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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.
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
Answer : A
Explanation
Putting y = x+3 in 2x+3y = 29, we get : 2x+3 (x+3) = 29 ⇒5x = 20 ⇒x= 4
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 - If x/4 + y/3= 5/12 and x/2+ y =1, then the estimation of (x+y) is:
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 - 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
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 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 x+2y = 3 and 2x+ 4y = 3 have:
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 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:
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.