List of top Mathematics Questions

Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) 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 of getting a sum greater than 7 when a pair of dice are thrown is:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king 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 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? 
 
The volume generated by the revolution of the cardioid \(r = a(1-\cosθ)\) about its axis 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 :
If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is:
The pair of equations \( x + 3y = 6 \) and \( 2x - 3y = 12 \) :
If a, b, c are nonzero vectors such that a=8b, and c= -7b, then the angle between a and c is:
The value of \( x \), if \( \left| 5^2 - 4 \right| = 12x - 4 \), is:
Find the equation of circle with center at \( (2, 5) \) and radius 5 units.
The integrating factor of the differential equation \( x^2 \left(\frac{dy}{dx}\right) - xy = 1 \) is:
If \( 4\cot^2 x - 16\cot x + 15 < 0 \) and x is real then cot x lies in the interval:
In how many ways we can select a group of 2 males and 2 females from the family of 5 males and 3 females?
In what ratio the segment joining \( (-1, -12) \) and \( (3, 4) \) divided by x-axis?
If \( \vec{A}, \vec{B} \) are unit vectors. If \( \vec{C} = \vec{A} + 2\vec{B} \) and \( \vec{D} = 5\vec{A} - 4\vec{B} \) are perpendicular, then angle between \( \vec{A} \) and \( \vec{B} \) is:
The coefficient of variation of the two frequency distributions is 60% and 40% respectively. Both series have the same mean = 15. What is their standard deviation?