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This mock test of Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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

Solution:

Toolbox:

Equation of a family of circles in (xâˆ’h)^2+(yâˆ’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

QUESTION: 2

If , then solution of above equation is

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QUESTION: 3

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QUESTION: 4

Differential equation for y = A cos αx + B sin αx where A and B are arbitrary constants is

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QUESTION: 5

The solution of the differential equation is

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QUESTION: 6

The integrating factor of the different equation dy/dx ( x log x ) + y = 2 log x is given by:

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QUESTION: 7

Solution of is

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QUESTION: 8

The solution is

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QUESTION: 9

Solution of differential equation xdy – ydx = 0 represents

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QUESTION: 10

Integration factor of is

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QUESTION: 11

A continuously differentiable function y = f(x) ∈ (0,π ) satisfying y = 1 + y, y (0) = 0 = y(π)is

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QUESTION: 12

The solution of is

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QUESTION: 13

A primitive of* sin x cos x* is

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QUESTION: 14

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QUESTION: 15

If then

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QUESTION: 16

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QUESTION: 17

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QUESTION: 18

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

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QUESTION: 19

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QUESTION: 20

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QUESTION: 21

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QUESTION: 22

The value of ( a x^{3} + bx + c) dx = depends on

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QUESTION: 23

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QUESTION: 24

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QUESTION: 25

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QUESTION: 26

Sin^{ 11} x dx =

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QUESTION: 27

Sin^{3} x cos^{2} x dx =

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QUESTION: 28

Cos^{3} x dx =

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QUESTION: 29

| Sin π x | dx =

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QUESTION: 30

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