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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 - On solving 2x+y=8 and 3y=4+4x, we get:

Answer : B

Explanation

The given equations are
2x+ y=8...  (1)     4x-3y=-4 ...(2)
On multiplying (1) by 3 and adding (2) to it, we get:
 10x= 20
 ⇒x= 2
Putting x= 2 in (1), we get: 4+ y = 8   ⇒y = 4
∴ x= 2, y= 4

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

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 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 2x+3y=2 and 3x+2y =2 can be spoken to by a point in the direction plane in:

Answer : A

Explanation

2x+3y = 2...(i) , 3x+2y= 2...(ii)
Multiplying (i) by 2 and (ii) by 3 and subtracting, we get: -5x= -2 ⇒x= 2/5
Putting x= 2/5 in (i), we get 4/5+3y= 2 ⇒3y = (2-4/5) = 6/5 ⇒y = 6/5*1/3 =2/5
∴ the solution can be represented by a point (2/5, 2/5) which lies in 1st quadrant.

Q 8 - The arrangement of mathematical statements 2x+ℏy= 11 and 5x-7y = 5 have no arrangement when:

Answer : C

Explanation

For no solution , we have a₁/a₂ = b₁/b₂ ≠c₁/c₂
i.e. 2/5 = ℏ/-7 ≠11/5 ⇒ℏ= -14/5

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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