List of top Mathematics Questions

Let f(x) = [2x2 + 1] and \(g(x)=\left\{\begin{matrix}  2x-3,\,x<0&\\2x+3,  x≥0 &\end{matrix}\right.\)where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.

Let z = a + ib, b≠ 0 be complex numbers satisfying
\(\begin{array}{l} z^2=\overline{z}\cdot 2^{1-\left|z\right|}.\end{array}\)
Then the least value of n∈ N, such that zn= (z + 1)n, is equal to _____.

If α, β are the roots of the equation
\(x^2-(5+3^{\sqrt{log_35}}-5^{\sqrt{log_53}})+3(3^{(log_35)^{\frac{1}{3}}}-5^{(log_53)^{\frac{2}{3}}}-1) = 0\)
then the equation, whose roots are α + 1/β and β + 1/α , is

If \( A = \{3, 5, 7\} \) and \( B = \{1, 2, 3, 5\} \), then \( A \times B \cap B \times A \) is equal to:
Let \(x(t)=2\sqrt2costsin\sqrt2t \) and \(y(t)=2\sqrt2sintsin\sqrt2t\) ,\(t ∈(0,\frac{π}{2})\)
 Then \(\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}\) at \(t=\frac{π}{4}\) is equal to
If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), and \( A_n = \alpha^n + \beta^n \), then Arithmetic mean of \( A_{n-1} \) and \( A_n \) is

If \( x^m y^n = (x+y)^{m+n} \), then \( \frac{dy}{dx} \) is
 

Let a, b, c be distinct non-negative numbers. If the vectors \( a\hat{i} + a\hat{j} + c\hat{k} \), \( \hat{i} + \hat{k} \) and \( c\hat{i} + c\hat{j} + b\hat{k} \) lie in a plane, then c is
The value of \( 3^{3-\log_3 5} \) is
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
Suppose that the temperature at a point (x, y) on a metal plate is \( T(x, y) = 4x^2 - 4xy + y^2 \). An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

If \( (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c}) \), then
 

If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is
If the foci of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} \) are coincide, then the value of \( b^2 \) is
Let a be the distance between the lines \( -2x + y = 2 \) and \( 2x - y = 2 \), and b be the distance between the lines \( 4x - 3y = 5 \) and \( 6y - 8x = 1 \), then
Coordinate of focus of the parabola \(4y^2 + 12x - 20y + 67 = 0\) is

The function \( f(x) = \begin{cases} (1+2x)^{1/x}, & x \neq 0 \\ e^2, & x=0 \end{cases} \) is
 

The value of \( \cot(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}) \) is
A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is

If \( D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2+x & 1 \\ 1 & 1 & 2+y \end{vmatrix} \) for \( x \neq 0, y \neq 0 \), then D is

If \( \vec{a} = \lambda\hat{i} + \hat{j} - 2\hat{k} \), \( \vec{b} = \hat{i} + \lambda\hat{j} - 2\hat{k} \), \( \vec{c} = \hat{i} + \hat{j} + \hat{k} \) and \( [\vec{a}\vec{b}\vec{c}] = 7 \), then the values of \( \lambda \) are
The correct expression for \( \cos^{-1}(-x) \) is
If \( \cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \phi \), then \( 9x^2 - 12xy\cos\phi + 4y^2 \) is equal to