Math Set a Question and Solution in DU

7/18/2019 Math Set a Question and Solution in DU

http://slidepdf.com/reader/full/math-set-a-question-and-solution-in-du 1/6

1. If g(x) = thenb x

x

x

a x,

−+

− ?)

2( =

+ ba g

a)2

2

a

ab b)

22

4

ba

ab

− c)

2

4

b

ad)

22

2

ba

ab

−

Solution:

2. Find the square root of ( )312

1−+−

(a) )31(2

1i+± (b) )31(

2

1i+± (c) )31(

2

1−+± (d) )31(

2

1i−±

Solution:

3. If A =

−

−

−

311

122

11

and !=

−

−−

131

312

321

, then A!=?

(a)

−−

312

2"#

33

(b)

−

−−

11"$

1"#

#%1

(c)

− 312

%42

#31

(d)

−

−−

312

1"#

33

Solution:

&sing 'acuator e get,

A! =

−

−−

312

1"#

33

4. If n*4 = 14 (n+1)*3 , then n = ?

(a) $ (b) " (c) (d) a and c



Solution:

)4)(3)(2(14)3)(2)(1( −−−=−−− nnnnnnn

#%1#2 =+−⇒ nn

))($( =−−⇒ nn

,$=⇒ n

#. -he 'oefficient of # x and 1# x are equa for the exansion of

1

3

22

+

x

p x , hat is the

ositi/e /aue of ?

(a)3

1(b) 3 (c)

3

1(d) 3

Solution:

%. -he 0idoint of the ine oining the oints A(1,2) and !(a,b) is (%,"), hat is the coordinate of

oint !?

(a) (1,%) (b) (11, 1%) (c) (11,+1%) (d) (+1, +%)

oution

%2

1=

+ a"

2

2=

+ b

11=⇒ a 1%=⇒ b

)%,11(=∴ B

$. Find the equation of a circe assing through the oint (1, +2) and has center at (",4).

(a) 3122 =−−−+ y x y x (b) 3122 =−−−+ y x y x

(c) 122 =−−+ y x y x (d) "22 =+ y x

Solution:

-he circe assing through the oint (1,+2) i satisf the equation of circe.



. A force of # 0agnitude is acting in east direction5 another 2 force is acting at %2

o

incination to east direction. 6hat is the ange beteen the resutant and # force?

(a) .11% (b) .21 (c) .

32 (d) .#1%

Solution:

". 13

#=θ Sin

and

∠∠θ

2 . ?

)(coscot

)sec(tan=

−+

−+

θ θ

θ θ

ec

(a)1

3− (b)

3

1− (c)

2##

11 (d)

1

3

Solution: use cacuator for required /aues.

1. ?cos

3

i0 =+→ X SinX

x7

(a) (b) 3 (c) 4 (d) 2

Solution:

11. If θ θ 3,cos Sin y x == then ?

2

2

=dx

yd

(a) θ 2cos3− (b)θ

θ

sin

2cos3 (c) θ 2sin

2

3− (d) none of these

Solution:



12. ∫ =−1

2?)1( dx x x

(a) 1 (b) (c)3

1 (d) +1

Solution:

13. 6hat is the soution of ?)( 44=− ya D (89 %4)

(a) = )sincos( 4321 axcaxcecec axax +++ −

(b) =ax xaxax ecececec sin

#

cos

421 ( +++ −

)

(c) = xa xaecec

22

21

−+

(d) one of these

Solution:

Auxiiar equation : 44 =− a D

( )22 a D +⇒ ( ) 22 =− a D

aia D ±±=⇒ ,

( )axcaxcecec y axax

sincos, 432 +++=∴ −

14. If .$12 ≤+ x hich one is correct?

(a) 34 ≤≤− x (b) 2≤ x (c) ## ≤≤− x (d) none of these

Solution:

( ) $12$ ≤+≤− x

1$21$ −≤≤−−⇒ x

%2 ≤≤−⇒ x

34 ≤≤−⇒ x

1#. 6hat is the correct binar con/ersion of 4%?

(a) 111111 (b) 111111 (c) 111111 (d) 1111111



Solution:

&sing scientific cacuator (4%)1= (111111)2

1%. 9quations of robabiit for e/ents A and ! are reated b ( ) ,3

1=∩ B A P ,

%

#)( =∪ B A P

,2

1)( = A P then ?)( = B P

(a)3

2 (b)

#

2 (c)

$

2 (d)

"

2

Solution:

( ) )()()( B A P B P A P B A P ∩−+=∪

3

1)(

2

1

%

#−+=⇒ B P

3

2

%

4

%

23#

3

1

2

1

%

#)( ==+−=+−=⇒ B P

1$. ∫ =+

?)2sin1( θ θ d

2

(a) 12−

(b) 1+

2

(c)

2

(d)

2

3

Solution:

using cacuated e get, I = 12

#$" −=⋅

o, Anser is (a).

1. For hat /aue of ;a<, tangent dran at (,) oint on the cur/e )1( xax y −= i 0ae an

ange % ith x+axis

(a) 2

1

(b) 2

3

(c) 3 (d) 2

1

Solution:

axaaxaxdx

d

dx

dy2)(

2 −=−=



at (,) ointdx

dy = a+2a. = a

soe = tan% 3=

According to question, a = 3

Ans: (c)

1". If ( ) x

a x x f += 2

has 0ini0u0 /aue at 2= x oint, then a=?

(a) (b) 1 (c) 1% (d) none of these.

Solution:

For 0ini0u0 /aue,

=dx

dy

3

2

2

2

2

2

xa

x x

a

x

a x

=⇒

=⇒

=−⇒

at 2= x int, po 1%22 3 =×=a

2. 8o0ain of tangent function is?

(a) R ( )

∈+− N nn Rb

212)( [ ]1,1)( −− Rc (d) R+(+1,1)

Solution:

tangent function is undefined at2

and odd 0utie of

2

>ence, do0ain is R

+ ( )

∈+ N nn

212

Documents

Math Set a Question and Solution in DU