List of practice Questions

In the detection of II group acid radical, the salt containing chloride is treated with concentrated sulphuric acid, the colourless gas is liberated. The name of the gas is

Given below are two statements :
Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number.
In the light of the above statements, choose the most appropriate answer from the options given below :

A cylindrical tube, with its base as shown in the figure, is filled with water It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ} P_{1}$ and $P_{2}$ are pressures at points $1$ and $2$, respectively located at the base of the tube. Let $\beta=\left(P_{1}-P_{2}\right) /(\rho g d)$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is(are) correct?

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed $v_0$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

A function $ f $ is defined on $[-3, 3]$ as $ f(x) = \begin{cases} \min\{|x|, 2-x^2\}, & -2 \le x \le 2 \\ |x|, & 2 < |x| \le 3 \end{cases} $, where $ [x] $ denotes the greatest integer $ \le x $. The number of points, where $ f $ is not differentiable in $(-3, 3)$ is ________ .

A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, -1, 1), then the projection of $\vec{OP}$ on this plane is of length :

The following system of linear equations
2x + 3y + 2z = 9
3x + 2y + 2z = 9
x - y + 4z = 8

If for the matrix, A = $ A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix} $, and $ A A^T = I_2 $, then the value of $ \alpha^4 + \beta^4 $ is :

The major product of the following reaction is :
(Image shows Benzene reacting with 2-nitropropene in presence of H$_2$SO$_4$)

The truth table for the following logic circuit is:

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30° in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be: