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

SSC CGL Previous Year Questions: Algebra- 3 for SSC CGL 2024 is part of SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) preparation. The SSC CGL Previous Year Questions: Algebra- 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The SSC CGL Previous Year Questions: Algebra- 3 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- 3 below.
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SSC CGL Previous Year Questions: Algebra- 3 - Question 1

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 for SSC CGL Previous Year Questions: Algebra- 3 - 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

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 for SSC CGL Previous Year Questions: Algebra- 3 - 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

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

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

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


x = – 1

SSC CGL Previous Year Questions: Algebra- 3 - Question 4

If x = 332, y = 333, z = 335, then the value of x3 + y3 + z3 – 3xyz is       (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 4

Using the formula,
 
 

SSC CGL Previous Year Questions: Algebra- 3 - Question 5

If  then the value of m is        (SSC CGL 1st Sit. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 5


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

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

2x – ky + 7 = 0 and 6x – 12y + 15 = 0 has no solution for        (SSC CGL 1st Sit. 2015)

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

For no solution, a = b

SSC CGL Previous Year Questions: Algebra- 3 - Question 7

If m = –4, n = –2, then the value of m3 – 3m2 + 3m + 3n + 3n2 + n3 is       (SSC CGL 1st Sit. 2015)

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

The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is       (SSC CGL 1st Sit. 2015)

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

If  is equal to        (SSC CHSL 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 9




= c– (c – 1)
= c – c + 1
= 1

SSC CGL Previous Year Questions: Algebra- 3 - Question 10

If (2a – 1)2 + (4b – 3)2 + (4c + 5)2 = 0 then the value of  is:        (SSC CHSL 2015)

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

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 for SSC CGL Previous Year Questions: Algebra- 3 - 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

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 for SSC CGL Previous Year Questions: Algebra- 3 - 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

If for non–zero x, x2 – 4x – 1 = 0 the value of x2 - (1/x2) is :        (SSC CHSL 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 13

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





= 1458 – 1440 = 18.

SSC CGL Previous Year Questions: Algebra- 3 - Question 14

If  then the value of  is :        (SSC CHSL 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 14




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

SSC CGL Previous Year Questions: Algebra- 3 - Question 15

If p = –0.12, q = –0.01 & r = –0.015, then the correct relationship among the three is :        (SSC CHSL 2015)

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

If x + (1/x)= 2, then the value of x7 + (1/x5) is:      (SSC Sub. Ins. 2015)

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

The term that should be added to (4x2 + 8x) so that resulting expression be a perfect square is:       (SSC Sub. Ins. 2015)

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

If 999x  + 888y = 1332
888x  + 999y = 555 then the value of x+y is:       (SSC Sub. Ins. 2015)

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

If  32x -y = 3x +y = √27 , then the value of  3x -y will be :        (SSC Sub. Ins. 2015)

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

The mean of x and 1/x is M. Then the mean of x2 and 1/x2 is.      (SSC Sub. Ins. 2015)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 20

Mean of x and (1/x) = M

Mean of x2 and 

SSC CGL Previous Year Questions: Algebra- 3 - Question 21

If  and x + y + z ≠ 0, then each ratio is        (SSC CHSL 2014)

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

If x = 3 + 2√2, then  is equal to       (SSC CHSL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 22

We have, x = 3 + 2√2


= 6[62 – 3] + 6 = 198 + 6 = 204

SSC CGL Previous Year Questions: Algebra- 3 - Question 23

If x = p + (1/p) and y = p – (1/p), then value of x4 – 2x2 y2 + y4 is       (SSC CHSL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 23

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

SSC CGL Previous Year Questions: Algebra- 3 - Question 24

If  then the value of  is       (SSC CHSL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 24


SSC CGL Previous Year Questions: Algebra- 3 - Question 25

If a = 331, b = 336 and c = – 667, then the value of a3 + b3  + c3 – 3abc is        (SSC Sub. Ins. 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 25

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

SSC CGL Previous Year Questions: Algebra- 3 - Question 26

If          (SSC Sub. Ins. 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 26


x2 –2x + 1 = 0; (x – 1)2 = 0 ; x = 1

= 1 + 1 = 2

SSC CGL Previous Year Questions: Algebra- 3 - Question 27

If p = 5/18 then  is equal to       (SSC Sub. Ins. 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 27


SSC CGL Previous Year Questions: Algebra- 3 - Question 28

If a =  then 2a2 – 5ab + 2b2 =       (SSC Sub. Ins. 2014)

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

If x : y ::2 : 3 and 2 : x :: 4 : 8 the value of y is       (SSC Sub. Ins. 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 29


x = 4

SSC CGL Previous Year Questions: Algebra- 3 - Question 30

If x + y + z = 0, then the value of  is       (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 30

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

SSC CGL Previous Year Questions: Algebra- 3 - Question 31

If a = 4.965, b = 2.343 and c = 2.622, then the value of a3 – b3 – c3 – 3abc is         (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 31

a = 4.965 ≈ 5, b = 2.343 ≈ 2
c = 2.622
a – b = c
taking cube both sides
a3 – b3 – 3a2b + 3ab2 = c3
a3 – b3 – c3 – 3ab(a – b) = 0
a3 – b3 – c3 – 3abc = 0

SSC CGL Previous Year Questions: Algebra- 3 - Question 32

If x = 2 + √3, then x2 + 1/(x2) is equal to       (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 32

x = 2 + √3


= 16 – 2 = 14

SSC CGL Previous Year Questions: Algebra- 3 - Question 33

For what value of k, the system of  equations kx + 2y = 2 and 3x + y = 1 will be coincident?       (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 33

kx + 2y = 2 ...(1)
3x + y = 1 ...(2)
divide eqn (1) by (2)
(k/2) + y = 1
for system of equation to be coincident
k/2 = 3
k = 6

SSC CGL Previous Year Questions: Algebra- 3 - Question 34

The total area (in sq. unit) of the triangles formed by the graph of 4x + 5y = 40, x-axis, y-axis and x = 5 and y = 4 is       (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 34


Area of ΔABC = (1/2) × base × height

Area = 10 sq unit.

SSC CGL Previous Year Questions: Algebra- 3 - Question 35

If a2 – 4a – 1 = 0,  then the value of a2 + 3a +  is            (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 35

a2 – 4a – 1 = 0
a2 – 4a = 1
a (a – 4) = 1
a – 4 = (1/a)
a - (1/a) = 4 ...(1)
We have 

42 + 3 × 4 + 2 = 30

SSC CGL Previous Year Questions: Algebra- 3 - Question 36

If a + b + c = 3, a+ b2 + c2 = 6 and  where a, b, c are all non-zero, then 'abc' is equal to      (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 36

a + b + c = 3
Squaring both sides
a2 + b2 + c2 + 2 (ab + bc + ac) = 9
6 + 2 (ab + bc + ca) = 9
ab + bc + ca = 3/2 ...(1)
given 
⇒ ab + bc + ac = abc = 3/2 [from (1)]

SSC CGL Previous Year Questions: Algebra- 3 - Question 37

If a2 + b2 + c2 = 2a – 2b – 2, then the value of 3a – 2b + c is        (SSC CGL 2014)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 37

a2 + b2 + c2 = 2a – 2b – 2
(a2 – 2a + 1) + (b2 + 2b + 1) + c2 = 0
(a – 1)2 + (b + 1)2 + c2 = 0
This equation is possible if
a – 1 = 0, b + 1 = 0 and c = 0
a = 1, b = –1, c = 0
3a – 2b + c = 3 × 1 – 2 × (–1) + 0 = 3 + 2 = 5

SSC CGL Previous Year Questions: Algebra- 3 - Question 38

The straight line 2x + 3y = 12 passes through :         (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 38

Putting y = 0 in 2x + 3y = 12, we get x = 6
Putting x = 0 in 2x + 3y = 12, we get, y = 4

SSC CGL Previous Year Questions: Algebra- 3 - Question 39

 What number must be added to the expression 16a2 –12a to make it a perfect square?       (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 39

a2 – 2ab + b2 = (a – b)2
∴ 16a2 – 12a
= (4a)2 – 2 × 4a × (3/2)
Hence, on adding 

SSC CGL Previous Year Questions: Algebra- 3 - Question 40

If  then the value of x2 + 1/x2 is       (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 3 - Question 40


On squaring both sides

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