List of top Mathematics Questions

The volume of the tetrahedron formed by the points $(1, 1, 1 ), (2, 1, 3), (3, 2, 2)$ and $(3, 3, 4)$ in cubic units is
The value of $\left(0.2\right)^{\log_{\sqrt{5}}\left(\frac{1}{4} + \frac{1}{8} + \frac{1}{6} + .... to \, \infty\right)}$
$\int \frac{x^{2}+1}{x^{4}+1}dx $
$\int e^{x} \left\{\frac{1+\sin x \cos x}{\cos^{2} x}\right\} dx = $
If $\tan A - \tan B = x$ and $\cot B - \cot A = y$, then $\cot (A- B) =$
The subtangent at $x = \pi /2$ on the curve $y = x \sin x$ is
The maximum value of $\left(\frac{1}{x}\right)^{2x^2}$ is
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
If $y =\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y}}}} +.....$ then $ \frac{dy}{dx} $
The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is
Which of the following functions is differentiable at $x = 0$ ?
If $x= a\left(\cos t+\log \tan \frac{t}{2}\right), y = a \sin t, $ then $ \frac{dy}{dx} $
Value of $1+cos56^{\circ}+cos58^{\circ}-cos66^{\circ}$ is
$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to
In a triangle $ABC$, if sin A sin $B =\frac{ab}{c^{2}}$, then the triangle is
The number of seven-digit integers, with sum of the digits equal to $10$ and formed by using the digits $1, 2$ and $3$ only, is
The locus of the orthocentre of the triangle formed by the lines $(1 + p )x -p y + p (1 + p) = 0 (1+ q)x-qy + < 7(1+ q) = 0$ and $y = 0$, where $p\ne q$ is
The image of the point $(1, 2, 3)$ in the plane $x + y + z + 3 = 0 $ is
An ellipse intersects the hyperbola $2x^2-2y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal to th a t of the hyperbola. If the axes of the ellipse are along the coordinate axes, then
Let $f$ be a non-negative function defined on the interval [0,1].if $\int_0^x \sqrt{1-(f'(t))^2}dt = \int_0^x f(t) dt , 0 \le x \le 1$ and $f (0) = 0$, then
In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then
A line with positive direction cosines passes through the point $P (2, -1, 2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x + y+ z = 9$ at point $Q$. The length of the line segment $PQ$ equals
In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then
If \(\vec{a},\vec{b},\vec{c}\) be three unit vectors such that \(\vec{a}\times(\vec{b}\times\vec{c})=\frac{1}{2}\vec{b}\), \(\vec{b}\) and \(\vec{c}\) being non-parallel. If \(\theta_1\) is the angle between \(\vec{a}\) and \(\vec{b}\) and \(\theta_2\) is the angle between \(\vec{a}\) and \(\vec{c}\), then
Probability of getting positive integral roots of the equation \(x^2-n=0\) for the integer \(n,\ 1\le n \le 40\) is