A steel wire of length \(4.7 \mathrm{~m}\) and cross-sectional area \(3.0 \times 10^{-5} \mathrm{~m}^{2}\) stretches by the same amount as a copper wire of length \(3.5 \mathrm{~m}\) and cross-sectional area of \(4.0 \times 10^{-5} \mathrm{~m}^{2}\) under a given load. What is the ratio of Young's modulus of steel to that of copper?

A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is \(2000 \times 10^{-6}\) weber. What is the induced emf in the secondary if the current through the primary increases at a rate of \(0.2 \mathrm{As}^{-1}\) ?

A block of wood floats in water with \((4 / 5)\) th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in \(\mathrm{kgm}^{-3}\))

The primary of a transformer when connected to a DC battery of \(10 \mathrm{~V}\) draws a current of \(1 \mathrm{~mA}\). The number of turns of the primary and secondary windings are 50 and 100 , respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively

\({ }_{92} \mathrm{U}^{235}\) undergoes successive disintegrations with the end product of \({ }_{82} \mathrm{~Pb}^{203}\). The number of \(\alpha\) and \(\beta\) particles emitted are

A wire is stretched to double of its length. The strain is

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

The stress verses strain graph of four metals A,B,C and D are as shown. Which of the graph represent the metal having greatest Young's modulus?

Three moles of \(\mathrm{PCl}_{5}\), three moles of \(\mathrm{PCl}_{3}\) and two moles of \(\mathrm{Cl}_{2}\) are taken in a closed vessel. If at equilibrium the vessel has \(1.5\) moles of \(\mathrm{PCl}_{5}\), the number of moles of \(\mathrm{PCl}_{3}\) present in it is

\(\text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is }\)

In Friedal-Crafts alkylation reaction of phenol with chloromethane, the product formed will be

The correct increasing order of basic strength of following amines,
\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}, \mathrm{NH}_{3},\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}_{6} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) in gaseous state is

A conducting circular loop is placed in a uniform magnetic field \(\mathrm{B}=0.125 \mathrm{~T}\) with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of \(2 \mathrm{~mm} \mathrm{~s}^{-1}\), then the induced emf when the radius is \(4 \mathrm{~cm}\) is