List of top Mathematics Questions

Evaluate:
\[ I = \int_2^4 \left( |x - 2| + |x - 3| + |x - 4| \right) dx \]

If sum of first 9 terms of an $A.P.$ is $81$ and the sum of first $17$ terms is $289$, find its first term and the common difference.
If \( 2P(A) = P(B) = \frac{5}{13} \) and \( P(A|B) = \frac{2}{5} \), then find \( P(A \cup B) \).
What is the value of \( \csc 31^\circ \sec 59^\circ \)?
$\cot(90^\circ - \theta) = ?$
The value of \( 1 + \sec 19^\circ \sin 71^\circ \) is:
The value of \( \frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} \) is:
The 6th term of the AP \( \sqrt{27}, \sqrt{75}, \sqrt{147}, \ldots \) is:
If \[ A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix} \] and \( A^T \) represents the transpose of \( A \), then calculate \( AA^T - A - A^T \).
Sumit can row a distance of 9 km in one hour in still water and he can now row the same distance in 45 minutes with the current. Find the total time taken by him to row 36 km with the current and return to the starting point.
For two invertible matrices A and B of order n, prove that \( (AB)^{-1} = B^{-1}A^{-1} \).
If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
Evaluate: \(\int \sqrt{3 - 2x - x^2} dx\).
Find the vector equation of a straight line passing through the point (5, 2, -4) and parallel to the vector \( 3\hat{i} + 2\hat{j} - 8\hat{k} \).
The number of ways of dividing 15 persons into 3 groups containing 3, 5 and 7 persons so that two particular persons are not included into the 5 persons group is
Raina is 1.5 m tall. At an instant, his shadow is 1.8 m long. At the same instant, the shadow of a pole is 9 m long. How tall is the pole?
If \( 3\overline{i} + \overline{j} + \overline{k} \), \( 2\overline{i} + \overline{k} \), and \( \overline{i} + 5\overline{j} \) are the position vectors of three non-collinear points A, B, C respectively. If the perpendicular drawn from C onto \( \overline{AB} \) meets \( \overline{AB} \) at the point \( a\overline{i} + b\overline{j} + c\overline{k} \), then \( a + b + c = \)
Let \( f, g : \mathbb{R} \to \mathbb{R} \) be two functions defined by \[ f(x) = \begin{cases} |x|^{1/8} \sin \tfrac{1}{|x|} \cos x & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases} \] and \[ g(x) = \begin{cases} e^x \cos \tfrac{1}{x} & \text{if } x \neq 0 \\ 1 & \text{if } x = 0 \end{cases} \] Then, which one of the following is TRUE?
The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:

A quadratic polynomial \( (x - \alpha)(x - \beta) \) over complex numbers is said to be square invariant if \[ (x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2). \] Suppose from the set of all square invariant quadratic polynomials we choose one at random. The probability that the roots of the chosen polynomial are equal is ___________. (rounded off to one decimal place) 

The domain of the real valued function $ f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x) $ is
What is the next number in the sequence? 2, 6, 12, 20, 30, ?

For the curve \( \sqrt{x} + \sqrt{y} = 1 \), find the value of \( \frac{dy}{dx} \) at the point \( \left(\frac{1}{9}, \frac{1}{9}\right) \).

A batch of 36 school children goes for an excursion trip to Nainital. When one 10-year-old child is replaced with another child, the average age of the children in the batch increases by \( 2\frac{1}{2} \) months. What is the age of the new child?
A number is selected randomly from each of the following two sets:
{1, 2, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8, 9}
What is the probability that the sum of the numbers is 9?