Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

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`.

If y = (tan^–1 x)², show that (x² + 1)² y₂ + 2x (x² + 1) y₁ = 2

Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `P(2veca + vecb)` and `Q(veca - 3vecb)` externally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.

Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx