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

A - x=3, y=-4

B - x=2, y=4

C - x=1, y=4

D - x=4, y=1

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:

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

A - 14

B - 15

C - 16

D - 17

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

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:

A - a=2, b=3

B - a=-2, b=3

C - a=2, b=-3

D - a=3, b=2

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) =?

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

A - First quadrant

B - second quadrant

C - third quadrant

D - fourth quadrant

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 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 3 seats and 1 table expense Rs. 900 and 5 seats and 3 tables cost Rs. 2100, then the expense of 4 seats and 1 table is:

A - Rs. 1000

B - Rs. 1050

C - Rs. 1100

D - Rs. 1150

Answer : B

Explanation

Let cost of 1 chair =Rs x and cost of 1 table =Rs y. Then,
3x+y=900   ...(i)             5x+3y=2100      ...(ii)
On multiplying (i) by 3 and subtracting (ii) from it, we get: 4x=600⇒x=150.
Putting x=150 in (i), we get: 3*150+y=900⇒y= (900-450) =450.
Cost of (4 chairs+1 table) =Rs (4*150+1*450) =Rs (600+450) =Rs1050.


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