List of top Mathematics Questions

The probability that at least one of \( A \) or \( B \) occurs is 0.6. If \( A \) and \( B \) occur simultaneously with probability 0.2, then \( P(A') + P(B') \) is:
sin\(^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right) \) is equal to:
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 area of the region bounded by the curve \( y = 3x^2 \) and the x-axis, between \( x = -1 \) and \( x = 1 \), is:
The general solution of the differential equation \( (x + y)^2 \frac{dy}{dx} = 1 \) is:
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):
Let \( P \) and \( Q \) be two finite sets having 3 elements each. The total number of mappings from \( P \) to \( Q \) is
The value of \( \int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\tan x + \sin x}{1 + \cos^2 x} \, dx \) is equal to:
The order and degree of the following differential equation: \( \frac{d^2 y}{dx^2} - 2x = \sqrt{y} + \frac{dy}{dx} \), respectively, are:
The solution of the differential equation \( x + y \frac{dy}{dx} = 0 \), given that at \( x = 0 \), \( y = 5 \), is:
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
If the mean of five observations \( x, 2x+5, 13, 2x-7, \) and 9 is 22, then the value of \( x \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) 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 \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
The derivative of \( t^2 + t \) with respect to \( t-1 \) at \( t = -2 \), is equal to:
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
The common ratio of a G.P. is 10. Then the ratio between its 11th term and its 6th term is:
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
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 \( x_1, i=2, 3, \ldots, n \) 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: