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Sample Paper 2020
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Q29 of 36 Page 1

Solve the differential equation

Given:


We need to solve the differential equation.



⇒


⇒


Put y = vx and differentiating both sides,


⇒


Now, putting the value in the equation,


⇒


⇒


⇒


Integrating both sides,


⇒


⇒


Putting the value of v,


⇒


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27

Let be a function defined as f(x) = , where and . Is the function one-one or onto? Is f invertible? If yes, then find its inverse.

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If , then prove that .

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If x = a(cos2θ + 2θsin2θ) and y = a(sin2θ – 2θcos2θ), find at θ = .


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Evaluate

31

Two numbers are selected at random (without replacement) from first 7 natural numbers. If X denotes the smaller of the two numbers obtained, find the probability distribution of X. Also, find mean of the distribution.

OR


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Questions · 36
Sample Paper 2020
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