List of top Mathematics Questions

If \( A \) and \( B \) are two events such that \( P(A) = 0.3, P(B) = 0.4, P(A \cap \bar{B}) = 0.5 \), then find the value of \( P(B \cap \bar{A}) \)
If \( \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^3}{x^2 - k^2} \), then the value of \( k \) is:
If a quadratic function in \( x \) has the value 19 when \( x = 1 \) and has a maximum value 20 when \( x = 2 \), then the function is
The solution of the differential equation: \( x\cos y\,dy = (xe^x\log x + e^x)dx \) is
Given that \( z \) is a real number and \( z = \frac{\lambda + 4i}{1+\lambda i} \) where \( \lambda \in R \), then the possible value of \( \lambda \) is:
\( \sin^{-1}(x - 1) + \cos^{-1}(x - 3) + \tan^{-1}\!\left(\frac{x}{2 - x^2}\right) = \cos^{-1} k + \pi \), then the value of \( k \) is __________.
If \( z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5 \), then
If the function \( f(x) = \mu \sin x + \frac{1}{3} \sin 3x \) has its derivative equal to zero at \( x = \frac{\pi}{3} \), then the value of \( \mu \) is __________.
The relationship between \( a \) and \( b \) for the continuity of the function \( f(x) = \begin{cases} ax + 1, & x \leq 3 \\ bx + 3, & x \gt 3 \end{cases} \) at \( x = 3 \) is __________.
A man is moving away from a tower 41.6 m high at a rate of 2 m/sIf the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance 30 m from the foot of the tower is:
\( \int_{0}^{1} x(1 - x)^{99} \, dx = \)
Given \( Z = 80x + 120y \), subject to constraints are \( x + 3y \leq 30; 3x + 4y \leq 60; x \geq 0; y \geq 0 \). \( P \) is one of the corner points of the feasible region for the given Linear Programming Problem. Then the coordinate of \( P \) is
The angle between two lines is \(45^\circ\) and slope of one line is \( \frac{1}{4} \) then which is the possible value of the slope of the other line.
If \( \sin x + \sin^2 x = 1 \) then \( \cos^8 x + 2\cos^6 x + \cos^4 x \) is equal to:
Let \( f(x) = x\sqrt{4ax - x^2, \; a > 0 \) then \( f'(x) \) at \( x = 2a \) is:}
Value of the determinant of a matrix \( A \) of order \( 3 \times 3 \) is 7Then the value of the determinant formed by the cofactors of matrix \( A \) is
The area of a triangle formed by the lines joining the vertex of the parabola \( x^2 = \lambda y \) to the ends of its latus rectum is 18 sq units then the value of \( \lambda \) is
If \( X = \begin{bmatrix} 1 & 0 0 & 1 \end{bmatrix} \) and \( Y = \begin{bmatrix} 0 & 1 -1 & 0 \end{bmatrix} \) and \( B = \begin{bmatrix} \cos \theta & \sin \theta -\sin \theta & \cos \theta \end{bmatrix} \), then \( B \) equals:
If the standard deviation of \( 0,1,2,3,\ldots,9 \) is \( k \), then the standard deviation of \( 10,11,12,13,\ldots,19 \) will be:
Two numbers are selected at random from integers 1 to 9. If their sum is even, what is the probability that both the numbers are odd?
Kiran purchased 3 pencils, 2 notebooks and one pen for INR 41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for INR 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for INR 44. The above situation can be represented in matrix form as \( AX = B \). Then \( \text{adj}(A) \) is equal to
If \( A = \begin{bmatrix} a & b \\ b & a \end{bmatrix} \) and \( (AI)^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix} \), where \( I \) is the identity matrix, then __________.
The solution for the following system of inequalities \( 3x - 7 < 5 + x \) and \( 11 - 5x \leq 1 \) on a real number line is
The value of \( \frac{\sin^2 20^\circ + \cos^4 20^\circ}{\sin^4 20^\circ + \cos^2 20^\circ} \) is :
A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is