List of top Mathematics Questions

A rectangle ABCD with ABCD with AB = 2 and BC = 4 is inscribed in rectangle PQRS such that vertices of ABCD lie on sides of PQRS then maximum possible area(in sq. unit) of rectangle PQRS is :
Two lines passing through (2, 3) parallel to coordinate axes. A circle of unit radius touches both the lines and lies on the origin side. Then the shortest distance of point (5,5) from the circle is:
$ \lim_{t \rightarrow x} \frac{t^2f(x) - x^2 f(t)}{t-x} = 1$, then 2f(2) + 3f(3) equals to:
If a, b, c are in increasing A.P. and a + 1, b, c + 3 are in G.P. If A.M. of a, b, c is 8. Find cube of G.M. of a, b, c.
A parabola $y^2 = 12x$ has a chord PQ with mid-point (4, 1) then equation of PQ passes through
Team A plays 10 matches, probability of winning is $\frac1{3}$ and losing is $\frac2{3}$. They win x matches and lose y matches. Probability such that $|x – y| ≤ 2$ is P then find 3$^9P$.
For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2}=1, C_1$ is a circle touching hyperbola having centre at origin and $C_2$ is circle centred at four and touching hyperbola at vertices, if area of $C_1= 36π$ and area of $C_2 = 4π$. Find $a_2 + b_2 $= ?
$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to
$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to
The radius of a circle is $\sqrt{10} .\,\, x + y = 4$ is the line intersecting the circle at P & Q. A chord MN is of length 2 m having slope –1. Find perpendicular distance between the two chords PQ and MN.
If $ f(x) =\begin{cases}\frac{(72)^x - 9^x -8^x+1}{\sqrt2-\sqrt{1+cosx}} &; x ≠0\\a\,log2\,log3 &  ; x=0\end{cases} $ is continuous at x = 0. Then $a^2$ equals to
If a, b, c are in A. P. and a + 1, b, c + 3 are in G. P., arithmetic mean of a, b, c is 8, then the value of cube of geometric mean of a, b, c is:
If (z)2+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α2+β2)
The coefficient of x7 in (1-x-x2+x3)6
\(f(x)=\frac{2x^2-3x+8}{2x^2+3x+8}\), Then sum of maximum and minimum values of f(x) is:
Find \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{\sin^2x}{1+2^x} \;dx\)
Three urn A, B, C, A has 7 red and 5 black balls, B has 5 red and 7 black balls, C has 6 red and 6 black balls. One urn is selected and black ball is taken out. Find probability that the selected urn is A.
Find the number of rational numbers in the expansion of \((2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}\).
If \(f(x) =   \begin{cases}  x-2       & \quad 0\leq x\leq2\\     -2  & \quad -2\leq x\leq0   \end{cases}\) and \(h(x) = f(|x|) + |f(x)|, \int\limits^{k}_{0} h(x) dx\) is equal to _____.(k>0)
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if 
(i) 4 letters are used at a time, 
(ii) all letters are used at a time, 
(iii) all letters are used but first letter is a vowel.
How many chords can be drawn through 21 points on a circle?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Find \( \frac {dy}{dx}:\) \(sin^2y+cos\ xy=\pi\)
If the third term of a G.P. is 3, then the product of its first 5 terms is
$sin\left\{2\,cos^{-1}\left(- \frac{3}{5}\right)\right\}$ is equal to