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List of top Mathematics Questions

If $x\begin{bmatrix} 3 \\ 2 \end{bmatrix}+y\begin{bmatrix} 1 \\ -1 \end{bmatrix}=\begin{bmatrix} 15 \\ 5\end{bmatrix}$ then the value of x and y are

If A = $\begin{bmatrix} 0 & 3\\ 0 & 0 \end{bmatrix}$and f(x) = x+x²+x³+.....+x²⁰²³, then f(A)+I =

Let $k$ be a real number such that $\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}$.Then the value of $4k$ is

if $2x^y+3y^x=20$ then $\frac{dy}{dx}$ at (2,2) is equal to:

$I(x) = \int \frac{x^2(xsec^2x + tanx)}{(xtanx+1)^2} dx$. If $I(0)=1$ then $I(\frac{\pi}{4})$ is equal to

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

If x = 3 tan t and y = 3 sec t, then find $\frac{d^2y}{dx^2} \, at\,t=\frac{\pi}{4}$, is:

If z₁ and z₂ are two complex numbers satisfying the equation$|\frac{z_1+z_2}{z_1-z_2}|=1$, then $\frac{z_1}{z_2}$ may be

Let f : (0,1) → R be the function defined as f(x) = √n if x ∈ [$\frac{1}{n+1},\frac{1}{n}$] where n ∈ N. Let g : (0,1) → R be a function such that $\int_{x^2}^{x}\sqrt{\frac{1-t}{t}}dt<g(x)<2\sqrt x$ for all x ∈ (0,1).
Then $\lim_{x\rightarrow0}f(x)g(x)$

Let $\alpha\ and\ \beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$. If $\sin (\alpha+\beta)=\frac{1}{3}\ and\ \cos (\alpha-\beta)=\frac{2}{3}$, then the greatest integer less than or equal to
$\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2$ is ____

Let $S=\left\{\alpha: \log _2\left(9^{2 \alpha-4}+13\right)-\log _2\left(\frac{5}{2} \cdot 3^{2 \alpha-4}+1\right)=2\right\}$ Then the maximum value of $\beta$ for which the equation $x^2-2\left(\displaystyle\sum_{\alpha \in s} \alpha\right)^2 x+\displaystyle\sum_{\alpha \in s}(\alpha+1)^2 \beta=0$ has real roots, is _____

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$.
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$
then $n + a + b$ is equal to _________.

The number of ways in which the letter of the word 'VERTICAL' can be arranged without changing the order of the vowels is

Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$, then the product of all possible values of $a$ is_____

Let $ 0 < z < y < x $ be three real numbers such that $ \frac{1}{x}, \frac{1}{y}, \frac{1}{z} $ are in an arithmetic progression and $ x, \sqrt{2}y, z $ are in a geometric progression. If $ xy + yz + zx = \frac{3}{\sqrt{2}} xyz $, then $ 3(x + y + z)^2 $ is equal to ____________.

Let $\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c$, where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______

Let $ w_1 $ be the point obtained by the rotation of $ z_1 = 5 + 4i $ about the origin through a right angle in the anticlockwise direction, and $ w_2 $ be the point obtained by the rotation of $ z_2 = 3 + 5i $ about the origin through a right angle in the clockwise direction. Then the principal argument of $ w_1 - w_2 $ is equal to:

Let $\alpha \in(0,1)$ and $\beta=\log _e(1-\alpha)$ Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int\limits_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to

Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d(b-c)=b c(a-d)$ Then $R$ is

Let R=$\begin{pmatrix}a&3&b\\c&2&d\\0&5&0\end{pmatrix}$: a,b,c,d ∈ {0,3,5,7,11,13,17,19}. Then the number of invertible matrices in R is

The derivative $\frac{dy}{dx} $ of the function y = sin(cos(log(x))) is,

Let f : (-2, 2) → IR be defined by $f(x) = \begin{cases} x[x] & \quad -2<x<0\\ (x-1)[x], & \quad 0\leq x<2 \end{cases}$
Where [x] denotes the greatest integer function. If m and n respectively are the number of points in (-2, 2) at which y = |f(x)| is not continuous and not differentiable, then m + n is equal to ______.

The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?

If A is a square matrix of order 3 and $|A| = 6$, then the value of $|\text{adj} A|$ is: