SSC CGL Previous Year Questions: Algebra- 2 - SSC CGL MCQ

# SSC CGL Previous Year Questions: Algebra- 2 - SSC CGL MCQ

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## 40 Questions MCQ Test SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) - SSC CGL Previous Year Questions: Algebra- 2

SSC CGL Previous Year Questions: Algebra- 2 for SSC CGL 2024 is part of SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) preparation. The SSC CGL Previous Year Questions: Algebra- 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The SSC CGL Previous Year Questions: Algebra- 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for SSC CGL Previous Year Questions: Algebra- 2 below.
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SSC CGL Previous Year Questions: Algebra- 2 - Question 1

### If 3x – 8(2 – x) = –19, then the value of x is       (SSC CHSL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 1

3x – 8 (2 – x) = –19
3x – 16 + 8x = – 19
11x = – 3
∴ x = (-3)/11

SSC CGL Previous Year Questions: Algebra- 2 - Question 2

### If  then what two values of x - (1/x)?       (SSC CGL 2017)

SSC CGL Previous Year Questions: Algebra- 2 - Question 3

### What is the value of x in the equation     (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 3

By squaring both sides

⇒ 13x2 + 13x = 12x2 + 12x + 6
⇒ x2 + 3x – 2x – 6 = 0
⇒ x (x + 3) – 2 (x + 3) = 0
⇒ (x – 2) (x + 3) = 0
⇒ x – 2 = 0 ∴ x = 2
⇒ x + 3 = 0 ∴ x = – 3

SSC CGL Previous Year Questions: Algebra- 2 - Question 4

If x + (1/x) = 17, then what is the value of       (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 4

Here,
x + (1/x) = 17

= 1/14 (4913-3x17)
⇒ (1/14) x 4862 = 2431/7

SSC CGL Previous Year Questions: Algebra- 2 - Question 5

What is the value of         (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 5

SSC CGL Previous Year Questions: Algebra- 2 - Question 6

If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 +  5t2) / (3q2 + 4s2 + 5u2)]?       (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 6

Here,

then,

SSC CGL Previous Year Questions: Algebra- 2 - Question 7

If x – y – √18 = – 1 and x + y – 3√2 = 1, then what is the value of 12xy (x2 – y2)?       (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 7

According to question,
x - y - √18 = -1 ...(i)
x + y - 3√2 = 1 ...(ii)
From equation (i) and (ii),
We get,
x = 3√2 and y = 1
then,
12xy (x2 – y2)
⇒ 12x3√2 x1[(3√2)2 - (1)2 ]
⇒ 36√2 x 17 = 612√2

SSC CGL Previous Year Questions: Algebra- 2 - Question 8

If (x – y) = 7, th en wh at is the value of (x – 15)3 – (y – 8)3?      (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 8

Here,
(x – y) = 7
then,
∴ a3 – b3 = (a – b) (a2 + ab + b2)
(x – 15)3 – (y – 8)3 = ?
⇒ (x – 15 – y + 8) [(x –15)2 + (x – 15) (y – 8) + (y – 8)2]
⇒ (x – y – 7)[ (x – 15)2 + (x – 15) (y – 8) + (y – 8)2]
⇒ (7 – 7) [(x – 15)2 + (x – 15) (y – 8) + (y – 8)2]
⇒ 0 × [(x – 15)2 + (x – 15) (y – 8) + (y – 8)2]
⇒ 0

SSC CGL Previous Year Questions: Algebra- 2 - Question 9

If (x – 2) an d (x + 3 ) are th e factor s of the equat ion x2 + k1x + k2 = 0, then what are the values of k1 and k2?      (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 9

∵ If x – 2 = 0
∴ x = 2
then,
x2 + k1x + k2 = 0
(2)2 + k1 × 2 + k2 = 0
2k1 + k2 = – 4 ...(i)
If x + 3 = 0
∴ x = –3
then,
x2 + k1x + k2 = 0
(–3)2 + k1x – 3 + k2 = 0
∴ 3k1 – k2 = 9 ...(ii)
From equation (i) and (ii),
we get k 1 = 1 and k2 = – 6

SSC CGL Previous Year Questions: Algebra- 2 - Question 10

If  then what is the value of       (SSC CGL 2017)

SSC CGL Previous Year Questions: Algebra- 2 - Question 11

If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7) (b – 9) (c – 11)?        (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 11

According to question,
a + b + c = 27
(a – 7) + (b – 9) + (c – 11) = 27 – 7 – 9 – 11
(a – 7) + (b – 9) + (c – 11) = 0
∴ a + b + c = 0
then
a3 + b3 + c3 – 3abc = 0

SSC CGL Previous Year Questions: Algebra- 2 - Question 12

If x = 6+ 2√6, then what is the value of        (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 12

x = 6 + 2√6
Subtraction by 1 in both side.
x -1 = 6 + 2√6 - 1
x -1 = 5 + 2√6 ⇒ 3 + 2√6

Now,

SSC CGL Previous Year Questions: Algebra- 2 - Question 13

If x + (1/x) = 2, then what is the value of x64 + x121?        (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 13

According to question,

⇒ x2 + 1 = 2x
⇒ x2 – 2x + 1 = (x – 1)2
∴ x – 1 = 0 ∴ x = 1
∴ x64 + x121 = 1 + 1 = 2.

SSC CGL Previous Year Questions: Algebra- 2 - Question 14

If x + (1/x) = 4, then what is the value of x6 + (1//x6)?       (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 14

x + (1/x)= 4
then,
x6 + (1/x6) = ?
Let x + (1/x) = a

⇒ ((4)3 – 3 × 4 )2 – 2
⇒ (64 – 12)2 – 2 = (2704 – 2) = 2702

SSC CGL Previous Year Questions: Algebra- 2 - Question 15

If  then what is the value of      (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 15

SSC CGL Previous Year Questions: Algebra- 2 - Question 16

If  then what is the value of x + (1/x)?      (SSC CGL 2017)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 16

Here,

SSC CGL Previous Year Questions: Algebra- 2 - Question 17

If 3x + y = 81 and 81x - y = 3, then the value of x/y is       (SSC Sub. Inspector 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 17

SSC CGL Previous Year Questions: Algebra- 2 - Question 18

If p, q, r are all real numbers, then (p – q)3 + (q – r)3 + (r – p)3 is equal to       (SSC Sub. Inspector 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 18

If a + b + c = 0 then a3 + b3 + c3 = 3abc
let, a = (p – q), b = (q – r), c - (r – p)
than, a + b + c = p – q + q – r + r – p = 0
∴ (p – q)3 + (q – r)2 + (r – p)3
= 3(p – q) (q – r) (r – p) = 0

SSC CGL Previous Year Questions: Algebra- 2 - Question 19

If x = 31/3 – 3–1/3 then 3x3 + 9x is equal to       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 19

x = 31/3 – 3–1/3
Cubing on both sides

3x3 + 9x = 8

SSC CGL Previous Year Questions: Algebra- 2 - Question 20

If x = 222, y = 223, z = 225 then the value of x3 + y3 + z3 – 3xyz is          (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 20

x3 + y3 + z3 – 3xyz = 1/2(x + y + z)
[(x – y)2 + (y – z)2 + (z – x)2]
= 1/2(222 + 223 + 225)
[(222 – 223)2 + (223 – 225)2 + (225 – 222)2]
⇒ 1/2[670][1+4+9] = 335 [14] = 4690

SSC CGL Previous Year Questions: Algebra- 2 - Question 21

If  then the value of  is equal to       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 21

Cubing both Sides

SSC CGL Previous Year Questions: Algebra- 2 - Question 22

If 4x + (1/x) = 5, x ≠ 0, then the value of  is       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 22

⇒ 4x2 + 1 = 5x

SSC CGL Previous Year Questions: Algebra- 2 - Question 23

If  then the value of x3 + 5x2 + 12x is       (SSC CGL  1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 23

(Cubing both sides)
(x + 2)3 = x2 + 11
x3 + 8 + 6x2 + 12x = x2 + 11
x3 + 5x2 + 12x = 3

SSC CGL Previous Year Questions: Algebra- 2 - Question 24

If x =  then the value of x4 + y4 – 2x2y2 is       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 24

x4 + y4 – 2 x2y2
= (x2 – y2)2

SSC CGL Previous Year Questions: Algebra- 2 - Question 25

When  then value of  is        (SSC CGL  1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 25

Dividing eq by 2
Cubing both sides

SSC CGL Previous Year Questions: Algebra- 2 - Question 26

If (x – 2) (x – p) = x2 – ax + b, then the value of (a – p) is        (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 26

(x – 2) (x – p) = x2 – ax + b
x2 + ( – 2 – p)x + (– P) (–2) = x2 – ax + b
– (2 + p) = – a
2 = a – p

SSC CGL Previous Year Questions: Algebra- 2 - Question 27

If x + y + z = 1,  and xyz = – 1, then x3 + y3 + zis equal to       (SSC CGL  1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 27

x + y + z = 1,

xy + yz + zx = – 1
(x + y + z)2 = 1
x2 + y2 + z2 + 2xy + 2yz + 2zx = 1
x2 + y2 +z2 + 2(–1) = 1
x2 + y2 +z2 = 3
x3 + y3 + z3 – 3xyz
= (x + y + z) (x2 + y2 +z2 + xy – yz – zx)
x3 + y3 + z3 – 3(–1) = (1) [(3 – (–1)]
x3 + y3 + z3 + 3 = 4
= 4 – 3 = 1

SSC CGL Previous Year Questions: Algebra- 2 - Question 28

If  then the value of  is       (SSC CGL   1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 28

SSC CGL Previous Year Questions: Algebra- 2 - Question 29

The length of the base of an isosceles triangle is 2x – 2y + 4z, and its perimeter is 4x – 2y + 6z. Then the length of each of the equal sides is        (SSC CGL  1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 29

Base side of isosceles Δ = 2x – 2y + 4z
Perimeter = 4x – 2y + 6z
Remaining two sides are = (P-B)/2

SSC CGL Previous Year Questions: Algebra- 2 - Question 30

If x2 – 3x + 1 = 0, (x ≠ 0), then the value of x + (1/x) is       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 30

x2 – 3x + 1 = 0
Dividing Equation by x
x - 3 + (1/x) = 0
x + (1/x) = 3

SSC CGL Previous Year Questions: Algebra- 2 - Question 31

If  a3 – b3 = 56 and a – b = 2 then what is the value of a2 + b2?       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 31

(a – b) = 2, a3 – b3 = 56
(a – b)3 = a3 – b3 – 3ab (a – b)
8 = 56 – 3ab (2)
– 48 = – 6ab
∴ ab = 8
(a – b)2 = a2 + b2 – 2ab
4 = a2 + b2 – 16
20 = a2 + b2

SSC CGL Previous Year Questions: Algebra- 2 - Question 32

If  then the value of   is       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 32

Now

SSC CGL Previous Year Questions: Algebra- 2 - Question 33

If  then        (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 33

SSC CGL Previous Year Questions: Algebra- 2 - Question 34

If then the value of  is       (SSC CGL  1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 34

dividing Eq. by 2
Squaring on both sides

SSC CGL Previous Year Questions: Algebra- 2 - Question 35

If  then the value of  is       (SSC CGL 1st Sit. 2016)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 35

SSC CGL Previous Year Questions: Algebra- 2 - Question 36

If x = 2 then the value of x3 + 27x2 + 243x + 631        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 36

Given x = 2
then x3 + 27x2 + 243x + 631
= 8 + 108 + 486 + 631
= 1233

SSC CGL Previous Year Questions: Algebra- 2 - Question 37

If p = 99 then the value of p (p2 + 3p + 3)        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 37

Given p = 99
then p(p2 + 3p + 3)
= p((p + 1)2 + p + 2)
= 99 ((99 + 1)2 + 101)
= 99 × (10000 + 101)
= 999999

SSC CGL Previous Year Questions: Algebra- 2 - Question 38

If 5x + 9y = 5 and 125x3 + 729y3 = 120 then the value of the product of x and y is        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 38

5x +9y = 5 ...(i)
125x3 + 729y3 =120 ...(ii)
Now cube both sides of equation (i), we get
⇒ (5x + 9y)3 = (5)3
⇒ 125x3 + 729y3 +135xy(5x + 9y) =125
⇒ 125x3 + 729y3 +135xy x 5 =125
Now, put the value of equation (i)
120 + 135 xy × 5 = 125
⇒ 135 × 5xy = 125 – 120
⇒ 135 × 5xy = 5

SSC CGL Previous Year Questions: Algebra- 2 - Question 39

If x =  then the value of        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 39

Given that

On cubing both sides we get

SSC CGL Previous Year Questions: Algebra- 2 - Question 40

The HCF of x8 – 1 and x4 + 2x3 – 2x – 1 is:        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 2 - Question 40

Given fraction
x8 -1 = (x4 +1)(x2 +1)(x -1)(x +1)
x4 + 2x3 - 2x -1 = (x -1)(x +1)3
HCF of Given fractor
= (x -1)(x +1) = x2 -1

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