41. ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?
Answer:
Explanation:Join OE and OD.
Internal angle of regular pentagon = 108°
∠EAB = ∠EDC = 108°
∠OAB = 60°
∠EAO = 48°
AO = OB = AB as the triangle is equilateral. AB = AE as this is a regular pentagon.
Triangle AEO is isosceles as AO = EA.
∠AEO = ∠AOE = x (say)
In triangle AEO,
∠OAE + 2x = 180° 48° + 2x = 180°
2x = 132°, or x = 66°
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42. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the centre of the circle than the periphery?
Answer:
Explanation:0.25.
Total area of board = Pi*1^2= Pi Preferred are =Pi (1/2)^2= Pi/4
So prob = (pi/4)/pi =1/4= 0.25
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43. Six friends decide to share a big cake. Since all of them like the cake, they begin quarrelling as to who gets to first cut and has a piece of the cake. One friend suggests that they blindfold a friend and then choose from a well shuffled set of cards numbered from one to six. You check and find that this method works as it should be simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfolding and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums up to a number between 2 and 12. Which total would be likely to appear more often 8, 9 or 10?
Answer:
Explanation:The best solution will be 7, and there will be total 6 cases for this choice (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)but this one is not in the choices so out of the 4 choices given 8 will be the best choice. For this choice there are 5 methods (2,6), (3,5), (4,4), (5,3), (6,2)
Similarly for 9 there are 4 choices (3,6), (4,5), (5,4),
(6,3) for 10 there are 3 choices (4,6), (5,5), (4,6)
Answer is 8.
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44. One the Planet, Oz, there are 8 days in a week - Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hours has 90 min while each minute has 60 sec. As on earth, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when time is
14.40 am
Answer:
Explanation:Hour hand=> 18hrs=360 deg=> 1hr=20 deg 90mins=20 deg=> 1min=2/9 deg
Minute hand=> 90mins=360 deg=> 1min=4 deg Angle= (14*20+40*2/9)-40*4
= 280+80(8.8)/9-160
= 289-160
Angle= 129 deg.
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45. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque with his neighbour and gave change to John. After 2 days, it is known that cheque is bounced. Shop keeper paid the amount to his neighbour. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper?
Answer:
Explanation:CP of cycle = $19 SP of cycle = $31
Profit for the shopkeeper = $31 - $19 = $12 Again, shopkeeper gave $35 to neighbour. Loss = $35
So, net loss = $35 - $12 = $23
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46. A game is played between 2 players and one player is declared as winner. All the winners from first round, played in the second round. All the winners from second round played in third round and so on. If 8 rounds were played to declare only one player as winner, how many players played in first round?
Answer:
Explanation:8 rounds means 128-64-32-16-8-4-2-1
So 128 matches were played in first round teams= 128*2=256
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47. Alok is attending a workshop "How to do more with less" and today's theme is working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4?Can you help Alok find the answer?
Answer:
Explanation:For a number to be divisible by 4,we must check that the last two digits should be divisible by 4.
The combinations of digits formed by 1,2,3,4,5 which are divisible by 4 are (1,2),(2,4),(3,2)(4,4),(5,2)
So out of these 5 pairs we must select 1 pair for the number to be divisible by 4.
So probability is 5C1 =5
Now we have to select the first 3 digits in a number. They can be any digits i.e. (1, 2, 3, 4, 5) because repetition is allowed
Number of possibilities for 1st place =5 Number of possibilities for 2nd place =5 Number of possibilities for 3rd place =5
So total possibilities at 1st, 2nd, 3rd place =5^3 Total probability is=5^3+5C1 = 5^4= 625.
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48. If 5 Neptunians can destroy 5 small plutos in 5 solar years. How long will 7 Neptunians take to destroy 7 small plutos (in solar years)?
Answer:
Explanation:Using chain Rule, 5*7*5=7*5*x x=(5*7*5)/(7*5)=5.
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49. A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
Answer:
Explanation:"The first 13 statements are true and the rest are false." is the correct answer.
All others do not satisfy the rule and contradict itself.
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50. The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P= 180 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 120 cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed kmph.
Answer:
Explanation:n/P = 180 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 120cm.
Number of steps in one minute = 180*1.2
Distance travelled in 1 minute = 180*1.2*1.2 metres Distance travelled in one hr = 180*1.2*1.2*60/1000 km = 15.55 km approx
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