List of top Mathematics Questions

To maximize the objective function $z = 2x + 3y $ under the constraints $x + y \leq 30, x - y \geq 0 , y \leq 12, x \leq 20 , y \geq 3$ and $x ,y \geq 0 $

To derive the tangent formula, the following steps are given: 1. $\tan\left(A + B\right) = \frac{\frac{\sin A \cos B}{\cos A \cos B} + \frac{\cos A \sin B}{\cos A \cos B}}{\frac{\cos A \cos B}{\sin A \sin B} + \frac{\sin A \sin B}{\cos A \cos B}}$ 2. $\tan\left(A + B\right) = \frac{\sin\left(A + B\right)}{\cos\left(A + B\right)} $ 3. $\tan\left(A + B\right) = \frac{\sin A \cos B + \cos A \sin B}{\cos A \cos B - \sin A \sin B}$ 4.$ \tan\left(A + B\right) = \frac{\tan A + \tan B}{1- \tan A \tan B} $ Their correct and proper sequential form to derive the formula is:

Tickets are numbered from 1 to 100. They are well shuffled and a ticket is drawn at random. Probability that the drawn ticket has a number 5 or multiple of 5 is

Three points $(2, -1,3)$, $(3, -5,1)$ and $(-1, 11, 9)$ are

Three numbers are chosen from 1 to 30. The probability that they are not consecutive is

Three non-zero real numbers form an $A.P$. and the square of the numbers taken in the same order constitute a $G.P$. Then the number of all possible common ratios of the $G.P$. are

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.

Three faces of a fair dice are yellow, two faces red and only one is blue. The dice is tossed three times. The probability that the colour yellow, red and blue appears in the first, second and the third tosses respectively is:

Three cards drawn successively, without replacement from a pack of $52$ well shuffled cards, then the probability that first two cards are kings and the third card drawn is an ace, is

These organisms have chlorophyll - a similar to that of higher plants.

There are three coplanar parallel lines. If any $P$ points are taken on each of the lines, the maximum number of triangles with vertices at these points, is

There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceding vector at angle $\frac{2 \pi}{N} .$ What is the magnitude of their resultant?

There are $15$ points in a plane, no three of which are in a straight line, except $6$, all of which are in a st. line. The number of st. lines which can be drawn by joining them is

There are $25$ points in a plane, of which $10$ are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is

There are $10$ points in a plane of which $4$ are collinear. The number of quadrilaterals that can be formed is

There are 10 true-false questions in a examination. Then these questions can be answered in:

The weighted mean of first n natural numbers, whose weights are proportional to the corresponding numbers, is

The volume V and depth x of water in a vessl are connected by the relation $V = 5x - \frac{x^2}{6}$ and the volume of water is increasing , at the rate of $5 \, cm^3/sec$, when x = 2 cm. The rate at which the depth of water is increasing, is

The volume of the tetrahedron whose coterminous edges are $ \hat{j}+\hat{k}$, $ \hat{i}+\hat{k}$, $\hat{i}+\hat{j}$ is

The variance of random variable $X$ i.e. $\sigma^{2}_{x}$ or var$(X)$ is equal to

The variance of first 25 natural numbers is

The variance of first n natural numbers is :

The variance of the numbers $2, 3, 11 $ and $x$ is $\frac{49}{4}$. Find the value of $x$.

The values of x satisfying $| x - 4 | + | x - 9 | = 5$, is :

The values of the determinant $ \begin{vmatrix} x+1& x+2 &x+4 \\[0.3em] x+3 & x+5 & x+8 & \\[0.3em] x+7 & x+10 & x+14 \end{vmatrix}$