List of top Mathematics Questions

The value of the integral \(\int\limits^6_3\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt x}dx\) is

Let \(f:R\rightarrow R\) be defined by \(f(x) = \begin{cases} k-2x,x\le-1\\ 2x+3,x\gt-1   \end{cases}\). If f(x) has a local minimum at x=- 1, then a possible value of k is

If \((\displaystyle\int_0^axdx)\le(a+4)\), then

\(lt_{x\rightarrow\infin}(\frac{x^2+5x+3}{x^2+x+3})^{\frac{1}{3}}\) is

Find \(Lt_{x\rightarrow\infin}(\frac{x}{2+x})^{2x}\)

A missile fired from ground level rises x metres vertically upwards in 't' seconds and x = t( 100-12.5t). Then the maximum height reached by the missile is

\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{(3n-1)(3n+2)}\) is equal to

How many positive integers n can be formed using the digits 3,4,4,5,5,6,7, if n has to exceed 50,00,000?

If \(f(x) = \begin{cases}  1 + x & \text{if } 0 \leq x \leq 2 \\ 3 - x & \text{if } 2 < x \leq 3  \end{cases}\) , then \(f[f(x)]\) is

The points representing the complex numbers Z for which |Z + 4|² - |Z - 4|² = 8 lie on

If A+B=\(\begin{pmatrix} 2&-4 \\4&0 \end{pmatrix}\) and 3B=\(\begin{pmatrix}  -9&6 \\3&12 \end{pmatrix}\) then A+4B is

If A is a non-singular matrix such that AA^T = A^TA and B = A^-1A^T , then matrix B is

If I is the unit matrix of order n, where K≠0 is a constant, then adj(KI) =

If \(\Delta_1=\begin{vmatrix} x&b&b \\a&x&b\\a&a&x\end{vmatrix}\) and \(\Delta_2=\begin{vmatrix} x&b \\a&x\end{vmatrix}\), then \(\frac{d}{dx}(\Delta_1)\) is equal to

Number of integral values of x satisfying x² - 4x - 21 > 0 and x² - 9x + 8 < 0 is

If \(i=\sqrt{-1}\), then \(4+5(\frac{-1}{2}+\frac{i\sqrt3}{2})^{334}+3(\frac{-1}{2}+\frac{i\sqrt3}{2})^{265}\) is equal to

The values of is

If two sides of a triangle are the roots of the equation \(4x^2 - (2\sqrt{6})x + 1 = 0\) and the included angle is 60⁰ , then the third side is

If $0 \le x < \frac{\pi}{2}$ , then the number of values of $ x$ for which $sin \,x-sin\,2x+sin\,3x = 0$, is

Two vertices of a triangle are $(0,2)$ and $(4,3)$ . If its orthocentre is at the origin, then its third vertex lies in which quadrant ?

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

$\displaystyle\lim_{x\to0} \frac{\sin^{2}x}{\sqrt{2} - \sqrt{1+\cos x}} $ equals :

$\int\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} dx $ is equal to : (where $c$ is a constant of integration)

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 :

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-