List of practice Questions

Probability of getting a head in a fair coin toss:

Direction ratios of x-axis are:

Equation of line with slope 2 passing through origin:

Distance between points (1,2) and (4,6) is:

Number of permutations of 5 distinct objects is:

If $\log_a b = 2$, then $b = ?$

If $a + b = 5$ and $ab = 6$, find $a^2 + b^2$:

If a function is increasing, then its derivative is:

Evaluate: $\int x \, dx$

The derivative of $\sin x$ is:

If $f(x) = x^2 + 3x$, then $f'(x)$ is:

The interval in which \( y = x^2 e^x \) is decreasing is _____

The maximum value of the function \( f(x) = -|x+1| + 3, \; x \in \mathbb{R} \) is _____

The total revenue in Rupees received from the sale of \( x \) units of a product is given by \( R(x) = 3x^2 + 36x + 5 \). The marginal revenue, when \( x = 15 \), is _____

If \( y = \log_{2026}(\log_{2025} x) \), then \( \frac{dy}{dx} \)= _____

If \( x = a t^2, \; y = 2at \), then \( \frac{d^2 y}{dx^2} =\) _____

If function \( f \) is continuous at point \( x = \pi \) and \[ f(x) = \begin{cases} kx + 1, & x \le \pi \\ \cos x, & x>\pi \end{cases} \] then the value of \( k \) is ______

If inverse matrix of \( A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix} \) is \( A^{-1} = \begin{bmatrix} a & \frac{3}{11} \\ \frac{1}{11} & b \end{bmatrix} \), then a + b = _____

If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix} \] then \( A^2 + B^2 = \underline{\hspace{2cm}} \)

If area of triangle is 35 sq. units with vertices \( (2,-6), (5,4) \) and \( (k,4) \), then \( k \) is _____

If \( A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} \), then \( A^2 + I = \) _____

If \( A \) and \( B \) are skew-symmetric matrices of same order, then \( AB - BA \) is a _____

If \( A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} \) is such that \( A^2 = I \), then _____