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Does the pressure difference between two points depends on the medium of fluid other than height??

Three simple harmonic motions of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is ${60}^{\circ }$ ahead of the first and the phase of the third motion is ${60}^{\circ }$ ahead of the second. Find the amplitude of the resultant motion.

Abiogenesis means

A particle moves such that its acceleration a is given by a=-bx, where x is the displacement from equilibrium position and b is a constant. The period of oscillation is

Whenyou are pedalling a bicycle, the force of friction exerted
by the ground on the two wheels is such that it acts

In the system shown in the figure $m_1>m_2$. System is held at rest by thread $BC$. Just after the thread $BC$ is cut:

(A) Acceleration of $m_2$ will be upwards
(B) Magnitude of acceleration of both blocks will be equal to $\left(\frac{m_1-m_2}{m_1+m_2}\right)g$
(C) Acceleration of $m_1$ will be equal to zero
(D) Magnitude of acceleration of two blocks will be non-zero and unequal.
From the above four statements we can conclude

If |Z| = 1 and Z $\ne$ 1, then all the values of $\frac{Z}{1-Z^2}$ lie on

An infinite number of charges, each equal to q, are placed along the x-axis at x =1, x=2, x=8, ... and so on. The potential at the point x =0 due to this set of charges is

Two rings have their moment of inertia in the ratio 2:1 and their diameters are in the ratio 2:1. The ratio of their masses will be:

A convex and a concave mirror of radii 10 cm each are facing each other and 15 cm apart. A point object is placed midway between them. Then position of the final image if the reflection first takes place at the concave mirror and then in the convex mirror is

In the adjoining figure, SS is a spherical surface separating two media of refractive indices n₁ and n₂ where n₁ > n₂. C is the centre of curvature of the spherical surface. An observer, keeping his eye beyond C in the medium of refractive index n₂ views the refracted image of an object AB placed as shown in the medium of refractive index n₁. The image will be:

Some derived quantity related to electric current?

A body is projected vertically up with certain velocity. At point $P$ in its path, the ratio of its potential energy to kinetic energy is $36:64$. The ratio of velocity of projection to velocity at $P$ is

A body is rolling without slipping on a horizontal plane. The radius of body is $R$. If the ratio of rotational to translational kinetic energy is $\frac{9}{25}$, then the radius of gyration of the body is

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. What is the angle betwee the two vectors?

A merry- go- round ( diameter 4.0 m ) starts from rest and uniformly accelerates until it rotates at 0.8 rev/min. This occurs in 11s. Once it has reached this rate , it rotates at 0.8 rev/min uniformly . Determine the angular acceleration

A cricketer hits a ball from the ground level with a velocity of $\left(10\sqrt{2}\right)m{s}^{-1}$ at an angle of ${45}^{\circ }$ with the horizontal. What should be the minimum speed of the fielder standing [Along the direction in which ball is hit] at a distance of $5m$ from the batsman so as to catch the ball at ground level. Assume the direction of motion of the ball and the fielder are same.

Which is NOT a property of ferrimagnetism?

Two identical ladders are arranged as shown in figure. Mass of each ladder is $M$ and length is $L$. A load of mass $m$ has been attached at the touching point $\left(\text{O}\right)$ of the ladders, as shown in figure. The system is in equilibrium. Find the magnitude of static frictional force acting at either point $A$ and $B$.

A glass prism of refractive index 1.5 is immersed in water $(\mu =\frac{4}{3})$. A light beam incident normally on the face AB is totally reflected to reach the face BC if

A cylinder rolls on a horizontal plane surface. If the speed of the centre is 25 m/s, what is the speed of the highest point ?

Suppose A and B be two non-singular matrices, such that $AB=B{A}^m$ and $B^n=I$ and $A^p=I$
Which of the following represents the correct relation between m, n and p?

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. The power of the pulse is 30 mW and the speed of light is $3\times {10}^8$ m/s. The final momentum of the object is

A uniform magnetic field B exists in a cylindrical region of radius 10 cm as shown in figure. A uniform vire of length 80 cm and resistance 4.0 $Omega$ is bent into a square frame and id placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of 0.010 T/s, find the current induced in the frame.

If a gas has ${}^{\prime }{f}^{\prime }$ degree of freedom, the ratio of specific heats of the gas $\left(\frac{C_P}{C_V}\right)$ is

X-ray beam of intensity $I_0$ passes through an absorption plate of thickness d. If absorption coefficient of material of plate is $\mu$, the correct statement regarding the transmitted intensity I of X-ray is

Calculate the increase in the internal energy of 10 g of water when it is heated from $0^{\circ }C$ to ${100}^{\circ }C$ and converted into steam at 100 kPa. The density of steam $=0.6kg{m}^{-3}$. Specific heat capacity of water $=4200\text{J}k{g}^{-1}{}^{\circ }{C}^{-1}$ and the latent heat of vaporization of water $=2.25\times 106\text{J}k{g}^{-1}$.

Column-I contains organisms and column-II contains their excretory structures. Choose the correct match form the options given below.
$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ & \text{(Organism)}& & \text{(Excretory structure)}\\ \text{A.}& \text{Cockroach}& \text{I.}& \text{Nephridia}\\ \text{B.}& \text{Cat fish}& \text{II.}& \text{Malpighian tubules}\\ \text{C.}& \text{Earthworm}& \text{III.}& \text{Kidneys}\\ \text{D.}& \text{Balanoglossus}& \text{IV.}& \text{Flame cells}\\ \text{E.}& \text{Flatworm}& \text{V.}& \text{Proboscis gland}\end{array}$

For component of vector $\overrightarrow{P}=\hat{i}+2\hat{j}-3\hat{k}$ values are in column - II, then the correct match is:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{a)}& \text{X-axis}& \text{p)}& 1\\ \text{b)}& \text{Along vector}& \text{q)}& \sqrt{14}\\ & \overrightarrow{q}=\hat{i}+2\hat{j}+\frac{5}{3}\hat{k}& & \\ \text{c)}& \text{Along vector}& \text{r)}& 0\\ & \overrightarrow{r}=2\hat{i}+4\hat{j}-6\hat{k}& & \\ \text{d)}& \text{Along vector}& \text{s)}& \sqrt{7}\\ & \overrightarrow{s}=\frac{\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{14}}& & \end{array}$

A driver, having a definite reaction time, is capable of stopping over a distance of $30\text{m}$ on seeing a red traffic light when speed of the car is $72\text{km/hr}$ and over a distance of $10\text{m}$ when the speed is $36\text{km/hr}$. Assuming that his reaction time and the acceleration of the car remain the same in all cases, find the distance over which he can stop the car when he is going at $54\text{km/hr}$.

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\dot{A}$ and ${\lambda }_2=5000\dot{A}$ then ratio of their respective resolving power is

A bar magnet falls with its North Pole pointing down through the axis of a copper ring. When viewed from above, the current in the ring will be

The current flowing through a wire depends on time as $I=3t^2+2t+5.$ The charge flowing through the cross-section of the wire in time from t = 0 to t = 2s is:

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth

A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

In the $n^{th}$ orbit, the energy of an electron $E_n=-\frac{13.6}{n^2}\text{eV}$ for hydrogen atom. The energy required to take the electron from first orbit to second orbit will be

Find the radius of gyration of a thin uniform rod of mass $M$ and length $L=3\text{m}$ about an axis passing through one end and perpendicular to rod as shown in figure.

A conducting ring of mass $2kg$ and radius $0.5m$ is placed on a smooth horizontal plane. The ring carries a current of $i=4A$.
A horizontal magnetic field $B=10T$ is switched on at time $t=0$ as shown in figure. The initial angular acceleration of the ring will be:

The displacement of the particle is given by $x=3t^2+2t$ in $\text{m}$. The average speed of the particle in $4\text{sec}$ is

Two blocks A and B of masses $m$ & $2m$ placed on smooth horizontal surface are connect with a light spring. The two blocks are given velocities as shown when spring is at natural length. Find maximum extension in the spring.

A ball is thrown from the ground to just clear a wall 3 m high at a distance of 6 m and falls 18 m away from the wall. The angle of projection of ball is