List of top Mathematics Questions

If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?

$\left( 1 + \sqrt{5} + i \sqrt{10 - 2\sqrt{5}} \right)^5$

A circle passing through the point (1,0) makes an intercept of length 4 units on X-axis and an intercept of length \(2\sqrt{11}\) units on Y-axis. If the centre of the circle lies in the fourth quadrant, then the radius of the circle is
If $ A = \begin{bmatrix} -1 & x & -3 \\ 2 & 4 & z \\ y & 5 & -6 \end{bmatrix} $ is symmetric and $ B = \begin{bmatrix} 0 & 2 & q \\ p & 0 & 4 \\ -3 & r & s \end{bmatrix} $ is skew-symmetric, then find $ |A| + |B| - |AB| $
The minimum value of \( |z - 1| + |z - 5| \) is:
If $$ \int \frac{a \cos x + 3 \sin x}{5 \cos x + 2 \sin x} dx = \frac{26}{29} x - \frac{k}{29} \log |5 \cos x + 2 \sin x| + c, $$ then find $ |a + k| $.
Given \(f(x) = x^2 - 5x + 4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
Consider the following statements
Statement-I: A function \( f: A \rightarrow B \) is said to be one-one if and only if \[ f(x) = f(y) \Rightarrow x = y \]
Statement-II: A relation \( f: A \rightarrow B \) is said to be a function if \[ x = y \Rightarrow f(x) \neq f(y) \]
Then which one of the following is true?
If all possible 4-digit numbers are formed by choosing 4 different digits from the given digits $ 1, 2, 3, 5, 8 $, then the sum of all such 4-digit numbers is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]
If the roots of the quadratic equation \( 2x^2 - 4x + k = 0 \) are real and equal, find the value of \( k \).
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
Evaluate: \( \int_0^{400\pi} \sqrt{1 - \cos 2x} \, dx \)
If $x>\sqrt{3$ and $\frac{x^2+1}{(x^2+2)(x^2+3)}$ is expanded in terms of powers of $x$, then the coefficient of $x^{-8}$ is}
If \( \alpha, \beta \) are the acute angles such that \( \frac{\sin \alpha}{\sin \beta} = \frac{6}{5} \) and \( \frac{\cos \alpha}{\cos \beta} = \frac{9}{5\sqrt{5}} \) then \( \sin \alpha = \)
If \[ \int \frac{dx}{(x \tan x + 1)^2} = f(x) + c, \] then \(\lim_{x \to \frac{\pi}{2}} f(x)\) is?
If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
The slope of one of the direct common tangents drawn to the circles \(x^2 + y^2 - 2x + 4y + 1 = 0\) and \(x^2 + y^2 - 4x - 2y + 4 = 0\) is
The general solution of the equation \( \cos(2x) = \frac{1}{2} \) is:
If P(\(\alpha, \beta\)) is the radical centre of the circles \(S=x^2+y^2+4x+7=0\), \(S'=2x^2+2y^2+3x+5y+9=0\) and \(S''=x^2+y^2+y=0\), then the length of the tangent drawn from P to S' = 0 is
If the average number of accidents occurring at a particular junction on a highway in a week is 5, then the probability that at most one accident occurs in a particular week is:
Evaluate the limit: \[ \lim_{x \to \infty} \frac{3x+4\cos^2x}{\sqrt{x^2-5\sin^2x}} \]
$\int \frac{\sin 2x}{\sin^2 x + 3 \cos x - 3} \, dx =$
Identify the correct option from the following:
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)