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Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation

25 Questions MCQ Test Mock Test Series for JEE Main & Advanced 2022 | Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation

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Attempt Mathematics Test 5 - Definite And Indefinite Integration, Differential Equation | 25 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mock Test Series for JEE Main & Advanced 2022 for JEE Exam | Download free PDF with solutions
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

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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 Solution:
QUESTION: 15
If then
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QUESTION: 16 Solution:
QUESTION: 17 Solution:
QUESTION: 18

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

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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) + 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
QUESTION: 23

If the foci of the ellipse and the hyperbola coincide, then the value of b2 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 4y2 = x2 (4 – x2) is :-

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