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Question 1 of 10
1. Question
Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:
I. x – 9 √3x + 60 = 0
II. y – 14 √2y + 96 = 0
Correct
x– 5 √3x – 4 √3x + 60 = 0
⇒ (√x – 4 √3)( √x – 5 √3)
⇒ √x = 4 √3 , 5 √3
⇒ x = 48, 75
II. y – 8 √2y – 6 √2y + 96 = 0
⇒ ( √y – 8 √2 )(√ y – 6 √2) = 0
⇒√y = 8 √2 , 6 √2
⇒ y = 128, 72
So, No relationship between x and y exists.
Incorrect
x– 5 √3x – 4 √3x + 60 = 0
⇒ (√x – 4 √3)( √x – 5 √3)
⇒ √x = 4 √3 , 5 √3
⇒ x = 48, 75
II. y – 8 √2y – 6 √2y + 96 = 0
⇒ ( √y – 8 √2 )(√ y – 6 √2) = 0
⇒√y = 8 √2 , 6 √2
⇒ y = 128, 72
So, No relationship between x and y exists.
Question 2 of 10
2. Question
Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:
I. 20 x^{2} – 159x + 304 = 0
II. 25 y^{2} – 120y + 108 = 0
Correct
I. 20x^{2} – 64 x – 95 x + 304 = 0
⇒ (5x – 16) (4x – 19) = 0
⇒ x = ^{16}/_{5},^{19}/_{4}
II. 25y2 – 30y – 90y + 108 = 0
⇒(5y – 18) (5y – 6) = 0
⇒y =^{18}/_{5},^{6}/_{5}
No relationship between x and y exists
Incorrect
I. 20x^{2} – 64 x – 95 x + 304 = 0
⇒ (5x – 16) (4x – 19) = 0
⇒ x = ^{16}/_{5},^{19}/_{4}
II. 25y2 – 30y – 90y + 108 = 0
⇒(5y – 18) (5y – 6) = 0
⇒y =^{18}/_{5},^{6}/_{5}
No relationship between x and y exists
Question 3 of 10
3. Question
Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:
I. x^{2} –5 √5 x + 30 = 0
II. y^{2} – 7 √7 y + 84 = 0
Correct
y > x or x < y
Incorrect
y > x or x < y
Question 4 of 10
4. Question
Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:
I. x^{2} – 14x + 45 = 0
II. y^{2} – 20y + 99 = 0
Correct
i. x^{2} – 5x – 9x + 45 = 0
⇒ (x – 5) (x – 9) = 0
⇒ x = 5, 9
II. y^{2} – 11y – 9y + 99 = 0
⇒ (y –11) (y –9) = 0
⇒ y = 11, 9
So, y ≥ x or x ≤ y
Incorrect
i. x^{2} – 5x – 9x + 45 = 0
⇒ (x – 5) (x – 9) = 0
⇒ x = 5, 9
II. y^{2} – 11y – 9y + 99 = 0
⇒ (y –11) (y –9) = 0
⇒ y = 11, 9
So, y ≥ x or x ≤ y
Question 5 of 10
5. Question
Directions: In the following number series one number is wrong. Find out the wrong number.
289, 360, 529, 841, 961, 1369
Correct
The series is 17^{2} = 289 ,
19^{2} = 361,
23^{2} = 529,
29^{2} = 841,
31^{2} = 961,
37^{2} = 1369 (squares of prime number)
⇒ The wrong number in the series is 360.
Incorrect
The series is 17^{2} = 289 ,
19^{2} = 361,
23^{2} = 529,
29^{2} = 841,
31^{2} = 961,
37^{2} = 1369 (squares of prime number)
⇒ The wrong number in the series is 360.
Question 6 of 10
6. Question
Directions: In the following number series one number is wrong. Find out the wrong number.
197, 233, 297, 396, 541, 737
Correct
The series is +6^{2}, +8^{2}, +10^{2}, + 12^{2}, +14^{2}, +16^{2}….
Incorrect
The series is +6^{2}, +8^{2}, +10^{2}, + 12^{2}, +14^{2}, +16^{2}….
Question 7 of 10
7. Question
Directions: In the following number series one number is wrong. Find out the wrong number.
157, 183, 210, 241, 273, 307
Correct
The series is:
13^{2} –12 = 157
14^{2} – 13 = 183
15^{2} – 14 = 211 ≠ 210
16^{2} – 15 = 241
17^{2}– 16 = 273
18^{2} – 17 = 307
Incorrect
The series is:
13^{2} –12 = 157
14^{2} – 13 = 183
15^{2} – 14 = 211 ≠ 210
16^{2} – 15 = 241
17^{2}– 16 = 273
18^{2} – 17 = 307
Question 8 of 10
8. Question
Biswas borrowed a sum of Rs 30,000. He took a part of it at 12% per annum rate of simple interest and the remaining at 10% per annum. At the end of two years, he returned Rs 36480 and discharged his loan. What was the sum borrowed at 12% per annum rate of interest?
Correct
Incorrect
Question 9 of 10
9. Question
The numerator of a fraction is increased by ^{1}/_{4} and the denominator is decreased by ^{1}/_{3} , the fraction thus obtained is ^{33}/_{64} . What was the original fraction?
Correct
Incorrect
Question 10 of 10
10. Question
A train leaves P for Q at the same time that a train leaves Q for P. The two trains meet at the end of 6 hours. The train from P to Q travelles 8 kilometres an hour more than the other. What would be the speed of the slower train if the distance from P to Q is 528 kilometres?