List of top Mathematics Questions

Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

For a Linear Programming Problem (LPP), the given objective function is $Z = x + 2y$. The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph.

The point $P = ( \frac{3}{13}, \frac{24}{13} )$, $Q = ( \frac{3}{15}, \frac{15}{4} )$, $R = ( \frac{7}{3}, \frac{3}{2} )$, $S = ( \frac{18}{7}, \frac{7}{7} )$. Which of the following statements is correct?

In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints:

\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.

The solution for the differential equation $\log \left( \frac{dy}{dx} \right) = 3x + 4y$ is:
The order and degree of the following differential equation are, respectively: \[ \frac{d^4y}{dx^4} + 2 \frac{d^2y}{dx^2} + y^2 = 0. \]
\[ \int \frac{x + 5}{(x + 6)^2} e^x \, dx \] is equal to:
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:
If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?
If \[ f(x) = \begin{cases} \frac{\log(1 + ax) + \log(1 - bx)}{x}, & \text{for } x \neq 0 \\ k, & \text{for } x = 0 \end{cases} \] is continuous at $x = 0$, then the value of $k$ is:
\[ \sec^{-1} \left( -\sqrt{2} \right) - \tan^{-1} \left( \frac{1}{\sqrt{3}} \right) \] is equal to:
If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:

The following graph is a combination of:

Sum of two skew-symmetric matrices of the same order is always a/an:
If \[ A = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{pmatrix} \] then $A$ is a/an:
The probability of a component being defective is 0.01. There are 100 such components in a machine. Then the probability of two or more defective components in the machine is _______
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?
If the function \( f(z) = -x^2 + xy + y^2 + i(ax^2 + bxy + cy^2) \) of complex variable \(z = x + iy\) is analytic in the complex plane, then the values of \(a, b, c\) are _______
Let \( A \) be a \(3 \times 3\) matrix and \( B = 2A^2 + A^{-1} - I \), where \( I \) is a \(3 \times 3\) identity matrix. If the eigenvalues of \( A \) are 1, –1 and 2, then the trace of \( B \) is ________
Let \( A = \begin{bmatrix} a+1 & b & c \\ a & b+1 & c \\ a & b & c+1 \end{bmatrix} \). If determinant of the matrix \( A \) is zero, then \( (a + b + c)^3 = \_\_\_\_\_\_ \)
If the function \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \), where \( a>0 \), attains its local maximum and minimum at \( p \) and \( q \), respectively, such that \( p^2 = q \), then \( f(3) \) is equal to:
The general solution of the differential equation \( x^2 y'' - xy' + 5y = 0 \) is _______
The value of the real variable \( x>0 \) that minimizes the function \( f(x) = x^x e^{-x} \) is ________
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).