List of top Mathematics Questions

If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
In \( \triangle ABC \), if the midpoints of the sides \( AB, BC, CA \) are respectively \( (l, 0, 0), (0, m, 0), (0, 0, n) \), then: \[ \frac{AB^2 + BC^2 + CA^2}{l^2 + m^2 + n^2} = ? \]
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
If A is a non singular square matrix of order 3 such that \(A^3 = 4A^2\) then value of |A| is:
Derivative of \(2x^2\) with respect to \(5x^4\) is:
Le L be the set of all lines in a plane and R be the relation in L. defined as R = {(\(L_1, L_2\)): \(L_1\) is perpendicular to \(L_2\)} then R is:
A) Reflexive
B) Symmetric
C) Neither reflexive nor transitive
D) Transitive
E) Neither reflexive nor symmetric
Choose the correct answer from the options given below:
Consider the non-empty set consisting of children in a family and a relation R is defined as aRb if a is a brother of b. Then R is:
The value of the expression sin \([cot^{-1}(cos (tan^{-1}1))]\) is:
If \(x = \sqrt{a^{sin^{-1} t}}\), \(y = \sqrt{a^{ cos^{-1}t}}\) then \(\frac{dy}{dx}\) is:
Two cards are drawn without replacement. The probability distribution of number of aces is given by:
The solution set of the inequality \(2x + 3y < 4\) is:
The corner points of the feasible region determined by the system of linear inequalities are (0,0), (4, 0), (2, 4) and (0.5). If the maximum value of Z = ax + by where a, \(b > 0\) occurs at both (2, 4) and (4.0), then
The area bounded by x = 1, x = 2, xy = 1 and x-axis is:
If, A is a square matrix of order 3 and |A| = -2 then. \(|-2 \ A^{-1}|\) is:
The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by
The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = x + 1\) is:
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:
Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. If the tailors A and B work for x and y days respectively. To maximize the earning for producing at least 60 shirts and 32 pants, the LPP is:
If y = x + tan x, then value of \(\frac{d^2y}{dx^2}\) at \(x= \frac{\pi}{4}\) is:
Differential coefficient of see (\(tan^{-1} x\)) with respect to x is:
The direction cosines of z-axis are:
If \(\begin{bmatrix}      1 & 3 & 5          \\[0.3em]      1 & 0   &3 \\[0.3em]        0 &1 &0      \end{bmatrix}\),then \(|(adjA)| \) is:
for which value of \(\lambda\) is the function ,\(f(x) = \begin{cases} \lambda(x^2-2x) & \text{if } x \leq 0 \\ 4x+1& \text{if } x > 0 \end{cases}\) continuous at \(x=0 ?\)
The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is:
The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is: