When a strip made or iron `(alpha_(1))` and copper `(alpha_(2)),(alpha_(2) gt alpha_(1))` is heated

A bimetallic strip of thickness d and length L is clamped at one end at temperature t_(1) . Find the radius of curvature of the strip if it consists of two different metals of expansivity alpha_(1) and alpha_(2) (alpha_(1) gt alpha_(2) ) when its temperature rises to t_(2) "^(@)C .

If f(x+y)=f(x).f(y) for all x and y, f(1) =2 and alpha_(n)=f(n),n""inN , then the equation of the circle having (alpha_(1),alpha_(2))and(alpha_(3),alpha_(4)) as the ends of its one diameter is

If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

A bimetallic strip made of aluminium and steel (alpha_(Al) gt alpha_(steel)) on heating the strip will

A bimetallic strip made of aluminum and steel (alpha_(Al) gt alpha_(steel)) on heating the strip will a) remain straight b) get twisted c) will bend with aluminum on concave side d) will bend with steel on concave side.

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

If 1, alpha_(1), alpha_(2), alpha_(3),…….,alpha_(s) are ninth roots of unity (taken in counter -clockwise sequence in the Argard plane). Then find the value of |(2-alpha_(1))(2-alpha_(3)),(2-alpha_(5))(2-alpha_(7)) |.

The maximum value of (cosalpha_(1))(cos alpha_(2))...(cosalpha_(n)), under the restrictions 0lealpha_(1),alpha_(2)...,alpha_(n)le(pi)/(2) and (cotalpha_(1))(cotalpha_(2))......(cotalpha_(n))=1 is

The variance of observation x_(1), x_(2),x_(3),…,x_(n) is sigma^(2) then the variance of alpha x_(1), alpha x_(2), alpha x_(3),….,alpha x_(n), (alpha != 0) is

let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4)) be an identity in x, where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are independent of x. Then find the value of alpha_(1)alpha_(2)alpha_(3)alpha_(4)