List of top Mathematics Questions

The number of values of $r \in\{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is :

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

For all $z \in C$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$ Then:

Let α and β be real numbers. Consider a \(3 \times 3\) matrix A such that \(A^2 = 3A + \alpha I\). If \(A^4 = 21A + \beta I\), then

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α2 + β2 + γ2) is equal to
The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :
\( \sin^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \sin^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} = \)
If the equation of the tangent drawn at \((h, k)\) to the hyperbola \(\frac{(x - 1)^2}{1} - \frac{(y - 2)^2}{2} = 1\) is \(x = 2\), then \(h + k =\)
If $ O $ is the origin and $ P, Q $ are points on the line $ 3x + 4y + 15 = 0 $ such that $ OP = OQ = 9 $, then the area of $ \triangle OPQ $ is:
If the difference between the mean and variance of a binomial variate is \( \dfrac{5}{9} \), then the probability of getting 2 successes for an event when the experiment is conducted 5 times is:
In \(\triangle ABC\), if \(\cos A + \cos C = 4 \sin^2 \frac{B}{2}\), then the ratio between the perimeter of the triangle and \((a + c)\) is
The Cartesian form of the curve given by \( x = \frac{a}{2}\left(t + \frac{1}{t}\right) \), \( y = \frac{a}{2}\left(t - \frac{1}{t}\right) \), where \( t \) is a parameter, is:
The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter 6, then the probability that at least one and at most five persons join the queue in a particular minute is
The number of arrangements of the word KANGAROO in which the A's do not appear together is:
Evaluate the following expression: \[ (1+i)^{2024} + (1-i)^{2024} \]
In a matrix \( A \), if all the sub matrices of \( k^{th} \) order are singular and there is one non-singular sub matrix of order \( r \) \( (r<k) \), then the rank \( (\rho) \) of the matrix \( A \)
If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point P, lying in the first quadrant, is a horizontal line, then the equation of the normal at the point P is
If a function defined by \( f(x) = \frac{(3^x - 1)^2}{\sin x \cdot \log(1+x)}, x \neq 0 \) is continuous at \(x = 0\), then \(f(0) =\) ?

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).

Let \( \vec{b} = 3i - 2j + k \) and \( \vec{c} = i - j - k \) be two vectors. If \( \vec{a} \) is a vector such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), then \( | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | \) is:
In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
If \( f(x) = \int_0^x \frac{5t^8 + 7t^6}{(t^2 + 2t + 1)^2} dt \) and \( f(0) = 0 \), then the value of \( f(1) \) is:
Let $ S $ be a circle concentric with the circle $ 3x^2 + 3y^2 + x + y - 1 = 0 $. If the length of the tangent drawn from a point $ (2, -2) $ to the given circle is the radius of the circle $ S $, then the power of the point $ (2, 1) $ with respect to the circle $ S $ is
In a test, a student either guesses, copies, or knows the answer to a multiple-choice question with four choices. The probability that he makes a guess is \( \frac{1}{3} \), and the probability that he copies is \( \frac{1}{6} \). The probability that his answer is correct, given that he guessed it, is \( \frac{1}{4} \), and the probability that he copied it and it is correct is \( \frac{1}{8} \). The probability that he knew the answer to the question, given that he answered it correctly, is: