List of top Mathematics Questions

A stick of length $r$ units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
If the point \( P(\sin\alpha, \cos\alpha) \) lies inside the triangle formed by the vertices \( (0, 0), \left(\frac{\sqrt{3}}{2}, 0\right), (0, \frac{\sqrt{3}}{2}) \), then \( \alpha \) lies in the interval:
The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
In quadrilateral ABCD, $\vec{AB} = \vec{a},\ \vec{BC} = \vec{b},\ \vec{DA} = \vec{a} - \vec{b}$. M is midpoint of BC and X lies on DM such that $\vec{DX} = \dfrac{4}{5}\vec{DM}$. Then the points A, X and C:
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
If $ \sin\theta + \csc\theta = 4 $, then find: $$ \sin^2\theta + \csc^2\theta = ? $$
In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]
If $\displaystyle \lim_{x \to 0} \dfrac{|x|}{\sqrt{x^4 + 4x^2 + 5}} = k$, $\displaystyle \lim_{x \to 0} x^4 \sin\left(\dfrac{1}{3\sqrt{x}}\right) = l$, Then $k + l = $
The function $ y = x^3 - ax^2 + 48x + 7 $ is increasing for all real values of $ x $. Find the interval in which $ a $ lies:
Suppose a point \( P \) moves such that: \[ BP^2 - AP^2 = 121 \] where \( A = (2, 5) \), \( B = (5, 11) \). Then the locus of \( P \) is a straight line. What is the slope of this line?
The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2 + (y \pm 1)^2 = 1\) is (The equation \((x \pm 1)^2 + (y \pm 1)^2 = 1\) represents four circles with radius 1, centered at (1,1), (1,-1), (-1,1), (-1,-1).)
If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?
In a Binomial distribution $B(n, p)$, if the mean and variance are 15 and 10 respectively, then the value of the parameter $n$ is
A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:
The locus of the point of intersection on the line \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different real values of k is a hyperbola H. If e is the eccentricity of H then \(4e^2 = \)
For any real number $t$, the point $\left( \dfrac{8t}{1 + t^2}, \dfrac{4(1 - t^2)}{1 + t^2} \right)$ lies on a/an
The total number of positive integral solutions \((x, y, z)\) of \( xyz = 24 \) is:
If $P$, $Q$ are two points on the curve $y = 2x^2$ in the rectangular Cartesian coordinate system such that $\vec{OP} \cdot \vec{i} = -1$, $\vec{OQ} \cdot \vec{i} = 2$, then $\vec{OQ} - 4\vec{OP} =$