List of top Mathematics Questions

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:
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:
If \( \log_3 2, \log_3 (2^x - 5), \log_3 \left(2^x - \frac{7}{2}\right) \) are in A.P., then \(x\) is:
The value of \( \sum_{a,b,c} \frac{1}{1 + \log_a bc} \) is:
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?
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
If the cost price of an article is ₹632, selling price of an article is ₹765 and total profit earned is ₹1596, then the number of articles sold are:
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:
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:
If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
Reena is twice as old as Sunitha. Three years ago, she was three times as old as Sunitha. How old is Reena now?

If the origin is shifted to a point \( P \) by the translation of axes to remove the \( y \)-term from the equation \( x^2 - y^2 + 2y - 1 = 0 \), then the transformed equation of it is: 

The point of inflexion for the curve \(y = (x - a)^n\), where \(n\) is odd integer and \(n \ge 3\), is:
The population \( p(t) \) at time \( t \) of a certain mouse species satisfies the differential equation:
\[ \frac{d p(t)}{dt} = 0.5p(t) - 450. \] If \( p(0) = 850 \), then the time at which the population becomes zero is:
Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]
Evaluate the integral: \[ \int \sqrt{x + \sqrt{x^2 + 2}} \, dx. \]
The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is:
The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:
The value of definite integral \( \int_0^{\pi/2} \log(\tan x) dx \) is:
Evaluate the integral: \[ \int_{5}^{9} \frac{\log 3x^2}{\log 3x^2 + \log (588 - 84x + 3x^2)} dx \]
Evaluate the integral: \[ \int \frac{x^2 (x \sec^2 x + \tan x)}{(x \tan x + 1)^2} dx \]

Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.

The value of \( \int_0^{\frac{\pi}{2}} \frac{\sin\left( \frac{\pi}{4} + x \right) + \sin\left( \frac{3\pi}{4} + x \right)}{\cos x + \sin x} \, dx \) is: