List of top Mathematics Questions

The probability that a person goes to college by car,\(\frac{1}{5}\) bus,\(\frac{2}{5}\) or train \(\frac{3}{5}\) is given. If he reaches college on time, find the probability he traveled by car.
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
Find the value of \( x \) satisfying: \[ 1 + \sin x + \sin^2 x + \sin^3 x + \dots = 4 + 2\sqrt{3} \] where \( 0x\pi, x \neq \frac{\pi}{2} \).
The coefficient of \( x^5 \) in the expansion of \( (3 + x + x^2)^6 \) is:
In \( \triangle ABC \), \( (r_2 + r_3) \csc^2 \frac{A}{2} =\)
\[ f(x) = \begin{cases} \frac{x - |x|}{x}, & x \neq 0 \\[8pt] 2, & x = 0 \end{cases} \] Which of the following is true for \( f(x) \)
Evaluate the integral: \[ \int \sin^{-1} \left( \sqrt{\frac{x - a}{x}} \right) dx \]
The differential equation for which \( ax + by = 1 \) is the general solution is:
The solution of the differential equation \( e^x y dx + e^x dy + xdx = 0 \) is:
If the angle \( \theta \) between the line \( \frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2} \) and the plane \( 2x - y + \sqrt{\lambda}z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( \lambda \) is:
The area of the quadrilateral formed with the foci of the hyperbola \[ \frac{x^2}{16} - \frac{y^2}{9} = 1 \] and its conjugate hyperbola is (in square units):
The length of the internal bisector of angle A in \( \triangle ABC \) with vertices \( A(4,7,8) \), \( B(2,3,4) \), and \( C(2,5,7) \) is:
If the direction cosines of two lines are given by \[ l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0, \] then the acute angle between those lines is:
The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve \( x^2 + y^2 + xy + x + 3y + 1 = 0 \) and the line \( x + y + 2 = 0 \) is:
If the straight line passing through \( P(3,4) \) makes an angle \( \frac{\pi}{6} \) with the positive x-axis in the anticlockwise direction and meets the line \( 12x + 5y + 10 = 0 \) at \( Q \), then the length of the segment \( PQ \) is:
Bag A contains 2 white and 3 red balls, and Bag B contains 4 white and 5 red balls. If one ball is drawn at random from one of the bags and is found to be red, then the probability that it was drawn from Bag B is:
In a Binomial distribution \( B(n,p) \), the sum and product of the mean and the variance are 5 and 6 respectively, then \( 6(n + p - q) = \):
The mean of a binomial variate \( X \sim B(n, p) \) is 1. If \( n>2 \) and \( P(X = 2) = \frac{27}{128} \), then the variance of the distribution is:}

The limit: \[ \lim_{x \to 0} \frac{\sin \left( \pi \sin^2 x \right)}{x^2} \] is equal to:

When \( y = vx \), the differential equation \[ \frac{dy}{dx} = \frac{y}{x} + \frac{f\left( \frac{y}{x} \right)}{f'\left( \frac{y}{x} \right)} \] reduces to:
The integral

\[ \int \frac{dx}{x^8 \left( 1 + x^7 \right)^{2/3}} \] is equal to:
If \[ \lim_{x \to 1} \frac{x^2 - ax - b}{x - 1} = 5, { then } a + b = ? \]
The value of \[ \int_0^{\frac{\pi}{2}} \frac{\cos^{2024} x}{\sin^{2024} x + \cos^{2024} x} \, dx \] is equal to:
The solution of \( \frac{dy}{\cos y} = dx \) is: