List of top Mathematics Questions

Evaluate the integral  \(\int_{0}^{1} \frac{1}{\sqrt{3+x} + \sqrt{1+x}} \, dx\) Given that the integral can be expressed in the form \(a + b\sqrt{2} + c\sqrt{3}\), where \(a, b, c\) are rational numbers, find the value of \(2a + 3b - 4c\).
Let \( f(x) = x^5 + 2x^3 + 3x + 1 \), \( x \in \mathbb{R} \), and \( g(x) \) be a function such that \( g(f(x)) = x \) for all \( x \in \mathbb{R} \). Then \( \frac{g(7)}{g'(7)} \) is equal to:
Let \( C: x^2 + y^2 = 4 \) and \( C': x^2 + y^2 - 4\lambda x + 9 = 0 \) be two circles. If the set of all values of \( \lambda \) such that the circles \( C \) and \( C' \) intersect at two distinct points is \( R = [a, b] \), then the point \( (8a + 12, 16b - 20) \) lies on the curve:
The solution of the differential equation: \[ x^4 \frac{dy}{dx} + x^3 y + \csc(xy) = 0 \] is equal to:
Quartile coefficient of skewness is
The angle between \( x^2 = y \) and \( y^2 = x \) at \( (1, 1) \) is:
Reena is twice as old as Sunitha. Three years ago, she was three times as old as Sunitha. How old is Reena now?
The probability that A passes a test is \( \frac{2}{3} \) and the probability that B passes the same test is \( \frac{3}{5} \). The probability that only one passes is
In the expansion of \( \left( x - \frac{3}{x^2} \right)^9 \), the constant term is:
A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is:
If \( \cot^{-1}(n)>\frac{\pi}{6} \), \( n \in N \), then the maximum value of n is
If the sum of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is equal to the sum of the square of their reciprocals, then \( \frac{a}{c}, \frac{b}{a}, \frac{c}{b} \) are in:
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and him in 8 seconds. The length of the train is:
Four milkmen rented a pasture. A grazed 24 cows for 3 months, B, 10 cows for 5 months, C, 35 cows for 4 months and D, 21 cows for 3 months. If A’s share of rent is ₹720, then the total rent of the field is:
The value of \( \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \) is
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is equal to
If \( \cos B = \frac{\sin A}{2 \sin C} \), then the triangle is
The value of \( \frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} \) is equal to
What is the annual income derived by investing ₹6800 in 10\% stock at 136?
If the height of a pole is \( 2\sqrt{3} \) metres and the length of its shadow is 2 metres, what is the angle of elevation of the sun?
The probability that a person aged 60 years will live up to 70 is 0.65. What is the probability that out of 10 persons aged 60, at least 7 of them will live up to 70?
If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:
The equation of the tangent at \( (2, -3) \) on the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is:
The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is: