List of top Mathematics Questions

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \{- | x |,- \sqrt{ 1- x^2} \}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :

Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g : N \to N$ such that : $f(n) = \begin{cases} \frac{n+1}{2} & \quad \text{if } n \text{ is odd}\\ \frac{n}{2} & \quad \text{if } n \text{ is even} \end{cases}$ and $g(n) = n-(-1)^n$. The $fog$ is :

If $f\left(x\right) = \frac{2- x\cos x}{2+x \cos x}$ and $ g\left(x\right) =\log_{e}x ., \left(x>0\right) $ then the value of integral $\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}} g\left(f\left(x\right)\right)dx $ is :

If $ \int \frac{\sqrt{1-x^{2}}}{x^{4}} dx = A \left(x\right)\left(\sqrt{1-x^{2}}\right)^{m} + C $ , for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant of integration then $(A(x))^m$ equals :

The number of integral values of m for which the equation $(1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0$ has no real root is :

Considering only the principal values of inverse functions, the set $A = \{ x \ge 0 : \tan^{-1} (2x) + \tan^{-1} (3x) = \frac{\pi}{4} \}$

If $\int \frac{dx}{x^{3}\left(1+x^{6}\right)^{\frac{2}{3}}}=f \left(x\right)\left(1+x ^{6}\right)^{\frac{1}{3}}+C$, where C is a constant of integration, then the function $f \left(x\right)$ is equal to-

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is

Let $a_1, a_2 , ....... , a_{30}$ be an $A. P$., $S =\displaystyle \sum^{30}_{i=1} a_i $ and $T = \displaystyle\sum^{15}_{i=1} a_{(2i -1)}$. If $a_5 = 27$ and $S - 2T = 75, $ then $a_{10}$ is equal to :

A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is

If \(log_8 x+log_4 x+log_2 x=11,x=?\)

If a²-b² = 8 and a*b = 2, find a⁴+b⁴.

In $\triangle ABC$, $\angle CAB=60^\circ$, $BC=a$, $AC=b$, $AB=c$. Which relation is correct? \includegraphics[width=0.5\linewidth]{image83.png}

In a regular hexagon, ropes are tied to connect every pair of vertices (all sides and all diagonals). How many distinct intersection points do the ropes create?

The inverse of the function \(f(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}+2\) is given by

The integral $\int \cos( \log \; x)dx$ is equal to : (where C is a constant of integration)

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =

A tangent is drawn from an external point P to a circle of 8 cm radius. If the length of the tangent is 15 cm then the distance between the centre of the circle and point P is

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then |d| equals :

Find the value of log_y(x⁴) if log_x(y³) = 2