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10 resistors, each of resistance $R$ are connected in series to a battery of emf $E$ and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased $n$ times. The value of $n$ is
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are
Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is $0.15$ ($g = 10 \text{ m s}^{-2}$).
In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)? $n_1 = 1.5$, $n_2 = 1.6$, $R_1 = R_2 = 20$ cm
A bullet is fired from a gun at the speed of $280 \text{ m s}^{-1}$ in the direction $30^\circ$ above the horizontal. The maximum height attained by the bullet is ($g = 9.8 \text{ m s}^{-2}$, $\sin 30^\circ = 0.5$)
An electric dipole is placed as shown in the figure. The electric potential (in $10^2$ V) at point $P$ due to the dipole is ($\epsilon_0$ = permittivity of free space and $\frac{1}{4\pi\epsilon_0} = K$)
A very long conducting wire is bent in a semi-circular shape from $A$ to $B$ as shown in figure. The magnetic field at point $P$ for steady current configuration is given by
A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24$ cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is
A speed motorcyclist sees a traffic jam ahead of him. He slows down to $36 \text{ km/h}$. He finds that traffic has eased and a car moving in front of him at $18 \text{ km/h}$ is honking at a frequency of $1392 \text{ Hz}$. If the speed of sound is $343 \text{ m/s}$, the frequency of the honk as heard by him will be
If the nucleus $^{27}_{13}\mathrm{Al}$ has a nuclear radius of about 3.6 fermis, then $^{125}_{52}\mathrm{Te}$ would have its radius approximately as:
If $n_1, n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50 \text{ cm}$. The next larger length of the column resonating with the same tuning fork is
$4.0 \text{ g}$ of a gas occupies $22.4 \text{ L}$ at NTP. The specific heat capacity of the gas at constant volume is $5.0 \text{ J K}^{-1}\text{mol}^{-1}$. If the speed of sound in this gas at NTP is $952 \text{ ms}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant $R = 8.3 \text{ J K}^{-1}\text{mol}^{-1}$)
Sound waves travel at $350 \text{ m/s}$ through warm air and at $3500 \text{ m/s}$ through brass. The wavelength of a $700 \text{ Hz}$ acoustic wave as it enters brass from warm air:
The output ($Y$) of the given logic gate is similar to the output of an/a:
An infinite line charge produces a field of $9 \times 10^4$ N/C at a distance of 2 cm. The linear charge density is:
For which one of the following is the Bohr model not valid?
An alpha nucleus of energy 1/2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
Which colour of the light has the longest wavelength?
An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state: (a) the electron would not move in circular orbits. (b) the energy would be 2⁴ times that of a H-atom. (c) the electron's orbit would go around the protons. (d) the molecule will soon decay in a proton and a H-atom. Choose the correct option: