List of top Mathematics Questions

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} $,

The value of $ \tan( 1^\circ) +\, tan(89^\circ)$ is

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is