List of top Mathematics Questions

If \( \Delta r = \left| \sum_{r=1}^{n} r \right| \), then \( \sum_{r=1}^{n} \Delta r \) is equal to

If \( A = \begin{pmatrix} 1 & 2
3 & 1 \end{pmatrix} \), then rank \( A \) is

The mean square deviation of a set of $n$ observation $x_{1}, x_{2},... x_{n}$ about a point $c$ is defined as $\frac{1}{n} \displaystyle\sum_{i=1}^{n}\left(x_{i}-c\right)^{2}$.The mean square deviations about $- 2$ and $2$ are $18$ and $10$ respectively, the standard deviation of this set of observations is

Let $M$ be a $3 \times 3$ non-singular matrix with $det(M)=\alpha$. If $\left[M^{-1} adj(adj(M)]=K I\right.$, then the value of $K$ is

The number of real roots of the equation $e^{x-1} + x - 2 = 0$ is

A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is.

The arithmetic mean of the data $0,1,2, \ldots \ldots, n$ with frequencies $1,{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ is

Let $S$ be the focus of the parabola $y ^{2}=8 x$ and let $PQ$ be the common chord of the circle $x^{2}+y^{2}-2 x-4 y=0$ and the given parabola. The area of the $\Delta PQS$ is

If a function $f(x)$ is given by $f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2 x+1)}+\frac{x}{(2 x+1)(3 x+1)}+\ldots \infty$ then at $x =0$, $f(x)$

The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman. is :

The total number of $4$-digit numbers in which the digits are in descending order, is

If $\omega$ is the complex cube root of unity, then the value of $\omega+\omega\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\frac{27}{128}+\ldots \ldots\right)$

Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is :

If a line segment OP makes angles of $ \frac{\pi}{4}$ and $\frac{\pi }{3}$ with X-axis and Y-axis, respectively. Then, the direction cosines are

If $N$ is a set of natural numbers, then under binary operation $a ?b =a + b, (N, ?)$ is

The normal at the point $(at_1^2 ,\, 2at_1)$ on the parabola meets the parabola again in the point $(at_1^2 ,\, 2at_2)$ , then

On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

The two lines $x = my + n, z = py + q$ and $x = m'y + n',\, z = p'y + q'$ are perpendicular to each other, if

If p, q, r are simple propositions with truth values T, F, T, then the truth value of $\left(\sim p \vee q\right) \wedge \sim r \Rightarrow p $ is

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is

The area bounded by the curves $y = cos\, x$ and $y = sin \,x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is

If $12$ identical balls are to be placed in $3$ different boxes, then the probability that one of the boxes contains excatly $3$ balls, is

If A = $ \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end {bmatrix}$ is a matrix satisfying the equation $AA^T =9 I,$ where, $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

The solution set of the inequation $\frac {x^2+6x-7}{|x+4|}<0$ is

If $ f(x) = 2-2x^2,$ find $\frac {f(3,8)-f(4)} {3.8-4} $,