`3^r` divides `50!` then maximum value of `r=`

Express 2cos theta + 3 sin theta in the form r cos ( theta - alpha ), where r is positive, stating the values of r and alpha. What is the maximum value of 2 cos theta + 3 sin theta ?

If 2p+3q+4r=15, the maximum value of p^(3)q^(5)r^(7) will be

If theta in [0,5pi] and r in R such that 2sintheta=r^4-2r^2+3 then the maximum number of values of the pair (r,theta) is.....

If theta in [0,5pi] and r in R such that 2sintheta=r^4-2r^2+3 then the maximum number of values of the pair (r,theta) is.....

If theta in [0,5pi] and r in R such that 2sintheta=r^4-2r^2+3 then the maximum number of values of the pair (r,theta) is.....

If theta in [0, 5 pi] and r in R such that 2 sin theta = r^(4) - 2 r^(2) + 3 then the maximum number of values of the pair (r, theta) is

If theta in[0,5 pi] and r in R such that 2sin theta=r^(4)-2r^(2)+3 then the maximum number of values of the pair (r,theta) is....

If R is remainder when 6^(83)+8^(83) is divided by 49, then the value of R//5 is.