List of top Mathematics Questions

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:
If \(\frac{2}{\sqrt{x}} = 2\) and \(\frac{4}{\sqrt{y}} = -1\), then
How many two-digit numbers are divisible by 3?
In a G.P. the 3rd term is 24 and 6th is 192, then the 10th term is:
Rainfall of a town in a week is 4 cm, 5 cm, 12 cm, 3 cm, 6 cm, 8 cm, and 4 cm, then the average rainfall per day is:
A Kiddy bank contains hundred 50 paise coins, fifty ₹1 coins, twenty ₹2 coins, and ten ₹5 coins. If one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is a ₹5 coin?
From a helicopter, a person observes an object on the ground at an angle of depression of \(30^\circ\). If the helicopter is flying at a height of 500 m from the ground, then the distance between the person and the object is:
A boy observed the top of an electric pole at an angle of elevation of \(60^\circ\) when the observation point is 6 meters away from the foot of the pole, then the height of the pole is:
A chord of a circle of radius 4 cm is making an angle 60° at the centre, then the length of the chord is:
The volume of a right circular cone with radius 6 cm and height 7 cm is:
(use \(\pi = \frac{22}{7}\))
If two cubes each of volume 64 cm\(^3\) are joined end to end together, then the surface area of the resulting cuboid is: