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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.
| 201. |
`int(1)/((a^(2)+b^(2))-(a^(2)-b^(2))cosx)dx=`A. `(1)/(ab)tan^(-1)[(a)/(b)tan((x)/(2))]+c`B. `(a)/(b)tan^(-1)[ab tan((x)/(2))]+c`C. `tan^(-1)[(a)/(b)tan((x)/(2))]+c`D. `(a)/(b)tan^(-1)[2ab tan((x)/(2))]+c` |
| Answer» Correct Answer - A | |
| 202. |
`int[lim_(hrarr0)(sec(x+h)-secx)/(h)]dx=`A. `secx+c`B. `-secx+c`C. `secx tan x+c`D. `-sec xtanx+c` |
| Answer» Correct Answer - A | |
| 203. |
`inte^(x)tanx(1+tanx)dx=`A. `e^(x)(tanx-1)+c`B. `e^(x)(tanx+1)+c`C. `e^(-x)(tanx-1)+c`D. `e^(x)(sec^(2)x-1)+c` |
| Answer» Correct Answer - A | |
| 204. |
`int tan^(-1)[(cosx)/(1-sinx)]dx=`A. `(x)/(4)(pi+x)+c`B. `(pi)/(4)(x+pi)+c`C. `(x)/(2)(pi+x)+c`D. `(x)/(4)(pi-x)+c` |
| Answer» Correct Answer - A | |
| 205. |
`(1+cos4x)/(cotx-tanx)`A. `(cos4x)/(8)+c`B. `(cos4x)/(4)+c`C. `-(cos4x)/(4)+c`D. `-(cos4x)/(8)+c` |
| Answer» Correct Answer - D | |
| 206. |
If `u=(d)/(dx)(e^(sinx)),v=lim_(hrarr0) (e^(sin(x+h))-e^(sinx))/(h)` and `w=inte^(sinx)cosxdx,` thenA. `u ne v`B. `v=w`C. `intwdx=v`D. `(dw)/(dx)=w` |
| Answer» Correct Answer - D | |
| 207. |
`inte^(-x)(cosx-sinx)dx=`A. `e^(-x)sinx+c`B. `e^(x)sinx+c`C. `-e^(x)sinx+c`D. `-e^(-x)sinx+c` |
| Answer» Correct Answer - A | |
| 208. |
`inte^(x)(1-sinx)/(1-cosx)dx=`A. `e^(x).cotx+c`B. `e^(x).tan((x)/(2))+c`C. `-e^(x).cot((x)/(2))+c`D. `e^(x).cot((x)/(2))+c` |
| Answer» Correct Answer - C | |
| 209. |
`inte^(x)((1+sinx)/(1+cosx))dx=?`A. `e^(x//2).tanx+c`B. `e^(x).tan((x)/(2))+c`C. `-e^(x).cot((x)/(2))+c`D. `e^(x).sec^(2)((x)/(2))+c` |
| Answer» Correct Answer - B | |
| 210. |
`inte^(x)(sinx-cosx)/(sin^(2)x)dx=`A. `e^(x).secx+c`B. `e^(x).cosecx+c`C. `e^(x).tanx+c`D. `e^(x).cotx+c` |
| Answer» Correct Answer - B | |
| 211. |
if `inte^(2x)sinxcosxdx=u/8e^(2x)+c` then `u`A. `sinx-cosx`B. `sin2x-cos 2x`C. `sin2x+cos 2x`D. `cos 2x-sin2x` |
| Answer» Correct Answer - B | |
| 212. |
Evaluate the following integrals: `int(logx)/((1+logx)^(2))dx`A. `(1)/(1+logx)+c`B. `(logx)/(1+logx)+c`C. `(x-1)/(1+logx)+c`D. `(x)/(1+logx)+c` |
| Answer» Correct Answer - D | |
| 213. |
`int(3^(x))/(sqrt(9^(x)-1))dx=`A. `log_(3)(3^(x)+sqrt(9^(x)-1))+c`B. `log_(3)(3^(x)-sqrt(9^(x)-1))+c`C. `log_(9)(3^(x)+sqrt(9^(x)-1))+c`D. `(1)/(log3)sec^(-1)(3^(x))+c` |
| Answer» Correct Answer - A | |
| 214. |
If `inte^(sinx).sin2xdx=-2u.e^(sinx)+c,` then `u=`A. `1+sinx`B. `1+cosx`C. `1-sinx`D. `1-cosx` |
| Answer» Correct Answer - C | |
| 215. |
If `f((3x-4)/(3x+4))=x+2`, then `int` f(x)dx is equal toA. `e^(x+2).log|(3x-4)/(3x+4)|+c`B. `-(8)/(3).log|1-x|+(2x)/(3)+c`C. `(8)/(3).log|x-1|+(x)/(3)+c`D. none of these |
| Answer» Correct Answer - B | |
| 216. |
`int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx=`A. `log(tan^(2)x+sqrt(1+tan^(4)x))+c`B. `(1)/(2).log(tan^(2)x+sqrt(1+tan^(4)x))+c`C. `(1)/(4).log(tan^(2)x-sqrt(1+tan^(4)x))+c`D. none of these |
| Answer» Correct Answer - B | |
| 217. |
`int(1)/(x.sqrt(1-x^(3)))dx=`A. `(1)/(3).log|(sqrt(1-x^(3))-1)/(sqrt(1-x^(2))+1)|+c`B. `(1)/(3).log|(sqrt(1-x^(3))+1)/(sqrt(1-x^(3))-1)|+c`C. `(1)/(3).log|(1)/(sqrt(1-x^(3)))|+c`D. none of these |
| Answer» Correct Answer - A | |
| 218. |
Evaluate `int(secx)/((secx+tanx)) dx`.A. `(-1)/(3(secx+tanx)^(3))+c`B. `(1)/(3(secx+tanx)^(3))+c`C. `(3)/(secx+tanx)+c`D. `secx-tanx+c` |
| Answer» Correct Answer - A | |
| 219. |
`int(1)/(x^(2)-x^(3))dx=`A. `log((1-x)/(x))-(1)/(x)+`B. `log((1-x)/(x))+(1)/(x)+c`C. `log((x)/(1+x))+c`D. `-log((1-x)/(x))-(1)/(x)+c` |
| Answer» Correct Answer - D | |
| 220. |
`int(x^8)/(x^6+1)dx=`A. `-(x^(3))/(3)+tan^(-1)(x^(3))+c`B. `(x^(3))/(3)-(1)/(3)tan^(-1)(x^(3))+c`C. `-(x^(3))/(3)-tan^(-1)(x^(3))+c`D. `x^(2).tan^(-1)(x^(3))+c` |
| Answer» Correct Answer - B | |
| 221. |
`int(1)/(x^(3)-x^(4))dx=`A. `log((x)/(1-x))+(2x+1)/(2x^(2))+c`B. `log((1-x)/(x))-(2x+1)/(2x^(2))+c`C. `log((x)/(1-x))-(2x+1)/(2x^(2))+c`D. `(x^(-1))/(-1)-(x^(-2))/(-2)+c` |
| Answer» Correct Answer - C | |
| 222. |
`int sec x log(secx+tanx)dx=`A. `(secx+tanx)log(secx+tanx)+c`B. `log[log(sec x+tanx)+c`C. `(1)/(2)[log(secx+tanx)]^(2)+c`D. `(1)/(2)[sec(logx)]^(2)+c` |
| Answer» Correct Answer - C | |
| 223. |
If `int(u(dv)/(dx))dx=uv-intwdx,` then `w=`A. `(du)/(dx)(dv)/(dx)`B. `v(du)/(dx)`C. `(d)/(dx)(uv)`D. `uv` |
| Answer» Correct Answer - B | |
| 224. |
`int(1)/(sqrt(a^(2)-b^(2)x^(2)))dx=`A. `(1)/(ab)sin^(-1)((bx)/(a))+c`B. `(1)/(ab)sin^(-1)((ax)/(b))+c`C. `(1)/(b)sin^(-1)((bx)/(a))+c`D. `(1)/(a)sin^(-1)((bx)/(a))+c` |
| Answer» Correct Answer - C | |
| 225. |
`int(sin(x-a))/(sin(x+a))dx=`A. `x sin 2a-cos 2a. Log[sin(x+a)]+c`B. `x cos 2a+sin 2a.log[sin(x+a)]+c`C. `x cos 2a-sin 2a.log[sin(x-a)]+c`D. `x cos 2a-sin2a.log[sin(x+a)]+c` |
| Answer» Correct Answer - D | |
| 226. |
`int(cos (x-a))/(cos(x-b))dx=`A. `xcos(a-b)+sin(b-a).log[sec(x-b)]+c`B. `xsin(a-b)+cos(a-b).log[sec(x-b)]+c`C. `xcos(a-b)+sin(a-b).log[sec(x-b)]+c`D. `xcos(b-a)+sin(b-a).log[sec(x-b)]+c` |
| Answer» Correct Answer - C | |
| 227. |
`int(u(v(du)/(dx)-u(dv)/(dx)))/(v^(3))dx=`A. `log((u)/(v))+c`B. `(u^(2)v^(2))/(2)+c`C. `(u^(2))/(2v^(2))+c`D. `(u)/(2v)+c` |
| Answer» Correct Answer - C | |
| 228. |
If `int(x)/(1+sinx)dx=logu-x(secx-tanx)+c,` then `u=`A. `(1)/(1+sinx)`B. `(1)/(1-sinx)`C. `1-sinx`D. `1+sinx` |
| Answer» Correct Answer - D | |
| 229. |
`int(udv+vdu)/(sqrt(uv))=`A. `(2)/(3)(uv)^(3//2)+c`B. `2sqrt(uv)+c`C. `(2)/(3)sqrt((u)/(v))+c`D. `(2)/(3sqrt(uv))+c` |
| Answer» Correct Answer - B | |
| 230. |
If `int(sinx)/(cos(x-a))dx=kx+n.log[sec(x-a)]+p,` then `(k, n)-=`A. `(-sina, cosa)`B. `(cosa, sina)`C. `(sina, cosa)`D. `(sina, -cos a)` |
| Answer» Correct Answer - C | |
| 231. |
`int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx` is equal toA. `(sqrt(2x^(4)-2x^(2)+1))/(x^(2))+c`B. `(sqrt(2x^(4)-2x^(2)+1))/(x^(3))+c`C. `(sqrt(2x^(4)-2x^(2)+1))/(x)+c`D. `(sqrt(2x^(4)-2x^(2)+1))/(2x^(2))+c` |
| Answer» Correct Answer - D | |
| 232. |
If `I_(n)=int(sinnx)/(sinx)dx,` then `I_(5)-I_(3)=`A. `-(sin4x)/(4)+c`B. `sin4x+c`C. `(sin4x)/(2)+c`D. `-(sin4x)/(2)+c` |
| Answer» Correct Answer - C | |
| 233. |
`intsec^(4)xdx=`A. `(4sinx)/(cos^(5)x)+c`B. `tanx+(1)/(3)tan^(3)x+c`C. `4sec^(3)xlog(secx+tanx)+c`D. `(sec^(5)x)/(5)+c` |
| Answer» Correct Answer - B | |
| 234. |
If `alpha, beta` are roots of `ax^(2)+bx+c=0`, then : `int((x-alpha)(x-beta))/(ax^(2)+bx+c)dx=`A. `oo.x+k`B. `ax+c`C. 0D. `(x)/(a)+c` |
| Answer» Correct Answer - D | |
| 235. |
If `int(dx)/(root3(sin^(11)xcosx))=-[(3)/(8)f(x)+(3)/(2)g(x)]+C`, thenA. `f(x)=tan^(-8//3)x, g(x)=tan^(-2//3)x`B. `f(x)=tan^(8//3)x, g(x)=tan^(-2//3)x`C. `f(x)=tan^(-8//3)x, g(x)=tan^(2//3)x`D. none of these |
| Answer» Correct Answer - A | |
| 236. |
`int(cos^(3)x)e^(log(sinx))dx=`A. `-(sin^(4)x)/(4)+c`B. `-(cos^(4)x)/(4)+c`C. `(e^(sinx))/(4)+c`D. `(sin^(4)x)/(4)+c` |
| Answer» Correct Answer - B | |
| 237. |
If `int(sinx)/(cos^(5)x)dx=intu^(3)du`, then `u=`A. `sinx`B. `cos x`C. `secx`D. `cosx` |
| Answer» Correct Answer - C | |
| 238. |
`int(e^(x)(1+x))/(cos^(2)(xe^(x)))dx=`A. `e^(x)tan(xe^(x))`B. `e^(x)tan(xe^(-x))`C. `-cot(xe^(x))`D. `tan(xe^(x))` |
| Answer» Correct Answer - D | |
| 239. |
`int(x+1)(x+2)^7(x+3)dx` is equal toA. `((x+2)^(10))/(10)-((x+2)^(8))/(8)+c`B. `((x+2)^(2))/(2)-((x+2)^(8))/(8)-((x+3)^(2))/(2)+c`C. `((x+2)^(10))/(10)+c`D. `((x+1)^(2))/(2)+((x+2)^(8))/(8)-((x+3)^(2))/(2)+c` |
| Answer» Correct Answer - A | |
| 240. |
`int(xe^(x))/((x+2)^(3))dx=`A. `(e^(x))/(x+2)+c`B. `(e^(x))/((x+2)^(2))+c`C. `(e^(x))/((x+2)^(3))+c`D. `(xe^(x))/((x+2)^(2))+c` |
| Answer» Correct Answer - B | |
| 241. |
`int((x-1).e^(x))/((x+1)^(3))dx=`A. `(e^(x))/(x+1)+c`B. `(e^(x))/((x+1)^(2))+c`C. `e^(x).(x+1)^(3)+c`D. none of these |
| Answer» Correct Answer - B | |
| 242. |
If `f(x) = co s x-cos^2 x + cos^3 x-....to oo` then `int f(x) dx` is equal toA. `tan.(x)/(2)`B. `x+tan.(x)/(2)`C. `x-(1)/(2)tan.(x)/(2)`D. `x-tan.(x)/(2)` |
| Answer» Correct Answer - D | |
| 243. |
`int(x+1)/(x-2)dx=`A. `3x+log(x-2)+c`B. `x+3log(x-2)+c`C. `3+xlog(x-2)+c`D. `x^(3)+log(x-2)+c` |
| Answer» Correct Answer - B | |
| 244. |
`int(1+tan^(2)x)/(1+tanx)dx=`A. `sinx+cosx+c`B. `cosx-sinx+c`C. `log(1+tanx)+c`D. `log(cosx+sinx)+c` |
| Answer» Correct Answer - C | |
| 245. |
If `int(5cos x+4sinx)/(3sinx+2cos x)dx=ax+blog(3sinx+2cos x)+c,` then `(a,b)-=`A. `((22)/(13),(-7)/(13))`B. `((23)/(12),(-7)/(12))`C. `((-22)/(13),(-7)/(13))`D. `((22)/(13),(7)/(13))` |
| Answer» Correct Answer - D | |
| 246. |
Evaluate:`int(x^3)/((x^2+1)^3)dx`A. `3log(x^(2)+1)+c`B. `x^(2)-log(x^(2)+1)+c`C. `(x^(2))/(2)-tan^(-1)x+c`D. `(x^(2))/(2)-(1)/(2)log(x^(2)+1)+c` |
| Answer» Correct Answer - D | |
| 247. |
`int(x^(3)+3x^(2)+3x+1)/((x+1)^(5))dx=`A. `(-1)/(x+1)+c`B. `(1)/(5)log(x+1)+c`C. `log(x+1)+c`D. `tan^(-1)x+c` |
| Answer» Correct Answer - A | |
| 248. |
If `int(2x+5)/(5x+1)dx=ax+b log(5x+1)+c`, then `(a, b)-=`A. `((2)/(5),(23)/(25))`B. `((5)/(2),(23)/(2))`C. `((-2)/(5),(2)/(23))`D. `((2)/(5),-(2)/(23))` |
| Answer» Correct Answer - A | |
| 249. |
If `int(3e^(x)+4e^(-x))/(5e^(x)+6e^(-x))=ax+b log(5e^(2x)+6)+c,` thenA. `a=(2)/(3), b=-30`B. `a=(3)/(2), b=(-1)/(30)`C. `a=(2)/(3), b=(-1)/(30)`D. `a=-(3)/(2), b=-30` |
| Answer» Correct Answer - C | |
| 250. |
If `int(3x+4)/(5x-7)dx=ax+b.log(5x-7)+c`, then `(a, b)-=`A. `((5)/(3),(25)/(41))`B. `((3)/(5),(41)/(25))`C. `(3, 41)`D. `(5, 25)` |
| Answer» Correct Answer - B | |