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JAGRUTI CLASSES
First Floor Only, Chaturbhai Complex – 2, Harni – Warshiya Ring
Road, Vadodara Std 9 English Mohinder Sir – +91 97146 30799 SA
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Chapter:- 1 Set Operations
� Select proper option (A), (B), (C) or (D) from giv en options
and write in the box given on the right so that the statement
becomes correct. 1. If U= {x / x ∈ N, x < 5), A = {x / x ∈ N, x
< 2) then A’= ................ a) {1,2} b) {1,2,3,4,5} c) {3,4}
d) {3,4,5} 2. ∅ ............. {∅} a) ⊂ b) ∉ c) = d) ⊄ 3. If A=
{1,2,3), B= {3,4,5} then A∪B= ........... a) {1,2,3,4,5} b) {3} c)
{1,2} d) ∅ 4. If A= {x / x ∈ N, x < 7) and B = {2,4,6} then B=
.......... A. a) = b) ⊂ c) ⊄ d) ~ 5. If A = {1,2, 3} B = {2,3,4} ,
C= {3,4,5} then (A∩B) ∩ C’ = ........ where U = {1,2,3,4,5}. a) {1}
b) {2} c) {1, 2} d) {2, 3} 6. If A= {x / x ∈ N, x < 3) B =
{1,2,3}, U = N, then A and B are .......... sets. a) equal b)
singleton
c) null d) complements of each-other 7. If A= {1,2,3,4}
.......... is a correct statement. a) 3 ∉ A b) {1} ∈ A c) {2} ∈ A
d) {3,4} ⊂ A 8. If A = {1,2,3,4}, then number of subsets of A are =
........... a) 2 b) 4 c) 8 d) 16 9. ........... is a singleton. a)
A= {x ∈ R ; x2 – x = 0} b) B= {x / x ∈ N , 2x =3} c) C= {x / x ∈ R
, x2 = -4}
d) B= {x / x ∈ Z , x is a neither positive nor negative} 10.If A
= {0,1, 2, 4} B = {1, 3, 5, 7, 9} , C= {0, 1, 4, 3, 9} then (A∩B) ∩
C =
........ a) A b) B c) C d) A U B 11.If A ∪ B = ∅, then
............. a) A ≠ ∅ and B ≠ ∅ b) A = ∅ and B ≠ ∅ c) A ≠ ∅ and B
= ∅ d) A = ∅ and B = ∅ 12.If A= {x / x ∈ N, x < 4), B =
{-1,0,1,2,3}, C = {0,1,2}, then (A ∪ B) ∩ (A
∪ C) =........... a) {1,2,3,4} b) {0,1,2} c) {0,1,2,3,4} d) {-1,
0, 1, 2, 3, 4} 13.If A = {1, 2, 3, 4}, B= {2, 4, 5, 6}, U = {1, 2,
3, 4, 5, 6, 7}, then A’ ∩
B’ = .............
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a) ∅ b) {1,2,3,4,5,6} c) {7} d) {3, 4, 5, 6} 14.∅ ∩ U’ =
............... a) ∅ b) U c) {U} d) {∅} 15.(A ∩ B’)’ =
.............. a) A ∪ B’ b) A’ ∪ B c) A ∪ B d) A ∩ B
BASED ON EXERCISE : 1.1 �Answer the following questions by
selecting appropriate alternative
from alternatives given in questions: 1. The theory of sets was
developed by ............... a) R. Dedekind b) Bhaskaracharya c)
Newton d) George Cantor 2. ............... collection of objects or
things is considered as a set. a) An undefined b) A defined c) A
well-defined d) Any 3. A set without any number is called a
........... set. a) universal b) sub- c) null d) singleton 4. A set
having only one member is called ............. set. a) a finite b)
a singleton c) an empty d) a well-defined 5. If x is a member of
set A, this fact is denoted by x ...........A.
a) ∈ b) ⊂ c) ∉ d) ⊄ 6. If x is not a member of set A, we write
as x ...........A.
a) ∈ b) ⊂ c) ⊄ d) ∉ 7. A set whose number of member of members
is a positive integer is called .... a) an infinite set b) an empty
set c) a finite set d) universal set 8. A is subset of B. This fact
is denoted by ............. a) A ⊃ B b) A ∋ B c) A ∈ B d) A ⊂ B 9.
A ............. A is true. a) ⊂ b) ⊄ c) ∈ d) ∉ 10.If A is any set
and null set is denoted by then ∅ = .............A. a) ∈ b) ⊂ c) ∉
d) ⊄ 11.If the set A has n elements then number of subsets is
........... a) n2 b) 2n c) n + 2 d) 2n 12.The universal set is
denoted by ............. a) S b) P c) U d) Vn 13. A ∪ A’ =
.............. and A ∩ A’ = ............. a) U, U b) U, ∅ c) ∅, U
d) ∅, ∅ 14.If A ........... B and B ......... A then A = B. a) ⊂ ,
⊄ b) ⊄ , ⊂ c) ⊂ , ⊂ d) ⊄ ,⊄ 15.If A= {x / x ∈ N, x < 5) and B =
{1,2,3,4} then A .......... B. a) ⊄ b) ∈ c) = d) ≠ 16.If A =
{a,b,c} and B = {3,2,1} then the sets A and B are called .......
sets.
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a) equal b) equivalent c) complementary d) universal
17............... is true. a) {a,b} ⊄ {b,c,a} b) {b, c} ⊄ {b, c, a}
c) {c, a} ⊄ {b, c, a} d) {a, b, c} ⊂ {b, c, a} 18............ is
false. a) ∅ ~ {∅} b) ∅ ∈ {∅} c) ∅ ≠ {∅} d) ∅ ∉ {∅}
19............... is true. a) {3} ⊂ {1, 2, {3}, 4} b) 3 ∈ {1, 2,
{3}, 4} c) {3} ∈ {1, 2, {3}, 4} d) {1, 2, 3, 4} ⊂ {1, 2, {3},
4}
BASED ON EXERCISE : 1.2 �Answer the following questions by
selecting appropriate alternative from alternatives given in
questions: 1. A ∪ B = .............. a) {x/ x ∈ A and x ∈ B} b) {x/
x ∉ A and x ∉ B} c) {x/ x ∈ A or x ∈ B} d) {x/ x ∉ A or x ∈ B} 2.
If P = set of the letters of the word DAHOD and Q= set of the
letters of the
word BARODA then P ∪ Q = ............. a) {A, D, O} b) {A, B, D,
H, O, R} c) {B, H, R} d) {O} 3. If A ⊂ N and N = U then A ∪ A =
............ a) ∅ b) A’ c) U d) A 4. If A ⊂ B then A ∪ B =
............ a) = A b) = B c) = U d) = ∅ 5. A ∪ U = .............
a) ∅ b) A c) U d) A’ 6. A ∪ ∅ = ............. a) A b) A’ c) U d) ∅
7. A ∩ B = .............. a) {x/ x ∈ A or x ∈ B} b) {x/ x ∉ A and x
∉ B} c) {x/ x ∈ A or x ∈ B} d) {x/ x ∉ A or x ∉ B} 8. If A = N and
B= W then A ∩ B = ........... a) N b) W c) Z d) Q 9. If A = Q and
B= W then A ∩ B = ........... a) R b) Z c) W d) N 10.If A ⊂ U and
B⊂ U then A ∩ B = ............ a) ⊄ A b) ⊄ B c) =∅ d) ⊂ U 11.The
rule (A∩ B) ∩ C = A ∩ (B∩C)’ is termed as ............. a)
Commutative law b) Associative law c) Idempotent law d)
Distributive law 12.If A ⊂ B then A ∩ B = ............ a) A b) B c)
U d) ∅
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13.A ∩ ∅ = ..............and A a) ∅, ∅ b) A, ∅14.If A and B are
disjoint sets then A a) A b) B 15.A ∪ (B ∩ C) = {a, b, c} then (A
a) {a} b) {b, c}16.A ∩ (B ∪ C) ......... (A∩ a) ≠ b) ⊄
17.Venn-diagram of (A∪B)
a)
A B
C
A B
c)
C
18. Venn-diagram of (A
a)
A B
C
A B
c)
C
19.If A = {x / x ∈ N, is a prime factor of 12} and B = {factor
of 20} then A ∩ B = .............
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= ..............and A ∩ U = ......... ∅ c) ∅, A d)
If A and B are disjoint sets then A ∩ B = ......... c) U d)
C) = {a, b, c} then (A∪ B) ∩ (A ∪ C) = ..........{b, c} c) ∅ d)
∩ B) ∪ (A ∩ C)
c) ∈ d) B) ∩ (A∪C) is .........
U b)
B A
C
U A
d)
C
diagram of (A∩B) ∪ (A∩C) is .........
U b)
B A
C
U A
d)
C
N, is a prime factor of 12} and B = {x ∩ B = .............
A, A
∅ C) = ..........
{a, b, c}
=
U
B
B U
C
U
B
B U
C
/ x ∈ N, is a prime
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a) {1, 2, 3} b) {2, 3, 5} c) {1, 5} d) {2} 20.If A = {x / x ∈ N,
is a factor of 12} B = {x / x ∈ N, 2 < x < 7} then A ∩ B
=
............. a) {2, 3, 4, 6} b) {3, 4, 5, 6} c) {3, 4, 6} d)
{1, 2, 3, 4, 5, 6, 12} 21.If A = {1, 2, 3, 4}, B = {x / x ∈ N, 4
< x < 6} then ............. a) A ⊂ B b) B ⊂ A
c) A, B are not equivalent set d) A and B are not disjoint sets
BASED ON EXERCISE: 1.3
�Answer the following questions by selecting appropriate
alternative from alternatives given in questions: 1. A ∪ A’ =
.............. and A ∩ A’ = ............... (Given : U is universal
set) a) U, U b) ∅, ∅ c) U, ∅ d) ∅, U 2. (A’)’ = .............. a) ∅
b) A c) A’ d) U 3. U’ = ............. and ∅’ = .............. a) U,
U b) ∅, ∅ c) ∅, U d) U, ∅ 4. If N is set of natural numbers and U =
W = set of whole numbers then N’ =
.................. a) 0 b) ∅ c) W d) {0} 5. If A = {a, c, e} and
U = {a, b, c, d, e} then A’ = ........... a) ∅ b) {b} c) {e} d) {b,
d} 6. If A ⊂ U and B ⊂ U then (A ∩ B)’ = ......... a) A ∪ B b) A’∪
B c) A∪ B’ d) A’ ∪ B’ 7. If A ⊂ U and B ⊂ U then (A ∪ B)’ =
......... a) A’ ∩ B’ b) A’∩ B c) A∩ B’ d) A∩B 8. Number of subsets
of the set A = {x / x ∈ Z, -3 < x < 3} is ............. a) 8
b) 16 c) 32 d) 64
SELF ASSESSMENT TEST: 1 �Selecting a proper answer from the
given brackets fill in the blanks. 1. .......... is a symbol of
Empty set. a) 0 b) { } c) {∅} d) U 2. ∅ is .......... set. a)
finite b) infinite c) equal d) undefined 3. A = {2, 3} and B = {1,
2, 3} ∴ A ...........B. a) ∩ b) ∪ c) ⊂ d) ⊄ 4. Set of Natural
Numbers is ........... a) finite b) infinite c) null d) whole 5.
Formula of finding the number of subsets of a set having n element
is .... a) 2n b) n2 c) 2n d) n+2 6. {1, 2, 3} and {4,5,6} are
......... sets. a) equal b) equivalent c) infinite d) similar
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7. If A = {10, 20, 30, 40} and B = {10, 20, 30} th a) A b) B 8.
Number of subsets of {x, y, z} = .............. a) 6 b) 8 9. If U =
{1, 2, 3, 4, 5}, A = {1, 3, 5} then A’ = .............. a) {2, 4}
b) {1, 3, 5}10.If A ~ B and n (A) = 5 then a) 5 b) 10 11.Most of
the basic work in set a) George Cantor b) 12.If A ⊂ B and B ⊂ A
then ........... a) A~B b) A 13.A’ ∩ B’ = ........... a) (A∪B)’ b)
(A∩14.Every set has at least ............. subsets. a) 0 b) 1 15.A
non-empty set has at least .......... subsets. a) 0 b) 1 16.If A ⊂
B then ........... a) A’⊂ B’ b) B’ 17.If A = (7,8,9), B = (7, 9,
10) and a) 7 b) 8 18.If A ∪ B = B then ........... a) B ⊂ A b) A
⊂19.If A ≠ ∅ and A ∩ B = ∅ a) B = ∅
c) A and B are disjoint20.If A ⊂ B then ........... is false. a)
A ∪ B = B b) 21.If U = {a, b, c, d, e, f}, A = {a, b, f} and B =
{c, e} then .........is true. a) A’ = B’ b) A ⊂22.In the following
figure the shaded region represents ................
A B
C
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If A = {10, 20, 30, 40} and B = {10, 20, 30} then A ∩ B =
.......... c) ∅ d) U , y, z} = ..............
c) 3 d) 9 If U = {1, 2, 3, 4, 5}, A = {1, 3, 5} then A’ =
..............
{1, 3, 5} c) A d) {0}(A) = 5 then n(B) = ...........
c) 25 d) 1 Most of the basic work in set-theory is done by
.............
Galeleo c) Archimedes A then ...........
⊄ B c) A= B d) B ⊄
∩B)’ c) ∅ d) U Every set has at least ............. subsets.
c) 2 d) ∞ (infinite)empty set has at least ..........
subsets.
c) 2 d) 3
⊂ A’ c) A’ = B d) A ~ BIf A = (7,8,9), B = (7, 9, 10) and x ∈ A
∪ B but x ∉ B then
c) 9 d) 10 ........
⊂ B c) A ∩ B ⊄ B d) ∅, for B we have ........... is false.
b) A ∪ B = B e disjoint d) B= A’
B then ........... is false. A ∩ B = A c) B’ ⊂ A’
If U = {a, b, c, d, e, f}, A = {a, b, f} and B = {c, e} then
.........is true.⊂ B’ c) B’ ⊂ A d) B’
In the following figure the shaded region represents
................
U a) (A ∩ B’) ∪ C
B b) A ∪ C
c) (A ∩ B)’ ∪ C
d) (A ∪ C) ∩ B’
∩ B = ..........
{0}
theory is done by ............. d) Ramanujan
⊄ A
∞ (infinite)
A ~ B B then x = ...........
B⊂ A ∩ B
d) A = B If U = {a, b, c, d, e, f}, A = {a, b, f} and B = {c, e}
then .........is true.
B’ ⊂ A’ In the following figure the shaded region represents
................
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23.In the following figure the shaded region represents
................
A
24.In the following figure the shaded regi
A B
C
25. In the figure (A ∪ B)’ is represented by
................
A
R1 R2 R3
Chapter:� Select proper option (A), (B), (C) or (D) from give n
options and write in the box given on the right so that1. Set of
all natural number is denoted by ........... a) N b) W 2. Set of
whole numbers is denoted by ........... a) N b) W 3. Set of all
integers is denoted by ......... a) N b) W 4. Set of all rational
numbers is denoted by ......... a) N b) W 5. ............... is a
true statement. a) Every whole number is a natural number b) Every
integer is a rational number
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23.In the following figure the shaded region represents
................
U
B a) (A ∪ B)’
c) (A ∩ B)’
In the following figure the shaded region
represents................
U
B a) (A ∩ B) ∩ C
b) A ∩ C
c) (A ∪ B)
d) (A ∪ B) ∩ C
B)’ is represented by ................
U
B a) R1, R3 and R4
b) R1, R2 and R3
R4 c) R4
d) R2, R3 and R4
Chapter: - 2 Number System Select proper option (A), (B), (C) or
(D) from give n options and write
in the box given on the right so that the statement becomes
correct. Set of all natural number is denoted by ...........
c) Z d) R Set of whole numbers is denoted by ...........
c) Z d) Q Set of all integers is denoted by .........
c) Z d) Q Set of all rational numbers is denoted by
.........
c) Z d) Q ............... is a true statement.
Every whole number is a natural number Every integer is a
rational number
23.In the following figure the shaded region represents
................
b) A’ ∪ B’
d) (A’ ∩ B’)’
represents................
Select proper option (A), (B), (C) or (D) from give n options
and write the statement becomes correct.
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c) Every rational number is an integer. d) Every integer is a
rational number
6. The number 3
4 is ...........
a) a natural number b) an integer c) a whole number d) a
rational number 7. The pair of equivalent rational numbers is
.............
a) 4
7 and 104
182 b)
5
2 and
155
64
c) 144
169 and
169
225 d)
8
27 and
125
216
8. ............. is a rational number between 10 and 11.
a) 21
4 b) 87
8 c)
97
8 d)
47
4
9. 9 = ............. a) 3 b) -3
c) 3 and -3 d) All (A). (B). (C) are true 10.There are
........... rational numbers between two given numbers. a) two b)
can’t say c) finitely many d) infinitely many 11. 2 belongs to
....... a) the set of whole numbers b) the set of rational numbers
c) the set of infinite numbers d) the set of natural numbers 12.The
collection of rational numbers and irrational numbers together
is
called..... a) the set of whole numbers b) the set of real
numbers c) the set of finite numbers d) the set of infinite numbers
13. 16 is not ....... a) a natural number b) a real number c) an
irrational number d) a whole number
14.The decimal expansion of 7
4is ......
a) terminating b) non-terminating recurring c) non-terminating
and non-recurring d) infine 15.44.7232323..... can be written
as.......
a) 44.723 b) 44.723 c) 44.723 d) 44.723 16.The number 0.235 is
...... a) a natural number b) an integer c) an irrational number d)
a rational number
17.The p
q form of 0.35 is......
a) 16
45 b) 176
495 c) 35
99 d)
16
495
18.The p
q form of 0.01 is......
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a) 199
b) 1099
c) 10099
d) 101
99 19.............. is an irrational number. a) 0.3786 b) 225 c)
1.010010001... d) 0.2353535...
20.If 2
0.285714,7
= then 67
= ..............
a) 0.571428 b) 0.142857 c) 0. 857142 d) 0. 095235
21. ( ) ( )6 6+ − is .............. a) a natural number b) an
irrational number c) a whole number d) an infinite number
22.3 3
.2 2
is ..............
a) an irrational number b) a rational number c) a whole number
d) a natural number 23. 3 . 6 is .............
a) a whole number b) a natural number c) an irrational number d)
a rational number 24. 5 29+ is .............
a) an integer b) an irrational number c) a whole number d) a
rational number 25. 3 3+ is .............
a) an integer b) an irrational number c) a rational number d) a
whole number 26.6 5 .3 5 is not .............
a) a natural number b) an irrational number c) a whole number d)
a rational number 27.8 8 3 2÷ is .............
a) an integer b) a rational number c) a whole number d) a
irrational number 28.8 15 2 5÷ is .............
a) a irrational number b) an integer c) a whole number d) a
rational number
29. ( ) ( )10 3 10 3− − =- .............. a) 0 b) 13 - 2 30 c) 7
- 2 30 d) 7 + 2 30
30. ( ) ( )7 7 7 7+ − =- .............. a) 0 b) 2 7 c) 7 7 d)
42
31. ( )25 2− = ............... a) a natural number b) an
irrational number c) a whole number d) a rational number
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32.3
2 5− is rationalized by ...........
a) -3 b) 2 - 5 c) 2 + 5 d) -2 + 5
33. An equivalent expression of 5
7 4 5+ after rationalizing the denominator is
..............
a) 20 5 3531
− b) 20 5 35129
− c) 35 20 531
− d) 35 20 5129
−
34.If 2n a b= then b2n = ........... (a, b > 0, n ∈ N)
a) a b) 2( )n
a c) a2n d) a4
35. 3 64 = .............
a) 8 b) 4 c) 2 d) not possible
36.4
π is .................
a) a natural number b) an irrational number c) a rational number
d) a whole number
BASED ON EXERCISE: 2.1 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions. 1. {1, 2, 3, 4, ........} = ........... a) R b) W c) Z
d) N 2. {0, 1, 2, 3, ........} = ........... a) Q b) R c) W d) N 3.
{......., -3, -2, -1, 0, 1, 2, 3, ........} = ........... a) N b) Q
c) Z d) R
4. { | , ,p
p Z q N p and qq
∈ ∈ are co-prime}
a) R b) Z c) W d) Q 5. ......... are equivalent rational
numbers.
a) 3 9,5 15
b) 3 9,5 5
c) 6 7
,10 10
d) 12 15
,20 20
6. To obtain n rational number between two rational numbers a
and b(a < b) we shall write a as .........
a) 1
an
n+ b) ( 1)
1
a n
n
++
c) a p
q d)
2
2
( 1)
1
a n
n
++
BASED ON EXERCISE: 2.2 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions. 1. R includes ......... too. a) whole numbers and
integer b) Z and Q c) rational and irrational d) Q and N 2.
.......... were the first to discover the numbers which were not
rationals.
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a) Indians b) Pythagoreans c) Americans d) Arabians 3. In ∆ABC
with m∠B= 90, if AC = 5 then AB = .......... and BC= .......... a)
1, 4 b) 2, 3 c) 2.5, 2.5 d) 2, 1 4. There are ........
correspondence between set of real numbers and the set
of points on the number line. a) one-many b) one-one c) many one
d) no 5. ............. showed that corresponding to every real
number, there is a point on the real number line, there exists a
unique real number. a) Pythagoras and Archimedes b) Newton and Rene
Descartes c) Ramanujan and Bhaskaracharya d) G. Cantor and R.
Dedekind
BASED ON EXERCISE: 2.3 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions.
1. p
q ∈ Q form 0. 6 is .............
a) 23
b) 3
5 c)
66
100 d)
666
1000
2. ......... is not rational.
a) 0. 3 b) 22
7 c) π d) 4
3.Decimal expansion of 8
7 is ...........
a) terminating b) terminating and recurring c) non-terminating
d) non-terminating and recurring 4. The decimal expansion
of........are either terminating or non-terminating
recurring. a) whole numbers b) Real number c) Rational numbers
d) Irrational numbers
5. In p
q, q = 2m, p = 5n m, n ∈ N then
p
q has ......... expression.
a) terminating and recurring b) terminating expression and not
otherwise
c) non-terminating and recurring. d) non-terminating and non-
recurring
6. p
q form of 2. 237 is .............
a) 223599
b) 223799
c) 2237
999 d) 2235
999
7. p
q form of 3. 123 is .............
a) 1546495
b) 1549
495 c)
3123
100 d)
347
111
8. A number is an irrational if and only if its decimal
expansion is ........... a) terminating and recurring b)
non-terminating and recurring.
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c) terminating and non-recurring
d) non-terminating and non- recurring 9. 0.303303330........ is
.......... a) a rational number b) an irrational number c) a
positive integer d) a whole number
10.π ............... 22
7.
a) = b) > c) < d) - 11.One can obtain.......irrational
numbers between any two rational numbers. a) at the most two b)
finite number of c) infinitely many d) exactly two 12.π
............... a) 3.141592 b) 3.141546 c) 3.151429 d) 3.140845
13.22
7 = ................
a) 3.114829 b) 3.142857 c) 3.141592 d) 3.428571 BASED ON
EXERCISE: 2.4
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions. 1. The real
number with terminating decimal or non-terminating decimal or
non-terminating recurring decimal expansion can be represented
on the number line by successive .............
a) addition b) subtraction c) magnification d) minimization
2. To locate the numbers 3.556 we have to magnify the subset of
number line between.............
a) 3 and 4 b) 3.55 and 3.56 c) 3.5 and 3.6 d) 3.554 and 3.557 3.
......... the following is satisfied by the rational numbers. a)
Only commutative law for addition and multiplication b) Only
associative law for addition and multiplication c) Only
distributive law d) All to the above laws
BASED ON EXERCISE: 2.5 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions. 1. The sum of rational number is ..........number. a) a
real b) a rational c) an irrational d) an integer 2. Positive nth
root of x = n a then n ∈ N and x ∈ ............. a) Z b) Q c) R d)
R+ 3. 0n ............... a) > 0 b) < 0 c) = 0 d) not defined
4. 0n ................ a) is undefined b) is infinite c) > 0 d)
= 0
-
13
5. The sum, difference product and quotient of irrational
numbers ......... a) is a rational number b) is an integer c) is an
irrational number d) may not be an irrational number.
6. ( ) ( )7 3 7 3+ − is not .............. a) a real number b) a
positive integer c) a rational number d) an irrational number 7. 25
......... a) < 0 b) > 0 c) is an irrational number d) = 0 8.
........... is a rationalizing factor of 2 - 3 .
a) -2 + 3 b) 2+ 3 c) 3 -2 d) 2 + 3
9. ........... is a rationalizing factor of 3 .
a) 3 b) 1
3 c) 3 d) 1
10............ is a rationalizing factor of 1
1 2−.
a) 2 - 1 b) 1
1 2+ c)
2 1
2 1
++
d) 1 + 2
11.If a, b are positive real numbers, then .......... is
incorrect.
a) a a
b b= b) ( ) ( )a b a b a b+ − = −
c) ( ) ( ) 2 2a b a b a b+ − = − d) ( ) ( )a b a b a b− + = −
12.(5 + 7 ) (2 + 5 ) = .............
a) 5 5 + 2 7 b) 10 + 35
c) 10 + 5 5 + 2 7 + 35 d) 10 + 25+ 14 + 35
13. ( ) ( )7 3 7 3+ − = .............. a) 0 b) 7 3 c) 4 d) 7 +
3
BASED ON EXERCISE: 2.6 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions. 1. If am-n = 1, then m.......... n a) > b) < c) =
d) ≠ 2. a-n = ............. a) a – n b) n – a c) a – b d) b – a
3. 1
a
b
−
= ..............
a) a
b b) b
a c) a – b d) b - a
4. 1
na = ...........
a) 1
an b) a n c) n a d) n . a 5. (ap)q = .............
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14
a) ap + q b) ap – q c) p
qa d) apq
6. Which of the following is false? a) am . an = am + n b) (am)n
= amn
c) am . bn = (ab)mn d) ,m
m nn
aa m n
a−= >
7. 02 = ............. a) 1 b) 0 c) undefined d) finite number 8.
2-3 = ...........
a) -8 b) 8 c) 18 d) -
1
8
9. 1
128= ...........
a) 16-2 b) 2-7 c) 8-3 d) 4-4 SELF ASSESSMENT TEST: 2
� Selecting a proper answer from the given brackets fill in the
blanks. 1. 8 is ................ a) a rational number b) an
irrational number c) a whole number d) an integer 2. (5 - 5 ) (5 +
5 ) is not ............. a) whole number b) a rational number c) an
integer d) an irrational number
3. To rationalize the denominator of 1 2
3 2 2 3
−−
........... is the rationalizing
factor.
a) 2 + 1 b) 2 3 - 3 2 c) 3 2 + 2 3 d) 2 - 1
4. 0.32......... 0.32 a) < b) > c) = d) equivalent
5. 1 1 1 1
4 4 4 4x y x y
+ −
= ..............
a) 1 1
8 8x y− b) 1 1
2 2x y+ c) x y− d) x y+
6. p
q form of 0.001.
a) 1000
999 b) 1
999 c)
1
99 d)
100
999
7. 7 7.3 3
is .............
a) a rational number b) a whole number c) an integer d) an
irrational number 8. 5-3 = .........
a) - 125 b) 125 c) -1
125 d) 1
125
9. 5 x- 3 = 1 then ...........
a) x > 3 b) x < 3 c) x = 3 d) x = 2
-
15
10. 3 729 = ...........
a) 3 b) 9 c) 27 d) 81
11.If p
q∈ Z then p ∈ Z and q ..........
a) ∈ N b) > 1 c) < 1 d) = 1
12.If 3 62 = b, then b = ...........
a) 2 b) 4 c) 8 d) 16 Chapter: 3 Polynomials
� Select proper option (A), (B), (C) or (D) from giv en options
and write in the box given on the right so that the statement
becomes correct. 1. If p (3) = 0, then factor of p(x) is ..........
a) (x - 3) b) (x – 2) c) (x + 3) d) (x + 2) 2. If x3 + 2x2- 6x + 9
is divided by x-2, then ........... is the remainder. a) -13 b) 13
c) 9 d) -16 3. The degree of the polynomial x5 + 3x3 – 7x2 + 9x +
11 is .......... a) 1 b) 2 c) 3 d) 5 4. If x – 2 is a factor of 3x4
– 2x3 + 7x2 – 21x + k, then the value of k is ........ a) 2 b) 9 c)
18 d) -18 5. The zero of 7x – 3 is ..........
a) 37
− b) 37
c) 73
d) 73
−
6. If x2 + 6x + 7 is divided by (x+1), then the remainder is
......... a) 1 b) 2 c) 5 d) 7 7. Factors of y2 + 10y + 21 are
........... a) (y + 3) and (y – 7) b) (y - 3) and (y + 7) c) (y -
3) and (y – 7) d) (y + 3) and (y + 7) 8. If a – b = 2 and ab = 3,
then a3 – b3 = ............. a) 8 b) 27 c) 26 d) 6 9. If a = b = c,
then a3 + b3 + c3 – 3abc = ......... a) a3 b) 2a3 c) 3a3 d) 0 10.If
one factor of the polynomial x3 + 4x2 – 3x – 18 is (x + 3), then
the other
factor is .............. a) x2 + x b) x2 + x + 6 c) x2 + x – 6
d) x2 – x + 6 11.If (x3 + 28) is divided by (x+3), then the
remainder is .......... a) 0 b) 1 c) -1 d) 2 12......... should be
added to x3 – 76 so that the resulting polynomial is divisible
by x – 4. a) 5 b) -5 c) 12 d) -12 13.If 25x2 – 49y2 has one
factor (5x – 7y), then the other factor is ........ a) 7x + 5y b)
-7x – 5y c) 5x + 7y d) -5x + 7y 14.If p (x) = x3 – 2x2 – 7x – 6,
then a zero of p (x) is ..........
-
16
a) 0 b) 1 c) 2 d) 3 15.If the cost of one mathematics text-book
is Rs. (x+4), then..........text-books
can be purchased by Rs. (x3 + 64). a) x2 + 8x + 16 b) x2 - 8x –
16 c) x2 - 4x + 16 d) x2 - 4x – 16 16.(4x – 7y)3 = ............. a)
4x3 – 7y3 + 84xy b) 16x3 + 49y3 + 84xy c) 64x3 – 343y3 - 336x2y +
588xy2
d) 64x3 + 343y3 - 336x2y + 588xy2
BASED ON EXERCISE : 3.1 �Answer the following questions by
selecting appropriate alternative from alternative given in
questions: 1. If p(x) = 3x5 then p (x) is .......... a) Trinomial
b) Binomial
c) Monomial d) Constant Polynomial 2. The degree of a polynomial
x2 + 2x4 + 3x3 + 4x + 5 is ............. a) 0 b) 2 c) 1 d) 5 3. The
degree of a non-zero constant polynomial is .......... a) -1 b) 0
c) 2 d) undefined 4. The degree of a zero polynomial is ..........
a) 0 b) undefined c) infinitely many d) ∞ 5. A polynomial of degree
1 is called a ........... a) Monomial b) Binomial c) Linear
polynomial d) Constant polynomial 6. .......... is a cubic
polynomial. a) ax + by + c b) ax2 + by + c c) ax3 + bx2 + cx d) ax
+ by + cz 7. ............. is a quadratic polynomial. a) 2x + 3 b)
3x3 + 4 c) 3x4 + 2x3 + 1 d) 3x2 + 2x + 1 8. 0 is called a
............. a) quadratic polynomial b) cubic polynomial c)
monomial d) zero polynomial 9. ........... is a linear polynomial.
a) x3 + 27 b) (x-1) (x + 2) c) 2011x + 2010 d) x(x -1) (x-2)
10............. is not a polynomial.
a) 0 b) 7 c) 2
2 33ax x x b+ + + d) 2ax bx c+ +
11.The degree of 5 + x + 3x2 + x5 a) 3 b) 5 c) 2 d) 1 12.14
(x2)12 + 11(x3)8 – 10(x4)6 + 10(x6)4 + 45 has degree ..............
a) 4 b) 6 c) 12 d) 24
-
17
13. 2 3 6x x+ + is ............. a) monomial b) binomial c)
trinomial d) not a polynomial
BASED ON EXERCISE : 3.2 �Answer the following questions by
selecting appropriate alternative from alternative given in
questions: 1. For a p (x) if p (a) = 0 then a is called the
........... of p (x). a) co-efficient b) degree c) zero d) variable
2. If p (x) = 3x2 – 7x + 5 then p (2) = ........... a) 2 b) 3 c) 7
d) -5 3. Zeroes of p (x) = x (x2 – 9) are ........... a) -2 0 2 b)
-1, 0, 1 c) -3 0 3 d) -3, 3 4. Zero of p (x) = ax + b are
...........
a) ab
b) -ab
c) -ba
d) ba
5. Zeroes p (x) = x2 – 8 are ...........
a) 2, 3 b) +2 2 , -2 2 c) 1, -1 d) 32 -2 3 6. Zeroes p(x) = (x3
– 8) (x + 3), where x ∈ R are........... a) 2 2 , -2 2 b) +2, -2 c)
3, -2 d) 2, -3 7. 2x4 + x3 + 54x + 27 has zeroes ........ and
..........
a) ½ and 3 b) ½ , 3 c) ½ and -3 d) - ½ , -3 8. If p (x) = x
(x+2) (3x-7), where x ∈ W or x ∉ Z zeroes of p(x) are........and
.....
a) 2, 73
b) -2, -73
c) 0, 73
d) 0, 73
−
BASED ON EXERCISE : 3.3 �Answer the following questions by
selecting appropriate alternative from alternative given in
questions: 1. If a polynomial p (x) is divided by another
polynomial g(x) ≠ 0, q(x) and r(x)
are the quotient and remainder then ............ a) q(x) . r(x)
= p (x) + g (x) b) g(x) . r(x) = p (x) + q (x) c) p(x) = g(x) . q
(x) + r (x) d) r(x) = g(x) . q (x) + p (x) 2. We know the quotient
law in usual notations p (x) = q(x) . g (x) + r (x),
where q (x) is quotient, r(x) is remainder and g(x) divisor,
then degree of r(x) ........... degree of g (x).
a) > b) < c) 0 d) ~ 3. When p (x) is divided by x – a,
then the remainder r (x) is a ........... a) monomial b) zero
polynomial c) linear polynomial d) constant polynomial 4. If m3 –
2m2 – 2m – 42 is divided by m -3, then remainder = ......... a) 120
b) 0 c) -120 d) -174 5. If y4 + y3 + 8y2 + py + q is divisible by
y2 +1, then p + q = ..........
-
18
a) -6 b) 6 c) 7 d) 8 6. x3 – 4x2 – 14x -4 is divided by x +2,
then the quotient is ......... a) x2 + 6x + 2 b) x2 - 6x - 2 c) x2
+ 6x - 2 d) x2 - 6x + 2 7. The product of two polynomials is x3- 8x
– 12 + x2. If one of the polynomial is x + 2 then the other
polynomial is ........ a) x2 + x + 6 b) x2 + x - 6 c) x2 - x + 6 d)
x2 - x - 6
BASED ON EXERCISE: 3.4 �Answer the following questions by
selecting appropriate alternative from alternative given in
questions: 1. If ax – b is a factor of p(x), then p(.......) =
0.
a) ba
b) - ba
c) ab
d) -ab
2. If mx + n is a factor of p (x), then p (........) =0.
a) nm
b) -nm
c) mn
d) -mn
3. If x-1 is a factor of p (x) = ax3 + bx2 + cx + d, then
.......... a) a + c = b + d b) p (-1) = 0 c) a + b = c + d d) a + b
+ c + d = 0 4. If (x + 1) is a factor of p (x) = ax3 + bx2 + cx +
d, then ............. a) a + b + c + d = 0 b) p (1) = 0 c) a + c =
b + d d) a + d = b + c 5. If (x – 2) is a factor of p (x) = x2 + kx
+ 2, then k = .......... a) -1 b) -2 c) -3 d) -4 6. If (px + l) and
(qx + m) are the factors of ax2 + bx + c, then c = .......... a) pq
b) pm c) lq d) lm 7. If ax2 + bx + c = (px + 1) (qx + m), then b
=............. a) pq + lm b) pm + lq c) pl + qm d) l + m 8. If 7x +
6 is a factor of kx2 – 8x – 12, then k = ........... a) 4 b) 6 c) 7
d) 8 9. ........... has the factor (x- 1). a) 3 32 7 2x x x+ − − b)
2x3 – 3x2 + 3x -2
c) x5 – 7x6 + 4x3 + x4 – x + 1 d) 2x6 + 5x4 – 2x2 – 3 10.
Factors of 21x2 + 16x – 5 are ........... and ......... a) (7x + 1)
and (3x – 5) b) (7x - 5) and (3x – 1) c) (x + 5) and (21x + 1) d)
(21x - 5) and (x + 1)
BASED ON EXERCISE : 3.5 �Answer the following questions by
selecting appropriate alternative from alternative given in
questions: 1. 105 x 95 = ...........
-
19
a) 9875 b) 9925 c) 9975 d) 9825 2. 107 x 102 = .......... a)
11414 b) 10702 c) 10207 d) 11014 3. 373 + 133 + 3 x 37 x 13(37 +
13) = ......... a) 64000 b) 125000 c) 216000 d) 27000 4. 213 – 3 x
21 x 121 + 3 x 441 x 11 – 1331 = ........... a) 512 b) 27000 c)
8000 d) 1000 5. (110)3 = ............. a) 1111000 b) 1221000 c)
1331000 d) 1441000 6. (29)3 – (25)3 – (4)3 = ........... a) 5700 b)
8700 c) 729 d) 11700 7. a2 + b2 + c2 + 2ab – 2bc – 2ca =
(.........)2 a) a + b + c b) -a + b + c c) a – b + c d) a + b – c
8. a2 + b2 + c2 - 2ab + 2bc – 2ca = (.........)2 a) a - b + c b) a
+ b - c c) -a – b + c d) a - b – c
SELF ASSESSMENT TEST: 3 �Selecting a proper answer from the
given brackets fill in the blanks. 1. Degree of a0 + arx
r + anxn is .............. (where r < n, r, n ∈ N)
a) 0 b) 1 c) r d) n 2. If p(x) = 3 + 2011x then p(x) is called
........... a) monomial b) binomial c) constant polynomial d) zero
polynomial 3. x + 2 is .......... a) a linear polynomial b) a
binomial c) not a polynomial d) a constant polynomial 4. Zeroes of
x3 + 3x2 + 2x are ........... a) 1, -3, 2 b) 0, 1, 2 c) 0, -1, -2
d) 0, -1, 2 5. If zero polynomial is divided by a constant
polynomial then remainder is
........ a) 1 b) ∞ c) 0 d) not defined 6. If a – b = 5 and ab =
2 then a3 – b3 = ........... a) 125 b) 135 c) 145 d) 155 7. x2 + 9x
+ k has one factor (x+4) then c = ......... a) 20 b) -20 c) 14 d)
-10 8. x3 - 3x2 + 5x -7 is divided by x - 3 then remainder =
......... a) 3 b) -3 c) 8 d) -8 9. If p(x) = x3 + 3x2 – 4x – 12
then p (-3) = .......... a) 1 b) -1 c) 0 d) 2
10.If p 32
−
= 0 then one factor of p (x) is ..........
a) 2x – 3 b) 2x + 3 c) 3x + 2 d) 3x -2
-
20
11.(12)3 + (13)3 + (-25)3 = .......... a) 11700 b) -11700 c)
71100 d) -71100 12.(1.3)3 - (0.6)3 – (0.7)3 = ............ a)
-1.638 b) -16.38 c) 1.638 d) 16.38
Chapter- 4 - Co-ordinate Geometry � Select proper option (A),
(B), (C) or (D) from giv en options and write in the box given on
the right so that the statement becomes correct. 1. Point (4, 0)
lies on ...........
a) 'OXuuuur
b) OYuuur
c) OXuuur
d) 'OYuuuur
2. For a point, if the abscissa is -3 and ordinate is 5, then it
lies in the ......... a) I b) II c) III d) IV 3. The point of
intersection of the axes has co-ordinates ............. a) (0,1) b)
(1, 0) c) (0, 0) d) (0, -1) 4. The point (-2, 0) lies
on.............
a) OYuuur
b) 'OXuuuur
c) 1st quadrant d) OXuuur
5. Point (5, -2) lies in the ........... quadrant. a) I b) II c)
III d) IV 6. For the point (7, -4), the abscissa is .......... a)
-4 b) -7 c) 4 d) 7 7. For the point (3, -5), the ordinate is
.......... a) 3 b) 5 c) -3 d) -5 8. For the origin O, abscissa and
ordinate are both .......... a) 1 b) -1 c) 0 d) 0.5 9. The 3rd
quadrant is the interior of .......... a) ∠YOX’ b) ∠X’OY’ c) ∠Y’OX
d) ∠XOY 10.The co-ordinates of any point on the Y-axis are of the
form (0, b), where
|b| is the distance of the point from the .......... a) Y-axis
b) X-axis c) (0, 1) d) (1, 0)
11. The measure of the angle between the lines 'X Xsuuuur
and 'Y Ysuuur
is ......... a) 90 b) 0 c) 180 d) 60 12.For x= 3, y = 2, u = -9,
v = 13 the point (x + y, u + v) lies in the........
quadrant. a) III b) II c) IV d) I 13.In the plane, (x ,y) = (y,
x) if .......... a) x =3, y = 3 b) x = 3, y = 2 c) x =2, y = 3 d) x
= 1 , y = 0 14.If the co-ordinates of the point are of the same
sign (both positive or both
negative) then points lies in the ........... quadrants. a) I
and II b) I and III c) I and IV d) II and IV 15.The point having
co-ordinates of the opposite signs lies in.........
a) I and II b) I and III c) I and IV d) II and IV 16.Any point
on the X-axis is of the type.......... a) (0, x) b) (0, y) c) (0,
1) d) (a, 0)
-
21
17.The co-ordinate axes divide plane into ........... parts
called quadrants. a) two b) five c) four d) six 18.X-axis is a
horizontal line passing through ........... a) Point (0, 1) b)
origin c) Point (0, -1) d) quadrant-I 19.The vertical line through
the origin is called the ...........
a) X- axis b) XY-plane c) Y- axis d) line 'Y Ysuuur
20.The .............quadrant is bounded by the negative X-axis
and the positive
Y- axis. a) 1st b) 3rd c) 2nd d) 4th 21.In the plane origin O
(0, 0) lies on the ........... a) X-axis only b) Y-axis only c) 1st
quadrant d) X-axis and Y-axis both 22.The point (0, 3) lies on the
...........
a) X- axis b) 'Y Ysuuur
c) 1st quadrant d) 2nd quadrant 23.The point (-4, 0) lies on the
...........
a) 2nd quadrant b) OXuuur
c) 3rd quadrant d) 'OXuuuur
24.The point (0, -2) lies on the ...........
a) Y- axis b) X- axis c) 1st and 4th quadrant d) 3rd
quadrant
25.The point (-3, 4) lies in the ........... a) 1st quadrant b)
3rd quadrant
c) interior of ∠YOX’ d) interior of ∠Y’OX BASED ON EXERCISE:
4.1
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions: 1. Co-ordinate
Geometry, was initially developed by French Philosopher and
Mathematician ........... a) R. Cantor b) Newton c) Rene
De-scartes d) Euclid 2. If a > 0 and b > 0 the point (a, b)
lies in the .......... quadrant. a) 1st b) 2nd c) 3rd d) 4 th 3. If
(2x- 1, 1) = (-3, 3y, -2) then (x, y) = ............. a) (1, -1) b)
(2, -2) c) (3, -3) d) (-1, 1)
4. 35,2
− −
lies in the ..............quadrant.
a) 4th b) 3rd c) 2nd d) 1st BASED ON EXERCISE : 4.2
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions: 1. The point
......... is in the II-quadrant. a) (3, -3) b) (-3, -3) c) (-3, 3)
d) (3, 3) 2. The point (0, 5) is on ..........
a) OYuuur
b) 'OYuuuur
c) OXuuur
d) 'OXuuuur
3. (x, y) and (y, x) represent the same point if ...........
-
22
a) x > y b) x < y c) x = y d) x ≠ y 4. The point .......
lies in the lower half plane of X-axis and to the right hand
side of Y-axis. a) (-4, -5) b) (4, -5) c) (-4, 5) d) (4, 5)
SELF ASSESSMENT: 4 � Selecting a proper answer from the given
brackets fill in the blanks. 1. ........... is on the X-axis. a)
(0, -5) b) (-5, 0) c) (5, -5) d) (5, 5) 2. O (0, 0) is ..........
a) Only on X-axis b) only on Y-axis c) in all quadrants d) on both
the axes 3. Point P (a, b) where a > 0, b < 0 is in
.......... quadrant. a) III b) I c) II d) IV 4. ......... is in II
quadrant. a) (2, 2) b) (2, -2) c) (-2, 2) d) (-2, -2) 5. Interior
of ∠X’OY’ is called ........... quadrant. a) III b) II c) I d) IV
6. (2y +1, 5x -2) = (5, x + 10) then (x, y) = .......... a) (-2,
-3) b) (2, 3) c) (3, 2) d) (-3, -2) 7. If A = {1, 2} and B = {3, 5}
then (5, 2) ∈ .......... a) A x A b) B x A c) A x B d) B x B 8. (5,
-3) is in interior of .......... a) ∠XOY b) ∠X’OY c) ∠X’OY’ d)
∠XOY’ 9. Cartesian co-ordinate plane is a union of actually
.........sets. a) two b) four c) five d) six 10.If U = Cartesian
co-ordinate plane, set A= points on X-axis and B = points
on Y-axis then (A ∪ B)’ = .......... a) ∅ b) {(0, 0)}
c) union of any two quadrants d) union of four quadrants
11.Abscissa of (3, 5) is ......... a) 8 b) 3 c) 2 d) 5 12.Ordinate
of (3, 5) is ............. a) 8 b) 3 c) 2 d) 5
Chapter- 5 Linear Equations in Two Variables MCQs � Select
proper option (A), (B), (C) or (D) from giv en options and write in
the box given on the right so that the statement becomes correct.
1. Graph of the equation y = x passes through the........quadrants
and the origin. a) I and II b) II and III c) I and III d) III and
IV 2. Line x + y = 2 passes though the ...........quadrants. a) 1st
and 3rd both b) 2nd and 3rd c) 3rd and 4th both d) 1st, 2nd and 4th
3. x + y = 0 passes through ......... quadrants. a) I and II b) I
and III c) II and IV d) III and IV
-
23
4. ax + by = c, a2 + b2 ≠ 0, passes through origin, if
........... a) a = 0, c ≠ 0 b) b = 0, c ≠ 0 c) c = 0 d) a ≠ 0, c ≠
0 5. The linear equation 4x –y + 8 = 0 has .......... a) no
solution b) unique solution c) only two solution d) infinitely many
solutions 6. If x = 2, y =5 is a solution of the 5x + 7y – k = 0,
then the value of k is...... a) 12 b) 35 c) 45 d) -45
7. If the equation is F = 95
C + 32 then C ..........
a) 5F – 160 b) 19(5F – 160) c) 5
9F – 32 d) 5
9 (F – 32)
8. If the equation is F = 95
C + 32 F = C ..........
a) is impossible b) if C = 40 c) if C = -40 d) if F = 32
9. If F = 95
C + 32, and F = -274, then C ..........
a) -338 b) -274 c) -170 d) -170 10.In the plane the equation y =
mx represents ............for different values of m. a)
perpendicular lines b) parallel lines c) lines through origin d)
lines through the point other than origin 11.Line y = 4 is
......... a) parallel to Y-axis b) intersects both the axis c)
parallel through (0, 0) d) passing through (0, 0) 12.Line x = -2 is
......... a) parallel to X-axis b) parallel to Y-axis c) passing
through the origin d) Intersecting Y-axis 13.One of the solutions
of the linear equation 2x + 3y = 7 is ........ a) (1, 2) b) (-1, 3)
c) (-2, 5) d) (-2, 4) 14.The graph of the equation ........ is a
line parallel to Y-axis. a) x – 3 = 0 b) x – y =1 c) y = 1 d) x + y
= 1 15.The graph of the equation ........ is a line passing through
the origin. a) x + y = 0 b) x + y =1 c) 2y – 3 = 0 d) 2x - 2y =
1
BASED ON EXERCISE: 5.1 �Answer the following questions by
selecting appropriate alternative from alternatives given in
questions. 1. The standard form of linear equation in one variable
is ........... a) x = a b) ax + b = 0
c) ax + b = c d) (A), (B) & (C) all 2. ax + b = c, a ≠ 0 has
............. solution/ solutions. a) unique b) two c) no d)
infinitely many 3. If ax + b = c is a standard form of a linear
equation in one variable then...
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24
a) c ≠ 0 b) b ≠ 0 c) a = 0 d) a ≠ 0 4. Solution of 3x – 5 = 7 is
x = ............. a) 3 b) 4 c) 5 d) 6
5. Solution of 3 52 1
x
x
++
= 2 is x = .............
a) 2 b) 3 c) 1 d) 4 6. ........... is a linear equation in one
variable. a) x2 + x + 1 = 0 b) x + y + c = 0 c) xy = 1 d) 6y = 2 7.
......... is not a linear equation in two variables. a) x = k b) y
= 5 c) xy = 1 d) x + y + 1 = 0 8. ......... is a linear equation in
two variables.
a) x2 + y2 = 9 b) xy = 2 c) x2 + y + 1 = 0 d) xy = 2
BASED ON EXERCISE : 5.2 �Answer the following questions by
selecting appropriate alternative from alternatives given in
questions. 1. A linear equation in two variables has .......... a)
only one solution b) at least one solution c) at the most one
solution d) infinitely many solutions. 2. Standard form of a linear
equation in two variable is ax + by + c = 0 where
........... a) a, b, c ∈ N b) a, b, c ∈ Z c) a, b, c ∈ Q d) a,
b, c ∈ R 3. ............ is one of the solutions of 4x + 3y = 12.
a) (0, 0) b) (0, 3) c) (4, 0) d) (3, 0) 4. ........... is one of
the solutions of 3x + 2 y = 5.
a) (1, 1) b) (0, 0) c) ( 3 , 2 ) d) ( 2 , 3) 5. If (2, 5) is a
solution of 4x + ky = 13k then k = ........... a) 3 b) 3 c) 2 d) 1
6. The equation ax + by + c = 0 a, b, c are real numbers is not
linear if ......... a) a = 0, b = 0 b) a = 0, b ≠ 0 c) a ≠ 0, b = 0
d) a ≠ 0, b ≠ 0 7. If x = 1 and y = 3 is a solution of 3x + ky = 9
then k = .......... a) 1 b) 2 c) 3 d) 4 8. If kx + 5y = 11 has a
solution (4, -1) then k = .......... a) 3 b) 4 c) 1 d) 2
BASED ON EXERCISE : 5.3 �Answer the following questions by
selecting appropriate alternative from alternatives given in
questions. 1. Graph of 2x – 3y = 0 passes through ..........
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25
a) (2, 3) b) Origin c) X- axis d) Y-axis 2. Graph of 3x – 1 = 5
is perpendicular to .......... a) X- axis b) Y-axis c) Graph of x =
2 d) Co-ordinate plane 3. Graph of 3y – 1 = 5 is parallel to
.......... a) Origin b) Y-axis c) X- axis d) Graph of x = 2 4. If c
= 0 then the graph of ax + by + c = 0 passes through
...........
a) (a, a) b) (b, b) c) (0, 0) d) ,b aa b
5. If F = 95 C + 32 and F = 212 then C = .............
a) 273 b) 0 c) 180 d) 100 6. 60 is divided into two parts such
that the larger part is 3 times the smaller
part then two parts are .............. a) 20, 3 b) 45, 15 c) 15,
4 d) 18, 15 7. Graph of y = x + 1 and x + y – 3 = 0 intersect at
the point .......... a) (1, 1) b) (0, 0) c) (1, 2) d) (2, 1) 8. The
cost of a note-book is twice the cost of a pen. Write a linear
equation to
represent this statement. Where cost of note-book and a pen are
x, y respectively.
a) 2x = y b) x = 2y c) x = ½ y d) x = y + 2 BASED ON EXERCISE :
5.4
�Answer the following questions by selecting appropriate
alternative from alternatives given in questions.
1. The graphs of y = 3
x and y = -3x on the Cartesian planer are lines ........
a) parallel to Y-axis b) parallel to X-axis c) perpendicular to
each other at the point (3, -3) d) perpendicular to each other at
the point (0, 0) 2. For the equation ax + by = c = 0 if a = 0 and c
= 0 then its graph is ....... a) X-axis b) Y- axis c) a line
parallel to X-axis d) a line parallel to Y-axis 3. In the equation
ax + by = c = 0 if b = 0 and c ≠ 0 then its graph is ....... a) a
line through (0, 0) b) a line perpendicular to X-axis c) not
possible d) a line perpendicular to Y-axis 4. The graphs of ax + by
= 0 is ........... a) a family of lines parallel to X-axis b) a
family of lines parallel to Y-axis c) a family of lines
perpendicular to the co-ordinate plane. d) a family of lines
passing through the origin. 5. The sum of the ages of Raj, Ram and
Rubin is x years today then after 3
years the sum of their ages will be ...........
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26
a) 3x + 3 b) 3x + 9 c) x + 9 d) x + 18 6. ............. is a
linear equation in two variable.
a) x y+ = 1 b) xy + y = k c) 35 y = 6 d) 3 3x y+ = 2
SELF ASSESSMENT TEST: 5 �Selecting a proper answer from the
given brackets fill in the blanks.
1. Solution of 11
x
x
+−
= 2 is ...........
a) 4 b) 3 c) 2 d) 1 2. 2x = 3y passes through .............. a)
(2, 3) b) (2, 0) c) (3, 0) d) (0, 0) 3. ax + by + c is a linear
equation if ........... a) a2 + b2 = 0 b) a2 + b2 ≠ 0
c) a2 - b2 = 0 d) a2 - b2 = 0 4. Solution of 3x + my = 10 is (0,
5) then m = ........... a) 0 b) -2 c) 2 d) 1 5. ........... is a
linear equation in two variable.
a) x2 + x + 5 = 0 b) x2 + x + y + y2 = c c) x = y d) xy = 1
6. 3x + 2y + 1 = 0 has .......... solution/ solutions. a)
infinitely many b) only one c) no d) at the most two 7. Solution of
5x + 2my = 4m is (2, -3) then m = .......... a) 5 b) 1 c) 3 d) 6 8.
Graph of x + y = 0 pass through (0, 0) and lies in ...........
quadrants. a) I and II b) I and III c) I and IV d) II and IV 9. x =
y has ............... solutions/ solution. a) unique b) at least
three c) at the most one d) infinite number of
10.F = 95C + 32. If F = 5 then C = ...........
a) -5 b) -15 c) 15 d) 5 Chapter- 6 Structure of Geometry
� Select proper option (A), (B), (C) or (D) from giv en options
and write in the box given on the right so that the statement
becomes correct. 1. The three steps from solid to point are
.......... a) Solid- Surface – Line – Point
b) Line- Point- Surface- Solid c) Surface – Point- Line - Solid
d) Point – Surface – Line- Solid
2. The number of dimensions a point has is ........... a) 1 b) 4
c) 0 d) 2
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27
3. The number of dimensions a surface has is ........... a) 3 b)
1 c) 0 d) 2 4. Euclid divided his famous treatise “the elements”
into: The number of
dimensions a point has is ........... a) 12 Chapters b) 13
Chapters
c) 9 Chapters d) 11 Chapters 5. Pythagoras was a student of :
The number of dimensions a point has is ........... a) Euclid b)
Thales c) Ramanujan d) Bhaskaracharya 6. Which of the following
needs a proof? a) Axiom b) Postulate c) Definition d) Theorem 7.
Euclid stated that all right angles are equal to each other in the
form of: a) a proof b) a definition c) a postulate d) an axiom 8.
‘Lines are parallel to each other if they do not intersect’ is
stated in the
form of: a) a definition b) an axiom c) a postulate d) a
proof
BASED ON EXERCISE: 6.1 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. Boundaries of surface are ........... a) lines b)
points c) solids d) curves 2. Thales belongs to the country
.......... a) Greece b) Babylon c) India d) Egypt
SELF ASSESSMENT TEST: 6 � Selecting a proper answer from the
given brackets fill in the blanks. 1. “For every line l and every
point P not lying on l, there exists unique line m
passing through P and parallel to l” is ........... a)
Pythagoras theorem b) Postulate by Euclid c) Playfair’s Axiom d)
Thale’s Theorem 2. ........... modified the approach of Euclidean
geometry and made it more
logical and abstract. a) Thales b) Devid Hibert c) Pythagoras d)
Aryabhatta 3. Dimensions of a point is .......... a) 0 b) 1 c) 2 d)
3 4. Dimensions of a solid is .......... a) 0 b) 1 c) 2 d) 3 5.
Euclid deducted........... propositions. a) 456 b) 465 c) 654 d)
546 6. Equivalent verson of Euclid’s fifth postulate was given as
an axiom
by........... a) Pythagoras b) Playfair c) Thales d) Newton 7.
“All right angles are equal to one another” is the ..............
postulate given
by Euclid. a) 2nd b) 3rd c) 4 th d) 5th 8. Non-Euclidean
Geometry is in fact ................ Geometry.
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28
a) Plane b) Co-ordinate c) Spherical d) Vector 9. Two acute
angles can not be a pair of ............. angles. a) Complementary
b) Supplementary c) Vertically opposite d) Alternate 10.“Jinal is
at most 27 years old.” It means the age of Jinal might be
.........years. a) 32 b) 30 c) 28 d) 26
Chapter – 7 Some Primary Concepts in Geometry: 1 � Select proper
option (A), (B), (C) or (D) from giv en options and write in the
box given on the right so that the statement becomes correct. 1. In
P-Q-R, ............. is the ray opposite to QR
uuur.
a) PQuuur
b) QPuuur
c) RQuuur
d) RPuuur
2. If PQ= 9 and RS = 9, we can write ...........
a) PQ RS≅ b) PQ = RS c) PQuuur
= RS d) PQ ≅ RS
3. ............ represents ray XY.
a) XY b) YXuuur
c) XYuuur
d) XYsuur
4. If AB AC=uuur uuur
, then .............. is not possible.
a) A-B-C b) A-C-B c) B-A-C d) AB AC AB∩ =uuur uuur uuur
5. If P-Q-R then point ............. on PQuuur
can not lie between any two other
points of PQuuur
.
a) R b) P c) Q d) all 6. If AB
uuur and AC
uuur are opposite rays, then AB AC∩
uuur uuur= ..............
a) {A} b) AC c) AB d) ∅ 7. If X-Y-Z, then XZ
uuur= ..............
a) YZsur
b) ZXsuur
c) XYuuur
d) YXuuur
8. If X-Y-Z, then YZ ZY∩uur uuur
= ..............
a) YZsur
b) YZuur
c) YZ d) XY
9. Every line has at least ............. distinct points. a) 2
b) 2 c) 3 d) 4
BASED ON EXERCISE : 7.1 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. There are .......... basic concepts in geometry. a)
4 b) 3 c) 2 d) 1 2. In the study of geometry ........ is taken as
universal set. a) point b) space c) line d) plane 3. In the study
of geometry space is taken as ............. set. a) a null b)
singleton c) disjoint d) universal 4. The ......... has no length,
breadth and thickness. a) line b) plane c) point d) space 5. A line
is ..........set.
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29
a) an empty b) a singleton c) a finite d) an infinite 6.
........... distinct points determine a line. a) 3 b) 4 c) 2 d) 5
7. A line passing through the points A and B is denoted by
.........
a) ABuuur
b) BAuuur
c) AB d) ABsuur
8. In the adjoining figure points .......... are collinear. A B
C D
a) A, B, C b) A, C, D c) B, C, D d) A, B, D 9. A line has
.......... end points. a) two b) finite number of c) no d)
infinitely many
BASED ON EXERCISE: 7.2
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions:- 1. Intersection
of two distinct line is ........ a) an empty set b) an infinite set
c) a singleton set d) a universal set 2. In adjoining figure l ∩ m
is ........ A D m O C B l
a) {A, O, B} b) {C, O, D} c) {A, C, O, B, D} d) {O} 3. In
adjoining figure l ∩ m is ........ l m
l || m a) a singleton b) a null set c) an infinite set d)
disjoint sets 4. In adjoining figure l ∩ m is ........ l m a) an
empty set b) a subset
c) an infinite set d) a finite set
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30
5. If l = m then l ∩ m = .............. a) ∅ b) U c) m d) does
not exist
BASED ON EXERCISE : 7.3 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. Distance between two distinct points is associated
with ......... a) 0 b) non-negative real number c) an integer only
d) a definite non-negative real number 2. For any three points P,
Q, R, PQ + QR ........... PR. a) < b) > c) > d) < 3.
For two distinct points A and B, AB ........0. a) < b) < c)
> d) > 4. The measure of distance between two distinct points
P and Q is denoted
by ........... a) PQ b) PQ
suur c) PQ d) QP
uuur
5. |a| = - a if a ........... 0. a) > b) > c) < d) <
0 6. If a < b then | a – b| = ........... where a, b ∈ R. a) a –
b b) 0 c) ab d) b – a 7. On a line l, M corresponds to m ∈ R and N
corresponds to n ∈ R then MN
= .............. a) m – n b) n- m c) | m – n| d) 0 8. On a line
l if M is associated with -5 and N is associated with -3 then MN
=
............. a) 8 b) -8 c) -2 d) 2 9. If PQ= |p –x | = 3 and p
= 6.3 then x = ........... a) 3.3 b) 9.3 c) 3.3 or 3.9 d) 3.3 or
9.3 10.If A-P-B and A, P, B on a line correspond to real numbers a,
p, b
respectively then .......... a) a < b < p b) p < a <
b c) a < p < b d) a < p < b or a < p < b 11.If on
a line, point B is between the points A and C then .......... a) AB
+ BC = AC b) AB + AC = BC c) BC + AC = AB d) AB + BC + CA = 0
12.Given P-Q-R. Let -3.7 and 7.8 correspond to the points P and
R
respectively. If PQ= 5.6 then QR= ..... a) 2.2 b) 5.9 c) 11.5 d)
5.6 13.|7 – a | = 10 then a = ..... a) 3 or -17 b) -3 or 17 c) 3 or
17 d) -3 or -17 14.On a line l, let the points L, M, N correspond
to 10, -7, 15 respectively
then ...... a) L-M-N b) L-N-M c) M-L-N d) M-N-L
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31
BASED ON EXERCISE: 7.4
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions:- 1. PQ ..........
PQ
suur
a) ⊄ b) ⊂ c) ∈ d) ∉ 2. PQ
suur .......... PQ
a) ⊄ b) ⊂ c) ∈ d) ∉ 3. A line segment has ......... end points.
a) one b) two c) three d) no 4. {P, Q} ......... PQ
a) ∈ b) ∉ c) ⊂ d) ⊄ 5. A line segment AB is represented by
......
a) AB b) ABsuur
c) AB d) {P I A-P-B}
6. Length of AB denoted by ......
a) ABsuur
b) x c) AB d) AB 7. On a line let A, B correspond to real
numbers a, b respectively then AB =
.......... a) a – b b) b – a c) | a – b| d) | ab | 8. If AB = x
, PQ = x where x ∈ R then PQ ....... AB a) ~ b) ⊂ c) = d) ≅ 9. PQ =
...........
a) PQ b) {X | P-X-Q} c) {P, Q} ∪ {X | P-X-Q} d) P ∪ Q ∪ {X |
P-X-Q} 10.Every line-segment has ......... mid-point. a) at least
one b) at most one c) one had only one d) two 11.On a line, let
points P and Q correspond 7 and 13 respectively. Then mid-
point of PQ correspond to.........
a) 6 b) -6 c) 10 d) -10 12.If M is a mid-point of PQ and M, P
correspond to 15, 8 respectively then Q
corresponds to ...... a) 7 b) 22 c) 23 d) 11.5
13.Let A and P correspond to -7 and 3 respectively. If P is the
mid-point AB then AB = ......
a) 16 b) 5 c) 8 d) 20
14.Let A and B be correspond to 3 and 15. If M is the mid-point
of AB, then BM = ......
a) 6 b) 12 c) 3 d) 18 BASED ON EXERCISE: 7.5
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions:- 1. The bisector
of a line-segment passes through the mid-point of the...... a) line
b) ray c) line-segment d) plane
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32
SELF ASSESSMENT TEST : 7
� Selecting a proper answer from the given brackets fill in the
blanks. 1. On a line l, point A corresponds to -3 and AB = 5 then
the point B
corresponds to .......... a) 1 or -4 b) 2 or -8 c) -3 or 5 d) 8
or -2 2. If A-B-C, BC= 3 and AC= 9 then AB = ....... a) 12 b) 15 c)
6 d) 18 3. If A, B, C are three distinct points they determine at
the most ....... line-
segments. a) 1 b) 2 c) 3 d) 4 4. Four distinct co-planar points
determine at most ....line segments.
a) 5 b) 1 c) 4 d) 6 5. Five distinct co-planar points determine
at most ...... line-segments.
a) 8 b) 10 c) 12 d) 20 6. Real number a, b and x corresponds to
the points A, C, B respectively. If B
is mid-point of AC then x = .......
a) a + b b) | a - b | c) 2
a b+ d)
2
a b−
7. | x - 7| = 2 then x = ....... a) -4.5 or 4.5 b) 5 or 9 c) 5
or -9 d) -5 or 9
8. If A-M-B then AB ....... AMuuuur
. a) ⊂ b) ∈ c) ∉ d) ⊄ 9. If P-Q-R then pair of opposite rays is
.........
a) RPuuur
and PRuuur
b) PRuuur
and QPuuur
c) QPuuur
and QRuuur
b) QRuuur
and RPuuur
10.If P-Q-R then PRuuur
∩ RPuuur
= ......
a) PQ b) QR c) PR d) ∅
11.If P,Q,R non-collinear points then PQuuur
∩ PRuuur
.
a) ∅ b) PRuuur
c) PQuuur
d) {P}
12. PQ PQ∩uuur
= .........
a) ∅ b) PQsuur
c) PQ d) QPuuur
13. PQ PQ∪uuur
= .........
a) PQ b) PQsuur
c) {P, Q} d) PQuuur
14. ABsuur
is bisector of PQ then ........passes through the mid-point of
PQ.
a) APuuur
b) BPuuur
c) ABuuur
d) ABsuur
15.If A ∈ BC then AB AC∩uuur uuuur
is ..........
a) ∅ b) {A} c) ABuuur
d) ACuuur
16.For two distinct points A and B = .......
a) ABsuur
⊂ {A, B} b) ABsuur
⊂ ABuuur
c) ABsuur
⊂ AB d) ABsuur
⊂ ABsuur
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33
17.For two distinct points A and B, AB BA∪
uuur uuur= ..........
a) {A, B} b) AB c) ABsuur
d) ABuuur
18.In a geometry ...... is taken as universal set. a) a point b)
a line c) a space d) a plane 19.For two distinct point A and B,
AB
uuur⊂ .......
a) {A} b) {A, B} c) BAuuur
d) ABsuur
20.If a AB
uuurbisects PQ in a point M then ..... is between P and Q.
a) A b) B c) M d) Q Chapter- 8 Some Primary Concepts in Geometry
: 2
� Select proper option (A), (B), (C) or (D) from giv en options
and write in the box given on the right so that the statement
becomes correct. 1. An angle is a union of ...... a) lines b)
line-segments
c) rays d) a line segment and a ray 2. The measure of an angle
always lies between ......... a) 0 and 90 b) 90 and 180 c) 0 and
100 d) 0 and 180 3. If m∠A = 81 and m∠B = ......... then they are
complementary angles. a) 99 b) 19 c) 81 d) 9 4. BA
uuur and BC
uuur are distinct rays. If ......... then they determine a plane
uniquely.
a) they are opposite rays b) they lie in the same line c) they
are not opposite rays d) they are identical rays
5. If distinct points A and B lie in a plane X, then X ∩
ABsuur
= .........
a) {A, B} b) ABsuur
c) plane X d) PQ
6. If two lines cannot lie in the same plane, they are called
.......lines. a) disjoint b) skew c) parallel d) coplanar 7. The
supplementary angle of the complementary angle having measure
23
has measure ........ a) 67 b) 90 c) 113 d) 23 8. The
complementary angle of an angle having measure x + 30 has
measure ........ a) -( x - 60) b) 60 + x c) x - 60 d) -60 - x 9.
If one angle of linear pair is acute, then other angle is .......
a) congruent b) acute c) obtuse d) right angle 10.If t is a
transversal for two parallel lines l and m, interior angles on
the
same side of the transversal are ......... a) supplementary b)
linear pair c) complementary d) congruent 11.If two angles forming
a linear pair have measures (6y + 30) and 4ym then
y = ......... a) 30 b) 15 c) 60 d) 90
12.An angle has measure equal to 1
3rd measure of its supplementary any
angle, then the angle has measure .......
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34
a) 15 b) 30 c) 45 d) 60
BASED ON EXERCISE: 8.1 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. A plane is .......... a) a null set b) a singleton
set c) a universal set d) a points set 2. A line in a plane
partitions the plane into...........mutually disjoint subsets of
points of the plane. a) 4 b) 3 c) 2 d) 1 3. If α and β are
half-planes in a plane because of a line I in the plane X then
α ∩ β = ......... a) ∅ b) l c) X d) space 4. If P and Q are in
different half planes X1 and X2 made by line l then PQ l∩ =
............... a) ∅ b) a singleton set c) l d) PQ
suur
5. .............. distinct non-collinear points determine a
plane. a) Two b) Three c) Four d) Five 6. .......... determine a
plane. a) Two skew lines b) Four non-collinear points c) Two
intersecting lines d) A point and two lines 7. In a plane X and Y
are closed half plane as the plane α is partitioned by a
line l then X ∩ Y = ........... and X ∪ Y = ................ a)
X, l b) ∅, α c) l, α d) X or Y, α 8. ............. determine a
plane. a) Two non- intersecting lines b) A pair of parallel lines
c) Two skew lines d) Four non-collinear points 9. Intersection of
two distinct non-parallel planes is a .............. a) Either of
the given planes b) Two distinct lines c) A unique line d) A unique
point 10.If three planes intersect each-other then there exist at
the most ........lines. a) 3 b) 2 c) 1 d) 0 11. If a line m
intersects the plane X then n(l ∩ x) = ............. is false. a) ∞
b) 1 c) n (l) d) 0 12.In the given figure P Q ................. =
∅. . .
l X
a) l ∩ x b) PQsuur
∩ l c) PQ X∩ d) PQ l∩
BASED ON EXERCISE : 8.2 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:-
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35
1. ∠ABC = ..................
a) AB BC∪suur suur
b) AB BC∪ c) {B} d) BA BC∪uuur uuur
2. If D is in interior of ∠ABC then ADuuur
intersects .................
a) ABuuur
b) BC c) ACuuur
d) DBuuur
3. If D is in interior of ∠ABC then .............. is called the
vertex of ∠ABC. a) A b) B c) C d) D 4. If P QR∈
uuur and P-M-R then M is in the interior of .............
a) ∠PMR b) ∠PQR c) ∠PRQ d) ∠QPR 5. If D is in interior of ∠ABC
and B-D-C then. D ∈ ................
a) ABuuur
b) BCuuur
c) ∠ABC d) BC
BASED ON EXERCISE: 8.3 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. Associate with each angle there is one and only one
real number x such
that ........... called the measure of that angle. a) 0 < x
< 180 b) 0 < x < 180 c) 0 < x < 180 d) 0 < x <
180 2. In adjoining figure x = ............., given that m∠BOA= 60.
a) 12 b) 24 B c) 36 d) 6 C 3x
2x A O 3. In adjoining figure x = 3y and m∠BOA= 60 then m∠AOC=
......... a) 15 b) 45 B c) 30 d) 5 C y x O A 4. If m∠ABC= 37 then
∠ABC is ........... a) an obtuse angle b) a right angle c) an acute
angle d)) a congruent angle 5. If m∠ABC= 91then ∠ABC is ...........
a) an acute angle b) a right angle c) an obtuse angle d)) a
congruent angle 6. Two angles are said to be...........to each
other if the sum of their measures
is 90. a) congruent b) similar
c) supplementary d) complementary 7. If m∠ABC= 115 and m∠PQR =
65 then they are called........... angles.
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36
a) complementary b) supplementary c) congruent d)) adjacent 8.
If m∠ABC= m∠PQR then ∠ABC and ∠PQR are called ............. a)
congruent b) complementary c) vertically opposite d)) supplementary
9. If two adjacent angles from a linear pair of angles then they
are also a pair
of ............... a) complementary angles b) vertically
opposite angles c) supplementary angles d) congruent angles 10.The
measure of an angle is five time the measure of its complementary
angle then the measure of the angle .............. a) 15 b) 30 c)
45 d) 75 11.In adjoining figure y = ............. a) 15 b) 30 5y 2y
c) 60 d) 75 5y 12.In adjoining figure x = ............... a) 19 b)
38 c) 57 d) 76 3 x – 10 2x 13.In adjoining figure c =
............... if a : b = 2 :3 a) 136 b) 144 c) 72 d) 126 a b 90 c
14.In adjoining figure 2x = ............... a) y + z b) y – 2z
c) y – z d) 3y – 2z x y z
O 15.If two supplementary angles are congruent then the measure
of each
angle is ............... a) 45 b) 90 c) 60 d) 135 16.The m∠A
measure of its supplementary angle differ by 34 then m∠A =
............. (where m∠A is greater). a) 73 b) 97 c) 107 d) 78
17.∠A is complementary angle of supplementary angle of the angle
having
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measure 125. ∴ m∠A = ...............
a) 35 b) 45 c) 65 d) 25 18.∠A is complementary angle of the
angle with measure 10 + x then m∠A =
............... a) 90 + x b) 80 + x c) 80 - x d) 90 - x 19.∠A is
supplementary angle of the angle with measure y – 30 then m∠A =
............... a) y+ 60 b) 210 - y c) 150 + y d) 180 - y 20.A
pair of supplementary angle is also a pair of congruent angles
measure
of each angle is ............... a) 45 b) 135 c) 90 d) 120
21.∠AOC and ∠BOD are vertically opposite angels such that m∠AOC = a
+ 20, m∠BOD = 2a – 50. m∠AOD= .............. a) 60 b) 70 c) 90 d)
110 22.For a linear pair of angles ∠XOY and ∠YOZ m∠XOY:m∠YOZ = 2:3,
then
n∠YOZ = ................ a) 72 b) 108 c) 36 d) 54 23.Disjoint
angles of measure 115 and 65 are a pair of .............. angles.
a) Supplementary b) Complementary c) Linear pair d) Vertically
opposite angles
BASED ON EXERCISE: 8.4 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:-
1. If l1, l2 , l3 are three distinct co-planar line such that l1
|| l2 and l3 || l2 then l1 ∩ l3 = ....................
a) l1 b) l2 c) l3 d) ∅ � Following Figure for MCQ No. 2, 3 and
4. A P Q B R C S D 2. In the adjoining figure ∠PBC and ∠RCD form a
pair of .............. angles. a) Alternative b) Corresponding c)
Interior angles on the same side of the transversal
d) Adjacent 3. In the adjoining figure ∠QBC and ∠RCB form a pair
of ........... angles.
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a) Alternative b) Corresponding c) Complementary d) Vertically
opposite 4. In the adjoining figure ∠QBC and ∠BCS form a pair of
............ a) Vertically opposite angles b) Alternate opposite
angles c) Corresponding opposite angles
d) Interior angles on the same side of the transver sal �
Following Figure for MCQ No. 5 and 6. E A B F m C G D n H 5. In the
adjoining figure m || n and m∠EFB = 65 then m∠CGF = ..............
a) 25 b) 115 c) 75 d) 135 6. In the adjoining figure m∠EGD = 5x,
m∠EFB = 120 - x and m || n then
m∠EFB = .............. a) 90 b) 75 c) 100 d) 105
BASED ON EXERCISE: 8.5 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions:- 1. Angles in each pair of alternate angles formed by a
transversal to two
parallel lines are ................ a) complementary b)
congruent c) supplementary d) disjoint 2. Bisectors of alternate
angles formed by two parallel lines and their
transversal are ............... a) parallel to each other b)
intersecting each other c) skew rays d) identical rays 3. In the
adjoining figure m∠DEF = ........... a) 30 b) 60 A B
c) 90 d) 120 60 C D F
E
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BASED ON EXERCISE: 8.4 & 8.5
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions:- 1. Interior
angles on one side of a transversal to two parallel lines are......
a) Adjacent b) Complementary
c) Supplementary d) Congruent 2. In the adjoining figure m∠XYR +
m∠YRQ + m∠PQR = ...........where l || m. X Y l R P Q m
a) 180 b) 360 c) 90 d) 120
3. In the adjoining figure if m∠P = 40 then m∠QTR = ..........
where QTuuur
and RTuuur
are the bisectors of ∠EQR and ∠FRQ respectively.
P
40 Q R o o x x E ? F
T a) 70 b) 60 c) 140 d) 30
4. In adjoining figure , ||AB AD AB DC⊥suur suur suur suur
m∠DBC = 28, m∠BCE = 65
∴ y – x = ....... A B x
a) 8 b) 64 c) 32 d) 16 28 y 65 D C E
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SELF ASSESSMENT TEST: 8
� Selecting a proper answer from the given brackets fill in the
blanks. 1. In the adjoining figure m∠AOB = ........... where l ||
m. A l 55 O 38 m B
a) 74 b) 66 c) 93 d) 90 2. In the adjoining figure m∠ACB =
........... where m∠B = 55, CE
uuuris bisector of
∠ACD and ||CE BAuuur uuur
. A
a) 55 b) 70 E c) 110 d) 125
55 B C D
3. In the adjoining figure m∠AOC = ........... where ||AC BDsuur
suur
.
a) 80 b) 20 A D c) 40 d) 60 50
70 O C B 4. If ............... two lines do not intersect each
other then they are parallel. a) skew b) non-coplanar c)
perpendicular d) co-planar 5. If two distinct l and m are
perpendicular to a line l then ..............where, l,
m, t are co-planar. a) l ⊥ m b) l || m c) l ∩ m = l d) l ∩ m = ∅
6. ∠A is complement of ∠B and ∠C is suppleme nt of ∠B if m∠A = 35
then
m∠C = ................ a) 125 b) 135 c) 155 d) 160 7. In
adjoining figure x = .............. where l || m.
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a) 36 b) 20 c) 40 d) 72
7x 2x 8. In adjoining figure y = .............. where l ||
m.
a) 25 b) 45 c) 55 d) 35 155
l y m 9. A pair of alternate angles from by two parallel lines
and a transversal form
a pair of ............... a) complemental angles b)
supplementary angles c) congruent angles d) adjacent angles
10.Measure of obtuse angle ............. measure of acute angle. a)
= b) < c) > d) >
Chapter – 9 Triangle � Select proper option (A), (B), (C) or (D)
from giv en options and write in the box given on the right so that
the statement becomes correct. 1. For ∆ABC, the side opposite to ∠A
is .............
a) AB b) BC c) CA d) ACuuur
2. For ∆ABC ......... is included by the sides the side BC and
AC . a) ∠A b) ∠B c) ∠C d) exterior angle of ∠D
3. If ∠ACD is an exterior angle of ∆ABC and m∠ACD= 105, then
m∠ACB = ..............
a) 105 b) 75 c) 100 d) less than 75 4. For the correspondence
BAC ↔YXZ between ∆ABC and ∆XYZ, the angle
∠............. correspondence to ∠Z. a) B b) A c) C d) Y 5. For
∆ABC, if D ∈ BC
uuur such that B-C-D then..........is exterior angle of
∆ABC.
a) ∠ABC b) ∠ACB c) ∠ACD d) ∠BAD
6. The measure of congruent angles in ∆ABC (where AB≅ AC ) is
.......... where m∠A= 60.
a) 35 b) 45 c) 60 d) 90 7. For ∆ABC, ∠A ≅ ∠C. If BC= 3, AC- 4,
then perimeter of ∆ABC = ........... a) 10 b) 12 c) 14 d) 7 8. ∆ABC
is ...........
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42
a) AB∪ BC b) ∠A ∪ ∠B c) AB∪ BC∪ AC d) ∠A ∪ ∠B ∪ ∠C 9. From the
following which condition is not possible for the congruence of
two triangles? a) ASA b) AAS c) AAA d) SSS 10.For ∆ABC
.............. is true. (If it is not a right triangled) a) AB2 +
BC2 = AC2 b) AB + BC = AC c) AC > AB + BC d) AC < AB + BC
11.For ∆ABC, m∠A= 40, m∠C= 50, then the smallest side of ∆ABC is
.......
a) AB b) BC c) AC d) BC 12.For ∆ABC, ∠B ≅ ∠C, then .........
sides are congruence.
a) ABand BC b) ABand AC c) BC and AC d) any two 13.For ∆ ABC,
the bisectors of ∠B and ∠C intersect at the point P. If m∠A =
70, then m∠BPC= ........... a) 50 b) 75 c) 100 d) 125 14.For ∆
ABC, if m∠B = 2x, m∠A = x, m∠C = y and 2x - y = 40, then ∆ ABC
is
........... a) scalene b) right angled c) isosceles d)
equilateral 15.If the measure of the angles of ∆ ABC are in
proportion 1:2:3, then the
measure of the smallest angle is ........... a) 30 b) 60 c) 90
d) 120 16.For ∆ ABC, BC ........... ∆ ABC. a) ∈ b) ∉ c) ⊂ d) ⊄
17.In ∆ ABC if m∠A + m∠B = 120 then m∠C = ........... a) 20 b) 40
c) 60 d) 80
BASED ON EXERCISE : 9.1 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions: 1. ∆ PQR = ..........
a) PQ QR PR∩ ∩ b) PQ QR PR∩ ∪
c) PQ QR PR∪ ∪ d) PQ QR PR∪ ∩
2. For a ∆ PQR, ∠PQR .......... a) ⊂ ∆ PQR b) ⊂ {P, Q, R} c) ⊂
PQ QR∪ d) ⊄ ∆ PQR 3. Each triangle has ............... parts. a)
two b) three c) five d) six 4. For ∆ PQR, ∠Q is called the included
angle of the .............
a) sides PQ and QR b) sides QR and PR
c) sides RP and PQ d) side PR and vertex Q
5. The plane containing a triangle is partitioned
into.........parts by the triangle. a) two b) three c) five d) six
6. The interior of ∠P, ∠Q, ∠R are respectively I1, I 2, I 3; and
the interior of ∆ PQR is I then I = ........... a) I1 ∪ I2 ∪ I3 b)
I1 ∩ I2 ∪ I3
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43
c) I 1 ∩ I 2 ∩ I 3 d) I1 ∪ I2 ∩ I3
7. If P is a vertex of ∆ PQR in plane α then P ...... a) ∈
Interior of ∆ PQR b) ∈ α c) ∈ Exterior of ∆ PQR d) ∈ ∆ PQR 8. The
exterior and the interior of ∆ PQR in a plane α are denoted by E
and I
respectively then I ∪ E ∪ ∆ PQR = ............. a) I b) E c) ∆
PQR d) α 9. The exterior and the interior of ∆ PQR in a plane α are
denoted by E and I
then E ∩ I = ........... a) ∆ PQR b) I c) ∅ d) α 10.At each
vertex of a triangle, there are ......... exterior angles of the
triangle. a) one b) two c) three d) four 11.A triangle has in all
...........exterior angles. a) three b) six c) nine d) twelve 12.In
the adjoining figure .............of ∆ PQR are called the interior
opposite
angles of ∆ PRS. P
a) ∠R and ∠Q b) ∠P and ∠R c) ∠PRQ and ∠PRS d) ∠P and ∠Q
Q R S 13.If ∠PRS is an exterior angle of ∆ PQR the m∠PRS = .....
a) m∠P + m∠Q b) m∠Q + m∠R c) m∠R + m∠P d) 90 14.In the adjoining
figure if ||PQ RY
uuur the m∠Q = .... when m∠PRS = 120.
a) 50 b) 60 P c) 70 d) 90
50 Q R S 15.In ∆ ABC, m∠A = 2, m∠B = 6, then m∠C= ........ a) 18
b) 36 c) 54 d) 108 16.If the measure of the angles are in
pro-portion 4:5:6 then measure of the
smallest angel is ...... a) 24 b) 48 c) 60 d) 72 17.For ∆ ABC if
m∠C = 120, m∠A - m∠B = 20, then m∠A= ........ a) 100 b) 80 c) 40 d)
60 18.In the adjoining figure m∠BDA = ........... A a) 60 b) 100 30
D c) 80 d) 75 �
B � 50
Y
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19.The sum of the measure of all the exterior angles of a
triangle is ...... a) 180 b) 360 c) 540 d) 720 20.The measure of an
exterior angle ∠ACD of ∆ABC is 105 and m∠B = 35
then m∠A = .......... a) 140 b) 35 c) 70 d) 75 21.In adjoining
figure BE AC⊥ , B-D-C, m∠EBC = 40 and m∠DAC = 30 then
m∠ADC = ................. A a) 70 b) 80 c) 100 d) 120 30 E B 40
D C 22.If the measure of the angles of the triangle are in
proportion 2:3:5 then the
triangle is .............. a) acute angled triangle b) right
angles triangle c) obtuse angles triangle d) Isosceles angled
triangle 23.Compute the value of x for the adjoining figure. a) 75
b) 65 110 A c) 45 d) 35 B x 105
C 24.In ∆ABC if m∠A- m∠B = 70 and m∠B - m∠C v= 40 then m∠B =
............. a) 30 b) 40 c) 50 d) 70
25.In ∆ABC if m∠A = 2 2
m B m C∠ ∠= then m∠A = = .............
a) 30 b) 40 c) 45 d) 60 26.For ∆ABC, ∠ABE and ∠CAD are exterior
angles and their measures are
100 and 125 respectively then m∠ACB =............. a) 55 b) 35
c) 45 d) 65
BASED ON EXERCISE : 9.2 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions: 1. For correspondence ABC ↔ ........... ∠B ↔ ∠P. ∠C ↔
∠R, ∠A ↔ ∠Q. a) PQR b) QPR c) PRQ d) QRP 2. For ∆DEF and ∆XYZ if ,
,DE XY E Y EF YZ≅ ∠ ≅ ∠ ≅ then correspondence
..............is a congruence. a) DEF ↔ XZY b) DEF ↔ ZXY c) DFE
↔ XYZ d) DEF ↔ XYZ
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BASED ON EXERCISE : 9.3
� Answer the following questions by selecting approp riate
alternative from alternatives given in questions: 1. For ∆ABC if
,AB AC≅ and 50m B then m A∠ = ∠ = ................. a) 50 b) 100 c)
80 d) 60
2. In ∆ABC, BEsuur
is the bisector of ∠B and .AB AC≅ if m∠ABE = 40 then m∠C=
................. a) 40 b) 60 c) 70 d) 80
3. In an isosceles ∆XYZ, ,XY XZ≅ If M and N are the points on YZ
such that
YN = MZ. If XM = 12 cm then XN = ........... cm. a) 3 b) 6 c) 9
d) 12 4. For a ∆ABC if m∠A= x, m∠B = 3x , m∠C = y and 3y – 5x = 30
then ∆ABC
is ............ a) obtuse angles triangle b) isosceles c) right
angled triangle d) equilateral triangle
BASED ON EXERCISE : 9.4 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions: 1. For a ∆ABC if D ∈ BC such that AD = BD = CD then m∠A=
.................. a) 90 b) 60 c) 45 d) 30 2. In ∆PQR, bisector of
∠P is ⊥ to QR. ∴ ∆PQR is ..................
a) obtuse angled triangle b) scalene c) right angled triangle d)
isosceles triangle 3. If a point P is in interior of ∆ABC. If PA =
PB = PC and m∠A = 70 then
m∠BPC = ............... a) 35 b) 125 c) 65 d) 140 4. In the
adjoining figure if AB = AC, AF= AE and BE = 12 then CF = ...... a)
3 b) 6 A c) 12 d) 9 F P E B C
BASED ON EXERCISE: 9.5 � Answer the following questions by
selecting approp riate alternative from alternatives given in
questions: 1. In ∆ABC, AB = BC and m∠A = 50. ∴ Measure of exterior
∠ACD = ........ a) 95 b) 105 c) 115 d) 125 2. For ∆ABC, AB= 4, BC=
6 then AC = .............. a) < 2 b) > 4 c) ∈ (4, 6) d) ∈ (2,
10)
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SELF ASSESSMENT TEST: 9
� Selecting a proper answer from the given brackets fill in the
blanks. 1. In ∆ABC if m∠B = m∠A + m∠C then m∠B = ..................
a) 60 b) 90 c) 100 d) 50 2. In ∆ABC, AB BC⊥ then AB ..........
AC.
a) > b) < c) = d) ≅ 3. For ∆PQR, vif QR > PQ>PR then
the smallest side is ..........
a) PRuuur
b) PRsuur
c) PR d) PR 4. In ∆ABC, m∠B = 100, m∠A = 50 then BC
................ AC. a) = b) > c) < d) = 5. In ∆ABC, m∠A =
120 ∴ the largest side is ...........
a) BC b) AB c) AC d) BC 6. In ∆ABC, AB = 12, BC= 8 then AC
