Linear Equations Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts
LINEAR EQUATIONS PRACTICE TEST [1 - EXERCISES]
Linear Equations Model Questions Set 1
Question : 1
The value of k, for which the system of equation 3x – ky – 20 = 0 and 6x – 10y + 40 = 0 has no solution, is
a) 6
b) 5
c) 10
d) 3
Answer »Answer: (b)
Given that system of equations has no solution
⇒ |A| = 0
|A| = – 30 + 6 k
But |A| = 0
⇒ 6k – 30 = 0
⇒ k = 5
∴ Option (b) is correct.
Question : 2
It is given that the equations $x^2 – y^2$ = 0 and $(x – a)^2 + y^2$ = 1 have single positive solution. For this, the value of 'a' is
a) 2
b) - $√2$
c) $√2$
d) 1
Answer »Answer: (c)
$x^2 – y^2$ = 0
(Equation of y = |x|)
$(x – a)^2 + y^2$ = 1
[Equation of a circle with centre (a, 0) and radius 1]
These have single positive solution
⇒ y = |x| to be tangent to the circle
AB = radius of circle
∠AOB = 45°
∠OAB = 90°
[tangent to the circle]
∠ABO = 45°
Length of OB = $√{AB^2 + OA^2} = √{1^2 + 1^2}$
OB = $√2$
Question : 3
If 65x – 33y = 97 and 33x – 65y = 1, then what is xy equal to?
a) 3
b) –2
c) 2
d) –3
Answer »Answer: (c)
65x – 33y = 97 .... (i)
(given)
33x – 65y = 1 ....(ii)
(given)
From eq (i) + eq (ii)
98x – 98y = 98
98(x – y) = 98 ∴ x – y = 1 ....(iii)
Now
From eq (i) × 1 – eq (iii) × 33
65x - 33y = 97
- 33x + 33y = - 33
32x = 64
∴ $x = 64/32$ = 2
From eq (iii)
x – y = 1
2 – y = 1
∴ y = 2 – 1 = 1
Hence, xy = 2 × 1 = 2
Question : 4
The sum of digits of a two-digit number is 8 and the difference between the number and that formed by reversing the digits is 18. What is the difference between the digits of the number?
a) 2
b) 3
c) 1
d) 4
Answer »Answer: (a)
Let x be the first digit and y be the second digit of two digit number.
According to question,
x + y = 8 ... (i)
(10x + y) – (10y + x) = 18
⇒9x – 9y = 18
⇒x – y = 2 ... (ii)
Adding (i) and (ii),
x + y = 8
x - y = 2
We get
2x = 10
⇒ x = 5
⇒ y = 8 – 5 = 3
⇒ x = 5 and y = 3
∴ Required difference of digits, x – y
= 5 – 3 = 2.
Question : 5
If 2x + 3y = 87 and 3x – 3y = 48, what is the value of x?
a) 29
b) 11
c) 72
d) 28
e) None of these
Answer »Answer: (d)
2x | + | 3y | = | 87 |
3x | - | 3y | = | 48 |
5x | = | 135 |
∴ x = ${135}/5$ = 27
IMPORTANT QUANTITATIVE APTITUDE EXERCISES
Linear Equations Model Questions Set 1 Online Quiz
Click to Start..QUANTITATIVE APTITUDE CATEGORIES
-
» Number System
-
» Average
-
» LCM & HCF
-
» Percentage
-
» Profit & Loss
-
» Time & Work
-
» Pipes & Cisterns
-
» Time & Distance
-
» Trains
-
» Compound Interest
-
» Simplification
-
» Discount
-
» Power
-
» Permutations & Combination
-
» Ratio & Proportion
-
» Advance Math
-
» Algebraic Expressions
-
» Trigonometric Ratios & Identities
-
» Simple Interest
-
» Alligation & Mixtures
-
» Boats & Streams
-
» Set Theory
-
» Linear Equations
-
» Quadratic Equations
-
» Mensuration
-
» Squareroots & Cuberoots
-
» Data Sufficiency
-
» Logarithm
-
» Probability
-
» Statistics
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
IBPS PO MAINS 2025: Sentence Improvement Questions PDF
Get Free PDF of Sentence Improvement English Questions Answer with practice Mock Test and explore various examples for IBPS PO MAINS 2025, Bank, Govt Exams
Continue Reading »
IBPS PO MAINS 2025: One Word Substitution Mock Test, PDF
Get Free PDF of One Word Substitution English Questions Answer with practice Mock Test and explore various examples for IBPS PO MAINS 2025, Bank, Govt Exams
Continue Reading »
100+ Para Jumbles Mock Test, PDF for IBPS PO MAINS 2025
Get a Free PDF of Para Jumbles General English Questions Answer with practice Mock Test and explore various examples for IBPS PO MAINS 2025, Bank, Govt Exams
Continue Reading »
Coded Inequality Mock Test, PDF for IBPS PO MAINS 2025
Get a Free PDF of Coded Inequality Reasoning Questions Answer with practice Mock Test and explore various examples for IBPS PO MAINS 2025, Bank, Govt Exams
Continue Reading »