MCQs Preparation
In the following question, two equations are given. On their basis you have to determine the relation between x and y and then give answer I. 3x^2 – 7x + 2 = 0 II. 2y^2 – 11y + 15 = 0
A. x < y
B. x > y
C. x ≤ y
D. x ≥ y
A. x < y
Equation I
3x² – 7x + 2 = 0
3x²-6x-x+2=0
3x (x-2)-1(x-2)=0
(3x -1)(x – 2) = 0
3x -1 = 0
3x =1
x = 1/3 , x-2=0
x = 2
Equation II
2y² -11y +15 = 0
2y² – 6y – 5y +15 = 0
2y (y-3)-5(y-3)=0
(2y- 5)(y-3)= 0
(2y-5)=0
y = 5/2
Also (y – 3) = 0
y=3
Now comparing x and y
x = 1/3 is smaller than 5/2 and 3
x= 2 is smaller than 3 and 5/2
Thus we see that x is smaller than y
x<y
In the following question, there are two equations. Solve them and give answer I. 20P^2 + 31P + 12 = 0 II. 21Q^2 + 23Q + 6 = 0
A. P > Q
B. P < Q
C. P ≤ Q
D. P ≥ Q
B. P < Q
I. 20P²+31P+ 12 = 0
On doing factorization
20P²+15P+16P+12 = 0
5P (4P + 3) + 4 (4P + 3) = 0
(4P + 3) (5P + 4) = 0
P = -3/4, -4/5 P — 0.75, -0.80
II. 21Q² + 23Q + 6 = 0
On doing factorization
21Q² + 9Q + 14Q + 6 = 0
3Q (7Q + 3) + 2 (7Q + 3) = 0
(7Q + 3)(3Q + 2) = 0
Q = -3/7, -2/3 Q = – 0.43, -0.66
On taking Q = – 0.43
P < Q (for both the values of P) equation I
On taking Q = -0.66
P < Q (for both the values of P) equation II
From equation I and II
P < Q
In the following question, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer. I. x^2 + 3x + 2 = 0 II. 2y^2 = 5y
A. x < y
B. x > y
C. x ≤ y
D. x = y
A. x < y
We will separately solve both equations
Equation 1:
x²+3x+2=0
x²+2x+x+2=0
x (x + 2)+1 (x +2)= 0
(x + 2) * (x + 1)= 0
x=-2 , x=-1
Equation 2:
2y² = 5y
2y² – 5y = 0
2y * (y – 5/2) = 0
y=0 , y= 5/2
Both values of y are positive while both values of x are negative
x<y