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1. 22

The moment of force $\hat{i}+\hat{j}+\hat{k}$ acting through the point $A\left(\overrightarrow{a}\right)=-2\hat{i}+3\hat{j}+\hat{k}$ about the point $B\left(\overrightarrow{b}\right)=\hat{i}+2\hat{j}+3\hat{k}$ is

A plot of potential energy function $U\left(x\right)=k{x}^2$, where $x$ is the displacement and $k=$ constant is shown below. The correct conservative force function $F\left(x\right)$ is

A parallel plate capacitor made of circular plates each of radius $R=6.0\text{cm}$ has a capacitance $C=100\text{pF}$. The capacitor is connected to a $230\text{V}$ AC supply with an angular frequency of $300\text{rad/s}$. The displacement current is -

Pair the following with the next shape in the pattern.

Consider the circuit shown in the figure below:



The value of voltage gain $A_V=\frac{V_o}{V_i}$ is equal to $(\text{Assume}{V}_{Th}=25V)$

A person of mass $10\text{kg}$ jumps from a stationary helicopter with the parachute open. As he falls through $50\text{m}$ height, the gains a speed of $20\text{m/s}$. The work done by the viscous air drag is

The light from the sun is found to have a maximum intensity near the wavelength of $470\text{nm}$. Assuming that the surface of the sun emits as a blackbody, calculate the temperature of the surface of the sun. Given: $b\left(\text{Wein's constant}\right)=0.288\text{cm}K$

The fixed end moment of a uniform beam of span l and fixed at the ends, subjected to central point load P is

A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. (a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? (b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produced by the whistle equal to $\frac{1}{20}$ or 0.05 Hz?

1. 120

If a workpiece is moved by 50 mm in 10 s by a piston of diameter 100 mm, the hydraulic liquid flow rate is nearly

A convex lens of focal length $10\text{cm}$ is placed $30\text{cm}$ in front of a second convex lens also of the same focal length. A plane mirror is placed after the two lenses. Where should a point object be placed in front of the first lens so that it images on to itself ?

A plastic disc of diameter $22cm$ and thickness $\frac{3}{4}cm$ has a mass of $125g$. For the disc to float on a liquid, which of the following cannot be the value of density of the liquid?

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

The equation for the first law of thermodynamics is given as;

$\Delta U=q+W$

Where,

A uniform rod $AB$ is hinged at end $A$ in horizontal position as shown in figure. The other end is connected to a block through a massless pulley- string arrangement as shown in figure. The acceleration of block just after release from the shown position is

Five capacitors are connected as shown in the figure. Initially, all capacitors are uncharged and $S$ is open. When $S$ is closed, then the potential difference between points $\text{M}$ and $\text{N}$ is :

[assume steady state to be achieved after $S$ closes]

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between T_A and T_B?

The temperature of gas is increased from $200\text{K}$ to $600\text{K}$ at a constant pressure. If initially the volume of gas is $10\text{cc}$, then the final volume of the gas will be (in $\text{cc}$)

A ball of mass $m=2\text{kg}$ is projected at an angle $\theta ={45}^{\circ }$ with initial velocity of $u=10\text{m/s}$ as shown in figure. Find the torque acting on the particle due to gravity about origin at it's maximum height.
(Take $g=10m/s^2$)

The
half-life for radioactive decay of ¹⁴C
is 5730 years. An archaeological artifact containing wood had only
80% of the ¹⁴C
found in a living tree. Estimate the age of the sample.

The equivalent capacitance of the combination shown in the figure is

Consider the situation shown in figure. The system is released from rest and the block of mass 1.0 kg is found to have a speed 0.3 $\frac{m}{s}$ after it has descended through a distance of 1m. Find the coefficient of kinetic friction between the block and the table.

The time period of small oscillation of block along y-axis is given by ________. (Neglect gravity)

1. 0.5

Find the potential difference between the points A and B and between the points B and C of figure (32-E33) in steady state.

Figure 32-E33

A thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma \left(r\right)=k{r}^2$ where $r$ is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is