Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.

The value of `int sinx^@ dx` isA. ` pi/180 cos x^(@) + c`B. ` 180/pi cos x^(@) + c `C. ` - 180 /pi cos x^(@) + c`D. ` - 180/pi cos x^(@) + c`

Answer» Correct Answer - C
Discussion
2.

`int sec^(2) x " cosec"^(2) xdx ` is a function of -A. tan xB. sin xC. cos xD. none of these

Answer» Correct Answer - A
Discussion
3.

If ` (dy)/(dx) = 3x^(2) - 2 ` , then the value of y is -A. `x^(3)- 2x + c `B. ` x^(3)- 2c `C. `3/2 x^(2) - 2x + c`D. `x^(3)- 2x^(2)+c`

Answer» Correct Answer - A
Discussion
4.

The value of `int 2^(3x)dx ` is -A. `(2^(3x))/(3log 2)`B. `(2^(3x))/(3 log 2 ) + c`C. ` (3 xx 2^(3x))/(log 2 )`D. ` 3 log 2 xx 2^(3x) + c`

Answer» Correct Answer - B
Discussion
5.

If `int (cos 4x+1)/(cot x - tan x ) dx ` = A f(x) + B , then -A. `A= -1/8`B. `B=1/2`C. f(x) has fundamental period `pi/2`D. f(x) is an odd function

Answer» Correct Answer - A::C
Discussion
6.

Let `f(x) = cos 7 x cos 3x and g(x) = sin 7 x sin 3x ` ` int g(x) dx = `A. ` 1/8 sin 4x - 1/20 sin 10 x+c`B. ` 1/4 sin 4x - 1/10 sin 10 x + c`C. ` 1/4 sin 4x + 1/20 sin 10 x + c `D. ` 1/4 sin 4x + 1/10 sin 10 x + c`

Answer» Correct Answer - A
Discussion
7.

Let `f(x) = cos 7 x cos 3x and g(x) = sin 7 x sin 3x ` ` int {f(x) + g(x) } dx = `A. `1/8 sin 4x+ c `B. `1/10 sin 10x + c `C. ` 1/4 sin 4x + c`D. `1/20 sin 10 x + c `

Answer» Correct Answer - C
Discussion
8.

If ` m != 0 ` , then the value of ` int sec mx tan mx dx ` is -A. ` "m sec " mx + c `B. ` m tan mx + c `C. ` (sec mx )/m + c `D. `(tan mx )/m + c`

Answer» Correct Answer - C
Discussion
9.

Let `f(x) = cos 7 x cos 3x and g(x) = sin 7 x sin 3x ` ` int f(x) dx = `A. ` 1/4 sin 4x + 1/10 sin 10 x + c `B. ` 1/8 sin 4x + 1/20 sin 10x + c `C. `1/8 sin 4x + 1/20 sin 10 x + c`D. none of these

Answer» Correct Answer - B
Discussion
10.

The value of `int e^(5logx)` dx is -A. ` (e^(5 log x))/5`B. ` (e^(5 log x ))/(5 log x ) +c`C. `(x^(5))/5 + c `D. ` (x^(6))/6 + c `

Answer» Correct Answer - D
Discussion
11.

If `f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n``f(x)`is an odd function`f(x)`has range `R``f(x)`has at least one real root`f(x)`is amonotonic function.A. f(x) is an odd functtionB. f(x) has range RC. f(x) has at least one real rootD. f(x) is monotonic function

Answer» Correct Answer - A::B
Discussion
12.

If `I = int sec^(2) x "cosec"^(4) xdx = A cot^(3) x + B tan x + C cot x + D ` ,A. `A=-1/3`B. B=2C. `C=-2`D. none of these

Answer» Correct Answer - A::C
Discussion
13.

If `intsinx d(secx)=f(x)-g(x)+c ,t h e n``f(x)=secx`(b) `f(x)=tanx``g(x)=2x`(d) `g(x)=x`A. f(x) = sec xB. f(x) = tan xC. g(x) = 2xD. g(x) = x

Answer» Correct Answer - B::D
Discussion
14.

The value of `int ("cosec" 2x cot 2x) ` dx is -A. ` - (cot 2x)/2 + c `B. ` 2 cot 2x + c`C. ` - 2 " cosec " 2x + c `D. ` - ("cosec"2x)/2 +c`

Answer» Correct Answer - D
Discussion
15.

Let `f(x) = tan^(-1) ((1+cos x)/(sinx)) and g (x) = tan^(-1) ((sinx)/(1-cos x))` `int {f(x) - g (x)}dx = `A. `pix+c`B. `(x^(2))/2+c`C. 0D. `pix+x^(2)+c`

Answer» Correct Answer - C
Discussion
16.

If the derivative of a function is `sqrt(x)` , then the function is -A. ` 1/(2sqrt(3))+c `B. ` 2/3 x^(3/2) +c`C. ` 3/2 x^(3/2 )+c`D. ` 2/(3sqrt(x))+c`

Answer» Correct Answer - B
Discussion
17.

` int (x^(2)+1)/(x) ` dx is equal to -A. ` 1/2 x^(2) = log |x| + c `B. ` log x + 1/2 x^(2)+c`C. ` x + log | x | + c `D. `x^(2) + log |x|+c`

Answer» Correct Answer - A
Discussion
18.

Let F(x) be an indefinite integral of `sin^(2) x ` Statement - I : The function F(x) satisfies `F(x+pi) = F(x)` for all real x Statement - II : `sin^(2) (pi+x) = sin^(2) x ` for all real xA. Statement - I is True , Statement - II is True , Statement - II is a correct explanation for Statement -IB. Statement - I is True , Statement - II is True , Statement - II is not a correct explanation fo Statement - IC. Statement - I is True , Statement - II is FalseD. Statement - I is False , Statement - II is True .

Answer» Correct Answer - D
Discussion