The instantaneous magnetic flux linked with a coil is given by \(\phi = (15t^3 - 100t^2 + 40)\) Wb. The emf induced in the coil at time \(t = 1\) s is :

With the rise in temperature, the electrical resistance

A Convex mirror produces the magnification \( \frac{1}{3} \) and \( \frac{1}{4} \) when the object is placed at the points P and Q in front of the mirror.

In a Young's double-slit experiment, the slits are separated by 0.56 mm and the screen is placed 2.8 m away from the slits. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

'n' identical small drops are charged to V volt each. They coalesce to form a bigger drop. The potential of the bigger drop will be:

The work function for a metallic surface is 4.0 eV. The longest wavelength of light that can cause photoelectron emission is approximately:

The frequency of a photon whose energy is 66.3 eV would be
(Given \( h = 6.63 \times 10^{-34} \text{ Js} \))

Consider the Linear Programming Problem
Maximize \(z=x+y\)
Subject to the constraints \(x-y \leq-1, x \geq y, x \geq 0, y \geq 0\)
Then which one of the following is TRUE?

Match List-I with List-II

List-I (Compound)	List-II (Use)
(A) Dichloromethane	(I) in the manufacturing of propellants for aerosol cans
(B) DDT	(II) in the production of the Freon refrigerant R-22
(C) Trichloromethane	(III) as a paint remover
(D) Tetrachloromethane	(IV) as an insecticide

Choose the correct answer from the options given below:

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :

The matrix \(A=\left[\begin{array}{ccc}0 & 1 & -3 \\ -1 & 0 & 0 \\ 3 & 0 & 0\end{array}\right]\) is a :

A parallel plate capacitor is charged by battery. While the battery remains connected and dielectric slab of dielectric constant 'k' is inserted between the plates of capacitor then,
A. Charge increases and becomes k times.
B. Capacitance decreases becomes times 1/k
C. Energy stored in capacitor increases to \(k\) times.
D. Potential difference increases to \(k\) times.
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases
with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\left(\Lambda_m^0\right)\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per
molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law
finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The unit of constant A is :