List of top Mathematics Questions

Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?

If the integers \( m \) and \( n \) are chosen at random from 1 to 100, then the probability that a number of the form \( 7m + 7n \) is divisible by 5, equals to?

Let \( X \) denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of \( X \) are?

A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd is?

The vertices of a triangle are \( A(0,4,1) \), \( B(2,-3,-1) \), and \( C(4,5,0) \), then the orthocenter of ABC is?

The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?

The solution of \( \frac{dy}{dx} = \frac{x^2 + y^2 + 1}{2xy} \), satisfying \( y(1) = 0 \), is given by?

If \( x \frac{dy}{dx} = x \cdot f(xy) \), then \( f(xy) \) is equal to?

The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is?

The angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$, is

If M. D. is $12$, the value of S.D. will be

If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :

In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is $9$ meter and the highest part of the bridge is $3$ meter from the horizontal; the best approximation of the height of the arch. $2$ meter from the centre of the base is

Consider $\frac{x}{2} + \frac{y}{4} \ge1 $ and $\frac{x}{3} + \frac{y}{2} \le 1 , x ,y \ge0 $. Then number of possible solutions are :

A coin is tossed $7$ times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

If $\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$ is square root of identity matrix of order $2$ then

The complex number $z = z + iy$ which satisfies the equation $\left| \frac{z-3i}{z+3i}\right| = 1 $, lies on

If $T_0, T_1, T_2.....T_n$ represent the terms in the expansion of $ (x + a)^n$, then $(T_0 -T_2 + T_4 - .......)^2 + (T_1 - T_3 + T_5 - .....)^2 =$

The number of all three elements subsets of the set $\{a_1, a_2, a_3 . . . a_n\}$ which contain $a_3$ is

If the $(2p)^{th}$ term of a H.P. is $q$ and the $(2q)^{th}$ term is $p$, then the $2(p + q)^{th}$ term is-

If $\frac{1}{a} , \frac{1}{b} , \frac{1}{c} $ are in A. P., then $\left(\frac{1}{a} + \frac{1}{b} - \frac{1}{c}\right) \left(\frac{1}{b} + \frac{1}{c} - \frac{1}{a}\right) $ is equal to