List of top Mathematics Questions

If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are in A.P. where $a_{i}>0$ for all $i$, then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+$ $\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}$ is?

The locus of the mid-point of a chord of the circle $x^2+ y^2 = 4$, which subtends a right angle at the origin is

A bag contains $2n$ coins out of which $n-1$ are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is $\frac{41}{56}$, then the number of unfair coins in the bag is

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

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

Equation of two straight lines are $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ .Then

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 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

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

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 __________

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 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

\(\displaystyle\int\frac{dx}{cosx-sinx}\) is equal to

\(\int \sec xdx\) is

The value of the integral \(\int\limits^6_3\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt x}dx\) is