List of top Mathematics Questions

Two spinning machines A and B can together produce 3,00,000 metres of cloth in 10 hours. If machine B alone can produce the same amount of cloth in 15 hours, then how much cloth can machine A produce alone in 10 hours?

In a class of 50 students, 23 speak English, 15 speak Hindi and 18 speak Punjabi. 3 speak only English and Hindi, 6 speak only Hindi and Punjabi and 6 speak only English and Punjabi. If 9 can speak only English, then how many students speak all the three languages?

The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.

If $(0, 6)$ and $(0, 3)$ are respectively the vertex and focus of a parabola then its equation is

If the foci of the ellipse $ \frac {x^{2}} {{16}}$+$ \frac {y^{2} }{{b}^2} $=1 and hyperbola $\frac {x^{2}} {144} - \frac {y^{2}}{81}=\frac {1}{25}$ coincide then the value of $b^2$ is

If $w= \frac {-1+\sqrt {3i}}{2} $ then $(3+w+3w^2)^4 $

If $Cos^{-1} p + Cos ^{-1} q + Cos ^{-1} r = \pi $ then $p^{2} + q^{2} +r^{2} +2pqr=$

The differential coefficient of $f (Sin \,x)$ w.r.t. $x$ where $f (x) = \log\, x$ is

The smallest positive integer $n$ for which $(1+i)^{2n} = (1-i)^{2n}$ is

If $0 \leq x \leq \pi$ and +$81^{sin^2x}+81^{Cos^2x}=30$ then $x=$

The radius of the circle passing through the point $(6, 2)$ and two of whose diameters are $x + y = 6$ and $x + 2y = 4$ is

The coaxal system of circles given by $x^{2} + y^{2} + 2gx + c = 0$ for $c < 0$ represents.

The equation of the director circle of the hyperbola $\frac {x^{2}} {16}-\frac{y^{2}} {4}=1$ is given by .............

The value of $k$ so that $x^{2} + y^{2} + kx + 4y + 2 = 0 $ and $2(x^{2}+y^{2})- 4x - 3y + k = 0$ cut orthogonally is

If $Sin^{-1} \frac {x}{5}+Cosec^{-1} \frac {5}{4}=\frac {\pi}{2}$ then $x=$

If the lines $\frac{x-1}{2}=\frac{y+3}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of k is

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation R is

If $a_1, a_2, a_3,......, a_n $,.... are in G.P., then the value of the determinant $\begin{vmatrix}\log a_{n}& \log a_{n+1}&\log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}&\log a_{n+5}\\ \log a_{n+6} &\log a_{n+7}& \log a_{n+8}\end{vmatrix} $, is

The set of all integral multiples of $5$ is a subgroup of

If $(1 - p)$ is a root of quadratic equation $x^2 + px + (1- p) = 0$, then its roots are

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is

The range of the function $f\left(x\right) = ^{7-x}P_{x-3}$ is

If $\displaystyle\lim_{x \to\infty} \left(1+ \frac{a}{x} + \frac{b}{x^{2}}\right)^{2x} = e^{2} $ , then the values of a and b, are

The coefficient of the middle term in the binomial expansion in powers of x of $(1+ \alpha x)^4$ and of $ (1 - \alpha x)^6$ is the same if $\alpha$ equals

The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is