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JEE Exam  >  JEE Tests  >  Mock Tests for JEE Main and Advanced 2025  >  JEE Main Maths Test- 5 - JEE MCQ

JEE Main Maths Test- 5 - JEE MCQ


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25 Questions MCQ Test Mock Tests for JEE Main and Advanced 2025 - JEE Main Maths Test- 5

JEE Main Maths Test- 5 for JEE 2024 is part of Mock Tests for JEE Main and Advanced 2025 preparation. The JEE Main Maths Test- 5 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Maths Test- 5 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Maths Test- 5 below.
Solutions of JEE Main Maths Test- 5 questions in English are available as part of our Mock Tests for JEE Main and Advanced 2025 for JEE & JEE Main Maths Test- 5 solutions in Hindi for Mock Tests for JEE Main and Advanced 2025 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt JEE Main Maths Test- 5 | 25 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mock Tests for JEE Main and Advanced 2025 for JEE Exam | Download free PDF with solutions
JEE Main Maths Test- 5 - Question 1
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The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

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Equation of a family of circles in (x−h)^2+(y−k)^2=a^2 where (h,k) are the centers and a is the radius.
If the given equation has 'n' arbitary constants, then the given equation will be of h order

We are asked to form the differential equations of all circles which pass through the orgin and whose centers lies on y-axis
Since it is given that the center lies on the y-axis, the sketch of the circle is as shown


JEE Main Maths Test- 5 - Question 2
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If  , then solution of above equation is 

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JEE Main Maths Test- 5 - Question 3
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Order and degree of differential equation

 are

JEE Main Maths Test- 5 - Question 4
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Differential equation for y = A cos αx + B sin αx where A and B are arbitrary constants is
JEE Main Maths Test- 5 - Question 5
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The solution of the differential equation   is 
JEE Main Maths Test- 5 - Question 6
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The integrating factor of the different equation dy/dx ( x log x ) + y = 2 log x is given by:
JEE Main Maths Test- 5 - Question 7
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Solution of   is 
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JEE Main Maths Test- 5 - Question 8
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The solution   is 
JEE Main Maths Test- 5 - Question 9
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Solution of differential equation xdy – ydx = 0 represents 
JEE Main Maths Test- 5 - Question 10
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Integration factor of   is 
JEE Main Maths Test- 5 - Question 11
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A continuously differentiable function  y = f(x) ∈ (0,π ) satisfying  y = 1 + y, y (0) = 0 = y(π)is 
JEE Main Maths Test- 5 - Question 12
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The solution of   is 
JEE Main Maths Test- 5 - Question 13
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A primitive of sin x cos x is
JEE Main Maths Test- 5 - Question 14
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JEE Main Maths Test- 5 - Question 15
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If   then
JEE Main Maths Test- 5 - Question 16
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JEE Main Maths Test- 5 - Question 17
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JEE Main Maths Test- 5 - Question 18
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The primitive of | x |, when x < 0 is
JEE Main Maths Test- 5 - Question 19
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JEE Main Maths Test- 5 - Question 20
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*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 21
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If  is differentiable at x = 1, then the value of (A + 4B) is

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ƒ(x) is continuous  A + B = A + 3 – B
⇒ B = 3/2
ƒ(x) is differentiable 2B = 6 + A 
⇒ A = –3

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JEE Main Maths Test- 5 - Question 22
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A function y = ƒ(x) satisfies the differential equation  The value of |ƒ"(1)| is

Detailed Solution for JEE Main Maths Test- 5 - Question 22

ƒ'(x) + x2ƒ(x) = –2x, ƒ(1) = 1
⇒    ƒ'(1) + 1 = –2     ⇒    ƒ'(1) = –3
ƒ''(x) + 2xƒ(x) + x2ƒ'(x) = –2
ƒ''(1) + 2ƒ(1) + ƒ'(1) = –2
ƒ''(1) = 3 – 4 = –1  ⇒ |ƒ''(1)| = 1

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JEE Main Maths Test- 5 - Question 23
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If the foci of the ellipse  and the hyperbola  coincide, then the value of b2 is :-

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JEE Main Maths Test- 5 - Question 24
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Let f(x) = min.  for all x ≤ 1. Then the area bounded by y = f(x) and the x-axis is :-

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JEE Main Maths Test- 5 - Question 25
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The area bounded by the loop of the curve 4y2 = x2 (4 – x2) is :-

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