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.
| 51. |
`int_(0) ^(pi//2) (cos^(2) x)/(sin x + cos x ) dx = `A. `1/(2sqrt(2)) log ((sqrt(2)-1)/(sqrt(2)+1))`B. `1/(2sqrt(2)) log ((sqrt(2)+1)/(sqrt(2)-1))`C. `1/(sqrt(2)) log ((sqrt(2)-1)/(sqrt(2)+1))`D. `1/(sqrt(2)) log ((sqrt(2)+1)/(sqrt(2)-1))` |
| Answer» Correct Answer - B | |
| 52. |
`int_(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta = ` |
| Answer» Correct Answer - A | |
| 53. |
`int_(0)^(pi//4)x^(2) sinx " " dx = `A. `sqrt(2) + 2 + pi/(2sqrt(2) )+ pi^(2) / (16sqrt2) `B. `sqrt(2) + 2 -pi/(2sqrt(2) )+ pi^(2) / (16sqrt2) `C. `sqrt(2) - 2 +pi/(2sqrt(2) )+ pi^(2) / (16sqrt2) `D. `sqrt(2) - 2 +pi/(2sqrt(2) )- pi^(2) / (16sqrt2) ` |
| Answer» Correct Answer - D | |
| 54. |
`int_(0) ^(pi//2) cos^(2) theta d theta =` |
| Answer» Correct Answer - C | |
| 55. |
`int_(0)^(pi//2) (sinx )/(sin x + cos x ) dx=`A. `pi/4`B. `pi/2`C. `(3pi)/4`D. `(3pi)/2` |
| Answer» Correct Answer - A | |
| 56. |
`int_(-pi//4)^(pi//4) dx/(1+sin x)=`A. `2- sqrt(2)`B. `2 + sqrt(2)`C. `sqrt(2)`D. 2 |
| Answer» Correct Answer - D | |
| 57. |
`int_(0)^(pi) dx/(1-sin x)=` |
| Answer» Correct Answer - D | |
| 58. |
`int_(0)^(pi//2) x^(2) sin x " " dx= `A. `pi + 2`B. `pi- 2`C. `pi/2+1`D. `pi/2 -1` |
| Answer» Correct Answer - B | |
| 59. |
`int _(0) ^(2) x e^(2) dx= `A. `e^(2) -1`B. `e-1`C. `e^(2) + 1`D. `e +1` |
| Answer» Correct Answer - C | |
| 60. |
`int _(0)^(pi//2)(dx)/(1+ cos x)`A. 1B. `pi`C. 2D. `2pi` |
| Answer» Correct Answer - A | |
| 61. |
The value of the integral ` int _(0)^(pi//2) (sin ^(100)x - cos^(100)x) dx ` isA. `1/100`B. `100/(100)^(100)`C. `pi/100`D. `0` |
| Answer» Correct Answer - D | |
| 62. |
`int_(-pi//4)^(pi//4) dx/(1-sin x)=`A. 2B. `-2`C. `sqrt(2)`D. `-sqrt(2)` |
| Answer» Correct Answer - A | |
| 63. |
` int _(0)^(pi//6) (2+3x^(2))cos 3 xdx ` is equal toA. `4/9-pi^(2)/18`B. `4/9+pi^(2)/18`C. `4/9-pi^(2)/36`D. `4/9+pi^(2)/36` |
| Answer» Correct Answer - D | |
| 64. |
`int _(0) ^(pi//2) (sin x +cos x)/ sqrt(1+sin 2x )" "dx=` |
| Answer» Correct Answer - D | |
| 65. |
`int_(0)^(pi//2)(sin x - cos x)/(1-sin x cos x)dx=`A. `pi/2`B. `(3pi)/2`C. `pi`D. 0 |
| Answer» Correct Answer - D | |
| 66. |
`int _(0) ^(pi//2) sqrt(1-cos x )" "dx=`A. `sqrt^(2)-2`B. `sqrt(2) +2`C. `2sqrt(2)-2`D. `2sqrt(2) +2` |
| Answer» Correct Answer - C | |
| 67. |
`int_(0)^(pi) dx/(3+2sin x + cos x) = `A. `(-pi)/2`B. `pi/2`C. `(-pi)/4`D. `pi/4` |
| Answer» Correct Answer - D | |
| 68. |
The value of `int_(1)^(4)(dx)/(xsqrt(x))` is-A. `(1)/(2)`B. `(3)/(2)`C. 2D. 1 |
| Answer» Correct Answer - D | |
| 69. |
if `f(x) = a+bx +cx^(2)`, then what is `int_(0)^(1)f(x) dx` equal to ?A. `f (0) + 4 f (1/2) + f(1)`B. `1/6(f (0) + 4 f (1/2) + f(1))`C. `1/3(f (0) + 4 f (1/2) + f(1))`D. `1/2(f (0) + 4 f (1/2) + f(1))` |
| Answer» Correct Answer - B | |
| 70. |
`int_(1)^(2) (dx)/(2x+5)= `A. `1/2 log (5/7)`B. `1/2 log (7/5)`C. `2 log(5/7)`D. `2 log (7/5)` |
| Answer» Correct Answer - B | |
| 71. |
`int_(-2)^(3) (dx)/(x+5)= `A. `log(2/3)`B. `log(4/3)`C. `log(8/3)`D. `log16/3)` |
| Answer» Correct Answer - C | |
| 72. |
The value of `int_(2)^(3)(dx)/(2x+1)` is-A. `log.(7)/(5)`B. `2log.(7)/(5)`C. `(1)/(2)log.(7)/(5)`D. `(3)/(2)log.(7)/(5)` |
| Answer» Correct Answer - C | |
| 73. |
The value of `int_(1)^(2)(x+1)/(x^(3))dx` is-A. `(7)/(8)`B. `(7)/(4)`C. `(5)/(8)`D. `(5)/(4)` |
| Answer» Correct Answer - A | |
| 74. |
`int_(0)^(2) (dx)/(4+x-x^(2))= `A. `1/(2sqrt(17))log ((5+sqrt(17))/(5-sqrt(17)))`B. `1/(2sqrt(17))log ((5-sqrt(17))/(5+sqrt(17)))`C. `1/(sqrt(17))log ((5+sqrt(17))/(5-sqrt(17)))`D. `1/(sqrt(17))log ((5-sqrt(17))/(5+sqrt(17)))` |
| Answer» Correct Answer - C | |
| 75. |
`int_0^a(dx)/(x+sqrt(a^2-x^2))`A. `pi/2`B. `pi/4`C. `(3pi)/2`D. `(3pi)/4` |
| Answer» Correct Answer - B | |
| 76. |
If `I_(1) int_(1)^(2) dx/sqrt(1+x^(2)) and I_(1) = int _(1)^(2) dx/x` thenA. `I_(1)gtI_(2)`B. `I_(1)ltI_(2)`C. `I_(1)=I_(2)`D. `I_(1)gt2I_(2)` |
| Answer» Correct Answer - B | |
| 77. |
`int_(2)^(3) x/(x^(2)-1) dx = `A. `1/2 log (3/8)`B. `1/2 log (8/3)`C. `1/2 log (3/4)`D. `1/2 log (4/3)` |
| Answer» Correct Answer - B | |
| 78. |
`int_(0)^(a)(dx)/((ax+a^(2)-x^(2)))`A. `(-1)/(asqrt(5))log((7+3sqrt(5))/2)`B. `(1)/(asqrt(5))log((7+3sqrt(5))/2)`C. `(-2)/(asqrt(5))log((7+3sqrt(5))/2)`D. `(2)/(asqrt(5))log((7+3sqrt(5))/2)` |
| Answer» Correct Answer - B | |
| 79. |
`int_0^1sqrt((1-x)/(1+x))dx`A. `pi/2 + 1`B. `pi/2-1`C. `pi/2+2`D. `pi/2-2` |
| Answer» Correct Answer - B | |
| 80. |
Evaluate the following : `int_(1)^(2)(x^(2))/(x^(2)+4x+3)dx`A. `1-2log (8/10) + 5/2 log (6/5)`B. `1+2log (8/10) - 5/2 log (6/5)`C. `1+2log (8/10) + 5/2 log (6/5)`D. `1-2log (8/10) - 5/2 log (6/5)` |
| Answer» Correct Answer - C | |
| 81. |
`int_(-1)^(1) (1+x^(3))/(9-x^(2)) dx =`A. `2/3 log 2`B. `1/6 log 2`C. `1/3 log 2`D. `3/2 log 2` |
| Answer» Correct Answer - C | |
| 82. |
`int_(0)^(1)x^(2)sqrt(1-x^(2))dx=`A. `8/21`B. `16/21`C. `8/105`D. `16/105` |
| Answer» Correct Answer - D | |
| 83. |
`int_(-1//2) ^(1//2) (1+x^(3)) /(4-x^(2)) dx =`A. `1/2 log (5/3)`B. `1/2 log (3/5)`C. `1/4 log (5/3)`D. `1/4log (3/5)` |
| Answer» Correct Answer - A | |
| 84. |
`int_(0)^(3) abs(5x-3) dx=`A. `(-13)/10`B. `13/10`C. `(-13)/5`D. `13/5` |
| Answer» Correct Answer - B | |
| 85. |
`int_(0)^(2pi)(sinx+ abs(sinx)) dx =`A. oB. 1C. 4D. 8 |
| Answer» Correct Answer - C | |
| 86. |
`int_(0)^(pi//2) abs(sinx-cosx) dx=` |
| Answer» Correct Answer - C | |
| 87. |
`int_(0)^(pi//2) abs(sin(x-pi/4)) dx=`A. `2+sqrt(2)`B. `2-sqrt(2)`C. `-2+sqrt(2)`D. `-2-sqrt(2)` |
| Answer» Correct Answer - B | |
| 88. |
`int_(-2)^(2) abs(1-x^(2)) dx=`A. 2B. 4C. 6D. 8 |
| Answer» Correct Answer - B | |
| 89. |
`int_(0)^(pi)x sin^(2)x dx=`A. `pi/2`B. `pi/4`C. `pi^(2)/2`D. `pi^(2)/4` |
| Answer» Correct Answer - D | |
| 90. |
`int_(0)^( pi/2)sin^(2)x cos x dx`A. `(-2pi)/5`B. `(-pi)/5`C. `(2pi)/5`D. `pi/5` |
| Answer» Correct Answer - D | |
| 91. |
`int _(0)^(pi//2) dx/(4cosx+9sinx)=`A. `1/sqrt(97) log ((13-sqrt(97))/(13+sqrt(97)))`B. `1/sqrt(97) log ((13+sqrt(97))/(13-sqrt(97)))`C. `1/(2sqrt(97)) log ((13-sqrt(97))/(13+sqrt(97)))`D. `1/(2sqrt(97)) log ((13+sqrt(97))/(13-sqrt(97)))` |
| Answer» Correct Answer - B | |
| 92. |
`int _(0)^(pi//2) dx/(5+4sinx)=`A. `1/3tan ^(-1)3`B. `2/3 tan ^(-1) 3`C. `1/3 tan ^(-1)(1/3)`D. `2/3tan^(-1)(1/3)` |
| Answer» Correct Answer - D | |
| 93. |
`int_(0)^(pi//2) (cosx )/ (1+sin^(2)x)dx=`A. `(-pi)/2`B. `pi/2`C. `(-pi)/4`D. `pi/4` |
| Answer» Correct Answer - D | |
| 94. |
`int_(0)^(pi//2)(sin x) / (1+ cos^(2) x ) dx = `A. `(-pi)/2`B. `pi/2`C. `(-pi)/4`D. `pi/4` |
| Answer» Correct Answer - D | |
| 95. |
`int_(0)^(pi//2)(sin xcos x) / (1+ sin^(4) x ) dx = `A. `pi/8`B. `(-pi)/8`C. `pi/4`D. `(-pi)/4` |
| Answer» Correct Answer - A | |
| 96. |
`int_(0)^(pi//4)(sin 2 x)/(sin^(4) x + cos^(4) x ) dx = `A. `pi/2`B. `pi/4`C. `(3pi)/2`D. `(3pi)/4` |
| Answer» Correct Answer - B | |
| 97. |
`int_(0)^(pi//2) cos^(5) x " " dx=`A. `(8pi)/15`B. `(5pi)/32`C. `(8)/15`D. `5/32` |
| Answer» Correct Answer - C | |
| 98. |
`int_(0)^(pi//2) sin^(4) x " " dx =`A. `(3pi)/8`B. `(3pi)/16`C. `(3pi)/3`D. `(3pi)/32` |
| Answer» Correct Answer - B | |
| 99. |
The value of `int_(0)^(1)(dx)/(x^(2)+1)` is-A. `(pi)/(2)`B. `(pi)/(4)`C. `pi`D. `(3pi)/(4)` |
| Answer» Correct Answer - B | |
| 100. |
Evaluate : `(i) int_(0)^(pi//2)cos^(3)xdx` `(ii) int_(0)^(pi//2)sin^(4)xdx`A. `2/3`B. `5/6`C. `(-2)/3`D. `(-5)/6` |
| Answer» Correct Answer - A | |