Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

Find the second order derivative of the function.

x² + 3x + 2

Find the second order derivative of the function.

x²⁰

Find the second order derivative of the function.

x . cos x

Find the second order derivative of the function.

log x

Find the second order derivative of the function.

x³ log x

Find the second order derivative of the function.

e^x sin 5x

Find the second order derivative of the function.

e^6x cos 3x

Find the second order derivative of the function.

tan^–1 x

Find the second order derivative of the function.

log (log x)

Find the second order derivative of the function.

sin (log x)

If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.

If y = cos^–1 x, find `(d^2y)/dx^2` in terms of y alone.

If y = 3 cos (log x) + 4 sin (log x), show that x²y₂ + xy₁ + y = 0.

If y = Ae^mx + Be^nx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.

If y = 500e^7x + 600e^–7x, show that `(d^2y)/(dx^2)` = 49y.

If e^y (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.