List of top Mathematics Questions

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?
$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is
If $g$ is the inverse function of $f$ and $f'(x) = \frac{1}{ 1+x^n} $ , then the value of $g'(x)$ is
$\displaystyle\lim_{x \to \infty} \left( \frac{x+6}{x+1}\right)^{x+4} =$
If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $
If $ f(x) = x^m$, where $m$ is a positive integer then the value of $m$ for which $f'(\alpha + \beta) = f'(\alpha ) + f'(\beta)$ for all $ \alpha , \beta > 0$ is
The points of discontinuities of $f(x) = \left(\frac{\pi x}{x+1} \right)$ other than $x = -1$ are
$f(x) = \begin{cases} x , \text{if } x \text{ is rational}\\ 0, \text{if } x \text{ is rational} \end{cases}$ then $f$ is
A plane passes through $ (1 ,-2 ,1 )$ and is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4, $ then the distance of the plane from the point $ (1, 2, 2)$ is
For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is
Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is
If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then
If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is
If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is
If $a, b$ and $c \in N$ which one of the following is not true ?
If $2A+3B =\begin{bmatrix} {2}&{-1} &{4}\\ {3}&{2}& {5} \\ \end{bmatrix} $ and $A+2B \begin{bmatrix} {5}&{0} &{3}\\ {1}&{6}& {2} \\ \end{bmatrix} $then $B =$
The number of common tangents to circle $x^{2}+y^{2}+2 x+8 y-23=0$ and $x^{2}+y^{2}-4 x-10 y+9=0$, is.
The largest value of $2x^3 - 3x^2 - 12x + 5$ for $-2 \leq x \leq 4$ occurs at $x$ is equal to :
The shortest distance from the point $(3, 0)$ to the parabola $y = x^2$ is.
The tangents from a point $(2 \sqrt{2}, 1)$ to the hyperbola $16 x ^{2}-25 y ^{2}=400$ include an angle equal to.
The degree of the differential equation $y(x)=1 +\frac{dy}{dx}+\frac{1}{1.2}\left(\frac{dy}{dx}\right)^2+\frac{1}{1.2.3}\left(\frac{dy}{dx}\right)^3+.........$ is
Total number of books is $2n + 1$. One is allowed to select a minimum of the one book and a maximum of $n$ books. If total number of selections if $63$, then value of $n$ is :
The equation of plane passing through a point $A (2,-1,3)$ and parallel to the vectors $a =(3,0,-1)$ and $b =(-3,2,2)$ is:
Let $\alpha, \beta, \gamma$ and $\delta$ are four positive real number such that their product is unity, then the least value of $(1+\alpha)(1+\beta)(1+\gamma)(1+\delta)$ is:
Given function $f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$ is.