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## Algebra Level 2 Test 3

Congratulations - you have completed Algebra Level 2 Test 3. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
If the roots of the equation (c2 - ab) x2 - 2 (a2 - bc) x + (b2 - ac) = 0 for a is not equal to 0 are real and equal, then the value of a3 + b3 + c3 is
 A abc B 3abc C zero D None of these
Question 1 Explanation:
We are given by that the roots are real and equal, that means we have
= b2- 4ac = 0
Therefore the equation becomes
[-2(a2 - cb) ]2 - 4 (c2 - ba) (b2 - ac) = 0
On solving we have
4a (a3 + b3 + c3 â€“ 3abc) = 0
Therefore the value of a3 + b3 + c3 = 3abc
 Question 2
If 2x2 -7xy + 3y2 = 0, then the value of x: y is
 A 3 : 2 B 2 : 3 C 3 : 1 and 1 : 2 D 5 : 6
Question 2 Explanation:
2x2 -7xy + 3y2 = 0
2 (x/y)2 â€“ 7(x/y) +3 = 0
x/y = {-b + ^(b2 â€“ 4ac) } / 2a
= {7 + ^(49 â€“ 24)} / 2 x 2 = (7+ 5) / 4 = 3, Â½
Therefore the value of x/y = 3/1 and x/y = Â½
 Question 3
If (a + b + 2c + 3d) (a - b â€“ 2c + 3d) = (a - b + 2c - 3d) x (a + b â€“ 2c - 3d), then 2bc is equal to
 A 3ad B 3/2 C a2d2 D 3a/2d
Question 3 Explanation:
(a + b + 2c + 3d) (a - b â€“ 2c + 3d) = (a - b + 2c - 3d) x (a + b â€“ 2c - 3d)
Therefore [(a+b) + (2c -3d) x (a + b â€“ 2c - 3d)
= Â Â [(a-b) + (2c -3d)] x [(a + b â€“ (2c - 3d)]
=(a+b)(a-b) â€“ (a+b)(2c â€“ 3d) + (a â€“ b)(2c â€“ 3d) â€“ (2c +3d)(2c -3d)
OnÂ  further solving
= 2ac +3ad -2bc -3bd = 2ac - 3ad + 2bc - 3bd
 Question 4
If X=4ab/(a+b), a+-b, then the value of (x +2a)/(x â€“ 2a) + (x +2b)/(x â€“ 2b) is
 A 0 B 1 C 2 D None of these
Question 4 Explanation:
(x +2a)/(x â€“ 2a) + (x +2b)/(x â€“ 2b
Put values of x in the expression we will get
[{(6ab + 2a2)/(a+b)} / {(2ab â€“ 2a2)/(a+b)}] + [{(6b2 + 2ab)/(a+b)} / {(2ab â€“ 2b2)/(a+b)}]
= {2a(3b + a)/2a(b â€“ a)} + {2b (3b+a) / 2b (a â€“ b)}
(3b + a)/ (b â€“ a) â€“ (3b + a)/ (b â€“ a) = 0
 Question 5
Richa's age is1/6th of Natasha 'sage. Natasha 's age will be twice of Sona 's age after 10 yr. If Sona' s eight birthday was celebrated two yr ago, then the present age of Richa Â must be
 A 5 yr B 10 yr C 15 yr D 20 yr
Question 5 Explanation:
Given that Age of Richa = 1/6 age of Natasha
Present age of Sona = 10 years
That means
Natasha + 10 = 2( Sona + 10)
Therefore Natasha + 10 = 40
Natasha = 30
Therefore the age of Richa = 5 years
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