$\begin{align}  & {{4243}_{5}} \\ & \underline{13x{{4}_{5}}} \\ & \underline{y{{344}_{5}}} \\\end{align}$Find x and y respectively in the subtraction above carried out in base 5.

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64cm.long, find the length of a pendulum whose period is 9sec.

Find the sum to infinity $\tfrac{1}{2},\tfrac{1}{6},\tfrac{1}{18}---$

Factorize completely $ac-2bc-{{a}^{2}}+4{{b}^{2}}$

if $P=\left( \begin{matrix}   1 & 0 & -1  \\   3 & 4 & 5  \\   -1 & 0 & 1  \\\end{matrix} \right)$, then $\left| P \right|$ is

The n^th term of two sequences are ${{Q}_{n}}=3\cdot {{2}^{n+2}}$ and ${{U}_{m}}=3\cdot {{2}^{2m-3}}$. Find the product of Q₂ and U₂

Find the remainder when $3{{x}^{3}}+5{{x}^{2}}-11x+4$is divided by x + 3

If the operation * on the set of integer is defined by $p*q=\sqrt{pq}$, find the value of $4*(8*32)$

The shaded area in the diagram above is represented by

Given that the first and fourth term of a G.P are 6 and 162 respectively. Find the sum of the first three term of the progression