List of top Mathematics Questions asked in CBSE CLASS XII

For \( f(x) = x + \frac{1{x} \), (\( x \neq 0 \))}

If \( \begin{vmatrix} -1 & -2 & 5 \\ -2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = -86 \), then the sum of all possible values of \( a \) is

\( \int \frac{dx}{\sec x + \tan x} \) is equal to

If \( A = \begin{bmatrix} \tan x & \cot x \\ -\cot x & \tan x \end{bmatrix} \) and \( A + A' = 2I \), then value of \( x \in [0, \pi/2] \) is

If \( x + y = xy \), then \( \frac{dy}{dx} \) is

For a square matrix \( A \), \( (3A)^{-1 = \)}

A relation \( R \) on set \( A = \{1, 2, 3\} \) is defined as \( R = \{(1, 3), (3, 3), (1, 1), (2, 2), (3, 1)\ \) is}

If \( A = \begin{bmatrix} 1 & a & b \\ -1 & 2 & c \\ 0 & 5 & 3 \end{bmatrix} \) is a symmetric matrix, then the value of \( 3a + b + c \) is

If \( A \) and \( B \) are square matrices of same order, then which of the following statements is/are always true?
(i) $(A+B)(A-B)=A^2-B^2$
(ii) $AB=BA$
(iii) $(A+B)^2=A^2+AB+BA+B^2$
(iv) $AB=0\Rightarrow A=0\text{ or }B=0$}

Direction cosines of line \( \frac{1 - x}{0} = y = z \) are

In a linear programming problem, the linear function which has to be maximized or minimized is called

For the feasible region shown below, the non-trivial constraints of the linear programming problem are

For two events \( A \) and \( B \) such that \( P(A) \neq 0 \) and \( P(B) \neq 1 \), \( P(A' / B') = \)

If \( x = a(\sin t - t \cos t) \) and \( y = b(\cos t + t \sin t) \), then find \( \frac{dy}{dx} \) and \( \frac{d^2y}{dx^2} \).

Solve the following linear programming problem graphically :
Minimize \( Z = 13x - 15y \)
Subject to constraints
\( x + y \leq 7, \)
\( 2x - 3y + 6 \geq 0, \)
\( x \geq 0, y \geq 0 \)

If \( \begin{bmatrix} 3 & -1 & \sin 3x \\ -7 & 4 & \cos 2x \\ -11 & 7 & 2 \end{bmatrix} \) is a singular matrix, then find all values of \( x \) where \( x \in [0, \pi/2] \).

A relation \(R\) is defined on \(Z\), the set of integers, as \[ R = \{(x,y) : |x-y| \text{ is divisible by a prime number } 'p', x,y \in Z\}. \] Check whether \(R\) is an equivalence relation or not.

Show that line \( AB \) passing through points \( A(0, 4, 1), B(2, 3, -1) \) and the line \( CD \) passing through points \( C(4, 5, 0), D(2, 6, 2) \) are parallel. Also, find distance between them.

A function \( f : R - \{3/5\} \to R - \{3/5\} \) is defined as \( f(x) = \frac{3x + 2{5x - 3} \). Show that \( f \) is one-one and onto.}

If \( A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix} \), find \( A^{-1} \) and use it to solve the following system of equations :
\( -2y + z = 7, 2x - y - z = 8, x - 2y = 10 \)

Find the general solution of the differential equation \( (y^2 - x^2)dx = 2xy dy \)

If \( I_1 = \int_{-\pi/4}^{\pi/4} \frac{dx}{1 + \cos 2x} \) and \( I_2 = \int_{-1/2}^{1/2} |x| dx \), then show that \( I_1 - 4I_2 = 0 \).

Find : \( \int \frac{x^2}{(x^2 + 9)(x^2 + 16) dx \)}

Find \( \int \sqrt{\frac{x + 2}{x - 2}} dx \)

Find the particular solution of the differential equation \( (1 + e^{2x})dy + (1 + y^2)e^x dx = 0 \), given that \( y(1) = 0 \).