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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.
| 51. |
If `int(k)/(sin(x-a)cos(x-b))dx=log[(sin(x-a))/(cos(x-b))]+c`, then `k=`A. `sin(a-b)`B. `cos(a-b)`C. `tan(a-b)`D. `sec(a-b)` |
| Answer» Correct Answer - B | |
| 52. |
If `int g(x)dx=f(x)`, then : `intf(x).g(x)dx=`A. `log[f(x)]+c`B. `(1)/(2)[g(x)]^(2)+c`C. `(1)/(2)[f(x)]^(2)+c`D. `[g(x)]^(2)+c` |
| Answer» Correct Answer - C | |
| 53. |
If `f(x)=x, g(x)=sinx,` then `intf[g(x)]dx` is equal toA. `sinx+c`B. `-cos+c`C. `(x^(2))/(2)+c`D. `xsinx+c` |
| Answer» Correct Answer - B | |
| 54. |
If `intf(x)dx=2 {f(x)}^(3)+C` , then f (x) isA. `(x)/(2)`B. `x^(3)`C. `(1)/(sqrtx)`D. `sqrt((x)/(3))` |
| Answer» Correct Answer - D | |
| 55. |
`int(dx)/(sinx+sqrt3.cosx)=`A. `log[tan((x)/(2)+(pi)/(2))]+c`B. `(1)/(2).log[tan((x)/(2)+(pi)/(6))]+c`C. `log[cot((x)/(2)+(pi)/(6))]+c`D. `(1)/(2).log[cot((x)/(2)+(pi)/(6))]+c` |
| Answer» Correct Answer - B | |
| 56. |
If `int(1)/(sin(x-a)cos(x-a))dx=log[f(x)]+c`, then `f(x)=`A. `sin(x-a)`B. `cos(x-a)`C. `tan(x-a)`D. `cot(x-a)` |
| Answer» Correct Answer - C | |
| 57. |
`int(1)/(sqrt((log.(1)/(2))^(2)-x^(2)))dx=`A. `sin^(-1)((x)/(log2))+c`B. `-sin^(-1)((x)/(log2))+c`C. `-2sin^(-1)((log2)/(x))+c`D. `2.sin^(-1)((log2)/(x))+c` |
| Answer» Correct Answer - A | |
| 58. |
`int(1)/(x^(2)+6x+10)dx=`A. `(1)/(2)log[(x+3)/(x-3)]+c`B. `sin^(-1)(x+3)+c`C. `log(x+sqrt(x+3))+c`D. `tan^(-1)(x+3c` |
| Answer» Correct Answer - D | |
| 59. |
`int(1)/(2x+log(x^(x)))dx=`A. `(log2).log(logx)`B. `log(2+logx)`C. `log(2.logx)`D. `2+log(logx)` |
| Answer» Correct Answer - B | |
| 60. |
`intsqrt(1+sinx)dx`A. `2(sin.(x)/(2)-cos.(x)/(2))`B. `2(sin.(x)/(2)+cos.(x)/(2))`C. `2(cos.(x)/(2)-sin.(x)/(2))`D. `sqrt2(cos.(x)/(2)-sin.(x)/(2))+c` |
| Answer» Correct Answer - A | |
| 61. |
`int(sinx)/(sqrt(9-sin^(2)x))dx=`A. `log(sinx+sqrt(9-sin^(2)x))+c`B. `-log(cosx-sqrt(9-sin^(2)x))+c`C. `log(sinx+sqrt(8+cos^(2)x))+c`D. `-log(sqrt(1-sin^(2)x)+sqrt(9-sin^(2)x))+c` |
| Answer» Correct Answer - D | |
| 62. |
`int((1+3x^(3))^(2//3))/(x^(6))dx=`A. `((1+3x^(3))^(3//5))/(3x^(3))+c`B. `(-(1+3x^(3))^(5//3))/(5x^(5))+c`C. `((x^(-3)+3)^(3//2))/(5x^(5))+c`D. `(-(x^(-3)+3)^(5//3))/(3x^(5))+c` |
| Answer» Correct Answer - B | |
| 63. |
`int(e^(2x)+1)/(e^(2x)-1)dx=`A. `log(e^(x)-e^(-x))+alpha`B. `log(e^(x)+e^(-x))+beta`C. `log(e^(2x)-1)+x+gamma`D. `log(e^(2x)-1)+delta` |
| Answer» Correct Answer - A | |
| 64. |
The value of `int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2))` is equal toA. `sin^(-1)[(1)/(c)(ax+(b)/(x))]+k`B. `sin^(-1)[(1)/(c)(ax^(2)+(b)/(x^(2))]+k`C. `cos^(-1)[(1)/(c)(ax+(b)/(x))]+k`D. `cos^(-1)[(1)/(c)(ax^(2)+(b)/(x^(2)))]+k` |
| Answer» Correct Answer - A | |
| 65. |
`int sin x d(cosx)=`A. `(sin2x)/(2)+c`B. `(1)/(2)((sin2x)/(2)-x)+c`C. `(1)/(2)((sin2x)/(2)+x)+c`D. `(cos2x)/(2)+c` |
| Answer» Correct Answer - B | |
| 66. |
`int(tanx)/(secx+tanx)dx=`A. `secx-tanx+c`B. `x+secx+tanx`C. `x-secx+tanx`D. `x+secx-tanx` |
| Answer» Correct Answer - D | |
| 67. |
`int(1)/(xsin^(2)(logx))dx=`A. `tan(logx)`B. `-cot(logx)`C. `cos(2logx)+c`D. `-log(cotx)` |
| Answer» Correct Answer - B | |
| 68. |
`int(cosx)/(sqrt(17-cos^(2)x))dx=`A. `log(sinx-sqrt(17-cos^(2)x))+c`B. `log(sinx+sqrt(16+sin^(2)x))+c`C. `log(sqrt(17-cos^(2)x)-sqrt(1-cos^(2)x))+c`D. `4tan^(-1)(2cos x)+c` |
| Answer» Correct Answer - B | |
| 69. |
`int(1)/(cosx sqrt(cos2x))dx=`A. `sqrt2[sqrt(tanx)+(1)/(5)tan^(5//2)x]+c`B. `sqrt2[sqrt(cotx)+(1)/(5)tan^(5//2)x]+c`C. `sqrt2[sqrt(tanx)-(1)/(5)tan^(5//2)x]+c`D. `sin^(-1)(tanx)+c` |
| Answer» Correct Answer - D | |
| 70. |
If `int(sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)dx=A sin 2x+B,` then A =A. `-(1)/(2)`B. `(1)/(2)`C. `-1`D. 1 |
| Answer» Correct Answer - A | |
| 71. |
`int(sinx)/(sqrt(cos2x))dx=`A. `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(cos2x)]+c`B. `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(2sin^(2)x-1)]+c`C. `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(1-2cos^(2)x)]+c`D. `(-1)/(sqrt2)sec^(-1)(2cos^(2)x-1)+c` |
| Answer» Correct Answer - A | |
| 72. |
`intsin4x. Sin 7xdx=`A. `(sin3x)/(6)-(sin11x)/(22)`B. `(sin3x)/(6)+(sin11x)/(22)`C. `(cos3x)/(6)-(cos11x)/(22)`D. `(cos4x.cos7x)/(28)` |
| Answer» Correct Answer - A | |
| 73. |
`int(4x+6)/(sqrt(x^(2)+3x-2))dx=`A. `2sqrt(x^(2)+3x-2)`B. `4sqrt(x^(2)+3x-2)`C. `sqrt(x^(2)+3x-2)`D. `(x^(2)+3x-2)^(3//2)` |
| Answer» Correct Answer - B | |
| 74. |
`int(sinx)/(sin(x-a))dx-int(cosx)/(cos(x-a))dx=`A. `2sina log(tanx)+c`B. `2sinalog[tan(x-a)]+c`C. `2log[tan(x-a)]+c`D. `2cosa log[sec(x-a)]+c` |
| Answer» Correct Answer - B | |
| 75. |
`int(1)/(sinxsin(x+a))dx=`A. `cos a log[(sinx)/(sin(x+a))]+c`B. `cos alog[(sinx)/(sin(x+a))]+c`C. `cosx alog [(sec(x+a))/(secx)]+c`D. `cos a log[(secx)/(sec(x+a))]+c` |
| Answer» Correct Answer - B | |
| 76. |
`int(1)/(x^(2)+(a+b)x+ab)dx=`A. `(1)/(b-a)log[(x+b)/(x+a)]+c`B. `(1)/(b-a)log[(x+a)/(x+b)]+c`C. `(1)/(ab)tan^(-1)[(ax)/(b)]+c`D. `(1)/(ab)tan^(-1)[(bx)/(a)]+c` |
| Answer» Correct Answer - B | |
| 77. |
`int(1)/(x^(4)+(a^(2)+b^(2))x^(2)+a^(2)b^(2))dx=`A. `(1)/(a^(2)-b^(2))[(1)/(a)tan^(-1)((x)/(a))-(1)/(b)tan^(-1)((x)/(b))]+c`B. `(1)/(a^(2)-b^(2))[tan^(-1)((x)/(a))-tan^(-1)((x)/(b))]+c`C. `(1)/(b^(2)-a^(2))[(1)/(a)tan^(-1)((x)/(a))-(1)/(b)tan^(-1)((x)/(b))]+c`D. `2x[log(x^(2)+a^(2))-log(x^(2)+b^(2))]+c` |
| Answer» Correct Answer - C | |
| 78. |
`int(1)/(x^(3)(1-x))dx=`A. `log((x)/(1-x))-(2x+1)/(2x^(2))+c`B. `log((1-x)/(x^(3)))+c`C. `log((x^(3))/(1-x))+c`D. `(x^(-2))/(-2)-log(1-x)+c` |
| Answer» Correct Answer - A | |
| 79. |
`int(1)/(x(1+x^(3)))dx=`A. `log((1+x^(3))/(x^(3)))+c`B. `log((x^(3))/(1+x^(3)))+c`C. `(1)/(3)log((x^(3))/(1+x^(3)))+c`D. `3log((x^(3))/(1+x^(3)))+c` |
| Answer» Correct Answer - C | |
| 80. |
`int(1)/(x(1-x^(5)))dx=`A. `(-1)/(5)log((x^(5))/(1-x^(5)))+c`B. `(1)/(5)log((x^(5))/(1-x^(5)))+c`C. `-5log((x^(5))/(1-x^(5)))+c`D. `logx-x-(x^(6)/(6))+c` |
| Answer» Correct Answer - B | |
| 81. |
`int(2x^(2)+a^(2))/(x^(2)(x^(2)+a^(2)))dx=`A. `(-1)/(x)+(1)/(a)log((x)/(a))+c`B. `(-1)/(x)-tan^(-1)((x)/(a))+c`C. `(-1)/(x)+(1)/(a)tan^(-1)((x)/(a))+c`D. `2x^(2)+(a^(2))/(2)tan^(-1)((x)/(a))+c` |
| Answer» Correct Answer - C | |
| 82. |
`int x/(1+x^4) dx`A. `(1)/(2)tan^(-1)(x^(2))+c`B. `(1)/(4)log(1+x^(4))+c`C. `(1)/(3)log(1+x^(3))+c`D. `(1)/(4x^(2))log(1+x^(4))+c` |
| Answer» Correct Answer - A | |
| 83. |
If `int(x^(2)+a^(2))/(x+a)dx=((x+a)^(2))/(2)+hx+klog(x+a)+c`, then `2ah+k=`A. `a^(2)`B. `2a^(2)`C. `-2a^(2)`D. 0 |
| Answer» Correct Answer - D | |
| 84. |
`int ((sin^2xcos^2x)/(sin^3x+cos^3x))dx`=A. `(1)/(3(1+tan^(3)x))+c`B. `(-1)/(3(1+tan^(3)x))+c`C. `(1)/(1+tan^(3)x)+c`D. `(-1)/(1+tan^(3)x)+c` |
| Answer» Correct Answer - B | |
| 85. |
`int(secxcosecx)/(log(tanx))dx=`A. `(1)/(2)[log(tanx)]^(2)+c`B. `log[log(tanx)]+c`C. `(-1)/(log(tanx))+c`D. `log[tan(logx)]+c` |
| Answer» Correct Answer - B | |
| 86. |
`int5sin^(3//2)x cos x dx=`A. `5sin^(5//2)x+c`B. `2sin^(5//2)x+c`C. `(5)/(2)sin^(5//2)x+c`D. `(2)/(5)sin^(5//2)x+c` |
| Answer» Correct Answer - B | |
| 87. |
`int5(2x^(2)+3x-4)^(2//3)(4x+3)dx=`A. `3(2x^(2)+3x-4)^(-1//3)`B. `sqrt(2x^(2)+3x-4)`C. `3(2x^(2)+3x-4)^(5//3)`D. `(2x^(2)+3x-4)^(2//3)` |
| Answer» Correct Answer - C | |
| 88. |
`int(1-cossqrtx)/(sqrtx)dx=A. `sqrtx-2sin sqrtx`B. `2(sqrtx-sin sqrtx)+c`C. `2sqrtx+sin sqrtx`D. `sqrtx+2sin sqrtx+c` |
| Answer» Correct Answer - B | |
| 89. |
`int(1)/(x+x^(-3))dx=`A. `tan^(-1)(x^(2))+c`B. `log(x+x^(-3))+c`C. `(-1)/(1+x^(4))+c`D. `0.25log(1+x^(4))+c` |
| Answer» Correct Answer - D | |
| 90. |
`int(1)/(sqrtx+x)dx=`A. `log((sqrtx)/(1+sqrtx))`B. `log(1+sqrtx)+c`C. `2log(1+sqrtx)`D. `(2)/(3)x^(3//2)-(x^(2))/(2)+c` |
| Answer» Correct Answer - C | |
| 91. |
`int((7-3sqrtx)^(5//2))/(sqrtx)dx=`A. `(-4)/(21)(7-3sqrtx)^(7//2)`B. `(5)/(2)(7-3sqrtx)^(3//2)`C. `(21)/(4)(7-3sqrtx)^(7//2)`D. `(21)/(4)(7-3x)^(2//7)` |
| Answer» Correct Answer - A | |
| 92. |
If `intf(x)dx=h(x) and intf(x)dx=g(x)` as well, thenA. `h(x)=g(x)`B. `h(x)+g(x)`= constantC. `h(x).g(x)=`constantD. `h(x)-g(x)=` constant |
| Answer» Correct Answer - D | |
| 93. |
`intx sqrtx dx=`A. `1.5sqrtx`B. `2.5x^(1.5)`C. `0.4x^(2.5)`D. `0.4 x sqrtx` |
| Answer» Correct Answer - C | |
| 94. |
`int(x x^(3)x^(5)x^(7)…" to n terms")dx=`A. `((x^(n+1))/(n+1))^(2)+c`B. `(x^(2n+1))/(2n+1)+c`C. `(x^(n^(2)+1))/(n^(2)+1)+c`D. `(x^(n(n+1)))/(2)+c` |
| Answer» Correct Answer - C | |
| 95. |
`intx(x+1)(x+2)dx=`A. `x^(4)+x^(3)+x^(2)+c`B. `(x^(4))/(4)+(x^(3))/(3)+(x^(2))/(2)+c`C. `x^(4)+x^(3)+(x^(2))/(2)+c`D. `(x^(4))/(4)+x^(3)+x^(2)+c` |
| Answer» Correct Answer - D | |
| 96. |
`int((x+1)(x+2))/(x)dx=`A. `x^(2)+x+logx+c`B. `(x^(2))/(2)+3x+2logx+c`C. `2x^(2)+(x)/(3)+(1)/(2)logx+c`D. `(x^(2))/(2)+3logx+2x+c` |
| Answer» Correct Answer - B | |
| 97. |
`intx cos x dx=`A. `sinx+x cos x+c`B. `x sin x+cosx+c`C. `cos x-x sin x+c`D. does not exist |
| Answer» Correct Answer - B | |
| 98. |
`intx tanx dx=`A. `x tanx+cotx+c`B. `xlog(secx)+c`C. `x-log(cosx)+c`D. does not exist |
| Answer» Correct Answer - D | |
| 99. |
`int(1)/(x sqrt(x^(6)-16))dx=`A. `sec^(-1)((x^(3))/(4))+c`B. `(1)/(12)sec^(-1)((x^(3))/(4))+c`C. `(1)/(3)sec^(-1)((x^(3))/(4))+c`D. `(1)/(3)sin^(-1)((x^(3))/(4))+c` |
| Answer» Correct Answer - C | |
| 100. |
`int(x+(1)/(x))^(2)dx=`A. `(x^(3))/(3)-(1)/(x)+2x+x`B. `2x-(x^(3))/(3)-(1)/(x)+c`C. `(x^(3))/(3)+(1)/(x)-2x+c`D. `(x^(3))/(3)-2x-(1)/(x)+c` |
| Answer» Correct Answer - A | |