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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. The product of two consecutive odd numbers is 19043. Which is the smaller one?
Options- A. 137
- B. 131
- C. 133
- D. 129 Discuss
- 2. The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :
Options- A. b tan ? cosec B
- B. a tan ? cosec A 2
- C. c tan ? cosec C 2
- D. None of these Discuss
- 3. From a point on a circular tract 5 Km long A, B and C started running in the same direction at the same time with speeds of 2 1? 2 Km/h, 3 Km/h and 2 Km/h. respectively. Then on the starting point all three will meet again after :
Options- A. 30 hours
- B. 6 hours
- C. 10 hours
- D. 15 hours Discuss
- 4. The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is?
Options- A. 29.46 km/hr.
- B. 31.68 km/hr.
- C. 36.25 km/hr.
- D. 32.72 km/hr. Discuss
- 5. A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated?
Options- A. 120
- B. 180
- C. 160
- D. 140 Discuss
- 6. Find the LCM of 1/3, 2/9, 5/6 and 4/27.
Options- A. 1/54
- B. 10/27
- C. 20/3
- D. 3/20 Discuss
- 7. A runs 1 3? 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:
Options- A. 360 m
- B. 440 m
- C. 460 m
- D. 380 m Discuss
- 8. 124.35 % 8096 =?
Options- A. 2000
- B. 10000
- C. 1000
- D. 12000 Discuss
- 9. Given that log 10 2 = 0.3010 the value of log 10 5 is?
Options- A. 0.3241
- B. 0.6911
- C. 0.6990
- D. 0.7525 Discuss
- 10. In a month of 31 days, third Thursday falls on 16th. What will be the last day of the month?
Options- A. 5th Friday
- B. 4th Saterday
- C. 5th Wednesday
- D. 5th Thirsday Discuss
More questions
Correct Answer: 137
Explanation:
Let the two consecutive numbers are N and N+2
According to the question
N (N + 2) = 19043
? N2 + 2N - 19043 = 0
? N2 + 139N - 137N - 19043= 0
? N( N + 139) - 137 ( N - 137 ) = 0
? N( N + 139) ( N - 137) = 0
? N = 137 and N = - 139
? N = 137
Correct Answer: a tan ? cosec A 2
Explanation:
Correct Answer: 10 hours
Explanation:
A will reach at starting point in 5 * 2 / 5 = 2 hours ;
B will reach at starting point in 5 / 3 hours ;
C will reach at starting point in 5 / 2 hours ;
Then, on the starting point all three will meet after the L.C.M. of 2, 5 / 3, 5 / 2, 10 / 1 = 10 hours.
Correct Answer: 31.68 km/hr.
Explanation:
Circumference = 2?r
= 2 x (22 / 7) x 70 cm
= 440 cm
Distance travelled in 10 revolutions = 440 x 10 cm
= 4400 cm
= 44 m
? Speed = distance / time
= 44 / 5 m/sec
= (44 / 5) x (18 / 5) km/hr
= 31.68 km/hr
Correct Answer: 120
Explanation:
Regarding all copies of the same book as one book, we have only 5 books. These 5 books can be arranged in 5! ways. But all copies of the same book being identical can be arranged in only one way.
? Required number = 5! x 1! x 1! x 1! x 1! = 120
Correct Answer: 20/3
Explanation:
We known that,
LCM of fractions = (LCM of numerators) / (HCF of denominators)
? Required LCM = (LCM of 1, 2, 5, and 4) / (HCF of 3, 9, 6 and 27)
? = 20/3
Correct Answer: 440 m
Explanation:
The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.
Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
? P / 11 = (P - 120) / 8
? P / 11 = (P - 120 / 8
? 8P = 11 x (P - 120 )
? 8P = 11P - 120 x 11
? 11P - 8P = 120 x 11
? 3P = 11 × 120
? P = 440.
Correct Answer: 10000
Explanation:
? = 124.35% of 8096
= (8096 x 124.35)/100 = 1006737.6/100
= 10067.376 = 10000
Correct Answer: 0.6990
Explanation:
log105 = log10(10/2)
= log1010 - log102
= 1-0.3010
= 0.6990
Correct Answer: 5th Friday
Explanation:
Friday will fall on 3, 10, 17, 24, 31
So, it will be 5th Friday on 31 st
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