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| MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals With Answers PDF |
MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals With Answers PDF: Multiple Choice Questions (MCQs) are a popular method of testing a student's understanding of a particular subject. They are widely used in school and college exams as they are a quick and efficient way to assess a student's knowledge.
An MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals consists of a question or statement, followed by several answer options, of which the student must choose the correct one. The answer options are usually presented as a list of possible choices, such as A, B, C or D.
MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals With Answers PDF
MCQ On Application Of Integration Class 12 Chapter 8 Question 1.
The area of the y = cos x and y = sin x, 0 ≤ x ≤ π2 is
(A) 2–√ sq units
(B) (2–√+1) sq units
(C) (2–√−1) sq units
(D) (22–√−1)
Answer:
(C) (2–√−1) sq units
Explanation:
We have y = cos x and y = sin x
Where o ≤ x ≤ π2
we get cos x = sin π
⇒ x = π4
From the figure, area of the shaded region,
A = ∫π/40(cosx+sinx)dx
= [sinx+cosx]π/40
= [sinπ4+cosπ4−sin0−cos0]
= 12√+12√−1
= (2–√−1) sq units
Application Of Integrals Class 12 MCQ Chapter 8 Question 2.
The area of the region bounded by the curve x2 = 4y and the straight-line x = 4y – 2 is
(A) 38 sq units
(B) 58 sq units
(C) 78 sq units
(D) 98 sq units
Answer:
(D) 98 sq units
Explanation:
x2 = x + 2
x2 – x – 2 = 0
(x – 2)(x + 1) = 0
x = -1, 2
For x = -1, y = 14 and for x = 2, y = 1
Points of intersection are (-1, 14) and (2, 1).
Graphs of parabola x2=4y and x =4y – 2 are shown in the following figure:
A = ∫2−1[x+24−x24]dx
= 14[x22+2x−x33]2−1
= 14[8−12−3]
= 14[8−12−3]
= 98 sq units
Application Of Integration MCQ Maths Class 12 Chapter 8 Question 3.
Area of the region in the first quadrant endosed by the x-axis, the line y = x and the circle x2 + y2 = 32 is
(A) 16π sq units
(B) 4π sq units
(C) 32π sq units
(D) 24π sq units
Answer:
(B) 4π sq units
Explanation:
We have y = 0,y = x and the circle
x2 + y2 = 32 in the frist quadrant.
Solving y = x with thedrcle
x2 + x2 = 32
x2 = 16
x = 4 (In the first quadrant)
When x = 4, y = 4 for the point of intersection of the circle with the x-axis.
Put y = 0
x2 + 0 = 32
x = ±42–√
So, the drde intersects the x-axis. at (±42–√, 0).
From the above figure, area oi the shaded region,
A = ∫40xdx+∫42√4(42–√)2−x2−−−−−−−−−−√dx
= [x22]40+[x2(42–√)2−x2−−−−−−−−−−√+(42√)22sin−1x42√]42√4
= [162]+⎡⎣⎢0+16sin−11−42(42–√)2−162−−−−−−−−−−−√−16sin−1442√⎤⎦⎥
= 8 + [16π2−216−−√−16π4]
= 8 + [8π – 8 – 4π]
= 4π sq units
Application Of Integrals MCQ Class 12 Chapter 8 Question 4.
Area of the region bounded by the curve y = cos x between x = 0 and x = π is
(A) 2 sq units
(B) 4 sq units
(C) 3 sq units
(D) 1 sq unit
Answer:
(A) 2 sq units
Explanation:
We have y = cos x, x = 0, x = π
From the figure, area of the shaded region,
A = ∫π0|cosx|dx+∫π/20cosxdx
A = 2[sinx]π/20
= 2 sq units
Benefits of MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals
One of the benefits of using MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals is that they are easy to grade. The correct answer is already provided, so the teacher or exam proctor simply needs to check that the student has chosen the correct option. This makes MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals more efficient than open-ended questions, which require more time and effort to grade.
Another benefit of MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals is that they can test a wide range of knowledge, including factual information, concepts, and problem-solving skills. They can also be used to test a student's ability to apply knowledge to new situations, rather than just recall information.
Conclusion of MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals With Answers PDF
In conclusion, MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals are a popular method of testing a student's understanding of a particular subject. They are widely used in school and college exams as they are a quick and efficient way to assess a student's knowledge. But to minimize the drawbacks, it is important to write good MCQs and use a variety of question types. They can test a wide range of knowledge, including factual information, concepts, and problem-solving skills, but they should not be the only method of assessment, it's important to use different types of questions to evaluate a student's understanding of a subject.
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