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If vectors $\overrightarrow{A}=\cos wt\hat{i}+\sin wt\hat{j}$ and $\overrightarrow{B}=\cos wt/2\hat{i}+\sin wt/2\hat{j}$ are functions of time , then the value of $t$ at which they are orthogonal to each other is

Two masses M and m are connected by a light string going over a pulley of radius r. The pulley is free to rotate about its axis which is kept horizontal. The moment of inertia of the pulley about the axis is I. The system is released from rest. Find the angular momentum of the system when the mass M has descended through a height h. The string does not slip over the pulley.

The lowest frequency of light that will cause the emission of photoelectrons from the surface of a metal (for which work function is 1.65 eV) will be

Two blocks A and B of equal mass m=1 kg are lying on a smooth horizontal surface as shown below A spring of force constant k = 200 N/m is fixed at one end of block 'A'. Block 'B' collides with 'A' with velocity V₀ = 2 m/s. The maximum compression of the spring is

A boy can throw a stone up to a maximum height of 10m .The maximum horizontal distance that the boy can throw the same stone up to will be

Ans:20

But I calculated it using R/H=4/tan(45)

Since maximum range I took tan45...The answer came out to be 40m ...COuld you please tell me what is wrong with the method I used...

A particle is moving along positive $x$-axis and at $t=0$, the particle is at $x=0$. The acceleration of the particle is a function of time. The acceleration at any time $t$ is given by $a=2(1–[t\left]\right)$ where $\left[t\right]$ is the greatest integer function . Assuming that the particle is at rest initially, the average speed of the particle for the interval $t=0s\text{to}t=4s$ is

What is the black body radiation. I didn't understand it clearly

The area of the region bounded by the curve $y=x^2$ and $y={\text{sec}}^{-1}[-{\text{sin}}^{2}x]$, (where [.] denotes the greatest integer function), is

What do you mean by magnitude

If motion of a particle is represented by $s=e^t+4t^3-\cos t$, then the acceleration of the particle at any time $t$ is
[Hint: Acceleration of the particle is $\frac{d^{2}s}{d{t}^2}$]

What is parallelogram law and triangular law and cross or dot product

The unit of self inductance of a coil is

Is there friction present outside the earth?That is in space?

The wave number of the first line on the Balmer series of hydrogen is 15200$c{m}^{-1}$. What would be the wave number of the first line in the Lyman series of the $B{e}^{3+}$ ion?

A man starts from the point $P(4,-3)$ and reaches the point $Q(1,0)$ touching $y-$axis at $R$ such that $PR+RQ$ is minimum, then the point $R$ is:

When a system is taken through the process abc shown in figure, 80 J of heat is absorbed by the system and 30 J of work is done by it. If the system does 10 J of work during the process adc, how much heat flows into it during the process ?

In the arrangement shown in figure, slits $S_1$ and $S_4$ are having a variable separation Z. Point O on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.
When $Z=\frac{\lambda D}{2d^{\prime }}$ the intensity measured at O is $I_0$. The intensity at O when $Z=\frac{2\lambda D}{d}$ is

The magnetic field due to current element depends upon which of the following factors:

A bird fly east at $10\text{m/s}$ for $100\text{m}$. It then turns around flies at $20\text{m/s}$ for $15\text{s}$. Neglect time taken for turning, find its magnitude of average velocity.

When a dolphin glides through air, it experiences an external pressure of $0.75\text{m}$ of mercury. The absolute pressure on dolphin when it is $4\text{m}$ below the free surface of the water is
$[\text{Take}g=10{\text{m/s}}^2]$

When a body is projected with velocity $\overrightarrow{v},$ horizontally from a height $h$.

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) The speed of body at any time}t\text{is}& \text{(p)}\sqrt{\frac{2gh}{u^2}}\\ \text{(b) It will strike the ground after time}t\text{is equal to}& \text{(q)}\sqrt{\frac{2h}{g}}\\ \text{(c) The path followed by the body is expressed as}y\text{equal to}& \text{(r)}\frac{1}{2}g\frac{x^2}{u^2}\\ \text{(d) The value of}\tan \theta \text{, where}\theta \text{is the angle made by velocity striking the ground with horizontal is equal to}& \text{(s)}\sqrt{v^2+g^2{t}^2}\end{array}$

A tuning fork of frequency $300\text{Hz}$ is vibrated on arm-$1$, then the air column vibrates in fundamental mode. If the same tuning fork is vibrated on arm-$2$, the air column vibrates in first overtone. Both the arms are of length $1\text{m}$. If velocity of sound is $300\text{m/s},g=10{\text{m/s}}^2$ and density of water is ${10}^3{\text{kg/m}}^3$ then the density of the unknown liquid is
$($Neglect surface tension and end corrections$)$

A particle is executing linear SHM of amplitude $A$ and time period $T$. If $v$ refers to the average speed of the particle during any time interval of $\frac{T}{3}$, then the maximum possible value of $v$ in terms of $A$ is

Two non - zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. Find angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^3$/sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2$\frac{A}{3}$. The velocity of liquid at Q is $V_Q$ and Velocity at P is $V_P$ (The cross-sectional area of the main is A)

A block of ice with mass m falls into a lake. After impact, a mass of ice melts. Both the block of ice and the lake have a temperature of 0⁰C. If L represents the latent heat of fusion, the distance the ice falls before striking the surface is

A block of mass m is suspended from a spring. Its frequency of oscillation is f. The spring is cut into two identical halves and the same block is suspended from one of the two pieces of the spring such that it just touches the other spring below in its equilibrium position. The frequency of small oscillations of the mass will be

A particle performing SHM with amplitude $A$ and time period $T$ starts from mean position towards the positive extreme point as shown in the figure. Find the time taken by the particle (in seconds) to reach $x=\frac{A}{2}.$

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant k. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. Then the angular frequency of oscillation of $m_2$ is

Two perfectly elastic particles P and Q of equal mass travelling along the line joining them with velocities 15 m/sec and 10 m/sec. After collision, their velocities respectively (in m/sec) will be

A system goes from A to B via two process I and II. If $\Delta V_1$ and $\Delta V_2$ are changes in internal emerges in the process I and II respectively, then

A body takes time ‘t’ to reach the bottom of an inclined plane of angle $\theta$ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is:

A current of I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius r. The magnetic field at any point outside the cylinder at a distance x form the axis is

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

Which of the points marked in the figure below are in phase?

(a) What are the features of a good table? Any 3 point.

(b) Explain any 3 merits of direct personal investigation.

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B = $B_0{e}^{-t}$ is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

A point source emitting light uniformly in directions is placed 60 cm above-top. The illuminance at a point on the table-top , directly below the source, is 15 lux .Find the illuminance at a point on the table-top 80 cm away from the first point.

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross – section and Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period given by

A train moves towards a stationary observer with a speed of $34\text{m/s}$. The train sounds a whistle and its frequency registered by the observer is $f_1$ . If the train speed is reduced to $17\text{m/s}$, the frequency registered is $f_2$. If the speed of sound is $340\text{m/s}$, then the ratio $\frac{f_1}{f_2}$ is

A $1\text{m}$ long horizontal rope, having a mass of $40\text{g}$, is fixed at one end and is tied to a light string at the other end. The tension in the rope is $400\text{N}$. What will be the wavelengths (in $\text{metres}$) in the first and second overtone ?

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$ . The force exerted by the liquid at the other end is

A bucket full of hot water cools from ${75}^{\circ }C$ to ${70}^{\circ }C$

in time $T_1$ , from ${70}^{\circ }C$ to ${65}^{\circ }C$ in time $T_2$ and

from ${65}^{\circ }C$ to ${60}^{\circ }C$ in time $T_3$, then

Two parallel glass plates are dipped partly in the liquid of density 'd' keeping them vertical. If the distance between the plates is 'x', surface tension for liquids is T and angle of contact is θ , then rise of liquid between the plates due to capillary will be