List of top Mathematics Questions

Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

If \[ \frac{(2 - i)\,x + (1 + i)}{2 + i} \;+\; \frac{(1 - 2i)\,y + (1 - i)}{1 + 2i} \;=\; 1 - 2i, \quad\text{then}\quad 2x + 4y =\;? \]

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)

Find the number of rational numbers in the expansion of \((2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}\).

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 \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{\sin^2x}{1+2^x} \;dx\)

\(f(x)=\frac{2x^2-3x+8}{2x^2+3x+8}\), Then sum of maximum and minimum values of f(x) is:

The coefficient of x⁷ in (1-x-x²+x³)⁶

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)

If the length of focal chord of y² = 12x is 15 and if the distance of the focal chord from origin is p then 10p² is equal to:

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

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 $ 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

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.

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.

In group A there are 4 men and 5 women and in group B there are 5 men and 4 women, if 4 people are selected from each group. Find a number of ways to select 4 men and 4 women.

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$

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 $= ?

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$^9P$.

A parabola $y^2 = 12x$ has a chord PQ with mid-point (4, 1) then equation of PQ passes through