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. |
`int_(0)^(pi//4) (dx)/(1+x^(2))` |
| Answer» Correct Answer - C | |
| 152. |
If `int_(0)^(a) 4x^(3) dx =16, and agt 0 , " then " a=` |
| Answer» Correct Answer - C | |
| 153. |
Evaluate the following : `int_(0)^(pi//2)(root3(secx))/(root3(secx)+root3("cosec x"))dx`A. `pi/2`B. `(3pi)/2`C. `pi/4`D. `(3pi)/4` |
| Answer» Correct Answer - C | |
| 154. |
Evaluate the following : `int_(0)^(pi)(x tan x)/(secx+cos x)dx`A. `pi^(2)/2`B. `pi^(2)/4`C. `pi/2`D. `pi/4` |
| Answer» Correct Answer - B | |
| 155. |
Evaluate: `int_(-pi//2)^(pi//2)(cosx)/(1+e^x)dx` |
| Answer» Correct Answer - C | |
| 156. |
Evaluate:`int_0^1xsqrt((1-x^2)/(1+x^2))dx`A. `pi/4 +1/2`B. `pi/4-1/2`C. `pi/2 + 1/2`D. `pi/2-1/2` |
| Answer» Correct Answer - B | |
| 157. |
`int_(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx = ` |
| Answer» Correct Answer - C | |
| 158. |
if `int_0^k (dx)/(2+8x^2)=pi/16` then find the value of `k`A. `1/2`B. `(-1)/2`C. `pi/2`D. `(-pi)/2` |
| Answer» Correct Answer - A | |
| 159. |
Evaluate the following : `int_(-2)^(1)(dx)/(x^(2)+4x+13)`A. `pi/4`B. `pi/3`C. `pi/6`D. `pi/12` |
| Answer» Correct Answer - D | |
| 160. |
The value of `int _(0)^(pi//2) log ("cosec "x) dx` isA. `pi/2 log 2`B. `(-pi)/2log2`C. `pi/4log2`D. `(-pi)/4 log 2` |
| Answer» Correct Answer - A | |
| 161. |
Evaluate the following : `int_(0)^(1)tan^(-1)((2x)/(1-x^(2)))dx`A. `pi/2 - log 2`B. `pi/4- log 2`C. `pi/2 - log sqrt(2)`D. `pi/4-log sqrt(2)` |
| Answer» Correct Answer - A | |
| 162. |
`int_(1)^(2)(dx)/(x(1+logx)^(2))`A. `(2(1+log 2))/(log2)`B. `(2log2)/(1+log2)`C. `(1+log2)/log2`D. `(log2)/(1+log2)` |
| Answer» Correct Answer - D | |
| 163. |
If`int_0^asqrt(x)dx=2aint_0^(pi//2)sin^3xdx`findthe value of integral `int_a^(a+1)xdxdot`A. `(-1)/2, (-9)/2`B. `(1)/2, (9)/2`C. `(-1)/2, (9)/2`D. `(1)/2, (-9)/2` |
| Answer» Correct Answer - B | |
| 164. |
Evaluate the following definite integral: `int_0^1 1/(2x^2+x+1)dx`A. `1/sqrt(7) tan ^(-1) (sqrt(7)/6)`B. `1/sqrt(7) tan ^(-1) (sqrt(7)/3)`C. `2/sqrt(7) tan ^(-1) (sqrt(7)/6)`D. `2/sqrt(7) tan ^(-1) (sqrt(7)/3)` |
| Answer» Correct Answer - D | |
| 165. |
`int_(0)^(1)tan ^(-1) (x/sqrt(1-x^(2)))dx=`A. `pi/2-1`B. `1-pi/2`C. `pi/2-2`D. `2-pi/2` |
| Answer» Correct Answer - A | |
| 166. |
Evaluate :`int_0^1x(1-x)^5dx`A. `1/42`B. `13/42`C. `1/6`D. `1/7` |
| Answer» Correct Answer - A | |
| 167. |
The value of the integral `int_0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx`A. `4 - pi`B. `4+pi`C. `2-pi`D. `2+pi` |
| Answer» Correct Answer - A | |
| 168. |
The greater of `int_(0)^(pi//2)(sinx)/x dx and pi/2 ` isA. `pi/2`B. `int_(0)^(pi//2)(sinx)/x dx`C. nothing can be saidD. both are equal |
| Answer» Correct Answer - A | |
| 169. |
Evaluate: `int_0^1(x t a n^(-1)x)/((1+x^2)^(3//2))dx`A. `(4-pi)/(2sqrt(2))`B. `(4+pi)/(2sqrt(2))`C. `(4-pi)/(4sqrt(2))`D. `(4+pi)/(4sqrt(2))` |
| Answer» Correct Answer - C | |
| 170. |
Evaluate : `(i) int_(0)^(pi//2)(cosx)/((cos.(x)/(2)+sin.(x)/(2)))dx` `(ii) int_(0)^(pi//2)(cosx)/((1+cosx+sinx))dx`A. `pi/2+log sqrt(2)`B. `pi/2-log sqrt(2)`C. `pi/4+log sqrt(2)`D. `pi/4-log sqrt(2)` |
| Answer» Correct Answer - D | |
| 171. |
`int_(0)^(pi//2) (sin x) / ((sinx + cosx)^(2) ) dx =`A. `pi/2`B. `pi/4`C. `1/2`D. `1/4` |
| Answer» Correct Answer - C | |
| 172. |
If `f(a+b-x)=f(x)`, then `int_(a)^(b)x f(x)dx=`A. `(a+b)/2 int_(a)^(b) f (b-x) dx`B. `(a+b)/2 int_(a)^(b) f(x) dx`C. `(b-a)/2 int_(a)^(b) f(x) dx`D. `(b-a)/2 int_(a)^(b) f(b-x) dx` |
| Answer» Correct Answer - B | |
| 173. |
`int_(0)^(a) (f(a+x) + f(a-x) ) dx =`A. `2int_(0)^(2a) f(x) dx`B. `int_(0) ^(2a) f(x) dx`C. `2int_(0) ^(a) f(x) dx`D. `int_(0) ^(a) f(x) dx` |
| Answer» Correct Answer - B | |
| 174. |
`int_(0)^(pi)(x sinx)/((1+sinx))dx=pi((pi)/(2)-1)`A. `pi^(2)/4 + pi`B. `pi^(2)/4 - pi`C. `pi^(2)/2+ pi`D. `pi^(2)/2- pi` |
| Answer» Correct Answer - D | |
| 175. |
Evaluate the following : `int_(pi//2)^(pi)e^(x)((1-sinx)/(1-cosx))dx.`A. `-e^(pi)`B. `e^(pi)`C. `-e^(pi/2)`D. `e^(pi/2)` |
| Answer» Correct Answer - D | |
| 176. |
If `int_(0)^(pi) x f (cos^(2) x + tan ^(4) x ) dx` `= k int_(0)^(pi//2) f(cos^(2) x + tan ^(4) x ) dx` then k =A. `pi/2`B. `pi/4`C. `pi`D. 1 |
| Answer» Correct Answer - C | |
| 177. |
`int_(0)^(pi//2) sin 2x tan^(-1) (sinx)dx = `A. `pi/2-1`B. `1-pi/2`C. `pi/4-1`D. `1-pi/4` |
| Answer» Correct Answer - A | |
| 178. |
`int_(1)^(2) e^(x)(1/x-1/x^(2))dx= `A. `e^(2) /2 +e`B. `e^(2) /2 -e`C. `e-e^(2) /2 `D. `-e-e^(2) /2 ` |
| Answer» Correct Answer - B | |
| 179. |
`int_(0)^(pi//4)e^(x)(1+tan x + tan^(2)x)dx=`A. `-e^(pi/4)`B. `e^(pi/4)`C. `-4e^(pi/4)`D. `4e^(pi/4)` |
| Answer» Correct Answer - B | |
| 180. |
Evaluate the following definite integral: `int_1^2e^(2x)(1/x-1/(2x^2))dx`A. `e^(2)/2(e^(2)/2-1)`B. `e^(2)/2(1-e^(2)/2)`C. `e^(2)/4(e^(2)/2-1)`D. `e^(2)/4(1-e^(2)/2)` |
| Answer» Correct Answer - A | |
| 181. |
Evaluate: `int_1^2(logx)/(x^2)dx`A. `1/2 log (2/e)`B. `1/2log (e/2)`C. `2log (2/e)`D. `2log (e/2)` |
| Answer» Correct Answer - B | |
| 182. |
`int_0^1log(1+x)/(1+x^2)dx`A. `pi/2 log 2`B. `pi/4 log 2`C. `pi/8 log2`D. `pi/16 log 2` |
| Answer» Correct Answer - C | |
| 183. |
`int_0^pixlogsinx dx`A. `(-pi^(2))/2log2`B. `pi^(2)/2log2`C. `(-pi)/2log 2`D. `pi/2log 2` |
| Answer» Correct Answer - A | |
| 184. |
`int_0^pix/(a^2cos^2x+b^2sin^2x)dx`A. `pi/(2ab)`B. `pi/(4ab)`C. `pi^(2)/(2ab)`D. `pi^(2)/(4ab)` |
| Answer» Correct Answer - C | |
| 185. |
If `f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty` for `olt x lt pi/4 , "than" int_(0)^(pi//4) f (x) dx=`A. `1/2`B. `1/4`C. 0D. 1 |
| Answer» Correct Answer - B | |
| 186. |
Evaluate the following : `int_(0)^(pi)x sin^(3)x dx`A. `(4pi)/3`B. `(2pi)/3`C. `4pi`D. `2pi` |
| Answer» Correct Answer - B | |
| 187. |
Evaluate the following : `int_(0)^(a)x^(2)(a-x)^((3)/(2))dx.`A. `8 /315 a^(9/2)`B. `16/315a^(9/2)`C. `8/315 a^(5/2)`D. `16/315a^(5/2)` |
| Answer» Correct Answer - B | |
| 188. |
`int_(0)^(3) abs(x-2) dx=`A. `3/2`B. `3/4`C. `5/2`D. `5/4` |
| Answer» Correct Answer - C | |
| 189. |
`f(x) = {(1-2x", for " x le0),(1+2x", for "xgt0):}` then `int_(-1) ^(1) f(x) dx=`A. 4B. `-4`C. 2D. `-2` |
| Answer» Correct Answer - A | |
| 190. |
`int_- 1^1|x|dx=?`A. 1B. `-1`C. 2D. 0 |
| Answer» Correct Answer - A | |
| 191. |
If `int_(-1) ^(4) f(x) dx=4and int_(2)^(4) (3-f(x))dx=7,` then `int_(-1) ^(2) f(x) dx=`A. `-2`B. 3C. 4D. 5 |
| Answer» Correct Answer - D | |
| 192. |
`int_(-9) ^(9) (x^(3))/(4-x^(2)) dx =` |
| Answer» Correct Answer - A | |
| 193. |
`int_(-1)^(1) (sqrt(1+x+x^(2))-sqrt(1-x+x^(2))) dx =` |
| Answer» Correct Answer - A | |
| 194. |
`int_0^9(dx)/(1+sqrt(x))`A. `6-4log 2`B. `3-4log 2`C. `6-2log 2`D. `3-2lo2` |
| Answer» Correct Answer - A | |
| 195. |
`int_(0)^(1)(dx)/([ax+(1-x)b]^(2))=`A. `a/b`B. `b/a`C. `ab`D. `1/(ab)` |
| Answer» Correct Answer - D | |
| 196. |
The value of `int_(-3)^(3)(ax^()+bx^(3)+cx+k)dx`, where a,b,c,k are constants, depends only on. . . .A. `a and k `B. `a and b`C. `a, b and c`D. `k` |
| Answer» Correct Answer - D | |
| 197. |
`int_(-pi//2) ^(pi//2)sin^(3) xdx=`A. `pi/4`B. `pi/2`C. 0D. `pi` |
| Answer» Correct Answer - C | |
| 198. |
`int_(a)^(b)f(x)dx` is equal to-A. `underset(hrarro)limunderset(r=0)overset(n-1)Sigmaf(rh)`, where nh = b - aB. `underset(hrarro)limunderset(r=0)overset(n-1)Sigmaf(a+rh)`, where nh = b - aC. `underset(hrarro)limhunderset(r=0)overset(n-1)Sigmaf(a+rh)`, where nh = b - aD. none of these |
| Answer» Correct Answer - C | |
| 199. |
To evaluate `int_(0)^((pi)/(2))sin^(6)xcos^(3)xdx` we put-A. sin x = zB. cos x = zC. tan x = zD. none of these |
| Answer» Correct Answer - A | |
| 200. |
If `n(ne0)` is an integer, then the value of `int_(0)^(pi)sin^(2)nxdx` is-A. `pi`B. `(pi)/(2)`C. 0D. `(1)/(2)` |
| Answer» Correct Answer - B | |