SSC CGL Previous Year Questions: Algebra- 6

# SSC CGL Previous Year Questions: Algebra- 6 - SSC CGL

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## 26 Questions MCQ Test SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) - SSC CGL Previous Year Questions: Algebra- 6

SSC CGL Previous Year Questions: Algebra- 6 for SSC CGL 2023 is part of SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) preparation. The SSC CGL Previous Year Questions: Algebra- 6 questions and answers have been prepared according to the SSC CGL exam syllabus.The SSC CGL Previous Year Questions: Algebra- 6 MCQs are made for SSC CGL 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for SSC CGL Previous Year Questions: Algebra- 6 below.
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SSC CGL Previous Year Questions: Algebra- 6 - Question 1

### If x = 2+√3, then the value of is:        (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 1  SSC CGL Previous Year Questions: Algebra- 6 - Question 2

### If then the value of a3 is:       (SSC CGL  2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 2 a2 + 1 = a
a2 – a + 1 = 0
Multiplying both side by (a + 1)
(a + 1) (a2 – a + 1) = 0
a3 + 1
a3 = –1

SSC CGL Previous Year Questions: Algebra- 6 - Question 3

### If ax + by = 6, bx – ay = 2 and x2 + y2 = 4, then the value of (a2 + b2) would be:        (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 3

ax + by = 6 ...(i)
bx – ay = 2 ...(ii)
a2x2 + b2y2 + 2abxy + b2x2 + a2y2 – 2abxy
= 36 + 4
⇒ x2 (a2 + b2) + y2 (a2 + b2) = 40
⇒ (a2 + b2) (x2 + y2) = 40
⇒ (a2 + b2) × 4 = 40
⇒ a2 + b2 = 10

SSC CGL Previous Year Questions: Algebra- 6 - Question 4

If then the value of is:       (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 4  = 103 – 3 × 10 = 1000 – 30 = 970

SSC CGL Previous Year Questions: Algebra- 6 - Question 5

If (5x2 – 3y2) : xy = 11 : 2, then the postive value of x/y is:       (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 5 10x2 – 6y2 = 11xy
10x2 – 11xy – 6y2 = 0
10x2 – 15xy + 4xy – 6y2 = 0
5x(2x – 3y) + 2y(2x – 3y) = 0
(5x + 2y) (2x – 3y)
5x ≠ 2y, 2x = 3y SSC CGL Previous Year Questions: Algebra- 6 - Question 6

If (a – b) = 3, (b – c) = 5 and (c – a) = 1, then the value of is      (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 6 a3 + b3 + c3 – 3abc=  SSC CGL Previous Year Questions: Algebra- 6 - Question 7

In the xy–coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y – 7, then k = ?        (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 7

Points (a, b) and [(a + 3), (b + k)] will satisfy the equation
x – 3y + 7 = 0.
∴ a – 3b + 7 = 0 ......(i)
and a + 3 – 3 (b + k) + 7 = 0
⇒ a + 3 – 3b – 3 k + 7 = 0
⇒ a – 3b + 7 + 3 – 3 k = 0
⇒ 3 – 3k = 0 ⇒ 3k = 3
⇒ k = 3/3 = 1 [∵ a - 3b + 7 = 0]

SSC CGL Previous Year Questions: Algebra- 6 - Question 8

If a + b + 1 = 0, then the value of (a3 + b3 + 1 – 3ab) is        (SSC CGL 1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 8

If a + b + c = 0
then a3 + b3 + c3 – 3abc = 0
Now,
a + b + 1 = 0
∴ a3 + b3 + 1 – 3ab = 0

SSC CGL Previous Year Questions: Algebra- 6 - Question 9

If x + (1/x) = 3, the value of x5 + (1/)x5)) is      (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 9 On squaring,  SSC CGL Previous Year Questions: Algebra- 6 - Question 10

If then the value of will be       (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 10 SSC CGL Previous Year Questions: Algebra- 6 - Question 11

In xy–plane, P and Q are two points having co–ordinates (2, 0) and (5, 4) respectively. Then the numerical value of the area of the circle with radius PQ is        (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 11  ∴ Area of circle = πr2
= 25 π sq. units

SSC CGL Previous Year Questions: Algebra- 6 - Question 12

If x = (0.08)2, y = and z = (1 – 0.08)2 – 1, then out of the following the true relation is      (SSC CGL 1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 12

x = (0.08)2 Z = (1 – 0.08)2 – 1
= 1 + (0.08)2 – 2 × 0.08 – 1 = (0.08)2 – 2 × 0.08
Clearly, z < x < y

SSC CGL Previous Year Questions: Algebra- 6 - Question 13

The sum of two numbers is 24 and their product is 143. The sum of their squares is      (SSC CGL 2nd Sit. 2011)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 13

Let the two numbers be x and y.
∴ x + y = 24
and, xy = 143
∴ x2 + y2 = (x + y)2 – 2xy
= (24)2 – 2 × 143 = 576 – 286 = 290

SSC CGL Previous Year Questions: Algebra- 6 - Question 14

If then the value of x is      (SSC CGL  2nd Sit. 2011)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 14 Squaring on both sides,  SSC CGL Previous Year Questions: Algebra- 6 - Question 15

If value of a/b is     (SSC CGL  2nd Sit. 2011)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 15 On squaring,
0.03 × 0.3 × a = 0.09 × 0.09 × b SSC CGL Previous Year Questions: Algebra- 6 - Question 16

If 1.5x = 0.04y, then the value of is        (SSC CGL  2nd Sit. 2011)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 16  Now  SSC CGL Previous Year Questions: Algebra- 6 - Question 17

In an examination a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempts correctly is        (SSC CGL 1st Sit. 2011)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 17

Let the number of correct answers be x.
∴ x + 4 – (75 – x) × 1 = 125
⇒ 4x – 75 + x = 125
⇒ 5x = 125 + 75 = 200 SSC CGL Previous Year Questions: Algebra- 6 - Question 18

If p and q represent digits, what is the possible maximum value of q in the statement 5p9 + 327 + 2q8 = 1114?       (SSC CGL  2nd Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 18 If p = 0, then q’s maximum value = 7.

SSC CGL Previous Year Questions: Algebra- 6 - Question 19

It the value of is        (SSC CGL 2nd  Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 19  SSC CGL Previous Year Questions: Algebra- 6 - Question 20

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored, in all 200 marks. The number of questions, he answered correctly was         (SSC CGL 2nd Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 20

If the number of correct answers be x, then
x × 4 – 1. (200 – x) = 200
⇒ 4x – 200 + x = 200
⇒ 5x = 400 SSC CGL Previous Year Questions: Algebra- 6 - Question 21 then x is equal to      (SSC CGL 1st Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 21 By componendo and dividendo, Squaring both sides, SSC CGL Previous Year Questions: Algebra- 6 - Question 22

Two natural numbers are in the ratio 3 : 5 and their product is 2160. The smaller of the numbers is        (SSC CGL 1st Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 22

Let the numbers be 3x and 5x.
∴ 3x × 5x = 2160 ⇒ x = 12
∴ Smaller number = 3x = 3 × 12 = 36

SSC CGL Previous Year Questions: Algebra- 6 - Question 23

If a and b be positive integers such that a2 – b2 = 19, then the value of a is      (SSC CGL 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 23

a2 – b2 = 19
⇒ 102 – 92 = 19
⇒ a = 10

SSC CGL Previous Year Questions: Algebra- 6 - Question 24

If a = 11 and b = 9, then the value of is       (SSC CGL 1st Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 24  SSC CGL Previous Year Questions: Algebra- 6 - Question 25

If a and b are two odd positive integers, by which of the following integers is (a4 – b4) always divisible?      (SSC CGL 1st Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 25

a4 – b4 = (a2 + b2) (a + b) (a – b)
∴ Required number = (3 + 1) ( 3 – 1) = 8

SSC CGL Previous Year Questions: Algebra- 6 - Question 26

If then x is equal to       (SSC CGL 1st Sit. 2010)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 6 - Question 26 ⇒ 2x – 1 = –3
⇒ 2x = –3 + 1 = –2
⇒ x = –1

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