List of top Mathematics Questions

Let a and b are roots of \(x^2 – 7x – 1 = 0\). The value of \(\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}\) is?
$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let $R$ 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
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
The derivative \(\frac{dy}{dx} \) of the function y = sin(cos(log(x))) is,
Let \(f(x)\) be a quadratic polynomial with leading coefficient 1 such that \(f(0) = p, p≠0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x) = 0\) and \(fofofof(x) = 0\) have a common real root, then \(f(–3)\) is equal to.......................
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 ______.
Let $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then
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 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:
Let \(f: R \rightarrow R\) be a function defined by\(f(x)=\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}\), for some \(m\), such that the range of \(f\) is \([0,2]\) Then the value of \(m\) is_____
If ABCD is a parallelogram and AC and BD are its diagonals, then $\overrightarrow{AC} + \overrightarrow{BD}$ is:
Function f is defined as: \[ f(x) = \begin{cases} 2x + 2, & x<2 \\ k, & x = 2 \\ 3x, & x>2. \end{cases} \text{Find the value of } k \text{ for which } f \text{ is continuous at } x = 2. \]
Let \(x = 2\) be a root of the equation \(x^2 + px + q = 0\) and \(f(x)=\begin{cases}\frac{1-cos(x^2-4px+q^2+8q+16)}{(x-2p)^4} & x≠2p\\0 & x=2p\end{cases}\).
Then \(lim_{x \rightarrow 2p}[f(x)]\), where [·] denotes greatest integer function, is
Let the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements 
(S1) : A ∩ B = (1, ∞) – N and  
(S2) : A ∪ B = (1, ∞) 
Evaluate $\displaystyle \int \frac{\cos 2x}{\sin^2 x \cdot \cos^2 x} dx$
The modulus of the complex number \(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\) is

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

The mean deviation about the median for the data \(3,5,9,3,8,10,7\) is ?
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{T _{\subseteq} A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is _______ .
Let $f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______ .
Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.