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

What is the value of the determinant \[\begin{vmatrix}0 & 2 & 0 \\ 2 & 3 & 4 \\ 4 & 5 & 6\end{vmatrix} ?\]

Write the value of the determinant \[\begin{vmatrix}p & p + 1 \\ p - 1 & p\end{vmatrix}\]

Write the value of the determinant \[\begin{vmatrix}x + y & y + z & z + x \\ z & x & y \\ - 3 & - 3 & - 3\end{vmatrix}\]

Prove that the function 

If the determinant \[\begin{vmatrix}0 & x^2 - a & x^3 - b \\ x^2 + a & 0 & x^2 + c \\ x^4 + b & x - c & 0\end{vmatrix} = 0 \text{ is }\] 

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

If \[A_r = \begin{vmatrix}1 & r & 2^r \\ 2 & n & n^2 \\ n & \frac{n \left( n + 1 \right)}{2} & 2^{n + 1}\end{vmatrix}\] , then the value of \[\sum^n_{r = 1} A_r\] is

For what value of λ is the function 
\[f\left( x \right) = \begin{cases}\lambda( x^2 - 2x), & \text{ if }  x \leq 0 \\ 4x + 1 , & \text{  if } x > 0\end{cases}\]continuous at x = 0? What about continuity at x = ± 1?

Find the relationship between 'a' and 'b' so that the function 'f' defined by 

Find the points of discontinuity, if any, of the following functions: 

Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}2x , & \text{ if }  & x < 0 \\ 0 , & \text{ if }  & 0 \leq x \leq 1 \\ 4x , & \text{ if }  & x > 1\end{cases}\]

Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}x^{10} - 1, & \text{ if }  x \leq 1 \\ x^2 , & \text{ if } x > 1\end{cases}\]

Find the points of discontinuity, if any, of the following functions:  \[f\left( x \right) = \begin{cases}- 2 , & \text{ if }& x \leq - 1 \\ 2x , & \text{ if } & - 1 < x < 1 \\ 2 , & \text{ if }  & x \geq 1\end{cases}\]

In the following, determine the value of constant involved in the definition so that the given function is continuou: 

The function f (x) = tan x is discontinuous on the set