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Test: Area Between A Curve And A Line - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Area Between A Curve And A Line

Test: Area Between A Curve And A Line for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Area Between A Curve And A Line questions and answers have been prepared according to the JEE exam syllabus.The Test: Area Between A Curve And A Line MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Area Between A Curve And A Line below.
Solutions of Test: Area Between A Curve And A Line questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Test: Area Between A Curve And A Line solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Area Between A Curve And A Line | 10 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
Test: Area Between A Curve And A Line - Question 1
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The area enclosed between the lines x = 2 and x = 7 is​

Detailed Solution for Test: Area Between A Curve And A Line - Question 1

Area enclosed between the lines x = 2 and x = 7 is Infinite.

Test: Area Between A Curve And A Line - Question 2
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If the area of y = f(x) between x = a and x = b is   then the point c is the point of intersection of the curve with:

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Test: Area Between A Curve And A Line - Question 3
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Area under the circle x2 + y2 = 16 is​

Test: Area Between A Curve And A Line - Question 4
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Area of the shaded region in the given figure is :

​

Test: Area Between A Curve And A Line - Question 5
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Area of the region bounded by the curve y2 = 2y – x and y-axis is:​
Detailed Solution for Test: Area Between A Curve And A Line - Question 5

y2 = 2y−x
⇒ x = 2y − y2
Curve meets y−axis where x= 0
2y − y2 = 0
⇒ y (2−y) = 0
y = 0 or y = 2
Area =∣∫(0 to 2) x.dy∣
=|∫(0 to 2) (2y − y2).dy∣
=∣[y2 − y3/3] (0 to 2) |[4−8/3]−0|
=4/3 unit2

Test: Area Between A Curve And A Line - Question 6
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The area of the region bounded between the line x=9 and the parabola y2=16x is​
Detailed Solution for Test: Area Between A Curve And A Line - Question 6

Correct Answer : a

Explanation : Equation of the parabola is

y2 = 16x .... (i)

Required area =2∫(0 to 9) ydx

[by symmetry about x-axis]

= 2∫(0 to 9) 4(x)1/2 dx

= 8∫(0 to 9) (x)1/2 dx

​= 8[(x3/2)/(3/2)](0 to 9)

​= 16/3[x3/2](0 to 9)

= 144 sq unit.

Test: Area Between A Curve And A Line - Question 7
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Area of the region  is : 
Test: Area Between A Curve And A Line - Question 8
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If the area above x-axis, bounded by the curves y = 2kx, x = 0 and x = 2 is then k = ?​
Test: Area Between A Curve And A Line - Question 9
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Write the shaded region as an integral
Test: Area Between A Curve And A Line - Question 10
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The area bounded by the curve:

 y = cos2 x between x = 0, x = π and x axis
Detailed Solution for Test: Area Between A Curve And A Line - Question 10

y = cos2 x [0,π]
∫(0 to π/2)cos2 xdx + ∫(π/2 to π)cos2 xdx
= 1/2∫(1 + cos 2x)
= [½(x + sin(2x)/2](0 to π/2] + [1/2(x + sin(2x)/2](π/2 to π)
= ½|π + 0 - 0 - 0| + 1/2|(π + 0) - π/2|
= π/4 + π/4 = π/2

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