Math Class 12 New Book Chapter 4 MCQs Federal Board
Math Class 12 New Book Chapter 4 MCQs Federal Board
(i)
The order of differential equation
$$x\;\frac{d^3y}{dx^3}-2{(\frac{dy}{dx})}^4+\;y=0,$$ is:
a) 1
b) 2
c) 3
d) 4
Correct option is (c)
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(ii)
The degree of differential equation
$$\frac{d^2y}{dx^2}\;+9y^3=\sin\;x,$$ is:
a) 0
b) 1
c) 2
d) 3
Correct option is (b)
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(iii)
y = 8 is a solution of the differential equation:
$$a)\;\frac{dy}{dx}+8y=32\\b)\;\frac{dy}{dx}+6y=32\\c)\;\frac{dy}{dx}+5y=32\\d)\;\frac{dy}{dx}+4y=32$$
Correct option is (d)
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(iv)
$$f(x,\;y)\;=\;\frac{x^3-y^3}{x-y}$$ is a homogeneous function of degree:
a) 1
b) 2
c) 3
d) 4
Correct option is (b)
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(v)
The solution of the differential equation dy = dx is:
$$a)\;y=x+c\\b)\;y=x^2+c\\c)\;y^2=x^2+c\\d)\;y^2=x+c$$
Correct option is (a)
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(vi)
The number of arbitrary constants present in the general solution of a differential equation of first order is:
a) 1
b) 2
c) 3
d) 0
Correct option is (a)
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(vii)
The differential equation
$$\frac{dy}{dx}=e^{x+y}$$ has solution:
$$a)\;e^{-x-y}=c\\b)\;e^{-x}+e^y=c\\c)\;e^x+e^y=c\\d)\;e^x+e^{-y}=c$$
Correct option is (d)
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(viii)
The general solution of
$$y^2dy-x^2dx=0$$ is:
$$a)\;x^2-y^2=c\\b)\;x^3+y^3=c\\c)\;x^3-y^3=c\\d)\;x^2+y^2=c$$
Correct option is (c)
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(ix)
The solution of cos x sin y dx + sin x cos y dy = 0 is:
a) sin x cos y = c
b) cos x cos y = c
c) cos x sin y = c
d) sin x sin y = c
Correct option is (d)
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(x)
Which of the following cannot be the order of differential equation?
a) -1
b) 1
c) 10
d) 100
Correct option is (a)
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