List of top Mathematics Questions

The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:

The 25th term of $9, 3, 1, \frac{1}{3}, \frac{1}{9}, \ldots$ is:

Real part of $\frac{1+\sin\frac{2\pi}{27}-i\cos\frac{2\pi}{27}}{1+\sin\frac{2\pi}{27}+i\cos\frac{2\pi}{27}}$ is equal to:

Let $z$ be a complex number such that $z^{3}+iz^{2}-iz+1=0$ where $i^{2}=-1$. Then $|z|=$

Let $z=x+iy$ be a complex number, where $i=\sqrt{-1}$ is the complex unit. Then $|z-1+i|=5$ is a circle with:

Let $s, t, r$ be non-zero distinct positive real numbers. If the complex number $z=x+iy$ satisfies $sz+t\overline{z}+r=0$, then $z$ lies on:

The range of the function $f(x)=\sqrt{x^{2}+4x+4}$ is:

The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:

If two sets A and B are having 11 elements in common, then the number of elements common to $A\times B$ and $B\times A$ is:

The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is:

In the graphical method of a linear programming problem, the optimal solution lies

The integrating factor of the differential equation \( \sin x\, dy = \frac{1}{2}(\sin2x + 2y\cos x)\,dx \) is

If \( y'(x) = 2y \), \( y(x) \ge 0 \) and \( y(0) = e^2 \), then \( y(x) = \)

\( \int_{0}^{1} \frac{3^{2x}}{3^x + 1}\,dx = \)

The area of the region bounded by \( y = x^{5/2} \) and \( y = x \) (in square units) is

The value of \( \int_{\pi/10}^{2\pi/5} \frac{\cot^3 x}{1+\cot^3 x}\,dx \) is equal to

If \( \int_{-\sqrt{3}}^{1} (-6x^2 + 18)\,dx = \alpha + \beta\sqrt{3} \), then the value of \( \alpha + \beta \) is equal to

\( \int e^x(x^2-2)\cos(e^x(x^2-2x)) dx = \)

\( \int e^x \sec x (1+\tan x) dx = \)

\( \int x^7 (x^8 + 1)^{-3/4} \, dx = \)

\( \int \frac{\sin^{-1}x}{\sqrt{1-x^2}} \, dx = \)

\( \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx = \)

Let \( f(x) = x^2 + ax + \beta \). If \( f \) has a local minimum at \( (2,6) \), then \( f(0) \) is equal to

The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in

The surface area of a solid hemisphere is increasing at the rate of \( 8 \, \text{cm}^2/\text{sec} \) (retaining its shape). Then the rate of change of its volume (in \( \text{cm}^3/\text{sec} \)), when the radius is \( 5 \,\text{cm} \), is