List of top Mathematics Questions

The corner points of the feasible region determined by the system of linear inequalities are (0,0), (4, 0), (2, 4) and (0.5). If the maximum value of Z = ax + by where a, \(b > 0\) occurs at both (2, 4) and (4.0), then

The area bounded by x = 1, x = 2, xy = 1 and x-axis is:

If, A is a square matrix of order 3 and |A| = -2 then. \(|-2 \ A^{-1}|\) is:

The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by

The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = x + 1\) is:

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:

Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. If the tailors A and B work for x and y days respectively. To maximize the earning for producing at least 60 shirts and 32 pants, the LPP is:

If y = x + tan x, then value of \(\frac{d^2y}{dx^2}\) at \(x= \frac{\pi}{4}\) is:

Differential coefficient of see (\(tan^{-1} x\)) with respect to x is:

The direction cosines of z-axis are:

If \(\begin{bmatrix}      1 & 3 & 5          \\[0.3em]      1 & 0   &3 \\[0.3em]        0 &1 &0      \end{bmatrix}\),then \(|(adjA)| \) is:

for which value of \(\lambda\) is the function ,\(f(x) = \begin{cases} \lambda(x^2-2x) & \text{if } x \leq 0 \\ 4x+1& \text{if } x > 0 \end{cases}\) continuous at \(x=0 ?\)

The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is:

The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is:

For the LPP
Maximise z=x+y
subject to x-y≤-1, x+y≤2, x, y≥0, z has:

If \( f(x) = \begin{cases} \sqrt{\pi - \cos^{-1} x}, & x = -1 \\ \frac{\sqrt{2(1 + x)}}{\pi + \cos^{-1} x}, & x \neq -1 \end{cases} \) is right continuous at \( x = -1 \), then \( \lambda = \)

If \( y = y(x) \) is the solution of \( \frac{dy}{dx} = \frac{x - y \cos x}{1 + \sin x} \), \( y\left(\frac{\pi}{2}\right) = \frac{\pi^2}{8} \), then \( y(\pi) = \)

Given that \( \frac{d}{dx} \left[ \int_0^{\phi(x)} f(t) dt \right] = \phi'(x) f(\phi(x)) \). If \( \int_0^{x^3} f(t) dt = x^2 \sin 2\pi x \), then the value of \( f(8) \) is

\( \lim_{n \to \infty} \frac{1}{n} \left( \frac{1}{e^{1/n}} + \frac{1}{e^{2/n}} + \frac{1}{e^{3/n}} + \dots + \frac{1}{e^{n/n}} \right) = \)

\( \int_0^{1/2} \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx = \)

\( \int \frac{x^2 - 1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} dx = \)

Let \( f(x) = \max\{\cos x, \sin x, 0\} \). If the number of points at which \( f(x) \) is not differentiable in \( (0, 2024\pi) \) is \( 1012k \), then \( k = \)

The points on the curve \( y^2 = x + \sin x \) at which the normal is parallel to the Y-axis lie on

If the tangent drawn at \( A(2, 1) \) to the curve \( x = 1 + \frac{1}{y^2} \) meets the curve again at \( B \), then

If \( \theta \) is the angle between the asymptotes of the hyperbola \( \frac{x^2}{9} - \frac{(y - 2)^2}{16} = 1 \) and \( \cos \theta = \frac{a^2}{b^2} \), then \( a^2 = \)