Statement-I : If 27 abc ≥ (a + b + c)³ and 3a + 4b + 5c = 12 then  where a, b, c are positive real numbers.
Statement-II : For positive real numbers A.M. ≥ G.M.

Statement-I : Minimum value of  
Statement-II : The least value of a sin q + b cosq is 

At point of intersection of the two curves shown, the conc. of B is given by …….. For,:

Following is the graph between log and log a (a initial concentration) for a given reaction at 27^oC. Hence, order is

Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed

inradius is the radius of the circle inscribed inside a polygon.

Statement-I : For n  N, 2n > 1 + n 
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2

for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1

Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.

the mathematical reasoning can be proved by observing the term of the sequences

Let p, q, r  R+ and 27 pqr ≥ (p + q + r)³ and 3p + 4q + 5r = 12 then p³ + q⁴ + r⁵ is equal to -

for real and positive numbers, we can use the property AM>=GM

For the chemical reaction , the rate of formation of  is 0.04 mole lit^-1sec^-1. Determine the rate of disappearance of 

If a homogenous catalytic reaction follows three alternative paths and then which of the following indicates the relative ease with which the reaction moves?

For the reaction (g), at 900 K. following data are observed.

Find out the rate law and order of reaction -

During the transformation of the number of emitted is

For which positive integers n is the ratio, an integer?

an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements. the variable n is generalized using an AP as well.

A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, unit up, unit to the right, unit down, unit to the right etc. The length of each move is half the length of the previous move and movement continues in the ‘zigzag’ manner indefinitely. The co-ordinates of the point to which the ‘zigzag’ converges is

the problem states that the particle’s movement follows a geometric progression with the first term being 1 and the ratio being ½ and the particle moves infinitely.
The ratio in the x direction is ¼ . The ratio in the y direction is -1/4

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

the Am- Gm relation is a handy tool for solving sequence related problems. it is applicable to any sequence of numbers.

Let and are two arithmetic sequences such that and then the value of is

an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements