List of top Mathematics Questions

Let \(I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx\), x>0. If \(\lim\limits_{x\rightarrow\infin}I(x)=0\), then I(1) is equal to

Let S_K = \(\frac{1+2+...+ K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)\), where A,B,C,D∈N and A has least value. Then

If the coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:5:20, then the coefficient of the fourth term of the expansion is?

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

Let P = \(\left[\begin{matrix}   \frac{\sqrt3}{2} & \frac{1}{2} \\   -\frac{1}{2} & \frac{\sqrt3}{2}  \end{matrix}\right]\) A = \(\left[\begin{matrix}   1 & 1 \\   0 & 1  \end{matrix}\right]\) and Q = PAP^T. If P^TQ²⁰⁰⁷P = \(\left[\begin{matrix}   a & b \\   c & d  \end{matrix}\right]\), then 2a+b-3c-4d equal to

Let α, β, γ be the three roots of the equation x³+bx+c=0. If βγ =1=-α, then b³+2c³-3α³-6β³-8γ³ is equal to

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$ Then $(\vec{a} \cdot \vec{b})^2$ is equal to

If 5f(x) + 4f (\(\frac{1}{x}\)) = \(\frac{1}{x}\)+ 3, then \(18\int_{1}^{2}\) f(x)dx is:

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

The remainder on dividing $5^{99}$ by 11 is

Let $\alpha>0$, be the smallest number such that the expansion of $\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}$ has a term $\beta x^{-a}, \beta \in N$.
Then \(α\) is equal to _________. 

Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ is equal to

Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ at the point $P$ Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$ If $\alpha$ is the area of triangle $P Q R$, then $\alpha^2$ is equal to

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} $ 

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

If the variance of the frequency distribution

is 3 , then $\alpha$ is equal to