Test: Application of Integrals- Case Based Type Questions - JEE MCQ

# Test: Application of Integrals- Case Based Type Questions - JEE MCQ

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## 15 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Application of Integrals- Case Based Type Questions

Test: Application of Integrals- Case Based Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Application of Integrals- Case Based Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Application of Integrals- Case Based Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Application of Integrals- Case Based Type Questions below.
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Test: Application of Integrals- Case Based Type Questions - Question 1

### Direction: Read the following text and answer the following questions on the basis of the same:In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.Q. Ar (BAMB) = _______ sq. units

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 1

Test: Application of Integrals- Case Based Type Questions - Question 2

### Direction: Read the following text and answer the following questions on the basis of the same:In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.Q. The co-ordinates of B are _______.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 2
x2 + y2 = 32 ...(i)

y = x ...(ii)

Solving (i) and (ii),

⇒ x2 + y2 = 32

⇒ x2 = 16

⇒ x = 4,

⇒ y = x = 4

∴ B = (4, 4)

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Test: Application of Integrals- Case Based Type Questions - Question 3

### Direction: Read the following text and answer the following questions on the basis of the same:In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.Q. The equation of the circle is _______.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 3
Centre = (0, 0),

r = 4√2

Equation of circle is x2 + y2 = (4√2)2

⇒ x2 + y2 = 32

Test: Application of Integrals- Case Based Type Questions - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.

Q. Area of DOBM is _______ sq. units

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 4

= 8 sq. units

Test: Application of Integrals- Case Based Type Questions - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.

Q. Area of the shaded region is _______ sq. units.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 5

= Ar (ΔOBM) + Ar (BAMB)

= 8 + 4π – 8

= 4π sq. units

Test: Application of Integrals- Case Based Type Questions - Question 6

Direction: Read the following text and answer the following questions on the basis of the same:

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Q. The area formed by the curve x2 = 250y, x-axis, y = 0 and y = 10 is

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 6
x2 = 250 y

at = y = 0 x = 0

at y = 10 x = 50, -50

∴ Area formed by curve

Test: Application of Integrals- Case Based Type Questions - Question 7

Direction: Read the following text and answer the following questions on the basis of the same:

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Q. The value of the integral

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 7

Test: Application of Integrals- Case Based Type Questions - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Q. The equation of the parabola designed on the bridge is

Test: Application of Integrals- Case Based Type Questions - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Q. The integrand of the integral

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 9
f(x) = x2

f(-x) = x2

∴ f(x) is even function.

Test: Application of Integrals- Case Based Type Questions - Question 10

Direction: Read the following text and answer the following questions on the basis of the same:

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Q. The area formed between x2 = 250y, y-axis, y = 2 and y = 4 is

Test: Application of Integrals- Case Based Type Questions - Question 11

Direction: Read the following text and answer the following questions on the basis of the same:

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

Q. Area received by son A is _______ sq. units.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 11

Test: Application of Integrals- Case Based Type Questions - Question 12

Direction: Read the following text and answer the following questions on the basis of the same:

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

Q. The coordinates of Q are _______.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 12
Q = (4, 4)
Test: Application of Integrals- Case Based Type Questions - Question 13

Direction: Read the following text and answer the following questions on the basis of the same:

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

Q. Equation of PQ is _______.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 13
Equation of PQ is x = 4.
Test: Application of Integrals- Case Based Type Questions - Question 14

Direction: Read the following text and answer the following questions on the basis of the same:

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

Q. Area received by son B is _______ sq. units.

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 14

Test: Application of Integrals- Case Based Type Questions - Question 15

Direction: Read the following text and answer the following questions on the basis of the same:

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

Q. Total area of the square field is _______ sq. units

Detailed Solution for Test: Application of Integrals- Case Based Type Questions - Question 15
Total area = 4 × 4

= 16 sq. units

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests
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## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests