List of top Mathematics Questions

If the line $2x - 3y = k$ touches the parabola $y^2 = 6x$, then find the value of $k$.

If x satisfies $| 3 x - 2 | + | 3x - 4 | + | 3x - 6 | \ge 12$, then

Let $f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right), g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)$ and let $h(x)$ be such that $f(x)=g(x) h(x)$. Then $\displaystyle\lim _{x \rightarrow 1} h(x)$ is

Find the variance of the data given below

Occurance $(x_i)$	Frequency $(f_i)$	Freq $\ast (x_i)$	$(x_i-mean)$	$(x_i-mean)^2$	$f_i(x_i-mean)^2$
3.5	3	10.5	-3.59	12.887	38.661
4.5	7	31.5	-2.59	6.707	46.952
5.5	22	121	121	2.528	55.609
6.5	60	390	-0.59	0.348	20.876
7.5	85	637.5	0.41	0.168	14.298
8.5	32	272	1.41	1.988	63.632
9.5	8	76	2.41	5.809	46.47
Total	217	1538.5	-	-	286.498

$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis. If $STB$ is an equilateral triangle, then the eccentricity of the ellipse is

Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is

An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is

In the truth table for the statement $(p \wedge q) \rightarrow(q \vee \sim p)$, the last column has the truth value in the following order is

For $k=1,2,3$ the box $Bk$ contains $k$ red balls and $(k+1)$ white balls. Let $P\left(B_{1}\right)=\frac{1}{2}, P\left(B_{2}\right)=\frac{1}{3}=\frac{1}{3}$ and $P\left(B_{3}\right)=\frac{1}{6} .$ A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_{2}$, is

A pair of tangents are drawn from the origin to the circle $x^2 + y^2+ 20 (x + y) + 20 = 0$, then the equation of the pair of tangent are

The value of $\cos \left[ \frac{1}{2} \cos^{-1}\left(\cos\left(\sin^{-1} \frac{\sqrt{63}}{8}\right)\right)\right] $ is -

If $1.0$ mole of $I_{2}$ is introduced into $1.0$ litre flask at $1000\, K$, at equilibrium $\left(K_{c}=10^{-6}\right)$, which one is correct?

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n =10$ then the value of $n$ is

The solution of the differential equation $\frac{dy}{dx}=\frac{yf '\left(x\right)-y^{2}}{f \left(x\right)}$ is

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b=0$ and if $\alpha^{n}+\beta^{n}=V_{_n},$ then

The sum of the series $ \displaystyle\sum_{r = 0}^{n}\left(-1\right)^{r}\, ^{n}C_{r}\left(\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+...m \text{terms}\right)$ is

If $\int \frac{dx}{x+x^{7}} = p\left(x\right)$ then, $\int \frac{x^{6}}{x+x^{7}}dx$ is equal to:

If a tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^{2}}{18}+\frac{y^{2}}{34}=1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to (O is the centre of the ellipse)

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777,....,$ is

If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8\, cm^2/s$, then the rate of change of its volume is :

If the integral $\int \frac{cos 8x+1}{cot 2x-tan 2x} dx=A cos 8x+k,$ where $k$ is an arbitrary constant, then $A$ is equal to:

On the sides $AB, BC, CA$ of a $\Delta ABC, 3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices a re :

If the value of mode and mean is $60$ and $66$ respectively, then the value of median is

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$