List of top Mathematics Questions

If the average of 5 numbers is 18, what is their total sum?
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is:
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
What is the distance between the points $(3, -2)$ and $(-1, 4)$?
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
The sum of the least positive integer and the greatest negative integer in the range of the function \( f(x) = \dfrac{x^2 - 5x + 7}{x^2 - 5x - 7} \) is:
The point P(4, 1) undergoes the following transformations in succession: (i) origin is shifted to the point (1, 6) by translation of axes, (ii) translation through a distance of 2 units along the positive direction of the x-axis, (iii) rotation of axes through an angle of $90^\circ$ in the positive direction. Then the coordinates of the point P in its final position are
\[ \text{If } y = |\cos x - \sin x| + |\tan x - \cot x|, \text{ then } \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{3}} + \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{6}} = \]
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)
The general solution of the differential equation $\left( x \sin \frac{y}{x} \right) \frac{dy}{dx} = y \sin \frac{y}{x} - x$ is
Identify the correct option from the following:
Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \[ \lim_{x \to 2^+} \left( \frac{[x]^3}{3} - \left[ \frac{x^3}{3} \right] \right) \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \]
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is
If $-\frac{2}{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is
If 3 sisters and 8 brothers are together playing a game, then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the three sisters are not seated together is
If \(k\) is a positive integer and \(10^k\) is a divisor of the number \(9^{11} + 11^9\), then the greatest value of \(k\) is:
If the vectors \(2\vec{i} + 3\vec{j} + k\), \(-3\vec{i} - 2\vec{j} - 4k\), and \(l\vec{i} - \vec{j} + 3\vec{k}\) form a right-angled triangle for a positive value of \(l\), then the length of its hypotenuse is
In a shoe rack there are 4 pairs of shoes and 4 shoes are drawn one after the other at random without replacement. Then the probability of getting at least one correct pair of shoes among the four shoes drawn is:
The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.
Points \( P \) and \( Q \) are given by \( \vec{OP} = \vec{i} - \vec{j} - \vec{k} \) and \( \vec{OQ} = -\vec{i} + \vec{j} + \vec{k} \). A line along the vector \( \vec{a} = \vec{i} + \vec{j} \) passes through point \( P \), and another line along the vector \( \vec{b} = \vec{j} - \vec{k} \) passes through point \( Q \). If a line along the vector \( \vec{c} = \vec{i} - \vec{j} + \vec{k} \) intersects both the lines along \( \vec{a} \) and \( \vec{b} \) at \( L \) and \( M \) respectively, then \( \vec{PM} = \) ?
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
Let \[ A = \begin{bmatrix} 0 & k & k \\ k & -4 & -6 \\ k & -3 & -5 \end{bmatrix} \text{be a singular matrix for} \]