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[WpProQuiz 7360]Quadratic equations
Directions (1 – 5): Following question contains two equations as I and II. You have to solve both equations and determine the relationship between them and give answer as,
1)
I) 14x² – 5√15 x – 90 = 0
II) 6y² + √21 y – 21 = 0
a) x > y
b) x ≥ y
c) x = y or relationship cannot be determined.
d) x < y
e) x ≤ y
2)
I)  3x2– 13√2x + 24 = 0 Â
II) y2– 4√2y + 6 = 0
a) x > y
b) x ≥ y
c) x = y or relationship cannot be determined.
d) x < y
e) x ≤ y
3)
I) 3x2– (6 + √5)x + 2√5 = 0Â
II) 8y2– (16 + 3√5)y + 6√5 = 0
a) x > y
b) x ≥ y
c) x = y or relationship cannot be determined.
d) x < y
e) x ≤ y
4)
I) 18x² – 63x + 40 = 0
II) 12y² + 47y + 45 = 0
a) x > y
b) x ≥ y
c) x = y or relationship cannot be determined.
d) x < y
e) x ≤ y
5)
I) 20x²-119x+176=0
II) 45x²+200x+155=0
a) x > y
b) x ≥ y
c) x = y or relationship cannot be determined.
d) x < y
e) x ≤ y
Caselet
Directions (6 – 10): Study the following information carefully and answer the questions given below.
The population of village A and Village B is 2400 and 2100 respectively. The percentage of Labours in village A is 33.33% and that of village B is 42.85%. The ratio of male and female labours in village A is 3:2 and that in village B is 5:4. The male labours and female labours of village A work for 9 hours in a day and the male labours and female labours of village B work for 7 hours in a day.
6) The total number of male labours from village A is what percent of total number of female labours in village B?
a) 130%
b) 120%
c) 125%
d) 135%
e) None of these
7) Total male labours from both villages is how much approx percentage more or less than the total female labours from both villages?
a) 36% more
b) 40% more
c) 39% less
d) 35% less
e) None of these
8) How many hours the total male labours works in a day from both the villages?
a) 8500
b) 8250
c) 7820
d) 8900
e) None of these
9) Find the total numbers of peoples who are not labours in both the villages.
a) 1600
b) 2800
c) 3200
d) 2400
e) None of these
10) Find the difference between the male labours in both the villages to that of female labours in both the villages?
a) 260
b) 300
c) 280
d) 320
e) None of these
Answers :
Directions (1-5) :
1) Answer: c
I) 14x²-5√15 x-90=0
14x²-12√15 x+7√15 x – 90 = 0
2x(7x – 6√15)+ √15(7x – 6√15) = 0
(2x + √15)(7x – 6√15) = 0
x = -√15/2, (6√15)/7
II) 6y²+√21 y-21=0
6y²+3√21 y-2√21 y -21=0
3y(2y+√21)- √21(2y+√21)=0
(3y- √21)(2y+√21)=0
y =√21/3 ,-√21/2
Hence, relationship between x and y cannot be determined
2) Answer: c
I) 3x2– 13√2x + 24 = 0
3x2 – 9√2x – 4√2x + 24 = 0
3x(x – 3√2) – 4√2 (x – 3√2) = 0
(3x – 4√2)(x – 3√2) = 0
x = 4√2/3, 3√2
II)y2– 4√2y + 6 = 0
y2 – √2y – 3√2y + 6 = 0
y(y – √2) – 3√2 (y – √2) = 0
(y – √2) (y – 3√2) = 0
y = √2, 3√2
Hence, relationship between x and y cannot be determined
3) Answer: c
I) 3x2– (6 + √5)x + 2√5 = 0Â
3x2 – 6x – √5x + 2√5 = 0
3x (x – 2) – √5 (x – 2) = 0
(3x – √5) (x – 2) = 0
x = √5/3,2
II) 8y2– (16 + 3√5)y + 6√5 = 0
8y2 – 16y – 3√5y + 6√5 = 0
8y (y – 2) – 3√5 (y – 2) = 0
(8y – 3√5) (y – 2) = 0
y = (3√5)/8, 2
Hence, relationship between x and y cannot be determined
4) Answer: a)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
I) 18x² – 63x + 40 = 0
18x²-15x-48x+40=0
3x(6x-5)-8(6x-5)=0
(3x-8)(6x-5)=0
x=8/3,5/6
II) 12y²+47y+45=0
12y²+27y+20y+45=0
3y(4y+9)+5(4y+9)=0
(3y+5)(4y+9)=0
Y =-5/3,-9/4
Hence, x > y
5) Answer: a)
I) 20x²-119x+176=0
20x²-64x-55x+176=0
4x(5x-16)-11(5x-16)=0
(4x-11)(5x-16)=0
x=11/4,16/5
II) 45x²+200x+155=0
45x²+45x+155x+155=0
45x(x+1)+155(x+1)=0
(45x+155)(x+1)=0
x=-155/45,-1
Hence, x > y
Directions (6 – 10) :
Total population of village A = 2400
Population labours in village A = 33.33% of 2400 = 1/3 * 2400 = 800
Male labours in village A = 800 * 3/5 = 480
Female labours in village A = 800 * 2/5 = 320
Total population of village B = 2100
Population labours in village B = 42.85% of 2400 = 3/7 * 2100 = 900
Male labours in village B = 900 * 5/9 = 500
Female labours in village A = 900 * 4/9 = 400
6) Answer: b)
Required percentage = 480/400 * 100 = 120%
7) Answer: a)
Total male labours from both villages = 480 + 500 = 980
Total female labours from both villages = 320 + 400 = 720
Required percentage = (980 – 720)/720 * 100
= (260 * 100)/720 = 36.11 % = 36% approx
8) Answer: c)
Total hours of male labours from both the villages = 480 * 9 + 500 * 7 = 7820 hours.
9) Answer: b)
Required numbers of peoples = (2400 + 2100) – (800 + 900) = 2800
10) Answer: a)
Required difference = (480 + 500) – (320 + 400) = 260
