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JEE Main Maths Test- 5 - JEE MCQ


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25 Questions MCQ Test Mock Tests for JEE Main and Advanced 2024 - JEE Main Maths Test- 5

JEE Main Maths Test- 5 for JEE 2024 is part of Mock Tests for JEE Main and Advanced 2024 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.
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JEE Main Maths Test- 5 - Question 1

The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

Detailed Solution for JEE Main Maths Test- 5 - Question 1
Toolbox:
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

If  , then solution of above equation is 

JEE Main Maths Test- 5 - Question 3

Order and degree of differential equation

 are

JEE Main Maths Test- 5 - Question 4

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
The solution of the differential equation   is 
JEE Main Maths Test- 5 - Question 6

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

Solution of   is 

Detailed Solution for JEE Main Maths Test- 5 - Question 7

JEE Main Maths Test- 5 - Question 8

The solution   is 

JEE Main Maths Test- 5 - Question 9

Solution of differential equation xdy – ydx = 0 represents 

JEE Main Maths Test- 5 - Question 10

Integration factor of   is 

JEE Main Maths Test- 5 - Question 11

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

The solution of   is 

JEE Main Maths Test- 5 - Question 13
A primitive of sin x cos x is
JEE Main Maths Test- 5 - Question 14
JEE Main Maths Test- 5 - Question 15
If   then
JEE Main Maths Test- 5 - Question 16

JEE Main Maths Test- 5 - Question 17
JEE Main Maths Test- 5 - Question 18

The primitive of | x |, when x < 0 is

JEE Main Maths Test- 5 - Question 19
JEE Main Maths Test- 5 - Question 20
*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 21

If  is differentiable at x = 1, then the value of (A + 4B) is


Detailed Solution for JEE Main Maths Test- 5 - Question 21

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

*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 22

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

*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 23

If the foci of the ellipse  and the hyperbola  coincide, then the value of b2 is :-


*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 24

Let f(x) = min.  for all x ≤ 1. Then the area bounded by y = f(x) and the x-axis is :-


Detailed Solution for JEE Main Maths Test- 5 - Question 24

*Answer can only contain numeric values
JEE Main Maths Test- 5 - Question 25

The area bounded by the loop of the curve 4y2 = x2 (4 – x2) is :-


Detailed Solution for JEE Main Maths Test- 5 - Question 25

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