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

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.

In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

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.

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 

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to \[ \frac{2}{3} \] of the diameter of the sphere.

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is \[\cot^{- 1} \left( \sqrt{2} \right)\] .

A given quantity of metal is to be cast into a half cylinder with a rectangular base and semicircular ends. Show that in order that the total surface area may be minimum the ratio of the length of the cylinder to the diameter of its semi-circular ends is \[\pi : (\pi + 2)\].

If P(A) = 0·4, P(B) = p, P(A ⋃ B) = 0·6 and A and B are given to be independent events, find the value of 'p'.