In the following circuit, the magnitude of current \(I _{ l }\), is \(............A\).

Identify the correct statements from the following: \((A)\) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. \((B)\) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. \((C)\) Work done by friction on a body sliding down an inclined plane is positive. \((D)\) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero. \((E)\) Work done by the air resistance on an oscillating pendulum in negative. Choose the correct answer from the options given below:

Assuming the nitrogen molecule is moving with \(r.m.s.\) velocity at \(400\, K\), the de\(-\)Broglie wavelength of nitrogen molecule is close to\(......\mathring {A}\) (Given : nitrogen molecule weight : \(4.64 \times 10^{-26}\, kg ,\) Boltzman constant : \(1.38 \times 10^{-23}\, J / K ,\) Planck constant : \(\left.6.63 \times 10^{-34}\, J . s \right)\)

A particle starts with an initial velocity of \(10.0\,ms ^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0\,ms ^{-2}\). The time taken by the particle to reach the velocity of \(60.0\,ms ^{-1}\) is \(.......\,s\)

A student in the laboratory measures thickness of a wire using screw gauge. The readings are \(1.22\,mm , 1.23\,mm , 1.19\,mm\) and \(1.20\,mm\). The percentage error is \(\frac{ x }{121} \%\). The value of \(x\) is ..............

The \(V-I\) characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\)

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below.

The resistance of a wire is \(5 \Omega\). It's new resistance in ohm if stretched to \(5\) times of it's original length will be :

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

As shown in figure, a \(70\,kg\) garden roller is pushed with a force of \(\overrightarrow{ F }=200\,N\) at an angle of \(30^{\circ}\) with horizontal. The normal reaction on the roller is \(.......\,N\) \(\left(\right.\) Given \(\left.g =10\,m s ^{-2}\right)\)

A wire of resistance \(9 \Omega\) is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.