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A boat which has a speed $5\text{km/h}$ in still water crosses a river of width $100\text{m}$ along the shortest possible path in $1.5\text{min}$. The velocity of river water in $\text{km/h}$ is

Question 3

What is the far point and near point of the human eye with normal vision?

A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is

A lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. Now Focal length of lens and intensity of image will be respectively

Electromagnetic wave of intensity $1400{\text{W/m}}^2$ falls on metal surface on area $1.5{\text{m}}^2$ is completely absorbed by it. Find out the force exerted by the beam.

An object is put at a distance 25 cm from the optical centre of a convex lens. If it's real image is formed at a distance 30 cm from the lens to its focal length is about

(1) 10 cm

(2) 14 cm

(3) 12 cm

(4) 20 cm

A car of mass $1000\text{kg}$ moves in a circular path with a constant speed of $12\text{m/s}$. It is turned by ${180}^{\circ }$, while travelling a distance of $628\text{m}$ on the road. The centripetal force acting on the car is

If $\overrightarrow{x}+\overrightarrow{c}\times \overrightarrow{y}=\overrightarrow{a}$ and $\overrightarrow{y}+\overrightarrow{c}\times \overrightarrow{x}=\overrightarrow{b}$, where $\overrightarrow{c}$ is a non - zero vector, then which of the following is correct

If a photon of intensity $I$ falls on a surface at an angle ${60}^{\circ }$ making with it having absorption coefficient $0.4$, then radiation pressure exerted on the surface is-

The space between two large horizontal metal plates 6cm apart is filled with a liquid of viscosity $0.8Ns/m^2$ . A thin planck of surface area $1m^2$ is moved parallel to the length of the plates such that the planck is at a distance of 2cm from one plate and 4cm from the other.The force F required to drag it with a constant speed of is $1m{s}^{-}1$ is

A solid sphere of mass M rolls without slipping and presses a spring of spring constant K as shown in the figure. Then the compression in the spring will be

In the figure shown, a ring A is initially rolling without sliding with a velocity v on the horizontal surface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity what will be the maximum height reached by A on B.

A block of mass $0.50\text{kg}$ is moving with a speed of $2.00{\text{ms}}^{-1}$ on a smooth surface. it strikes another mass of $1.00\text{kg}$ and then they move together as a single body. The energy loss during the collision is

A student wants to calculate the refractive index of NaCl crystal with accurate measurements. He gets different values of refractive index for different directions. Reason for this is

The graph shows three waves travelling with same velocity, that are separately sent along a string, which is under a certain tension along $x-$axis. If ${\omega }_1,{\omega }_2$ and ${\omega }_3$ are their angular frequencies respectively, then,

A car, moving with a speed of $50km/hr$, can be stopped by brakes after at least $6m$. If the same car is moving at a speed of $100km/hr$, the minimum stopping distance is

A bar is subjected to equal and opposite forces as shown in the figure. PQRS is a plane making angle $\theta$ with the cross-section of the bar. If the area of cross-section be ‘A’, then when is the shearing stress maximum

If area $\left(A\right)$, time $\left(T\right)$ and momentum $\left(P\right)$ are assumed as fundamental quantities, then dimensional formula for energy will be

A pulling force of $100\text{N}$ is acting at an angle of ${30}^0$with the horizontal on a body of mass $50\text{kg}$ placed on a rough horizontal surface. Will the same force cause the body to move if it is a pushing force for the body? If not, what should be the value of the force (acting at the same angle) to cause the body to just move? Take $g=10{\text{m/s}}^2$.

In the shown figure, block moves downwards with velocity $v_1$, the wedge moves rightwards with velocity $v_2$. The correct relation between $v_1$ and $v_2$ is

A galvanometer whose resistance is $50\Omega$ has $25$ divisions in it . When a current 0f $4\times {10}^{-4}\text{A}$ passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range $5\text{V}$, it should be connected to a resistance of

A ground to ground projectile is at point A at t $=\frac{T}{3}$, is at point B at $t=\frac{5T}{6}$ and reaches the ground at $t=T$. The difference in heights between points A and B is

1. 3

Light of wavelength $4000\stackrel{\circ }{A}$ is incident on a sodium surface for which the threshold wave length of photo – electrons is $5420\stackrel{\circ }{A}$. The work function of sodium is

For the 4 bit DAC shown below, the Analog output voltage is (Assume ideal Op-amp).

A pulley of $10cm$ diameter is wrapped with a cord of length $2m$ around its periphery. If pulley is initially at rest and is given an angular acceleration of $0.5rad/s^2$, then total angular displacement of the pulley for the cord to unwind completely and the time taken by the cord to unwind completely are

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are $Q_1=5960\text{J}$, $Q_2=-5585\text{J}$, $Q_3=-2980\text{J}$ and $Q_4=3645\text{J}$ respectively. The corresponding quantities of work involved are $W_1=2200\text{J}$, $W_2=-825\text{J},W_3=-1100\text{J}$ and $W_4$ respectively . Find the efficiency of the cycle.