99 + Interview Questions in APPLICATIONS-OF-DEFINITE-INTEGRALS IN GENERAL AWARENESS Page 2 InterviewSolution

51.	`y=3-2x-x^(2), … x=-1, x = 2`A. 9B. 3C. 25D. 36
Answer» Correct Answer - B

Discussion

52.	Area bounded between the curve `x^(2)=y` and the line y = 4x isA. `(32)/(3)`B. `(2)/(3)`C. `(3)/(2)`D. `(1)/(7)`
Answer» Correct Answer - A

Discussion

53.	The area bounded by the x-axis and the curve `y = 4x - x^2 - 3` isA. `(3)/(2)`B. `(3)/(4)`C. `(4)/(3)`D. 7
Answer» Correct Answer - C

Discussion

54.	Area between the parabola `y^(2)=x` and the line x = 3 isA. `4sqrt(3)`B. `2sqrt(3)`C. `6sqrt(3)`D. `5sqrt(3)`
Answer» Correct Answer - A

Discussion

55.	x=0 एवं `x=2pi` के मध्य वक्र `y=cos x` से घिरे क्षेत्र का क्षेत्रफल ज्ञात कीजिए \|A. 2B. 4C. 3D. 5
Answer» Correct Answer - B

Discussion

56.	x=0 एवं `x=2pi` के मध्य वक्र `y=cos x` से घिरे क्षेत्र का क्षेत्रफल ज्ञात कीजिए \|A. 2B. 4C. 6D. 8
Answer» Correct Answer - D

Discussion

57.	`y=(x-1)(2-x), ….. x= 1, x = 2`A. `(1)/(3)`B. `(1)/(4)`C. `(1)/(5)`D. `(1)/(6)`
Answer» Correct Answer - D

Discussion

58.	`y=sin x, ….. x = 0, x = (2pi)/(3)`A. `(1)/(3)`B. `(3)/(2)`C. 1D. 2
Answer» Correct Answer - B

Discussion

59.	Area under the curve `y=sqrt(16-x^(2))` between x = 0 and x = 4 in the first quadrant isA. `8pi`B. `16pi`C. `4pi`D. `(8pi)/(3)`
Answer» Correct Answer - C

Discussion

60.	The area bounded by the curve `y = 2x - x^(2)` and the line y = - x isA. `(9)/(2)`B. `(43)/(6)`C. `(35)/(6)`D. `pi^(2)`
Answer» Correct Answer - A

Discussion

61.	The area bounded by the curve `x=2-y-y^(2)` and Y-axis isA. `(9)/(2)`B. `(7)/(2)`C. `(5)/(2)`D. `(3)/(2)`
Answer» Correct Answer - A

Discussion

62.	What is the area bounded by the curves `y=e^x ,y =e^-x` and the straight line `x=1` ?A. `e+(1)/(e )+2`B. `e+(1)/(e )-2`C. `e-(1)/(e )+2`D. `e-(1)/(e )-2`
Answer» Correct Answer - B

Discussion

63.	Area bounded by the curve `y=2+x, y=2-x` and x = 2 isA. 3B. 4C. 8D. None of these
Answer» Correct Answer - B

Discussion

64.	If `a lt b`, then area under the curve `xy=c^(2)`, the X-axis and the ordinates at a and b isA. `c^(2).log((a)/(b))`B. `c^(2).log((b)/(a))`C. `c^(2).log(ab)`D. `c^(2).log(b-a)`
Answer» Correct Answer - B

Discussion

65.	If the area above the x-axis, bounded by the curves `y = 2^(kx)` and x = 0, and x = 2 is `3/(log_e(2))`, then the value of k isA. `(1)/(2)`B. 1C. `-1`D. 2
Answer» Correct Answer - B

Discussion

66.	`xy=c^(2), …. x=c, x= 2c` where c>0A. `2c^(2)`B. `c^(2).log 2`C. `2c.log 32`D. `c^(2).log 4`
Answer» Correct Answer - B

Discussion

67.	Area bounded by the curve `y=x^(2)+x-6` and the X-axis isA. `(127)/(6)`B. `(225)/(6)`C. `(125)/(6)`D. `(123)/(6)`
Answer» Correct Answer - C

Discussion

68.	`xy=c^(2), …. x=c, x= 2c`A. `2c^(2)`B. `c^(2).log2`C. `2x.log2`D. `c^(2).log 4`
Answer» Correct Answer - B

Discussion

69.	The ratio of the areas between the curves `y=cos x and y=cos 2x` and x-axis from `x=0` to `x=pi/3` isA. `1 : 2`B. `2 : 1`C. `sqrt(3) : 1`D. `1 : sqrt(3)`
Answer» Correct Answer - B corrrect option is B

Discussion

70.	Area of the region bounded by the curves y = tan x, y = cot x and X-axis in `0 le x le (pi)/(2)` isA. 3 log 2B. log 2C. 2 log 2D. `(pi)/(8)` log 2
Answer» Correct Answer - B

Discussion

71.	`y=sin^(2)x,…..x=0,x=(pi)/(4)`A. `(pi)/(8)-(1)/(4)`B. `(pi)/(4)-(1)/(8)`C. `(pi)/(32)`D. `(1)/(2)+(pi)/(4)`
Answer» Correct Answer - A

Discussion

72.	Area bounded by the parabola `x^(2)=16 y` and the line `x-2y=0` isA. `(16)/(3)`B. 6C. 10D. 24
Answer» Correct Answer - A

Discussion

73.	`y=x + sin x,…. x = 0, x=(pi)/(2)`A. `(pi)/(4)+1`B. `(pi)/(4)-1`C. `(pi^(2))/(4)+1`D. `(pi^(2))/(8)+1`
Answer» Correct Answer - D

Discussion

74.	Area bounded by parabola `x^(2)=y`, the Y-axis and the lines y = 0, y = 4 isA. `(8)/(3)`B. `(16)/(3)`C. 6D. 8
Answer» Correct Answer - B

Discussion

75.	Area bounded by the parabola `x^(2)=-4y`, the X-axis and the lines x = 0, x = 4 isA. `(16)/(3)`B. `(8)/(3)`C. 8D. 6
Answer» Correct Answer - A

Discussion

76.	the area formed by the lines `x^2-y^2=0` and `x+8=0` isA. 16B. 32C. 64D. 128
Answer» Correct Answer - C

Discussion

77.	Find the area included between the line `y=x` and the parabola `x^2=4y`.A. `(32)/(3)` sq. unitsB. `(23)/(3)` sq. unitsC. `(29)/(3)` sq. unitsD. `(31)/(3)` sq. units
Answer» Correct Answer - A

Discussion

78.	Area bounded by the lines `y=2x, y=4x` and x = 2 isA. 8B. 4C. 5D. 3
Answer» Correct Answer - B

Discussion

79.	FInd the area bounded by the curves `y^2=9xandx^2=9y.`A. 36B. 18C. 12D. 6
Answer» Correct Answer - C

Discussion

80.	Area bounded by the parabolas `y=4x^(2), 9y=x^(2)` and the line y = 2 isA. `(20sqrt(2))/(3)`B. `(10sqrt(2))/(3)`C. `(40sqrt(2))/(3)`D. None of these
Answer» Correct Answer - A

Discussion

81.	Area bounded by the curve `y = sin^(-1)x`, the X-axis and the line 2x = 1 isA. `(pi)/(12)+(sqrt(3))/(2)`B. `(pi)/(12)-(sqrt(3))/(2)`C. `(pi)/(12)-1`D. `(pi)/(12)+(sqrt(3))/(2)-1`
Answer» Correct Answer - D

Discussion

82.	The area of bounded by the curve `y = log x,` the x-axis and the line `x = e` isA. 4B. `(1)/(2)`C. 1D. `(1)/(e )`
Answer» Correct Answer - C

Discussion

83.	The area of bounded by the curve `y = log x,` the x-axis and the line `x = e` isA. eB. 1C. `1-(1)/(e )`D. `1+(1)/(e )`
Answer» Correct Answer - B

Discussion

84.	Area bounded by the curve `y = tan^(-1)x`, the X-axis and the line x = 1 isA. `(pi)/(4)+log sqrt(2)`B. `(pi)/(4)-sqrt(2)`C. `(pi)/(4)-log sqrt(2)`D. `(pi)/(2)-log sqrt(2)`
Answer» Correct Answer - C

Discussion

85.	Area under the curve `y = x sin x^(2)`, bounded by the lines x = 0 and `x= sqrt(pi//2)` isA. `0.3`B. `0.4`C. `0.5`D. 1
Answer» Correct Answer - C

Discussion

86.	Area bounded by the curve y = log x, the X-axis and the lines x = e, x = 2e isA. eB. log 2C. e . log 2D. 2e . log 2
Answer» Correct Answer - D

Discussion

87.	Area bounded by the curve y = log x, the X-axis and the line x = 1, x = 3 isA. 2 + log 27B. `-2 +` log 9C. `-2 +` log 27D. log 18
Answer» Correct Answer - C

Discussion

88.	Area bounded by the curve `y=e^(x)`, the X-axis and the lines x = 0, x = 2 isA. `e^(2)+1`B. `e-1`C. 2eD. `e^(2)-1`
Answer» Correct Answer - D

Discussion

89.	Area bounded by the curve xy = 16, the X-axis and the lines x = 2, x = 4 isA. 2 + 4 log 3B. 8 log 2C. 16 log 2D. 4 log 2
Answer» Correct Answer - C

Discussion

90.	Area bounded by the curve `xy=x+4`, the X-axis and the lines x = 1, x = 4 isA. 3 + 5 log 4B. 4 + 4 log 4C. 3 + 4 log 4D. 3 + 3 log 4
Answer» Correct Answer - C

Discussion

91.	Area bounded by the `xy^(2)=1`, X-axis and the lines x = 1, x = 2 isA. `4(sqrt(2)-1)`B. `4(sqrt(2)+1)`C. `2(sqrt(2)-1)`D. `2(sqrt(2)+1)`
Answer» Correct Answer - A

Discussion

92.	If a curve `y = asqrt(x)+bx` passes through the point (1,2) and the area bounded by the curve, line x = 4 and X-axis is 8 sq units, thenA. `a=3, b=1`B. `a=3, b=-1`C. `a=-3, b=1`D. `a=-3, b=-1`
Answer» Correct Answer - B

Discussion

93.	Area bounded by the line `2x+y=4`, the X-axis and the ordinate at `x=-2` isA. 12B. 15C. 16D. None of these
Answer» Correct Answer - C

Discussion

94.	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. `sqrt(2)`B. `2sqrt(2)`C. `3sqrt(2)`D. `4sqrt(2)`
Answer» Correct Answer - B

Discussion

95.	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).cos(3x+4)`D. none of these
Answer» Correct Answer - C

Discussion

96.	Area bounded by the curve `{:(y =x^(2)", if " x lt 0),(" "=2x", if " x ge 0","):}` and the line y = 9 isA. `(155)/(4)`B. `(153)/(4)`C. `(151)/(4)`D. None of these
Answer» Correct Answer - B

Discussion

97.	Area of the region enclosed between the curve `x =1-y^(2)` and the Y-axis isA. `(5)/(3)`B. `(4)/(3)`C. `(2)/(3)`D. `(1)/(3)`
Answer» Correct Answer - B

Discussion

98.	If the area of the region enclosed between the curve `y=3x^(2)-4x+c`, the X-axis and the ordinates at x = 1, x = 3 is 20, then : c =
Answer» Correct Answer - D

Discussion

99.	Smaller area enclosed by the circle `x^(2)+y^(2)=a^(2)` and the line `x+y=a` isA. `(a^(2))/(4)(pi-2)`B. `(a^(2))/(4)(pi+2)`C. `(a^(2))/(4)(2-pi)`D. `(a^(2))/(4)(pi-2)`
Answer» Correct Answer - A

Discussion

Explore topic-wise InterviewSolutions in .

`y=3-2x-x^(2), … x=-1, x = 2`A. 9B. 3C. 25D. 36

Area bounded between the curve `x^(2)=y` and the line y = 4x isA. `(32)/(3)`B. `(2)/(3)`C. `(3)/(2)`D. `(1)/(7)`

The area bounded by the x-axis and the curve `y = 4x - x^2 - 3` isA. `(3)/(2)`B. `(3)/(4)`C. `(4)/(3)`D. 7

Area between the parabola `y^(2)=x` and the line x = 3 isA. `4sqrt(3)`B. `2sqrt(3)`C. `6sqrt(3)`D. `5sqrt(3)`

x=0 एवं `x=2pi` के मध्य वक्र `y=cos x` से घिरे क्षेत्र का क्षेत्रफल ज्ञात कीजिए |A. 2B. 4C. 3D. 5

x=0 एवं `x=2pi` के मध्य वक्र `y=cos x` से घिरे क्षेत्र का क्षेत्रफल ज्ञात कीजिए |A. 2B. 4C. 6D. 8

`y=(x-1)(2-x), ….. x= 1, x = 2`A. `(1)/(3)`B. `(1)/(4)`C. `(1)/(5)`D. `(1)/(6)`

`y=sin x, ….. x = 0, x = (2pi)/(3)`A. `(1)/(3)`B. `(3)/(2)`C. 1D. 2

Area under the curve `y=sqrt(16-x^(2))` between x = 0 and x = 4 in the first quadrant isA. `8pi`B. `16pi`C. `4pi`D. `(8pi)/(3)`

The area bounded by the curve `y = 2x - x^(2)` and the line y = - x isA. `(9)/(2)`B. `(43)/(6)`C. `(35)/(6)`D. `pi^(2)`

The area bounded by the curve `x=2-y-y^(2)` and Y-axis isA. `(9)/(2)`B. `(7)/(2)`C. `(5)/(2)`D. `(3)/(2)`

What is the area bounded by the curves `y=e^x ,y =e^-x` and the straight line `x=1` ?A. `e+(1)/(e )+2`B. `e+(1)/(e )-2`C. `e-(1)/(e )+2`D. `e-(1)/(e )-2`

Area bounded by the curve `y=2+x, y=2-x` and x = 2 isA. 3B. 4C. 8D. None of these

If `a lt b`, then area under the curve `xy=c^(2)`, the X-axis and the ordinates at a and b isA. `c^(2).log((a)/(b))`B. `c^(2).log((b)/(a))`C. `c^(2).log(ab)`D. `c^(2).log(b-a)`

If the area above the x-axis, bounded by the curves `y = 2^(kx)` and x = 0, and x = 2 is `3/(log_e(2))`, then the value of k isA. `(1)/(2)`B. 1C. `-1`D. 2

`xy=c^(2), …. x=c, x= 2c` where c>0A. `2c^(2)`B. `c^(2).log 2`C. `2c.log 32`D. `c^(2).log 4`

Area bounded by the curve `y=x^(2)+x-6` and the X-axis isA. `(127)/(6)`B. `(225)/(6)`C. `(125)/(6)`D. `(123)/(6)`

`xy=c^(2), …. x=c, x= 2c`A. `2c^(2)`B. `c^(2).log2`C. `2x.log2`D. `c^(2).log 4`

The ratio of the areas between the curves `y=cos x and y=cos 2x` and x-axis from `x=0` to `x=pi/3` isA. `1 : 2`B. `2 : 1`C. `sqrt(3) : 1`D. `1 : sqrt(3)`

Area of the region bounded by the curves y = tan x, y = cot x and X-axis in `0 le x le (pi)/(2)` isA. 3 log 2B. log 2C. 2 log 2D. `(pi)/(8)` log 2

`y=sin^(2)x,…..x=0,x=(pi)/(4)`A. `(pi)/(8)-(1)/(4)`B. `(pi)/(4)-(1)/(8)`C. `(pi)/(32)`D. `(1)/(2)+(pi)/(4)`

Area bounded by the parabola `x^(2)=16 y` and the line `x-2y=0` isA. `(16)/(3)`B. 6C. 10D. 24

`y=x + sin x,…. x = 0, x=(pi)/(2)`A. `(pi)/(4)+1`B. `(pi)/(4)-1`C. `(pi^(2))/(4)+1`D. `(pi^(2))/(8)+1`

Area bounded by parabola `x^(2)=y`, the Y-axis and the lines y = 0, y = 4 isA. `(8)/(3)`B. `(16)/(3)`C. 6D. 8

Area bounded by the parabola `x^(2)=-4y`, the X-axis and the lines x = 0, x = 4 isA. `(16)/(3)`B. `(8)/(3)`C. 8D. 6

the area formed by the lines `x^2-y^2=0` and `x+8=0` isA. 16B. 32C. 64D. 128

Find the area included between the line `y=x` and the parabola `x^2=4y`.A. `(32)/(3)` sq. unitsB. `(23)/(3)` sq. unitsC. `(29)/(3)` sq. unitsD. `(31)/(3)` sq. units

Area bounded by the lines `y=2x, y=4x` and x = 2 isA. 8B. 4C. 5D. 3

FInd the area bounded by the curves `y^2=9xandx^2=9y.`A. 36B. 18C. 12D. 6

Area bounded by the parabolas `y=4x^(2), 9y=x^(2)` and the line y = 2 isA. `(20sqrt(2))/(3)`B. `(10sqrt(2))/(3)`C. `(40sqrt(2))/(3)`D. None of these

Area bounded by the curve `y = sin^(-1)x`, the X-axis and the line 2x = 1 isA. `(pi)/(12)+(sqrt(3))/(2)`B. `(pi)/(12)-(sqrt(3))/(2)`C. `(pi)/(12)-1`D. `(pi)/(12)+(sqrt(3))/(2)-1`

The area of bounded by the curve `y = log x,` the x-axis and the line `x = e` isA. 4B. `(1)/(2)`C. 1D. `(1)/(e )`

The area of bounded by the curve `y = log x,` the x-axis and the line `x = e` isA. eB. 1C. `1-(1)/(e )`D. `1+(1)/(e )`

Area bounded by the curve `y = tan^(-1)x`, the X-axis and the line x = 1 isA. `(pi)/(4)+log sqrt(2)`B. `(pi)/(4)-sqrt(2)`C. `(pi)/(4)-log sqrt(2)`D. `(pi)/(2)-log sqrt(2)`

Area under the curve `y = x sin x^(2)`, bounded by the lines x = 0 and `x= sqrt(pi//2)` isA. `0.3`B. `0.4`C. `0.5`D. 1

Area bounded by the curve y = log x, the X-axis and the lines x = e, x = 2e isA. eB. log 2C. e . log 2D. 2e . log 2

Area bounded by the curve y = log x, the X-axis and the line x = 1, x = 3 isA. 2 + log 27B. `-2 +` log 9C. `-2 +` log 27D. log 18

Area bounded by the curve `y=e^(x)`, the X-axis and the lines x = 0, x = 2 isA. `e^(2)+1`B. `e-1`C. 2eD. `e^(2)-1`

Area bounded by the curve xy = 16, the X-axis and the lines x = 2, x = 4 isA. 2 + 4 log 3B. 8 log 2C. 16 log 2D. 4 log 2

Area bounded by the curve `xy=x+4`, the X-axis and the lines x = 1, x = 4 isA. 3 + 5 log 4B. 4 + 4 log 4C. 3 + 4 log 4D. 3 + 3 log 4

Area bounded by the `xy^(2)=1`, X-axis and the lines x = 1, x = 2 isA. `4(sqrt(2)-1)`B. `4(sqrt(2)+1)`C. `2(sqrt(2)-1)`D. `2(sqrt(2)+1)`

If a curve `y = asqrt(x)+bx` passes through the point (1,2) and the area bounded by the curve, line x = 4 and X-axis is 8 sq units, thenA. `a=3, b=1`B. `a=3, b=-1`C. `a=-3, b=1`D. `a=-3, b=-1`

Area bounded by the line `2x+y=4`, the X-axis and the ordinate at `x=-2` isA. 12B. 15C. 16D. None of these

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. `sqrt(2)`B. `2sqrt(2)`C. `3sqrt(2)`D. `4sqrt(2)`

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).cos(3x+4)`D. none of these

Area bounded by the curve `{:(y =x^(2)", if " x lt 0),(" "=2x", if " x ge 0","):}` and the line y = 9 isA. `(155)/(4)`B. `(153)/(4)`C. `(151)/(4)`D. None of these

Area of the region enclosed between the curve `x =1-y^(2)` and the Y-axis isA. `(5)/(3)`B. `(4)/(3)`C. `(2)/(3)`D. `(1)/(3)`

If the area of the region enclosed between the curve `y=3x^(2)-4x+c`, the X-axis and the ordinates at x = 1, x = 3 is 20, then : c =

Smaller area enclosed by the circle `x^(2)+y^(2)=a^(2)` and the line `x+y=a` isA. `(a^(2))/(4)(pi-2)`B. `(a^(2))/(4)(pi+2)`C. `(a^(2))/(4)(2-pi)`D. `(a^(2))/(4)(pi-2)`