List of top Mathematics Questions

For a Linear Programming Problem (LPP), the given objective function \( Z = 3x + 2y \) is subject to constraints: \[ x + 2y \leq 10, \] \[ 3x + y \leq 15, \] \[ x, y \geq 0. \]

The correct feasible region is:

The integrating factor of the differential equation \[ e^{-\frac{2x}{\sqrt{x}}} \, \frac{dy}{dx} = 1 \] is:
Assertion (A): Let \( A = \{ x \in \mathbb{R} : -1 \leq x \leq 1 \} \). If \( f : A \to A \) be defined as \( f(x) = x^2 \), then \( f \) is not an onto function.
Reason (R): If \( y = -1 \in A \), then \( x = \pm \sqrt{-1} \notin A \).
The integral \[ \int \sqrt{1 + \sin x} \, dx \] is equal to:

The area of the region enclosed between the curve \( y = |x| \), x-axis, \( x = -2 \)} and \( x = 2 \) is:

The function $f$ defined by \[ f(x) = \begin{cases} x, & \text{if } x \leq 1 \\ 5, & \text{if } x>1 \end{cases} \] is not continuous at :
If $f(x) = 2x + \cos x$, then $f(x)$ :
The area of the region enclosed by the curve $y = \sqrt{x}$ and the lines $x = 0$ and $x = 4$ and the x-axis is :
\[ \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \] is equal to :
Assertion : In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution.
Reason (R): A feasible region is defined as the region that satisfies all the constraints.
For real $x$, let $f(x) = x^3 + 5x + 1$. Then :
If \( E \) and \( F \) are two events such that \( P(E)>0 \) and \( P(F) \neq 1 \), then \( P(E \,|\, F) \) is:
A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \( Z = 5x + 7y \), where \( x \) and \( y \) are the number of units of X and Y respectively sold. Which of the following statements is correct?
The function \( f(x) = x^2 - 4x + 6 \) is increasing in the interval:
Assertion (A): Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R): The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.
The integral \( \int \frac{dx}{\sin^2 x \cos^2 x} \) is equal to
The principal value of \( \sin^{-1} \left( \cos \frac{43\pi}{5} \right) \) is
The values of \(x\) for which the angle between the vectors \( \vec{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k} \) and \( \vec{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k} \) is obtuse, is:
The equation of a line parallel to the vector \( 3 \hat{i} + \hat{j} + 2 \hat{k} \) and passing through the point \( (4, -3, 7) \) is:
If \( \vec{PQ} \times \vec{PR} = 4 \hat{i} + 8 \hat{j} - 8 \hat{k} \), then the area \( (\triangle PQR) \) is
The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
The area of the shaded region
In the following probability distribution, the value of p is:
probability distribution
If A denotes the set of continuous functions and B denotes the set of differentiable functions, then which of the following depicts the correct relation between set A and B?
set of continuous functions
Let \( |z_1 - 8 - 2i| \leq 1 \) and \( |z_2 - 2 + 6i| \leq 2 \), where \( z_1, z_2 \in \mathbb{C} \). Then the minimum value of \( |z_1 - z_2| \) is: