List of top Mathematics Questions

If \[ q_1x + b_1y + c_1z = 0, \quad a_2x + b_2y + c_2z = 0, \quad a_3x + b_3y + c_3z = 0 \] then the given system has:
Let \( A \) be a square matrix all of whose entries are integers. Then, which one of the following is true?
The value of \[ \left| \begin{array}{ccc} (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 \end{array} \right| \] is:
$\int \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x}$ is equal to:
The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
Let R be the set of real numbers A = {(x, y) $\in$ R $\times$ R : y - x is an integer} is an equivalence relation on R. B = {(x, y) $\in$ R $\times$ R : x = $\alpha$y for some rational number $\alpha$} is an equivalence relation on R.
$\int \frac{e^{x} \left(1 +\sin x\right)}{1+\cos x}dx= $
If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ is
Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is
If the area of a circle increases at a uniform rate, then its perimeter varies
If $x = 2y + 3$ is a focal chord of the ellipse with eccentricity 3/4, then the lengths of the major and minor axes are
$\begin{vmatrix}a&b&c&d\\ -a&b&c&d\\ -a&-b&c&d\\ -a&-b&-c&d\end{vmatrix} = $
$1 + 3 + 5 + 7 + ... + 29 + 30 +31 + 32 + ... + 60 =$
$\frac{1}{\sin\theta}- \frac{\sqrt{3}}{\cos \theta}=$
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
If $y =\frac{\sec x +\tan x}{\sec x - \tan x} $ , then $\frac{dy}{dx} = $
$\sin10^{\circ} +\sin 20^{\circ }+\sin 30^{\circ }+...+\sin360^{\circ } =$
If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $
The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is
Let [ ?] denote the greatest integer function and $f (x) = [\tan^2 x]$. Then
The constraints of the L.P. problem given by x₁+2x₂\le2000, x₁+x₂\le1500 and x₂\le600, x₁,x₂\ge0, which of the following points does not lie in the positive bounded region?
In an equilateral triangle, the inradius, circumradius and one of the ex-radii are in the ratio:
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60^ with the horizontal and height of the house is 6\sqrt3 meters, then the length of the ladder is:
Given the line L:(x-1)/(3)=(y+1)/(2)=(z-3)/(-1) and the plane π:x-2y-z=0. Of the following assertions, the only one that is always true is:
The degree of the differential equation ((d²y)/(dx²))³+4-3d²ydx²+5(dy)/(dx)=0 is: