List of practice Questions

The time required for 100% completion of a zero order reaction is
[$R$]$_0$ = Initial concentration of reactant, R

The conjugate base of phosphorus acid is $ x $. The conjugate base of oleum is $ y $. What are $ x $ and $ y $, respectively?

If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}

Evaluate \[ \sum_{k=0}^{12} \sin\left( (k+1) \frac{\pi}{6} + \frac{\pi}{4} \right) \sin \left( \frac{k \pi}{6} + \frac{\pi}{4} \right) \]

If the displacement \( y \) (in cm) of a particle executing simple harmonic motion is given by the equation: \[ y = 5 \sin(3 \pi t) + 5 \sqrt{3} \cos(3 \pi t) \] then the amplitude of the particle is:

If the function \(y = \sin(x)(1 - \cos x)\) is defined in the interval \([-\pi, \pi]\), then y is strictly increasing in the interval

The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is

A body of mass $1~\text{kg$ is attached to the lower end of a vertically suspended spring of force constant $600~\text{N/m}$. If another body of mass $0.5~\text{kg}$ moving vertically upward hits the suspended body with a velocity $3~\text{m/s}$ and is embedded in it, then the frequency of the oscillation is}