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

Using determinants, find the equation of the line joining the points

(1, 2) and (3, 6)

Using determinants, find the equation of the line joining the points

(3, 1) and (9, 3)

Find values of k, if area of triangle is 4 square units whose vertices are 
(k, 0), (4, 0), (0, 2)

Find values of k, if area of triangle is 4 square units whose vertices are 

(−2, 0), (0, 4), (0, k)

x − 2y = 4
−3x + 5y = −7

2x − y = 1
7x − 2y = −7

Find the values of x and y, if \[2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]

Prove that :

Prove that :

Prove that :

Prove that :

If  \[x\binom{2}{3} + y\binom{ - 1}{1} = \binom{10}{5}\] , find the value of x.

If  \[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] , find x − y.

If  \[\begin{bmatrix}xy & 4 \\ z + 6 & x + y\end{bmatrix} = \begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}\] , write the value of (x + y + z).

If  \[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\] , then write the value of (x, y).

Prove that :

Prove that :

Prove that :

Prove that :

\[\begin{vmatrix}\left( b + c \right)^2 & a^2 & bc \\ \left( c + a \right)^2 & b^2 & ca \\ \left( a + b \right)^2 & c^2 & ab\end{vmatrix} = \left( a - b \right) \left( b - c \right) \left( c - a \right) \left( a + b + c \right) \left( a^2 + b^2 + c^2 \right)\]

Prove that :