List of top Mathematics Questions

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

The value of $\tan^2(\sec^{-1}2)+\cot^2(cosec^{-1}3)$ is

If $f(a) = a^2 , \phi (a) = b^2 $ and $f'(a) = 3 \phi '(a)$ then $Lt_{x \to a} \frac{\sqrt{ f(x)} - a}{ \sqrt{\phi (x)} - b}$ is

Solution set of the inequality $\frac{1}{2^{x}-1} > \frac{1}{1-2^{x-1}}$ is

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?