Small Quiz

3

QUESTION 1

If x²-3x + 1 = 0, then the value of x²+x+1/x+1/x²  is?

10
 

2
 

 6
 

8

QUESTION 2

If xy + yz + zx = 0, then (1/(x²-yz)+1/(y²-zx)+1/(z²-xy)) (x, y, z ≠ 0)?

 3
 

 1
 

 x + y + z
 

 0

QUESTION 3

If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a²+b²+c² is

 100
 

 9
 

27
 

81

QUESTION 4

If x ≠ 0, y ≠ 0 and z ≠ 0 and 1/x² +1/y² +1/z² =1/xy+1/yz+1/zx then the relation among x, y, z is

x + y + z = 0
 

 x + y = z
 

 1/x+1/y+1/z=0
 

x = y = z

QUESTION 5

If a + b = 1, c + d = 1 and a – b = d/c, then the value of c²-d²

 a/b
 

 b/a
 

 1
 

 -1

QUESTION 6

 If x = 3t, y = 1/2(t + 1), then the value of t for which x = 2y is

) 1


 

1/2


 

-1
 

 2/3

 

QUESTION 7

If the equation 2x²-7x+12=0 has two roots α and β, then the value of α/β+β/α is

7/2
 

1/24
 

7/24
 

 97/24

QUESTION 8

If x=?5+2, then the value of x³-6x²+12x-13

 -1
 

 1
 

 2
 

 0

QUESTION 9

If x²+9y²=6xy, then x : y is

 1 : 3
 

3 : 2
 

 3 : 1
 

 2 : 3

QUESTION 10

Internal bisectors of angle B and C of triangle ABC intersect at O. If angle BOC = 102°, then the value of angle BAC is

 12°
 

 24°
 

48°
 

 60°