List of top Mathematics Questions asked in CBSE CLASS XII

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+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

Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to

For the matrix A=\(\begin{bmatrix}3&2\\1&1\end{bmatrix}\),find the numbers a and b such that A²+ aA+bI=O. 

Let A=\(\begin{bmatrix}3&7\\2&5\end{bmatrix}\)and B=\(\begin{bmatrix}6&8\\7&9\end{bmatrix}\),Verify that (AB)^-1=B^-1A^-1.

Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&0&0\\0& \cos\alpha& \sin\alpha\\0&\sin\alpha&-\cos\alpha\end{bmatrix}\)

Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\)

Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)

Find the inverse of each of the matrices (if it exists). \(\begin{bmatrix}1&0&0\\3&3&0\\5&2&-1\end{bmatrix}\)

Find adjoint of each of the matrices. \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\)

For the matrices A and B, verify that (AB)′=B'A' where
I. A=\(\begin{bmatrix}1\\-4\\3\end{bmatrix}\),B=\(\begin{bmatrix}-1&2&1\end{bmatrix}\) 

II. A= \(\begin{bmatrix}0\\1\\2\end{bmatrix}\),B=\(\begin{bmatrix}1&5&7\end{bmatrix}\)

Using Cofactors of elements of second row, evaluate △=\(\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}\)

Consider f: R₊\(\to\) [−5,∞) given by f(x) = 9x² + 6x − 5. Show that f is invertible with 
\(f^{-1}(y) = \frac {(\sqrt {y+6})-1}{3}\)

Consider f: {1, 2, 3} \(\to\) {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f⁻¹ and show that (f⁻¹)⁻¹= f.