List of top Mathematics Questions

Given \( Z = 80x + 120y \), subject to constraints are \( x + 3y \leq 30; 3x + 4y \leq 60; x \geq 0; y \geq 0 \). \( P \) is one of the corner points of the feasible region for the given Linear Programming Problem. Then the coordinate of \( P \) is

The angle between two lines is \(45^\circ\) and slope of one line is \( \frac{1}{4} \) then which is the possible value of the slope of the other line.

Let \( f(x) = x\sqrt{4ax - x^2, \; a > 0 \) then \( f'(x) \) at \( x = 2a \) is:}

Value of the determinant of a matrix \( A \) of order \( 3 \times 3 \) is 7Then the value of the determinant formed by the cofactors of matrix \( A \) is

If \( \sin x + \sin^2 x = 1 \) then \( \cos^8 x + 2\cos^6 x + \cos^4 x \) is equal to:

If the standard deviation of \( 0,1,2,3,\ldots,9 \) is \( k \), then the standard deviation of \( 10,11,12,13,\ldots,19 \) will be:

Two numbers are selected at random from integers 1 to 9. If their sum is even, what is the probability that both the numbers are odd?

Kiran purchased 3 pencils, 2 notebooks and one pen for INR 41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for INR 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for INR 44. The above situation can be represented in matrix form as \( AX = B \). Then \( \text{adj}(A) \) is equal to

The area of a triangle formed by the lines joining the vertex of the parabola \( x^2 = \lambda y \) to the ends of its latus rectum is 18 sq units then the value of \( \lambda \) is

If \( X = \begin{bmatrix} 1 & 0 0 & 1 \end{bmatrix} \) and \( Y = \begin{bmatrix} 0 & 1 -1 & 0 \end{bmatrix} \) and \( B = \begin{bmatrix} \cos \theta & \sin \theta -\sin \theta & \cos \theta \end{bmatrix} \), then \( B \) equals:

The value of \( \frac{\sin^2 20^\circ + \cos^4 20^\circ}{\sin^4 20^\circ + \cos^2 20^\circ} \) is :

A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is

If \( \frac{x^2-3}{(x+2)(x^2+1)} = \frac{A}{x+2} + \frac{Bx+C}{x^2+1} \), then \( 3A+2B-C = \)

The equation of the circle which touches the circle $S \equiv x^2+y^2-10x-4y+19=0$ at the point (2,3) internally and having radius equal to half of the radius of the circle S=0 is

The foci of the conic \( 25x^2 + 16y^2 - 150x = 175 \) are

The differential equation of the family of all circles of radius 'a' is

If \(\alpha, \beta, \gamma, \delta, \epsilon\) are the roots of the equation \(x^5 + x^4 - 13x^3 - 13x^2 + 36x + 36 = 0\) and \(\alpha<\beta<\gamma<\delta<\epsilon\) then \( \frac{\epsilon}{\alpha} + \frac{\delta}{\beta} + \frac{1}{\gamma} = \)

The domain of the real valued function \( f(x) = \log_{5}(\sqrt{x^2+x} + \sqrt{x^2-x}) \) is

If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:

Using matrices and determinants, find the value(s) of $k$ for which the pair of equations \[ 5x - ky = 2; \quad 7x - 5y = 3 \] has a unique solution.