List of practice Questions

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then

A wire when connected to $220\, V$ mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2 \, then \, P_2 : P_1$ is

Consider the two cells having emf $E_{1}$ and $E_{2}\left(E_{1}>E_{2}\right)$ connected as shown in the figure. A potentiometer is used to measure potential difference between $P$ and $Q$ and the balancing length of the potentiometer wire is $0.8\, m$. Same potentiometer is then used to measure potential difference between $P$ and $R$ and the balancing length is $0.2\, m$. Then, the ratio $E_{1} / E_{2}$ is

In an aluminum $(Al)$ bar of square cross section, a square hole is drilled and is filled with iron $(Fe)$ as shown in the figure. The electrical resistivities of $Al$ and Fe are $2.7 ? 10^{-8 }\, \Omega m$ and $1.0 ? 10^{-7}\, \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is

A metal wire of circular cross-section has a resistance $R_1$. The wire is now stretched without breaking so that its length is doubled and the density is assumed to remain the same. If the resistance of the wire now becomes $R_2$ then $R_2 : R_1$ is

If a wire is stretched to make it $0.1\%$ longer, its resistance will

The effective resistance across the points P and Q is

A $ 50\,\Omega $ galvanometer is shunted by a resistance of $ 5\,\Omega . $ The percentage of the total current, which passes through the galvanometer is

Silicon doped with arsenic is

For a given circuit, it is observed that the current $I$ is independent of the value of the resistance $R_6$. Then, the resistance values must satisfy

The resistivity of the material of a potentiometer wire is $5 \times 10^{-6} \Omega\, m$ and its area of cross section is $5 \times 10^{-6} \; m^2$. If $0.2\, A$ current is flowing through the wire, then the potential drop per metre length of the wire is

The pair of compound which cannot exist together in solution is

$ 0.6 \,mL $ of acetic acid is dissolved in $ 1 \,L $ of water. The value of van?t Hoff factor is $ 1.04 $ . What will be the degree of dissociation of the acetic acid?

What is the mole fraction of the solute in $ 2.5 $ molal aqueous solution?

Which of the following statement is true ?

Boiling point of chloroform was raised by $0.323 \,K$, when $0.5143\, g$ of anthracene was dissolved in its $35 \,g$. Molecular mass of anthracene is $(K_b$ for $CHCl_3 = 3.9 \,K \,kg\,, mol^{-1})$

Setting of plaster of Paris is

When two displacements represented by $ y_1 = a \sin \, (\omega \, t)$ and $ y_2 = b \, cos \, ( \omega \, t )$ are superimposed the motion is

The displacement of a particle varies according to the relation $x = 4(\cos \, \pi t + \sin \, \pi t)$. The amplitude of the particle is

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $?_1$ and $?_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta p with positions x are shown in the figures. If $\frac{a}{b} = n^{2}$ and $\frac{a}{R} = n, $ then the correct equation(s) is(are)

A disc of radius a and mass m is pivoted at the rim and is set in small oscillation. If a simple pendulum have the same period as that of the disc, then the length of the simple pendulum should be

A catalyst only

For which of the following order of reaction, half-life is independent of initial concentration?

Match items in Column I with those in Column II and select the correct option.

Which of the following groups of algae produces algin?