Aptitude - Questions & Answers

Basic Equations - Online Quiz

Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Basic Equations. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - The arrangement of x/2+ y/9 = 11 and x/3 + y/6 =9 are:

Answer : C

Explanation

The given equations are
9x+ 2y = 198...(i)
2x+y =54...(iii)
On multiplying (ii) by 2 and subtracting it from (i), we get: 5x= 90 ⇒x= 18
Putting x=18 in (ii), we get: 36+y = 54 ⇒y = 18
∴x = 18, y= 18

Q 2 - On solving 4/x+5y=7 and 3/x+4y =5 we, get:

Answer : C

Explanation

Given equations are 4/x+5 y= 7 ...(i)
3/x+4y = 5  ...(ii)
On multiplying (i) by 3, (ii) by 4 and subtracting, we get -y =1 ⇒y= -1
Putting y= -1 in (i), we get 4/x-5 = 7 ⇒4/x= 12 ⇒12x= 4 ⇒x= 1/3
∴x= 1/3, y= -1

Q 3 - If (5, ℏ) is an answer of 2x+y-6 =0 then ℏ=?

Answer : A

Explanation

Clearly x= 5 and y= ℏ satisfies 2x+y- 6 = 0
∴ 2*5+ ℏ-6= 0 ⇒ 10+ℏ- 6= 0 ⇒ℏ+4= 0 ⇒ ℏ= -4

Q 4 - On solving p/x+q/y = m, q/x+p/y = n, we get:

A - x=(q²-p²)/(mp-nq) , y = (q²-p²)/(np-mq)

B - x=(p²-q²)/(mp-nq), y=(p²-q²)/(np-mq)

C - x=(p²-q²)/(mp-nq) , y= (q²-p²)/(np-mq)

D - x=(q²-p²)/(mp-nq), y = (p²-q²)/(np-mq)

Answer : B

Explanation

Given equations are p/x+q/y = m...(i),   q/x+ p/y = n ...(ii)
On multiplying (i) by q, (ii) by p and subtracting, we get:
q²/y- p²/y = mq-np
⇒y (mp-np) = (q²- p²)
⇒y = (q²-p²)/(mq- np)
= (p²- q²)/(np-mq)
On multiplying (i) by p, (ii) by q and subtracting, we get:
p²/x - q²/x = mp- nq
⇒ (p²- q²) = x (mp- nq)
⇒x = (p²- q²)/ (mp-nq)
∴ x= (p²-q²)/(mp-nq) , y = (p²-q²)/(np- mq)

Q 5 - On the off chance that 2a+3 b= 17 and 2a+2-3b+1= 5 then:

Answer : D

Explanation

Given equation are  2a +3b = 17 ...(i)
2a*2²- 3b*3ⁱ= 5   ⇒4*2a- 3*3b= 5 ...(ii)
Putting 2a = x and 3b= y, we get:
x+y= 17 ...(iii)     4x-3y = 5...(iv)
Multiplying (iii) by 3 and adding (iv) to it, we get: 7x= 56
⇒x= 8
Putting x= 8 in (iii), we get: 8+ y = 17 ⇒y = 9
∴ (2a= 8 = 2³ ⇒a = 3) and (3b= 9= 3² ⇒b= 2)
∴ a= 3, b= 2

Q 6 - On the off chance that 4x+6y =32 and 4x-2y= 4, then 8y =?

Answer : D

Explanation

4x+6y = 32...(i) 4x-2y = 4...(ii)
On subtracting (ii) from (i), we get: 8 y= 28

Q 7 - The arrangement of x/2+y/3 =4 and x+y = 10 are given by:

Answer : C

Explanation

Given equation are 3x+2y = 24 ...(i), x+y =10 ...(ii)
On multiplying (ii) by 2 and subtracting from (i), we get: x=4
Putting x= 4 in (ii), we get: y = (10-4) = 6

Q 8 - The System of mathematical statements ℏx-y= 2 and 6x-2y =3 have an exceptional arrangement when:

Answer : D

Explanation

For a unique solution , we must have  ℏ/6 ≠-1/-2 ⇒ ℏ≠(6*1/2 )= 3

Q 9 - The arrangement of comparisons 4x+7y= 10 and 10x+ky= 25 have boundless number of arrangements, when:

Answer : D

Explanation

For infinite number of solutions, we have a₁/a₂ = b₁/b₂ =c₁/c₂
∴ 4/10 = 7/ℏ= 10/25 ⇒7/ℏ= 2/5 ⇒ℏ= 35/2

Q 10 - In the event that 3x-5y = 5 and x/x+y = 5/7, then (x-y) =?

Answer : A

Explanation

3x -5y=5 ...(i), 7x=5x+5y⇒2x-5y=0 ...(ii)
On subtracting (ii) from (i), we get=5.
3*5-5y=5⇒5y=10⇒y=2.
∴(x-y) = (5-2) =3.

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