Basic Equations - Online Quiz


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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.

Questions and Answers

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

A - x=36, y=9

B - x=9, y=9

C - x=18, y=18

D - x=18, y=9

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:

A - x=1/3, y=1

B - x=- 1/3, y=-1

C - x=1/3, y=-1

D - x=- 1/3, y=1

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=?

A - -4

B - -3

C - 4

D - 6

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 - If x/4 + y/3= 5/12 and x/2+ y =1, then the estimation of (x+y) is:

A - 1/2

B - 1

C - 3/2

D - 2

Answer : C

Explanation

Given equations are 3x+4y= 5 ...(i) and x+2y =2 ...(ii)
On multiplying (ii) by 3 and subtracting (i) from it, we get 2y = 1 ⇒y = 1/2
Putting y = 1/2 in (ii), we get x+2*1/2 = 2 ⇒x+1= 2 ⇒x =1
∴(x+y ) = (1+1/2 ) = 3/2

Q 5 - The arrangement of 3x-y+1/3 = 2x+y+2/5 = 3x+2y+1/6 are given by:

A - x=1, y=2

B - x=-1, y=-1

C - x=1, y=1

D - x=2 , y=1

Answer : C

Explanation

We have (3x-y+1)/3= (2x+y+2)/5
⇒5 (3x-y+1) =3(2x+y+2)
⇒15x-5y+5 = 6x+3y+6
⇒9x-8y -1 = 0 ⇒9x-8y = 1 ...(i)
And (2x+y+2)/5 = (3x+2y+1)/6
⇒ 6 (2x+y+2) = 5(3x+2y+1)
⇒12x+6y +12=   15x+10 y+5
⇒3x+ 4y= 7...(ii)
Multiplying (ii) by 2 and adding (i) to it, we get: 15x= 15 ⇒x= 1
Putting x =1 in .., (ii), we get 3*1+4y= 7 ⇒4y = 4 ⇒y = 1
∴ x= 1, y = 1

Q 6 - On the off chance that x+1/y= 5, 2x+ 3/y= 13, then (2x-3y) =?

A - 1

B - 2

C - 3

D - 5

Answer : C

Explanation

X+1/y = 5...(i),     2x+3/y =13 ...(ii)
On multiplying (i) by 3 and subtracting (ii) from it, we get: x=2
Putting x= 2 in (i), we get 1/y =3 ⇒3y= 1 ⇒y = 1/3
∴ (2x-3y) = (2*2-3*1/3) = (4-1) = 3

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

A - x=6, y=-4

B - x=-6, y=4

C - x=4, y=6

D - x=6, y=4

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:

A - ℏ=0

B - ℏ≠0

C - ℏ=3

D - ℏ≠3

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:

A - ℏ=17/2

B - ℏ=5

C - ℏ=27/2

D - ℏ=35/2

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) =?

A - 3

B - 4

C - 6

D - 9

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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