In the arrangement shown in figure. The ratio of velocity V₁ & V₂ of block (1) & (2) is

Moment of inertia of a thin uniform semicircular wire having mass M, radius R and centre C about an axis passing through point O and perpendicular to its plane is

A uniform rod having length L, is made of material having density , coefficient of thermal expansion and young's modulus Y. It is placed between two vertical walls having separation L and coefficient of friction . What is the minimum rise in temperature so that the rod does not falls down on releasing

A block of mass m moving on the horizontal x-y plane having coefficient of friction . The particle has a velocity and acceleration Unit vector along the direction of friction force acting on the particle is

In wave, displacement of origin is varying according to of disturbance is propagating in + x direction with speed 2 cm/sec, then displacement of particle at x = 4 cm at t = 5 sec. is

A point-like object of mass 2.0 kg moves along the x-axis with a velocity of + 4.0 m/s. A net horizontal force acting along the x-axis is applied to the object with the force-time profile shown. What is the total work that was done by the force?

A mass on the end of a spring oscillates with the displacement versus time graph shown to the right. Which of the following statements about its motion is CORRECT?

Consider the cyclic process ABCA shown in figure, performed on a sample of 1 mole of an ideal gas. A total of 1000 J of heat is withdrawn from the sample in the process, the work done on the gas during part BC is 1830 J, the value of T_b is (R = 8.3 J/K-mole)

A rubber ball bounces on the ground as shown. After each bounce, the ball reaches one-half the highest of the bounce before it. If the time the ball was in the air between the first and second bounce was 1 second, what would be the time between the second and third bounce?

A monatomic ideal gas is used as the working substance for the Carnot cycle shown in the figure. Processes AB and CD are isothermal, while processes BC and DA are adiabatic. During process AB, 400 J of work is done by the gas on the surroundings. How much heat is expelled by the gas during process CD?

A projectle is fired horizontally from an inclined plane (of inclination 30° with horizontal) with speed = 50 m/s. If , range of the projectile measured along the incline is

The two points A and B in a plane are such that for all points P lies on circle satisfied  , then k will not be equal to

So here we have given the two points A and B in a plane are such that for all points P lies on circle satisfied . We can also use equation of circle to find the answer. So here the correct option is none of these.

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius. The locus of the centre of the circle is

So here we have given to find the locus is in which form. We used the concept of circles and solved the question. We can also use equation of circle to find the answer. So the locus is x²-10y+5=0, this is the representation of parabola, so correct answer is parabola. 

If d is the distance between the centres of two circles,  are their radii and , then

For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.

Assertion (A): The curve touches the x-axis.
Reason(R): touches the x-axis if

Assertion (A): When a>0 and has complex roots.
Reason(R): The graph of cuts x-axis.