Identify the correct statements among the following.
(A) The number of electrons (\( n_e \)) is more than the number of holes (\( n_h \)) in intrinsic conductors.
(B) Semiconductors are elements (Si, Ge) type as well as compounds (GaAs, CdS).
(C) The number of charge carriers can be changed by 'doping' of a suitable impurity in pure semiconductors.
(D) Holes are essentially electron vacancies in a valence band.
Choose the correct answer from the options given below:

A moving coil galvanometer has N number of turns in the coil with area A. It carries a current I and the magnetic field is B. The torque acting on the coil is :

The resistance of a wire is \( R \, \Omega \). What will be its new resistance \( R_{new} \) if it is stretched to n times its original length?

The self-inductance (L) of a long solenoid on doubling its number of turns and length, keeping other factors constant, will become

Two concentric coils \(X\) and \(Y\), each of radius \(2 \pi cm\), are placed at right angles to each other. If \(X\) and \(Y\) carry 4 A and 3 A currents, respectively, then the value of the magnetic field (in \(Wb m ^{-2}\) ) at the centre of the coils is (Take \(\mu_0=4 \pi \times 10^{-7} Wb A ^{-1} m^{-1}\) )

A long solenoid with 30 turns/cm has a small loop of area \( 3 \text{ cm}^2 \) placed inside it normal to its axis. If the current in the solenoid changes steadily from 3.0 A to 6.0 A in 0.1 s, the induced emf in the loop is :

A proton is accelerated by a potential V and the de-Broglie wavelength associated with it is \(\lambda\). By how much potential a deuteron should be accelerated to acquire the same de-Broglie wavelength as that of a proton?

The slope of the normal to the curve \(y=x^3-4 \sin x\) at \(x=0\) is:

Two solutions 'A' and 'B' are taken and diluted. On dilution, it was seen that the limiting molar conductivity of 'B' increases to a smaller extent while that of 'A' increases to a much larger extent comparatively, which of the two is a strong electrolyte ?

A, B, and C are parallel conductors of equal lengths carrying current I, 2I and 3I respectively, as shown in the figure. \( F_1 \) is the force exerted by B on A and \( F_2 \) is the force exerted by C on A. Choose the correct answer

The value of \(\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|\) is

"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Which of the following compounds would have the smallest value of \(\text{pKa}\)?"

(A) The degree of differential equation \(\frac{d^2 y}{d x^2}+\sin \left(\frac{d y}{d x}\right)=0\) is 2
(B) The degree of differential equation \(\frac{d}{d x}\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3+\sin x=0\) is 1
(C) The order of differential equation \(2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0\) is 2
(D) The number of arbitrary constants in a particular solution of a differential equation of third order are 3
(E) The integrating factor of the differential equation \(\frac{d y}{d x}-y=\cos x\) is \(e^{-x}\)
Choose the correct answer from the options given below: