Algebra - Online Test
Q1. If x2 + y2 = 29 and xy = 10, where x>0, y>0, x>y then the value of c
is
is
Answer : Option B
Explaination / Solution:
Given, x2 + y2 = 29 and xy = 10, where x > 0, y > 0, x > y
Q2. What will be the value of 
if a+b+c = 0 and a2+b2+c2 = 2abc ?
if a+b+c = 0 and a2+b2+c2 = 2abc ?
Answer : Option B
Explaination / Solution:
Given a+b+c = 0
⇒b+c = -a
⇒(b+c)2 = a2
⇒b2 + c2 + 2bc = a2
⇒a2 + b2 + c2 = 2(a2 - bc)
⇒(a2 - bc) = (1/2)(a2 + b2 + c2)
Similarly,
(b2 - ac) = (1/2)(a2 + b2 + c2)
And, (c2 - ab) = (1/2)(a2 + b2 + c2)
Now,
Q3. If p3 – q3 = (p – q) {(p + q )2 – x p q} then the value of x is
Answer : Option A
Explaination / Solution:
On comparing the coefficient, we get
Q4. LCM of two polynomials is x3 + x2 - 4x - 4 is and their HCF is (x-2) and one of the polynomials is (x2-4) then which of the following is the 2nd polynomial?
Answer : Option A
Explaination / Solution:
LCM = x3 + x2 - 4x - 4 = x(x2-4)+1(x2-4) = (x+1)(x-2)(x+2)
HCF = (x-2)
Som 2nd polynomials = (x+1)(x-2)(x+2)(x-2)/(x2-4) = (x+1)(x-2) = x2-x-2
Q5. If 
then the value of (a4 – a) is:
then the value of (a4 – a) is:
Answer : Option A
Explaination / Solution:
Q6. What is the value of m in the quadratic equation x2 + mx +24=0 if one of its roots is 
Answer : Option D
Explaination / Solution:
X =
3/2 in x2 +
mx + 24 = 0
(3/2) + m*(3/2) + 24 = 0
(9/4) + (3m/2) + 24 = 0
Q7. a = 1000, b = 1001, c = 1002. then find the value of 
.
.
Answer : Option D
Explaination / Solution:
Q8. Sum of three consecutive even integers is 54. Find the least among them
Answer : Option D
Explaination / Solution:
Let three consecutive even integers by 2x, 2x + 2 and 2x + 4. respectively
2x + 2x + 2 + 2x + 4 = 54
6x + 6 = 54
Q9. 
+ 
= ?
+ = ?
Answer : Option A
Explaination / Solution:
+ 
+ 
= 1
+ + = 1
Q10. If 
+ 
= 2 and 
+ 
= 1 than find (ZQ – PX)2 + (ZX + PQ)2
+ = 2 and + = 1 than find (ZQ – PX)2 + (ZX + PQ)2
Answer : Option D
Explaination / Solution:
Z2 + P2 = 2 ; X2 + Q2 = 1
Let Z = 1 and X = 1/√2
P = 1 Q = 1/√2
(ZQ – PX )2 + (ZX + PQ)2 = ((1/√2) - (1/√2)2 + ((1/√2) + (1/√2))2
0 + (4/2) = 2
