Practice Aptitude Questions (Algebra) With Solutions Set-61:
Dear Readers, Important Aptitude Questions for SSC/FCI Exam was given here with solutions, candidates those who are preparing for those exams can use this material.
1).If
a + [1 / (a – 2) ] = 4, then the value of (a – 2)2 + [ 1 / (a – 2) ]2
is
a)
0
b)
2
c)
- 2
d)
4
2).If
a + b + c = 2s, then
[ (s – a)2 + (s – b)2 +
(s – c)2 + s2 ] / (a2 + b2 + c2
) is equal to
a)
a2 + a2 + a2
b)
0
c)
1
d)
2
3).If
xy (x + y) = 1 the, the value of [1 / (x3 y3) ] - (x3
- y3) is
a)
3
b)
-3
c)
1
d)
-1
4).If
(a3 – b3 – c3 ) = 0 then the value of a9
– b9 – c9 - 3a3 b3
c3
a)
1
b)
2
c)
0
d)
-1
5).The
minimum value of (x – 2)(x – 9) is
a)
– (11 / 4)
b)
49 / 4
c)
0
d)
– (49 / 4)
6).If
x + y + z = 6 and (x2 + y2 + z2 ) = 20 then
the value of x3 + y3 + z3 – 3xyz is
a)
64
b)
70
c)
72
d)
76
7).The
third proportional to [ (x / y) + (x / y) ] and √(x2 + y2)
is
a)
xy
b)
√xy
c)
3√xy
d)
4√xy
8).If
a : b = 2 : 3, b : c = 4 : 5 and c : d =
6 : 7, then a : d =
a)
12 : 35
b)
24 : 35
c)
16 : 35
d)
24 : 25
9).The
value of √(3√0.000729) is
a)
0.03
b)
0.09
c)
0.9
d)
0.3
10).If
the average of x and 1 / x be 1, then the value of x10 + (1 / x10)
a)
-2
b)
2
c)
0
d)
1
Answers:
1).
b) 2). c) 3).
a) 4). c) 5).
d) 6). c) 7).
a) 8). b) 9).
d) 10). b)
Solution:
1).
a + 1 ( a – 2) = 4
=
( a – 2) + (1 / ( a – 2) ) = 4 – 2 = 2
On
squaring
=
(a – 2)2 + (1 / ( a – 2)2 ) + 2 = 4
=
(a – 2)2 + (1 / ( a – 2)2 ) = 2
Answer: b)
2).
[ (s – a)2 + (s – b)2 + (s – c)2 + s2 ]
/ (a2 + b2 + c2 )
=
[ s2 + 2sa + a2 + s2 + b2 – 2sb + s2
– 2sc + c2 + s2 ] / (a2 + b2 + c2
)
=
[ 4s2 + a2 + b2 + c2 – 2s (a + b +
c) ] / (a2 + b2 + c2 )
=
[ 4s2 + a2 + b2 + c2 – 4s2
] / (a2 + b2 + c2 ) = 1
Answer: c)
3).
xy (x + y) = 1
=>
x + y = 1 / xy
Cubing
both sides,
x3
+ y3 + 3xy (x + y) = 1
/ x3 y3
=
x3 + y3 + 3 × 1 =
1 / x3 y3
=
(1 / x3 y3 ) - x3
- x3 = 3
Answer: a)
4).
If a + b + c =0, then a3 + b3 + c3 – 3abc = 0
Answer: c)
5).
Expression = (x – 2)(x – 9)
=
x2 – 11x + 18 = ax2 + bx + c
Minimum Value =
(4ac – b2) / 4a
= (4 × 1 × 18 –
121) / 4 = -(49 / 4)
Answer: d)
6).
x + y + z = 6
On
squaring,
x2
+ y2 + z2 + 2xy + 2zy + 2zx = 36
ð 20 + 2 (xy + yz + zx) = 36
ð xy + yz + zx = 8
∴x3
+ y3 + z3 – 3xyz
=
(x + y + z) (x2 + y2 + z2 - xy - zy – zx)
=
6 (20 – 8) = 72
Answer: c)
7).
Third proportional of a and b
=
b2 / a = {[ ( √x2 + x2 ) ]2 } / [
(x / y) + (y / x) ]
=
(x2 + y2) / [(x2 + y2) / xy ] = xy
Answer: a)
8).
(a
/ b) = 2 / 3
(b
/ c) = 4 / 5
(c
/ d) = 6 / 7
⇒(a
/ b) ×(b / c) × (c / d) = (2 / 3) × (4 /
5) × (6 / 7)
=
a / d = 24 / 35
Answer: b)
9).
√3√0.000729
= √3√(0.09)3
= √0.3
Answer: d)
10).
[ x + (1 / x) ] / 2 = 1
x
+ (1 / x) = 2
x2
+ 1 = 2x
x2
- 2x + 1 = 0
(x
– 1)2 = 0
x
= 1
x10
+ (1 / x10) = 1 + 1 = 2
