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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(1)/(sqrt(x+a)-sqrt(x+b))dx=`A. `(2)/(3(a-b))[(x+a)^(3//2)+(x+b)^(3//2)]+c`B. `(2)/(3(a-b))[(x+a)^(3//2)-(x+b)^(3//2)]+c`C. `(2)/(3(a+b))[(x+a)^(3//2)-(x=b)^(3//2)]+c`D. `(2)/(3(a+b))[(x+a)^(3//2)+(x-b)^(3//2)]+c` |
| Answer» Correct Answer - A | |
| 152. |
`int(2tanx)/(2+3tan^(2)x)dx=`A. `(1)/(3)log(2+3tan^(2)x)`B. `log(2cos^(2)x+3sin^(2)x)+c`C. `tan^(-1)(tan^(2)x)+c`D. `2x+3secx+c` |
| Answer» Correct Answer - A | |
| 153. |
`int(1-tanx)/(1+tanx)dx=`A. `sec^(2)((pi)/(4)-x)+c`B. `log(secx-sinx)+c`C. `log(sinx+cosx)-k`D. `log[sec((pi)/(4)-x)]+c` |
| Answer» Correct Answer - C | |
| 154. |
`int{1 + tan x.tan(x+alpha)}dx= `A. `cot alpha.log|(sinx)/(sin(x+alpha))|+c`B. `tan alpha.log|(sinx)/(sin(x+alpha))|+c`C. `cot alpha.log|(sin(x+alpha))/(sinx)|+c`D. none of these |
| Answer» Correct Answer - C | |
| 155. |
`int(cosx)/(1+cosx)dx=`A. `x+tan((x)/(2))+c`B. `(x)/(2)-tanx+c`C. `x-tan((x)/(2))+c`D. `(x)/(2)+tanx+c` |
| Answer» Correct Answer - C | |
| 156. |
`intsqrt(1-sinx)dx=`A. `2sqrt(1-sinx)+c`B. `2sqrt(1+sinx)+c`C. `2[sin((x)/(2))-cos((x)/(2))]+c`D. `x+cosx+c` |
| Answer» Correct Answer - B | |
| 157. |
`int(a^(4)-x^(4))/(a-x)dx=`A. `x^(4)+ax^(3)+a^(2)x^(2)+a^(3)x+c`B. `(x^(4))/(4)+(ax^(3))/(3)+(a^(2)x^(2))/(2)+a^(3)x+c`C. `(x^(4))/(4)-(ax^(3))/(3)+(a^(2)x^(2))/(2)-a^(3)x+c`D. `(x^(4))/(4)+(ax^(3))/(3)-(a^(2)x^(2))/(2)+a^(3)x+c` |
| Answer» Correct Answer - B | |
| 158. |
`int(d(cosx))/(sqrt(1-cos^(2)x))=`A. `sin^(-1)x+c`B. `cos^(-1)x+c`C. `log(sinx+cosx)+c`D. `-x+c` |
| Answer» Correct Answer - D | |
| 159. |
`int(1+x+x^(2))/(1+x^(2))e^(tan^(-1)x)dx=`A. `xe^(tan^(-1)x)+c`B. `x^(2)e^(tan^(-1)x)+c`C. `x^(-1)e^(tan^(-1)x)+c`D. `(1+x^(2))e^(tan^(-1))+c` |
| Answer» Correct Answer - A | |
| 160. |
`int((x^(3)+1)^(2))/(x^(2))dx=`A. `(x^(5))/(5)-x^(2)+(1)/(x)+c`B. `x^(2)-(x^(5))/(5)logx+c`C. `(x^(5))/(5)+x^(2)+(1)/(x)+c`D. `(x^(5))/(5)+x^(2)-(1)/(x)+c` |
| Answer» Correct Answer - D | |
| 161. |
`int(tan^(-1)x)/(1+x^(2))dx=`A. `log(tan^(-1)x)+c`B. `0.5(tan^(-1)x)^(2)+c`C. `log(1+x^(2))+c`D. `tan^(-1)(logx)+c` |
| Answer» Correct Answer - B | |
| 162. |
`int(xsin^(-1)(x^(2)))/(sqrt(1-x^(4)))dx=`A. `2sin^(-1)(x^(2))+c`B. `0.25sin^(-2)(x^(2))+c`C. `0.25(sin^(-1)x^(2))^(2)+c`D. `2xsin^(-1)(x^(2))+c` |
| Answer» Correct Answer - C | |
| 163. |
`int9^(log_(3)(secx))dx=`A. `secx+tanx+c`B. `cotx+c`C. `tanx+c`D. `-tanx+c` |
| Answer» Correct Answer - C | |
| 164. |
`int(1)/(sqrt(1+cos5x))dx=`A. `(sqrt2)/(5)log(sin5x)+c`B. `(5)/(2)log(secx+tanx)+c`C. `5sqrt2 sec5x+tan5x+c`D. `(sqrt2)/(5)log(sec.(5x)/(2)+tan.(5x)/(2))+c` |
| Answer» Correct Answer - D | |
| 165. |
`int(log(x//e))/((logx)^(2))dx=`A. `(x+1)/((logx)^(2))+c`B. `(x-1)/((logx)^(2))+c`C. `(x)/(logx)+c`D. `(logx)/(x)+c` |
| Answer» Correct Answer - C | |
| 166. |
`int(dx)/(x.logx.log(logx))=`A. `(logx)^(3)+c`B. `3log(logx)+c`C. `log[log(logx)]+c`D. `(x.logx)^(2)+c` |
| Answer» Correct Answer - C | |
| 167. |
`int(6x^(2)tan^(-1)(x^(3)))/(1+x^(6))dx=`A. `(tan^(-1)x^(3))^(2)+c`B. `tan^(-2)(x^(3))+c`C. `log(tan^(-1)x^(3))+c`D. `tan^(-1)(logx)^(3)+c` |
| Answer» Correct Answer - A | |
| 168. |
`int((1-x)^(2))/(x(1+x^(2)))dx=`A. `tan^(-1)x-2logx+c`B. `log x-2tan^(-1)x+c`C. `logx+2 tan^(-1)x+c`D. `2logx-tan^(-1)x+c` |
| Answer» Correct Answer - B | |
| 169. |
`int(tanax-cotbx)/(1+tanaxcotbx)dx=`A. `(-1)/(a+b)log{sin[(a+b)x]}+c`B. `(-1)/(a-b)log{cos[(a-b)x]}+c`C. `(-1)/(a+b)log{[cos(a+b)x]}+c`D. `(1)/(a-b)log[secax-secbx]+c` |
| Answer» Correct Answer - A | |
| 170. |
If `intf(x)sec^(2)xdx=(1)/(2)[f(x)]^(2)+c,` then : `f(x)` can beA. `cos^(5)x`B. `tanx+c`C. `cotx`D. `tanx` |
| Answer» Correct Answer - D | |
| 171. |
`intsqrt(1+cos5x)dx=`A. `(2)/(5)sin((5x)/(2))+c`B. `(sqrt2)/(5)sin((5x)/(2))+c`C. `(2sqrt2)/(5)sin((5x)/(2))+c`D. `(2sqrt2)/(5)cos((5x)/(2))+c` |
| Answer» Correct Answer - C | |
| 172. |
`intsqrt((1-cos2x)/(1+cos 2x))dx=`A. `sec^(2)x+c`B. `log(secx)+c`C. `secx+tanx+c`D. `log(tanx)+c` |
| Answer» Correct Answer - B | |
| 173. |
`intsqrt(1+sin((x)/(2)))dx=`A. `4[sin((x)/(2))+cos((x)/(2))]+c`B. `4[sin((x)/(4))-cos((x)/(4))]+c`C. `sqrt(1-sin((x)/(2)))+c`D. none of these |
| Answer» Correct Answer - B | |
| 174. |
`intsqrt((a-x)/(a+x))dx-int sqrt((a+x)/(a-x))dx=`A. `sqrt(a^(2)-x^(2))+c`B. `-2sqrt(a^(2)-x^(2))+c`C. `-sqrt(a^(2)-x^(2))+c`D. `2sqrt(a^(2)-x^(2))+c` |
| Answer» Correct Answer - D | |
| 175. |
`intsqrt(2+sqrt(2+sqrt(2+2cos8x)))dx=`A. `sqrt2 sinx+c`B. `2sqrt(sinx)+c`C. `2sinx+c`D. `sqrt(2sinx)+c` |
| Answer» Correct Answer - C | |
| 176. |
`intsqrt(1-cosx)dx=?`A. `-2cos((x)/(2))+c`B. `-2sqrt2cos((x)/(2))+c`C. `-sqrt2cos((x)/(2))+c`D. `-2sqrt2 sin((x)/(2))+c` |
| Answer» Correct Answer - B | |
| 177. |
Integral of `(1)/(sqrt(x^(2)+4))` w.r.t. `(x^(2)+3)` isA. `sqrt(x^(2)+4)+c`B. `(1)/(sqrt(x^(2)+4))+c`C. `2sqrt(x^(2)+4)+c`D. `3sqrt(x^(2)+3)+c` |
| Answer» Correct Answer - C | |
| 178. |
`intsqrt((1+cos 3x)/(1-cos3x))dx=`A. `cot((3x)/(2))+c`B. `tan((3x)/(2))+c`C. `(2)/(3)log[sin((3x)/(2))]+c`D. `3log(sin 3x)+c` |
| Answer» Correct Answer - C | |
| 179. |
`int(1)/(1-sinx) dx`A. `secx+tanx`B. `secx-tanx`C. `cosx+cotx`D. `cosx-cotx` |
| Answer» Correct Answer - A | |
| 180. |
Integrate `w.r.t x, x^3[(x-a)(x-b)(x-c)]^-1` given that `1/A=((a-b)(a-c))/a^3, 1/B=((b-a)(b-c))/b^3, 1/C=((c-a)(c-b))/c^3`A. `x+A.log(x-a)+B.log(x-b)+C.log(x-c)+C`B. `A.log(x-a)+B.log(x-b)+C.log(x-c)+D`C. `1+A.log(x-a)+B.log(x-b)+C.log(x-c)+D`D. `(1)/(A)log(x-a)+(1)/(B)log(x-b)` |
| Answer» Correct Answer - B | |
| 181. |
`int(1)/(1-cos3x)dx=`A. `3cot((3x)/(2))+c`B. `(1)/(3)cot((3x)/(2))+c`C. `-(1)/(3)cot((3x)/(2))+c`D. `-(1)/(3)cos((3x)/(2))+c` |
| Answer» Correct Answer - C | |
| 182. |
`intlogxdx=?`A. `(1)/(x)+c`B. `xlog((x)/(e))+c`C. `xlog((e)/(x))+c`D. `e^(logx)+c` |
| Answer» Correct Answer - B | |
| 183. |
`int(1+sinx)/((x-cosx)^(3))dx=`A. `(-1//2)/((x-cosx)^(2))+c`B. `(1)/(2(x-cosx)^(2))+c`C. `(1)/((x-cosx)^(2))+c`D. `(1)/((x-cosx)^(3))+c` |
| Answer» Correct Answer - A | |
| 184. |
`int(1+tanx)/(e^(-x)cosx)dx` is equal toA. `e^(-x).tanx+c`B. `e^(-x).secx+c`C. `e^(x).secx+c`D. `e^(x).tanx+c` |
| Answer» Correct Answer - C | |
| 185. |
`int(sin^3x)/(cos^5x)dx`A. `3sec^(2)xtan^(2)x+c`B. `(1)/(3)tan^(3)x+c`C. `(1)/(4)tan^(4)x+c`D. `(1)/(3)tan4x+c` |
| Answer» Correct Answer - C | |
| 186. |
`int(logx)^(2)dx=ux+c,` then `u=`A. 2B. `(logx)^(2)-2logx-2`C. `(logx)^(2)-2logx+2`D. `e^(x)(2logx-1)+c` |
| Answer» Correct Answer - C | |
| 187. |
`int(1)/(1+cosx)dx=`A. `tan((x)/(2))+c`B. `2tan((x)/(2))+c`C. `-cot((x)/(2))+c`D. `-2cot((x)/(2))+c` |
| Answer» Correct Answer - A | |
| 188. |
`int(sin2xcos2x)/(sin^(4)2x+cos^(4)2x)dx=`A. `(1)/(2)cot^(-1)(sin^(2)x)+c`B. `(1)/(2)cot^(-1)(sin^(2)x)+c`C. `(1)/(2)tan^(-1)(sin^(2)x)+c`D. `-(1)/(2)cot^(-1)(sin^(2)x)+c` |
| Answer» Correct Answer - D | |
| 189. |
`int(cos^(2)x)/(sin^(4)x)=`A. `(1)/(3)tan^(3)x+c`B. `-(1)/(3)cot^(3)x+c`C. `-2cos^(2)xcotx+c`D. `-(1)/(3)cot3x+c` |
| Answer» Correct Answer - B | |
| 190. |
If `I_(1)=intsin^(-1)xdx and I_(2)sin^(-1)sqrt(-x^(2))dx,` thenA. `I_(1)=I_(2)`B. `I_(2):I_(1)=(pi)/(2)`C. `I_(1)+I_(2)=(pi)/(2)`D. `I_(1)+I_(2)=(pi)/(2)x` |
| Answer» Correct Answer - D | |
| 191. |
`intsin^(2)xdx-(x)/(2)=`A. `(x)/(2)+intcos^(2)xdx+c`B. `(x)/(2)-intcos^(2)xdx+c`C. `-(x)/(2)+intcos^(2)xdx+c`D. `-(x)/(2)-intcos^(2)xdx+c` |
| Answer» Correct Answer - B | |
| 192. |
`int(secx+tanx)^(2)dx=`A. `x+secx+tanx`B. `2(secx+tanx)-x`C. `2(secx-tanx)+x`D. `2(secx-tanx)+x` |
| Answer» Correct Answer - B | |
| 193. |
If `intsin^(-1)xdx=x sin^(-1)x+u+c,` then `u=`A. `sqrt(1-x^(2))`B. `-sqrt(1-x^(2))`C. `2sqrt(1-x^(2))`D. `-sqrt(x^(2)-1)` |
| Answer» Correct Answer - A | |
| 194. |
`int(sin^(4)x+cos^(4)x)dx=`A. `(3x)/(4)-(sin4x)/(16)+c`B. `(sin4x)/(16)-(3x)/(4)+c`C. `(3x)/(4)+(sin4x)/(16)`D. `4sin^(3)x+4cos^(3)x+c` |
| Answer» Correct Answer - C | |
| 195. |
if `inte^(sqrtx)dx=2ue^(sqrtx)+c` then `u`A. `sqrtx-1`B. `sqrtx+1`C. `1-sqrtx`D. `2sqrtx+1` |
| Answer» Correct Answer - A | |
| 196. |
`intcot^(2)((x)/(3))dx=`A. `x+3cot((x)/(3))`B. `x-3cot((x)/(3))`C. `x+3cotx`D. `-x-3cot((x)/(3))` |
| Answer» Correct Answer - D | |
| 197. |
If `inttan^(-1)sqrtx dx=u tan^(-1)sqrtx-sqrtx+c,` then `u=`A. `x-1`B. `1-x`C. `1+x`D. `2sqrtx-1` |
| Answer» Correct Answer - C | |
| 198. |
`inttan^(2)((x)/(2))dx=`A. `(1)/(2)tan((x)/(2))+c`B. `2tan((x)/(2))-x+c`C. `sec((x)/(2))+c`D. `2sec((x)/(2))+c` |
| Answer» Correct Answer - B | |
| 199. |
`int(1)/(sqrt(sin^(2)x cos^(2)x-sin^(4)x))dx=`A. `cos^(-1)(cotx)+c`B. `cos^(-1)(cotx+c`C. `-log(cotx+sqrt(cot^(x)-1))+c`D. `sin^(-1)(sqrt(cot^(2)x-1))+c` |
| Answer» Correct Answer - C | |
| 200. |
`intcos.(x)/(16)cos.(x)/(8)cos.(x)/(4)cos.(x)/(2)sin.(x)/(16)dx=`A. `(1)/(256)cos16x+c`B. `(-1)/(256)cos16x+c`C. `(1)/(256)sin16x+c`D. `(-1)/(16)cosx+c` |
| Answer» Correct Answer - D | |