61. A sheet of paper has statements numbered from 1 to N. For each value of n from 1 to 40, statement N says "Exactly N of the statements on this sheet is false." Which statements are true and which are false?
Answer:
Explanation:For this type of Questions, follow this:
At least- 1st half are true, last half are false
Exactly- Last second one is true or (N-1)th Statement is true
Almost- All are true.
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62. The points A (-5,4), B (-7,6) and C (5,2) are the co- ordinates of a right angled triangle. Which of the following angle is a right angle?
Answer:
Explanation:Distance between any two points (x1,y1) and (x2,y2) is given by the formula [ (x2 - x1)2 - (y2 - y1)2 ]1/2 Distance between A and B in the given question is (8)1/2
Similarly, Distance between B and C is (160)1/2 Distance between A and C is (104)1/2
For any right angled triangle, hypotenuse is the largest side. Thus for our triangle ABC, BC is the hypotenuse. So the angle opposite to hypotenuse is the right angle. So A is the right angle
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63. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 19, 19 and 19, the number of points equidistant from all the 3 lines is
Answer:
Explanation:Ans is 4 because 1 for incentre and other 3 for excentres .So total no of points equidistant from the 3 lines is 4.
Note:-Every triangle has three excenters and three excircles. The excircle which is tangent to one side of the triangle and the extensions of the other two sides and the centre of the excircle is known as excentre
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64. Jenny made a block with small cubes of 9 cubic cm volume. To make the block she used 4 small cubes long, 8 small cubes wide and 16 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to look like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to take out so that the bigger cube is hollow?
Answer:
Explanation:The total volume (in terms of number of cubes) of the solid = 4*8*16= 512
The total volume (in terms of number of cubes) of the hollow = (4-2)*(8-2)*(16-2) = 168
i.e. 168 smaller cubes must be removed from the cube in order to make a hollow block.
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65. Pointing out to a photograph a man tells his friend, "She is the daughter of the only son of my father's wife". How is the girl in photograph related to the man?
Answer:
Explanation:From the given information,
The Only son of my father's wife is the man Daughter of the only son of my father's wife is the man's daughter.
So, the girl is the daughter of that man.
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66. The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than the age of my youngest grandchild and my eldest grandchild's age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?
Answer:
Explanation:Youngest be x, then eldest = 3x. 3x = y + x + 2 => y = 2x -2
So ages are 3x, 2x-2 and x respectively.
Now check the options. 10 and 13 are not suitable in place of 3x so on taking 12 for 3x, x=4 so ages are 12,6,4 but this answer is not possible according to the condition- The difference between the ages of two of my three grandchildren is 3
So take 3x=15, x=5 so ages are 15, 8, 5 and 8-5 =3 so 15 is the correct answer.
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67. What will be the remainder when (1234567890123456789)24 is divided by 2187?
Answer:
Explanation:1234567890123456789 can be expressed as (9k) 24. 1234567890123456789 is divisible by 9.
2187=37
(Because sum of the digits is divisible by 9)So it is divisible by 3. Thus the remainder will be zero.
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68. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?
A) All suspects are lying
B) The leftmost suspect is guilty
C) Rightmost suspect is guilty
Answer:
Explanation:If first is victim then all suspects are lying. Here you should remember that the rightmost person is not questioned.
If any of the person leaving leftmost is victim then the leftmost suspect is innocent. But "and" should not be used between the conditions because leftmost is not innocent necessarily.
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69. Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes 4/5th of the original speed. So, he travels the rest of the distance at a constant speed 4/5th of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?
Answer:
Explanation:Let the distance from Delhi to Gurgaon be 'd' km. The first 30 km he travels at his usual speed. However, the remaining'd-30' km he travels at a reduced speed.
To travel 'd' km he usually takes T hr. Therefore, to travel 'd - 30' km he should ideally take (d−30)xT/d hr. However, this is only if he travels at his usual speed. It is given that he travelled only at 4/5th of his usual speed. Because of this he would have taken 5/4th of the time to travel the remaining distance, i.e., he takes 1/4th of the time extra. This is given to be 45 minutes (or 3/4th hr)
1/4x(d−30)xT/d = 3/4 (1)
On the other hand, had the same thing happened after he travelled 48 km, he would have reached only 36 minutes or 34 hrs late. Hence,
1/4x(d−48)xT/d = 3/5 (2)
Dividing (1) by (2) and solving for d, we get d = 120 km.
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70. A pipe can fill a tank in 3 hrs .Due to a leakage in the tank it takes 3.5 hrs to fill the same tank. Then how many hours will the leakage can empty the tank.
Answer:
Explanation:The electric pump can fill the tank in 3 hrs. Because of the leak it took 3.5 hrs.
Now, if there is no leak and the electric pump works for 3.5 hrs instead of 3 hrs, 0.5/3 = 1/6 of the tank must have been overflown. But we are unable to see the overflow because this 1/6 is emptied by the leak of course working for 3.5 hrs.
Hence the leak can empty 1/6 of the tank in 3.5 hours. So it can empty a full tank in 21 hrs.
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