List of top Mathematics Questions

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 :

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

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

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :