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For the given figure List - I gives acceleration of blocks of masses $m_1,m_2,m_3\&m_4$ and List - II gives their magnitudes. Here $m_1=m_2=2m$ and $m_3=m_4=m$



$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{(I)}{a}_1& \text{(P)}2g\\ \text{(II)}{a}_2& \text{(Q)}g\\ \text{(III)}{a}_3& \text{(R)}\frac{g}{2}\\ \text{(IV)}{a}_4& \text{(S)}\frac{g}{4}\\ & \text{(T)}0\\ & \text{(U)}\text{None}\end{array}$

Just after cutting string connecting $m_1$ and $m_2$ correct match for accelerations of blocks is

The length of the compound microscope is $20\text{cm}$. The focal length of the eyepiece is $5\text{cm}$. If the magnifying power for the relaxed eye is $25$, then find the object distance from the objective lens.

Calculate the rms speed of nitrogen at STP (pressure = 1 atm and temperature = $0^{\circ }C$). The density of nitrogen in these conditions is $1.25kg{m}^{-3}$.

The moment of inertia of a solid cylinder of radius $a$, mass $M$ and height $h$ about an axis parallel to the axis of the cylinder and at distance $b$ from its centre is :

[Assume $b>a$]

A person travels $100\text{km}$ in the North direction and then turns right and travels $100\text{km}$. Consider the starting point as origin, North direction as positive y direction and East direction as positive x direction. The final position of the person is

1. 100

If $\underset{x\to 1}{lim}\left(\sec \frac{\pi }{2x}\right)\cdot \ln x=L,$ then the value of $\left[L\right]$ is

(where $[.]$ represents the greatest integer function)

A charge particle (q, m) enters normally inside an external uniform magnetic field of magnitude B which exists only in region (II) as shown. Find minimum value of D so that charge particle comes back in the region (I).



एक आवेश कण (q, m) परिमाण B वाले किसी बाह्य एकसमान चुम्बकीय क्षेत्र जो दर्शाए अनुसार केवल क्षेत्र (II) में उपस्थित है, के अन्दर अभिलम्बवत् प्रवेश करता है। D का न्यूनतम मान ज्ञात कीजिए ताकि आवेश कण क्षेत्र (I) में वापस लौटे?

A player stops a football weighing $0.5\text{kg}$ which comes flying towards him with a velocity of $10\text{m/s}$. If the impact lasts for $1/50\text{th}$ sec. and the ball bounces back with a velocity of $15\text{m/s}$, then the average force involved is

If $a=(3t^2+2t+1)m/s^2$ is the expression according to which the acceleration of a particle moving along a straight line varies, then the expression for instantaneous velocity at any time $t$ will be (if the particle was initially at rest)

The derivative of $\ln (1+x^2)$ with respect to ${\tan }^{-1}x$ is



[1 mark]

A radio station has two channels. One is AM at 1020 kHz and the other FM at 89.5 MHz. For good results you will use

A particle travels along the X-axis. Its velocity time graph is shown above.

In which direction was the particle headed at t = 16 sec?

Two concentric shells of radii 1 cm and 2 cm are charged to 3V and 5V, respectively. The charge on the inner shell is

If the momentum of a body is increased by 100 %, then the percentage increase in the kinetic energy is

An isolated and charged spherical soap bubble has a radius $r$ and the pressure outside is atmospheric. If $T$ is the surface tension of soap solution, then charge on drop is

The ratio of minimum to maximum wavelength of radiation emitted by transition of an electron, to ground state of Bohr's hydrogen atom is,

A skater is moving on ice at a velocity of $15\text{m/s}$ in a circle of radius $22.5\text{m}$. What is the angle the person makes with the ground?

Consider a situation as shown in figure. Find the minimum value of $m$ so that the blocks do not move.

In equation, $r=m^2\sin \left(\pi t\right)$, where $t$ represents time. If the unit of $m$ is $\text{N}$, then the unit of $r$ is

The area bounded by the y-axis, y = cos x and y = sin x when 0 $\le x\le \frac{\pi }{2}$ is

1. 286.56

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes $\frac{5T}{3}$. Then the ratio of $\frac{m}{M}$ is

Consider a square loop of side $4\text{cm}$ is positioned in a uniform magnetic field of magnitude $0.5\text{T}$ so that the plane of the loop makes an angle of ${30}^{\circ }$ with the magnetic field. Calculate amount of flux passing through the square loop.