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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
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
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)
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 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 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.
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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