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

If $n_1$, $n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

A parallel plate capacitor of capacitance $90\text{pF}$ is connected to a battery of emf $20\text{V}$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the flow of charge through the cell after insertion of dielectric will be

A square plate of edge $d$and a circular disc of diameter $d$ are placed touching each other at the midpoint of an edge of plate as shown. Then center of mass of the combination will be at (assume same mass per unit area for the two plates):

For the given circuit, the input digital signals are applied at the terminals $A,B$ and $C$. What would be the output at the terminal $y$?

Two metallic spheres of radii $1cm$ and $3cm$ are given charges of $-1\times {10}^{-2}C$ and $5\times {10}^{-2}C$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

A block is tied to one end of a light string of length l whose other end is fixed to a rigid support. The block is given a speed of $\sqrt{\frac{7gl}{2}}$ from the lowermost position. Find the height at which the block leaves the circle.

A person was moving at a uniform speed, but suddenly he comes to rest. What will be his acceleration at rest?

A series R - C circuit is excited by a $1\angle 0V$ sinusoidal ac voltage source. The locus diagram of the phasor current $I=(x+jy)A.$ When C is varied, while keeping R fixed, is

Two conducting spheres of radii r1 and r2 are equally charged.The ratio of their potential is?

In the given circuit the power generated in $5\Omega$ resistance will be maximum for $x$ equal to

A particle of mass 'm' moving with velocity 'V', hits to a stationary disc of mass M and radius R and sticks to the disc on its rim. The angular velocity of the disc with which it starts to rotate about its centre is

If $|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{3.}\overrightarrow{A}.\overrightarrow{B},$ then the value of $|\overrightarrow{A}+\overrightarrow{B}|$ is

A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the earth is

A ball of mass $2\text{kg}$ is on a frictionless horizontal surface. It is attached to one end of a string and rotates about a fixed other end at an angular velocity $2\text{rev/sec}$. If the length of the string is doubled and angular velocity is halved, the tension in the string is equal to (Let initial tension be $T_0$ )

Given in the figure are two blocks A and B of weight $20N$ and $100N$ respectively. The blocks are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15$, the frictional force applied by the wall on block B is

A coil having inductance $L$ and resistance $R$, is connected to a battery of emf $E$ and the circuit is closed at time, $t=0$. If $t_1$ and $t_2$ are time instants for $90\%$ and $99\%$ completion of current growth in the circuit, then $\frac{t_1}{t_2}$ will be equal to -

Rishi walks to his school which is at a distance of 4.5 km from his home in 45 minutes. On reaching he finds that the school is closed and comes back by bus and reaches home in 15 minutes. Find his average speed in km/h.

A concave lens made of material of refractive index 1.6 is immersed in a medium of refractive index 2.0. The two surfaces of the concave lens have the same radius of curvature 0.2 m. The lens will behave as a

Consider two rods of same length and different specific heats ($S_1$ and $S_2$), conductivities $K_1$ and $K_2$ and areas of cross section ($A_1$ and $A_2$) and both having temperature $T_1$ and $T_2$ at their ends. If the rate of heat loss due to conduction is equal, then

14. The temperature co-efficient of resistance of a wire at 0^° C is 0.00125 ^° C-1. At 25^° C its resistance is one ohm. The resistance of the wire will be 1.2 ohm at (1) 225 K (2) 190^° C (3) 260^° C (4) 185 K

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors perpendicular to each other and $|\overrightarrow{a}|=|\overrightarrow{b}|=1$ . Determine the angle between $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{2a}+\overrightarrow{b}$

Find the ratio of the tension $T_1$ and $T_2$ in the string as shown in the figure. Take $g=10{\text{m/s}}^2$.

1 liter of dry air at STP expands adiabatically to a volume of $3$ litres. If $\gamma =1.4$, the work done by air is ($3^{1.4}=4.655$) (take air to be an ideal gas)

A spool is pulled at an angle $\theta$ with the horizontal on a rough horizontal surface as shown in the figure. If the spool remains at rest, the angle $\theta$ is

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 body of mass M is kept on a rough horizontal surface (friction coefficient = $\mu$). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F, where

The potential difference between the terminals of an electric heater is $60\text{V}$ and draws a current of $4\text{A}$ from the source. What current the heater will draw if the potential difference is increased to $90\text{V}?$

A disc revolves with a speed of $33\frac{1}{3}$ rev/min, and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record?