List of top Mathematics Questions

Out of 8 students in a classroom, 4 of them are chosen and they are arranged around a table. If the remaining 4 are arranged in a row, then the total number of arrangements that can be made with those 8 students is
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
Tangents are drawn at three points P($t_1$), Q($t_2$), R($t_3$) on the parabola $y^2 = x$. Let these tangents intersect each other at the points L, M, N. If $t_1 = 2$, $t_2 = -4$, $t_3 = 6$, then the area of the triangle LMN is
The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants between any two vowels is:
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
The interval in which the curve represented by \( f(x) = 2x + \log\left(\frac{x}{2 + x}\right) \) is increasing is

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

If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
If \( \vec{a} = 2\vec{i} - \vec{j} + 6\vec{k} \); \( \vec{b} = \vec{i} - \vec{j} + \vec{k} \) and \( \vec{c} = 3\vec{j} - \vec{k} \), then \( \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \)
The triangle formed by the lines \( 2x^2 + xy - 6y^2 = 0 \) and \( x+y-1=0 \) is:
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?
If \(2\sin x - \cos 2x = 1\), then \( (3 - 2\sin^2x) = \)
Evaluate: \(\tan\left(2\tan^{-1}\left(-\frac{1}{3}\right) + \tan^{-1}\left(\frac{1}{7}\right)\right) =\)
If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$
A rational number is selected at random from the distinct rational numbers of the form \( \frac{p}{q} \) formed with \( p \) and \( q \) belonging to the set \( \{1,2,3,4,5,6\} \). The probability that the rational number selected is a proper fraction is:
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
If the angle between the lines joining the origin to the points of intersection of \( x + 2y + \lambda = 0 \) and \( 2x^2 - 2xy + 3y^2 + 2x - y - 1 = 0 \) is \( \dfrac{\pi}{2} \), then a value of \( \lambda \) is:
Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]
If two sides of a triangle are represented by \( 3x^2 - 5xy + 2y^2 = 0 \) and its orthocentre is (2,1), then the equation of the third side is
In triangle $ ABC $, $ 2A + C = 300^\circ $. If the circumradius is 8 times the inradius, then $ \sin\frac{C}{2} = ? $
In triangle \(ABC\), if \(a = 6\), \(b = 8\), and \(c = 10\), then \(\dfrac{2r_1}{r_2} =\)
Evaluate: \(\tanh^{-1}\left(\frac{1}{3}\right) + \coth^{-1}(3) =\)
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| $
If the equation of the circle having the common chord to the circles $$ x^2 + y^2 + x - 3y - 10 = 0 $$ and $$ x^2 + y^2 + 2x - y - 20 = 0 $$ as its diameter is $$ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, $$ then find $ \alpha + 2\beta + \gamma $.