The rate of change of  with respect to  at  is

If  then    is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

The domain of the function is

Range of the function is

The domain of the function is

Let , and , then dom is given by

In the adjacent diagram, represents a wavefront and and , the corresponding two rays. Find the condition on for constructive interference at P between the ray and reflected ray

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

is relation on given by Which of the following belongs to ?

Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle under the influence of magnets. The ratio of distances d₁ and d₂ will be

Two small magnets X and Y of dipole moments M₁ and M₂ are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is

Find the resultant magnetic moment for the following arrangement

A modulating signal is a square wave as shown in the figure

The carrier wave is given by The modulation index is

In the P-V diagram shown in figure ABC is a semicircle. The work done in the process ABC is