In which year were the National Awards to Teachers first

The ratio of roots of the equation mx² + nx + n = 0 is α/ β = a/b, then find the value of `sqrt(a/b)+sqrt(b/a)+sqrt(n/m)`

If (5√P - 7√Q) = 5, [1.5P = 4Q-(R/3)+9] and (√P/√Q) = 1.6, then find out the value of ‘R’.

The slope of the equation  24x+ 8y =56 is

I. p² – 5p + 6 = 0                  

II. 36q² = 81

If, x - y radic; 3 = 23 and radic; 3x + y = 35

Find the angle between both the lines when they intersect each other.

If x - √3 y = 8 Find the slope in angle?

I. 8/(√x) + 6/(√x) = √x

II. y ³- (14)^7/2 /(√y) = 0

If in two linear equations ax + by = c and dx + ey = f and a/d = b/e = c/f  then, which of the following is true about the two equations?

For which value of m, there is no solution to the equation -

a – b = 5

ma – 4b = 1