Test: Application of Integrals - 3

Question 1

For which one of the following function Rolle's theorem is applicable?

Accepted Answer

Answer

f(x) = 3x² – 2, on [2, 3]

Answer

f(x) = | x – 1 |, on [0, 2]

Answer

f(x) = | sgn x |, on [–1, 1]

Question 2

Accepted Answer

Answer

Answer

Answer

Question 3

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 4

Accepted Answer

Answer

Answer

Answer

Question 5

The length of a longest interval in which the function f (x) = 3 sinx – 4 sin3x is increasing, is

Accepted Answer

π/3

Answer

π/2

Answer

3π/2

Answer

π

Question 6

Accepted Answer

Answer

Answer

Answer

Question 7

Accepted Answer

√3

Answer

2

Answer

1/√3

Answer

2/√3

Question 8

Accepted Answer

Answer

Answer

Answer

Question 9

A dynamite blast blows a heavy rock straight up with a launch velocity of 160 m/sec. It reaches a height of s = 160 t = 16t² after t sec. The velocity of the rock when it is 256 m above the ground on the way up is

Accepted Answer

96 m/s

Answer

98 m/s

Answer

104 m/s

Answer

48 m/s

Question 10

Find the area (in sq. units) of the largest rectangle with lower base on the x-axis & upper vertices on thecurve y = 12 – x².

Accepted Answer

32

Answer

31

Answer

33

Answer

34

Question 11

Accepted Answer

Answer

Answer

Answer

Question 12

If the point P(a, b) lies on the curve 9y² = x³ such that the normal to the curve at P makes equal intercepts with the axes. The value of

(a + 3b) is

Accepted Answer

12

Answer

11

Answer

13

Answer

14

Question 13

Two curves C1 : y = x² – 3 and C² : y = kx² , intersect each other at two different points. The tangent drawn to C² at one of the points of intersection A (a,y¹) , (a > 0) meets C¹ again at B(1,y²) . The value of ‘a’ is

Accepted Answer

3

Answer

1

Answer

5

Answer

7

Question 14

Accepted Answer

Question 15

Accepted Answer

Question 16

Accepted Answer

Question 17

Accepted Answer

Answer

Answer

Answer

Question 18

Accepted Answer

0

Answer

4

Answer

–8

Answer

–4

Question 19

If M (x₀, y₀) is the point on the curve 3x² – 4y² = 72, which is nearest to the line 3x + 2y + 1 = 0, then the value of (x₀ + y₀) is equal to

Accepted Answer

–3

Answer

3

Answer

9

Answer

–9

Question 20

Accepted Answer

x = 2r

Answer

2x = r

Answer

2x = (π + 4)r

Answer

(4 – π) x = πr

Question 21

Accepted Answer

Answer

Answer

Answer

Question 22

Accepted Answer

Answer

Answer

Answer

Question 23

Accepted Answer

Answer

Answer

Answer

Question 24

Accepted Answer

1/4

Answer

0

Answer

1/2

Answer

1/3

Question 25

If the exhaustive set of all possible values of c such that f(x) = e^2x – (c + 1) ex + 2x + cos 2 + sin 1, is monotonically increasing for all x ∈ R, is (–∞, λ], then find the value of λ.

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 26

Accepted Answer

Question 27

Accepted Answer

1

Answer

–1

Answer

–3/4

Answer

4/3

Question 28

Accepted Answer

Question 29

Accepted Answer

9

Answer

8

Answer

10

Answer

11

Question 30

Accepted Answer

Answer

Answer

Answer

Application of Integrals - 3 - Free MCQ Practice Test with solutions, JEE

MCQ Practice Test & Solutions: Test: Application of Integrals - 3 (30 Questions)

For which one of the following function Rolle's theorem is applicable?

The length of a longest interval in which the function f (x) = 3 sinx – 4 sin3x is increasing, is

A dynamite blast blows a heavy rock straight up with a launch velocity of 160 m/sec. It reaches a height of s = 160 t = 16t² after t sec. The velocity of the rock when it is 256 m above the ground on the way up is

Find the area (in sq. units) of the largest rectangle with lower base on the x-axis & upper vertices on thecurve y = 12 – x².

If the point P(a, b) lies on the curve 9y² = x³ such that the normal to the curve at P makes equal intercepts with the axes. The value of
(a + 3b) is

Two curves C1 : y = x² – 3 and C² : y = kx² , intersect each other at two different points. The tangent drawn to C² at one of the points of intersection A (a,y¹) , (a > 0) meets C¹ again at B(1,y²) . The value of ‘a’ is

If M (x₀, y₀) is the point on the curve 3x² – 4y² = 72, which is nearest to the line 3x + 2y + 1 = 0, then the value of (x₀ + y₀) is equal to

If the exhaustive set of all possible values of c such that f(x) = e^2x – (c + 1) ex + 2x + cos 2 + sin 1, is monotonically increasing for all x ∈ R, is (–∞, λ], then find the value of λ.

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Application of Integrals - 3 - Free MCQ Practice Test with solutions, JEE

MCQ Practice Test & Solutions: Test: Application of Integrals - 3 (30 Questions)

For which one of the following function Rolle's theorem is applicable?

The length of a longest interval in which the function f (x) = 3 sinx – 4 sin3x is increasing, is

A dynamite blast blows a heavy rock straight up with a launch velocity of 160 m/sec. It reaches a height of s = 160 t = 16t2 after t sec. The velocity of the rock when it is 256 m above the ground on the way up is

Find the area (in sq. units) of the largest rectangle with lower base on the x-axis & upper vertices on thecurve y = 12 – x2.

If the point P(a, b) lies on the curve 9y2 = x3 such that the normal to the curve at P makes equal intercepts with the axes. The value of(a + 3b) is

Two curves C1 : y = x2 – 3 and C2 : y = kx2 , intersect each other at two different points. The tangent drawn to C2 at one of the points of intersection A (a,y1) , (a > 0) meets C1 again at B(1,y2) . The value of ‘a’ is

If M (x0, y0) is the point on the curve 3x2 – 4y2 = 72, which is nearest to the line 3x + 2y + 1 = 0, then the value of (x0 + y0) is equal to

If the exhaustive set of all possible values of c such that f(x) = e2x – (c + 1) ex + 2x + cos 2 + sin 1, is monotonically increasing for all x ∈ R, is (–∞, λ], then find the value of λ.

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

A dynamite blast blows a heavy rock straight up with a launch velocity of 160 m/sec. It reaches a height of s = 160 t = 16t² after t sec. The velocity of the rock when it is 256 m above the ground on the way up is

Find the area (in sq. units) of the largest rectangle with lower base on the x-axis & upper vertices on thecurve y = 12 – x².

If the point P(a, b) lies on the curve 9y² = x³ such that the normal to the curve at P makes equal intercepts with the axes. The value of
(a + 3b) is

Two curves C1 : y = x² – 3 and C² : y = kx² , intersect each other at two different points. The tangent drawn to C² at one of the points of intersection A (a,y¹) , (a > 0) meets C¹ again at B(1,y²) . The value of ‘a’ is

If M (x₀, y₀) is the point on the curve 3x² – 4y² = 72, which is nearest to the line 3x + 2y + 1 = 0, then the value of (x₀ + y₀) is equal to

If the exhaustive set of all possible values of c such that f(x) = e^2x – (c + 1) ex + 2x + cos 2 + sin 1, is monotonically increasing for all x ∈ R, is (–∞, λ], then find the value of λ.