Algebra - Online Test

Q1. Simplify: 
Answer : Option C
Explaination / Solution:



Q2. If  then:
Answer : Option D
Explaination / Solution:



Q3. If  then y is equal to
Answer : Option D
Explaination / Solution:



Q4. If and the value of is
Answer : Option C
Explaination / Solution:

X+y=5 
Cubing both sides, we get:
x3+y3+3xy(x+y)=125 OR xy = 6
((1/x) + (1/y)) = (x+y)/xy=5/6

Q5. If  and xyz = 288, the value of 
Answer : Option B
Explaination / Solution:




Q6. If ab + bc + ca = 0, then the value of  is
Answer : Option C
Explaination / Solution:

ab + bc + ca = 0 ⇒ bc = -ab –ac and similar for others 
Hence 


Q7. If  and the value of  is
Answer : Option A
Explaination / Solution:



Q8. If  then the value of is
Answer : Option B
Explaination / Solution:



Q9. If (2x)(2y) = 8 and (9x)(3y) = 81, then (x, y) is :
Answer : Option A
Explaination / Solution:

(2x)(2y) = 8 = 23
Applying the law of indices 
x + y = 3----- eqn 1 
(9x)(3y) = 81 = 34 
2x + y = 4----- eqn 2 
Solving the two equations simultaneously we get x=1 
And substituting the value of x in any of the two equations y=2 

Hence option A is correct

Q10. If , then the value of  is
Answer : Option B
Explaination / Solution: