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- Question
- If one of the roots of the equation x 2 - bx + c = 0 is the square of the other, then which of the following option is correct?
Options- A. b3 = 3bc + c2 + c
- B. c3 = 3bc + b2 + b
- C. 3bc = c3 + b2 + b
- D. 3bc = c3 + b3 + b2
- Correct Answer
- b3 = 3bc + c2 + c
ExplanationGiven that, one root of the equation
x2 - bx + c = 0 is square of other root of this equation i.e., roots (?, ?2).
? Sum of roots = ? + ?2 = -(-b)/1
? ? (? + 1) = b .......(i)
and product of roots= ?. ?2 = c/1
? ?3 = c ? = c1/3 ....(ii)
From Eqs. (i) and (ii).
c1/3 (c1/3 + 1) = b ....(iii)
On cubing both sides, we get
c(c1/3 + 1)3 = b3
? c {c + 1 + 3c1/3 (c1/3 + 1)} = b3
? c {c + 1 = 3b} = b3 [from Eq. (iii)]
? b3 = 3bc + c2 + c - 1. ?. x 4 ? 227 = 398
?. y 2 + 321 = 346
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 2. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Options- A. Sunday
- B. Saturday
- C. Tuesday
- D. Wednesday Discuss
- 3. 1, 4, 9, 16, 23, 25, 36
Options- A. 9
- B. 23
- C. 25
- D. 36 Discuss
- 4. A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?
Options- A. ? 2500
- B. ? 2000
- C. ? 1500
- D. Couldn't be determined Discuss
- 5. If a : b = b : c, then ratio a 4 : b 4 is equal to
Options- A. ac : b2
- B. a2 : c2
- C. c2 : a2
- D. b2 : ac Discuss
- 6. A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.
Options- A. 3 km/h
- B. 4 km/h
- C. 4.5 km/h
- D. 9 km/h Discuss
- 7. A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?
Options- A. 2 h
- B. 21/2 h
- C. 51/2 h
- D. 4 h Discuss
- 8. Find the least number by which 175760 be devided to make it a perfect cube.
Options- A. 10
- B. 20
- C. 100
- D. 5 Discuss
- 9. The roots of the equation x2 + px + q = 0 are equal if :
Options- A. p2 = 2q
- B. p2 = 4q
- C. p2 = - 4q
- D. p2 = - 2q Discuss
- 10. Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?
Options- A. 1 : 3
- B. 1 : 8
- C. 1 : 9
- D. 1 : 18 Discuss
More questions
Correct Answer:
Explanation:
According to question ,we can say that
From equation ?. x4 = 398 + 227 = 625
? x4 = 54
From equation ?. y2 = 346 - 321 = 25
? y2 = 52
Correct Answer: Sunday
Explanation:
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
∴ The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
∴ 6th March, 2004 is Sunday (1 day before to 6th March, 2005).
Correct Answer: 23
Explanation:
Correct Answer: Couldn't be determined
Explanation:
Couldn't be determined, since the total amount of money is not given in either of the case
Correct Answer: a2 : c2
Explanation:
Given that a /b = b/c
? b2 = ac
? a4 : b4 = a4 : a2 c2 = a2 : c2
Correct Answer: 4 km/h
Explanation:
Given, A = 6 km/h, B = 3 km/ h
According to the formula, Average speed = 2AB/(A + B)
? Required average speed = 2 x 6 x 3/(6 + 3)
= 36/9 = 4 km/h
Correct Answer: 2 h
Explanation:
Given that, W + D = 6 ...(i)
[ w = Time taken while walking and
D = Time taken while driving ]
From Eq. (i)
5 +D = 6
? D = 1
2D = 2 x 1 = 2
? He will take 2 h to drive both ways.
Correct Answer: 10
Explanation:
175760 = 24 x 5 x 13 3
= 23 x 2 x 5 x 133
To make perfect cube, it must be divided by 2 x 5 = 10
Correct Answer: p2 = 4q
Explanation:
On comparing it with ax2 + bx + c = 0 , we get a = 1, b = p, c = q
The roots of the equation x2 + px + q = 0 are equal if
b2 - 4ac = 0
? p2 - 4q = 0 ? p2 = 4q.
Thus , required answer is option B .
Correct Answer: 1 : 9
Explanation:
Let the volume be x3 and 27x3
? Their edges are x and 3x
Now Ratio of their surface area = 6x2 : 54x2 = 1 : 9
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