When a parachutist jumps from a height, its speed first increases with the distance fallen and then becomes constant. So, the graph given in option (d) best represents the given situation.

Brahmagupta was an Indian mathematician and astronomer who had written numerous important books on mathematics and astronomy. He anticipated Newton by declaring that all things gravitate to the earth.

If a fluid flows such that its velocity at a point is always the same in magnitude and direction, the fluid is said to have a streamline flow. The type of flow in a fluid system is characterized by the presence of laminae, or parallel streams of fluid. A streamline is a straight or curved path such that tangent to it at a point gives the direction of flow of liquid at that point. Thus, according to question the flow profile is best represented by figure (a).

As,
d = ut + (1/2)gt²
u = 0 (given)
d = (1/2)gt²
d ∞ t²

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. Thus, simple machine helps us in doing same amount of work with lesser force. Few examples of simple machines are pulley, lever, wheel, screw, etc.

It is observed that liquid drop tend to contract and appear spherical when it is set free from external forces like gravity, etc. Surface tension is the property among liquids due to which they tend to occupy minimum surface area. That’s why water droplet appears spherical because for a given volume, a sphere has minimum surface area. Due to this property of surface tension liquid surface stretches and behaves like a stretched membrane.

Scalars are quantities that have magnitude only; they are independent of direction. Vectors have both magnitude and direction. Momentum is the product of the mass and velocity of an object (p = mv). Momentum is a vector quantity, since it has a direction as well as a magnitude. The rest of quantities in option pressure, work and energy have magnitude but not direction.

Effective length is the length of point of suspension to the centre of gravity(mass) of a body. Let it be l when the girl is sitting and l’ when girl stands up. Here l > l’. Thus, the time period of swing will decrease because time period of swing is given by formula
T = 2π√(l/g)
So, it is clear from above formula that the time period of system is directly proportional to effective length.

Washing machine works on the principle of centrifugation. Centrifugation is a process that involves the use of the centrifugal force for the separation of mixtures with a centrifuge, used in industry and in laboratory settings. More-dense components of the mixture migrate away from the axis of the centrifuge, while less-dense components of the mixture migrate towards the axis.

An object on an inclined plane with inclination ? moves with an acceleration g sin q down the plane. The time taken to reach the bottom is given by

The velocity after time t is given by
v = u + gt
Here, u = 0, t = 2s, g = 9.8 m/s²
.’. v = 0 + (9.8*2) = 19.6 m/s

As monkey and bullet both fall under the same gravitational force, so bullet will hit exactly the same point it has been aimed.

Capillary action, or capillarity, is a phenomenon where liquid spontaneously rises in a narrow space such as a thin tube, or in porous materials such as paper or in some non-porous materials such as liquified carbon fibre. This effect can cause liquids to flow against the force of gravity or the magnetic field induction. In blotting of ink, spread of water drop on a cotton cloth and the rising of water from the roots of a plant to its foliage.

A “streamlined” design is one in which objects that move through a gas or liquid are shaped to match these lines, and therefore, reduce the energy required to produce that motion. Multi point fuel injection system injects fuel into individual cylinders, based on commands from the ‘on board engine management system computer—popularly known as the Engine Control Unit/ECU. These techniques result not only in better ‘power balance’ amongst the cylinders but also in higher output from each one of them, along with faster throttle response. The other two options radial tyres and catalytic converter with exhaust do not contribute to make the car more fuel efficient.

First statement can be explained on the basis of laws of motion. First statement involves the use of Newton’s third law of motion, “For every action there is an equal and opposite reaction”. In first case while whistling a man uses his breathe as a propellant to propel himself. The second statement can be explained on the basis of law of conservation of linear momentum according to which the momentum of body remains conserved until any external force acts upon it.

Mass is a universal constant. The mass of a body remains unchanged in any part of universe. Mass of a body does not change with respect to gravity. It is the weight that changes with gravity.

The bob of a simple pendulum is attached to a string which pulls the bob along its length.
Here B and C are extreme positions whereas A is mean position.The speed of the bob increases as it approaches the mean position A and continues to move till it reaches C. At C the speed becomes zero. Due to the unbalanced force the bob moves towards the mean position. The speed of the bob is maximum at the mean position and is zero at the extreme positions. Thus, it is clear that in each cycle bob velocity increases from zero to maximum. This means that it attains a given velocity twice. Suppose the bob of the pendulum reaches up to B while oscillating, then AB is the amplitude. For the next oscillation the bob fails to reach B but it will reverse the direction from point B¢ instead of B. The amplitude of oscillation in the second case is AB¢ which is less than AB. That means, a retarding force is acting on the bob thereby reducing the amplitude of oscillation. This retarding force is nothing but air-resistance or air-friction. At extreme position, acceleration is maximum. So statement 3 is not correct.

Figure (d) correctly represents the time-distance graph for one dimensional uniform motion.

Statement 1 is false. The temperature dependence of liquid viscosity is the phenomenon by which liquid viscosity tends to decrease (or, alternatively, its fluidity tends to increase) as its temperature increases. Thus, with increase of temperature viscosity of glycerine decrease. Statement 2 is correct because with the rise of temperature in case of liquid, the kinetic energy increases as kinetic energy of liquid molecules is directly proportional to absolute temperature.