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The values of sin105° is equal to

A thin circular ring of area $A$ is held perpendicular to a uniform magnetic field of induction $B.$ A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $R.$ When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

On one way traffic road, the speeds of overtaking and overtaken vehicles are 80 kmph and 50 kmph respectively. If the acceleration of the overtaking vehicle is 2.5 kmph per second, calculate the overtaking sight distance (Assume spacing between vehicles is 16 m, reaction time of driver is 2 seconds)

1. 191.05

A sono-meter wire supports a 4 kg load and vibrates in fundamental node with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental node, the load should be changed to

For the given curve between impedance $\left(Z\right)$ and frequency $\left(f\right)$ of a series LCR circuit, the value of resistance is -

Comment on the shape of the MR curve in case the TR curve is a

(i) positively sloped straight line, passing through the origin

(ii) horizontal straight line.

A small bar $\text{A}$ resting on a smooth horizontal plane is attached by threads to a point $\text{P}$ and by means of a weightless pulley, to a weight $\text{B}$ possessing the same mass as the bar itself. The bar is also attached to a point $\text{O}$ by means of a light non-deformed spring of length $l_0=\frac{32}{19}\text{cm}$ and stiffness $k=\frac{5mg}{l_0},$ where $m$ is the mass of the bar. The thread $\text{PA}$ having been burned, the bar starts moving to the right. Find its velocity at the moment when it breaks off the plane.(Take all the $g$ in ${\text{m/sec}}^2)$

A finite square grid with each link having resistance $r$ is fitted in a resistanceless conducting circular wire. The equivalent resistance between $\text{A}$ and $\text{B}$ will be:

$($Given, $r=80/7\Omega )$

Action and reaction forces are:

i. Equal

ii. Opposite

What is the number of protons in a magnesium atom?

A one kilowatt motor pumps out water from a $\text{10 m}$ deep well. Calculate the quantity of water pumped out per second.(Take $g=10\text{m}/{\text{s}}^2$)

A racing car driver drives his car on a flat circular track of radius $\frac{25}{3}$ m having a coefficient of friction 0.5.
The magnitude of its tangential acceleration at an instant when car starts slipping at a speed of 5 m/s is

In a rapid sand filter, the time for reaching particle break through ($T_B$) is defined as the time elapsed from start of filter run to the time at which the turbidity of the effluent from the filter is greater than 2.5 NTU. The time for reaching terminal head loss ($T_H)$ is defined as the time elapsed from the start of the filter run to the time when head loss across the filter is greater than 3 m.

The effect of increasing the filter loading rate (while keeping all other conditions same) on $T_B$ and $T_H$ is

A parallel plate condenser of capacity 5 $\mu$ F is kept connected to a battery of emf 10 V. If the space between the plates is filled with a medium of dielectric constant 12, then the additional charge taken from the battery is?

In a Carnot heat engine, the temperature of source and sink are ${827}^{\circ }\text{C}$ and ${27}^{\circ }\text{C}$. If the engine consumes $33\text{kJ}$ per cycle, then the heat rejected to the sink per cycle is

In Young's double-slit experiment, the intensity of light at a point on the screen, where the path difference is $\lambda$, is $I$. The intensity of light at a point where the path difference becomes $\frac{\lambda }{3}$ is :

One fourth of a sphere of radius R is removed as shown. An electric field E exists parallel to x – y plane. Find the flux through remaining curved part.

A block of mass 5.0 kg slides down an incline of inclination ${30}^{\circ }$ and length 10 m. Find the work done by the force of gravity.

The lateral strain produced in the wire is $0.01\times {10}^{-3}$. If Poisson's ratio is $0.4$, then find the longitudinal strain produced in the wire.

An uncharged capacitor of capacitance $100\mu \text{F}$ is connected to a battery of emf $20\text{V}$ at $t=0$ through a resistance $10\Omega$, then the maximum rate at which energy is stored in the capacitor is :

Find the range of frequenc of light that is visisble to an average human being (400 nm < \lambda < 700 nm.)

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

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

Match List I with List II.

Two capacitors of capacitance 1.0 micro farad and 2.0 micro farads are each charged by being connected across a 5.0-volt battery. they are disconnected from the battery and then connected to each other with resistivity wires so that plates of opposite charges are connected together. What will be the magnitude of the final voltage across the 2.0-micro farad capacitor?