List of top Mathematics Questions

The length of the intercept on the line $4x - 3y - 10 = 0$ by the circle $x^2 + y^2 - 2x + 4y - 26 = 0$ is
A line passing through $P(2, 3)$ and making an angle of $30^\circ$ with the positive direction of $x$-axis meets $x^2 - 2xy - y^2 = 0$ at $A$ and $B$. Then the value of $PA \cdot PB$ is
The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is:
The pairs of straight lines \( 2x^2 + axy + 3y^2 = 0 \) and \( 2x^2 + bxy - 3y^2 = 0 \) share a common line, and the other lines are perpendicular. Then values of \( a \) and \( b \) are?
If the angles of a triangle ABC are in the ratio 1:2:3, then the corresponding sides are in the ratio:
Let \( P_1, P_2, \ldots, P_{15} \) be 15 points on a circle. The number of distinct triangles formed by points \( P_i, P_j, P_k \) such that \( i + j + k \ne 15 \), is:
If $a = 2$, $b = 3$, $c = 4$ in a triangle $ABC$, then $\cos C =$
A farmer owns a triangular plot in Guntur. He measures the sides of the plot as 4 cm, 5 cm, and 7 cm. The area of the land (in sq. cm) is:
In triangle \( ABC \), if \( a = 2 \), \( b = 3 \) and \( \sin A = \frac{2}{3} \), then \( \angle B = \):
If a polygon of $n$ sides has 560 diagonals, then $n$ = ?
Two curves \( y = a^x \) and \( y = b^x \) intersect at some angle \( \alpha \). Find \( \tan \alpha \).
In a triangle ABC, let \(\angle C = \pi/2\). If r and R are respectively inradius and circumradius of ABC, then R + r =
Given points \( A(-3, 3), B(1, 1), C(1, -1), D(-2, -2) \), find the angle between diagonals \( AC \) and \( BD \).
The least value of $n$ so that ${}^{n-1}C_3 + {}^{n-1}C_4>{}^nC_3$ is
Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.
If \( \frac{d^n y}{dx^n} = y_n \) and \( y = e^{\sqrt{x}} + e^{-\sqrt{x}} \), then find the value of \( 4x y_2 + 2 y_1 \).
Let \[ f(x) = \begin{cases} \frac{1 - \sin^3 x}{3 \cos^2 x}, & x<\frac{\pi}{2} \\ \alpha, & x = \frac{\pi}{2} \\ \frac{\beta(1 - \sin x)}{(\pi - 2x)^2}, & x>\frac{\pi}{2} \end{cases} \] If \( f(x) \) is continuous at \( x = \frac{\pi}{2} \), find \( \alpha \beta \).
All pairs \( (x, y) \) that satisfy the inequality \[ 2\sqrt{\sin^2x - 2\sin x + 5} \cdot \frac{1}{4^{\sin^2 y}} \leq 1 \] also satisfy the equation:
If the position vectors of points \( A, B, C, D \) are: \[ \vec{A} = 7\hat{i} - 4\hat{j} + 7\hat{k},\quad \vec{B} = \hat{i} - 6\hat{j} + 10\hat{k},\quad \vec{C} = -\hat{i} - 3\hat{j} + 4\hat{k},\quad \vec{D} = 5\hat{i} - \hat{j} + 5\hat{k} \] Then the quadrilateral \( ABCD \) is:
If the slope of the line through \( (0, 0) \) which is tangent to the curve \( y = x^2 + x + 16 \) is \( m \), then find the value of \( m - 4 \).
If the line \( ax + by + c = 0 \) is a normal to the curve \( xy = 1 \), then which of the following is true?
A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:
A plane makes intercepts \(-2, \frac{4}{3}, \frac{-4}{5}\) on the X, Y, Z axes respectively. Find the direction cosines of a normal to the plane.
Evaluate the integral: \[ \int_{-\pi}^{\pi} \frac{2x(1 + \sin x)}{1 + \cos^2 x}\, dx \]
If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]