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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. |
Find the area common to two parabolas `x^2=4ay` and `y^2=4ax,` using integration.A. `(8a^(3))/(3)`B. `(16a^(2))/(3)`C. `(32a^(2))/(3)`D. `(64a^(2))/(3)` |
| Answer» Correct Answer - B | |
| 52. |
The area enclosed within the curve `|x|+|y|=1`, isA. 1B. 1.5C. 2D. 3 |
| Answer» Correct Answer - C | |
| 53. |
The area cut off from a parabola by any double ordinate is k time the corresponding rectangle contained by the double ordinate and its distance from the vertex. Find the value of k ?A. `2//3`B. `3//2`C. `1//3`D. 3 |
| Answer» Correct Answer - A | |
| 54. |
The area cut off a parabola `4y=3x^(2)` by the straight line `2y=3x+12` in square units, isA. 16B. 21C. 27D. 36 |
| Answer» Correct Answer - C | |
| 55. |
The area bounded by the curve `y=f(x)` (where `f(x) geq 0`), the co-ordinate axes & the line `x=x_1` is given by `x_1.e^(x_1)`. Therefore `f(x)` equalsA. `e^(x)`B. `xe^(x)`C. `xe^(x)-e^(x)`D. `xe^(x)+e^(x)` |
| Answer» Correct Answer - C | |
| 56. |
The area bounded by the x-axis, the curve `y=f(x),`and the lines `x=1,x=b`is equal to `sqrt(b^2+1)-sqrt(2)`for all `b >1,`then `f(x)`is`sqrt(x-1)`(b) `sqrt(x+1)``sqrt(x^2+1)`(d) `x/(sqrt(1+x^2))`A. `sqrt(x-1)`B. `sqrt(x+1)`C. `sqrt(x^(2)-1)`D. `x//sqrt(x^(2)+1)` |
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Answer» Correct Answer - d We have, `underset(1)overset(b)(int)f(x)dx=sqrt(b^(2)+1)-sqrt2` Differentiating w.r. to b, we get `f(b)=(b)/(sqrt(b^(2)+1))impliesf(x)=(x)/(x^(2)+1)` |
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| 57. |
Let f(x) be a continuous function such that the area bounded by the curve `y=f(x),` the x-axis, and the lines `x=0` and `x=a is 1+(a^(2))/(2)sin` a. Then,A. `((pi)/(2))=1+(pi^(2))/(8)`B. `f(a)=1+(a^(2))/(2)sina`C. `f(a)=asina+1/2cosa`D. none of these |
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Answer» Correct Answer - c It is given that `underset(0)overset(a)(int)f(x)dx=1+(a^(2))/(2)sina` Differentiationg this with respect to a, we get `f(a)=a sina+(a^(2))/(2)cosa` |
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| 58. |
The area cut off from a parabola by any double ordinate is k time the corresponding rectangle contained by the double ordinate and its distance from the vertex. Find the value of k ?A. `1//2`B. `1//3`C. `2//3`D. 1 |
| Answer» Correct Answer - C | |
| 59. |
The area bounded by the curves `y=x e^x ,y=x e^(-x)`and the line `x=1`is`2/e s qdotu n i t s`(b) `1-2/e s qdotu n i t s``1/e s qdotu n i t s`(d) `1-1/e s qdotu n i t s`A. `(2)/(e)`B. `1-(2)/(e)`C. `(1)/(e)`D. `1-(1)/(e)` |
| Answer» Correct Answer - A | |
| 60. |
The area of the loop between the curve `y=asinx` and x-axis is (A) `a` (B) `2a` (C) `3a` (D) none of theseA. aB. 2aC. 3aD. 4a |
| Answer» Correct Answer - B | |
| 61. |
Find the area bounded by the x-axis, part of the curve `y=(1-8/(x^2))`, and the ordinates at `x=2a n dx=4.`If the ordinate at `x=a`divides the area into two equal parts, then find `adot`A. `2sqrt(2)`B. `pm 2sqrt(2)`C. `pm sqrt(2)`D. `pm2` |
| Answer» Correct Answer - B | |
| 62. |
The area of the region bouned by the curve `y=2x-x^(2)` and the line `y=x` isA. `1//2`B. `1//3`C. `1//4`D. `1//6` |
| Answer» Correct Answer - D | |
| 63. |
The area of the region lying between the line `x-y+2=0` and the curve `x=sqrt(y)`, isA. 9B. `9//2`C. `10//3`D. `5//2` |
| Answer» Correct Answer - C | |
| 64. |
The area of the region bounded by `y=sinx`, `y=cosx` in the first quadrant isA. `2(sqrt(2)-1)`B. `sqrt(3)+1`C. `2(sqrt(3)-1)`D. none of these |
| Answer» Correct Answer - A | |
| 65. |
Area between the curve `y=4+3x-x^(2)` and x-axis in square units , isA. `125//3`B. `125//4`C. `125//6`D. `25` |
| Answer» Correct Answer - C | |
| 66. |
If A is the area lying between the curve `y=sin x and ` x-axis between x=0 `and x=pi//2` . Area of the region between the curve `y=sin 2x and x`-axis in the same interval is given byA. `A//2`B. AC. `2A`D. `3//2A` |
| Answer» Correct Answer - B | |
| 67. |
Find the area bounded by the curve `y=(x-1)(x-2)(x-3)`lying between the ordinates `x=0a n dx=3.`A. `9//4`B. `11/4`C. `11//2`D. `7//4` |
| Answer» Correct Answer - B | |
| 68. |
If `A_1` is the area of the parabola `y^2=4 ax` lying between vertex and the latusrectum and `A_2` is the area between the latusrectum and the double ordinate `x=2 a`, then `A_1/A_2` is equal toA. `2sqrt(2)-1`B. `(2sqrt(2)+1)//7`C. `(2sqrt(2)-1)//7`D. none of these |
| Answer» Correct Answer - B | |
| 69. |
Find the area of the closed figure bounded by the curves `y=sqrt(x),y=sqrt(4-3x)a n dy=0`A. `4//9`B. `8//9`C. `19//9`D. `5//9` |
| Answer» Correct Answer - B | |
| 70. |
The area bounded by the curve `x = a cos^3t,, y = a sin^3t, ` is :A. `(3pia^(2))/(8)`B. `(3pia^(2))/(16)`C. `(3pia^(2))/(32)`D. `3pia^(2)` |
| Answer» Correct Answer - A | |
| 71. |
What is the area bounded by the curves `y=e^x ,y =e^-x` and the straight line `x=1` ?A. `e+(1)/(e)`B. `e-(1)/(e)`C. `e+(1)/(e)-2`D. none of these |
| Answer» Correct Answer - A | |
| 72. |
Area lying between the curves `y^2=4x`and `y = 2x`is(A) `2/3` (B) `1/3` (C) `1/4` (D) `3/4`A. `2//3`B. `1//3`C. `1//4`D. `1//2` |
| Answer» Correct Answer - B | |
| 73. |
The area of the closed figure bounded by the curves `y=cosx,y =1+(2)/(pi)x and x=pi//2,` isA. `(pi+4)/(4)`B. `(3pi-4)/(4)`C. `(3pi)/(4)`D. `(pi)/(4)` |
| Answer» Correct Answer - B | |
| 74. |
Area bounded by the curves `y=|x-1|, y=0` and `|x|=2` is (A) `4` (B) `8` (C) `5` (D) `9`A. 4B. 5C. 3D. 6 |
| Answer» Correct Answer - B | |
| 75. |
The area bounded by the curves `y=e^(x),y=e^(-x)` and `y=2`, isA. log (16/e)B. log(4/e)C. 2log(4/e)D. log(8/e) |
| Answer» Correct Answer - C | |
| 76. |
The area bounded by the y-axis, y=cos x and `y=sin x, 0 le x le pi//4`, isA. `2(sqrt(2)-1)`B. `sqrt(2)-1`C. `sqrt(2)+1`D. `sqrt(2)` |
| Answer» Correct Answer - B | |
| 77. |
Find the area included between the curves `x^2=4y` and `y^2=4x`.A. `4//3`B. `1//3`C. `16//3`D. `8//3` |
| Answer» Correct Answer - C | |
| 78. |
For which of the following values of `m`is the area of the regions bounded by the curve `y=x-x^2`and the line `y=m x`equal `9/2?``-4`(b) `-2`(c) 2(d) 4A. `-4.4`B. `-2,2`C. `2,4`D. `-2,3` |
| Answer» Correct Answer - B | |
| 79. |
The area of the region on place bounded by max `(|x|,|y|) le 1/2` isA. `1//2+ln 2`B. `3+ln 2`C. `31//4`D. `1+2ln 2` |
| Answer» Correct Answer - B | |
| 80. |
The area bound by the curve `y=sec x,` then x-axis and the lines `x=0 and x=pi//4,` isA. `log (sqrt2+1)`B. `log (sqrt2-1)`C. `1/2 log 2`D. `sqrt2` |
| Answer» Correct Answer - A | |
| 81. |
The area between the curve `y=xsin x ` and x-axis where `o le x le 2 pi` , isA. `2pi`B. `3pi`C. `4pi`D. `pi` |
| Answer» Correct Answer - C | |
| 82. |
The area of the region included between the regions satisfying `min(|x|,|y|) geq1` and `x^2+y^2leq5` isA. `(5)/(2)(sin^(-1)(2)/(sqrt(5))-sin^(-1)(1)/(sqrt(5)))-4`B. `10(sin^(-1)(2)/(sqrt(5))-sin^(-1)(1)/(sqrt(5)))-4`C. `(2)/(5)(sin^(-1)(2)/(sqrt(5))-sin^(-1)(1)/(sqrt(5)))-4`D. `15(sin^(-1)(2)/(sqrt(5))-sin^(-1)(1)/(sqrt(5)))-4` |
| Answer» Correct Answer - B | |
| 83. |
If denotes the area bounded by `f(x)=|(sin x+ cos x)/(x)|` x-axis , `x=pi` and `x=3x` , thenA. `1 lt A lt 2`B. `0 lt A lt 2`C. `2 lt A lt 3`D. none of these |
| Answer» Correct Answer - D | |
| 84. |
Area (in square units) of the region bounded by `[x]^(2)=[y]^(2)` for `x in [1,5]` ,(where [`*`] denotes the greatest integer function) isA. 4B. 8C. 5D. 10 |
| Answer» Correct Answer - B | |
| 85. |
Find the area of the region bounded by the curves `y=x^2 and y = sec^-1[-sin^2x],` where [.] denotes G.I.F.A. `(1)/(3)(4-pi)^(3//2)`B. `(8(4-pi)^(3//2)`C. `(8)/(3)(4-pi)^(3//2)`D. `(8)/(3)(4-pi)^(1//2)` |
| Answer» Correct Answer - C | |
| 86. |
If A is the area between the curve `y=sin x` and x-axis in the interval `[0,pi//4]` , then in the same interval , area between the curve `y=cos x and ` x-axis, isA. AB. `pi//2-A`C. `1-A`D. `A-1` |
| Answer» Correct Answer - C | |
| 87. |
The area (in square units) bounded by curves y=sinx between the ordinates x=0, `x=pi` and the x-axis , isA. 2B. 4C. 3D. 1 |
| Answer» Correct Answer - A | |
| 88. |
The area bounded by the curves `y=f(x),`the x-axis, and the ordinates `x=1a n dx=b`is `(b-1)sin(3b+4)dot`Then `f(x)`is.`(x-1)cos(3x+4)``sin(3x+4)``sin(3x+4)+3(x-1)cos(3x+4)`None of theseA. `(x-1)cos (3x+4)`B. `sin(3x+4)`C. `sin(3x+4)+3(x-1)`D. none of these |
| Answer» Correct Answer - C | |