Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) An electric fan continues to rotate for some time after the current is switched off. Reason \(R:\) Fan continuous to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

In the given circuit, the current flowing through the resistance \(20\ \Omega\) is \(0.3 \mathrm{~A}\), while the ammeter reads \(0.9 \mathrm{~A}\). The value of \(\mathrm{R}_1\) is _______ \(\Omega\).

A steel wire having a radius of \(2.0\, mm\), carrying a load of \(4\, kg\), is hanging from a ceiling. Given that \(g = 3.1\pi \,m{s^{ - 2}}\) , what will be the tensile stress that would be developed in the wire?

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of \(10\, mV\) is added to the base-emitter voltage, the base current changes by \(10 \mu A\) and the collector current changes by \(1.5 \,mA\). The load resistance is \(5 \,k \Omega\). The voltage gain of the transistor will be

The angle between vector \(\vec{Q}\) and the resultant of \((2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})\) and \((2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})\) is _______.

A \(1\,m\) long copper wire carries a current of \(1\,A\). If the cross section of the wire is \(2.0\,mm ^{2}\) and the resistivity of copper is \(1.7 \times 10^{-8}\,\Omega\,m\). the force experienced by moving electron in the wire is \(\times 10^{-23}\,N\). (charge on electron \(=1.6 \times 10^{-19}\,C\) )

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi\  \mathrm{m}\) and \(R_2=4 \pi\  \mathrm{m}\) carrying current \(I=4 \mathrm{~A}\) as per figure given below is \(\alpha \times 10^{-7} \mathrm{~T}\). The value of \(\alpha\) is___________ (Centre \(\mathrm{O}\) is common for all segments)

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

If \(\mathop {\lim }\limits_{x - 1} \frac{{{x^4} - 1}}{{x - 1}} = \mathop {\lim }\limits_{x - k} \frac{{{x^3} - {k^3}}}{{{x^2} - {k^2}}}\), then \(k\) is

A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be

Let \(a , b\) and \(c\) be the length of sides of a triangle \(ABC\) such that \(\frac{ a + b }{7}=\frac{ b + c }{8}=\frac{ c + a }{9}\). If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle \(ABC\), respectively, then the value of \(\frac{R}{r}\) is equal to

Figure shows the variation in temperature \(\left( {\Delta T} \right)\) with the amount of heat supplied \((Q)\) in an isobaric process corresponding to a monoatomic \((M)\), diatomic \((D)\) and a polyatomic \((P)\) gas. The initial state of all the gases are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines \(a, b\) and \(c\) respectively correspond to