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List of top Mathematics Questions

If $y = 4t$ and $x = \dfrac{4}{t}$, then the value of $\dfrac{dy}{dx}$ will be:

Let $ R = \{a, b, c, d, e\} $ and $ S = \{1, 2, 3, 4\} $. Total number of onto functions $ f: R \to S $ such that $ f(a) \neq 1 $, is equal to:

For any $n≥0$ the value of $\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}$ is

The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

Let $\beta$ be a real number Consider the
$matrix\ A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}If A^7-(\beta-1) A^6-\beta A^5$ is a singular matrix, then the value of $9 \beta$ is _____

If $\overrightarrow F=2z\hat{i}-x\hat{j}+y\hat{k}$ and Vis the region bounded by the surface x=0,y=0,x=2,y=4,z=x²,z=2, then value of $\iiint\limits_V\overrightarrow FdV$is

Consider the Linear Programming Problem:
Minimize 3x₁+4x₂ +2x₃
subject to
x₁+x₂+x₃≤6
x₁+2x₂+x₃≤10
x₁,x₂,x₃≥0.
Then, the number of basic solutions are

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

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

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?

The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______

Let the area enclosed by the lines $ x + y = 2 $, $ y = 0 $, $ x = 0 $, and the curve $ f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} $, where $ [x] $ denotes the greatest integer less than or equal to $ x $, be $ A $. Then the value of $ 12A $ is ____________.

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

Let $ S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} $ be a sample space and $ A = \{ M \in S : M \text{ is invertible} \} $ be an event. Then $ P(A) $ is equal to:

Ki are possible values of K for which lines $Kx + 2y + 2 = 0$, $2x + Ky + 3 = 0$, $3x + 3y + K = 0$ are concurrent, then $∑k_i$ has value.

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:

If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___.

If $p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})$ are in A.P., then p, q, r