Test: Application of Integrals - 1

Question 1

The area of the smaller segment cut off from the circle x²+y² = 9by x = 1 is

Accepted Answer

9sec⁻¹(3)−√8

Answer

Answer

Answer

none of these

Question 2

The area bounded by the curve y² = x,line y = 4 and y – axis is equal to

Accepted Answer

64/3

Answer

7&radic;2

Answer

16/3

Answer

none of these

Question 3

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = π/2 is equal to

Accepted Answer

2(√2−1)sq. units

Answer

2(√2+1)sq. units

Answer

(4√2+1)sq. units

Answer

(4√2-1)sq. units

Question 4

The area bounded by the parabola y = x² and the line y = x is

Accepted Answer

1/6 sq. units

Answer

1/2 sq. units

Answer

1/3 sq. units

Answer

none of these

Question 5

The area common to the circle x²+y² = 16 and the parabola y²= 6x is

Accepted Answer

Answer

Answer

Answer

none of these

Question 6

The area of the region bounded by the curves y = |x−2|, x = 1 , x = 3 and the x – axis is

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 7

The area bounded by the curve y = | x | – 1 and y = – | x | + 1 is -

Accepted Answer

2

Answer

1

Answer

2√2

Answer

2√4

Question 8

Accepted Answer

5/12

Answer

5/3

Answer

5/4

Answer

12/5

Question 9

Accepted Answer

Answer

Answer

Answer

Question 10

The area bounded by the curve y = x|x|, x-axis and the ordinates x = 1, x = –1 is given by

Accepted Answer

2/3

Answer

0

Answer

1/3

Answer

None of these

Question 11

The ratio of the areas of two curves y = cos x and

y = cos 2x between x-axis from x = 0 to x = π/3 is

Accepted Answer

Answer

Answer

Answer

Question 12

Accepted Answer

Answer

Answer

Answer

Question 13

The area enclosed between the curves y = sin² x and y = cos²x in the interval 0 ≤ x ≤ π is -

Accepted Answer

1 sq unit

Answer

2 sq unit

Answer

1/2 sq unit

Answer

None of these

Question 14

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to-

Accepted Answer

4/3

Answer

1/3

Answer

2/3

Answer

5/3

Question 15

Area of the region bounded by the curves y = x² + 2, y = – x, x = 0 and x = 1 is -

Accepted Answer

17/6

Answer

5/16

Answer

3/16

Answer

None of these

Question 16

Accepted Answer

Answer

Answer

Answer

Question 17

Find the area bounded by x = 1/2, x = 2, y = log_e x and y = 2^x -

Accepted Answer

Answer

Answer

Answer

Question 18

Accepted Answer

1/3 sq. units

Answer

1/2 sq. units

Answer

1/4 sq. units

Answer

None of these

Question 19

The area bounded by the curves y² = 2x + 1 and x – y – 1 = 0 is -

Accepted Answer

16/3

Answer

2/3

Answer

4/3

Answer

8/3

Question 20

A region in the xy plane is bounded by the graph of y = 1/x , the x-axis, the line x = m, and the line x = 2m, m > 0. The area of this region

Accepted Answer

is independent of m

Answer

increases as m increases

Answer

decreases as m increases

Answer

decreases as m increases when m < 1/2 and increases as m increases when m > 1/2

Question 21

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 22

Accepted Answer

Answer

Answer

Answer

Question 23

The area enclosed by the curves 3x² + 5y = 32 and y = | x – 2 | is -

Accepted Answer

Answer

Answer

Answer

Question 24

The area of the region bounded by the curve a⁴y² = (2a – x) x⁵ is to that of the circle whose radius is a, is given by the ratio -

Accepted Answer

5 : 8

Answer

4 : 5

Answer

2 : 3

Answer

3 : 2

Question 25

Ratio of the area cut off a parabola by any double ordinate is that of the corresponding rectangle contained by that double ordinate and its distance from the vertex is -

Accepted Answer

2/3

Answer

1/2

Answer

1/3

Answer

1

Question 26

Area of region bounded by [x]² = [y]² if x ∈ [1, 5] where [.] represents the greatest integer function, is -

Accepted Answer

8 sq. units

Answer

10 sq. units

Answer

6 sq. units

Answer

5 sq. units

Question 27

Accepted Answer

4 sq. units

Answer

6 sq. units

Answer

10 sq. units

Answer

None of these

Question 28

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is-

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 29

The area of the bounded by y = cos x, y = 0, | x | = 1 is given by -

Accepted Answer

2 sin 1

Answer

sin 1

Answer

4 sin 1

Answer

None of these

Question 30

The value of m for which the area included between the curves y² = 4ax and y = mx equals a²/3 is

Accepted Answer

2

Answer

1

Answer

3

Answer

√3

Application of Integrals - 1 - Free MCQ Practice Test with solutions, JEE

MCQ Practice Test & Solutions: Test: Application of Integrals - 1 (30 Questions)

The area of the smaller segment cut off from the circle x²+y² = 9by x = 1 is

The area bounded by the curve y² = x,line y = 4 and y – axis is equal to

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = π/2 is equal to

The area bounded by the parabola y = x² and the line y = x is

The area common to the circle x²+y² = 16 and the parabola y²= 6x is

The area of the region bounded by the curves y = |x−2|, x = 1 , x = 3 and the x – axis is

The area bounded by the curve y = | x | – 1 and y = – | x | + 1 is -

The area bounded by the curve y = x|x|, x-axis and the ordinates x = 1, x = –1 is given by

The ratio of the areas of two curves y = cos x and
y = cos 2x between x-axis from x = 0 to x = π/3 is

The area enclosed between the curves y = sin² x and y = cos²x in the interval 0 ≤ x ≤ π is -

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to-

Area of the region bounded by the curves y = x² + 2, y = – x, x = 0 and x = 1 is -

Find the area bounded by x = 1/2, x = 2, y = log_e x and y = 2^x -

The area bounded by the curves y² = 2x + 1 and x – y – 1 = 0 is -

A region in the xy plane is bounded by the graph of y = 1/x , the x-axis, the line x = m, and the line x = 2m, m > 0. The area of this region

The area enclosed by the curves 3x² + 5y = 32 and y = | x – 2 | is -

The area of the region bounded by the curve a⁴y² = (2a – x) x⁵ is to that of the circle whose radius is a, is given by the ratio -

Ratio of the area cut off a parabola by any double ordinate is that of the corresponding rectangle contained by that double ordinate and its distance from the vertex is -

Area of region bounded by [x]² = [y]² if x ∈ [1, 5] where [.] represents the greatest integer function, is -

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is-

The area of the bounded by y = cos x, y = 0, | x | = 1 is given by -

The value of m for which the area included between the curves y² = 4ax and y = mx equals a²/3 is

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Application of Integrals - 1 - Free MCQ Practice Test with solutions, JEE

MCQ Practice Test & Solutions: Test: Application of Integrals - 1 (30 Questions)

The area of the smaller segment cut off from the circle x2+y2 = 9by x = 1 is

The area bounded by the curve y2 = x,line y = 4 and y – axis is equal to

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = π/2 is equal to

The area bounded by the parabola y = x2 and the line y = x is

The area common to the circle x2+y2 = 16 and the parabola y2 = 6x is

The area of the region bounded by the curves y = |x−2|, x = 1 , x = 3 and the x – axis is

The area bounded by the curve y = | x | – 1 and y = – | x | + 1 is -

The area bounded by the curve y = x|x|, x-axis and the ordinates x = 1, x = –1 is given by

The ratio of the areas of two curves y = cos x andy = cos 2x between x-axis from x = 0 to x = π/3 is

The area enclosed between the curves y = sin2 x and y = cos2x in the interval 0 ≤ x ≤ π is -

The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to-

Area of the region bounded by the curves y = x2 + 2, y = – x, x = 0 and x = 1 is -

Find the area bounded by x = 1/2, x = 2, y = loge x and y = 2x -

The area bounded by the curves y2 = 2x + 1 and x – y – 1 = 0 is -

A region in the xy plane is bounded by the graph of y = 1/x , the x-axis, the line x = m, and the line x = 2m, m > 0. The area of this region

The area enclosed by the curves 3x2 + 5y = 32 and y = | x – 2 | is -

The area of the region bounded by the curve a4y2 = (2a – x) x5 is to that of the circle whose radius is a, is given by the ratio -

Ratio of the area cut off a parabola by any double ordinate is that of the corresponding rectangle contained by that double ordinate and its distance from the vertex is -

Area of region bounded by [x]2 = [y]2 if x ∈ [1, 5] where [.] represents the greatest integer function, is -

The area enclosed between the curve y = loge(x + e) and the coordinate axes is-

The area of the bounded by y = cos x, y = 0, | x | = 1 is given by -

The value of m for which the area included between the curves y2 = 4ax and y = mx equals a2/3 is

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

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About this JEE Practice Test

Explore more JEE Study Resources

The area of the smaller segment cut off from the circle x²+y² = 9by x = 1 is

The area bounded by the curve y² = x,line y = 4 and y – axis is equal to

The area bounded by the parabola y = x² and the line y = x is

The area common to the circle x²+y² = 16 and the parabola y²= 6x is

The ratio of the areas of two curves y = cos x and
y = cos 2x between x-axis from x = 0 to x = π/3 is

The area enclosed between the curves y = sin² x and y = cos²x in the interval 0 ≤ x ≤ π is -

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to-

Area of the region bounded by the curves y = x² + 2, y = – x, x = 0 and x = 1 is -

Find the area bounded by x = 1/2, x = 2, y = log_e x and y = 2^x -

The area bounded by the curves y² = 2x + 1 and x – y – 1 = 0 is -

The area enclosed by the curves 3x² + 5y = 32 and y = | x – 2 | is -

The area of the region bounded by the curve a⁴y² = (2a – x) x⁵ is to that of the circle whose radius is a, is given by the ratio -

Area of region bounded by [x]² = [y]² if x ∈ [1, 5] where [.] represents the greatest integer function, is -

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is-

The value of m for which the area included between the curves y² = 4ax and y = mx equals a²/3 is