List of top Mathematics Questions

The directrix of the parabola y$^2$ + 4x + 3 = 0 is

The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$, is

The radius of the circle with the polar equation $r^2 - 8r( \sqrt{3} \, \cos \, \theta + \sin \, \theta) + 15 = 0$ is

The area of the region bounded by the curve \( x = 4 - y^{2} \) and the y-axis is:

The number of divisors of 360 (excluding 1 and 360) is:

The value of $\sin(45^{\circ} + \theta) - \cos(45^{\circ} - \theta)$ is:

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

A man walks 5 km South and then turns Right. After walking 3 km he turns Left and walks 5 km. Now in which direction is he from the starting place?

If 5 men can build a wall in 12 days, how many days will 10 men take?

A train 100m long passes a bridge in 10 seconds at 72 km/hr. The length of the bridge is:

A shopkeeper sold an item for Rs. 440 at a 10% profit. What was the Cost Price?

A boat goes 12 km/hr in still water. If the speed of the stream is 4 km/hr, what is the boat's speed downstream?

The value of \( \cos^{2} 48^\circ - \sin^{2} 12^\circ \) is:

The value of \( \cot 70^\circ + 4\cos 70^\circ \) is:

If \( \sin \theta \) and \( \cos \theta \) are the roots of the equation \( ax^{2} - bx + c = 0 \), then:

The value of \( \sum_{k=1}^{n} \frac{1}{\sqrt{a_{k}} + \sqrt{a_{k+1}}} \), where \( a_{1}, a_{2}, \dots, a_{n} \) are in A.P. with common difference \( d \), is:

If the sum of \( n \) terms of two A.P.s are in the ratio \( (3n + 8) : (7n + 15) \), then the ratio of their \( 12^{\text{th}} \) terms is:

The value of \( \sqrt{6 + \sqrt{6 + \sqrt{6 + \cdots}}} \) is:

The number of real solutions of \( x^{2} - 3|x| + 2 = 0 \) is:

If \( \log_{10} 2,\ \log_{10}(2^{x} - 1),\ \log_{10}(2^{x} + 3) \) are in A.P., then \( x \) is:

The eccentricity of the hyperbola \( x^{2} - 4y^{2} = 1 \) is:

The value of \( \lim_{x \to 0} \frac{1 - \cos x}{x^{2}} \) is:

If \( y = \tan^{-1}\left(\frac{3x - x^{3}}{1 - 3x^{2}}\right) \), then \( \frac{dy}{dx} \) is:

The derivative of \( e^{x^{3}} \) with respect to \( \log x \) is:

The value of \( \int \frac{1}{1 + e^{x}} \, dx \) is: