99 + Interview Questions in APPLICATIONS-OF-DEFINITE-INTEGRALS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	Find the area of the region enclosed by the curves `y=xlogxa n dy=2x-2x^2dot`A. `(7)/(12)`B. `(1)/(2)`C. `(5)/(12)`D. `(5)/(2)`
Answer» Correct Answer - A

Discussion

2.	Area between the parabolas `y^(2)=px` and `x^(2)=qy` isA. `(16pq)/(3)`B. `(pq)/(3)`C. `15pq`D. `2pq`
Answer» Correct Answer - B

Discussion

3.	The area of the figure bounded by right of the line `y = x + 1, y= cos x` and x-axis is :A. 1B. `(1)/(2)`C. `(3)/(2)`D. `(5)/(2)`
Answer» Correct Answer - C

Discussion

4.	Area bounded by the semi-sircle `y=sqrt(4-x^(2))`, and its diameter y = 0, isA. `2pi`B. `pi`C. `(pi)/(2)`D. `2pi^(2)`
Answer» Correct Answer - A

Discussion

5.	Find the area of the smaller region bounded by the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`and the line `x/a+y/b=1`A. `(1)/(2)pi ab`B. `(1)/(2)ab`C. `(1)/(4)pi ab - (1)/(2)ab`D. `(1)/(4)ab - (pi)/(4)`
Answer» Correct Answer - C

Discussion

6.	Area of smaller part in the first quadrant bounded by the semi-circle `y=sqrt(4-x^(2))`, the line `y = x sqrt(3)` and X -axis, isA. `(pi)/(3)`B. `(2pi)/(3)`C. `(4pi)/(3)`D. `4pi`
Answer» Correct Answer - B

Discussion

7.	Area bounded by the parabola `3y=x^(2)`, the X-axis and the lines x = 2, x = 3 isA. `(29)/(9)`B. `(17)/(9)`C. `(7)/(9)`D. `(19)/(9)`
Answer» Correct Answer - D

Discussion

8.	Area bounded by the lines `x=2y, y=2x` and x = 4 isA. 14B. 13C. 10D. 12
Answer» Correct Answer - D

Discussion

9.	The area bounded by the curves `y= "sin"` x, y= cos x and y-axis in 1 quadrant is -A. `3sqrt(2)-1`B. 2C. `2-sqrt(2)`D. `sqrt(2)-1`
Answer» Correct Answer - C

Discussion

10.	If the area bounded by the parabola `x^(2)=y` and the line y = 4 is divided into equal parts by the line y = c, then : c =A. 1B. `root(3)(4)`C. `root(3)(8)`D. `root(3)(16)`
Answer» Correct Answer - D

Discussion

11.	Find the area of the region included between theparabolas `y^2=4a xa n dx^2=4a y ,w h e r ea > 0.`A. `(16a^(2))/(3)`B. `(8a^(2))/(3)`C. `(4a^(2))/(3)`D. `(a^(2))/(3)`
Answer» Correct Answer - A

Discussion

12.	Area enclosed between the curve `y^(2)=x` and the line y = x isA. 1B. `(1)/(3)`C. `(1)/(6)`D. `(1)/(5)`
Answer» Correct Answer - C

Discussion

13.	Area bounded by the curve `y=(x-1) (x-5)` and the X-axis isA. `(32)/(3)`B. `(31)/(3)`C. `(29)/(3)`D. `(28)/(3)`
Answer» Correct Answer - A

Discussion

14.	Area of the region bounded by the curve `y=x^(2)-5x+4` and the X-axis isA. `(3)/(2)`B. `(5)/(2)`C. `(7)/(2)`D. `(9)/(2)`
Answer» Correct Answer - D

Discussion

15.	Find the area of the smaller part of the circle `x^2+y^2=a^2`cut off by the line `x=a/(sqrt(2))`A. `(a^(2))/(2)((pi)/(2)+1)`B. `(a^(2))/(2)((pi)/(2)-1)`C. `a^(2)((pi)/(2)-1)`D. `a^(2)(pi-1)`
Answer» Correct Answer - B

Discussion

16.	Find the area of one of the curvilinear triangles formed by the curves `y = sin x, x=cos^-1 y` and thex-axis.A. `2+sqrt(2)`B. `2-sqrt(2)`C. `2+2sqrt(2)`D. `2sqrt(2)`
Answer» Correct Answer - B

Discussion

17.	The area bounded by the parabola `y^(2)=8x,` the x-axis and the latusrectum, isA. `(1)/(2)`B. `(32)/(3)`C. `(23)/(3)`D. `(22)/(3)`
Answer» Correct Answer - B

Discussion

18.	Area enclosed between the curve `y^(2)=x` and the line y = x isA. 1B. `(1)/(3)`C. `(1)/(2)`D. `(1)/(5)`
Answer» Correct Answer - C

Discussion

19.	Area enclosed by the curve `y = sin^(2)x`, the X-axis and the lines `x=0, x=pi//2` isA. `(pi)/(2)`B. 1C. `(pi)/(4)`D. None of these
Answer» Correct Answer - C

Discussion

20.	Area enclosed by the curve `x^(2)y=36`, the X-axis and the lines x = 6 and x = 9, isA. 2B. 1C. 4D. None of these
Answer» Correct Answer - A

Discussion

21.	Area bounded by the parabola `x^(2)=4y` and its latusrectum isA. `(4)/(3)`B. `(8)/(3)`C. `(16)/(3)`D. `(5)/(3)`
Answer» Correct Answer - B

Discussion

22.	If the area bounded by the parabola `y^2 = 4ax` and the line y=mx is `a^2/12` sq. units, by using integration find the value of m.A. 1B. 2C. 3D. 4
Answer» Correct Answer - D

Discussion

23.	If the area bounded by the curves `y=x-x^2` and line `y=mx` is equal to `9/2` sq.units , then m may beA. `-4`B. `-2`C. 2D. 4
Answer» Correct Answer - D

Discussion

24.	Area under the line `4x-y+2=0`, above the X-axis, bounded by the lines x = 0 and x = 3 is (in sq. units)A. 12B. 24C. 25D. None of these
Answer» Correct Answer - B

Discussion

25.	If the area enclosed between the parabola `y^(2)=4x` and the line y = mx is (1/3) sq. unit, then : m =A. 1B. 2C. 3D. 4
Answer» Correct Answer - B

Discussion

26.	Area of the portion of the parabola `y^(2)=4ax` included between the X-axis, the ordinate at x = 2a and its latusrectum isA. `(a^(2)(2sqrt(2)-1))/(3)`B. `(4a^(2)(2sqrt(2)-1))/(3)`C. `(8a^(2)(2sqrt(2)-1))/(3)`D. None of these
Answer» Correct Answer - D

Discussion

27.	Area enclosed between the curve `x^(2)+4y=4` and the X-axis isA. `(32)/(3)`B. `(16)/(3)`C. `(8)/(3)`D. `(4)/(3)`
Answer» Correct Answer - A

Discussion

28.	Area enclosed between the curve `y=x^(2)-5x+15` and the line `y=3x+3` isA. `(32)/(3)`B. `(16)/(3)`C. `(8)/(3)`D. `(4)/(3)`
Answer» Correct Answer - A

Discussion

29.	Area above the X-axis, bounded by the circle `x^(2)+y^(2)-2ax=0` and the parabola `y^(2)=ax` isA. `a^(2)((pi)/(4)-(2)/(3))`B. `a^(2)((pi)/(4)+(2)/(3))`C. `2a^(2)((pi)/(4)+(2)/(3))`D. None of these
Answer» Correct Answer - A

Discussion

30.	Area enclosed between the curve `y^(2)=16x` and the chord BC, where `B-=(1, 4)` and `C-=(9,12)` isA. `(8)/(3)`B. `(32)/(3)`C. `(16)/(3)`D. None of these
Answer» Correct Answer - C

Discussion

31.	Area enclosed between the curve `x=2y-y^(2)` and the Y-axis isA. `(4)/(3)`B. `(5)/(3)`C. `(2)/(3)`D. `(7)/(3)`
Answer» Correct Answer - A

Discussion

32.	Area bounded by the parabola `ay^(2)=x`, the X-axis and the ordinate at x = a isA. `(2a^(2))/(3)`B. `(2a)/(3)`C. `(a^(2))/(2)`D. `(3a^(2))/(2)`
Answer» Correct Answer - B

Discussion

33.	Area enclosed between the curve `y=x^(2)` and the line y = x isA. `(1)/(8)`B. `(1)/(6)`C. `(3)/(2)`D. `(1)/(7)`
Answer» Correct Answer - B

Discussion

34.	Area enclosed between the curve `ay=3(a^(2)-x^(2))` and the X-axis isA. `4a^(2)`B. 8aC. `(3a^(2))/(2)`D. `(2a^(2))/(3)`
Answer» Correct Answer - A

Discussion

35.	Area bounded by the curve `y=x^(2)-2x` and the line y = 2x isA. `(125)/(6)`B. `(32)/(3)`C. 36D. 28
Answer» Correct Answer - B

Discussion

36.	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(1+x^(2)))`
Answer» Correct Answer - D

Discussion

37.	The area bounded by the curve `y = 2x - x^(2)` and the line y = - x isA. `(9)/(2)` sq. unitsB. `(43)/(6)` sq. unitsC. `(35)/(6)` sq. unitsD. none of these
Answer» Correct Answer - A

Discussion

38.	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. 2C. `2sqrt(2)`D. none of these
Answer» Correct Answer - C

Discussion

39.	Area of the region between the curve `y=x^(2)-3x` and the line y = 2x isA. `(125)/(6)`B. `(49)/(3)`C. `(64)/(3)`D. `(67)/(3)`
Answer» Correct Answer - A

Discussion

40.	Find the area bounded by the curve `x^2=4y`and the straight line `x=4y-2.`A. `(2)/(9)`B. `(4)/(9)`C. `(8)/(9)`D. `(9)/(8)`
Answer» Correct Answer - D

Discussion

41.	Area of the region bounded by the parabola `ay=x^(2)`, the X-axis and the ordinates at x = a, x = 2a isA. `(3a^(2))/(7)`B. `(3a)/(7)`C. `(7a)/(3)`D. `(7a^(2))/(3)`
Answer» Correct Answer - D

Discussion

42.	`y=x^(2)+1, …. x = 0, x = 3`A. 12B. 21C. 18D. 9
Answer» Correct Answer - A

Discussion

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

Discussion

44.	If `{:(f(x)=3x^(2)", if "0 le x le 2),(" "=16-2x", if " x ge 2","):}` then area bounded by the graph of `y=f(x)`, the X-axis and the line x = 3 is (in sq. u.)A. 12B. 19C. 17D. 24
Answer» Correct Answer - B

Discussion

45.	If `{:(f(x)=x^(2)", if "0 le x le 1),(" "=sqrt(x)", if " x ge 1","):}` then area above X-axis, bounded by the line x = 4 and the curve y = f(x) isA. 1B. 2C. 5D. None of these
Answer» Correct Answer - C

Discussion

46.	`y=(3)/(x^(2)), ….. x = 1, x = 2`A. 32B. 23C. `(3)/(2)`D. `(2)/(3)`
Answer» Correct Answer - C

Discussion

47.	Area above the X-axis, bounded by the parabola `y^(2)=9x` from x = 0 to x = 3 isA. `3sqrt(6)`B. `6sqrt(3)`C. `10sqrt(3)`D. None of these
Answer» Correct Answer - B

Discussion

48.	`y=4-x^(2), ….. x = 0, x = 1`A. 33B. `(11)/(3)`C. `3.3`D. `(3)/(11)`
Answer» Correct Answer - B

Discussion

49.	If the area bounded by the curve `y=x^(2)`, the X-axis and the line `x=2^(1//3)` is divided into two equal parts by the line x = a, then : a=A. `(1)/(6)`B. 1C. `(2)/(3)`D. `3^(1//3)`
Answer» Correct Answer - B

Discussion

50.	Area bounded by the curves `y = x-x^(2)` and X-axis, between Y-axis and the line x = 1, isA. `(5)/(6)`B. `(1)/(2)`C. `(1)/(3)`D. `(1)/(6)`
Answer» Correct Answer - D

Discussion

Explore topic-wise InterviewSolutions in .

Find the area of the region enclosed by the curves `y=xlogxa n dy=2x-2x^2dot`A. `(7)/(12)`B. `(1)/(2)`C. `(5)/(12)`D. `(5)/(2)`

Area between the parabolas `y^(2)=px` and `x^(2)=qy` isA. `(16pq)/(3)`B. `(pq)/(3)`C. `15pq`D. `2pq`

The area of the figure bounded by right of the line `y = x + 1, y= cos x` and x-axis is :A. 1B. `(1)/(2)`C. `(3)/(2)`D. `(5)/(2)`

Area bounded by the semi-sircle `y=sqrt(4-x^(2))`, and its diameter y = 0, isA. `2pi`B. `pi`C. `(pi)/(2)`D. `2pi^(2)`

Find the area of the smaller region bounded by the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`and the line `x/a+y/b=1`A. `(1)/(2)pi ab`B. `(1)/(2)ab`C. `(1)/(4)pi ab - (1)/(2)ab`D. `(1)/(4)ab - (pi)/(4)`

Area of smaller part in the first quadrant bounded by the semi-circle `y=sqrt(4-x^(2))`, the line `y = x sqrt(3)` and X -axis, isA. `(pi)/(3)`B. `(2pi)/(3)`C. `(4pi)/(3)`D. `4pi`

Area bounded by the parabola `3y=x^(2)`, the X-axis and the lines x = 2, x = 3 isA. `(29)/(9)`B. `(17)/(9)`C. `(7)/(9)`D. `(19)/(9)`

Area bounded by the lines `x=2y, y=2x` and x = 4 isA. 14B. 13C. 10D. 12

The area bounded by the curves `y= "sin"` x, y= cos x and y-axis in 1 quadrant is -A. `3sqrt(2)-1`B. 2C. `2-sqrt(2)`D. `sqrt(2)-1`

If the area bounded by the parabola `x^(2)=y` and the line y = 4 is divided into equal parts by the line y = c, then : c =A. 1B. `root(3)(4)`C. `root(3)(8)`D. `root(3)(16)`

Find the area of the region included between theparabolas `y^2=4a xa n dx^2=4a y ,w h e r ea > 0.`A. `(16a^(2))/(3)`B. `(8a^(2))/(3)`C. `(4a^(2))/(3)`D. `(a^(2))/(3)`

Area enclosed between the curve `y^(2)=x` and the line y = x isA. 1B. `(1)/(3)`C. `(1)/(6)`D. `(1)/(5)`

Area bounded by the curve `y=(x-1) (x-5)` and the X-axis isA. `(32)/(3)`B. `(31)/(3)`C. `(29)/(3)`D. `(28)/(3)`

Area of the region bounded by the curve `y=x^(2)-5x+4` and the X-axis isA. `(3)/(2)`B. `(5)/(2)`C. `(7)/(2)`D. `(9)/(2)`

Find the area of the smaller part of the circle `x^2+y^2=a^2`cut off by the line `x=a/(sqrt(2))`A. `(a^(2))/(2)((pi)/(2)+1)`B. `(a^(2))/(2)((pi)/(2)-1)`C. `a^(2)((pi)/(2)-1)`D. `a^(2)(pi-1)`

Find the area of one of the curvilinear triangles formed by the curves `y = sin x, x=cos^-1 y` and thex-axis.A. `2+sqrt(2)`B. `2-sqrt(2)`C. `2+2sqrt(2)`D. `2sqrt(2)`

The area bounded by the parabola `y^(2)=8x,` the x-axis and the latusrectum, isA. `(1)/(2)`B. `(32)/(3)`C. `(23)/(3)`D. `(22)/(3)`

Area enclosed between the curve `y^(2)=x` and the line y = x isA. 1B. `(1)/(3)`C. `(1)/(2)`D. `(1)/(5)`

Area enclosed by the curve `y = sin^(2)x`, the X-axis and the lines `x=0, x=pi//2` isA. `(pi)/(2)`B. 1C. `(pi)/(4)`D. None of these

Area enclosed by the curve `x^(2)y=36`, the X-axis and the lines x = 6 and x = 9, isA. 2B. 1C. 4D. None of these

Area bounded by the parabola `x^(2)=4y` and its latusrectum isA. `(4)/(3)`B. `(8)/(3)`C. `(16)/(3)`D. `(5)/(3)`

If the area bounded by the parabola `y^2 = 4ax` and the line y=mx is `a^2/12` sq. units, by using integration find the value of m.A. 1B. 2C. 3D. 4

If the area bounded by the curves `y=x-x^2` and line `y=mx` is equal to `9/2` sq.units , then m may beA. `-4`B. `-2`C. 2D. 4

Area under the line `4x-y+2=0`, above the X-axis, bounded by the lines x = 0 and x = 3 is (in sq. units)A. 12B. 24C. 25D. None of these

If the area enclosed between the parabola `y^(2)=4x` and the line y = mx is (1/3) sq. unit, then : m =A. 1B. 2C. 3D. 4

Area of the portion of the parabola `y^(2)=4ax` included between the X-axis, the ordinate at x = 2a and its latusrectum isA. `(a^(2)(2sqrt(2)-1))/(3)`B. `(4a^(2)(2sqrt(2)-1))/(3)`C. `(8a^(2)(2sqrt(2)-1))/(3)`D. None of these

Area enclosed between the curve `x^(2)+4y=4` and the X-axis isA. `(32)/(3)`B. `(16)/(3)`C. `(8)/(3)`D. `(4)/(3)`

Area enclosed between the curve `y=x^(2)-5x+15` and the line `y=3x+3` isA. `(32)/(3)`B. `(16)/(3)`C. `(8)/(3)`D. `(4)/(3)`

Area above the X-axis, bounded by the circle `x^(2)+y^(2)-2ax=0` and the parabola `y^(2)=ax` isA. `a^(2)((pi)/(4)-(2)/(3))`B. `a^(2)((pi)/(4)+(2)/(3))`C. `2a^(2)((pi)/(4)+(2)/(3))`D. None of these

Area enclosed between the curve `y^(2)=16x` and the chord BC, where `B-=(1, 4)` and `C-=(9,12)` isA. `(8)/(3)`B. `(32)/(3)`C. `(16)/(3)`D. None of these

Area enclosed between the curve `x=2y-y^(2)` and the Y-axis isA. `(4)/(3)`B. `(5)/(3)`C. `(2)/(3)`D. `(7)/(3)`

Area bounded by the parabola `ay^(2)=x`, the X-axis and the ordinate at x = a isA. `(2a^(2))/(3)`B. `(2a)/(3)`C. `(a^(2))/(2)`D. `(3a^(2))/(2)`

Area enclosed between the curve `y=x^(2)` and the line y = x isA. `(1)/(8)`B. `(1)/(6)`C. `(3)/(2)`D. `(1)/(7)`

Area enclosed between the curve `ay=3(a^(2)-x^(2))` and the X-axis isA. `4a^(2)`B. 8aC. `(3a^(2))/(2)`D. `(2a^(2))/(3)`

Area bounded by the curve `y=x^(2)-2x` and the line y = 2x isA. `(125)/(6)`B. `(32)/(3)`C. 36D. 28

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(1+x^(2)))`

The area bounded by the curve `y = 2x - x^(2)` and the line y = - x isA. `(9)/(2)` sq. unitsB. `(43)/(6)` sq. unitsC. `(35)/(6)` sq. unitsD. 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. 2C. `2sqrt(2)`D. none of these

Area of the region between the curve `y=x^(2)-3x` and the line y = 2x isA. `(125)/(6)`B. `(49)/(3)`C. `(64)/(3)`D. `(67)/(3)`

Find the area bounded by the curve `x^2=4y`and the straight line `x=4y-2.`A. `(2)/(9)`B. `(4)/(9)`C. `(8)/(9)`D. `(9)/(8)`

Area of the region bounded by the parabola `ay=x^(2)`, the X-axis and the ordinates at x = a, x = 2a isA. `(3a^(2))/(7)`B. `(3a)/(7)`C. `(7a)/(3)`D. `(7a^(2))/(3)`

`y=x^(2)+1, …. x = 0, x = 3`A. 12B. 21C. 18D. 9

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

If `{:(f(x)=3x^(2)", if "0 le x le 2),(" "=16-2x", if " x ge 2","):}` then area bounded by the graph of `y=f(x)`, the X-axis and the line x = 3 is (in sq. u.)A. 12B. 19C. 17D. 24

If `{:(f(x)=x^(2)", if "0 le x le 1),(" "=sqrt(x)", if " x ge 1","):}` then area above X-axis, bounded by the line x = 4 and the curve y = f(x) isA. 1B. 2C. 5D. None of these

`y=(3)/(x^(2)), ….. x = 1, x = 2`A. 32B. 23C. `(3)/(2)`D. `(2)/(3)`

Area above the X-axis, bounded by the parabola `y^(2)=9x` from x = 0 to x = 3 isA. `3sqrt(6)`B. `6sqrt(3)`C. `10sqrt(3)`D. None of these

`y=4-x^(2), ….. x = 0, x = 1`A. 33B. `(11)/(3)`C. `3.3`D. `(3)/(11)`

If the area bounded by the curve `y=x^(2)`, the X-axis and the line `x=2^(1//3)` is divided into two equal parts by the line x = a, then : a=A. `(1)/(6)`B. 1C. `(2)/(3)`D. `3^(1//3)`

Area bounded by the curves `y = x-x^(2)` and X-axis, between Y-axis and the line x = 1, isA. `(5)/(6)`B. `(1)/(2)`C. `(1)/(3)`D. `(1)/(6)`