The number of solutions of the equation $x ^2+ y ^2= a ^2+ b ^2+ c ^2$. where $x , y , a , b , c$ are all prime numbers, is
$0$
$1$
more than $1$ but finite
infinite
If $x$ is real and $k = \frac{{{x^2} - x + 1}}{{{x^2} + x + 1}},$ then
Number of integers satisfying inequality, $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}\,{x^3}}}{{{{\log }_3}\,\frac{1}{3}}} + 2 > 0$ is
If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is
If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$