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

SSC CGL Previous Year Questions: Algebra- 5 for SSC CGL 2024 is part of SSC CGL (Tier - 1) - Previous Year Papers (Topic Wise) preparation. The SSC CGL Previous Year Questions: Algebra- 5 questions and answers have been prepared according to the SSC CGL exam syllabus.The SSC CGL Previous Year Questions: Algebra- 5 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- 5 below.
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SSC CGL Previous Year Questions: Algebra- 5 - Question 1

The linear equation such that each point on its graph has an ordinate four times its abscissa is:        (SSC Sub. Ins. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 1

y = 4x,
When, x = 1, y = 4

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

If  x = a – b, y = b – c, z = c – a, then the numerical value of the algebraic expression  x3 + y3 + z3 – 3xyz will be         (SSC Sub. Ins. 2013)

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

x + y + z = a – b + b – c + c – a = 0
∴ x3 + y3 + z3 –3xyz = 0

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

If xy + yz + zx = 0, then  is equal to       (SSC CHSL 2013)

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

xy + yz + zn = 0

SSC CGL Previous Year Questions: Algebra- 5 - Question 4

If  then the value of a3 +b3 is       (SSC CHSL 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 4

Given 
We know, a3 +b3 = (a + b)(a2 +b2 - ab)
∴ (a + b) (ab – ab) ⇒ 0 (using given)

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

Let  Then point out the correct alternative among the four alternatives given below.           (SSC CHSL 2013)

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

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

If a2 + b2 + c2 = 2 (a – b – c) – 3, then the value of 2a – 3b + 4c is       (SSC CHSL 2013)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 6

a2 +b2 + c2 = 2(a -b - c) - 3
⇒ a2 + b2 + c2 - 2(a -b - c) + 3 = 0
⇒ a2 + b2 + c2 - 2a + 2b + 2c + 3 = 0
⇒ (a2 +1- 2a) + (b2 +1+ 2b) + (c2 +1+ 2c) = 0
⇒ (a -1)2 + (b +1)2 + (c +1)2 = 0
This is possible when (a -1)2 = 0,(b +1)2 = 0 and (c +1)2 = 0.
⇒ a = 1, b = –1, c = –1
Thus, 2a – 3b + 4c = 2(1) – 3(–1) + 4(–1)
= 2 + 3 – 4 = 1.

SSC CGL Previous Year Questions: Algebra- 5 - Question 7

If then the value of x3 - (1/x3) is:       (SSC CHSL 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 7


= a3 + b3 + 3a2b + 3b2 – (a3 – b3 – 3a2b + 3b2a)
= a3 + b3 + 3a2b + 3b2 – a3 + b3 + 3a2b – 3b2a

SSC CGL Previous Year Questions: Algebra- 5 - Question 8

If the difference of two numbers is 3 and the difference of their squares is 39; then the larger number is :       (SSC CHSL 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 8

Let the numbers are x, y.
x – y = 3 … (1)
x2 – y2 = 39
⇒ (x – y) (x + y) = 39
⇒ x + y = 13 … (2)
Adding eqn (1) and (2)
x + y + x – y = 16
⇒ x = 8
∴ y = 5
Hence, 8 is the larger number.

SSC CGL Previous Year Questions: Algebra- 5 - Question 9

If  then the value of x is :        (SSC CHSL 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 9


⇒ 9x + 15 = 10x – 4
⇒ 15 + 4 = 10x – 9x
⇒ x = 19

SSC CGL Previous Year Questions: Algebra- 5 - Question 10

If  then :        (SSC CHSL 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 10


So, x = k (b + c)
⇒ x – y = k (b + c) – k (c + a)
= k (b – a)
y = k (c + a)
⇒ y – z = k (c + a) – k (a + b)= k (c – b)
z = k (a + b) = z – x = k (a + b) – k (b + c) = k (a – c)
So,check option (a)

k = k = k
option (a) is true.

SSC CGL Previous Year Questions: Algebra- 5 - Question 11

The equation of this graph is           (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 11

Given equation is y=3x
When x=1,⇒y=3×1=3
When x=2,⇒y=3×2=6
When x=3,⇒y=3×3=9

Plot the points A(1,3), B(2,6), C(3,9) on the graph paper.Join these points by a straight line AC

SSC CGL Previous Year Questions: Algebra- 5 - Question 12

The graph of y = x + | x | is given by   (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 12

y = x + |x|
case 1, x>0
y = x + x = 2x
case 2, x<0
y = x - x = 0
so, the graph of y = x + |x| is lies in 

SSC CGL Previous Year Questions: Algebra- 5 - Question 13

The line passing through the points (– 2, 8) and (5, 7)       (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 13


As indicated in the graph, the line passing through the points cuts Y-axis only.

SSC CGL Previous Year Questions: Algebra- 5 - Question 14

If (3x – y) : (x + 5y) = 5 : 7, then the value of (x + y) : (x – y) is        (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 14


Þ 16x = 32y
 ...(1)
Now, to calculate value of  Divide numerator & denominator by y.

Putting value of x/y from equation (1)

SSC CGL Previous Year Questions: Algebra- 5 - Question 15

If a + b = 5, a2 + b2 = 13, the value of a – b (where a > b) is        (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 15

a + b = 5
Squaring on both sides
(a + b)2 = (5)2
a2 + b2 + 2ab = 25
13 + 2ab = 25
2ab = 25 – 13 = 12 ... (1)
Again, a2 + b2 = 13
Subtracting (– 2ab) from both sides
a2 + b2 – 2ab = 13 – 2ab
(a – b)2 = 13 – 12 from equation (1)
(a – b)2 = 1
TRICK Þ a = 3
b = 2 (a > b)
a – b = 1

SSC CGL Previous Year Questions: Algebra- 5 - Question 16

Minimum value of  is       (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 16


is minimum when x = 0

SSC CGL Previous Year Questions: Algebra- 5 - Question 17

If  then the value of  is          (SSC Sub. Ins. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 17


SSC CGL Previous Year Questions: Algebra- 5 - Question 18

If a, b, c are real and a3 + b3 + c3 = 3abc and a +b +c ≠ 0, then the relation between a, b, c will be        (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 18


fartrise the given expression

Therefore,

Multiply by 2 on both the sides

Seprate individual square

So, for Add equal to 0, individual becomes 0

from equation (1) & (2)
a=b=c 

SSC CGL Previous Year Questions: Algebra- 5 - Question 19

If a +b +c= 0 , the value of  is       (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 19

If a + b + c = 0
then a3 + b3 + c3 = 3abc
Dividing both sides by abc

SSC CGL Previous Year Questions: Algebra- 5 - Question 20

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 20

SSC CGL Previous Year Questions: Algebra- 5 - Question 21

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 21


Multiply by 3/5 on both sides

Squaring on both sides

SSC CGL Previous Year Questions: Algebra- 5 - Question 22

If  then the value of x4 + y4 – 2x2y2 is         (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 22

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

SSC CGL Previous Year Questions: Algebra- 5 - Question 23

If a + b + c = 8, then the value of (a – 4)3 + (b – 3)3 + (c – 1)3 – 3 (a – 4) (b – 3) (c – 1) is          (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 23

We have x3 + y3 + z3 – 3xyz = (x + y + z)
(x2 + y2 + z2–xy – yz - zx)
Here x = a – 4, y = b – 3, z = c –1
So, given expression is (x + y + z)
(x2 + y2 + z2 – xy – yz – zx)
= (a – 4 + b – 3 + c – 1) (x2 + y2 + z2 – xy – yz – zx)
= (a + b + c – 8) (x2 + y2 + z2 – xy – yz – zx)
= (8 – 8) (x2 + y2 + z2 – xy – yz – zx)
= 0

SSC CGL Previous Year Questions: Algebra- 5 - Question 24

The area (in sq. unit) of the triangle formed by the three graphs of the equations x = 4, y = 3, and 3x + 4y = 12, is       (SSC CGL  2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 24

x = 4 ...(1)
y = 3 ...(2)
3x + 4y = 12 ...(3)
Putting x = 0 in 3rd equation we get y = 3
Putting y = 0 in 3rd equation we get x = 4
The triangle will be formed by joining the points (3, 0) and (0, 4).
So, base = 3 and altitude = 4
Area = 

SSC CGL Previous Year Questions: Algebra- 5 - Question 25

If x = 997, y = 998, z = 999, then the value of x2 + y2 + z2  – xy – yz – zx will be        (SSC CGL  2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 25

x2 + y2 + z2 – xy – yz – zx

SSC CGL Previous Year Questions: Algebra- 5 - Question 26

If x = (4ab/a+b), then the value of  is        (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 26


Applying compodendo and Dividendo

SSC CGL Previous Year Questions: Algebra- 5 - Question 27

The area of the triangle formed by the lines 5x + 7y = 35, 4x + 3y = 12 and x-axis is        (SSC CGL 1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 27

5x + 7y = 35 ...(i)
4x + 3y = 12 ...(ii)
By equation (i) × 4 – (ii) × 5

⇒ y = 80/13 = Height of triangle
Point of intersection on x-axis of equation
5x + 7y = 35
⇒ 5x + 7 × 0 = 35
⇒ 5x = 35
⇒ x = 7
∴ (7, 0)
Similarly, point of intersection of
4x + 3y = 12 = (3, 0)
∴ Base = 7 – 3 = 4

SSC CGL Previous Year Questions: Algebra- 5 - Question 28

If  the value of is       (SSC CGL 1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 28


On multiplying by 3/5,

On squaring,

SSC CGL Previous Year Questions: Algebra- 5 - Question 29

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 29


 [on dividing by 2]
 [On Squaring]

SSC CGL Previous Year Questions: Algebra- 5 - Question 30

If a2 + b2 + c2 = 2(a – b – c) – 3 then the value of 2a – 3b + 4c is        (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 30

a2 + b2 + c2 = 2(a – b –c) –3
⇒ a2 + b2 + c2 – 2a + 2b + 2c + 3 = 0
⇒ a2 – 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⇒ (a –1)2 + (b + 1)2 + (c + 1)2 = 0
[If x2 + y2 + z2 = 0 ⇒ x = 0; y = 0; z =0]
∴ a – 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = – 1
c + 1 = 0 ⇒ c = – 1
∴ 2a – 3b + 4c = 2 + 3 – 4 = 1

SSC CGL Previous Year Questions: Algebra- 5 - Question 31

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 31

SSC CGL Previous Year Questions: Algebra- 5 - Question 32

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 32



= (1/2) x 110 = 55

SSC CGL Previous Year Questions: Algebra- 5 - Question 33

If 4x = 18y, then the value of (x/y)-1 is       (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 33

4x = 18y

SSC CGL Previous Year Questions: Algebra- 5 - Question 34

If the distance between two points (0,–5) and (x,0) is 13 unit, then x =        (SSC CGL  1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 34


⇒ x2 + 25 = 169
⇒ x2 = 169 – 25 = 144

SSC CGL Previous Year Questions: Algebra- 5 - Question 35

If x = 1 + √2 + √3, then the value of (2x4 – 8x3 – 5x2 + 26x – 28) is       (SSC CGL 1st Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 35


On squaring,
x2 – 2x + 1 = 2 + 3 + 2√6
⇒ x- 2x - 4 = 2√6
On squaring again,
x4 + 4x2 + 16 – 4x3 – 8x2 + 16x = 24
⇒ x4 – 4x3 – 4x2 + 16x – 8 = 0
⇒ 2x4 – 8x3 – 8x2 + 32x – 16 = 0
⇒ 2x4 – 8x3 – 5x2 + 26x – 28 – 3x2 + 6x + 12 = 0
⇒ 2x4 – 8x3 – 5x2 + 26x – 28
= 3x2 – 6x – 12
= 3 (x2 – 2x – 4)
 

SSC CGL Previous Year Questions: Algebra- 5 - Question 36

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 36


On cubing both sides, 

SSC CGL Previous Year Questions: Algebra- 5 - Question 37

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

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 37


On cubing,

 

SSC CGL Previous Year Questions: Algebra- 5 - Question 38

Area of the triangle formed by the graph of the line 2x – 3y + 6 = 0 along with the coordinate axes is:         (SSC CGL  2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 38

Putting x = 0 in
2x – 3y + 6 = 0
⇒ y = 2
Putting y = 0 in 2x + 3y + 6 = 0
⇒ x = – 3 

Area of ΔOAB

SSC CGL Previous Year Questions: Algebra- 5 - Question 39

Area of the trapezium formed by x-axis; y-axis and the lines 3x + 4y = 12 and 6x + 8y = 60 is:        (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 39

For 3x + 4y = 12,
By putting x = 0, y = 3
By putting, y = 0, x = 4
For 6x + 8y = 60,
By putting x = 0, y = 15/2
By putting y = 0, x = 10

∴ Area of ΔOCD

∴ Area of ΔOAB = 
∴ Area of trapezium = (75/2) - 6

SSC CGL Previous Year Questions: Algebra- 5 - Question 40

If a3 – b3 = 56 and a – b = 2, then the value of (a2 + b2) is:    (SSC CGL 2nd Sit. 2012)

Detailed Solution for SSC CGL Previous Year Questions: Algebra- 5 - Question 40

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

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