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- Question
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?
Options- A. ²²C?? + 1
- B. ²²C? + ¹?C?
- C. ²²C??
- D. ²²C?? - 1
- Correct Answer
- ²²C?? - 1
ExplanationThe total number of ways of forming the group of ten representatives is ²²C??.
The total number of ways of forming the group that consists of no seniors is ¹?C?? = 1 way
The required number of ways = ²²C?? - 1 - 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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