Applications of the Integrals Test

Result

Applications of the Integrals Test - 6

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Question 1
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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

A
A. 32 π

B
B. 4π

C
C. 8

D
D. 4π - 8

Solution
Question 2
1 / -0.25

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 _______.

A
A. (1, 1)

B
B. (2, 2)

C
C. (4√2 , 4√2)

D
D. (4, 4)

Solution

x² + y² = 32 ...(i)
y = x ...(ii)
Solving (i) and (ii),
⇒ x² + y² = 32
⇒ x² = 16
⇒ x = 4,
⇒ y = x = 4
∴ B = (4, 4)
Question 3
1 / -0.25

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 _______.

A
A. x² + y² = 4√2

B
B. x² + y² = 16

C
C. x² + y² = 32

D
D. (x − 4√2)² + 0

Solution

Centre = (0, 0),
r = 4√2
Equation of circle is x² + y² = (4√2)²
⇒ x² + y² = 32
Question 4
1 / -0.25

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

A
A. 8

B
B. 16

C
C. 32

D
D. 32π

Solution

= 8 sq. units
Question 5
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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.

A
A. 32π

B
B. 4π

C
C. 8

D
D. 4π - 8

Solution

Area of shaded region
= Ar (ΔOBM) + Ar (BAMB)
= 8 + 4π – 8
= 4π sq. units
Question 6
1 / -0.25

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

A
A. 1000√2/3

B
B. 4/3

C
C. 1000/3

D
D. 0

Solution

x² = 250 y
at = y = 0 x = 0
at y = 10 x = 50, -50
∴ Area formed by curve
Question 7
1 / -0.25

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

A
A. 1000/3

B
B. 250/3

C
C. 1200

D
D. 0

Solution
Question 8
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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

A
A. x² = 250y

B
B. x² =−250y

C
C. y² = 250x

D
D. y² = 250y
Question 9
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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

A
A. Even

B
B. Odd

C
C. Neither odd nor even

D
D. None of these

Solution

f(x) = x²
f(-x) = x²
∴ f(x) is even function.
Question 10
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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

A
A. 1000/3

B
B. 0

C
C. 1000√2/3

D
D. None of these
Question 11
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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.

A
A. 4

B
B. 16

C
C. 16/3

D
D. 8/3

Solution
Question 12
1 / -0.25

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 _______.

A
A. (2, 2)

B
B. (4, 4)

C
C. (1, 1)

D
D. (5, 5)

Solution

Q = (4, 4)
Question 13
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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 _______.

A
A. x = 0

B
B. x = 2

C
C. x = 4

D
D. y = 4

Solution

Equation of PQ is x = 4.
Question 14
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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.

A
A. 4

B
B. 16

C
C. 16/3

D
D. 8/3

Solution
Question 15
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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

A
A. 4

B
B. 16

C
C. 16/3

D
D. 8/3

Solution

Total area = 4 × 4
= 16 sq. units