, the probability of an event shown even

and odd number is:

A) 0 B) ½ C) 5/6 D) 1

Q16: If “A” is an event that occurs, then P not A is:

A) P A B) 1P A

C) 1P A D) 1 P A

Q17: Which of the following is true, for an event “A”

A) 0 100P A B) 0 1P A

C) 1 2P A D) 0 0.5P A

Q18: The probability of selecting a prime number from a list

of natural number 1,2,3,4,.....,33 is:

A) 1/2 B) 1 C) 1/4 D) 1/3

Q19: If there are 6 red balls out of 15 in a box, then the

probability that one ball drawn is red is:

A) 1/2 B) 2/5 C) 3/4 D) 5/2

Q20: If A and B are mutually disjoint events then

?P A B

A) P A B B) P A P B

C) .P A P B D) None of these

Answer Key

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Q1: cP A is equal to:

A) P A B) 1P A C) 1P A D) 1 P A

Q2: If 1,2,3,4,5,6S then probability of an event A

which denotes numbers less than 4 is:

A) 1

3P A B) 1

2P A

C) 3

4P A D) None of these

Q3: The probability that a three digit number taken at

random is divisible by 5 is:

A) 1/4 B) 11/5 C) 3/4 D) 1/5

Q4: If three coins are tossed, then what is the number of

elements in the sample space?

A) 90 B) 6 C) 8 D) 10

Q5: How many distinct permutations of the letter ENGIN

are possible?

A) 24 B) 120 C) 100 D) 96

Q6: The number of comities of 7 persons formed from a

group of 10 persons is:

A)130 B) 720 C) 120 D) 900

Q7: A dice is thrown, then the probability to get a number

divisible by 2 is:

A) 2/3 B) 1/3 C) 1/2 D) 3/5

Q8: How many distinct words are possible of the letters in

the word “PULLY”?

A) 50 B) 60 C) 120 D) 0 730

Q9:

3 !?

2 !

n

n

A) 2 !n B) 3 !n C) 3n D) 1n

Q10: 2 1 ?n n n

A) !n B) 2 !n C)

1 !

2 !

n

n

D)

2 !

1 !

n

n


Q11: 1

?4.3.2.1

n n

A) !n B) 4! 2 !

!

n

n

C)

!

4! 2 !

n

n D)

2 !

4! !

n

n

Q12: 10.9.8.7.6 ?

A) 10! 5! B) 10! 5! C) 10!

5! D)

5!

10!

Q13: 8.7.6

?3.2.1

A) 8!

3!5! B)

5!3!

8! C)

10!

2!8! D) 10!

Q14: 3 . 2 . 1 ........3.2.1 ?n n n

A) !n B) 1 !n

C) 3 !n D) 3 ! 3!n

Q15: 5 persons can be seated at a round table in:

A) 25 ways B) 24 ways

C) 20 ways D) 120 ways

Answer Key

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TYPE Objective Mathematical Induction and Binomial Theorem No 1

Q1: Which of the following is equal to 4a b ?

A) 4 3 2 2 3 44 6 4a a b a b ab b

B) 4 3 2 2 3 44 6 4a a b a b ab b

C) 4 3 2 2 3 44 12 4a a b a b ab b

D) 4 3 2 2 3 44 12 4a a b a b ab b

Q2: Which of the following is the binomial coefficients?

A) , , ,....,1 2 3

n n n n

n

B) , , ,....,0 1 2

n n n n

n

C) 1 2 3

, , ,....,n

n n n n

D) , , ,....,0 1 2

n n n n

n

Q3: The number of terms in the expansion 7a b is

equal to:

A) 7 B) 8 C) 6 D) 1n

Q4: The number of terms in the expansion n

a b is

....................... its index

A) one smaller than B) equal to

C) one greater than D) None of these

Q5: The sum of exponents of a and b in each term of the

expansion n

a b is equal to its:

A) 1n B) n C) 1n D) !n

Q6: The exponent of a in the expansion n

a b ............

from index to zero

A) increases B) decreases

C) doubled D) None of these

Q7: ?n

r

A) 1

n

r

B) 1

n

r

C) n

n r

D) n

n r

Q8: ?n

n r

A) 1

n

r

B) 1

n

r

C) n

r

D) n

r n

Q9: 11

?6

A) 11

5

B) 12

5

C) 10

5

D) 11

10

Q10: 3

nC exist when n is:

A) 2n B) 3n C) 3n D) 3n


Q11: 11

rC exist when r is:

A) 11r B) 12r

C) 11r D) Only when 11r

Q12: 11 11

4 3 ?C C

A) 11

4C B) 12

3C C) 12

4C D) 11

7C

Q13: The inequality 4 3 4n n is valid if:

A) 2n B) 2n C) 2n D) 2n

Q14: .... ?0 1 2

n n n n

n

A) !n B) 2n

C) 1

n n

n n

D) 1 !n

Q15: The inequality 2 2 1nn is valid if:

A) 3n B) 3n C) 3n D) 2n

Q16: If n is any positive integer, then 2 2 2 21 2 3 ..... ?n

A) 1 2 1

6

n n n B)

1 2 1

2

n n n

C) 1 2

6

n n n D)

1 2 1

3

n n n

Q17: If n is any positive integer, then

1 2 3 .......... ?n

A) 1

3

n n B)

1

2

n n

C) 2 1

3

n n D)

2 1

2

n n

Q18: If n is any positive integer, then 3 3 3 31 2 3 .......... ?n

A) 2

1

3

n n

B) 2

1

2

n n

C) 2

2 1

3

n n

D) 2

2 1

2

n n

Q19: If n is any positive integer, then

4 8 12 .......... 4 ?n

A) 4 1n n B) 2 1n n

C) 2 2 1n n D) 2 1n n

Q20: The inequality ! 2 1nn is valid if:

A) 3n B) 3n C) 4n D) 4n

Answer Key

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TYPE Objective Mathematical Induction and Binomial Theorem No 2

Q1: The inequality 1! 3n

n is valid if ........

A) 5n B) 5n C) 3n D) 3n

Answer Key

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TYPE Objective Fundamentals of Trigonometry No 1

Q1: The union of two non-collinear rays which have a

common endpoint is called:

A)Angle B) Radian

C) Degree D) Minute

Q2: The common end point of two rays is called:

A)Radian B) Degree

C) Vertex D) None of these

Q3: If the circumference of a circle is divided into 360

congruent parts, the angle subtended by one part at the centre of

the circle is called:

A)Angle B) Radian

C) Degree D) Minute

Q4: One degree is denoted by :

A)1 radian B) 1 C) 1 D) 01

Q5: The 60th part of one degree is called one:

A) Second B) Radian C) Degree D) Minute

Q6: One minute is denoted by:

A)1 radian B) 1 C) 1 D) 01

Q7: 01 is equal to:

A) 60 B) 60 C) 3600 D) 360

Q8: The 60th part of one minute is called one:

A) Second B) Radian

C) Degree D) Minute

Q9: One second is denoted by:

A) 1 radian B) 1 C) 1 D) 01

Q10: 1 is equal to:

A) 60 B) 60 C) 3600 D) 360


Q11: A right angle is the angle of measure:

A) 90 B) 90 C) 090 D)

0360

Q12: The system of measurement in which the angle is

measured in degrees, and its sub units, minutes and seconds is

called:

A) Circular System B) Sexagesimal System

C) M K S System D) CGS System

Q13: Which of the following trigonometric ratio is positive

in third quadrant?

A) Sin B) Cosine C) Tangent D) Secant


A) sin 23 sin 23 B) cos 20 cos20

C) tan0 0 D) cot 0 undefined

Q15: 2 2sin cos ?x x

A) 1 B) 0

C) 1 D) undefined

Q16: 2sec 1 ?x

A) 2cot x B)

2tan x

C) 1 D) 2tan x


A) 2 2tan 1 secx x B)

2 2cot 1 cscx x

C) 2 2tan cot 1x x D)

2 2sin cos 1x x

Q18: Which of the following trigonometric ratio is negative

in second quadrant?

A) Sine B) Cosine

C) Cosecant D) Nome of them

Q19: tan 45 cot 45 ?

A) 1 B) 2

C) 1 D) undefined

Q20: Which of the following is positive?

A) sin171 B) cos187

C) tan91 D) sin 30

Answer Key

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Q1: sin0 ..............

A) B) 0 C) 1 D) 1

Q2: sin30 ..............

A) 1 B) 3

2 C) 3 D)

1

2

Q3: sin 45 ..............

A) 2 B) 1

2 C)

2

2 D)

3

2

Q4: cos60 sin30 ?

A) 1 B) 2

2 C) 3 D)

1

2

Q5: sin ..............2

A) 1 B) 0

C) 1 D) Undefined

Q6: cos0 ..............

A) 1 B) 0

C) 1 D) Undefined

Q7: cos30 ..............

A) 1 B) 3

2 C) 3 D)

1

2

Q8: cos45 ..............

A) 2

2 B)

1

3 C)

2

2 D)

1

2

Q9: cos60 ..............

A) 2 B) 1

2 C)

2

2 D)

3

2

Q10: cos90 ..............

A) 1 B) 0

C) 1 D) Undefined


Q11: tan0 ..............

A) 1 B) 0

C) 1 D) Undefined

Q12: tan30 ..............

A) 2 B) 3 C) 2

2 D)

3

3

Q13: tan 45 ..............

A) 1 B) 3 C) 1 D) 2 3

Q14: tan60 ..............

A) 2 B) 3 C) 2

2 D)

3

3

Q15: tan90 ..............

A) 1 B) 0

C) 1 D) Undefined

Q16: cot 0 ..............

A) 1 B) 0

C) 1 D) Undefined

Q17: cot30 ..............

A) 2 B) 3 C) 2

2 D)

3

3

Q18: cot 45 ..............

A) 1 B) 3

C) 1 D) 2 3

Q19: cot 60 ..............

A) 2 B) 3 C) 2

2 D)

3

3

Q20: cot90 ..............

A) 1 B) 0

C) 1 D) Undefined

Answer Key

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Q1: sec0 ..............

A) 1 B) 0

C) 1 D) Undefined

Q2: sec30 ..............

A) 2 B) 3

2 C)

2

3 D) 2 3

Q3: sec45 ..............

A) 1 B) 2 C) 2

2 D) 2 2

Q4: sec60 ..............

A) 2 B) 3

2 C)

1

2 D) 2 3

Q5: sec90 ..............

A) 1 B) 0

C) 1 D) Undefined

Q6: csc0 ..............

A) 1 B) 0

C) 1 D) Undefined

Q7: csc30 ..............

A) 2 B) 3

2 C)

2

3 D)

1

2

Q8: csc45 ..............

A) 1 B) 2 C) 2

2 D) 2 2

Q9: csc60 ..............

A) 2 B) 3

2 C)

2

3 D) 2 3

Q10: csc90 ..............

A) 1 B) 0

C) 1 D) Undefined


Q11: sin180 ..............

A) 1 B) 0

C) 1 D) Undefined

Q12: sin 270 ..............

A) 1 B) 0

C) 1 D) Undefined

Q13: sin360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q14: cos180 ..............

A) 1 B) 0

C) 1 D) Undefined

Q15: cos270 ..............

A) 1 B) 0

C) 1 D) Undefined

Q16: cos360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q17: tan180 ..............

A) 1 B) 0

C) 1 D) Undefined

Q18: tan 270 ..............

A) 1 B) 0

C) 1 D) Undefined

Q19: tan360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q20: cot180 ..............

A) 1 B) 0

C) 1 D) Undefined

Answer Key

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Q1: cot360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q2: sec180 ..............

A) 1 B) 0

C) 1 D) Undefined

Q3: sec270 ..............

A) 1 B) 0

C) 1 D) Undefined

Q4: sec360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q5: csc180 ..............

A) 1 B) 0

C) 1 D) Undefined

Q6: csc270 ..............

A) 1 B) 0

C) 1 D) Undefined

Q7: csc360 ..............

A) 1 B) 0

C) 1 D) Undefined

Q8: sin .............

A) P

H B)

B

H C)

P

B D)

B

P

Q9: cos .............

A) P

H B)

B

H C)

P

B D)

B

P

Q10: tan .............

A) P

H B)

B

H C)

P

B D)

B

P


Q11: cot .............

A) P

H B)

B

H C)

P

B D)

B

P

Q12: sec .............

A) P

H B)

B

H C)

H

B D)

B

P

Q13: csc .............

A) P

H B)

B

H C)

P

B D)

H

P

Q14: sin720 ..............

A) 1 B) 0

C) 1 D) Undefined

Q15: cos210 ..............

A) 3

2 B)

3

2 C)

1

2 D)

1

2

Q16: tan300 ..............

A) 3 B) 3 C) 3

2 D)

3

2

Q17: cot120 ..............

A) 3 B) 3 C) 3

3 D)

3

3

Q18: sec450 ..............

A) 1 B) 0

C) 1 D) Undefined

Q19: csc150 ..............

A) 2 B) 2 C) 3

2 D)

3

2

Q20: tan3690 ..............

A) 1 B) 0

C) 1 D) Undefined

Answer Key

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Q1: sin 300 ..............

A) 1

2 B)

3

2 C)

3

2 D) 2

Q2: cos 330 ..............

A) 1

2 B)

3

2 C)

3

2 D) 2

Q3: tan 120 ..............

A) 3 B) 3

3 C) 3 D)

3

3

Q4: cot 135 ..............

A) 1 B) 3 C) 1 D) 3

Q5: sec 225 ..............

A) 2 3

4 B) 2 C) 2 D) 2

Q6: csc 390 ..............

A) 1 B) 0 C) 2 D) 2

Q7: In which quadrant sin is positive?

A) I and II B) I and III

C) I and IV D) All

Q8: In which quadrant cos is positive?


C) I and IV D) All

Q9: In which quadrant tan is positive?


C) I and IV D) All

Q10: In which quadrant cot is positive?


C) I and IV D) All


Q11: In which quadrant sec is positive?


C) I and IV D) All

Q12: In which quadrant csc is positive?


C) I and IV D) All

Q13: In which quadrant sin is negative?

A) II and II B) II and IV

C) III and IV D) All

Q14: In which quadrant cos is negative?



Q15: In which quadrant tan is negative?



Q16: In which quadrant cot is negative?



Q17: In which quadrant sec is negative?



Q18: In which quadrant csc is negative?



Q19: In which quadrant cos and tan are negative?

A) II B) III

C) IV D) I and II

Q20: In which quadrant all the trigonometric functions are

positive?

A) I-II-III and IV B) II and IV


Answer Key

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Q1 What is the circular measure of the angle between the

hands of a watch at 4 O’clock?

A) 120 B) 150 C) 90 D) 180

Q2: What is the length of the arc intercepted on a circle of

radius 14 cm by the arms of a central angle of 45

A) 11cm B) 22cm C) 26cm D) 6cm

Q3: If 12

sin13

and the terminal arm of the angle is in

first quadrant, then cos is:

A) 12

13 B)

5

13 C)

13

5 D)

5

12

Q4: If 12

sin13


first quadrant, then tan :

A) 12

5 B)

5

13 C)

13

5 D)

5

12

Q5: If 1

sin2 2


first quadrant, then cot :

A) 7

2 B) 7 C)

1

7 D)

2

7

Q6: If 5

sin13


first quadrant, then sec :

A) 12

13 B)

5

13 C)

13

12 D)

5

12

Q7: If 1

cos3


first quadrant, then sec :

A) 2 2 B) 3 C) 3

2 D)

1

3

Q8: If tan 1 and the terminal arm of the angle is in

fourth quadrant, then sin :

A) 2 2 B) 2 C) 1

2 D)

1

2

Q9: If 1

cos2


fourth quadrant, then tan :

A) 2 B) 0 C) 1 D) 1

Q10: If 9

cos41


fourth quadrant, then cot :

A) 9

40 B)

9

40 C)

40

9 D)

40

41


Q11: If 1

tan7

and terminal arm of the angle is not in

quad. III, then 2sec 1x :

A) 7 B) 1

7 C)

1

7 D) 7

Q12: 0 0 0 0sin 60 cos30 cos60 sin 30 :

A) sin30 B) sin 45 C) sin60 D) sin90

Q13: 0 01

2sin 45 csc 452

is:

A) 3 2

4 B) 3 2 C)

3

2 D)

4 2

3

Q14:

tan tan3 6

1 tan tan3 6

is:

A) 3

6 B)

3

3 C)

3

3 D)

3

3

Q15: if 2 0 2 0 0 0 0tan 45 cos 60 sin 45 cos 45 tan 60x Find

the value of x .

A) 1 B) 3 2 C) 3

2 D) 2

Q16: cos 330 ?

A) 1

2 B)

3

2 C)

1

2 D)

3

2

Q17: sin 765 ?

A) 2 B) 2 C) 1

2 D)

1

2

Q18: sin 675 ?

A) 2 2 B) 2 C) 1

2 D)

1

2

Q19: Which of the following is the circumference of a circle?

A) 2 r B) 2r C) r D)

22 r

Q20: Which of the following is the area of a circle?

A) 2 r B) 2r C) r D)

22 r

Answer Key

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Q1: tan cot ?

A) cos B) csc sec C) sin cos D) sin

Q2: cos tan sin ?

A) 1

cos B)

1

sin C) tan D) cot

Q3:

2

2

sin?

1 cos

A) 1 B) 1 C) sin D) cos

Q4: 2

2 tan?

1 tan

A) cot 2 B) tan 2 C) tan D) cot

Q5: 1 sin 1 sin ?

A) cos B) cos C) sin D) sin

Q6: sec tan sec tan

A) sec B) 1 C) 1 D) 0

Q7: tan cos .............

A) sin B) cos C) sec D) csc

Q8: sin 45 cos45 .............

A) 2

4 B) 2 2 C) 2 D)

2

2

Q9: 1

sin .............sin

A) tan cot B) cos tan

C) cos csc D) cos cot

Q10: 2 2tan cot 2 ?x x

A) 2 2sec cscx x B)

2 2sec cscx x

C) 2 2sec cscx x D)

2 2sec cscx x


Q11: What is the value of sin 47 if cos43 m ?

A) m B) 2 1m

C) 2 1m D)

21 m

Q12: In fourth quadrant psoitive functions are:

A) sin and csc B) cos and sec

C) tan and cot D) sin and cos

Q13: Value of 2 2 3cos sin cot

3 6 4

is:

A) 2

3 B)

3

2 C) 3 D) 2

Q14: Value of tan cot ?4 4

is:

A) 4 B) 1

2 C)

3

2 D) 2

Q15: 1

sin ?sin

x

x

A) 1

csccsc

x

x

B) 1

secsec

x

x

C) sec cscx x D) 1

coscos

x

x

Q16: Which of the following angles are coterminal?

A) 5

,3 3

B)4

,3 3

C) 17

,3 3

D) 13

,3 3

Q17: If cos 4r and sin 3r then r is:

A) 25 B) 5 C) 25 D) 25

Q18: 54 45 is ....... radians

A) 0.958 B) 0.0175

C) 0.65 D) None of these

Q19: If 3

cos2

and terminal side of the angle is not in

3rd quadrant then sin is:

A) 1

2 B)

1

2 C)

3

2 D)

3

2

Q20: If 2

tan5

and 02

then 2sec 1 is:

A) 8

5 B)

4

5 C)

4

25 D)

2

7

Answer Key

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TYPE Objective Trigonometric Identities No 1

Q1: Which of the following is the distance formula?

A) 2 2

1 2 1 2d x x y y

B) 2 2

1 2 1 2d x x y y

C) 1 2 1 2d x x y y

D) 2 2

1 1 2 2d x y x y

Q2: Find the distance between 3,8A and 5,6B

A) 6 B) 2 2 C) 2 D) 2 3

Q3: cos .............x y

A) cos cos sin .sinx y x y B) cos sin sin .cosx y x y

C) cos cos sin .sinx y x y D) sin cos cos .sinx y x y

Q4: cos .............x y

A) cos sin sin .cosx y x y B) cos cos sin .sinx y x y


Q5: sin .............x y

A) sin cos cos .sinx y x y B) cos sin sin .cosx y x y


Q6: sin .............x y

A) sin cos cos .sinx y x y B) cos sin sin .cosx y x y


Q7: Find the value of cos12

A) 3 1

2

B)

3 1

2 2

C)

3 1

2 2

D)

3 1

2

Q8: cos ...............2

A) sin B) cos C) sin D) cos

Q9: cos ...............2


Q10: cos ...............



Q11: cos ...............


Q12: 3

cos ...............2


Q13: 3

cos ...............2


Q14: cos 2 ...............


Q15: cos 2 ...............


Q16: sin ...............2


Q17: sin ...............2


Q18: sin ...............


Q19: sin ...............


Q20: 3

sin ...............2


Answer Key

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Q1: 3

sin ...............2


Q2: sin 2 ...............


Q3: sin 2 ...............


Q4: tan ...............2

A) tan B) cot C) tan D) cot

Q5: tan ...............2


Q6: tan ...............


Q7: tan ...............


Q8: 3

tan ...............2


Q9: 3

tan ...............2


Q10: tan 2 ...............



Q11: tan 2 ...............


Q12: Express sin5 sin7x x as a produc

A) 2sin3 cosx x B) 2sin cos6x x

C) 2sin6 cosx x D) sin cos6x x

Q13: cot ...............2


Q14: cot ...............2


Q15: cot ...............


Q16: cot ...............


Q17: 3

cot ...............2


Q18: 3

cot ...............2


Q19: cot 2 ...............


Q20: cot 2 ...............


Answer Key

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Q1: sec ...............2

A) sec B) sec C) csc D) csc

Q2: sec ...............2


Q3: sec ...............


Q4: sec ...............


Q5: 3

sec ...............2


Q6: 3

sec ...............2


Q7: sec 2 ...............


Q8: sec 2 ...............


Q9: csc ...............2


Q10: csc ...............2



Q11: csc ...............


Q12: csc ...............


Q13: 3

csc ...............2


Q14: 3

csc ...............2


Q15: csc 2 ...............


Q16: csc 2 ...............


Q17: 2

is in:

A) First Quadrant B) Second Quadrant

C) Third Quadrant D) Fourth Quadrant

Q18: 2

is in:



Q19: is in:



Q20: is in:



Answer Key

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Q1: 3

2

is in ..............



Q2: 3

2

is in ..............



Q3: 2 is in ..............



Q4: 2 is in ..............

A) First Quadrant !B) Second Quadrant


Q5: cos315 ..................

A) 1

2 B) 2 C)

1

2 D) 3

Q6: sin540 ..................

A) 1 B) 2

2 C) 1 D) 0

Q7: tan 135 ..................

A) 1 B) 1 C) 0 D) 3

Q8: sec 300 ..................

A) 2 B) 2 C) 3 D) 3

Q9: Express sin196 as a trigonometric function of

an angle of positive degree measure less than 45

A) sin16 B) cos16 C) sin16 D) cos16

Q10: Express cos147 as a trigonometric function

of an angle of positive degree measure less than 45

A) cos33 B) cos33 C) sin33 D) sin33


Q11: Express sin319 as a trigonometric function of an

angle of positive degree measure less than 45

A) sin 41 B) cos41 C) sin 41 D) cos41

Q12: Express cos254 as a trigonometric function of an


A) cos16 B) cos16 C) sin16 D) sin16

Q13: Express tan 294 as a trigonometric function of an


A) cot 24 B) tan 24 C) cot 24 D) tan 24

Q14: Express cos728 as a trigonometric function of an


A) sin8 B) cos8 C) sin8 D) cos8

Q15: Express sin 625 as a trigonometric function of an


A) sin5 B) cos5 C) cos5 D) sin5

Q16: Express cos 435 as a trigonometric function of an


A) 2 B) 2 C) sin15 D) 3

Q17: Express sin150 as a trigonometric function of an


A) 2 B) 2 C) 3 D) sin30

Q18: sin 180 sin 90 .............

A) sin cos B) sin cos

C) sin sin D) cos cos

Q19: sin780 sin 480 .............

A) 3

4 B)

1

4 C)

3

2 D)

1

2

Q20: cos120 sin30 .............

A) 1

4 B)

1

4 C)

1

2 D)

1

2

Answer Key

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Q1: cos11 sin11

............cos11 sin11

A) cot56 B) tan56 C) tan56 D) cot56

Q2: 2 2sin cos ..........

A) 1 B) 1 C) 0 D) cos2

Q3: sin .................

A) 21 cos B)

21 cos

C) 1 cos D) 1 cos

Q4: cos .................

A) 21 sin B)

21 sin

C) 1 sin D) 1 sin

Q5: 2 2sin 2 cos 2 ..........

A) 2 B) 1 C) 0 D) cos4

Q6: 2 2sin 20 cos 20 ..........

A) 1 B) 1 C) 0 D) 2

Q7: sin 45 ..............

A) 1sin cos

2 B) 1

sin cos2

C) 1sin cos

2 D) 1

sin cos2

Q8: cos 45 ..............

A) 1sin cos

2 B) 1

sin cos2

C) 1cos sin

2 D) 1

cos sin2

Q9: tan ...........

A) tan tan

1 tan .tan

B)

tan tan

1 tan .tan

C) tan tan

1 tan .tan

D)

tan tan

1 tan .tan

Q10: tan ...........

A) tan tan

1 tan .tan

B)

tan tan

1 tan .tan

C) tan tan

1 tan .tan

D)

tan tan

1 tan .tan


Q11: tan 2 ...........

A) 2

tan 2

1 tan

B) 2

tan 2

1 tan

C) 2

2 tan

1 tan

D) 2

2 tan

1 tan

Q12: sin cos ...........6 3

A) cos B) sin

C) sin D) cos

Q13: cos8 sin8

............cos8 sin8

A) cot37 B) tan37 C) tan37 D) cot37

Q14: sin 2 ............

A) sin cos B) sin cos

C) 2sin cos D) 4sin cos

Q15: cos2 ............

A) 2 2cos sin B)

2 2cos sin

C) 22sin 1 D)

21 2cos

Q16: cos2 ............

A) 2 2cos sin B) cos sin

C) cos sin D) 22cos 1

Q17: cos2 ............

A) 21 2sin B) cos sin

C) cos sin D) 2 2cos 2sin

Q18: cos ............2

A) 1 sin

2

B)

1 cos

2

C) 1 cos

2

D)

1 sin

2

Q19: sin ............2

A) 1 sin

2

B)

1 cos

2

C) 1 cos

2

D)

1 sin

2

Q20: tan ............2

A) 1 sin

sin

B)

1 cos

1 cos

C) 1 cos

1 cos

D)

1 sin

sin

Answer Key

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Q1: cot :2

A) 1 sin

sin

B)

1 cos

cos

C) 1 cos

cos

D)

1 sin

sin

Q2: sin3 :

A) 33sin 4sin B)

33sin sin

C) 34sin sin D)

34sin 3sin

Q3: cos3 :

A) 34cos 3cos B)

33cos 4cos

C) 34cos 3cos D)

33cos 4cos

Q4: tan3 :

A)

3

2

tan 3tan

1 3tan

B)

3

2

tan 3tan

3 tan

C)

3

2

3tan tan

3 tan

D)

3

2

3tan tan

1 3tan

Q5: 2sin cos :

A) sin sin B) sin sin

C) cos cos D) cos cos

Q6: 2cos sin ............


C) D) cos cos

Q7: 2cos cos ............



Q8: 2sin sin ............



Q9: sin sin :A B

A) 2sin cos2 2

A B A B B) 2cos sin

2 2

A B A B

C) 2cos cos2 2

A B A B D) 2sin sin

2 2

A B A B

Q10: sin sin :A B

A) 2sin cos2 2

A B A B B) 2cos sin

2 2

A B A B

C) 2cos cos2 2

A B A B D) 2sin sin

2 2

A B A B


Q11: cos cos :A B

A) 2sin cos2 2

A B A B B) 2cos sin

2 2

A B A B

C) 2cos cos2 2

A B A B D) 2sin sin

2 2

A B A B

Q12: cos cos :A B

A) 2sin cos2 2

A B A B B) 2cos sin

2 2

A B A B

C) 2cos cos2 2

A B A B D) 2sin sin

2 2

A B A B

Q13: 2 2sin cos ?

2 2

x x

A) 1

2 B) 2 C) 1 D) x

Q14: 2sin cos ?2 2

x x

A) sin 2x B) cos2x C) sin x D) cos x

Q15: 2 sin15 cos15 ?

A) 3 1

2

B)

3 1

2

C)

3

2 D)

1

2

Q16: 2 2cos 15 sin 15 ?

A) 3 1

2

B)

3 1

2

C)

3

2 D)

1

2

Q17: sin

sin 2 ?cos

x ax

x b

A) ab B) a b C) 2ab D) a

b

Q18:

2 2cos sin?

2sin cos

x x

x x

A) tan 2x B) tan x C) cot 2x D) cot x

Q19: 2

?sec cscx x

A) sin 2x B) cos2x C) sin x D) cos x

Q20: sin15 sin30 sin70 (cos20 cos75 ?

A) 2

3 B)

1

4 C)

3

2 D)

1

2

Answer Key

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TYPE Objective Trigonometric Functions and Their Graphs No 1

Q1: Which of the following is the domain of sine in real

numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q2: Which of the following is the domain of cosine in real

numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q3: Which of the following is the domain of tangent in real

numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q4: Which of the following is the domain of cotangent in

real numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q5: Which of the following is the domain of secant in real

numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q6: Which of the following is the domain of cosecant in

real numbers?

A) R

B) 2 1 ,2

R x x k k Z

C) ,R x x k k Z

D) None of them

Q7: Which of the following is the range of sine in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R

Q8: Which of the following is the range of cosine in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R


Q9: Which of the following is the range of tangent in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R

Q10: Which of the following is the range of cotangent in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R

Q11: Which of the following is the range of secant in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R

Q12: Which of the following is the range of cosecant in real

numbers?

A) 1 1x x R x

B) R

C) 1 1R x x

D) 1, 1R

Q13: A function is said to be ................. if x p D where

p is positive number f x p f x

A) Periodic function B) Range

C) Domain D) None of these

Q14: Which one of the following is periodic of sin

A) B) 2 C) 3 D) 2

Q15: Which one of the following is periodic of cos

A) B) 2 C) 3 D) 2

Q16: Which one of the following is periodic of tan

A) B) 2 C) 3 D) 2

Q17: Which one of the following is periodic of cot

A) B) 2 C) 3 D) 2

Q18: Which one of the following is periodic of sec

A) B) 2 C) 3 D) 2

Q19: Which one of the following is periodic of csc

A) B) 2 C) 3 D) 2

Q20: Find the period of sin3x

A) 2 B) 2

3

C)

3

2

D)

2

Answer Key

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TYPE Objective Trigonometric Functions and Their Graphs No 2

Q1: Find the period of cos2x

A) 2

B)

2

3

C) D) 2

Q2: Find the period of tan 4x

A) 3

2

B)

2

C) D)

4

Q3: Find the period of cot2

x

A) 2

B)

2

3

C) D) 2

Q4: Find the period of sin3

x

A) B) 2 C) 4 D) 6

Q5: Find the period of csc4

x

A) 8 B) 6 C) 4 D) 4

Q6: Find the period of sin5

x

A) 12 B) 10 C) 5 D) 6

Q7: Find the period of cos6

x

A) B) 6 C) 12 D) 16

Q8: Find the period of tan7

x

A) 3 B) 5 C) 7 D) 14

Q9: Find the period of cot8x

A) 3

B)

5

C)

4

5

D)

8

Q10: Find the period of sec9x

A) B) 2

9

C)

9

D)

3


Q11: Find the period of csc10x

A) B) 5

C) 5 D) 15

Q12: Find the period of 3sin x

A) B) 2 C) 4 D) 6

Q13: Find the period of 2cos x

A) 2 B) C) 3 D) 4

Q14: Find the period of 3cos5

x

A) 12 B) 10 C) 5 D) 6

Answer Key

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TYPE Objective Application of Trigonometry No 1

Q1: Find the value of sin38 24

A) 0.6262 B) 0.6211 C) 0.6112 D) 0.6012


A) 0.6212 B) 0.6240 C) 0.6220 D) 0.6230


A) 3.1235 B) 0.900 C) 1.1943 D) 0.909

Q4: If sin 0.5100x , find x

A) 30 40 B) 20 30 C) 10 45 D) 14 55


A) 0.0856 B) 0.6580 C) 0.5680 D) 0.8056

Q6: Find the value of cos36 20

A) 0.3456 B) 0.3541 C) 0.8055 D) 0.3241

Q7: Find the value of cot33 50

A) 1.4950 B) 1.4357 C) 2.0103 D) 3.1276

Q8: Find the value of tan65 30

A) 3.1235 B) 2.1943 C) 1.1943 D) 2.1345

Q9: If sin 0.5791 , find

A) 35 23 B) 33 22 C) 31 45 D) 34 51

Q10: If cos 0.5257 , find

A) 55 43 B) 55 26 C) 58 17 D) 58 51


Q11: If tan 1.705 , find

A) 45 43 B) 59 59 C) 59 36 D) 56 54

Q12: Find the value of c in ABC if 3.2a , 5.74b

and 90

A) 9.18 B) 6.73 C) 5.91 D) 6.98

Q13: Find the measure of 6.73 in given triangle?

A) 16 B) 4 2 C) 8 2 D) 16 2

Q14: Find the measure of 6.73 in given triangle?

A) 12 3 B) 9 3 C) 8 3 D) 4 3

Q15: A vertical pole is 8 m high and the length of its shadow

is 6 m. What is the angle of elevation of the Sun at that

moment?

A) 51 B) 52 C) 53 D) 54

Q16: A ladder leaning against a vertical wall makes an angle

of 24 with the wall. Its foot is 5 m from the wall. Find the

length.

A) 12.29m B) 12.12m C) 11.49m D) 10.64m

Q17:

tan2 ..................

tan2

A) b c

b c

B) a c

a c

C) b c

b c

D) a b

a b

Q18:

tan2 ..................

tan2

A) 2c

a b B)

a b

a b

C) 2

a b

c

D)

a b

a b

Q19:

tan2 ..................

tan2

A) c a

c a

B) c b

c b

C) a b

a b

D) a c

a c

Q20: Which of the following is the law of sines?

A) sin sin sin

a b c

B)

sin sin sin

b c a

C) 3 2 1

sin sin sin D)

sin 2 sin 2 sin 2

a b c

Answer Key

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Q1: If sin sin

a x

, then ?x

A) c B) 1 C) 0 D) b

Q2: Which of the following is the law of cosine?

A) 2 2 2 2 cosa b c bc B)

2 2 2 2 cosb a c bc

C) 2 2 2 cos2a b c bc D)

2 2 2 cosa b c bc

Q3: 2 2 2 cos ...............b c bc

A) a B) 2

a C) 3

a D) a

Q4: cos ...............

A)

2 2 2

2

c a b

ac

B)

2 2 2

2

a b c

ab

C)

2 2 2

2

b c a

bc

D)

2 2 2

2

c a b

abc

Q5: cos ...............

A)

2 2 2

2

c a b

ac

B)

2 2 2

2

a b c

ab

C)

2 2 2

2

b c a

bc

D)

2 2 2

2

c a b

abc

Q6: cos ...............

A)

2 2 2

2

c a b

ac

B)

2 2 2

2

a b c

ab

C)

2 2 2

2

b c a

bc

D)

2 2 2

2

c a b

abc

Q7: cos ...............2

A) s s a

bc

B)

s s b

ac

C) s s c

ab

D)

s s a

ac

Q8: cos ...............2

A) s s a

bc

B)

s s b

ac

C) s s c

ab

D)

s s a

ac

Q9: cos ...............2

A) s s a

bc

B)

s s b

ac

C) s s c

ab

D)

s s a

ac

Q10: ...............s

A) 2 a b c B) 2

a b c

C) 3

a b c D) 3 a b c


Q11: a b c

A) 2

s B) 2s C) 3s D) 4s

Q12: 2

a b c

A) s B) 2s C) 3s D) 4s

Q13: tan ............2

A)

s c s a

s s b

B)

s a s b

s s c

C)

s b s c

s s a

D)

.

s b s c

s a

Q14: tan ............2

A)

s c s a

s s b

B)

s a s b

s s c

C)

s b s c

s s a

D)

.

s b s c

s a

Q15: tan ............2

A)

s c s a

s s b

B)

s a s b

s s c

C)

s b s c

s s a

D)

.

s b s c

s a

Q16: tan ............2

A) r

s a B)

s a

r

C) r D) R

Q17: tan ............2

A) r

s b B)

s b

r

C) r D) R

Q18: tan ............2

A) r

s c B)

s c

r

C) r D) R

Q19: Area of ABC is ......

A) 1

sin4

bc B) 1

sin2

bc

C) sinbc D) 2 sinbc


A) 1

sin4

ac B) 1

sin2

ac

C) sinac D) sinac

Answer Key

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A) 1

sin4

ab B) 1

sin2

ab

C) sinab D) sinab


A) 2 sin sin

2sina

B) sin sin

2sina

C) 4 sin sin

2sina

D) sin sin

2sin


A) 2 sin sin

2sinb

B) sin sin

2sinb

C) 4 sin sin

2sinb

D) sin sin

2sin


A) 2 sin sin

2sinc

B) sin sin

2sinc

C) 4 sin sin

2sinc

D) sin sin

2sin

Q5: ............R

A) 2sin

a

B)

sin

a

C) sina D)

sin

r

Q6: ............R

A) 2sin

b

B)

sin

b

C) sinb D)

sin

r

Q7: ............R

A) 2sin

c

B)

sin

c

C) sinc D)

sin

r

Q8: ............r

A) s

B)

s a

C) s b

D) s c

Q9: 1 ............r

A) s

B)

s a

C) s b

D) s c

Q10: 2 ............r

A) s

B)

s a

C) s b

D) s c


Q11: 3 ............r

A) s

B)

s a

C) s b

D) s c

Q12: ............

A) s a s b s c B) s s a s b s c

C) s s a s b s c D) s a s b s c

Q13: Find the area of a triangle if 3cm , 4cm and 5cm

A) 6 B) 6 6 C) 6 2 D) 6 3

Q14: Which of the following is the area of an equilateral if

one side of the triangle is a cm?

A)

43

4

a B)

23

4

a C)

23

4

a D)

23

2

a

Q15: 1 1 1

.............ab bc ac

A) 1

2rR B)

1

r C)

1

rR D)

1

R

Q16: Find R if 13a , 14b and 15c

A) 8.13 B) 7.89 C) 8.90 D) 7.48

Q17: Find 1r if 13a , 14b and 15c

A) 7.5 B) 8.5 C) 10.5 D) 9.5


A) 10 B) 11 C) 12 D) 13


A) 14.4 B) 14.2 C) 14 D) 13.12

Q20: Find 2

3

r

r if 13a , 14b and 15c

A) 11

14 B)

6

7 C)

7

6 D)

13

14

Answer Key

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Q1: 1 2 3 ............rrr r

A) B) 2 C) D)

4

Q2: 1 2 3 ............rr r

A) rs B) 2

rs C) 3

rs D) 4

rs

Q3: s

A) r B) 1r C) 2r D) 3r

Q4: s a

A) r B) 1r C) 2r D) 3r

Q5: s b

A) r B) 1r C) 2r D) 3r

Q6: s c

A) r B) 1r C) 2r D) 3r

Q7: ...............4

abc

A) R B) S C) r D) rR

Q8: 4 ...............R

A) 4abc B) abc C) abcR D) R

Q9: 2 ...............S

A) a b c B) 2

a b c C) abc D) 4abc

Answer Key

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TYPE Objective Inverse Trigonometric Functions No 1

Q1: Evaluate 1sin 1 in the interval 0,

2

A) 2

B)

2

C)

3

D)

6

Q2: Evaluate 1sin 1 in the interval ,2 2

A) 3

B)

2

C)

3

D)

2

Q3: Evaluate 1 3

cos2

in the interval 0,

A) 3

B)

6

C)

6

D)

3

Q4: Evaluate 1 1

tan3

in the interval ,2 2

A) 3

B)

3

C)

6

D)

6

Q5: Evaluate 1 1

cos2

in the interval 0,

A) 3

B)

3

C)

6

D)

6

Q6: Evaluate 1 1

tan3


A) 3

B)

3

C)

6

D)

6

Q7: Evaluate 1cot 1 in the interval 0,

A) 3

B)

4

3

C)

3

4

D)

3

4

Q8: Evaluate 1 2

csc3


A) 3

B)

4

3

C)

3

4

D)

3

4

Q9: Evaluate 1 1

sin2


A) 3

B)

3

C)

4

D)

4

Q10: Find the value of 1 1

cos sin2

A) 1

2 B)

1

2 C) 2 D) 2



tan cos2

A) 1

3 B)

1

3 C) 3 D) 3

Q12: 1 1sin sin ................A B

A) 1 2 2sin 1 1A B B A

B) 1 2 2sin 1 1A B B A

C) 1 2 2sin 1 1A A B B

D) 1 2 2sin 1 1A B B A

Q13: Find the value of 1tan tan 1

A) 1 B) 1 C) 0 D) 3


sin sin2

A) 1

2 B)

1

2 C) 2 D) 2

Q15: 1 1cos cos ................A B

A) 1 2 2cos 1 1AB A B

B) 1 2 2cos 1 1AB A B

C) 1 2 2cos 1 1AB A B

D) 1 2 2cos 1 1AB A B

Q16: Find the value of 1sin tan 1

A) 1

2 B)

1

2 C) 2 D) 2


sec sin2

A) 2

3 B)

2

3 C)

2

2 D)

2

3

Q18: 1 1sin sin ................A B

A) 1 2 2sin 1 1A B B A

B) 1 2 2sin 1 1A B B A

C) 1 2 2sin 1 1A A B B

D) 1 2 2sin 1 1A B B A


tan sin2

A) 1

3 B)

1

3 C)

3

6 D)

2

3

Q20: 1 1cos cos ................A B

A) 1 2 2cos 1 1AB A B

B) 1 2 2cos 1 1AB A B

C) 1 2 2cos 1 1AB A B

D) 1 2 2cos 1 1AB A B

Answer Key

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TYPE Objective Inverse Trigonometric Functions No 2

Q1: 1 1tan tan ................A B

A) 1

A B

AB

B) 1

A B

AB

C) .

1

A B

A B D)

.

1

A B

A B

Q2: 1 1tan tan ................A B

A) 1

A B

AB

B) 1

A B

AB

C) .

1

A B

A B D)

.

1

A B

A B

Answer Key

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TYPE Objective Solution of Trigonometric Functions No 1

Q1: Factorize 2cos sin 1x x

A) sin sin 1 0x x B) sin cos 1 0x x

C) sin sin 1 0x x D) sin cos 1 0x

Q2: Find the solution set of sin 0x

A) n B) 2

n

C) 3

2

n

D) 2 1n

Q3: Find the solution set of sin 1 0x

A) 24

n

B) 3

n

C) n D) 22

n

Q4: Find the solution set of cos 0x

A) 24

n

B) 2

n

C) n D) 2n

Q5: Find the solution set of 1

cos 02

x

A) 2 4

2 23 3

n n

B) 4

2 23 3

n n

C) 2 3

2 23 2

n n

D) 2 4

3 3n n


sin2

x in 0,2

A) 4 5

,3 3

B) 3 3

,4 5

C) 4

,3 3

D) 2

,3

Q7: Find the solution set of csc 2x in 0,2

A) 4 7

,6 6

B) 5

,3 3

C) 5

,6 6

D) 5 2

,6 5


cot3

x in 0,2

A) 2 5

,3 3

B) 2

,3 3

C) 2 4

,3 3

D) 4

,3 3

Q9: What is the period of sin x in order to find the solution

set of any trigonometric equation?

A) B) 2 C) 2

D)

3

2

Q10: What is the period of cos x in order to find the solution


A) B) 2 C) 2

D)

3

2


Q11: What is the period of sec x in order to find the solution


A) B) 2 C) 2

D)

3

2

Q12: What is the period of csc x in order to find the solution


A) B) 2 C) 2

D)

3

2

Q13: What is the period of tan x in order to find the solution


A) B) 2 C) 2

D)

3

2

Q14: What is the period of cot x in order to find the solution


A) B) 2 C) 2

D)

3

2

Q15: What is the period of sin 2x in order to find the

solution set of any trigonometric equation?

A) B) 2 C) 2

D)

3

2

Q16: What is the period of cos2x in order to find the


A) B) 2 C) 2

D)

3

2

Q17: What is the period of sin3x in order to find the


A) B) 2 C) 2

3

D)

3

2

Q18: What is the period of cos3x in order to find the


A) B) 2 C) 2

2

D)

3

2

Q19: How many roots does 1

sin2

x have in the interval

0,2 ?

A) 1 B) 2 C) 3 D) 4


sin2

x in the interval

0,2 ?

A) 5

,6 6

B) 2

,3 3

C) 11

,6 6

D) 17

,6 6

Answer Key

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TYPE Objective Past Papers Year 2009

Q1: 1 1 i i is:

A) 1 B) 1 C) i D) i

Q2: Modulus of 8 15i is:

A) 8 B) 15 C) 17 D) 8 15i

Q3: If A has 3 elements and B has 6 elements, then

minimum number of elements in A B is:

A) 3 B) 6 C) 9 D) 18

Q4: A matrix whose determinant value is zero is known as:

A) Zero matrix B) Singular matrix

C) Non singular matrix D) identity matrix

Q5: If the sum of the roots of the equation 2 2 2 0ax x a is equal to their product, then the value of a

is:

A) 1 B) 2 C) 3 D) 4

Q6: The quotient of two polynomials

P x

Q x where

0Q x with no common factors is called a:

A) Rational fraction B) Irrational fraction

C) Polynomial D) None of these

Q7: The sum of series 2 7 12 ............... up to 12 terms

is:

A) 3 72

nn B) 3 7

2

nn

C) 3 33

nn D) None of these

Q8: What is the probability of getting a 3 when one die is

thrown?

A) 1

6 B)

1

2 C)

1

4 D)

1

3

Q9: An expression consisting or two terms is called:

A) Monomial B) Trinomial

C) Binomial D) None of these


3 6 4

is:

A) 2

3 B)

3

2 C) 3 D) 2


Q11: In fourth quadrant psoitive functions are:

A) sin and csc B) cos and sec

C) tan and cot D) None of these

Q12: cos cos ......................

A) 2cos sin B) 2sin cos

C) 2cos cos D) 2sin sin

Q13: tan 2 ...................

A) tan B) tan

C) cot D) cot

Q14: In any triangle ABC , 1 2 3 ......................r r r r

A) B) 2 C)

3 D) 4

Q15: 1tan ...................x

A) 1cot

2x

B) 1tan

2x

C) 1cot

2x

D) 1tan

2x

Q16: sin is .............

A) Odd function B) Even function

C) Both even and odd D) None of these

Q17: Roots of the equation 2 0ax bx c are rational if:

A) 2 4 0b ac B)

2 4 0b ac

C) 2 4 0b ac D)

2 4b ac is perfect

Q18: G.M between 5 and 80 are:

A) 85

2 B)

800

85


Q19: 10

7 ..................P

A) 604800 B) 60400


Q20: If A and B are any two matrices then:

A) 0AB B) AB BA

C) AB I D) AB may not be defined

Answer Key

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Q1: A decimal which has only finite number of decimal places is called ................. dcimal. A) Terminating B) Non terminating C) Recurring D) Non recurring

Q2: , ,a b c R , a b b c a c , this

inequality property of real number is ................. A) Reflexive B) Trichotomy C) Transitive D) Symmetric Q3: Multiplicative inverse of non zero complex number

,a b is:

A) 2 2 2 2

,a b

a b a b

B)2 2 2 2

,a b

a b a b

C) 2 2 2 2

,a b

a b a b

D) 2 2 2 2

,a b

a b a b

Q4: For the numbers a and b , 2

G is:..,,,444

A) A H B) A H

C) A H D) A

H

Q5: 9

2P i equal to:

A) 91 B) 6 C) -6 D) 72

Q6: An equation of the form ax by k is

homogeneous linear equation when:

A) 0, 0, 1a b k B) 0, 1, 2a b k C) 0, 0, 0a b k D) 0, 0, 0a b k

Q7: Number of roots contaning non zero imajinary part of cube roots of unity are: A) One B) Two C) Three D) Four

Q8: Partial fractions of

1

1x x are:

A) 1 1

1x x

B)

1 1

1x x

C) 1 2

1x x

D)

1 2

1x x

Q9: 1

5 and

1

8 are two terms of an H.P and their sum is

13

40, then sum of the corresponding terms of A.P will be:

A) 40

13 B)

1

13


Q10: The inequality ! 2 1nn is true for integral

values of:

A) 1n B) 2n C) 3n D) 4n


Q11: Which of the following angles are coterminal?

A) 5

,3 3

B)4

,3 3

C) 17

,3 3

D) 13

,3 3

Q12: If cos 7r and sin 3r then r is:

A) 9 B) 58 C) 58 D) 49

Q13: If is the period of tan x then period of tan3

x is:

A) 3 B) 2 C) D) 2

Q14: The circle passing through the vertices of a triangle is called a/an: A) In-circle B) Circum-circle C) Ex-circle D) Semi-circle Q15: For any equilateral triangle having sides measures

a , the value of S is:

A) 3

2

a B)

3

2

a C)

3

a D)

2

3

4a

Q16: s a

is the value of:

A) R B) r C) 1r D) 2r

Q17: Factorial form of 1n n is:

A)

1 !

2 !

n

n

B)

1 !

2 !

n

n

C)

1 !

1 !

n

n

D)

!

1 !

n

n

Q18: The matrix A is Skew Hermition when t

A is:

A) A B) A C) A D) tA

Q19: 1 1tan tan ?A B

A) 1tan1

A B

AB

B) 1tan1

A B

AB

C) 1 1

1 1

tan tan

1 tan tan

A B

A B

D) 1 1

1 1

tan tan

1 tan tan

A B

A B

Q20: Number of elements in the power set of set containing n elements is:

A) n n B) 2n C) 2n n D) 2n

Answer Key

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Q1: Multiplicative inverse of i is:

A) i B) i C) 1 D) 1 Q2: Contra positive of i is:

A) p q B) q p

C) p q D) None of these

Q3: If A is a matrix of order m n and B is a matrix

of order n p , the order of AB will be:

A) p m B) p n

C) m p D) None of these

Q4: When polynomial 3 24 2 5x x x is divided by

1x , the remainder is:

A) 6 B) 4 C) 8 D) 0

Q5: Partial fractions of

1

1x x are:

A) 1 1

1x x

B)

1 1

1x x

C) 1 2

1x x

D)

1 2

1x x

Q6: For what value of n , 1 1

n n

n n

a b

a b

is the positive

geometric mean between a and b ?

A) 1n B) 1 C) 1

2 D) 0

Q7: Factorial form of 1 1

3.2.1

n n n is:

A) 1 !

3!.2!

n B)

1 !

3! 2 !

n

n

C)

!

3! 2 !

n

n D) None of these

Q8: The sum of coefficients in the Binomial expansion is equal to:

A) 2n B) 2 1n C) 2n D) 0

Q9: 54 45 is ....... radians

A) 0.958 B) 0.0175 C) 0.65 D) None of these

Q10: For two mutually exclusive events A and B , we have:

A) A B B) A B

C) A B A B D) None of these


Q11: What is the middle term in the expansion of

na b for even values of n ?

A) 1

2

n B)

3

2

n

C) 2

n D) 1

2

n

Q12: Period of 3cos5

x is:

A) 10 B) 2 C) D) None of these

Q13: sin 2 ?

A) 2

2

1 tan

1 tan

B) 2

2 tan

1 tan

C) 2

2 tan

1 tan

D) None of these

Q14: The value of C in the given triangle is:

A) 4 2 B) 16

C) 8 2 D) None of these Q15: Hero's Formula is used to calculate: A) Area of triangle B) Sides of triangle C) Angles of triangle D) None of these

Q16: 12tan ?A

A) 1

2tan

1

A

A

B)

21tan1

A

A

C) 1

2

2tan

1

A

A

D) None of these

Q17: Solution set of equation 1 cos 0x is:

A) n B) 2 n

C) 2n D) 3

2n

Q18: Harmonic Mean between a and b is:

A) 2ab

a b B)

2

a b

C) 2

a b

ab

D) ab

Q19: If and are the roots of 2 0ax bx c , then

2 2 is:

A) b

a

B)

2

2

2b ac

a

C) 2

2

4b ac

a

D) None of these

Q20: A bijective function is: A) Both one-one and onto B) One-one but not onto C) Onto, but not one-one D) Neither one-one nor onto

Answer Key

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Q1: 18 ?i

A) 3 B) 2 C) 1 D) 1

Q2: 4

1 i is:

A) 1 i B) 1 i C) 2 1 i D) 2 1 i

Q3: C C

x y is:

A) X Y B) X Y

C) CX Y D) None of these

Q4: If 5 2 1 5

2 1 12 3X

, then X is:

A) 1 3

2 1

B) 1 3

2 1

C) 2 3

1 1

D) 2 3

1 1

Q5: For what value of m , the roots of the equation

21 2 3 8 0m x m x m are equal?

A) 1

2

B)

2

3

C) 1

3

D) None of these

Q6: If is the cube roots of unity, then a quadratic

equation whose roots are 2 and 22 is:

A) 2 2 4 0x x B)

2 2 4 0x x

C) 2 4 0x x D)

2 2 4 0x x

Q7: If degree of P x is 3 and degree of Q x is 4, then

P x

Q x will be:

A) Proper Rational Fraction B) Improper Rational Fraction

C) Polynomial D) None of these

Q8: If a , b , c are in G.P and 0a , 0b , 0c , then

the reciprocals of a , b , c form:

A) A.P B) G.P

C) H.P D) None of these

Q9: If a , b , c are in A.P , then the common difference is:

A) 2

a c

ac

B)

2ac

a c

C) 2

a c

ac

D)

2ac

a c

Q10: A card is drawn from a pack of 52 cards at random.

What is the probability that it is either a heart or a king?

A) 4

13 B)

1

13 C)

9

13 D)

2

13


Q11: The middle terms in the expansion of

12

2

2

2

x

x

will

be:

A) 5th term B) 7th term

C)8th term D) 6th term

Q12: Circular measure of the angle between the hands of a

watch at 4'O clock is :

A) 6

radians B)

2

3

radians

C) 3

4

radians D)

3

radians

Q13: If 2

tan5

and 02

then 4cos 3sin

cos sin

is:

A) 14

3 B)

26

3

C) 13

7 D) None of these

Q14: The angles 90 , 180 , 270 360

are the ...... angles

A) Composite B) Half

C) Quadrantal D) Allied

Q15: The period of 3cos5

x is:

A) 5 B) 2 C) 10 D) 6

Q16: The in-radius 3cos5

x of a triangle is given by:

A) s B) s

C) s

D) None of these

Q17: 1 3

sin cos ?2

A) 0 B) 1

2 C)

1

6 D)

3

2

Q18: If and are the roots of the equation

2 1 0x p c then 1 1 is:

A) 1 c B) 2c

C) c D) None of these

Q19: Which term of 64,60,56,52,....... is zero?

A) 16th B) 17th

C) 14th D) 15th

Q20: Multiplicative inverse of 1 2i is:

A) 1 2

5

i B)

1 2

5

i

C) 1 2

4

i D) None of these

Answer Key

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Q1: 20 ?i

A) 3 B) 2 C) 1 D) 0

Q2: 2

?1 i

A) 1 i B) 1 i C) 2 1 i D) 2 1 i

Q3: If A has 3 elements, B has 5 elements then maximum

number of elements in A B is:

A) 5 B) 3 C) 2 D) 8

Q4: If 1 1

Aa b

and 2

A I then a and b are:

A) 0, 1a b B) 1, 0a b

C) 2, 1a b D) 3, 0a b

Q5: For what value of k , the sum of roots of the equation 2 4 0x kx is equal to the product of its roots?

A) 1 B) 4 C) 4 D) 4

Q6: If the roots of 2 0x px q differ by unity then

2 4p q is:

A) 0 B) 1 C) 2 D) 1

Q7: The rational fraction

P x

Q x, where 0Q x , is

Proper Rational Fraction if:

A) Deg DegP x Q x B) Deg DegP x Q x

C) Deg DegP x Q x D) None of these

Q8: If 2 2 2, ,a b c are in A.P, then a b , c a ,b c are in:

A) A.P B) G.P

C) H.P D) None of these

Q9: If 1 1 1

, ,2 1 4 1k k k

are in H.P, then the value of k is:

A) 3 B) 2 C) 1 D) 4

Q10: A die is rolled, what is the probability of getting a

number which is even and greater than 2?

A) 1

2 B)

1

3 C)

1

6 D)

2

3


Q11: The expansion of 1

31 2x is valid if:

A) 1x B) 1x

C) 1

2x D)

1

2x

Q12: 1 is equal to:

A) radian180

B)

180radian

C) 1

radian180

D) 180 radian

Q13: If 3

cos2

and terminal side of the angle is not in

3rd quadrant then sin is:

A) 1

2 B)

1

2

C) 3

2 D) None of these

Q14: A reference angle is always:

A) 02

B) 2


Q15: The period of 5cos3

x is:

A) 3 B) 2 C) 6 D) 5

2

Q16: The in-radius 2 of a triangle is given by:

A) s

B)

4

abc

C) 2sin

c

r D)

1sin

2bc A

Q17: 1cos 2sin x

is equal to:

A) 21 2x B)

21 2x

C) 22 1x D)

21 x

Q18: If the roots of 2 0ax bx c are real an unequal

then:

A) 2 4 0b ac B)

2 4 0b ac

C) 2 4 0b ac D)

2 4 0b ab

Q19: 12 1 .........i

i

is in:

A) .A P B) .G P

C) .H P D) None of these

Q20: If 1 1 2z i and 2 2z i , then 1 2z z is:

A) 4 3

5

i B)

4 3

5

i

C) 5i D) None of these

Answer Key

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Q1: If a complex number 1 3z i then z is:

A) 4 B) 2 C) 3 D) 2i

Q2: If 1, 1, ,S i i , then set " "S is an abelian group

with respect to:

A) Addition B) Multiplication

C) Subtraction D) Division

Q3: The system of linear equations has unique solution if:

A) 0A B) 0A C) 0A D) 0A

Q4: If ij m n

A a

is a square matrix t

A A then A is:

A) Symmetric B) Skew Symmetric

C) Hermition D) None of these

Q5: The sum of cube roots of unity is:

A) 0 B) 1 C) 2 D) 3

Q6: If 2 4 0b ac then the roots of equation are:

A) Rational B) Distinct

C) Real and Equal D) Imaginary

Q7: A rational fraction

P x

Q x in which the degree of

P X is less than the degree of Q x is called:

A) Improper Fraction B) Proper Fraction

C) Common Fraction D) None of these

Q8: A.M between 2 and 3 2 is:

A) 4 2 B) 2 2


Q9: The sum of infinite G.P 2, 2,1,......... is:

A) 3 2 2 B) 2 2 2

C) 4 2 2 D) 5 2 2

Q10: The number of diagonals of a 6 sided figure is:

A) 9 B) 10 C) 11 D) 12


Q11: In expansion of Binomial Theorem, the general term is:

A) n r

na b

r

B) n r r

na b

r

C) r r

na b

r

D) None of these

Q12: 1

2sin 45 csc452

is equal to:

A) 3

2 B)

1

2 C) 2 D)

5

2

Q13: The measure of or 3

2

lies in the .......

quadrant

A) I B) II C) III D) IV

Q14: sin sin is equal to:

A) 2cos sin B) 2sin cos

C) 2cos cos D) 2sin sin

Q15: The period of tan3

x is:

A) 2 B) C) 3 D) 4

Q16: In a triangle ABC if vertex A is at origion then the law

of cosine is:

A) 2 2 2 2 cosa b c bc B)

2 2 2 2 cosa b c bc

C) 2 2 2 2 cosb a c ac D)

2 2 2 2 cosa b c bc

Q17: In a triangle ABC if one side c and two angles ,

are given then area will be:

A)

2 sin sin

2sin

a

B)

2 sin sin

2sin

b

C)

2 sin sin

2sin

c

D)

2 sin sin

2sin

c

Q18: Circum-centre of a circle is the point of intersection of

the:

A) Perpendiculars B) Right Bisectors

C) Angle Bisectors D) Sides Bisectors

Q19: Range of 1tan x

is:

A) 2 2

x B) 0 x

C) 0 x D) None of these

Q20: If 1

cot3

x then ...................x in interval

0,2

A) 4

,3 3

B)

5,

6 6

C) 2

3

D)

5

6

Answer Key

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TYPE Objective Past Papers Year 2013-2

Q1: Multiplicative inverse of non zero complex number

,a b is:

A) 2 2 2 2

,a b

a b a b

B)2 2 2 2

,a b

a b a b

C) 2 2 2 2

,a b

a b a b

D) 2 2 2 2

,a b

a b a b

Q2: If 2 3z i , then z z is:

A) 4 B) 6i C) 6i D) 4i

Q3: Contra positive of p q is:

A) q p B) p q

C) q p D) None of these

Q4: The set 1, 1, ,i i possess Closure Property with

respect to:

A) Addition B) Multiplication

C) Division D) Subtraction

Q5: If all elements in a square matrix ijA a below the

principal diagonal are zero i.e. 0ija i j is called:

A) Upper Triangular Matrix B) Triangular Matrix

C) Lower Triangular Matrix D) None of these

Q6: In a square matrix ijA a , if 0ija i j and

ija K , then matrix A is called:

A) Diagonal Matrix B) Scalar Matrix

C) Unit Matrix D) Null Matrix

Q7: 1 1 i i is:

A) 1 B) i C) i D) 1

Q8: If Discriminant 2 4b ac is a perfect square, then roots

are:

A) Irrational B) Rational

C) Imaginary D) Repeated Equal

Q9: If 1 2n na a n and 1 2a , then 3 ?a

A) 6 B) 4 C) 11 D) 17

Q10: The positive Geometric Mean of -2 and 8 is:

A) 4i B) 4i C) 4 D) 4


Q11: If a die is rolled, then the probability of the dots on the

top are greater than 4 is:

A) 1

6 B)

1

3 C)

1

4 D)

1

2

Q12: The sum of co-efficients in the binomial expansion is:

A) 12n B)

12n C) 1 2n

n D) 2n

Q13: 12n and

12n lie in ................. quadrant

A) I B) II C) III D) IV


3 6 4

is:

A) 2

3 B)

3

2 C) 3 D) 2

Q15: The angles associated with basic angles of the measure

to a right angle or its multiple are called ....... angles

A) Supplementary B) Complementary

C) Obtuse D) Allied

Q16: sin cos6 3

is equal to:

A) cos B) sin

C) sec D) csc

Q17: The period of trigonometric function 3cos5

x is:

A) 2 B) 10


Q18: In any triangle ABC , 1 2 3 ......................r r r

A) 2

rs B) 2

s C) 2 D)

2r

Q19: The value of 1 3

sin cos2

is:

A) 3

2 B)

1

2 C)

1

2 D)

1

3

Q20: The solution set of trigonometric equation

1 cos 0x is:

A) 2n B) 2n

C) 2 n D) None of these

Answer Key

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Q1: , ,a b R a b b a , this property is called:

A) Transitive B) Symmetric C) Reflexive D) Additive

Q2: 22 .......................i

A) i B) i C) 1 D) 1

Q3: If A B , then .................A B

A) A B) B C) D) X

Q4: If order of a matrix A is 2x3 and of matrix B is 3x3 the order of 'AB' is: A) 3x2 B) 2x2 C) 3x3 D) 2x3 Q5: The discriminate for equal roots is: A) >0 B) <0 C) =0 D) Perfect square

Q6: If 3 2 5ma n , its nth term is:

A) 2n+1 B) 2n+3 C) 2n-2 D) 2n-8 Q7: If a, A, b are in A)P) then 2A is:

A) a b B) 2

a b C) a b D) a b

Q8: The number of terms in the expansion of

____________n

a x

A) n+1 B)n-1 C) n D) 2n

Q9: 2!n n is true for integral value of n is:

A) 1 B) 2 C) 3 D) 4

Q10: If , , are the angles of a triangle than

tan tan ......................

A) 0 B) 1 C) 2 D) None of these


Q11: cos11 sin11

...............cos11 sin11

A) tan11 B) cot11 C) tan56 D) cot56

Q12: Sine is a periodic function and its period is:

A) B) 2


Q13: Geometric Means between -2 and 8 is:

A) 2 B) 8

C) 4 D) None of these Q14: All trigonometric functions are positive in quadrant:

A) I B) II C) III D) IV Q15: In a triangle ABC, the measures of the sides opposite to three angles are denoted by:

A) 1,2,3 B) A,B,C

C) , , D) a,b,c

Q16: 1 2 3. . . ............r r r r

A) s B) s-a C) D) 2

Q17: 1tan 1 ...............

A)4

B)

2

C)

4

D)

Q18: The graph of 1siny x is along the:

A) x-axis B) y-axis C) Both A and B D) None of these

Q19: In the binomial expansion of n

a b , n is called:

A) Root B) Element C) Index D) None of these

Q20: If 1r , then 1 ?n P

A) !n B) n

C) 1n D) None of these

Answer Key

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Documents

Hssc i objective workbook