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SSC CGL Exam  >  SSC CGL Test  >   Previous Year Papers  >  SSC CGL Previous Year Questions: Algebra- 3 - SSC CGL MCQ

SSC CGL Previous Year Questions: Algebra- 3 with solutions - Free MCQ Test


MCQ Practice Test & Solutions: SSC CGL Previous Year Questions: Algebra- 3 (40 Questions)

You can prepare effectively for SSC CGL SSC CGL Previous Year Papers with this dedicated MCQ Practice Test (available with solutions) on the important topic of "SSC CGL Previous Year Questions: Algebra- 3". These 40 questions have been designed by the experts with the latest curriculum of SSC CGL 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 40 minutes
  • - Number of Questions: 40

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SSC CGL Previous Year Questions: Algebra- 3 - Question 1
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Among the equations x + 2y + 9 = 0; 5x – 4 = 0; 2y – 13 = 0; 2x – 3y = 0, the equation of the straight line passing through origin is :       (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 1

2x – 3y = 0 is passing through origion because its satisfy x = 0 and y = 0.

SSC CGL Previous Year Questions: Algebra- 3 - Question 2
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The area of the triangle formed by the graphs of the equations x = 0, 2x + 3y = 6 and x + y = 3 is       (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 2

x = 0 ...(1)
2x + 3y = 6 ...(2)
x + y = 3 ...(3)

2x + 3y = 6 ...(ii)
x = 0, y = 2
x = 3, y = 0
From eqn. (iii) x+ y = 3
x = 0, y = 3
x = 3, y = 0
Area made by these three lines
= Area of triangle OBC – Area of OAC

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SSC CGL Previous Year Questions: Algebra- 3 - Question 3
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If  then the simplest value of x is         (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 3


x = – 1

SSC CGL Previous Year Questions: Algebra- 3 - Question 4
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If x = 332, y = 333, z = 335, then the value of x3 + y3 + z3 – 3xyz is       (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 4

Using the formula,
 
 

SSC CGL Previous Year Questions: Algebra- 3 - Question 5
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If  then the value of m is        (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 5


 
 = 0
m- a2 - b2 - c2 = 0
m = a2 + b2 + c2

SSC CGL Previous Year Questions: Algebra- 3 - Question 6
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2x – ky + 7 = 0 and 6x – 12y + 15 = 0 has no solution for        (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 6

For no solution, a = b

SSC CGL Previous Year Questions: Algebra- 3 - Question 7
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If m = –4, n = –2, then the value of m3 – 3m2 + 3m + 3n + 3n2 + n3 is       (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 7

m3 – 3m2 + 3m + 3n + 3n2 + n3
⇒ (– 4)3 – 3 (– 4)2 + 3 (– 4) + 3 (– 2) + 3 (– 2)2 + (– 2)3
⇒ – 64 – 48 – 12 – 6 + 12 – 8
⇒ – 126

SSC CGL Previous Year Questions: Algebra- 3 - Question 8
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The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is       (SSC CGL 1st Sit. 2015)

Detailed Solution: Question 8

Intercept can represent in the form of 
To get x and y intercept, we have
3x + 4y = 12

So, triplets of 3, 4 and 5.
Hence, 5 is the length of portion of straight line.

SSC CGL Previous Year Questions: Algebra- 3 - Question 9
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If  is equal to        (SSC CHSL 2015)

Detailed Solution: Question 9




= c– (c – 1)
= c – c + 1
= 1

SSC CGL Previous Year Questions: Algebra- 3 - Question 10
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If (2a – 1)2 + (4b – 3)2 + (4c + 5)2 = 0 then the value of  is:        (SSC CHSL 2015)

Detailed Solution: Question 10

(2a – 1)2 + (4b – 3)2 + (4c + 5)2 = 0

a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2+ c2 – ab – bc – ca)
But a + b + c = 0
So, a3 + b3 +c3 – 3abc = 0
So, 

SSC CGL Previous Year Questions: Algebra- 3 - Question 11
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Two positive whole numbers are such that  the sum of the first and twice the second number is 8 and their difference is 2. The numbers are :        (SSC CHSL 2015)

Detailed Solution: Question 11

Let the two numbers are x and y
So, x + 2y = 8 … (i)
x – y = 2 … (ii)
Solving both equations
x = 4; y = 2
So, numbers are 4, 2.

SSC CGL Previous Year Questions: Algebra- 3 - Question 12
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A number of boys raised ₹12,544 for a famine fund, each boy has given as many rupees as there were boys. The number of boys was:        (SSC CHSL 2015)

Detailed Solution: Question 12

Contribution of each boy = Number of boys
Total contribution raised = ₹ 12544
So, number of boys = 

SSC CGL Previous Year Questions: Algebra- 3 - Question 13
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If for non–zero x, x2 – 4x – 1 = 0 the value of x2 + (1/x2) is :        (SSC CHSL 2015)

Detailed Solution: Question 13

x2 – 4x – 1 = 0 can be written as x2 – 4x + 4 – 1 = 4
So (x - 2)2 – 1 = 4




SSC CGL Previous Year Questions: Algebra- 3 - Question 14
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If  then the value of  is :        (SSC CHSL 2015)

Detailed Solution: Question 14




= 125 + 125 + 360 + 360
= 250 + 720
= 970

SSC CGL Previous Year Questions: Algebra- 3 - Question 15
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If p = –0.12, q = –0.01 & r = –0.015, then the correct relationship among the three is :        (SSC CHSL 2015)

Detailed Solution: Question 15

p = – 0.12 ; q = – 0.01; r = – 0.015
So, p < r ; p < q
= p < r < q

SSC CGL Previous Year Questions: Algebra- 3 - Question 16
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If x + (1/x)= 2, then the value of x7 + (1/x5) is:      (SSC Sub. Ins. 2015)

Detailed Solution: Question 16

x + (1/x) = 2
Take cube on both sides

Squaring on both sides

Now multiplying both sides by x


x2 – 2x + 1 = 0
x2 – x – x +1 = 0
x(x – 1) –1(x – 1)
(x –1)2 = 0
x = 1
So 

SSC CGL Previous Year Questions: Algebra- 3 - Question 17
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The term that should be added to (4x2 + 8x) so that resulting expression be a perfect square is:       (SSC Sub. Ins. 2015)

Detailed Solution: Question 17

4x2 + 8x = (2x)2 + 2(2x) (2) + (2)2
= (2x + 2)2 ∴ x2 + y2 + 2xy = (x + y)2
So, 4 should be added to make if perfect square.

SSC CGL Previous Year Questions: Algebra- 3 - Question 18
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If 999x  + 888y = 1332
888x  + 999y = 555 then the value of x+y is:       (SSC Sub. Ins. 2015)

Detailed Solution: Question 18

999x + 888y = 1332
111(9x + 8y) = 1332
9x + 8y = 1332/111 = 12
9x + 8y = 12 ...(i)
888x + 999y = 555
8x + 9y = 5 ...(ii)
Solving (i) and (ii)
x = 4, y = – 3
x + y = 4 – 3 = 1

SSC CGL Previous Year Questions: Algebra- 3 - Question 19
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If  32x -y = 3x +y = √27 , then the value of  3x -y will be :        (SSC Sub. Ins. 2015)

Detailed Solution: Question 19

32x – y = 3x + y = √27 = 33/2

4x – 2y = 3 ...(i)
2x + 2y = 3 ...(ii)
Solving equation (i) and (ii)
x = 1 y = 1/2

SSC CGL Previous Year Questions: Algebra- 3 - Question 20
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The mean of x and 1/x is M. Then the mean of x2 and 1/x2 is.      (SSC Sub. Ins. 2015)

Detailed Solution: Question 20

Mean of x and (1/x) = M

Mean of x2 and 

SSC CGL Previous Year Questions: Algebra- 3 - Question 21
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If  and x + y + z ≠ 0, then each ratio is        (SSC CHSL 2014)

Detailed Solution: Question 21

Given,

We know that property of ratio,

So,

= (x + y + z)/(xa + xb + xc + ya + yb + yc + za + zb + zc)
⇒ x / (xa + yb + zc) = y / (ya + zb + xc) = z / (za + xb + yc)
= x / (xa + yb + zc) = y (ya + zb + xc) = z / (za + xb + yc)
= (x + y + z) / {x(a + b + c) + y(a + b + c) + z(a + b + c)}
⇒ x(xa + yb + zc) = y(ya + zb + xc) = z(za + xb + yc)
= (x + y + z) / {(a + b + c) (x + y + z)
⇒ x / (xa + yb + zc) = y / (ya + zb + xc) = z / (za + xb + yc)
= 

SSC CGL Previous Year Questions: Algebra- 3 - Question 22
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If x = 3 + 2√2, then  is equal to       (SSC CHSL 2014)

Detailed Solution: Question 22

We have, x = 3 + 2√2


= 6[62 – 3] + 6 = 198 + 6 = 204

SSC CGL Previous Year Questions: Algebra- 3 - Question 23
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If x = p + (1/p) and y = p – (1/p), then value of x4 – 2x2 y2 + y4 is       (SSC CHSL 2014)

Detailed Solution: Question 23

x4 – 2x2y2 + y4 = (x2 – y2)2 = [(x + y)(x – y)]2

SSC CGL Previous Year Questions: Algebra- 3 - Question 24
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If  then the value of  is       (SSC CHSL 2014)

Detailed Solution: Question 24


SSC CGL Previous Year Questions: Algebra- 3 - Question 25
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If a = 331, b = 336 and c = – 667, then the value of a3 + b3  + c3 – 3abc is        (SSC Sub. Ins. 2014)

Detailed Solution: Question 25

Here, a + b + c = 0
∴ a3 + b3 + c3 – 3abc = 0

SSC CGL Previous Year Questions: Algebra- 3 - Question 26
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If          (SSC Sub. Ins. 2014)

Detailed Solution: Question 26


x2 –2x + 1 = 0; (x – 1)2 = 0 ; x = 1

= 1 + 1 = 2

SSC CGL Previous Year Questions: Algebra- 3 - Question 27
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If p = 5/18 then  is equal to       (SSC Sub. Ins. 2014)

Detailed Solution: Question 27


SSC CGL Previous Year Questions: Algebra- 3 - Question 28
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If a =  then 2a2 – 5ab + 2b2 =       (SSC Sub. Ins. 2014)

Detailed Solution: Question 28

2a2 – 5ab + 2b2
2(a2 – 2ab + b2) – ab
2 (a – b)2 – ab

2 × 4 × 5 – 1 = 39

SSC CGL Previous Year Questions: Algebra- 3 - Question 29
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If x : y ::2 : 3 and 2 : x :: 4 : 8 the value of y is       (SSC Sub. Ins. 2014)

Detailed Solution: Question 29


x = 4

SSC CGL Previous Year Questions: Algebra- 3 - Question 30
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If x + y + z = 0, then the value of  is       (SSC CGL 2014)

Detailed Solution: Question 30

x + y + z = 0
y + z = –x
Squaring both sides
y2 + z2 + 2yz = x2
⇒ y2 + z2 = x2 – 2yz ...(1)

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