List of top Mathematics Questions

If \(A=\{x \mid x^2-5x+6=0\}\), \(B=\{2,4\}\), \(C=\{4,5\}\), then \(A \times (B \cap C)=\)
If the relation \(R: A \rightarrow B\) where \(A=\{1,2,3,4\}\), \(B=\{1,3,5\}\) is defined by \(R=\{(x,y): x<y,\; x\in A,\; y\in B\}\), then \(R\circ R^{-1}=\)
If \(2f(x)-3f\!\left(\dfrac{1}{x}\right)=x^2,\; x\neq 0\), then \(f(2)=\)
The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for 
The solution of \( e^{y-x} \frac{dy}{dx} = \frac{y(\sin x + \cos x)}{1 + y \log y} \)
If A and B are two matrices such that AB=B and BA=A then A2 + B2 =
Prove that, “Angles inscribed in the same arc are congruent.”
Find the differential equation of the family of curves \[ y = a \sin(x + b), \] where \( a \) and \( b \) are arbitrary constants.
Consider the Linear Programming Problem:
Minimize 3x1+4x2 +2x3
subject to
x1+x2+x3≤6
x1+2x2+x3≤10
x1,x2,x3≥0.
Then, the number of basic solutions are
Which of the following set is convex?
The modulus of the complex number \(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\) is
If \[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \] verify that \[ A(\text{adj}A) = (\text{adj}A)A = |A|I \]
A set A has 3 elements and another set B has 6 elements. Then:

The range of the function \( f(x) = \sqrt{3x^2 - 4x + 5} \) is: 
 

The roots of the given equation \( (p - q)x^2 + (q - r)x + (r - p) = 0 \) are:
If one root of the equation \( x^2 + px + 12 = 0 \) is \( 4 \), while the equation \( x^2 + px + q = 0 \) has equal roots, then the value of \( q \) is:
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:
If the eccentricity and length of the latus rectum of a hyperbola are \( \frac{\sqrt{13}}{3} \) and \( \frac{10}{3} \) units respectively, then what is the length of the transverse axis?
Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) is:
The coefficient of \( x^{50} \) in the expression of \[ (1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + \ldots + 1001x^{1000} \]
The sum of infinite terms of a decreasing GP is equal to the greatest value of the function \( f(x) = x^3 + 3x - 9 \) in the interval \([-2, 3]\), and the difference between the first two terms is \( f'(0) \). Then the common ratio of the GP is:
If \(a\), \(b\), \(c\), and \(d\) are in HP and the arithmetic mean of \(ab\), \(bc\), and \(cd\) is 9, then which of the following is the value of \(ad\)?

Select the correct relation between $E$ and $F$. $E=\dfrac{x}{1+x}$ and $F=\dfrac{-x}{\,1-x\,}$, with $x>1$.

The function
\[f(x,y) =   \begin{cases} \frac{x^3-y^3}{x^2+y^2} ,when \space x≠0, y≠0.\\ k, when \space x = 0, y=0   \end{cases}\]
is continuous at (0,0), then k is equal to:
The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is?