List of top Questions asked in CBSE CLASS XII

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.

Which of the following is correct?

Choose the correct answer. Let A be a square matrix of order 3×3,then IkAI is equal to 

By using properties of determinants, show that: \(\begin{vmatrix}1&x&x^2\\x^2&1&x\\x&x^2&1\end{vmatrix}\)=(1-x³)²

Consider f: R₊\(\to\)[4,∞) given by f(x) = x²+4. Show that f is invertible with the inverse f⁻¹ of given f by \(f^{-1}(y)= \sqrt {y-4}\) , where R₊is the set of all non-negative real numbers.

By using properties of determinants, show that: \(\begin{vmatrix}-a^2&ab&ac\\ba&-b^2&bc\\ca&cb&-c^2\end{vmatrix}\)=4a²b²c²

By using properties of determinants ,show that: \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)=0

Consider f: R\(\to\)R given by f(x) = 4x+3. Show that f is invertible. Find the inverse of f.

Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}2&7&65\\3&8&75\\5&9&86\end{vmatrix}\)=0

Show that the Signum Function f: R\(\to\)R, given by 

is neither one-one nor onto.

Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}=0\)

If \(\begin{vmatrix}x&2\\18&x\end{vmatrix}=\begin{vmatrix}6&2\\18&6\end{vmatrix}\),then x is equal to

Find values of x, if 
(i)\(\begin{vmatrix}2&4\\2&1\end{vmatrix}\)=\(\begin{vmatrix}2x&4\\6&x\end{vmatrix}\)

(ii)\(\begin{vmatrix}2&3\\4&5\end{vmatrix}\)=\(\begin{vmatrix}x&3\\2x&5\end{vmatrix}\)

Show that the Modulus Function f: R\(\to\)R given by f(x) = IxI, is neither one-one nor onto, where IxI is x, if x is positive or 0 and IxI is −x, if x is negative.

If A=\(\begin{bmatrix}1&0&1\\0&1&2\\0&0&4\end{bmatrix}\),then show that\(\mid A\mid=27\mid A \mid\)