List of top Mathematics Questions

Let \(f:R→R\) be a function defined by f(x)={\(3e^x \text{ if } x<0 x^2+3x+3  \text{ if  } 0≤x<1 x^2-3x-3\text{   if  } x≥1\)

If $\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}$, then the general value of $\theta$ is:

Let \(f(x)=αsin^{2}3x.\) If \(f'(π/12)=-3\) ,then the value of \(α \) is_____.

The coefficient of $x_n$ in the expansion of $\frac{e^{7x}+e^x}{e^{3x}}$ is

A problem is given to 3 students. Their chances of solving it individually are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ . The probability that the problem will be solved is

If the sums of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio between their 13^th terms is

The line passing through the points \((2,1,0) , (5,0,1)\) and \( (4,1,1)\) intersects the \(x-\)axis at

The equations of the lines through the point (3, 2) which make an angle of 45^o with the line x - 2y = 3 are

The signum function, $f$ : $R \to R$ is given by $f(x) = \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x=0 \\ -1, & \text{if } x < 0 \end{cases} $ is

Which one of the following statements is correct ? The power set of the null set is

The modulus of the complex number $z=\frac{\left(1-i\sqrt{3}\right)\left(cos\,\theta+i\, sin\,\theta\right)}{2\left(1-i\right)\left(cos\,\theta-i\, sin\,\theta\right)}$ is

The value of ${\cot }^{-1}9+\cos e{c}^{-1}\frac{\sqrt{41}}{4}$

The angle between the straight lines $x-y\sqrt{3}=5$ and $\sqrt{3}x+y=7$ is

The mode of the following series $ 3, 4, 2, 1, 7, 6, 7, 6, 8, 6, 5$ is

${\int }_0^{\pi /2}\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}$dx is equal to

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below. Which of these three subjects shows the highest variability in marks and which shows the lowest?

The maximum value of sin x + cos x is

$\displaystyle \lim_{x \to 2}$$\left[\frac{1}{x-2}-\frac{2\left(2x-3\right)}{x^{3}-3x^{2}+2x}\right]$ is equal to

If [x] denotes the greatest integer x, then $\left[\frac{2}{3}\right]+[\frac{2}{3}+\frac{1}{99}]+[\frac{2}{3}+\frac{2}{99}]+\dots ..+[\frac{2}{3}+\frac{98}{99}]$is equal to

The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? (Use $\pi = 3.14$)

The minimum value of the function $f \left(x\right)=x^{3/2}+x^{-3/2}-4\left(x+\frac{1}{x}\right)$ for all permissible real $x$, is

$\displaystyle \lim_{x \to 0}$ $\frac{cos\,ax-cos\,bx}{cos\,cx-1}=$