List of top Mathematics Questions

In a game, a man wins Rs. $100$ if he gets $5$ of $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/ loss (in rupees) is :

If $m$ is chosen in the quadratic equation $(m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :

The value of cos $^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}$

With the usual notation $\displaystyle \int_1^2 ([x^2]-[x]^2)dx$ is equal to

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

For the following feasible region, the linear constraints are

The coefficient of $x^2$ term in the binomial expansion of $\left(\frac{1}{3}x^{1/2}+x^{-1/4}\right)^{10}$ is :

The length of the chord of the parabola $x^2 = 4y$ having equation $x - \sqrt{2} y + 4 \sqrt{2} = 0$ is :

If a unit vector $\vec{a}$ makes angles $\pi/3$ with $\hat{i} , \pi /4$ with $\hat{j}$ and $\theta \in (0 , \pi)$ with $\hat{k}$, then a value of $\theta$ is : -

If the p^th, q^th, r^th terms of an A.P are in G.P, then the common ratio of the G.P is

Find the 4^th term in the expansion of (-3a - b)⁵

The coefficient of skewnes of a distribution is 0.32. If its standard deviation is 6.5 and mean is 29.6, then the mode of the distribution is given by

In a G.P if the (m+n)^th term is p and (m-n)^th term is q then its m^th term is

The equation of the second degree x²+2√2xy+2y²+4x+4√2y+1=0 represents a pair of straight lines, the distance between them is

If a,b,c are in AP, then a³+c³-8b³ is equal to

If the circles x² + y² + 2x + 2ky + 6 = 0, x² + y² + 2ky + k = 0 intersect orthogonally, then k is

A box contains 5 red and 4 white balls. Two balls are drawn successively from the box without replacement and it is noted that the second one is white. Then the probability that the first one is white is

Consider points A,B,C and D with position vectors \(7\vec{i}-4\vec{j}+7\vec{k}, \vec{i}-6\vec{j}+10\vec{k}, -\vec{i}-3\vec{j}+4\vec{k}\) and \(5\vec{i}-\vec{j}+5\vec{k}\) respectively, then ABCD is a

The centre and radius of the sphere \(|2\vec{r}=(J\vec{i}-\vec{j}+4\vec{k})|=4\) are __________

The line 4x+6y+9=0 touches y²=4x at the point

The circles x² + y² - 4x - 6y - 12 = 0 and x² + y² + 6x - 8y + 21 = 0

The eccentricity of a circle e is

ABCD is a square A = (1,2), B = (3,-4). If line CD passes through (3,8) then midpoint of CD is