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.
| 251. |
If `int(4cosx+3sinx)/(2sinx+cosx)dx=ax+b log (2sinx+cosx)+c,` thenA. `a=2, b=-1`B. `a=2, b=1`C. `a=b`D. `a=-2, b=1` |
| Answer» Correct Answer - B | |
| 252. |
`int(x-a)(x-b)dx=`A. constantB. `sc+sd+x`C. `x^(2)-ax`D. `e^(x)+c` |
| Answer» Correct Answer - A | |
| 253. |
`int(sin^(2)6x-cos^(2)7x)dx=`A. `c-(sin12x)/(24)-(sin14x)/(28)`B. `(cos6x)/(6)-(sin7x)/(7)+c`C. `(cos12x)/(12)-(sin14x)/(14)`D. `6sin12x+7sin14x+c` |
| Answer» Correct Answer - A | |
| 254. |
`int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx=`A. `(x^(2)+2x)/((x^(5)+x^(3)+1)^(2))+c`B. `(x^(10))/(2(x^(5)+x^()+1)^(2))+c`C. `ln|x^(5)+x^(3)+1|+sqrt(2x^(7)+5x^(4))+c`D. none of these |
| Answer» Correct Answer - B | |
| 255. |
`int(1+2x+0.5x^(2))e^(x)dx=`A. `(x+1)e^(x)+c`B. `(1+4x)e^(x)+c`C. `(x+0.5)e^(x)+c`D. `(x+0.5x^(2))e^(x)+c` |
| Answer» Correct Answer - D | |
| 256. |
If `int(x^(3)+4x^(2)-7x+5)/(x+2)dx=(x^(3))/(3)+ax^(2)-11x+b log(x+2)+c,` then `(a, b)-=`A. `(-1, 27)`B. `(1,-27)`C. `(-1, -27)`D. `(1, 27)` |
| Answer» Correct Answer - D | |
| 257. |
`int(log(3x)dx)/(log(9x)x)=`A. `log(3x)-log(9x)+c`B. `logx-log3.log(log9x)+c`C. `log9-logx.log(log3x)+c`D. `logx-log9.log(log3x)+c` |
| Answer» Correct Answer - B | |
| 258. |
`int(x^(2)+1)/(x(x^(2)-1))dx=`A. `log((x^(2)-1)/(x))+c`B. `-log((x^(2)-1)/(x))+c`C. `log((x)/(x^(2)+1))+c`D. `-log((x)/(x^(2)+1))+c` |
| Answer» Correct Answer - A | |
| 259. |
`int(x-1)e^(-x)dx=`A. `x.e^(-x)+c`B. `-x.e^(-x)+c`C. `x.e^(x)+c`D. `-x.e^(x)+c` |
| Answer» Correct Answer - B | |
| 260. |
If `f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0)`, and f(0) = 0, then the value of f(1) isA. `(x^(5))/(x^(2)+1+2x^(7))+c`B. `(-1)/(2x^(7)+x^(2)+1)+c`C. `(x^(5))/(2x^(7)+x^(2)+1)+c`D. `(x^(7))/(2x^(7)+x^(2)+1)+c` |
| Answer» Correct Answer - D | |
| 261. |
`int(1)/(sqrt(1+sqrtx))dx=`A. `(4)/(3)(x-2)sqrt(1+x)+c`B. `(4)/(3)(sqrtx-2)(1+sqrtx)+c`C. `(4)/(3)(sqrt(1+sqrtx))^(3)-4sqrt(1+sqrtx)+c`D. `2sqrt(1+sqrtx)+c` |
| Answer» Correct Answer - C | |
| 262. |
`int(1)/(1+sqrtx)dx=`A. `sqrtx-log(1+sqrtx)+c`B. `2sqrtx-2log(1+sqrtx)+c`C. `3sqrtx-3log(1+sqrtx)+c`D. `2sqrtx+log(sqrtx-1)+c` |
| Answer» Correct Answer - B | |
| 263. |
`int(1+x+sqrt(x+x^(2)))/(sqrtx+sqrt(1+x))dx=`A. `(1)/(2)sqrt(1+x)+c`B. `(2)/(3)(1+x)^(3//2)+c`C. `sqrt(1+x)+c`D. `2(1+x)^(3//2)+c` |
| Answer» Correct Answer - B | |
| 264. |
`int(1)/(sqrtx(x+9))dx=`A. `(2)/(3)tan^(-1)(sqrtx)+c`B. `(2)/(3)tan^(-1)((sqrtx)/(3))+c`C. `tan^(-1)(sqrtx)+c`D. `tan^(-1)((sqrtx)/(3))+c` |
| Answer» Correct Answer - B | |
| 265. |
`int(sqrt(1+sqrtx))/(sqrtx)dx=`A. `sqrt(logx+2sqrtx)+c`B. `(4)/(3)(1+sqrtx)^(3//2)+c`C. `(1)/(sqrt(logx+2sqrtx))+c`D. `(4)/(3(1+sqrtx)^(3//2))+c` |
| Answer» Correct Answer - B | |
| 266. |
`int(sqrtx)/(1+xsqrtx)dx-`A. `(3)/(2)tan^(-1)(sqrtx)+c`B. `(3)/(2)logx+c`C. `(2)/(3)log(1+xsqrtx)+c`D. `(2)/(3)tan^(-1)(sqrtx)+c` |
| Answer» Correct Answer - C | |
| 267. |
`int(1)/(16sin^(2)x+25cos^(2)x)dx=`A. `(1)/(20)tan^(-1)((4)/(5)tanx)+c`B. `(-1)/(20)tan^(-1)((4)/(5)tanx)+c`C. `-tan^(-1)((5)/(4)tanx)+c`D. `(1)/(20)log[4sinx+sqrt(16sin^(2)x+25cos^(2)x)]+c` |
| Answer» Correct Answer - A | |
| 268. |
If : `int(1+cos8x)/(tan2x-cot2x)dx=a.cos8x+c,` then : `a=`A. `-(1)/(16)`B. `(1)/(8)`C. `(1)/(16)`D. `-(1)/(8)` |
| Answer» Correct Answer - C | |
| 269. |
`int(2-sinx)/(2+cosx)dx=`A. `-(4)/(sqrt3).tan^(-1)((1)/(sqrt3).tan.(x)/(2))+log(2+cosx)+c`B. `(4)/(sqrt4).tan^(-1)((1)/(sqrt3).tan.(x)/(2))+log(2+cosx)+c`C. `(4)/(sqrt3).tan^(-1)((1)/(sqrt3).tan.(x)/(2))-log(2+cosx)+c`D. 0 |
| Answer» Correct Answer - B | |
| 270. |
`int(x^(2)-1)/(x^(4)+x^(2)+1)dx=`A. `(1)/(2).log((x^(2)+x+1)/(x^(2)-x+1))+c`B. `(1)/(2).log((x^(2)-x+1)/(x^(2)-x+1))+c`C. `log((x^(2)-x+1)/(x^(2)+x+1))+c`D. `(1)/(2).log((x^(2)-x+1)/(x^(2)+x+1))+c` |
| Answer» Correct Answer - D | |
| 271. |
`int(dx)/(sinx-cosx+sqrt2)` is equal toA. `-(1)/(sqrt2).tan((pi)/(8)+(x)/(2))+c`B. `(1)/(sqrt(2).tan((pi)/(8)+(x)/(2))`C. `(1)/(sqrt2).cot((pi)/(8)+(x)/(2))`D. `-(1)/(sqrt2).cot((pi)/(8)+(x)/(2))` |
| Answer» Correct Answer - D | |
| 272. |
The value of `sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx` , isA. `x+ln|sin(x-(pi)/(4))|+c`B. `x-ln|cos(x-(pi)/(4))|+c`C. `x+ln|cos(x-(pi)/(4))|+c`D. `x-ln|sin(x-(pi)/(4))|+c` |
| Answer» Correct Answer - A | |
| 273. |
The value of `sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx` , isA. `x-log|sin(x-(pi)/(4))|+c`B. `x+log|sin(x-(pi)/(4))|+c`C. `x-log|cos(x-(pi)/(4))|+c`D. `x+log|cos(x-(pi)/(4))|+c` |
| Answer» Correct Answer - B | |
| 274. |
`int(dx)/(sinx-cosx+sqrt2)` is equal toA. `-(1)/(sqrt2).tan((x)/(2)+(pi)/(8))+c`B. `(1)/(sqrt2).tan((x)/(2)+(pi)/(8))+c`C. `(1)/(sqrt2).cot((x)/(2)+(pi)/(8))+c`D. `-(1)/(sqrt2).cot((x)/(2)+(pi)/(8))+c` |
| Answer» Correct Answer - D | |
| 275. |
`int(1)/(sinx sqrt(sinx cos x))dx=`A. `sqrt(tanx)+c`B. `-sqrt(cosx)+c`C. `-2sqrt(cotx)+c`D. `sqrt(cotx)+c` |
| Answer» Correct Answer - C | |
| 276. |
`int(1)/(1+sinx+cosx)dx=`A. `log(1-tan.(x)/(2))+c`B. `log(1+tan.(x)/(2))+c`C. `log(2+tan.(x)/(2))+c`D. `log(2-tan.(x)/(2))+c` |
| Answer» Correct Answer - B | |
| 277. |
`int(cotx)/(1+sinx)dx=`A. `log((sinx)/(1-sinx))+c`B. `log((sinx)/(1+sinx))+c`C. `log((1+sinx)/(x))+c`D. `log(1+sinx)+c` |
| Answer» Correct Answer - B | |
| 278. |
`inte^(x)(1-cotx+cot^(2)x)dx=`A. `e^(-x).cotx+c`B. `-e^(x).cotx+c`C. `e^(x).cosx+c`D. `e^(-x).sinx+c` |
| Answer» Correct Answer - B | |
| 279. |
`int(1)/(sin2x-sin^(2)x)dx=`A. `log((tanx)/(tanx-2))+c`B. `(1)/(2)log((tanx)/(tanx-2))+c`C. `log((tanx-2)/(tanx))+c`D. `(1)/(2)tan^(-1)((tanx)/(2))+c` |
| Answer» Correct Answer - B | |
| 280. |
`int(1+tan^(2)x)/(1+cot^(2)x)dx-`A. `sinx-cos x+c`B. `secx-cos x+c`C. `tanx-cotx+c`D. `tanx-x+c` |
| Answer» Correct Answer - D | |
| 281. |
`int(tan^(2)x-cot^(2)x)dx=`A. `tanx+cotx+c`B. `tanx-cotx+c`C. `-tanx-cotx+4x+c`D. `cot2x+cotx+c` |
| Answer» Correct Answer - A | |
| 282. |
`int(1)/(1-sin2x)dx=`A. `(1)/(cosx-1)+c`B. `(cotx)/(cotx-1)+c`C. `(tanx)/(tanx-1)+c`D. `(tanx-1)/(tanx)+c` |
| Answer» Correct Answer - B | |
| 283. |
`int(tan(cos^(-1)x)+cot(sin^(-1)x))/(sqrt(1-x^(2)))dx=`A. `2logx+c`B. `logx+c`C. `-logx+c`D. `-2logx+c` |
| Answer» Correct Answer - A | |
| 284. |
`int(sqrt(tanx))/(sin2x)dx=`A. `sqrt((sinx)/(cosx))+c`B. `(1)/(sqrt(cosx))+c`C. `sqrt(cosx)+c`D. `sqrt((cos x)/(sinx))+c` |
| Answer» Correct Answer - A | |
| 285. |
If `int(1)/((x+1)sqrt(x-1))dx=k.tan^(-1)sqrt((x-1)/(2))+c` then `k = `A. `(1)/(sqrt2)`B. `(1)/(2)`C. `2sqrt2`D. `sqrt2` |
| Answer» Correct Answer - D | |
| 286. |
`int((1+x)^(2))/(x(1+x^(2)))dx=`A. `logx+c`B. `(logx)(tan^(-1)x)+c`C. `2logx+tan^(-1)x+c`D. `logx+2tan^(-1)x+c` |
| Answer» Correct Answer - D | |
| 287. |
if `int(dx)/((2x+1)sqrt(x-2))dx=sqrta.tan^-1sqrt(b(x-2))+c` thenA. `a lt b`B. `a gt b`C. `a=b`D. `a^(b)=100` |
| Answer» Correct Answer - C | |