Quiz 1

Discriminant = b² - 4ac

Given that a = 2k, b = 5k, c = 2

b² - 4ac = 0

(5k)² - 4(2k)(2) = 0

25k² - 16k = 0

k(25k - 16) = 0

k = 0 or 25k - 16 = 0

k = 0 or k = 16/25

Answer: k = 0 or k = 16/25

given, (m⁶ + m⁴ + m² + 1)/m³

=(m⁶/m³ + m⁴/m³ + m²/m³ + 1/m³)

=(m³ + m + 1/m + 1/m³)

now, m = (2 - √3)------------( 1 )

=>m³= (8 - 3√3 - 6√3(2 - √3)

=>m³ = (8 - 3√3 - 12√3 + 18)

=>m³= (26 - 15√3)-----------( 2 )

1/m = [1/(2 - √3)] * [(2 + √3)/(2 + √3)]

=>1/m= (2 + √3)/(4 - 3)

=>1/m= (2 + √3)------------( 3 )

1/m³= [1/(26 - 15√3)] * [(26 + 15√3)/(26 + 15√3)]

=>1/m³ = (26 + 15√3)/(676 - 675)

=>1/m³= (26 + 15√3)-------------( 4 )

adding------( 1 ) , --------( 2 ) , --------( 3 ) & --------( 4 )

(m + 1/m + m³ + 1/m³)

= (2 - √3 + 2 + √3 + 26 - 15√3 + 26 + 15√3)

= (4 + 52)

= 56

Hence, (m⁶ + m⁴ + m² + 1)/m³ = 56

d) none of these 

as :

y is always more than x becomes false in case of x=1 (y=1^1=1) (x becomes equal to y)

x is always more than y and x is always equal to y becomes false in case of x=2 (y=2^2=4)(y becomes greater than x)

(c) X is more than 0 but less than 1 

cause 

33×812×20/95 =535920/95 =5641.2632

D) NONE OF THESE

x/[(0.81)^1/2] =81

=>x = [(0.81)^1/2] x 81

=>x = 0.9 x 81

=>x=72.9

6^{x-3}=36^{x-5}

=>6^{x-3}=6^{2(x-5)}

=>x-3 = 2x - 10

=>x = 7

If there are \'x\' members in a family, father took 1/5 of the cake, so remaining 4/5 cake will be distributed among (x-1) members, so each member will get (4/5)/(x-1)

As 1/5 =4*(4/5)/(x-1)

x=17

0.1^{3}=1/x

x=1000

a^x = b^y

⇒log a^x=log b^y

⇒x(log a)=y(log b)

⇒log a/log b=y/x