A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below

A flexible chain of mass \(m\) hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is \(30^{\circ}\). Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is _________ .

The source that illuminates the double - slit in 'double - slit interference experiment' emits two distinct monochromatic waves of wavelength \(500\,nm\) and \(600\, nm\), each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to on wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in \(nm\) is

A parallel beam of monochromatic light of wavelength \(5000 \mathring A\) is incident normally on a single narrow slit of width \(0.001 \mathrm{~mm}\). The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of______________(degree).

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25 \%\) more charge from the battery. The dielectric constant of mica is ___________ .

A long straight wire of circular cross-section (radius \(a\)) is carrying steady current \(I\). The current \(I\) is uniformly distributed across this cross-section. The magnetic field is

Let \(O\) be the origin and \(OP\) and \(OQ\) be the tangents to the circle \(x^2+y^2-6 x+4 y+8=0\) at the point \(P\) and \(Q\) on it. If the circumcircle of the triangle OPQ passes through the point \(\left(\alpha, \frac{1}{2}\right)\), then a value of \(\alpha\) is

A tower \(T_1\) of height \(60\, m\) is located exactly opposite to a tower \(T_2\) of height \(80\, m\) on a straight road. From the top of \(T_1\) . if the angle of depression of the foot of \(T_2\) is twice the angle of elevation of the top of \(T_2\), then the width (in \(m\)) of the road between the feet of the towers \(T_1\) and \(T_2\) is

In the circuit, the logical value of \(A =1\) or \(B =1\) when potential at \(A\) or \(B\) is \(5\,V\) and the logical value of \(A=0\) or \(B=0\) when potential at \(A\) or \(B\) is \(0\,V\). The truth table of the given circuit will be :

A scientific committee is to be formed from \(6\) Indians and \(8\) foreigners, which includes at least \(2\) Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is

\(300 \,cal\). 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____\({ }^{\circ} C\).

Let \( S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+. \dots \) up to 13 terms. If \( 13S=\frac{2^{k}}{n!} \) where \( k\in N \), then \( n+k \) is equal to