Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation


30 Questions MCQ Test JEE Main Mock Test Series 2020 & Previous Year Papers | Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation


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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

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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


QUESTION: 2

If  , then solution of above equation is 

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QUESTION: 3

Order and degree of differential equation

 are

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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 x3 + 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

 Sin3 x cos2 x dx = 

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QUESTION: 28

 Cos3 x dx = 

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QUESTION: 29

 | Sin π x | dx = 

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QUESTION: 30

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