MCQ: Graphs of Linear Equations - 2 - SSC CGL MCQ

# MCQ: Graphs of Linear Equations - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Graphs of Linear Equations - 2

MCQ: Graphs of Linear Equations - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Graphs of Linear Equations - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Graphs of Linear Equations - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Graphs of Linear Equations - 2 below.
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MCQ: Graphs of Linear Equations - 2 - Question 1

### The solution set of the equations

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 1

the given equations becomes:

or 7u + 24v = 7 and 7u + 4v = 2.
Solving these, we get:

∴ 2x + 3y = 7 and 3x - 2y = 4.
Now solving these equations again, we get: x = 2 and y = 1.
∴ Solution set = {(2,1)}.
Hence, option D is correct.

MCQ: Graphs of Linear Equations - 2 - Question 2

### The solution of the equation x - y = 0.9 and

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 2

By cross multiplication, 2nd equation becomes 2x + 2y = 11.
Now multiplying 1st equation by 2 and adding to this equation, we get 4x = 12.8 or x = 3.2.
Putting x = 3.2 in 1st equation, we get y = 3.2 - 0.9 = 2.3.
Hence, option A is correct.

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MCQ: Graphs of Linear Equations - 2 - Question 3

### The value of y in the solution of the equation 2x + y = 2x – y = √8 is:

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 3

2x + y = 2x – y
2x + y = 2x - y = 8 = 23/2

Solving these equation we get:

Hence, option A is correct.

MCQ: Graphs of Linear Equations - 2 - Question 4

Find the value of the given below information
Solve:

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 4

Putting 1/x = u and 1/y = v, The given equation become:
6u + 3v = 7 and 3u + 9y = 11.
On solving these equations, we get: u = 2/3 and v = 1.

Hence, option A is correct.

MCQ: Graphs of Linear Equations - 2 - Question 5

Find the value of x and y from the given equation:
3x + 2y = 4, 8x + 5y = 9.

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 5

To eliminate x, we must make the coefficients of x equal in both of the given equation.
So, multiplying the first equation by 8, second equation by 3 and subtracting, we get: y = 5.
Putting y = 5 in first equations, we get 3x + 10 = 4 or 3x = – 6 or x = – 2.
∴ Solution set is {( – 2, 5)}.
Hence, option B is correct.

MCQ: Graphs of Linear Equations - 2 - Question 6

The straight line 4x + 3y = 12 passes through:

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 6

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

Hence, option B is correct.

MCQ: Graphs of Linear Equations - 2 - Question 7

The area of the triangle formed by the graph of 3x + 4y = 12, x-axis and y-axis (in sq. units) is

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 7

x-axis ⇒ y = 0, putting in equation 3x + 4y = 12
3x = 12 ⇒ x = 4
⇒ Co-ordinates of point of intersection on x-axis = (4, 0)
Putting on y-axis = (0, 3)
∴ (0, 3)
OA = 4
OB = 3

Hence, option C is correct.

MCQ: Graphs of Linear Equations - 2 - Question 8

The area bounded by the lines x = 0, y = 0, x + y = 1, 2x + 3y = 6 (in square units) is

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 8

x = 0 is the equation of y-axis.
y = 0 is the equation of x-axis.
Putting x = 0 in x + y = 1, y = 1
Putting y = 0 in x + y = 1, x = 1
Putting x = 0 in 2x + 3y = 6
3y = 6 ⇒ y = 2
Putting y = 0 in 2x + 3y = 6 ⇒ 2x = 6 ⇒ x = 3
∴ OB = 1; OA = 1 OD = 3; OC = 2 ∴ Required area = ΔOCD – ΔOAB

Hence, option C correct.

MCQ: Graphs of Linear Equations - 2 - Question 9

If 5x + 9y = 5 and 125x3 + 729y3 = 120 then the value of the product of x and y is:

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 9

Given,
5x + 9y = 5 .....(i)
125x3 + 729y3 = 120 ....(ii)
Make whole cube of 1st equation, we get
(5x + 9y)3 = (5)3
⇒ 125x3 + 729x3 + 3 × 5x × 9y (5x + 9y) = 125
Put the value of given terms in equation
⇒ 125x3 + 729x3 + 3 × 5x × 9y (5x + 9y) = 125
⇒ 120 + 135xy × 5 = 125
⇒ 135xy × 5 = 5
⇒ xy = 1/135.
Hence, option D is correct.

MCQ: Graphs of Linear Equations - 2 - Question 10

If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x + y) is equal to

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 10

x + y + z = 13
x2 + y2 + z2 = 69
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
⇒ (13)2 = 69 + 2[xy + z(x + y)]
⇒ 2[xy + z(x + y)] = 169 – 69 = 100
⇒ [xy + z(x + y)] = 100/2 = 50.
Hence, option C is correct.

MCQ: Graphs of Linear Equations - 2 - Question 11

If 6x – 5y = 13, 7x + 2y = 23 then 11x + 18y = ?

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 11

6x – 5y = 13 ...... (i)
7x + 2y = 23 ...... (ii)
By equation (i) × 2 & (ii) × 5,
12x – 10y = 26 ..... (iii)
35x + 10y = 115 ...... (iv)
by solving these equation we get
x = 3, y = 1
∴ 11x + 18y = 11 × 3 + 18 × 1 = 33 + 18 = 51.
Hence, option B is correct.

MCQ: Graphs of Linear Equations - 2 - Question 12

A person bought 5 tickets from a station P to a station Q and 10 tickets from the station P to a station R. He paid Rs. 350. If the sum of a ticket from P to Q and a ticket from P to R is Rs. 42, then what is the fare from P to Q?

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 12

Let the fare from station P to station Q is Rs. x and the fare from
station P to station R is Rs. y.
By given condition, x + y = 42 .....(i)
and 5x + 10y = 350 .... (ii)
On solving Eqs. (i) and (ii), we get
x = 14 and y = 28
Hence, fare from station P to station Q is Rs. 14.
Hence, option B is correct.

MCQ: Graphs of Linear Equations - 2 - Question 13

If one-third of a two-digit number exceeds its one-fourth by 8, then what is the sum of the digits of the number?

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 13

Let the number be y,

⇒ y = 12 × 8 = 96
∴ Sum of digits = 9 + 6 = 15.
Hence, option C is correct.

MCQ: Graphs of Linear Equations - 2 - Question 14

What is the sum of two numbers whose differences is 45 and the quotient of the greater number by the lesser number is 4?

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 14

Let the greater number be x and smaller number be y
∴ x – y = 45 ..... (i)
and x = 4y ..... (ii)
From eqs. (i) and (ii)
4y – y = 45
⇒ y = 45/3 = 15
On putting the value of y in Eq. (ii), we get
x = 4 × 15 = 60
Hence, required sum = x + y = 60 + 15 = 75.
Hence, option D is correct.

MCQ: Graphs of Linear Equations - 2 - Question 15

If a two-digit number is added to a number obtained by reversing the digits of the given number, then the sum is always divisible by which one of the following numbers?

Detailed Solution for MCQ: Graphs of Linear Equations - 2 - Question 15

Let a two-digit number be (10x + y) and reversing number be (10y + x)
∴ Required sum = 10x + y + 10y + x = 11x + 11y = 11(x + y)
Hence, it's divisible by 11.
Hence, option D is correct.

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests