List of top Mathematics Questions

The limit \( \lim_{x \to 0} \frac{3 \sin^2 2x}{x^2} \) is equal to:
If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
If the mean of five observations \( x, 2x+5, 13, 2x-7, \) and 9 is 22, then the value of \( x \) is:
The function \( f(x) = (x - 4)^2 (1 + x)^3 \) attains a local extremum at the point:
If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
Let \( f(x) = \cos^{-1} \left( \frac{1 - \tan^2 x}{1 + \tan^2 x} \right) \). Then \( f\left( \frac{\pi}{2} \right) \) is equal to:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
A vector of magnitude 6 and perpendicular to \( \vec{a} = 2i + 2j + k \) and \( \vec{b} = i - 2j + 2k \), is:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
The integral \( \int xe^x \, dx \) is equal to:
The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
If \( x = r \cos \theta, y = r \sin \theta \), then \( \frac{dy}{dx} \) at \( \theta = \frac{\pi}{4} \), where \( r \) is a constant and \( \theta \) is a parameter, is equal to:
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
The derivative of \( t^2 + t \) with respect to \( t-1 \) at \( t = -2 \), is equal to:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
tan\(^{-1} 2 - \) tan\(^{-1} \frac{1}{3}\) is equal to:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to:
If \( f(x) = \lfloor x \rfloor \), where \( \lfloor x \rfloor \) denotes the greatest integer function, and if the domain of \( f \) is \( \{-3.01, 2.99\} \), then the range of \( f \) is