
Q1. If x^2-3x + 1 = 0, then the value of x^2 + x + (1/x) + (1/x^2) is
(a) 10
(b) 2
(c) 6
(d) 8
Q3. If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a^2+b^2+c^2 is
(a) 100
(b) 9
(c) 27
(d) 81
Q5. If a + b = 1, c + d = 1 and (a – b) = (d/c), then the value of c^2 – d^2
(a) a/b
(b) b/a
(c) 1
(d) -1
Q8. If x=∛5+2, then the value of x^3-6x^2+12x-13
(a) -1
(b) 1
(c) 2
(d) 0
Q9. If x^2+9y^2=6xy, then x : y is
(a) 1 : 3
(b) 3 : 2
(c) 3 : 1
(d) 2 : 3
Solutions
S8. Ans.(d)
Sol. x = ∛5+2
⇒ x – 2 = ∛5
Take cube on both sides
⇒(x-2)^3=(∛5)^3
⇒x^3-8-3×2×x(x-2)=5
⇒x^3-8-6x^2+12x=5
∴x^3-6x^2+12x-13=0
S9. Ans.(c)
Sol. x^2+9y^2=6xy
⇒x^2+9y^2-6xy=0
⇒x^2+(3y)^2-2×3y×x=0
⇒(x-3y)^2=0
x-3y=0
⇒ x = 3y
∴ x : y = 3 : 1