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What is the difference between half-life and duration?

The duration is the time period and the half-life of a radioactive substance is the duration for half of the atomic nuclei of the radioactive... View Article

What is a diamagnetic ion?

A compound is diamagnetic if it does not have any unpaired electron. Zn2+ is an example of a diamagnetic compound.... View Article

How do plants use capillary action?

Capillary action is the movement of liquid along the surface of the solid caused by the attraction between the liquid molecules and the solid... View Article

Are all gases ideal

An ideal gas is a hypothetical concept that helps us learn the behaviour of real gases. At room temperature and at atmospheric pressure many of... View Article

Can I use a transformer as an inductor?

Yes, the transformer can be used as an inductor The connections can be made to one winding of the transformer to make it an inductor. The... View Article

Which current is used in home

Alternating current is the most commonly used form of current used at homes all around the world. The alternating current can be transmitted over... View Article

What does a diode do

The main purpose of a diode is to allow the flow of current in only one direction. The diode has minimum resistance in one direction and maximum... View Article

What is Rayleigh law?

Rayleigh scattering is the scattering of light by the particles present in the atmosphere. According to Rayleigh scattering law, the amount of... View Article

Can I use any transistor?

No. All the transistor parameters must match with the requirement only then it can be used. Different designs of the transistors have a different... View Article

How do you use Boolean logic?

Boolean logic is a form of algebra in which the variables have only two values 0 and 1. 1 is true and 0 is false. The boolean logic is applied by... View Article

What is the efficiency formula?

In science, efficiency is given by the ratio of the output energy to the input energy. The energy is in the form of heat or power. The energy... View Article

The points on the curve y³ + 3x² = 12y where the tangent is vertical (parallel to the y-axis), is (are)

1) (± 4 / √3, -2) 2) (± √11 / 3 + 1) 3) (0, 0) 4) (± 4 / √3, 2) Solution: (4) (± 4 / √3, 2) y3 + 3x2 = 12y 3y2 (dy / dx) + 6x =... View Article

If the normal to the curve y = f (x) at the point (3, 4) makes 3π / 4 with the postive x-axis then f’ (3) =

1) -1 2) -3 / 4 3) 4 / 3 4) 1 Solution: (4) 1 y = f (x) dy / dx = f’ (x) Slope of normal = -1 / f’ (x)3,4 = - 1 / f’ (3) - 1 /... View Article

At what points of the curve y = (2 / 3)x³ + (1 / 2)x², tangent makes the equal anlge with the axis

1) (1 / 2, 5 / 24) and (-1, -1 / 6) 2) (1 / 2, 4 / 9) and (-1, 0) 3) (1 / 3, 1 / 7) and (-3, 1 /2) 4) (1 / 3, 4 / 47) and (-1, -1 / 3)... View Article

If y = 4x – 5 is tangent to the curve y² = px³ + q at (2, 3), then

1) p = 2, q = –7 2) p = – 2, q = 7 3) p = –2, q = –7 4) p = 2, q = 7 Solution: (1) p = 2, q = –7 y2 = px3 + q 2y (dy / dx) = 3px2... View Article

The distance travelled s (in metre) by a particle in t seconds is given by, s = t³ + 2t² + t. The speed of the particle after 1 second will be

1) 8 cm/sec 2) 6 cm/sec` 3) 2 cm/sec 4) None of these Solution: (1) 8 cm/sec s = t3 + 2t2 + t v = ds / dt = 3t2 + 4t + 1 At t =... View Article

The radius of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is

1) (2 / 3) R 2) √(2 / 3) R 3) (3 / 4) R 4) √(3 / 4) R Solution: (2) √(2 / 3) R... View Article

A man height 1.8 metre is moving from a lamp post at the rate of 1.2 m/sec. If the height of the lamp post be 4.5 metre, then the rate at which the shadow of the man is lengthening is

1) 0.4 m/sec 2) 0.8 m/sec 3) 1.2 m/sec 4) None of these Solution: (2) 0.8 m/sec dy / dx = 1.2 According to the figure, (4.5 /... View Article

The volume of a spherical balloon is increasing at the rate of 40 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 8 centimetre, is

1) (5 / 2) sq.cm/min 2) 5 sq. cm/min 3) 10 sq.cm/min 4) 20 sq. cm/min Solution: (3) 10 sq.cm/min V = (4 / 3) πr3 and S = 4πr2... View Article

Let f : (0, + ∞) → R and F (x) = integral from 0 to x f (t) dt. If F (x²) = x² (1 +x), then f (4) =

1) 5 / 4 2) 7 3) 4 4) 2 Solution: (3) 4 x2 (1 + x) = ∫0x^2 f (t) dt 2x (1 + x) + x2 = f (x2) 2x f (x2) = 1 + x + (x / 2), x >... View Article

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