Linear Equations Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Linear Equations topic of quantitative aptitude
(a) 5
(b) 4
(c) 6
(d) 7
e) None of these
The correct answers to the above question in:
Answer: (c)
Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.
Let the number of spades be x. Then, number of clubs = (7 – x).
Number of diamonds = 2 x number of spades = 2x;
Number of hearts = 2 x number of diamonds = 4x.
Total number of cards = x + 2x + 4x + 7 – x – 6x + 7.
Therefore 6x + 7 = 13⇔6x = 6⇔x – 1.
Hence, number of clubs = (7 – x) = 6.
Discuss Form
Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
If x + $1/x$ = 2, then what is value of x – $1/x$ ?
a) 1
b) 2
c) 0
d) –2
Answer »Answer: (c)
Given that x + $1/x$ = 2 ... (i)
Squaring both sides, we get
$(x + 1/x)^2$ = 4
⇒ $x^2 + 1/{x^2}$ + 2 = 4
⇒ $x^2 + 1/{x^2}$ = 2 ... (ii)
Now, $(x - 1/x)^2 = (x^2 + 1/{x^2})$ – 2
= 2 – 2 = 0 [from equation (ii)]
∴ x – $1/x$ = 0
Question : 2
If ${5x - 7y + 10}/1 = {3x + 2y + 1}/8 = {11x + 4y - 10}/9$ then what is x + y equal to?
a) 2
b) 3
c) 1
d) –3
Answer »Answer: (b)
Given,
${5x - 7y + 10}/1 = {3x + 2y + 1}/8 = {11x + 4y - 10}/9$
= ${(5x + 10 - 7y) + (3x + 2y + 1) - (11x + 4y - 10)}/{(1 + 8) - 9}$
= ${- 3x - 9y + 21}/0$
⇒x + 3y = 7 ... (i)
On taking first two terms,
8(5x – 7y + 10) = 3x + 2y + 1
37x – 58y + 79 = 0 ... (ii)
From equation (i), on putting the value of x in equation (ii), we get
37(7 – 3y) – 58y + 79 = 0
⇒259 – 111y – 58y + 79 = 0
⇒169y = 338
⇒y = 2
From equation (i),
x = 7 – 3(2) = 1
∴ x + y = 1 + 2 = 3
Question : 3
The maximum marks in a Test are converted from 250 to 50 for the purpose of an Internal Assessment. The highest marks scored were 170 and lowest marks were 70. What is the difference between the maximum and minimum marks scored in the Internal Assessment ?
a) 17
b) 20
c) 15
d) 24
Answer »Answer: (b)
${170 - 70}/{250/50} = {100}/5$ = 20
Question : 4
Under what condition do the equations kx – y = 2 and 6x – 2y = 3 have a unique solution?
a) k ≠ 3
b) k = 0
c) k = 3
d) k ≠ 0
Answer »Answer: (a)
The equations kx – y = 2 and 6x – 2y = 3 have a unique solution. Then,
∴ $k/6 ≠ 1/2$ ⇒ k ≠ 3
Question : 5
The solution of linear inequalities x + y ≥ 5 and x – y ≤ 3 lies
a) In the first and second quadrants
b) In the second and third quadrants
c) Only in the first quadrant
d) In the third and fourth quadrants
Answer »Answer: (a)
x+ y ≥ 5
let first draw graph of x + y = 5 ... (i)
put y = 0 in (i)
x = 5
put x = 0 in (i)
y = 5
Checking for (0, 0)
x + y ≥ 5
0 ≥ 5, which is false
Hence, origin does not lie in x + y ≥ 5
Now,
x – y ≤ 3
let first drawn graph of x – y = 3 ...(ii)
put x = 0 in (ii)
y = –3
put y = 0 in (ii)
x = 3'
Checking for (0, 0)
x – y ≤ 3
0 ≤ 3, which is true
Hence, origin lies in x – y ≤ 3
So, shaded region will be the solution of these linear inequalities lies in the first and second quadrant.
Question : 6
Assertion (A) : The equations 2x – 3y = 5 and 6y – 4x = 11 cannot be solved graphically.
Reason (R) :The equations given above represent parallel lines.
a) A and R are correct but R is not correct explanation of A
b) A is correct but R is wrong
c) A and R are correct and R is correct explanation of A
d) A is wrong but R is correct
Answer »Answer: (c)
Given that,
2x – 3y = 5 ... (i)
and –4x + 6y = 11 ... (ii)
Also, ${a_1}/{a_2} = 2/{-4} = {-1}/2$
${b_1}/{b_2} = {-3}/6 = {-1}/2$
⇒${a_1}/{a_2} ={b_1}/{b_2} = {-1}/2 ≠ {c_1}/{c_2}$
So, both equations are in parallel. So, it is not solved graphically.
Hence, A and R are individually true and R is correct explanation of A.
GET Linear Equations PRACTICE TEST EXERCISES
Linear Equations Model Questions Set 1
Linear Equations Shortcuts and Techniques with Examples
Verbal Reasoning
Question & Answer Quiz
Non Verbal Reasoning
Question & Answer Quiz
Quantitative Aptitude
Question & Answer Quiz
Computer MCQ
Question & Answer Quiz
General English
Question & Answer Quiz
History GK
Question & Answer Quiz
Polity GK
Question & Answer Quiz
Geography GK
Question & Answer Quiz
Economy GK
Question & Answer Quiz
General Awareness GK
Question & Answer Quiz
Recently Added Subject & Categories For All Competitive Exams
100+ Quadratic Equation Questions Answers PDF for Bank
Quadratic Equation multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
IBPS Aptitude Linear Equations MCQ Questions Answers PDF
Linear equations multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »