InterviewSolution
Saved Bookmarks
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.
| 101. |
Evaluate the following integrals. `int (1)/(1-cosx)dx`A. `-cot2x-2x+c`B. `cot2x-2x+c`C. `-cot2x+2x+c`D. `cot2x+2x+c` |
| Answer» Correct Answer - A | |
| 102. |
`int xtan^2x dx=`A. does not existB. `xtanx-log(cosx)+c`C. `xtanx-log(secx)-(x^(2))/(2)+c`D. `x.sec^(2)x-x+c` |
| Answer» Correct Answer - C | |
| 103. |
`intsinx cos x(sec^(4)x)/(1+sec^(4)x)dx=`A. `-(1)/(2)tan^(-1)(x^(2))+c`B. `-(1)/(2)tan^(-1)(cos^(2)x)+c`C. `-cot^(-1)(sin^(2)x)+c`D. `tan^(-1)(sin^(2)x)+c` |
| Answer» Correct Answer - B | |
| 104. |
If `f(x)=(1)/(1-x)`, then `int(f(f(f(x))))dx=`A. `x+c`B. `(x^(2))/(2)+c`C. `(x^(3))/(3)+c`D. `(x^(4))/(4)+c` |
| Answer» Correct Answer - B | |
| 105. |
If `int(cosx)/(9-cos^(2)x)dx=m.tan^(-1)[m.f(x)]+c,` thenA. `m=2sqrt2, f(x)=cosx`B. `m=(1)/(2sqrt2), f(x)=sinx`C. `m=(1)/(2)sqrt2, f(x)=cosx`D. `m=2sqrt2, f(x)=sinx` |
| Answer» Correct Answer - B | |
| 106. |
`4int(sec^(2)xtan^(3)x+cosec^(2)xcot^(3)x)dx=`A. `tan^(4)x+cot^(4)x+c`B. `tan^(4)x-cot^(4)x+c`C. `-tan^(4)x-cot^(4)x+c`D. `sin^(4)x-cot^(4)x+c` |
| Answer» Correct Answer - B | |
| 107. |
`int(x+4)/(x+1)dx=`A. `3x+log(x+1)+c`B. `x-5log(x+4)+c`C. `x+3log(x+1)+c`D. `x^(3)+log(x+1)+c` |
| Answer» Correct Answer - C | |
| 108. |
`4int(1+sin^(2)2x)/(1+cos4x)dx=`A. `2tan2x-4x+c`B. `2tan2x-2x+c`C. `2tan2x+4x+c`D. `tan2x-x+c` |
| Answer» Correct Answer - B | |
| 109. |
`intsin^(2)4xdx=`A. `(x)/(2)+(sin8x)/(16)+c`B. `(x)/(2)-(sin8x)/(16)-c`C. `cos^(2)4x+c`D. `4sin8x+c` |
| Answer» Correct Answer - B | |
| 110. |
`int(x-2)/(x+3)dx=`A. `5x-log(x+3)+c`B. `x+5log(x+3)+c`C. `x+5log(x-2)+c`D. `x-5log(x+3)+c` |
| Answer» Correct Answer - D | |
| 111. |
Evaluate the following integrals :`int(1-cos2x)/(1+cos2x)dx`A. `-tanx-x+c`B. `tanx-x+c`C. `tanx+x+c`D. `-tanx+x+c` |
| Answer» Correct Answer - B | |
| 112. |
`2int(1+cos^(2)x)/(1+cos2x)dx=`A. `x-cotx+c`B. `tanx-x+c`C. `x+cotx+c`D. `x+tanx+c` |
| Answer» Correct Answer - D | |
| 113. |
`4int(sin^(3)x+cos^(3)x)/(sin^(2)2x)dx=`A. `secx-cosec x-c`B. `secx+cosx+c`C. `sinx-cosx+c^(3)`D. `secx-tanx+c` |
| Answer» Correct Answer - A | |
| 114. |
`int(2x+3)/(x)dx=`A. `3+2logx+c`B. `2-3logx+c`C. `2x-3logx+c`D. `2x+3logx+c` |
| Answer» Correct Answer - D | |
| 115. |
`int(sinx-cosx)^(2)dx=`A. `x-0.5cos 2x`B. `x+cos 2x+c`C. `x+0.5sin2x`D. `x+0.5cos 2x` |
| Answer» Correct Answer - D | |
| 116. |
`int(1)/((x-3)(x^(2)-7))dx=`A. `(1)/(2)((1)/(x-3)+(x+3)/(x^(2)-7))+c`B. `(1)/(2)log(x-3)-(1)/(4)log(x^(2)-7)-(3)/(4sqrt7)log((sqrt7+x)/(sqrt7-x))+c`C. `-(1)/(2)[(1)/(x-3)-(x+3)/(x^(2)-7)]+c`D. `(1)/(2)[(x+3)/(x^(2)-7)-(1)/(x-3)]+c` |
| Answer» Correct Answer - B | |
| 117. |
`int(1)/(cos2x+sin^(2)x)dx=`A. `sinx+c`B. `cosx+c`C. `tanx`D. `cotx` |
| Answer» Correct Answer - C | |
| 118. |
`int(1+cos^(2)x)/(1-cos2x)dx=`A. `-cotx-(x)/(2)+c`B. `cotx+(x)/(2)+c`C. `cotx-(x)/(2)+c`D. `-cotx+(x)/(2)+c` |
| Answer» Correct Answer - A | |
| 119. |
`int(sin^(4)x-cos^(4)x)dx=`A. `sinx-cosx`B. `sinx.cosx+c`C. `-sinx.cos x+c`D. `cos 2x+c` |
| Answer» Correct Answer - C | |
| 120. |
`int(1)/(sqrt(4x^(2)-4x+3))dx=`A. `(1)/(2)log[(x-(1)/(2))-sqrt(x^(2)-x+(3)/(4))]+c`B. `(1)/(2)log[(x-(1)/(2))+sqrt(x^(2)-x+(3)/(4))]+c`C. `(1)/(2)log[(x+(1)/(2))-sqrt(x^(2)+x-(3)/(4))]+c`D. `(1)/(2)tan^(-1)(4x^(2)-4x+3)+c` |
| Answer» Correct Answer - B | |
| 121. |
`int(4x+3)/(4x-1)dx=`A. `x+log(4x-1)+c`B. `4x+log(4x-1)+c`C. `x+4log(4x+3)+c`D. `x^($)+log(4x+3)+c` |
| Answer» Correct Answer - A | |
| 122. |
`int(1)/((x+5)(x^(2)+4))dx=`A. `(1)/(9)[(1)/(x+5)-(x-5)/(x^(2)+4)]+c`B. `(1)/(9)[(1)/(x-5)-(x+5)/(x^(2)-4)]+c`C. `-(1)/(9)[(1)/(x-5)-(x+5)/(x^(2)+4)]`D. `(1)/(9)log(x+5)-(1)/(18)log(x^(2)+4)+(5)/(18)tan^(-1)((x)/(2))+c` |
| Answer» Correct Answer - D | |
| 123. |
`inttanx sqrt(secx)dx=`A. `(2)/(3)sec^(3//2)x+c`B. `2sqrt(tanx)+c`C. `2sqrt(secx)+c`D. `2sqrt(cotx)+c` |
| Answer» Correct Answer - C | |
| 124. |
`int(tan^(m)x)/(sinx cos x)dx=`A. `(tan^(m+2)x)/(m+2)+c`B. `(tan^(m+1)x)/(m+1)+c`C. `tan^(m+1)x+c`D. `(tan^(m)x)/(m)+c` |
| Answer» Correct Answer - D | |
| 125. |
`int[(sin^(2).(x)/(2)-cos^(2).(x)/(2))^(2)+4sin^(2).(x)/(2).cos^(2).(x)/(2)]dx=` |
| Answer» Correct Answer - C | |
| 126. |
`int(cos2x)/(sin^(2)x.cos^(2)x)dx=`A. `tanx-cotx`B. `cotx-tanx`C. `tanx+cotx`D. `-(tanx+cotx)` |
| Answer» Correct Answer - D | |
| 127. |
`int(1)/((2x+3)^(2)(4x+5))dx=`A. `(1)/(2(2x+3))+(1)/(3)log((4x+5)/(2x+3))+c`B. `(1)/(2)[(1)/(2x+3)-log((4x+4)/(2x+3))]+c`C. `(1)/(2)[(1)/(2x+3)+log((4x+5)/(2x+3))]+c`D. `(1)/(2(2x+3))+log((4x+5)/(2x+3))+c` |
| Answer» Correct Answer - D | |
| 128. |
`int(1)/(5+4x-x^(2))dx=`A. `(1)/(6)log[(x-1)/(x-5)]+c`B. `(1)/(6)log[(x-5)/(x-1)]+c`C. `(1)/(6)log[(1+x)/(x-5)]+c`D. `(1)/(6)tan^(-1)[(x-5)/(x+1)]+c` |
| Answer» Correct Answer - C | |
| 129. |
`int (cos2x)/(cosx) dx=`A. `2sinx+log(cosx-cotx)+c`B. `log(cosx-cotx)+2cos x+c`C. `log(secx+tanx)+2cosx+c`D. `log(secx+tanx)-2sinx+c` |
| Answer» Correct Answer - B | |
| 130. |
`int(e^(2x)+e^(-2x))/(e^(x)+e^(-x))dx=`A. `e^(x)-e^(-x)-2 tan^(-1)(e^(x))+c`B. `e^(-x)+e^(x)+2 tan^(-1)(e^(-x))+c`C. `e^(-x)-e^(x)+2tan^(-1)(e^(x))+c`D. `e^(x)-e^(-x)+c` |
| Answer» Correct Answer - A | |
| 131. |
`int(sin^(m)x)/(cos^(m+2)x)dx=`A. `(tan^(m+1))/(m+1)+c`B. `(tan^(m)x)/(m)+c`C. `tan^(m)x+c`D. `(m)/(m+1)log(tanx)+c` |
| Answer» Correct Answer - A | |
| 132. |
`int(1)/(sinx*cos^(2)x)dx=`A. `log[tan((x)/(2))]-secx+c`B. `log[tan((x)/(2))]+secx+c`C. `log[tan((x)/(2))]+c`D. `log[cot((x)/(2))]+secx+c` |
| Answer» Correct Answer - B | |
| 133. |
`intx^(2)logxdx=`A. `(x^(3))/(9)(3logx-1)+c`B. `(x^(2))/(4)(2logx-1)+c`C. `x(logx-1)+c`D. `(x^(3))/(3)+(1)/(x)+c` |
| Answer» Correct Answer - A | |
| 134. |
`int(cos2x)/(sinx+cosx)dx=`A. `secx-cosx`B. `sinx-cosx`C. `sinx+cosx+c`D. `secx+tanx+c` |
| Answer» Correct Answer - C | |
| 135. |
`intx^(100x).(1+lnx)dx=`A. `int(x^(100)x)/(100)+c`B. `x^(100x)+c`C. `(x^(99x))/(99)+c`D. `dx^(99x).(1+ln x)+c` |
| Answer» Correct Answer - A | |
| 136. |
If `intx.f(x)dx=(1)/(2)f(x)+c`, then `f(x)=`A. `e^(2x)`B. `e^(x^(2))`C. `e^(x//2)`D. `e^(-x^(2))` |
| Answer» Correct Answer - B | |
| 137. |
`int(1)/(tanx+cotx)dx=`A. `log(secx+cosx)+c`B. `2cos 2x+c`C. `-(1)/(2)cos 2x+c`D. `(1)/(2)sin^(2)x+c` |
| Answer» Correct Answer - D | |
| 138. |
`int(1)/(4x^(2)+4x-15)dx=`A. `(1)/(16)log[(2x-3)/(2x+5)]+c`B. `(1)/(4)log[(2x+3)/(2x-5)]+c`C. `(1)/(4)log[(5+2x)/(3-2x)]+c`D. `(1)/(4)tan^(-1)[(2x-3)/(2x+5)]+c` |
| Answer» Correct Answer - A | |
| 139. |
`int6x sqrt(2x^(2)+5)dx=`A. `24x(2x^(2)+5)^(-1//2)`B. `(2x^(2)+5)^(3//2)`C. `1.5(2x^(2)+5)^(3//2)`D. `12(2x^(2)+5)^(3//2)` |
| Answer» Correct Answer - B | |
| 140. |
`int(1)/((e^(-mx))^(2))dx=`A. `(1)/(1+e^(2mx))+c`B. `(-1)/(2m(1+e^(2mx))+c`C. `(1)/(m(1+e^(2mx)))+c`D. `(2m)/(e^(2mx)+e^(-2mx))+c` |
| Answer» Correct Answer - B | |
| 141. |
`int(1)/((1+e^(mx))(1+e^(-mx)))dx=`A. `(m)/(1+e^(mx))+c`B. `(m)/(m(1+e^(mx))+c`C. `(1)/(1+e^(mx))+c`D. `(-1)/(m(1+e^(mx)))+c` |
| Answer» Correct Answer - D | |
| 142. |
`int(sqrt(1+cosx))/(1-cosx)dx=`A. `-sqrt2 cosec((x)/(2))+c`B. `sqrt2 cos ((x)/(2))+c`C. `-sqrt2 sec((x)/(2))+c`D. `log[cos((x)/(2))]+c` |
| Answer» Correct Answer - A | |
| 143. |
`int(cos2x)/((sinx+cosx)^(2))dx` is equal toA. `log(cotx)+c`B. `log(sinxcosx)+c`C. `log(sinx+cosx)+c`D. `log(cosx-sinx)+c` |
| Answer» Correct Answer - C | |
| 144. |
`int(cos2x)/(cosx-sinx)dx=`A. `sinx+cosx+c`B. `cosx-sinx+c`C. `sinx-cosx+c`D. `sinx.cosx+c` |
| Answer» Correct Answer - C | |
| 145. |
`int (cos2x)/(cosx) dx=`A. `2sinx-log(secx+tanx)+c`B. `2sinx+log(cos x+cotx)+c`C. `2cosx-log(cosx-cotx)+c`D. `2cosx-log(cos x -cotx)+c` |
| Answer» Correct Answer - A | |
| 146. |
`intx^(x)dx+intx^(x)logxdx=`A. `log(x^(x))+c`B. `e^(x^(x))+c`C. `(x x x …" n times")+c`D. `x^(x)+c` |
| Answer» Correct Answer - D | |
| 147. |
`int(1)/(secx+tanx)dx=`A. `(1)/(sec)+c`B. `secx+log(secx+tanx)+c`C. `cosx+log(cosx-cotx)+c`D. `log(secx)+c` |
| Answer» Correct Answer - C | |
| 148. |
`int6x e^(x^(2))dx=`A. `3e^(2x)`B. `2e^(x^(2))`C. `3e^(x^(2))`D. `x.e^(x^(2))` |
| Answer» Correct Answer - C | |
| 149. |
If `int(1)/(x^(2)-2 sin alpha+1)dx=sec alpha.tan^(-1)(mx+c)`, thenA. `m=sec alpha, c in R`B. `m=sec alpha, c = tan alpha`C. `m=sec alpha, c=-tan alpha`D. `m=tan alpha, c=sec alpha` |
| Answer» Correct Answer - C | |
| 150. |
`int(cosx)/(sqrt(cos2x))dx=`A. `(-1)/(sqrt2)log[sqrt2sinx+sqrt(cos2x)]+c`B. `(-1)/(sqrt2)sin^(-1)(sqrt2 cos x)+c`C. `(1)/(sqrt2)sin^(-1)(sqrt2 sinx)+c`D. `(1)/(sqrt2)sin^(-1)(sqrt2sinx)+c` |
| Answer» Correct Answer - D | |