List of top Mathematics Questions

The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] is:
If \( |\mathbf{a}| = 3 \), \( |\mathbf{b}| = 4 \), then the value of \( \lambda \) for which \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{a} - \lambda \mathbf{b} \) is:

The determinant of the matrix:

is:

If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:

If \[ \sin x + \cos x = \frac{1}{5} \] then \( \tan 2x \) is: 

If 

then \( {Adj} (A) \) is equal to:

If \[ \frac{a^n + b^n}{a^{n-1} + b^{n-1}} \] is the arithmetic mean (A.M.) between \( a \) and \( b \), then the value of \( n \) is:

The integral \[ \int x^n (1 + \log x) \, dx \] is equal to: 

Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:
If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:
Evaluate: \[ \tan (\cos^{-1} \frac{4}{5}) + \tan^{-1} \frac{2}{3} \]
The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:
The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:
The derivative of \[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \] with respect to \[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \] is equal to:
Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:
Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]
The general solution of the differential equation given by: \[ \tan^{-1} x + \tan^{-1} y = c \]
If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:
If the vertex of a parabola is \( (2, -1) \) and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:
The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m1 and m2 are the slopes of the lines l1 and l2, then the point of intersection of the line y = (m1 + m2)x with L lies on

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

Which of the following is an empty set ?