BASARA GNANA SARASWATHI CAMPUS KAKATIYA HILLS

Sec: Star SC Indefinite Integration Date: 28-08-2020

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SINGLE ANSWER TYPE
If  ln  sin x  .sin 2 x.dx  sin x  A ln  sin x  B   C then
sin x
1. 3

A) A > B B) A = B C) A is an integer D) B is an integer


and if   0  0 then the value of    equals
sin x
2. If  sin 3x dx    x  6
1 1 1 1
A) ln 2 B) ln 2 C) ln 2 D) ln 2
3 3 3 3
6  xy
3. If x  0, y  0, xy  xy  1  6 and if the value of  xy  y  1 dx  Ax
2
2
 Bx  C ln x  2  D then

A) A = 2 B) B = -2 C) C = 2 D) A=0
 
2
d
If  x 3 e x dx  e x . f  x  C then the local maximum value of f  x  equals  x  R 
2 2
4. 2
dx
A) 87/8 B) 2 C) 3 D) 0
tan 
5. If f     d is continuous function and f  0  0 then the value of
sin 2
 
2f    f   equals
 4  3

A) 3  1 B) 2  1 C)
1
2
 3 1 D)
1
2
 
2 1

ax 2  2bx  c
6. If   
dx B 2  AC is a rational function of x then which is necessarily true
 Ax 
2
2
 2 Bx  C

A) 2Bb = Ac + aC B) 2Bb =Aa + cC

C) 2Cc = Ab + Ba D) 2aA=bB+cC

7. If  e x x 4
2  dx 
e x f  x
 C then which is correct
1  x  2 5/ 2
1  x 
2 3/ 2

A) f 1  3 B) f  2  6 C) f 1  0  2 D) f  x  0x  R

8. If f ( x) is polynomial function such that f ( x )  f '( x)  f ''( x)  f '''( x)  x3 and

f ( x)
g ( x)   dx and g (1)  1 then g (e) 
x3
A) e  3 B) e  3 C) 1  e D) 1  e
  3x x
 x  x   l o g x  1
 
9.  4x
x 1
dx =, (‘c’ is integration constant)

1  x  1  1  x  1 
2x x
1 1
A) tan  c B) c
 2 x x 
tan 
2 2  2 x x 
   

1  x2 x  1 
C) 2 tan 
 x x 

c D) 2 tan 1 x x  1  c  
MULTIPLE ANSWER TYPE
e x f 11  x   e x f 1  x 
10. Let f be a differentiable function satisfying  1 and f  0  0, f 1  0  1
e2 x
then which is/are correct
xf 1  x  f  x
A)  1 x  0
x 2e x
B) For, x > 0, f(x) is increasing function
C) For x < 0, f(x) is decreasing function
D) Number of solutions of 3f(x) + 1 =0 is 2
3x 2 1
11. Let g  x  x3   x  then which is/are correct
2 4
1
A) The curve y  g  x is symmetric w.r.t x  line
2
1  g  x
B) f  x   dx and f 1  1 then f  2  2
g 1  x 

C) The curve y  g  x is symmetric w.r.t. x = 1 line

1
D) If g  g 1   g  t   1 then t 
2

12. The value of  cot x .e sin x

1  e  dx equals
sin x

 
2
1 e sin x

A) 2e sin x
c B) C
2

e   
2
C) e sin x sin x
2 C D) e sin x
1  C

cos 2 x sin 4 x
13. If  cos x 1  cos 
dx  A sec2 x  B ln 1  cos 2 x + C ln 1  cos 2 2 x  D then which is/are 
4 2
2x 
correct
A) A < B B) A = C C) A > C D) B > 1
14. If 
cos x 2
x
 
x ln x  1 dx  f ( x)  c (‘c,c| ’ is integration constant)

f (1)  cos1 and  f ( x )sec2 x dx  g ( x)  c '

g (1)  0 and L  lt g ( x ) then
x 0
x ln x
A) f ( x )  cos x 1  ln x   x sin x ln x B) g ( x) 
cos x
g ( x)
C) L  0 D) lt 0
x  x2

x2  x 1
15. If e  x  3/2
e x dx  f ( x)  c (‘c’ is constant of integration) and f (0)  1then
2
x 1
which of the following is/are true?
A) f ( x) is an even function
B) f ( x) is a bounded function
C) The range of f ( x) is (0,1]
D) f ( x) has two points of maxima
A2 A3
16. If A is square matix and e A  I  A    .............
2 3

1  f  x g  x x x
And e A    and A   ,
2  g  x f  x  x x 

0  x  1, I is a 2 x 2 identify matix then which of the following statement is/are true?

(‘c’ is integration constant)
g  x
A) 
f  x

dx  log e x  e x  c 
f  x  g  x
B)  dx  2e2 x  c
f  x  g  x

e2 x
C) g x  1 Sinx dx  2Sinx  Cosx  c
5
D) f  x   g  x  is an increasing function x  R
PASSAGE-1
1 1 
  2   x  1
x x
Let  1 dx  sec 1  f  x   c and f 1  2 . Then for x > 0
1
 4  2 
x x
x 4

 x3  x 2 x 4  x 3  x 2 
17. The minimum value of f  x equals
A) 2 B) 4 C) 2 2 D) 2
18. Which is correct

C) f    D) f   
3 13 3 2
A) f     f  e B) f     f  e
 2 6  2 3

PASSAGE-2
x7  x5  x3  x
If f  x   dx  Aln x8  x 6  x 4  x 2  1  Bln x 2  1  C , f  0  0 , then answer
x10  1
the following
19. f  x is

A) Even function B) Odd function

C) Neither even nor odd function D) Both even and odd functions
20. The value of A equals
1 1 4 1
A) B) C) D)
2 5 5 10
21. The value of B equals
1 2 3 4
A) B) C) D)
5 5 5 5
INTEGER ANSWER TYPE
sin 2 x  1  1 
22. If f  x   dx and if f    then the value of sum of digits of   is
 3  4 cos x  2  48  f  0 
3

. is GIF 
1 3   sin x  cos x B
23. If  dx  A.ln  B tan 1  sin x  cos x  C then   equals
sin x  sec x 3   sin x  cos x  A

. is GIF 
tan 4 x A
24. If  1  tan 2 x dx  A tan x  B ln sec 2 x  tan 2 x  C.x  D then the value of BC equals
x2
25. If f  x   dx and f  0  0 then the value of  f 1  equals . is GIF 
 
1  x2 1  1  x2 
26. If the integral I   x  x 2  3x dx on substitution t  x  x 2  3x takes the form



t4 t2  3  dt then the value of  equals
 
2
2t 2  3

cot x  tan x    

27. If  dx    x , x   0,  and     and maximum value of   x is 
2  cos x  sin x   2  4 2

then  5  equals . GIF 

 1  sin 2 x  cos x  cos 2 x  

2

 sin x  cos x 
28. If  ln    ln    dx = A.sin 2 x.ln    B ln  cos 2 x then the
 1  sin 2 x   1  sin 2 x   cos x  sin x
 

value of A + B equals