Class 11

Math

Algebra

Sequences and Series

If a, b, c are in AP, show that $(b+c−a),(c+a−b),(a+b−c)$ are in AP.

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Multiplied by 3 and then divided by 2.

If $32 ,k,85k $ are in A.P. then $k=$

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

The minimum value of $4e_{x}+9e_{−X}$ is

The minimum value of $a_{2}sec_{2}θ+b_{2}cosec_{2}θ$ is

Insert $x$ arithmetic means between $x_{2}$ and $1$.

In any $ΔABC,Π(sinAsin_{2}A+sinA+1 )$ is always greater than

Prove that the product of $n$ geometric mean between any two numbers is $nth$ power of their $G.M$.