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Three vectors $\overrightarrow{P},\overrightarrow{Q}$ and $\overrightarrow{R}$ are shown in the figure. Let $S$ be any point on the vector $\overrightarrow{R}$. The distance between the points $P$ and $S$ is $b|\overrightarrow{R}|$. The general relation among vectors $\overrightarrow{P},\overrightarrow{Q}$ and $\overrightarrow{S}$ is

The position vector $\overrightarrow{r}=5.00t\hat{i}+(et+f{t}^2)\hat{j}$ locates a particle as a function of time t. Vector $\overrightarrow{r}$ is in meters, t is in seconds, and factors e and f are constants. Below Diagram gives the angle $\theta$ of the particle's direction of travel as a function of t($\theta$) is measured from the positive x direction). What are 'e' and 'f', including units?

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Force F is applied perpendicularly to the end of a uniform rod (M, L) placed on smooth horizontal surface as shown. Magnitude of acceleration of end A and B just after the force is applied are a_A and a_B respectively, then



चिकने क्षैतिज पृष्ठ पर रखी एक समरूप छड़ (M, L) के सिरे के लम्बवत् दर्शाए अनुसार बल F आरोपित किया जाता है। बल आरोपित करने के ठीक बाद सिरे A तथा B के त्वरण के परिमाण क्रमशः a_A तथा a_B हैं, तब

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its centre of mass and perpendicular to its plane will be

The ratio of de-Broglie wavelength of a $\alpha$ -particle to that of a proton when they are subjected to the same magnetic field and their radii in the magnetic field are equal (assume the field induction vector $\overrightarrow{B}$ is perpendicular to the velocity vectors of the $\alpha$ -particle and the proton) is

Two identical circular loops are arranged such that their centres are at the origin and the loops are in $xy$ and $yz$ planes. The loops carry currents in directions shown in the diagram. The net magnetic dipole moment of this combination is

A slit of width $a$ is illuminated by white light. The first minimum for red light of wavelength $(\lambda =6500\mathring{\text{A}})$ will fall at $={30}^{\circ }.$ when $a$ is

The force $F$ acting on a particle of mass ${}^{\prime }{m}^{\prime }$ is indicated by the force - time graph shown below. The change in momentum of the particle over the time interval from zero to $8\text{s}$ is

A capacitor is connected to a $10\text{V}$ battery. When the medium is air, the charge on plates is $40\mu \text{C}$ . When the medium between plates is oil, the charge on plates becomes $100\mu \text{C}$ . The dielectric constant of oil is

For the given charge configuration consisting of charges $+q_1$ and $+q_2$ such that $q_1>q_2$, the relation between flux through two imaginary spheres $S_1$ and $S_2$ as shown in the figure will be

The velocity of the centre of mass of a system changes form $\overrightarrow{V_1}=8\hat{i}\text{m/s}$ to $\overrightarrow{V_2}=6\hat{j}\text{m/s}$ during time interval $△t=3\text{s}.$ If the mass of the system is $m=6\text{kg}$, the constant force acting on the system is

Two concentric spherical conducting shells of radii R and 2R carry charges Q and 2Q respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is$k=\frac{1}{4\pi {ϵ}_0}$

A projectile thrown with velocity $v$ making angle ${30}^{\circ }$ with vertical gains maximum height $100m$ in the time for which the projectile remains in air, the time of flight of the projectile in seconds is (take $g=10{m/s}^2$)

Two trains $\text{A}$ and $\text{B}$ have lengths $800\text{m}$ and $1000\text{m}$ respectively and are moving with the velocity of $25\text{m/s}$ and $15\text{m/s}$ respectively in the same direction. At time $t=0$ engine of train $\text{A}$ is just behind train $\text{B}$. Find time when train $\text{A}$ completely overtakes train $\text{B}$?

Axis of a solid cylinder of infinite length and radius $R$ lies along $y$-axis. It carries a uniformly distributed current $‘i^{\prime }$ along $+y$ direction. Magnetic field at a point $(\frac{R}{2},y,\frac{R}{2})$ is

Two copper circular discs are of the same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is

Suppose there are two coils of length 1m with 100 and 200 turns and area of cross section of 5 x 10^-3 m². Find the mutual inductance.

A man of mass 70 kg stands on a weighing scale in a lift which is moving
a) upwards with a uniform speed of $10m{s}^{-1}$,
b) downwards with a uniform acceleration of $5m{s}^{-1}$,
c) upwards with a uniform acceleration of $5m{s}^{-1}$.
What would be the readings on the scale in each case?
d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

A transformer is used to light a $100W$ and $110V$ lamp from a $220V$ main. If the main current is $0.5A,$ then efficiency of the transformer is approximately

Two identical short bar magnets of magnetic moment $M$ and $3M$ are placed at ${120}^{\circ }$ as shown in the figure. Find the magnetic induction at point $P$ on the angle bisector is

A body is projected at an angle${53}^0$ with velocity of 50 $m{s}^{-1}$. Calculate the time when speed becomes 4/5 of initial velocity.

How to draw the circuit diagram of a particular problem ?

When light rays are incident on a prism at an angle of ${45}^{\circ }$, the minimum deviation is obtained. If refractive index of the material of prism is $\sqrt{2}$ then the angle of prism will be ​

The temperature of a furnace is monitored at a distance of 50m away. The temperature transmitter has a range of $0-{500}^{o}C$ and provides 4-20 mA current output. The measured tempreature and the output current have a straight line relationship with positive slope. The tempertature is determined from the voltage meassured across a resistance of $500\Omega$ in the current loop. If the voltage meassured across the resistance is 4 V. The temperature of the furnace is

An object is at $2\text{m}$ at $t=0\text{sec}$. Its velocity is given by $v=2t+7$, its position at $t=5\text{sec}$ is

Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_1$ and $T_2$, rod $1$ takes twice the time as the other. Find the ratio of their lengths.

Which of the following graph is correct?



${\Lambda }_m$ - Molar conductivity

$C$ - concentration of electrolyte

A straight line source of sound of length $10\text{m}$ emits pulse that travels radially outward from the source. A detector is located at a perpendicular distance of $7\text{m}$ from the source. The total power emitted by the source in the form of sound wave is $2.2\times {10}^4\text{W}$. If the surface area of the acoustic detector is $1.2{\text{cm}}^2$, then the power (in $\text{mW}$) intercepted by the detector is
(Assume waves reaches surface of detector perpendicularly and take $\pi =\frac{22}{7}$)

Consider a parallel-plate capacitor of capacitance $10\mu F$ with air filled in the gap between the plates. Now, one half of the space between the plates is filled with a dielectric of dielectric constant 4 as shown in the figure. The capacitance of the capacitor changes to

A porter lifts a suitcase weighing 20 kg from the platform and puts it on his head 2.0 m above the platform. Calculate the work done by the porter on the suitcase.

Which of the following is the evidence to show that there must be a force acting on earth and directed towards the sun

In a Young's double slit experiment, the slits $S_1$ and $S_2$ are illuminated by a parallel beam of light of wavelength $4000\dot{A}$ from the medium of refractive index ${\mu }_1=1.2$. A thin film of thickness $1.2\mu \text{m}$ and refractive index $\mu =1.5$ is placed in front of $S_1$ perpendicular to the path of light. The refractive index of the medium between the plane of slits and screen is ${\mu }_2=1.4$. If the light coming from $S_1$ and $S_2$ have equal intensity $I$, then the intensity at the geometrical centre of screen $O$ is:

The amount of charge flowing through branches $\text{A}$, $\text{B}$ and $\text{C}$ when switch $S_n$ is closed as shown in figure are repectively

(Assume that the charge delivered by capacitor is negative)



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