List of top Mathematics Questions

What is the value of $\log_{X \to \infty} \left[ -(x + 1) \left( e^{x+1} - 1 \right) \right]$?

If \( \mathbf{a} = \hat{i} + \hat{j} + \hat{k}, \, \mathbf{b} = 2\hat{i} - \hat{j} + 3\hat{k}, \, \mathbf{c} = \hat{i} - 2\hat{j} + \hat{k} \), \(\text{ then a vector of magnitude }\) \( \sqrt{22} \) \(\text{ which is parallel to }\) \( 2\mathbf{a} - \mathbf{b} + \mathbf{c} \) is:

If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}| = 3$, $|\vec{b}| = 4$ and $|\vec{a} + \vec{b}| = 1$, then the value of $|\vec{a} \times \vec{b}|$ is:
 

There are two coins, say blue and red. For the blue coin, the probability of getting heads is 0.99 and for the red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting heads is:
There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals:

The length of the projection of \( \mathbf{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) \(\text{ on }\) \( \mathbf{b} = -2\hat{i} + \hat{j} + 2\hat{k} \) \(\text{ is equal to:}\)

Let E and F be two events such that \( P(E) > 0 \) and \( P(F) > 0 \). Which one of the following is NOT equivalent to the condition that \( P(E) = P(E \cap F) \)?
The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} \times \vec{b} = \vec{c}$, $\vec{a} \cdot \vec{c} = 2$ and $\vec{b} \cdot \vec{c} = 1$. If $|\vec{b}| = 1$, then the value of $|\vec{a}|$ is:
 

The area enclosed between the curve \( y = \sin x, y = \cos x \), \(\text{ for }\) \( 0 \leq x \leq \frac{\pi}{2} \) \(\text{ is:}\)

Suppose that C represents the set of all countries, R represents the set of all countries that have at least one river flowing through it, M represents the set of all countries that have at least one mountain in it, and D represents the set of all countries that have at least one desert in it. It is given that \( (R \cup M \cup D) = C \). Which one of the following gives the set of all countries that have either a mountain or a river, but does not have a desert in it? The notation \( D^c \) represents the complement of the set D with respect to the universal set C.
The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is:
An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes:
A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is
The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is
$\int(1+\tan^2 x)(1+2x\tan x)dx =$
$\int e^x(x^3-2x^2+3x-4)dx =$
$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $
$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$
$\int \frac{\log x}{(1+x)^2}dx = $
If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$
$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$
If a normal is drawn at a variable point P(x, y) on the curve $9x^2+16y^2-144=0$, then the maximum distance from the centre of the curve to the normal is
A real valued function
$f:[4, \infty) \to \mathbb{R}$ is defined as $f(x) = (x^2+x+1)^{(x^2-3x-4)}$, then f is