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Algebra
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Algebra
TEST : 4
# Algebra
# General Aptitude
Prepare / Learn
Q1.
If x
2
+ y
2
= 29 and xy = 10, where x>0, y>0, x>y then the value of c
is
A.
-7/3
B.
7/3
C.
3/7
D.
-3/7
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
Given, x
2
+ y
2
= 29 and xy = 10, where x > 0, y > 0, x > y
# Algebra
# General Aptitude
Prepare / Learn
Q2.
What will be the value of
if a+b+c = 0 and a
2
+b
2
+c
2
= 2abc ?
A.
abc
B.
a
2
b
2
c
2
C.
a
3
b
3
c
3
D.
4abc
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
Given a+b+c = 0
⇒b+c = -a
⇒(b+c)
2
= a
2
⇒b
2
+ c
2
+ 2bc = a
2
⇒a
2
+ b
2
+ c
2
= 2(a
2
- bc)
⇒(
a
2
- bc) = (1/2)(a
2
+ b
2
+ c
2
)
Similarly,
(b
2
- ac) = (1/2)(a
2
+ b
2
+ c
2
)
And, (c
2
- ab) = (1/2)(a
2
+ b
2
+ c
2
)
Now,
# Algebra
# General Aptitude
Prepare / Learn
Q3.
If p
3
– q
3
= (p – q) {(p + q )
2
– x p q} then the value of x is
A.
1
B.
-1
C.
2
D.
-2
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
On comparing the coefficient, we get
# Algebra
# General Aptitude
Prepare / Learn
Q4.
LCM of two polynomials is x
3
+ x
2
- 4x - 4 is and their HCF is (x-2) and one of the polynomials is (x
2
-4) then which of the following is the 2nd polynomial?
A.
x
2
-x-2
B.
x
2
-3x+2
C.
x
2
+x-6
D.
x
2
-5x+6
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
LCM =
x
3
+ x
2
- 4x - 4 = x(x
2
-4)+1(x
2
-4) = (x+1)(x-2)(x+2)
HCF = (x-2)
Som 2nd polynomials = (x+1)(x-2)(x+2)(x-2)/(x
2
-4) = (x+1)(x-2) = x
2
-x-2
# Algebra
# General Aptitude
Prepare / Learn
Q5.
If
then the value of (a
4
– a) is:
A.
0
B.
1
C.
2
D.
-1
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# Algebra
# General Aptitude
Prepare / Learn
Q6.
What is the value of m in the quadratic equation x
2
+ mx +24=0 if one of its roots is
A.
-45/2
B.
16
C.
-21/2
D.
-35/2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
X =
3/2 in x
2
+ mx + 24 = 0
(3/2) + m*(3/2) + 24 = 0
(9/4) + (3m/2) + 24 = 0
# Algebra
# General Aptitude
Prepare / Learn
Q7.
a = 1000, b = 1001, c = 1002. then find the value of
.
A.
0
B.
1
C.
2
D.
3
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Algebra
# General Aptitude
Prepare / Learn
Q8.
Sum of three consecutive even integers is 54. Find the least among them
A.
18
B.
15
C.
14
D.
16
View Solution
Add Work Space
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
# Algebra
# General Aptitude
Prepare / Learn
Q9.
+
= ?
A.
1
B.
0
C.
-1
D.
2
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
+
+
= 1
# Algebra
# General Aptitude
Prepare / Learn
Q10.
If
+
= 2 and
+
= 1 than find (ZQ – PX)
2
+ (ZX + PQ)
2
A.
-1
B.
0
C.
4/9
D.
2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
Z
2
+ P
2
= 2 ; X
2
+ Q
2
= 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
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