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Gadolinium belongs to 4f series. It’s atomic number is $64$. Which of the following is the correct electronic configuration of gadolinium?

Find out the solubility of $Ni(OH)_2$ in 0.1 M $NaOH$. Given that the ionic product of $Ni(OH)_2$ is $2 \times 10^{-15}$

Which one is malachite from the following?

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s² at a distance of 5 m from the mean position. The time period of oscillation is

Which of the following oxides is most acidic in nature?

A spherical conductor of radius 12 cm has a charge of $1.6 \times 10^{-7}$ C distributed uniformly on its surface. The electric field just outside the sphere is:

An electron (mass m) with an initial velocity v = v₀î (v₀ > 0) is in an electric field E = -E₀î (E₀ = constant > 0). Its de Broglie wavelength at the time t is given by:

An electron falls from rest through a vertical distance h in a uniform and vertically upward-directed electric field E. The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance h. The fall time of the electron in comparison to the fall time of the proton is:

A capacitor of capacitance $C$ is connected across an AC source of voltage $V$, given by; $V=V_0 \sin \omega t$. The displacement current between the plates of the capacitor would then be given by:

PQ is an infinite current carrying conductor carrying current $I$. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity $v$ as shown. The conductor EF is perpendicular to PQ and its ends are at distances $a$ and $b$ from the wire. The force needed to maintain constant speed of EF is:

The following metal ion activates many enzymes, participates in the oxidation of glucose to produce ATP and with Na, is responsible for the transmission of nerve signals.

In human beings, at the end of 12 weeks (first trimester) of pregnancy, the following is observed:

In DNA, the complementary bases are:-

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r (as shown in Fig. I). Now, as shown in Fig. II, the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:

An inductor coil of self-inductance $10 \text{ H}$ carries a current of $1 \text{ A}$. The magnetic field energy stored in the coil is:

A uniform magnetic field is restricted within a region of radius $r$. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 1 of radius $R$ ($R > r$) encloses the region $r$ and Loop 2 of radius $R$ is entirely outside the region of the magnetic field as shown in the figure. Then the electromotive force (emf) generated is:

A 800 turn coil of effective area $0.05 \text{ m}^2$ is kept perpendicular to a magnetic field $5 \times 10^{-5} \text{ T}$. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in $0.1 \text{ s}$, the emf induced in the coil will be:

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 \gg R_2$, the mutual inductance $M$ between them will be directly proportional to:

A car sometimes overturns while taking a turn. When it overturns, it is:

Match List-I with List-II (the symbols carry their usual meaning). **List-I** (A) $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$ (B) $\oint \vec{B} \cdot d\vec{A} = 0$ (C) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi}{dt}$ (D) $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ **List-II** (I) Ampere-Maxwell's law (II) Faraday's law (III) Gauss's law of electrostatics (IV) Gauss's law of magnetism