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Calculate the most probable speed of $O_2$ at STP

Two balls are projected upward simultaneously with speeds $40\text{m/s}$ and $60\text{m/s}$. Relative position $\left(x\right)$ of second ball w.r.t. first ball at time $t=5\text{s}$ is :

[Neglect air resistance]

A double-slit arrangement produces interference fringes for sodium light of, wavelength $589\text{nm}$. For what wavelength, would the fringe width, be $10$% greater?

For the velocity-time graph shown in figure, in a time interval from $t=0$ to $t=6\text{s}$, match the following



$\begin{array}{cc}\text{Table-1}& \text{Table-2}\\ \text{(A) Change in velocity}& \text{(P)}-\frac{5}{3}\text{SI unit}\\ \text{(B) Average acceleration}& \text{(Q)}-20\text{SI unit}\\ \text{(C) Total displacement}& \text{(R)}-10\text{SI unit}\\ \text{(D) Acceleration at}t=3\text{s}& \text{(S)}-5\text{SI unit}\end{array}$

A force $\overrightarrow{F}=2\hat{i}-\lambda \hat{j}+5\hat{k}$ is applied at the point $A(1,2,5)$. If its moment about the point $(-1,-2,3)$ is $16\hat{i}-6\hat{j}+2\lambda \hat{k},$ then $\lambda$ is equal to

A boat moves relative to water with a velocity $u$ and river is flowing with $2u$. At what angle with the stream should the boat move to have minimum drift ?

In the figure shown, string $AB$ and $BC$ have masses $m$ and $2m$ respectively. Both are of the same length $l$. Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room. A small jerk wave pulse is given at the end ${}^{\prime }{C}^{\prime }$. It goes up to upper end ${}^{\prime }{A}^{\prime }$ in time ${}^{\prime }{t}^{\prime }$. If $m=2\text{kg},l=\frac{9610}{1681}\text{m},g=10{\text{m/s}}^2,\sqrt{2}=1.4,\sqrt{3}=1.7$, then the value of ${}^{\prime }{t}^{\prime }$ is :-

A charge Q is placed at a distance a/2 above the centre of a horizontal, square of edge , a as shown in figure(30-E1). Find the flux of the electric field through the square surface.

If the third step of an input is “65 daily 12 tie 42 23 foreign urgent”, which of the following will definitely be the input?

A particle's motion is given by $s=a(t+b(e^{(-\frac{t}{b})}-1))$, where ($s$ is in metre, $a$ and $b$ are constants and $t$ is in sec). What will be the instantaneous speed of the particle at $t=\infty$

The slope of which line are we calculating?

A spring block system is compressed $x\text{m}$ from the mean position and released. Find out the total work done by the spring force when it reaches the other extreme point (fully stretched). Neglect friction.

A projectile is thrown from the base of an incline of ${30}^{\circ }$ as shown in the figure. It is thrown at an angle of ${60}^{\circ }$ from the horizontal direction at a speed of $10\text{m/s}$. The total time of flight is: $(g=10{\text{m/s}}^2)$

The specific heat of one mole of an ideal `gas at constant volume is $21.2J/mole{/}^{\circ }C$. If the temperature is increased by $1^{\circ }C$ keeping the volume constant, the change in its internal energy will be

Question 26

It is difficult to cut cloth using a pair of scissors with blunt blades. Explain.

The velocity of sound in air is $333\text{m/s}$. In order to produce the second overtone of frequency $999\text{Hz}$ in it, the length of the open organ pipe will be :

A house is built on the top of a hill with ${45}^{\circ }$ slope. Due to the sliding of material and sand from top to the bottom of hill, the slope angle has been reduced. If the coefficient of static friction between sand particles is $0.75$. what is the final angle attained by hill? $({\tan }^{-1}0.75={37}^{\circ })$

The following graph shows how the inverse of magnification $\frac{1}{m}$ produced by a thin convex lens varies with distance u. What is the focal length of lens used?

A straight metal wire of length $L$, cross-sectional area $A$ and resistivity $\rho$ is made into a square frame. A uniform magnetic field $B$ is perpendicular to the plane of the frame and is changing at a constant rate $\frac{dB}{dt}$. Find the current induced in the frame.

For the given system of charges, where should a third charge $+q$ be placed from negative charge, so that third charge experiences no net force?

Figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increase with time. $I_1$ and $I_2$ are the currents in the segments ab and cd. Then,

Out of the numbers: 6.26, 5.8, 0.00267, 0.03, the one with the least significant figures is:

Two blocks $\text{A}$ and $\text{B}$ of equal masses are released from an inclined plane of inclination ${45}^{\circ }$ at $t=0$. Both the blocks are initially at rest. The coefficient of kinetic friction between the block $\text{A}$ and the inclined plane is $0.2$ while it is $0.3$ for block $\text{B}$. Initially the block $\text{A}$ is $\sqrt{2}\text{m}$ behind the block $\text{B}$. When will their front faces come in a line?

A solenoid of $1000$ turns per metre has a core with relative permeability of $500$. Insulated windings of the solenoid carry an electric current of $5\text{A}$. The magnetic flux density produced by the solenoid is -



$($Permeability of free space $=4\pi \times {10}^{-7}\text{H/m})$

An asteroid is going to hit the Earth. To calculate its distance it is observed from 2 diametrically opposite points A, B on Earth. The angle subtended at the asteroid by these two directions of observations is $2^o$. Given the diameter of Earth to be about $1.276\times {10}^7$ m. compute the distance of the asteroid.

Two waves in the same medium are represented by $y-t$ curves in the figure. Find the ratio of their average intensities.

A $2\mu \text{F}$ capacitor is charged to a potential $10\text{V}.$ Another $4\mu \text{F}$ capacitor is charged to a potential $20\text{V}$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. Find heat developed in the circuit.

A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

Two stones each of mass 5kg fall on a wheel from a height of 10m. The wheel stirs 2kg water. The rise in temperature of water would be

Find the elastic potential energy stored in each spring shown in figure, when the block is in equilibrium. Also find the time period of vertical oscillation of the block.