Class 11

Math

Algebra

Sequences and Series

Sides of a triangle ABC are in A.P if a < minimum {b,c}, then cos A is equal to:

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Insert three arithmetic means between $23$ and $7$.

Find $x$, if the given numbers are in A.P. $(a+b)_{2},x,(a−b)_{2}$

In $△ABC,∑(sinAsin_{2}A+sinA+1 )$ is always greater than

If $a,b,c$ be positive and $ab(a+b)+bc(b+c)+ca(c+a)≥λ abc$, then value of $λ$ is

Let $A_{1}$ denotes arithmetic mean of two numbers $a=1$b=2. $A_{2}$ denotes arithmetic mean of $A_{1}$ and $b$. For $n≥3$,let $A_{n}$ is arithmetic mean of $A_{n}_{−1}$ and $b$ , then

The least value of $6tan_{2}ϕ+54cot_{2}ϕ$ is (I) $54$ when $A.M≥G.M$ is applicable for $6tan_{2}ϕ,54cot_{2}ϕ,18$(II) $54$ when $A.M≥G.M$ is applicable for $6tan_{2}ϕ,54cot_{2}ϕ,18$ is added further(III) $78$ when $tan_{2}ϕ=cot_{2}ϕ$

I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1II: If product of the two positive numbers is 400, then the minimum value of their sum is 20which of the above statements are true

Product of $n$ positive numbers is unit. The sum of these numbers can not be less than