List of top Mathematics Questions

Let $\alpha$ and $\beta$ be the distinct roots of $ax^2 + bx + c = 0$ , then $\displaystyle \lim_{x \to\alpha} \frac{1- \cos \left(ax^{2} + bx + c\right)}{\left(x-\alpha\right)^{2}} $ is equal to

$\displaystyle \lim_{n \to\infty} \left[\frac{1}{n^{2}} \sec^{2} \frac{1}{n^{2}} + \frac{2}{n^{2}} \sec^{2} \frac{4}{n^{2}}.......... + \frac{1}{n}\sec^{2} 1 \right] $ equals

If in a frequency distribution, the mean and median are $21 $ and $22$ respectively, then its mode is approximately

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{\left(1+x\right)^{\frac{3}{2}} - \left(1+ \frac{1}{2}x\right)^{3}}{\left(1-x\right)^{\frac{1}{2}}} $ may be approximated as

A real valued function $f (x) $.Satisfies the functional equation $f(x- y) =f (x) f(y)-f(a-x) f(a+y)$ where a is a given constant and $f(0) = 1$. Then $f(2a - x)$ is equal to

$A$ and$ B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance :

if $p=\begin {bmatrix} \sqrt 3 /2 & 1/2 \\ -1/2 & \sqrt 3/2 \end {bmatrix} , A=\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ and $ Q=PAP^T,\ then$ $P^TQ^{2005}P $ is

If $\int_{sin x}^1 \, t^2 f(t) dt =1-sin x, \forall x \in (0,\pi/2), \, then \, f\bigg(\frac{1}{\sqrt 3}\bigg)$ is

A variable plane $ \frac{x}{a}+ \frac{y}{b}+ \frac{z}{c} =1$ at a unit distance from origin cuts the coordinate axes at A. Band C. Centroid (x, y, z) satisfies the equation $ \frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2} =K.$ The value of K is

The number of ordered pairs $(\alpha, \beta), $ where $\alpha, \beta \in(-\pi, \pi)$ satisfying cos $(\alpha-\beta)=1 and cos (\alpha+\beta)=\frac{1}{e}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is

In a $\triangle$ ABC, among the following which one is true?

The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by

The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is

Let $f (x) = ax^2 + bx + c, a \ne 0$ and $\Delta =b^2 -4ac.$ If $a+ \beta,$ $a^2+ \beta^2$ and $a^3+ \beta^3$ are in GP, then

The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is

If f (x) is continuous and differentiable function and f (1/n) = 0 $\forall$ n $\ge$ 1and n $\in$ I, then

The value of $Cos (270^\circ +\theta )Cos (90^\circ - \theta ) - Sin (270^\circ - \theta )Cos \theta$ is

Train A travelling at 60km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the some time between Mumbai and Delhi, then what is the speed of Train C if the distance between Delhi and Mumbai is 1260 km?

A country follows a progressive taxation system under which the income tax rate applicable varies for different slabs of income. Total tax is computed by calculating the tax for each slab and adding them up. The rates applicable are as follows:

Annual income Slab (in Rs)	Tax rate Applicable
0 - 50,000	0%
50,001- 60,000	10%
60,001 - 1,50,00	20%
>1,50,000	30%

If my annual income is Rs. 1,70,000, then what is the tax payable by me?