Q2. If a ≠ b, then which of the following statements is true?
(a) (a+b)/2=√ab
(b) (a + b)/2<√ab
(c) (a + b)/2>√ab
(d) All of the above
Q6. If √x=√3-√5, then the value of x^2-16x+6 is
(a) 0
(b) -2
(c) 2
(d) 4
Q10. If √3tanθ = 3sinθ, then the value of (sin^2 θ-cos^2 θ ) is
(a) 1
(b) 3
(c) 1/3
(d) None of these
Solutions
S2. Ans.(c)
Sol. Given that a ≠ b
Let a = 16, b = 4
∴ by options
So, (a + b)/2=(16 + 4)/2 = 10
and √ab=√(16×4) = 8
∴ (a+b)/2>√ab
∴ option (c) is correct
S6. Ans.(c)
Sol. √x=√3-√5
x=3+5-2√3√5
x=8-2√5×√3
x-8=-2√15
(Squaring both sides)
x^2+64-16x=60
x^2+4-16x=0
x^2+6-16x=2
