Statement-I : If x₂y₃ = 6(x, y > 0), then the least value of 3x + 4y is 10
Statement-II : If m₁, m₂  N, a₁, a₂ > 0 then  and equality holds when a₁ = a₂.

Statement-I : If a, b, c are three distinct positive number in H.P., then 
Statement-II : Sum of any number and it's reciprocal is always greater than or equal to 2.

when some numbers are in HP, then their reciprocals are in AP.

Statement-I : In any ΔABC, maximum value of r₁ + r₂ + r₃ =9R/2.
Statement-II : In any ΔABC, R ≥ 2r.

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.

a,b,c are positive real numbers
=>  AM>= GM can be applied to these numbers
for real and positive numbers, we can use the property AM>=GM

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.