A body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3 H}{4}$ and $\frac{8 H}{9}$ from the ground is

The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y=3 x-0.8 x^2$. The time of flight of the projectile is (Acceleration due to gravity, $g=10 \mathrm{~ms}^{-2}$ )

A 100 kg cannon fires a ball of 1 kg horizontally from a cliff of height 500 m . It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A block of mass 5 kg is placed on a rough horizontal surface having coefficient of friction 0.5 . If a horizontal force of 60 N is acting on it, then the acceleration of the block is (Acceleration due ot gravity, $g=10 \mathrm{~ms}^{-2}$ )

A boy weighing 50 kg finished long jump at a distance of 8 m . Considering that he moved along a parabolic path and his angle of jump is $45^{\circ}$, his initial KE is

The moment of inetia of a rod about an axis passing through its centre and perpendicular to its length is $\frac{1}{12} M L^2$, where $M$ is the mass and $L$ is the length of the rod. The rod is bent in the middle, so that the two halves make an angle of $60^{\circ}$. The moment of inertia of the bent rod about the same axis would be

Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is

When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is

$$ \left(Y_{\text {Copper }}=10 \times 10^{10} \mathrm{Nm}^{-2} \text { and } g=10 \mathrm{~ms}^{-2}\right) $$

Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $10 \mathrm{~cm}^2$ and velocity $1 \mathrm{~ms}^{-1}$ is 2000 Pa , then the pressure of water at another point where the cross-sectional area $5 \mathrm{~cm}^2$ is

A metal ball of mass 100 g at $20^{\circ} \mathrm{C}$ is dropped in 200 g of water at $80^{\circ} \mathrm{C}$. If the resultant temperature is $70^{\circ} \mathrm{C}$, then the ratio of specific heat of the metal to that of water is

Initially the pressure of 1 mole of an ideal gas is $10^5 \mathrm{Nm}^{-2}$ and its volume is 16 L . When it is adiabatically compressed, its final volume is 2 L . Work-done on the gas is

An ideal gas is taken around $A B C A$ as shown in the $P^{\prime \prime}$ diagram. The work done during the cycle is

The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is

The vibrations of four air columns are shown below. The ratio of frequencies is

If a slit of width $x$ was illuminated by red light having wavelength $6500\mathop {\rm{A}}\limits^{\rm{^\circ }}$, the first minima was obtained at $\theta=30^{\circ}$. Then, the value of $x$ is

Eight capacitors each of capacity $2 \mu \mathrm{~F}$ are arranged as shown in figure. The effective capacitance between $A$ and $B$ is

If $E_1=4 \mathrm{~V}$ and $E_2=12 \mathrm{~V}$, the current in the circuit and potential difference between the points $P$ and $Q$ respectively are

Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. $I$ is current passing through each ring. The magnetic field value at the common centre is

One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased by 9 times the time period becomes

A coil of inductance $L$ is divided into 6 equal parts. All these are connected in parallel. The resultant inductance of this combination is

A 50 Hz AC circuit has a 10 mH inductor and a $2 \Omega$ resistor in series. The value of capacitance to be placed in series in the circuit to make the circuit power factor as unity is

The surface of a metal is first illuminated with a light of wavelength 300 nm and later illuminated by another light of wavelength 500 nm . It is observed that the ratio of maximum velocities of photoelectrons in two cases is 3 . The work function of metal value is close to

The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is

The half-life period of a radioactive element $A$ is 62 years. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in 1:15 ratio. The age of the sample is

The current gain of a transistor in common emitter configuration is 80 . The resistances in collector andbase sides of the circuit are $5 \mathrm{k} \Omega$ and $1 \mathrm{k} \Omega$ respectively. If the input voltage is 2 mV , the output voltage is

Four logic gates are connected as shown in the figure. If the inputs are $A=0, B=1$ and $C=1$, then the values of $Y_1$ and $Y_2$ respectively, are

The maximum distance between the transmitting and receiving antennas for satisfactory communication in line of sight mode is 57.6 km . If the height of the receiving antenna is 80 m , the height of the transmitting antenna is (radius of earth $=6.4 \times 10^6 \mathrm{~m}$ )