List of top Mathematics Questions

The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______
The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$ , is_________
$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$ and $D(4,5,0),|\lambda| \leq 5$ are the vertices of a quadrilateral $A B C D$ If its area is 18 square units, then $5-6 \lambda$ 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______
Let $f(x)=2 x+\tan ^{-1} x$ and $g(x)=\log _e\left(\sqrt{1+x^2}+x\right), x \in[0,3]$ Then
If $y=y(x)$ is the solution curve of the differential equation $\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1$ then $y\left(\frac{\pi}{6}\right)$ is equal to
If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to
The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is
For a triangle $A B C$, the value of $\cos 2 A+\cos 2 B+\cos 2 C$ is least If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?
Let $a, b, c>, a^3, b^3$ and $c^3$ be in AP, and $\log _a b, \log _c a$ and $\log _b c$ be in GP If the sum of first 20 terms of an AP, whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to:
If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then
The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is
For $\alpha, \beta \in R$, suppose the system of linear equations $ x-y+z=5 $ $2 x+2 y+\alpha z=8 $ $3 x-y+4 z=\beta$ has infinitely many solutions Then $\alpha$ and $\beta$ are the roots of
The solution of the differential equation $\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is
If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is
3 boys and 5 girls can complete one work in 8 days. 7 boys can complete the work in 4 days. Number of girls required to finish the work in half day is:

The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :

Among the relations 
$S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$ 
and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,

Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha$ (> 0 ), and the mean and standard deviation of marks of class B of $n$ students be respectively $55$ and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+ n$ students are respectively $50$ and $350$ , then the sum of variances of classes $A$ and $B$ is :

If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______
If for logcos x (cot x) - 4log(sin x) cot x = 1, x = sin-1 \((\frac{\alpha+\sqrt{\beta}}{2})\). Find (α + β), given x ∈ \((0,\frac{\pi}{2})\)
Suppose \( f: \mathbb{R} \to (0, \infty) \) be a differentiable function such that: \( 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} \). If \( f(3) = 320 \), then the value of:\( \sum_{n=0}^{5} f(n) \) is equal to:
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____
Let \( \lambda_1 < \lambda_2 \) be two values of \( \lambda \) such that the angle between the planes:
\( P_1 : \vec{r} \cdot (3\hat{i} - 5\hat{j} + \hat{k}) = 7 \) 
\( P_2 : \vec{r} \cdot (\lambda\hat{i} + \hat{j} - 3\hat{k}) = 9 \)
is \( \sin^{-1}\left(\frac{2\sqrt{6}}{5}\right) \). Then, the square of the length of the perpendicular from the point \( (38\lambda, 10\lambda, 2) \) to the plane \( P_1 \) is:
Let \( A = \begin{pmatrix} m & n \\ p & q \end{pmatrix} \), \( d = |A| \neq 0 \), and \( |A - d(\text{Adj}(A))| = 0 \). Then