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

Find the value of p, so that the lines `l_1:(1-x)/3=(7y-14)/p=(z-3)/2 and l_2=(7-7x)/3p=(y-5)/1=(6-z)/5 ` are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, – 4) and parallel to line l₁.

Integrate the functions:

`(1+ log x)^2/x`

Find x, y, a and b if

`[[2x-3y,a-b,3],[1,x+4y,3a+4b]]`=`[[1,-2,3],[1,6,29]]`

Find the values of a, b, c and d from the following equations:`[[2a + b,a-2b],[5c-d,4c + 3d ]]`= `[[4,- 3],[11,24]]`

Find x, y and z so that A = B, where`A= [[x-2,3,2x],[18z,y+2,6x]],``b=[[y,z,6],[6y,x,2y]]`

`If [[x,3x- y],[2x+z,3y -w ]]=[[3,2],[4,7]]` find x,y,z,w

`If [[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]`Find X,Y,Z,W.

`If [[x + 3 , z + 4 ,     2y-7 ],[4x + 6,a-1,0 ],[b-3,3b,z + 2c ]]= [[0,6,3y-2],[2x,-3,2c-2],[2b + 4,-21,0]]`Obtain the values of a, b, c, x, y and z.

`If [[2x +1    5x],[0     y^2 +1]]``= [[x+3   10],[0      26 ]]`, find the value of (x + y).

`If [[xy          4],[z+6     x+y ]]``=[[8     w],[0     6]]`, then find the values of X,Y,Z and W . 

Given an example of

a row matrix which is also a column matrix,

For what values of x and y are the following matrices equal?

`A=[[2x+1   2y],[0              y^2 - 5y]]``B=[[x + 3      y^2 +2],[0        -6]]`

Find the values of x and y if

`[[X + 10,Y^2 + 2Y],[0, -4]]`=`[[3x +4,3],[0,y^2-5y]]`

For what values of a and b if A = B, where

`A = [[a + 4        3b],[8        -6]]   B = [[2a +2              b^2+2],[8                    b^2  - 5b]]`

Disclaimer: There is a misprint in the question, b² − 5b should be written instead of b² − 56.

If  \[\begin{bmatrix}x + 3 & 4 \\ y - 4 & x + y\end{bmatrix} = \begin{bmatrix}5 & 4 \\ 3 & 9\end{bmatrix}\] , find x and y

Find the value of x from the following: `[[2x - y          5],[ 3                         y ]]` = `[[6            5 ],[3         - 2\]]`

Find the value of x, if  \[\begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]

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.