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The velocity of boat m still water is 10 ms $m{s}^{-1}$ ${}^{}$ . The river flow velocity is 5 ms $m{s}^{-1}.$ ${}^{}$

If ${}_{}$ $v_b$ ,= $$ velocity of boat with respect to river velocity, $v_b=$ ${}_{}$ actual velocity of boat (i.e. with respect to bank), $v_r=$ ${}_{}$ velocity of stream, then the value of $v_b$ ${}_{}$ is

A telescope with objective of focal length  $100cm$ and eyepiece of focal length $5cm$ is focused on a far object such that parallel rays emerge from eyepiece. If object subtends an angle of $1^0$  on objective, the angular size of image is

The correct graph between logeR and loge( - 0) during cooling of a body may be (R is the rate of cooling and 0 is surrounding temperature)

Resistance of given carbon resistor is

Deviation of light ray by a thin prism of refractive index $\mu$ and refracting angle $A$  is

If force (F), mass (M), length (L) are taken as fundamental quantities, dimensions of time will be

The radius of circle, the period of revolution $T$ , initial position and sense of revolution are indicated in the figure. x-projection of the radius vector of rotating particle $P$  is

What is the current through an ideal P – N junction diode shown in figure below?

The velocity of a particle is given by $\text{exception 25:}$ $v=\sqrt[]{180-16x}m/s$ . Its acceleration will be

The value of alternating emf (E) in the given circuit will be

Two conducting rods inclined at  $\text{'}\theta \text{'}$ angle from horizontal are kept parallel at separation $\text{'}l\text{'}$ to each other. A resistor of resistance $R$ joins the two rods at their topmost point. A metal bar of length $\text{'}l\text{'}$ is free to slide on the rods as shown in figure. on releasing from rest, the maximum speed that can be attained by the bar if a constant magnetic field $B$ exists vertically downwards, is

A farsighted person cannot focus distinctly objects closer than 100cm. The lens that will permit him to read from a distance of 50cm, will have a focal length:

Figure shown four plates each of area A and separated from another by a distance d. What is the capacitance between P and Q?

If $$ $a\cdot b=\left|a\times b\right|$ , then the $\theta$ angle $$ between a and b will be

Consider the following two statements .

(A)The gravitational force on a particle inside a spherical shell is zero.

(B) Total mechanical energy of a body on earth’s surface may be positive.

Which of the following options is correct?

A body possesses kinetic energy x, moving on a rough horizontal surface, is stopped in a distance y. The friction force exerted on the body is

A man who can swim with a speed of  $2kh/h$ wants to cross a river $200m$ wide. If the river is flowing with a speed of $3km/h$  then in what minimum time can the man cross the river?

A charged particle of mass m and charge q is released from rest in a uniform electric field E. The KE of particle after time t is:

For the arrangement shown in figure, the tension in the string to prevent it from sliding down, is (g = 10 m/s²)