List of top Questions asked in CBSE CLASS XII

If x \(\begin{bmatrix}2\\3\end{bmatrix}\)+y \(\begin{bmatrix}-1\\1\end{bmatrix}\)=\(\begin{bmatrix}10\\5\end{bmatrix}\),find values of x and y. 

Solve the equation for x,y,z and t if 2\(\begin{bmatrix}x&y\\y&t\end{bmatrix}\)+3\(\begin{bmatrix}1&-1\\0&2\end{bmatrix}\)=3\(\begin{bmatrix}3&5\\4&6\end{bmatrix}\)

Find x and y, if 2\(\begin{bmatrix}1&3\\0&x\end{bmatrix}\)+\(\begin{bmatrix}y&0\\1&2\end{bmatrix}\)=\(\begin{bmatrix}5&6\\1&8\end{bmatrix}\)

Simplify \(\cos\theta\) \(\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}\)+\(\sin\theta\) \(\begin{bmatrix}\sin\theta&-\cos\theta\\\cos\theta&\sin\theta\end{bmatrix}\)

Evaluate|x y x+y y x+y x x+y x y|
If a,b and c are real numbers,and determinant Δ=|b+c c+a a+b c+a a+b b+c a+b b+c c+a|=0.
Show that either a+b+c=0 or a=b=c. 
Solve the equation|x+a x x x x+a x x x x+a|=0,a≠0
Prove that|a2 bc ac+c2 a2+ab b2 ac ab b2+bc c2|=4a2b2c2
Let A=[1-21 -231 115]verify that
(i)[adjA]-1=adj(A-1)
(ii)(A-1)-1=A

Verify A(adj A)=(adj A)A=IAII. \(\begin{bmatrix}2&3\\-4&-6\end{bmatrix}\)

Find adjoint of each of the matrices \(\begin{bmatrix}1&-1&2\\2&3&5\\-2&0&1\end{bmatrix}\)

If A=\(\begin{bmatrix}2&3&5\\3&2&-4\\1&1&-2\end{bmatrix}\),find A-1.UsingA-1 solve the system of equations
2x-3y+5z=11
3x+2y-4z=-5
x+y-2z=-3

Solve system of linear equations, using matrix method.
 2x+3y+3z=5
 x-2y+z=-4
 3x-y-2z=3

Solve system of linear equations, using matrix method.
x-y+z=4
2x+y-3z=0 
x+y+z=2

Solve system of linear equations, using matrix method.
2x+y+z=1
x-2y-z=\(\frac{3}{2}\)
3y-5z=9

Solve system of linear equations, using matrix method.
4x-3y=3
3x-5y=7

Solve system of linear equations, using matrix method.
  2x-y=-2
  3x+4y=3

Solve system of linear equations, using matrix method.
 5x+2y=4,
 7x+3y=5

Examine the consistency of the system of equations.
 5x−y+4z=5,
 2x+3y+5z=2,
 5x−2y+6z=−1

Examine the consistency of the system of equations.
 3x-y−2z=2,
 2y−z=−1
 3x−5y=3

Examine the consistency of the system of equations.
x+y+z=12x+3y+2z=2,
ax+ay+2az=4

Examine the consistency of the system of equations.
x+3y=5,
2x+6y=8

If \(A = \begin{bmatrix}        \frac{2}{3} & 1 & \frac 53           \\[0.3em]        \frac{1}{3} & \frac 23           & \frac{4}{3} \\[0.3em]        \frac 73           & 2 & \frac{2}{3}      \end{bmatrix}\) and \(B = \begin{bmatrix}        \frac{2}{5} & \frac 35 & 1           \\[0.3em]        \frac{1}{5} & \frac 25           & \frac{4}{5} \\[0.3em]        \frac 75           & \frac 65 & \frac{2}{5}      \end{bmatrix}\) then compute 3A-5B.

Examine the consistency of the system of equations.
2x-y=5,
x+y=4

Examine the consistency of the system of equations. 
x+2y=2,
2x+3y=3