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- Question
- A point O in the interior of a rectangular ABCD is joined with each of the vertices A, B, C and D. Then :
Options- A. OA2 + OC2 = OB2 ? OD2
- B. OA2 + OC2 = OB2 + OD2
- C. OA2 = OB2 = OC2 + OD2
- D. OA2 + OD2 = OB2 + OC2
- Correct Answer
- OA2 + OC2 = OB2 + OD2
ExplanationAs per given figure , we can see that
Since the diagonals of a rectangle are equal and bisect each other. Let AC and BD intersect at M. Therefore M is the mid-point of AC and BD and AM = DM
From ?AOC, OA2 + OC2 = 2(AM2 + MO2) [Appollonius Theorem.] .......... ( 1 )
also in ?ODB, OB2 + OD2 = 2(MO2 + DM2) = 2(MO2 + AM2) .......... ( 2 )
From equations ( 1 ) and ( 2 ) .
? OA2 + OC2 = OB2 + OD2. - 1. Out of four number, the average of first three is 15 and that of the last three is 16, if the last number is 19, the first is?
Options- A. 15
- B. 16
- C. 18
- D. 19 Discuss
- 2. The average temperature of the first three days is 27° C and that of the next three is 29° C . If the average of the whole week is 28.5° C, the temperature of the last day of the week is?
Options- A. 10.5° C
- B. 21° C
- C. 31.5° C
- D. 42° C Discuss
- 3. The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is?
Options- A. 96 litres
- B. 98 litres
- C. 100 litres
- D. 102 litres Discuss
- 4. A batsman has a certain average runs for 11 innings . In the 12th innings he made a score of 90 runs and thereby decrease his average by 5 . His average after 12th innings is?
Options- A. 127
- B. 145
- C. 150
- D. 217 Discuss
- 5. The average age of A, B , C, D five years ago was 45 years . by including P, the present average age of all the five is 49 years . the present age of P is?
Options- A. 64 years
- B. 48 years
- C. 45 years
- D. 40 years Discuss
- 6. Out of three number, the first is twice the second and is half of the third. If the average of the three number is 56, the three number on order are?
Options- A. 48, 96, 24
- B. 48, 24, 96
- C. 96, 24,48
- D. 96, 48, 24 Discuss
- 7. The sum of seven numbers is 235. The average of the first three is 23 and that of the last three is 42. The fourth number is?
Options- A. 40
- B. 126
- C. 69
- D. 195 Discuss
- 8. Average to ten number is 7 . If every number is multiplied by 12, What will be the average of new numbers?
Options- A. 7
- B. 9
- C. 82
- D. 84 Discuss
- 9. The average weight of 60 students in a class was calculated to be 40 kg. Later it was found out that the weight of one of the students was calculated as 36 kg, whereas his actual weight was 33 kg. What is the actual average weight of the students in the class?
Options- A. 39.90 kg
- B. 39.95 kg
- C. 39 kg
- D. 38 kg Discuss
- 10. On a journey across Delhi, a taxi average 30 kmph for 60% of the distance, 20 kmph for 20% of it and 10 kmph for the remainder, the average speed for the whole journey is?
Options- A. 20 km/hr
- B. 22.5 km/hr
- C. 24.625 km/hr
- D. 25km/hr Discuss
More questions
Correct Answer: 16
Explanation:
Sum of four number = ( 15 x 3 + 19 ) = 64
Sum of last three number = ( 16 x 3 ) = 48
? first number = ( 64 ? 48 ) = 16
Correct Answer: 31.5° C
Explanation:
Temperature of last day = Sum of temperature of 7 days - sum of temperature of first 6 days.
= ( 7 x 28.5 ) - [( 3 x 27 ) + ( 3 x 29 )]
=31.5
? Temperature of last day = 31.5
Correct Answer: 100 litres
Explanation:
Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12
Average = ( 110 x 7 + 86 x 5 ) / 12
=(1200 / 12 = 100 liters
Correct Answer: 145
Explanation:
Let the average for first 11 innings is y
From question
11y + 90 = (y - 5) x 12
? y = 150
? Average after 12th inning = (150 - 5)= 145
Correct Answer: 45 years
Explanation:
Present age of P = [(49 x 5 ) - (4 x 45 + 4 x 5 ) ] years
= 45 years.
Correct Answer: 48, 24, 96
Explanation:
Let the numbers be 2y, y and 4y
? Average = (2y + y + 4y)/3
? 7y/3 = 56
? y = (3 x 56) / 7 = 24
Hence , the number in order are 48, 24 and 96
Correct Answer: 40
Explanation:
Sum of 7 numbers = sum of first 3 numbers + N4 + sum of last 3 numbers.
(23 x 3) + N4 + (42 x 3) = 235
? N4 = 40
? 4th number = 40
Correct Answer: 84
Explanation:
Here initial average = 7
As we know that, if all the numbers are multiple by a certain number, then their average must be a multiple of that number.
? New average = 7 x 12 = 84
Correct Answer: 39.95 kg
Explanation:
Total correct weight = (40 x 60) - 36 + 33 = 2400 - 3 = 2397 kg
? Required average weight = 2397/60 = 39.95 kg
Correct Answer: 20 km/hr
Explanation:
Let total journey = y km
Total time taken = time taken during 60% of distance + time taken during 20% of distance + time taken in remaining distance
= [( 60y / 100 ) / 30] + [( 20y / 100 ) / 20] + [( 20y / 100 ) / 10]
= ( y / 50 + y / 100 + y / 50 )hrs
= y/20 hours.
Average speed = total distance traveled / total time taken.
= [y / ( y/20 )] km/hr
=20 km/hr.
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