Jee 2014 Booklet5 Hwt Integral Calculus 1

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [1]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than One correct option. 1.

n cos n  1 x

 1  sin x n dx equals: (A)

*2.

1  sin x n

3t

a=b=c

 x 2t  x t





t 1 t

  2x

2t

(C)  3 xt  6

C





C

(D)

 sec x  tan x n  C

ab + bc + ca = 0

(D)

a 3  b 3  c 3  3a 1b 1c 1

1  sin x n

2 x . secb 3 x . secc 5 x  K . Then :

(B)

x

 cos n x

(C)



1 t dx

(B)

is :





t 1 2 x 2t  3 xt  6 x  C 6t

(D)

None of these

(B)

1   2 1  x  x 2  2 log  x   1  x  x 2   C 2  

(D)

2 1  x  x 2  2 log  1  x  x 2   C  

(C)

sec( e x x )  C

C

(B)

log

C

(D)

log



2 1  x  x 2  2 log  1  x  x 2   C  

e x 1  x 

 cos2  xe x  dx  (A)

tan e x  x  C

 

cos xe x

(B)

 

tan e x x  C

(D)

x 1

 x 1  xe x 2 dx is :   (A)

log

(C)

log

xe x 1  xe

x

1  xe x xe

7.

a

C

2 1 x3t  x 2t  xt  C t 1 2x  3 dx is: x2  x  1 1   (A) 1  x  x 2  2 log  x   1  x  x 2   C 2  

(C)

6.

1  sin x n

1 2 x3t  3 x 2t  6 xt 6  t  1

(C)

5.

sin n x

(B)

a, b, c are in H.P.

For any natural number t, (A)

4.

C

 tan 2 x tan 3x tan 5x dx  log sec (A)

3.

cos n x

x





1 1  xe

x

1 1  xe

x

xe x 1  xe x

1  xe x xe x





1 1  xe x

1 1  xe x

C

C

e x dx

  2  e x  e x  1 is : (A)

 e2  2  e x  1  C

(B)

 ex  1  C log   ex  2   

(C)

 ex  1  1 C log   ex  2  2  

(D)

 ex  2  C log   ex  1   

VMC/Integral Calculus-1

80

HWT/Mathematics

Vidyamandir Classes 8.

  x  5

1

10.

 e

dx is :

tan 1 x  4  C

(A)

9.

x4

x

(B)

2 tan 1 x  4  C (C)

 tan 1 x  4  C (D)

2 tan 1 x  4  C

sec x  e x . log  sec x  tan x   dx is : 

(A)

e x log  sec x  tan x   C

(B)

e x log  sec x  tan x   C

(C)

e x sec x  C

(D)

e x log  sec x  tan x   C

sin 1 x  cos 1 x

 sin1 (A) (C)

dx is : x  cos 1 x 2  2 x  1 sin 1 x  x 1  x   x  C   2  2 x  1 sin1 x  x 1  x   x  C  

VMC/Integral Calculus-1

(B) (D)

81

2  2 

 2 x  1 sin 1 x  x 1  x   x  C  

 2 x  1 sin 1 x  x 1  x   x  C  

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [2]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than One correct option. 1.

2.

3.

If



2x 1  4x

 

dx  k sin 1 2 x  C , then k equals :

(A)

log 2

(B)

(C)

1/3

(D)

If

x

dx 1 x

3

 k log

1  x3  1 1 x 1 3

(A)

log 2

(B)

(C)

1/3

(D)

6.

1/2 1 log 2

 C , then k equals : 1/2 1 log 2

*7.



dx  k  x  log sin x  cos x   C , then k 1  tan x equals:

If

(A)

log 2

(B)

(C)

1/3

(D)

1/2 1 log 2

8.

2 x  3 dx  k log  x  1   k  tan1  x     x 1  2    x2  1 x2  4     

  x  2

dx

then k equals :

5.

9.

(A)

log 2

(B)

(C)

1/3

(D)

 1 1 If log ex e .log 2 e dx  log  2 e x x  f 1  x  equals : lim x x0 (A) 0 (B) (C) e (D)



VMC/Integral Calculus-1

1/2 1 log 2

(B)

 x  3 1 log  C  x  3  1   

(C)

log

(D)

 x  3 1  log  C  x  3  1   

If



x dx 1 x

1 1/e

82

3







x  3 1  C

2 fog  x   c then : 3

(A)

f  x  x

(B)

g  x   cos 1 x

(C)

f  x   sin 1 x

(D)

g  x  x x

2

x x

e dx 

 2e  x

(A)

 2e  x  c

(B)

1  log 2 

(C)

 2e  x  1  c

(D)

None of these

x 1

 2 x2  x  1 dx  3 f 1

(C) 10.



x  3 1  C

log

(A)

f  x    C then f  x  



(A)

2

4.

is :

x3

1

tan 1 x sin

The value of

1

x

e

x

c

2x  1  c , then f (x) = 2  x  1

(B)

log x

(D)

None of these

sin e x dx is :

(A)

cos e x

(B)

 cos e x

(C)

(cos e x ) 1

(D)

sin e x

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [3]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If

e

x

 tan x  log cos x  dx  f  x  log sec x  c ,

range of f (x) is : (A) R (C) 2.

R

R  0

(D)

None

 5    2n  4 , 2n  4  (D)  

x

3 x2

e

2

x e  1 x2 2 e x 1 2



(C)



  1 



x  1 dx 1 .  cos 1    x  1 x2 x

(A) (C) 5.

 cos

x 1 x2 1 x

(B) (D)

ex  1

7.

x2

  1 

2

9.

x 1 x2

(B)

 x sin x  cos x   c  

(C)

2  x sin x  cos x   c  

None

None of

these

VMC/Integral Calculus-1

If



e (C)

10.

(D)

 x  1

14

4

(B)

C

14

 1   1   x4  

C



(A)

x dx  2  x sin x  cos x   c  

C

 1  (D) 1  4   C x   x  sin x dx is equal to : 1  cos x x (A) (B) x tan  C 2 (C) log 1  cos x   C (D) 2x 1  4x

x C 2 log  x  sin x   C cot

 

dx  K sin 1 2 x  C , then K is equal to

log 2

63

tan 1 x

1 log 2 2 1 log 2

(B)

1 2

(C)

2

(A)

dx is equal to :

 1  1  4  x  

(A)

2

x2

34

4

:

f  x   c , then f (x) =

(D)

 x  1

14

None of these

1 2 x e 2 

(B)

2

(C)

8.

2

1

14

dx is equal to : x2

x (A)

sin x  cos x sin x e cos x dx  e sin x  c , if x belongs 1  sin 2 x to : 3   (A) R (B)  2n  4 , 2n  4   

(A)

4.

(B)

6.



(C)

3.



then

(D)

 1  x  x2  dx is equal to :  2   1 x  1

xetan x  C 1 tan1 x e C x

1 x

C

(B)

x 2 etan

(D)

None of these

 g  x  dx  g  x  , then g  x   f  x   f   x  dx is equal to :  If

(A)

g  x f  x  g  x f  x  C

(B)

g  x f  x  C

(C)

g  x f  x  C

(D)

g  x f 2  x  C

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [4]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If

1 1   sinx  4 sin x  1 dx  A tan x  1  B tan  f  x   C , then : 1

2

2.

3.

(A)

1 2 4 tan x  3 A ,B , f  x  5 5 15 15

(C)

A

12

(B)

log cosec x  sec x  tan x   C

(C)

log sec x  sec x  tan x  C 

(D)

log  sec x  tan x   C

 sin x cos x dx is equal to : tan x

2 tan x  C

5

55

x

If

(B)

2 cot x  C

(C)

tan x C 2

(D)

None of these

(D)

None of these

(D)

None of these

x

. 55 . 5 x dx is equal to : 55

x

 log 53

C x

(B)

55

x

5

 log 5

3

5x

C

55

C

(C)

 log 53

(C)

a

(B)

f  x g  x  f  x g  x

(D)

f  x g  x  f  x g  x



 1  sin x dx  tan  2  a   b , then : 1

a

 ,bR 4

(B)

a

 ,bR 4

5 ,bR 4

  f  x  g   x   f   x  g  x  dx is equal to : f  x

(A)

g  x f  x g  x  f  x g  x

(C) 7.

dx is equal to :

log sec x  sec x  tan x   C

(A) 6.

(D)

(A)

(A)

5.

2 2 4 tan x  1 ,B , f  x  5 5 5

 1  2 tan x tan x  sec x 

(A) 4.

(B)

x 4 tan    1 2 15 x 4 tan  1 2 2 2 A ,B , f  x  5 5 15 15

1 1 A ,B , f  x  5 15

If

4e x  6e x

 9e

x

 4e x





dx  Ax  B log 9e2 x  4  C , then :

(A)

A

3 35 ,B ,C 0 2 36

(B)

A

(C)

A

3 35 ,B ,CR 2 36

(D)

None of these

VMC/Integral Calculus-1

63

35 3 ,B  ,CR 36 2

HWT/Mathematics

Vidyamandir Classes 8.

 x (A)

(C)

x2 2

 3x  3

10.

x 1

dx is equal to :

 x tan 1   3 3 x  1  

1

2 3

9.



   

 x  tan 1    x 1 

The value of the integral

(D)

1  x2

 1 x

4

 x tan 1   3 3 x  1  

2

(B)

None of these

dx is equal to :

(A)

tan 1 x 2  C

(B)

(C)

 x2  2 x  1  log  C  x2  2 x  1  2 2  

(D)

1

 x2  1  tan 1    2x  2  

1

None of these

If l r  x  means log log log . . . . x, the log being repeated r times, then

(A)

l r 1  x   C

VMC/Integral Calculus-1

(B)

   

l r 1  x  r 1

C

(C)

64

  x l  x  l lr  x  C

2

 x  l 3  x  . . . l r  x  (D)

1

dx is equal to :

None of these

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [5]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than One correct option. 1.

2.

x3  1

x

3

x



x  log x  log x 2  1  tan 1 x  C

(C)

x  log x 



x  log x 

(D)

None of these

 xn  1  1 log    xn  n  

(C)

 xn  log    C (D)  xn  1   

None of these

2a x C log a

(C)

2a

x

. log a  C

(D)

None of these

(C)

B

1 3

(D)

B



1 log x 2  1  tan 1 x  C 2

1

n



a

 xn  1 log    C (B)  xn  1  n  

If

x

x

dx is equal to : a x C log a

 5  4 cos x  Atan dx

(A)

*5.





1 log x 2  1  tan 1 x  C 2

(B)

 x  x  1 dx is equal to :

(A)

*4.



(A)

(A)

3.

dx is equal to :

(B) 1 

x  B tan 2   C , then :  

A=1

The value of the integral

(B)



A

log  x  1  log x x  x  1

2 3

2 3

dx is :

2 1 1 2 log  x  1    log x   log  x  1 log x  C 2 2

(A)



(B)

  log  x  1 

(C)





2   log x 2   log  x  1 . log x  C 2

6.

If



1  1  log 1     C 2   x 

x tan 1 x 1 x

2

(D)

None of these

dx  1  x 2 f  x   Alog  x  x 2  1   C then :  

(A)

f  x   tan 1 x, A  1

(B)

f  x   tan 1 x, A  1

(C)

f  x   2 tan 1 x, A  1

(D)

f  x   2 tan 1 x, A  1

VMC/Integral Calculus-1

65

HWT/Mathematics

Vidyamandir Classes 7.

If



f  x 

(A)

*8.

If



xe x 1 e

*10.

1 2 x 2

(B)

The value of

(B)

cos3 x  cos 5 x

 sin

2

x  sin 4 x

sin x  6 tan 1  sin x   C

(C)

sin x  2  sin x 

  x  1 x

(A)

 Ax  C , then :

g  x   log x

(C)

A=1

(D)

None of these

1

2

A

2

4



1 3

VMC/Integral Calculus-1

1

g  x 

1  ex  1

(C)

1  ex  1

g  x 

1  ex  1 1  ex  1

(D)

f  x   2  x  2

dx is :

(A)

If

2

dx  f  x  1  e x  2 log g  x   C , then :

x

f  x  x  1

(A)

9.

1

 x log 1  x  dx  f  x  .log  x  1  g  x  . x

 6 tan 1  sin x   C

dx  Atan 1 x  B tan 1

(B)

B

2 3

(B)

sin x  2  sin x 

1

C

(D)

sin x  2  sin x 

1

 5 tan 1  sin x   C

x  C , then : 2

(C)

66

A

1 3

(D)

B

1 6

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [6]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The value of



  sec

(C)



e sec x . sec3 x sin 2 x  cos x  sin x  sin x cos x dx is: 2

x



6.

x  sec x tan x  C

(A)

e sec x

(B)

e sec x  C

(C)

e sec x  sec x  tan x   C

(D)

None of these 7.

sin x  cos x 8

2.

 1  2 sin (C)

4.

8

2

x cos 2 x

The value of



dx  (B) (D)

 sin 2 x



x c x  ax  b 2 2

2

(A)

b   ax  x  1 sin    k (B)  c     

(C)

b   ax  x  1 cos    k (D)  c     

If

 9e

x

 4e x





2

8.

5.

 x  x  1 1

3

(A)

2x

9.

log

x3 x 1 3

C

dx  Alog x  1  C for x  1 , then

1 2

(B) (D)

The anti-derivative of f  x   e x

3e x

(B) (D)

1 x3  1 log  C (B) 3 x3

2e

2

x 2

2

whose graph passes

1

2

1

(B)

4e x

(D)

None of these

If f (x) is the anti-derivative of tan 1 x such that the



(A)

x tan 1 x  x  tan 1 x  2

(B)

x tan 1 x  x  tan 1 x  2

(C) (D)

x tan 1 x  2 None of these

e x dx



1  e2 x



35 36 35  36

   2e   C

   2e   C

(A)

sin 1 e x  C

(B)

cos 1 e x  C

(C)

sin 1

(D)

cos 1

(B)

ex C x2

 4  C , then A

1  x 

 2  x (A) (C)

dx  __________.

VMC/Integral Calculus-1

(D)

f (x) = ___________.

dx is :

 2 b   ax  2  1  x k sin c        2 b   ax  2  1  x k cos c      

dx  Ax  B log 9e

3  2 3 2

C

curve y  f  x  passes through the point (0, 2), then

10.

(C)

x  2x  1 A = _________. (A) 1 (C) 2

(C)

= (A)

1 2

(A) 1  sin 2 x 2

ax 2  b

4e x  6e x



3

through the point (0, 3) is _________.

1 sin 2 x 2 1  sin x 2

(A)

3.

x3  1

log

2

x

x

e x dx 

ex C x 1 ex

 x  12

C

(D)

ex

 x  2 2

C

1 x3 log 3 C 3 x 1

67

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [7]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

e

x

(A)

(C)

2.

3.

If



 x  2

3

dx  _____________.

ex C  x  2

e

x

 x  2 3

ex

(B)

C

6.

 x  2

(D)

2

(C)

None of these

(B)

A = 7, B = 6

(C)

A = 6, B = 14

(D)

A = 14, B = 6

e

8.

1

 e  1 dx is : log  e  e   C (B) log  e  e   C log  e  e   C (D)

The value of

5.

(A)

2e

(C)

ex

2

(A)

x

x

(C)

x

2

The anti-derivative of

9.

None of these 2

2

(B)

1

(D)

4

1 cos 2 x 1  tan x

, then its anti-derivative F(x)

x 2

(B)

2e

(D)

1 x e 2



2

If f  x  



2 1  tan x 3 2 3

(B)



1  tan x  1

(D)

1

None of these and its anti-derivative

4  3 cos 2 x  5 sin 2 x



1

2

1  tan x  4



1 F  x   tan 1 g  x   C then g (x) = 3

whose graph passes

5 2

10.

f  x   tan 1 x whose graph

(A)

3tan x

(B)

(C)

2tan x

(D)

If

f  x 

tan x sin x .cos x

2 tan x

None of these

and F(x) is its anti-derivative

  satisfying F    6 , then F(x) = 4

passes through the point (0, 2) is : (A)

x tan 1 x  x  2

(A)

(B)

tan 1 x  x  2

(C)

(C)

 x  1 tan1

(D)

None of these

VMC/Integral Calculus-1

1 2

If f  x  

x

through the point (0, 3) is : x 2

 

 Atan 1 e2 x  C , then A =

Let f  x   1  3x log 3 and F  x  be its anti-derivative

x

The anti-derivative of f  x   e x

 e2 x

satisfying F(0) = 4 is :

2x

x

dx 2x

which assumes the value 7 for x = 2. The value of x for which the curve F(x) cuts the x-axis is : (A) 0 (B) 1 (C) 2 (D) 3

x A dx  log , then : xB x 2  13 x  42

A = 6, B = 7

(C)

7.

1

2x

e (A)

C

(A)

(A)

4.

x

 2 2

 tan x  2  tan x  1



tan x  3



(B)

2

(D)

None of these

x  x 2

63

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [8]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

dx is :  5x2  4 1 1 1 x tan x  tan 1    C 3 2 2

(A)

(C)

5.

6.

(C)

f  x 

(D)









2  1  x2 3 

32

sin 2 x

 cos

7.

x (A) (B)

 3





1 log x 4  1  C (D) 4



2x  2x  1 2

x2 2 x4  2 x2  1 x3

VMC/Integral Calculus-1

C

Q  3  x  1

(D)

dx is a :

x

Polynomial of degree 5 in sin x Polynomial of degree 4 in tan x Polynomial of degree 5 in tan x Polynomial of degree 5 in cos x

e100 2

(A) (C)

  8 

8.

 x4  1 log  4 C  x 1 4  

9.

None of these

is equal to :

2 x4  2 x2  1

satisfy

derivatives at x  100 is :

If

10.

(B) (D)

x  sin x

x

(A)

f  x   x2

(B)

(C)

f  x   1  cos x

(D)

If

 tan

4

63

f  x  x

None of these

xdx  k tan3 x   tan x  f  x  , then : 2 3

(A)

k

(C)

f  x  x  C

(B)

  2

(D)

k

e3 x  e x

If the anti-derivative of then f  x  is equal to :

C

100 None of these

 1  cos x dx  f  x  . tan  2   C , then :

x 2  1 dx 4

Q

f  x   e x differ by 2, the difference of these anti-

4

(C)

and

C

If it is known that at the point x = 1 two anti-derivatives of

dx

 x4  1  1 log  4   C (B)  x  4  

6

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

 x  x  1 is equal to: (A)

4.



32  1 1  x2  7  3  3  1  f  x  sin x  6  2 3 2  1  f  x  1  x2  8 3  

(B)

3.



P

P  3  x  1

(C)

whose derivative is x 1  x 2 is given by :

f  x 

polynomials

2 x2

(ignore the constant of integration) then : (A) (B) Q  2 x P  3x  2

 7 The function f whose graph passes through  0,  and  3

(A)

If

2 x4  2 x2  1

 3x  1 cos x  1  2 x  sin x dx  P cos x  Q sin x

1 1 1 x tan x  tan 1    C 3 6 2

(D)

2 x4  2 x2  1  C (D) x

(C)

4

x  x 3 tan 1    2 tan 1    C 3 2 1 1 1 x   tan x  tan 1    C 3 6 2

(B)

2.

x

The value of

e

4x

 e2 x  1

4 3





is f e x  e  x  C

(A)

sin x

(B)

cos 1 x

(C)

tan 1 x

(D)

tan x

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [9]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If

3 cos x  2 sin x

 4 sin x  5 cos x dx  Ax  B log 4 sin x  5 cos x  C ,

x4  x2  1 C x

(A)

then :

23 ,B 41 11 A ,B 23 A

(A) (C)

2.

If



1 xx

2 3

7.

(D)

f  x 

is A 1  x  C then

 cos

9.

e

4

x  sin 4 x



f  x  x

(C)

f  x   sin x

2

x

x4  1 4



 x2  1

2

12

(C) 10.



(B)

f  x   cos x

(D)

f  x   tan 2 x

If



(A) (B) (C)

dx is equal to :

VMC/Integral Calculus-1



(D)

63

2

x tan 1   2 1





C

x4  x2  1 C x

 C (D)

 x   k , then g  x   1

(B)

x2  1

(D)

2 x2  1



x dx

2

tan 1 x

(A)

dx  tan 1 f  x   C , then :

(A)

x

If

1 4

32

x4  x2  1

None of these



 x2  k log x 2  4 x  8  tan 1  C ,  2   4x  8 then the value of k is : 1 (A) (B) 1 2 (C) 2 (D) None of these

x

8.

1 for all x   0,   x

sin 2 x



x2  1

(C)

Domain of f  x    0 ,  

g   x    cos ec 2 x





 x  12 dx  tan1 x  g

None of these

(B) (D)

(C)

If

(A)

Range of g  x   0,  

(B)

If

32



x x4  x2  1

(C)

 cos ec 2 x dx  f  g  x    C , then :

(A)

6.

(D)

2cos x

A= (A) (C)

5.

2 41 2 23

sin x x

(B)

If the anti-derivative of

If

(D)

sin x

(C)

4.

23 ,B 41 12 A ,B 23 A

(B)

f  x dx  2 cos x  C , then f  x  

(A)

3.

1 41 2 23

x2

(B)

 1  x  x2   1  x2 

etan

1 x

1  x2

x . etan dx 2  3x  x 2

  dx is equal to :  

C

1 x

C

xetan

(B) (D)

1 x

1  x2

C

None of these

 fog  x   C , then :

2x  3 17 2x  3 1 f  x   tan x, g  x   17 2x  3 1 f  x   sin x, g  x   17 None of these f  x   sin 1 x, g  x  

HWT/Mathematics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : IC-1 [10]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

cos 4 x  1

 cot x  tan x dx is equal to : 1 (A) (B) cos  4 x   C 2 1 (C) (D) sin  2 x   C 2 dx The value of is : 5  4 cos x 1 1  1  (A) tan  tan x   C 3 3 

1 cos  4 x   C 4 None of these



7.

(C)

2 1  tan 1  tan x   C 3 3  

(D)

2 1  1  x  tan  tan     C 3 3  2  

The value of



 x log 1

cos x dx is : sin x  cos x

8.

ex

(B)

log e  log e ex  1  C

(C)

log e  log e x  1  C

(D)

log e 1  log e x   C

The value of sec x



(C) (D) 4.

If



(A) (C) 5.

If f  x   then



2 k 3 2 k 3

x2 1  x2

(B) (D)

10.

 fog  x  cos x dx is :

(C) (D)

None of these

(B)

9.

2  3 1  6

and g  x   sin x ,

 sin x   C cos x  tan  cos x   C sin x  2 tan 1  sin x   C

(A)

sin x  tan

(A)

e sec x  sec x  tan x   C

(B)

e sec x sec 2 x  sec x . tan x  C

(C)

e sec x

(D)

None of these

  sec

2





x  tan x  C

Let f and g be two polynomials then

(C)

f  x g x  f  x g  x

(D)

f  x . g  x  f  x g  x



Let f  x   e x  x  1 x  2  dx . Then f decreases in the interval : (A)

  ,  2 

(B)

(C)

(1, 2)

(D)

If

1

(C)

63

sin 2 x

 1  sin

(A)

1

VMC/Integral Calculus-1



is equal to (ignoring the constant of integration) : f  x (A) (B) f  x  . g  x   f  x  g x  g x



None of these dx x  k tan 1 x   tan 1    C , then : 2 2 2 x 1 x  4





. sec3 x sin 2 x  cos x  sin x  sin x . cos x dx is :

  f  x  . g   x   f   x  . g  x  dx

x  log sin x  cos x  C 2 1 x  log sin x  cos x  C 2 2log sin x  cos x  x  C

(B)

is equal to :

log e 1  log e x   C

2

(A)

 e  dx

(A)

e

1 1  1  x  tan  tan     C 3 3  2  

(B)

3.

6.

2

x

 2,  1  2,  

dx  x  k tan 1  M tan x   C , then :

1 2 1 M 2 M

(B) (D)

1 2 1 K 2 K

HWT/Mathematics