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Two coils of self-inductance $2 \text{ mH}$ and $8 \text{ mH}$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at a constant speed of 4 m/s. The tension in the string is 6 N, when the stone is at (Take g = 10 m/s²):
When a body of mass $m$ just begins to slide as shown, match List-I with List-II: **List-I** (a) Normal reaction (b) Frictional force ($f_s$) (c) Weight ($mg$) (d) $mg \sin \theta$ **List-II** (i) $P$ (ii) $Q$ (iii) $R$ (iv) $S$
The electric field at a distance 3R/2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the centre of the sphere is
A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by
A uniform rope of length $l$ lies on a table. If the coefficient of friction is $\mu$, then the maximum length $l_1$ of the part of this rope which can overhang from the edge of the table without sliding down is:
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Pregnancy is characterised by metabolic changes in the mother. Reason (R): During pregnancy, the level of thyroxine is increased in the maternal blood. In the light of the above statements, choose the most appropriate answer from the options given below:
A ball of mass 0.1 kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 rpm. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:
A $1 \text{ kg}$ object strikes a wall with velocity $1 \text{ ms}^{-1}$ at an angle of $60^\circ$ with the wall and reflects at the same angle. If it remains in contact with the wall for $0.1 \text{ s}$, then the force exerted on the wall is:
Two masses of $5 \text{ kg}$ and $10 \text{ kg}$ are connected to a pulley as shown. What will be the acceleration of the system? ($g$ = acceleration due to gravity)
In a circuit shown in the figure, the heat produced in the 3 Ω resistance due to a current flowing in it is 12 J. The heat produced in the 4 Ω resistor is:
During the purification process for recombinant DNA technology, addition of chilled ethanol precipitates out :
The V-I graph for a conductor at temperatures $T_1$ and $T_2$ are as shown in the figure. The term $(T_2 - T_1)$ is proportional to:
The dependence of the short wavelength limit $\lambda_{min}$ on the accelerating potential $V$ is represented by the curve of figure:
Calculate the acceleration of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is $0.05$. (Take $g=10 \text{ m/s}^2$, the mass of the string is negligible and no other friction exists). [Note: Based on the answer, the mass of the hanging block is $2 \text{ kg}$ and the mass of the trolley is $10 \text{ kg}$].
A silver wire has a resistance of 2.1 Ω at 27.5°C, and a resistance of 2.7 Ω at 100°C. The temperature coefficient of resistivity of silver is:
In a meter bridge experiment, the null point is at a distance of 30 cm from A. If a resistance of 16 Ω is connected in parallel with resistance Y, the null point occurs at 50 cm from A. The value of the resistance Y is:
A long solenoid of diameter $0.1 \text{ m}$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius $0.01 \text{ m}$ is placed with its axis coinciding with the solenoid's axis. The current in the solenoid reduces at a constant rate to $0 \text{ A}$ from $4 \text{ A}$ in $0.05 \text{ s}$. If the resistance of the coil is $10\pi^2 \Omega$, the total charge flowing through the coil during this time is:
Two parallel metal plates having charges +Q and -Q faces each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
Among the following, the correct order of acidity is: