List of top Mathematics Questions

Find the area of the triangle whose sides are given by vectors: \[ \vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \vec{b} = \hat{i} - \hat{j} + 3\hat{k} \]
Using integration, find the area bounded by the circle \( x^2 + y^2 = 16 \) in the first quadrant.
Find the critical points of the function \( f(x) = 2x^3 - 3x^2 - 12x + 15 \):
Principal value of \( \sin^{-1}(1) \) is:
If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of matrix \( A^T \) is:
Evaluate \( \int_0^1 \frac{dx}{1 + x^2} \):
Evaluate \( \int_{\pi/6}^{\pi/3} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \):
Find the order of the differential equation \( \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 3y = 0 \):
If \( y = \log x \), then \( \frac{dy}{dx} \) is:
If \( A \) is a square matrix of order \( 2 \times 2 \) and \( |A| = 5 \), then \( | \text{Adj}(A) | \) is:
The radius of a circle is increasing at the rate of 2 m/s. The rate of change of its circumference is:
Vector equation of the line \( \frac{x - 5}{4} = \frac{y - 3}{5} = \frac{z + 3}{-8} \) is:
Objective function of a linear programming problem is:
Relation \( R = \{(x, y): x<y^2 \text{ where } x, y \in \mathbb{R}\} \) is:
Range of the function \( \cos^{-1} \):
If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:
Name of the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is:
Find the A.P. whose third term is 16 and seventh term exceeds the fifth term by 12. Also, find the sum of first 29 terms of the A.P.
Solve the equation \(4x^2 - 9x + 3 = 0\), using quadratic formula.
Check whether the following pair of equations is consistent or not. If consistent, solve graphically:
\[ x + 3y = 6\\ 3y - 2x = -12 \]
If \(\alpha, \beta\) are zeroes of the polynomial \(8x^2 - 5x - 1\), then form a quadratic polynomial in x whose zeroes are \(\frac{2}{\alpha}\) and \(\frac{2}{\beta}\).
If \( X \) is a continuous random variable whose probability density function is given by

\[ f_X(x) = \begin{cases} c x^3 + 0.25, & \text{for } 0 \leq x \leq 1,\ c \in \mathbb{R} \\ 0, & \text{elsewhere} \end{cases} \]

Then the value of \( c \) is ________________ (in integer).
If \( X \) is a continuous random variable whose probability density function is given by

\[ f_X(x) = \begin{cases} \dfrac{1}{x^2}, & \text{for } 1 < x < \infty \\ 0, & \text{elsewhere} \end{cases} \]

Then the median of \( X \) is ________________ (in integer).

Consider a lottery with three possible outcomes: 

The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.

Find a point \( P \) on the line \( \frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9} \) such that its distance from point \( Q(2, 4, -1) \) is 7 units. Also, find the equation of the line joining \( P \) and \( Q \).