List of top Mathematics Questions

Evaluate the limit: $$ \lim_{x \to 4} \left( \frac{1}{x - 4} - \frac{5}{x^2 - 3x - 4} \right) $$ is equal to 
Let \( z = x + iy \), where \( y>0 \). If \( z + \overline{z} = 6 \) and \( |z| + | \overline{z} | = 10 \), then \( z = \)
Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is
If \[ x^4 + 2\sqrt{y} + 1 = 3, \] then \( \frac{dy}{dx} \) at \( (1,0) \) is equal to
If \[ y = \log_e \left( \frac{1 + 2x^2}{1 - 3x^2} \right), \] then \( \frac{dy}{dx} \) is:
Evaluate the integral: \[ \int \frac{6x^3 + 9x^2}{x^4 + 3x^3 - 9x^2} dx. \]
If two dice are rolled simultaneously, then the probability that the difference of the numbers on the two dice equals to zero is
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
If \[ A = \begin{bmatrix} -7 & 3 \\ 3 & -1 \end{bmatrix} \] then \( \det(A^5) \) is equal to:

The area bounded by the parabola \( y = x^2 + 4 \) and the straight line passing through the points \( (-1,2) \quad {and} \quad (1,6) \) is (in square units)

If the complex number \( \frac{2 + i}{\lambda + i} \) lies on the line \( y = x \) of the first quadrant, then the value of \( \lambda \) is equal to
The relation \( R \) in the set of integers \( \mathbb{Z} \) is given by \( R = \{(a, b) : b = 2a + 3 \} \). Then the relation \( R \) is:
Let \( f(x) = ax^3 + bx^2 + cx + d \). If \( f \) has a local maximum value 21 at \( x = -1 \) and a local minimum value 7 at \( x = 1 \), then \( f(0) \) is equal to:
If \( (a,-6) \) lies on the perpendicular bisector of the line segment joining \( (-2,-1) \) and \( (4,-13) \), then the value of \( a \) is equal to
Find the equation of the line perpendicular to the line \[ 7x - 5y = 11 \] and passing through the point \( (7, -9) \).
The coordinates of the vertex of the parabola \[ y = 2x^2 - 12x + 26 \] are
Find the equation of the parabola with focus at \( (3,1) \) and vertex at \( (5,1) \).
The function \( f(x) = 6x^4 - 3x^2 - 5 \) is increasing in the set:
Evaluate the integral \[ \int x^5 e^{x^3} \,dx. \]
The value of \( \sin \left( 2 \cos^{-1} \left( \frac{5}{12} \right) + \sin^{-1} \left( \frac{5}{12} \right) \right) \) is equal to
The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{2}{3} \right) + \cot^{-1} \left( \frac{9}{7} \right) \] is equal to
The number of positive integers that have at most seven digits and contain only the digits 0 and 9 is
The eccentricity of the ellipse \[ p x^2 + 5y^2 = 80, \quad \text{where } p > 5, \] is \( \frac{\sqrt{3}}{2} \). Then the value of \( p \) is
For an ellipse, the foci are \( F(3,0) \) and \( F'(-3,0) \). If the length of the minor axis is 8, then the length of the major axis is equal to

Simplify: \( \tan x - \cot x + \csc x \sec x \)