List of top Mathematics Questions

If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) 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 equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) is
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
If \( \vec{a} = 2\vec i + 4\vec j + 7\vec k \) and \( \vec {b} = 4\vec i + 7\vec j + 2\vec k \), then the angle between \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) is equal to:
The integral \( \int xe^x \, dx \) is equal to:
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
The integral \( \int_5^{10} \left\lfloor x \right\rfloor dx \) is equal to (where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function):
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
Equation of the line parallel to the line \( \frac{x-2}{2} = \frac{y-2}{3} = \frac{z-1}{-2} \) and passing through the point \( (3, 2, -1) \) is:
Let \( a, b, c \) be positive numbers. If \( a + b + c \geq K \left[ (a + b)(b + c)(c + a) \right]^{1/3} \), then the maximum value of \( K \) is:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( \frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} + \frac{1}{\log_5 x} + \frac{1}{\log_6 x} = 1 \), then the value of \( x \) is
If the complex numbers \( (2 + i)x + (1 - i)y + 2i - 3 \) and \( x + (-1 + 2i)y + 1 + i \) are equal, then \( (x, y) \) is
The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:
The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to: