Class 11

Math

Algebra

Sequences and Series

The geometric mean of $6$ and $54$ is

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The geometric mean if the series $1,2,4,.....2_{n}$ is

Let $f(x)=x_{2}+x +x_{2}+x tan_{2}α ,αϵ(0,2π ).$ The value of $f(x)$ is always greater than or equal to

Assertion :Statement-1 : The least value of $(tanAtan_{2}A+tanA+1 )$ is $3$, where $A∈(π,23π )$. and Reason :Statement-2 : $A.M.≥G.M.$ for all positive numbers.

$(x−4)$ is geometric mean of $(x−5)$ and $(x−2)$ find $x$.

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 $tan_{2}ϕ=cot_{2}ϕ$

x and y are two +ve numbers suchs that xy =1. Then the minimum value of x + y is

If a, b, c are in AP; x is the GM between a and b; y is the GM between b and c; then show that $b_{2}$ is the AM between $x_{2}$ and $y_{2}$.

The least length of the thread required to construct a rectangle of area 256 $cm_{2}$ is