When was "Jana Gana Mana" officially adopted as India's

If (a + b) = 1 and (1/a) – 2b = 5/a then find the value of a² + b².

For which value of k does the quadratic equation

x² − 4(k + 1)x + (3k² + 8k + 4) = 0

have equal real roots?

Find the value of ‘x’ in the given expression:

(49/16)^x × (64/343)^x-1 = 4/7

If p = 40 - q - r and pq + r(q + p) = 432, then find the value of (p² + q² + r²).

If x = (2+√3)/(2-√3), y = (2-√3)/(2+√3)

Then find out the value of (x²+y²-xy)/(x²+y²+xy)

If p = 24 - q - r and pq + r(q + p) = 132, then find the value of (p² + q² + r²).

if a² + b² + c² = 2(4a -5b -6c)-77 , then a-b-c = ?

If 1/(x+ 1/(y+ 1/z)) = 13/30, then find x+y+z= ?

Simplify the following expression:  (8x - 6y - 5z)  ²

Solve the system:

x + 2y = 13

3x − y = 5

What is the value of 2x + y?