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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 25 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 (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

Solution:

QUESTION: 3

Solution:

QUESTION: 4

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

Solution:

QUESTION: 5

The solution of the differential equation is

Solution:

QUESTION: 6

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

Solution:

QUESTION: 7

Solution of is

Solution:

QUESTION: 8

The solution is

Solution:

QUESTION: 9

Solution of differential equation xdy – ydx = 0 represents

Solution:

QUESTION: 10

Integration factor of is

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

The solution of is

Solution:

QUESTION: 13

A primitive of* sin x cos x* is

Solution:

QUESTION: 14

Solution:

QUESTION: 15

If then

Solution:

QUESTION: 16

Solution:

QUESTION: 17

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Solution:

*Answer can only contain numeric values

QUESTION: 21

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

Solution:

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

QUESTION: 22

A function y = ƒ(x) satisfies the differential equation The value of |ƒ"(1)| is

Solution:

ƒ'(x) + x^{2}ƒ(x) = –2x, ƒ(1) = 1

⇒ ƒ'(1) + 1 = –2 ⇒ ƒ'(1) = –3

ƒ''(x) + 2xƒ(x) + x^{2}ƒ'(x) = –2

ƒ''(1) + 2ƒ(1) + ƒ'(1) = –2

ƒ''(1) = 3 – 4 = –1 ⇒ |ƒ''(1)| = 1

*Answer can only contain numeric values

QUESTION: 23

If the foci of the ellipse and the hyperbola coincide, then the value of b^{2} is :-

Solution:

*Answer can only contain numeric values

QUESTION: 24

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

Solution:

*Answer can only contain numeric values

QUESTION: 25

The area bounded by the loop of the curve 4y^{2} = x^{2} (4 – x^{2}) is :-

Solution:

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