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 : 6
A positive number, when increased by 10 equals 200 times its reciprocal. What is number?
a) 10
b) 20
c) 100
d) 200
Answer »Answer: (a)
Let the positive number be x.
According to the question,
x + 10 = ${200}/x$
⇒ $x^2$ + 10x = 200
⇒ $x^2$ + 10x – 200 = 0
⇒ (x – 10) (x + 20) = 0
∴ x = 10, –20
But x ≠ –20, since x is a positive number
The required number is 10.
Question : 7
If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?
1. a – b < a – c
2. If a < b then $a/c < b/c$
$1/b < 1/c$
Select the Correct answer using the code given below.
a) 2 only
b) 3 only
c) 1
d) 2 and 3
Answer »Answer: (a)
Since a, b are negative numbers.
a < 0 and b < 0
C is a positive real number
⇒ c > 0
(1) a – b < a – c
⇒ – b < – c
⇒ b > c
It is not true as b < c
(2) if a < b ⇒ $a/c < b/c$ this is true.
(3) $1/b < 1/c$
Since c > b ⇒ $1/c < 1/b$ this is not true.
∴ option (a) is correct.
Question : 8
A number consists of two digits, whose sum is 10. If 18 is subtracted from the number, digits of the number are reversed. What is the product?
a) 18
b) 24
c) 15
d) 32
Answer »Answer: (b)
Let the two-digit number be 10y + x.
According to question,
x + y = 10 ... (i)
and 10y + x – 18 = 10x + y
⇒9x – 9y = –18
⇒x – y = –2 ... (ii)
On solving equations (i) and (ii), we get
x = 4 and y = 6
∴ Required product = xy = 4 × 6 = 24.
Question : 9
In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is
a) 7
b) 3
c) 10
d) 12
e) None of these
Answer »Answer: (c)
Let there be (x + 1) members. Then,
Father's share = $1/4$ , share of each other member = $3/{4x}$.
∴ 3 $(3/{4x}) = 1/4$⇔4x = 36⇔x=9
Hence, total number of family member = 10.
Question : 10
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.
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