InterviewSolution
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InterviewSolution
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.
| 151. |
If `f(x)+f(2-x)=0`, then `int_(0)^(2)(1)/(1+2^(f(x)))dx=`A. 2B. 1C. f (2)D. `(1)/(2)f(2)` |
| Answer» Correct Answer - B | |
| 152. |
`int_(-1)^(1)(x^(2)+sin x)/(1+x^(2))dx=` |
| Answer» Correct Answer - D | |
| 153. |
`int_(0)^(pi//4)e^(x)sin x dx =`A. `(e^(pi//4))/(sqrt(2))`B. `(1)/(2)`C. `sqrt(2)e^(pi//4)`D. `e^(pi//4)` |
| Answer» Correct Answer - B | |
| 154. |
`int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=`A. `(a)/(2)`B. 2aC. aD. 3a |
| Answer» Correct Answer - A | |
| 155. |
If `int_(-1)^(4)f(x)dx=4` and `int_(2)^(4)[3-f(x)]dx=7`, then `int_(2)^(-1)f(x)dx=`A. 2B. `-3`C. `-5`D. 1 |
| Answer» Correct Answer - C | |
| 156. |
If `int_(0)^(1)f(x)dx=1` and `int_(1)^(2)f(y)dy=2`, then `int_(0)^(2)f(z)dz=`A. 1B. `-1`C. `-3`D. 3 |
| Answer» Correct Answer - D | |
| 157. |
If `int_(0)^(3)f(x)dx=1` and `int_(0)^(4)f(y)dy=2`, then `int_(3)^(4)f(z)dz=`A. 7B. `-1`C. 1D. 3 |
| Answer» Correct Answer - C | |
| 158. |
`int_(0)^(1)(1)/(x^(2)+4x+5)dx =`A. `tan^(-1)((1)/(7))`B. `log((1)/(7))`C. `sin^(-1)((1)/(7))`D. log 7 |
| Answer» Correct Answer - A | |
| 159. |
`int_(1)^(3)(1)/(x+x^(2))dx=`A. `log.(2)/(3)`B. `(log 2)/(log 3)`C. `log.(3)/(2)`D. `log_(2)3` |
| Answer» Correct Answer - C | |
| 160. |
`int_(-1)^(1)(x^(2)-1)/(x^(2)+1)dx=`A. `2-pi`B. `pi-2`C. `pi+2`D. `4-pi` |
| Answer» Correct Answer - A | |
| 161. |
`int_(0)^(1)(2-x^(2))/(1+x^(2))dx=`A. `(pi)/(4)-1`B. `(pi)/(2)-1`C. `1-(pi)/(2)`D. `(3pi)/(4)-1` |
| Answer» Correct Answer - D | |
| 162. |
Evaluate the following : `int_(0)^(1)(1-x^(2))/(1+x^(2))dx`A. `1-(pi)/(2)`B. `2-(pi)/(2)`C. `(pi)/(2)-1`D. `(pi)/(4)-1` |
| Answer» Correct Answer - C | |
| 163. |
`int_(0)^(1)(x)/(x+1)dx=`A. `1+log 2`B. `log 2-1`C. `log((e )/(2))`D. `1-log 2+e` |
| Answer» Correct Answer - C | |
| 164. |
Evaluate the following definite integral: `int_0^1 1/(1+x^2)dx`A. `(pi)/(4)`B. log 2C. `(pi)/(2)`D. `(pi)/(3)` |
| Answer» Correct Answer - A | |
| 165. |
`int_(0)^(pi)(cos x)/(x^(4)+(pi-x)^(4))dx=` |
| Answer» Correct Answer - A | |
| 166. |
Find the value of`int_0^1x(1-x)^ndx`A. `(n(n+1))/(2)`B. `(1)/((n+1)(n+2))`C. `((n+1)(n+2))/(3)`D. `n^(2)(n+1)` |
| Answer» Correct Answer - B | |
| 167. |
If `I_(n)=int_(0)^(pi//4)tan^(n)x dx`, where `n ge 2`, then : `I_(n-2)+I_(n)=`A. `(1)/(n)`B. `(1)/(n-1)`C. `(1)/(n)+(1)/(n-1)`D. `(1)/(n+1)` |
| Answer» Correct Answer - B | |
| 168. |
If `I_(1)=int_(0)^(pi//2)log (sin x)dx` and `I_(2)=int_(0)^(pi//2)log (sin 2x)dx`, thenA. `I_(1)lt I_(2)`B. `I_(1)=I_(2)`C. `I_(1)gt I_(2)`D. sin x = sin 2x |
| Answer» Correct Answer - B | |
| 169. |
`int_(0)^(pi//2)(e^(sin x)- e^(cos x)))dx=`A. 1B. `-1`C. 0D. `pi` |
| Answer» Correct Answer - C | |
| 170. |
If `I_(n)=int_(0)^(pi//4)tan^(n)x dx,` then `7(I_(6)+I_(8))=`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - A | |
| 171. |
`int_(0)^(pi//2)sin x.cos x. sqrt(a^(2).sin^(2)x+b^(2).cos^(2)x)dx=`A. `(a^(2)+ab+b^(2))/(2(a+b))`B. `(a^(2)+ab+b^(2))/(a+b)`C. `(a^(2)+ab+b^(2))/(3(a+b))`D. none of these |
| Answer» Correct Answer - C | |
| 172. |
If `int_(-2)^(lambda)(3x^(2)+2x+4)dx=32` then `lambda=`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 173. |
`int_(-pi//2)^(pi//2)cos^(6)x dx=`A. `(16)/(5)`B. `(5)/(16)`C. `(5pi)/(16)`D. `(16pi)/(5)` |
| Answer» Correct Answer - C | |
| 174. |
`int_(0)^(pi//2)sin^(4)xcos^(5)x dx=`A. `(8)/(315)`B. `(315)/(8)`C. `(256)/(5)`D. `(225)/(8)` |
| Answer» Correct Answer - A | |
| 175. |
`int_(0)^(pi//2) ""(sin x - cos x)/( 1-sin x * cos x) dx ` is equal toA. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. 0 |
| Answer» Correct Answer - D | |
| 176. |
`int_(-pi//2)^(pi//2)(sin^(2n-1)x)/(1+cos^(2n)x)dx=`A. `(pi)/(2)`B. `-(pi)/(2)`C. 0D. `pi` |
| Answer» Correct Answer - C | |
| 177. |
`int_(0)^(pi//2)(1)/(4-3 sin^(2)x)dx=`A. `pi`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(4)` |
| Answer» Correct Answer - D | |
| 178. |
`int_(0)^(pi//2)sin^(4)x cos^(6)x dx=`A. `(512pi)/(3)`B. `(3pi)/(512)`C. `(315pi)/(8)`D. `(3)/(512)` |
| Answer» Correct Answer - B | |
| 179. |
`int_(-pi//2)^(pi//2)sin^(7)x dx=`A. `(7pi)/(16)`B. `(2pi)/(35)`C. `2pi`D. 0 |
| Answer» Correct Answer - D | |
| 180. |
`int_(1)^(e^(99))(sin(pi.ln x))/(x)dx=` |
| Answer» Correct Answer - C | |
| 181. |
`int_(0)^(pi//2)sin^(3)x cos^(4)x dx=`A. `(2)/(35)`B. `(35)/(2)`C. `(35pi)/(2)`D. `(2pi)/(35)` |
| Answer» Correct Answer - A | |
| 182. |
`int_(0)^(pi//2)(cos x)/((3+sin x)(4+sin x))dx=`A. `log((4)/(3))`B. `log((16)/(15))`C. `log((15)/(16))`D. `log((3)/(4))` |
| Answer» Correct Answer - B | |
| 183. |
`lim_(n to oo)[(n)/(1+n^(2))+(n)/(4+n^(2))+(n)/(9+n^(2))+…+(1)/(2n^2)]=`A. `(pi)/(2)`B. `(pi)/(4)`C. 1D. none of these |
| Answer» Correct Answer - B | |
| 184. |
Evaluate : `lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5`A. `(1)/(30)`B. 0C. `(1)/(4)`D. `(1)/(5)` |
| Answer» Correct Answer - D | |
| 185. |
Evaluate` lim_(n->oo) [1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3) +..... 1/(2n) ]`A. `(1)/(3).log 3`B. `(1)/(3).log 2`C. `(1)/(3).log.(1)/(3)`D. none of these |
| Answer» Correct Answer - B | |
| 186. |
Evaluate the following : `int_(0)^(pi//4)(sin 2x)/(sin^(4)x+cos^(4)x)dx.`A. `pi`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(4)` |
| Answer» Correct Answer - D | |
| 187. |
Evaluate : `(i) int_(0)^(pi//2)cos^(3)xdx` `(ii) int_(0)^(pi//2)sin^(4)xdx`A. `(2)/(3)`B. `(3)/(4)`C. `(4)/(5)`D. `(5)/(6)` |
| Answer» Correct Answer - A | |
| 188. |
`If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx.` thenA. `(pi)/(4)-J`B. 2JC. JD. `(1)/(2).J` |
| Answer» Correct Answer - A | |
| 189. |
`int_(0)^(pi//4)(cos^(2)x-cos^(4)x)dx`A. `(pi)/(8)`B. `(pi)/(16)`C. `(pi)/(32)`D. `(pi)/(4)` |
| Answer» Correct Answer - C | |
| 190. |
`int_(0)^(pi//2)(sin x.cos x)/(1+sin^(4)x)dx=`A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(8)` |
| Answer» Correct Answer - D | |
| 191. |
`lim_(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)`A. `(1)/(p+1)`B. `(1)/(1-p)`C. `(1)/(p)-(1)/(1-p)`D. `(1)/(p+2)` |
| Answer» Correct Answer - A | |
| 192. |
integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`A. `2pi`B. `e^(pi)`C. 0D. `2sqrt(2)` |
| Answer» Correct Answer - C | |
| 193. |
Evaluate the following : `int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx`A. `(-pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(8)` |
| Answer» Correct Answer - A | |
| 194. |
`int_(pi//4)^(3pi//4)(dx)/(1+cos x)=`A. 2B. `-2`C. `(1)/(2)`D. `-(1)/(2)` |
| Answer» Correct Answer - A | |
| 195. |
If `int_(0)^(1)(x+4)/(x^(2)+5)dx = a log ((6)/(5))+b tan^(-1)((1)/(sqrt(5)))`, then `(a, b)-=`A. `((1)/(3), (3)/(sqrt(5)))`B. `((1)/(2), (4)/(sqrt(5)))`C. `((1)/(4), (2)/(sqrt(5)))`D. `(2, 4sqrt(5))` |
| Answer» Correct Answer - B | |
| 196. |
Evaluate:`int_0^(pi/2)log((4+3sinx)/(4+3cosx))dx`A. 2B. `3//4`C. 0D. none of these |
| Answer» Correct Answer - C | |
| 197. |
The solution for x of the equation `int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2`is:(1) 2 (2) `pi`(3)`(sqrt(3))/2`(4) `2sqrt(2)`A. `(sqrt(3))/(2)`B. `2sqrt(2)`C. 2D. `-sqrt(2)` |
| Answer» Correct Answer - D | |
| 198. |
`int_(sqrt(2)//3)^(sqrt(3)//3)(1)/(sqrt(4-9x^(2)))dx=`A. `(pi)/(36)`B. `(pi)/(9)`C. `(pi)/(12)`D. `(pi)/(4)` |
| Answer» Correct Answer - A | |
| 199. |
`int_(0)^(pi//2)((pi)/(4)-x)/(sqrt(sin x)+ sqrt(cos x))dx=`A. `(pi sqrt(2))/(4)`B. `(pi)/(4 sqrt(2))`C. 0D. `(pi)/(4)` |
| Answer» Correct Answer - C | |
| 200. |
The value `int_(-2)^(2) (plog ((1+x)/(1-x)) + q log ((1-x)/(1+x))^(-2) + r) dx ` depends on the value ofA. pB. qC. rD. p and q |
| Answer» Correct Answer - C | |