Tamil Nadu Board Solutions for Chapter: Algebra, Exercise 15: Exercise 3.4

Find the unit digit of ${124}^{128}\times {126}^{124}$.

Find the unit digit of the numeric expression ${16}^{23}+{71}^{48}+{59}^{61}$.

If $p=-2, q=1$ and $r=3$, then find the value of $3p^2{q}^{2}r$.

LEADERS is a WhatsApp group with $256$ members. Every one of its member is an admin for their own WhatsApp group with $256$ distinct members. When a message is posted in LEADERS and everybody forwards the same to their own group, then how many members in total will receive that message?

Find $x$, such that $3^{x+2}=3^x+216$.

If $X=5x^2+7x+8$ and $Y=4x^2-7x+3$, then find the degree of $X+Y$.

Find the degree of $\left(2a^2+3ab-b^2\right)-\left(3a^2-ab-3b^2\right)$.

Find the value of $w$, given that $x=3, y=4, z=-2$ and $w=x^2-y^2+z^2-xyz$.