List of practice Questions

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

1 mole of HI is heated in a closed container of capacity of 2 L. At equilibrium half a mole of HI is dissociated. The equilibrium constant of the reaction is

Beriberi is the disease caused by the deficiency of.............

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

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?

The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is

The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are

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

The value of \( 3^{3-\log_3 5} \) is

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

In the following figure, find the total number of squares.