List of top Mathematics Questions

Curve generated by a point on the circumference of a circle which rolls along a straight line is termed:
The solution of the differential equation \( \frac{d^2 y}{dx^2} - 3 \frac{dy}{dx} + 2y = 0 \) is given by
The solution of the differential equation \( \frac{dy}{dx} = \frac{x + y}{x} \) satisfying \( y(1) = 1 \) is
The solution of the differential equation \( y \, dx + (x + x^2 y) \, dy = 0 \) is
If the vectors \( 2\hat{i} - 3\hat{j} + \hat{k} \) and \( 3\hat{i} - 4\hat{j} - \hat{k} \) form three concurrent edges of a parallelepiped, then the volume of the parallelepiped is
Let \( \vec{x} \) and \( \vec{y} \) be two unit vectors and \( \theta \) is the angle between them. Then \( \vec{x} + \vec{y} \) is a unit vector if
For complex numbers \( z \), if \( |z| = 1 \), then the value of \( \frac{z-1}{z+1} \) is
If \( z = \cos\theta + i \sin\theta \), then the value of \( z^{100} + \frac{1}{z^{100}} \) is
If the line \( y = mx \) does not intersect the circle \( (x + 10)^2 + (y + 10)^2 = 180 \), then a possible value of \( m \) is
The distance between the lines \( 3x - 4y + 2 = 0 \) and \( 3x - 4y - 8 = 0 \) is
If \( (1+x)^n = C_0 + C_1 x + C_2 x^2 + \dots + C_n x^n \), then \( C_0 + \frac{C_1}{2} + \frac{C_2}{3} + \dots + \frac{C_{10}}{11} \) is
From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. The number of ways this can be done is
The number of 3 digit numbers that can be formed with \( S = \{0,1,2,3,\dots,8\} \) when repetitions are allowed is
The number of terms in the expansion of \( (2x + 3y + 5z)^5 \) is
The points on the curve \( y = 2x^3 + 3x^2 - 8x \) where the tangents are parallel to the line \( y = 4x + 3 \) are
The equation of the normal to the curve \( y = x + \frac{1}{x} \) at the point where \( x = 2 \) is
Local maximum and local minimum values of \( f(x) = (x-1)^2(x+2) \) are attained respectively at
The standard deviation of the observations 1; 2; 3; 4; 4; 5; 5; 5; 8 is
The position vectors of the vertices of a triangle are \( 4\hat{i} + 5\hat{j} + \hat{k} \), \( 2\hat{i} + 4\hat{j} - \hat{k} \) and \( 3\hat{i} + 6\hat{j} - 3\hat{k} \). Then the triangle is
Two dice are thrown together. The probability of getting a sum more than 8 is
The binary representation of the decimal number 125 is
The hexadecimal representation of the decimal number 2000 is
If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( x^2 \) is equal to
In a frequency distribution, the mean and median are 17 and 18 respectively. Then the mode of the distribution is
On a shelf, 2 books of History, 3 books of Philosophy, and 5 books of Economics are to be arranged in such a way that the books of any subject are kept together. The number of ways this can be done is