PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the value of y, if \[\begin{bmatrix}x - y & 2 \\ x & 5\end{bmatrix} = \begin{bmatrix}2 & 2 \\ 3 & 5\end{bmatrix}\]

if  \[\begin{bmatrix}2x + y & 3y \\ 0 & 4\end{bmatrix} = \begin{bmatrix}6 & 0 \\ 6 & 4\end{bmatrix}\]  , then find x.

If \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , find A + A^T.

If \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.

Which of the given values of x and y make the following pairs of matrices equal? \[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix}, \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\] 

If matrix  \[A = \left[ a_{ij} \right]_{2 \times 2}\] where 

If \[A = \frac{1}{\pi}\begin{bmatrix}\sin^{- 1} \left( \ pix \right) & \ tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & \cot^{- 1} \left( \ pix \right)\end{bmatrix}, B = \frac{1}{\pi}\begin{bmatrix}- \cos^{- 1} \left( \ pix \right) & \tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & - \tan^{- 1} \left( \ pix \right)\end{bmatrix}\]

A − B is equal to

Discuss the continuity and differentiability of the 

The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is

The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is

The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by

The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is

The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is

Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is

The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents

The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is

If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then