List of top Mathematics Questions

If A and B are the centres of similitude with respect to the circles \( x^2 + y^2 - 14x + 6y + 33 = 0 \) and \( x^2 + y^2 + 30x - 2y + 1 = 0 \), then midpoint of \( AB \) is:
If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
If the perpendicular distance from \( (1,2,4) \) to the plane \( 2x + 2y - z + k = 0 \) is 3, then \( k \) is:
If \( f(x) = \left(\frac{1+x}{1-x}\right)^{\frac{1}{x}} \) is continuous at \( x = 0 \), then \( f(0) \) is:
The function \( f(x) = |x - 24| \) is:
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
Displacement \( s \) of a particle at time \( t \) is expressed as \( s = 2t^3 - 9t \). Find the acceleration at the time when the velocity vanishes.
If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]
Evaluate the integral: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \,dx. \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]
The general solution of the differential equation: \[ (1 + \tan y) (dx - dy) + 2x \, dy = 0. \]
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{4 \cos^2 x + 3 \sin^2 x} dx \):
The sum of the order and degree of the differential equation: \[ x \left( \frac{d^2 y}{dx^2} \right)^{1/2} = \left( 1 + \frac{dy}{dx} \right)^{4/3} \] is:
The length of the tangent drawn from the point \( \left(\frac{k}{4}, \frac{k}{3}\right) \) to the circle \( x^2 + y^2 + 8x - 6y - 24 = 0 \) is:
Evaluate the expression \[ 2 \cot h^{-1}(4) + \sec h^{-1}\left( \frac{3}{5} \right). \]
If \( (a, \beta) \) is the orthocenter of the triangle with the vertices \( A(2, 5), B(1, 5), C(1, 4) \), then \( a + \beta = \):
If \( a \) is a rational number, then the roots of the equation \( x^2 - 3ax + a^2 - 2a - 4 = 0 \) are:
Evaluate the integral $$ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx $$
If \( x \) is real and \( \alpha, \beta \) are maximum and minimum values of \( \frac{x^2 - x + 1}{x^2 + x + 1} \) respectively, then \( \alpha + \beta = \):
Simplify the expression: \( 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + \cdots}}} \)
The length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm is:
The value of \(p\), for which the pair of equations \(3x + 4y + 2 = 0\) and \(9x + py + 8 = 0\) represents parallel lines, is:
The value of \(\log_6 2 + \log_6 3\) is:
H.C.F. of 2023, 2024, 2025 is: