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Basic Equations - Online 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 3x+7y= 75 and 5x-5y= 25, then what is the estimation of x+y?

Answer : D

Explanation

Given 3x+7y = 75  ...(i)
5x-5 y= 25 ⇒x-y = 5...(ii)
Multiplying (ii) by 7 and adding to (i), we get:
10 x = 110   ⇒x = 11
Putting x = 11 in (ii), we get: y=(11-5) = 6
∴ x+y = (11+6) = 17

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 x+1/y= 5, 2x+ 3/y= 13, then (2x-3y) =?

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 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 x+2y = 3 and 2x+ 4y = 3 have:

A - Precisely two arrangement

B - no arrangement

C - limitlessly numerous arrangement

D - an one of a kind arrangement

Answer : B

Explanation

Here a₁/a₂= 1/2, b₁/b₂=2/4=1/2 and c₁/c₂=3/3=1.
∴ a₁/a₂=b₁/b₂≠c₁/c₂.
∴Give system has no solution.

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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