List of top Mathematics Questions

A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:
A set A has 3 elements and another set B has 6 elements. Then:
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?
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) is:
The probability of getting a sum greater than 7 when a pair of dice are thrown 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 $x>1$.

If \(A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)\) are co-planer then \(\sum (\lambda_i + 2)^2\) is equal to
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 integral \(\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx\) 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? 
 
Let the line L pass through the point (0, 1, 2), intersect the line  \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is 

Let [t] denote the greatest integer ≤t. Then \(\frac{2}{π} \int\limits_{\frac{\pi}{6}}^{\frac{5\pi}{6}} (8 [cosec x]-5[cot x]) dx\)is equal to ______.

The volume generated by the revolution of the cardioid \(r = a(1-\cosθ)\) about its axis is:
The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :
If \( A \) is the set of even natural numbers less than 8 and \( B \) is the set of prime numbers less than 7, then the number of relations from \( A \) to \( B \) is:
If y intercept of a plane \( (x - y + z - 1) + q(x + y - z - 1) = 0 \) is 3 then q is :
The pair of equations \( x + 3y = 6 \) and \( 2x - 3y = 12 \) :
If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is:
Find the equation of circle with center at \( (2, 5) \) and radius 5 units.
If a, b, c are nonzero vectors such that a=8b, and c= -7b, then the angle between a and c is: