1. 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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2. 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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3. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?
Answer:
Explanation:Use the eqn (men*time)/work (p1*t1)/l1=(p2*t2)/l2 (12*12)/14=(72*t2)/72
12=t2
Time taken = 12
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4. 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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5. It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 26 red and 24 blue and 34 brown socks. How many socks do I have to take from the drawer to get at least two socks of the each colour?
Answer:
Explanation:Maximum of (red, blue, brown) + 2nd maximum of (red, blue, brown) + 2
36 + 24 + 2 = 62.
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6. It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says 'start' the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what will you say?
Answer:
Explanation:The series is like.. 1,4,7,10,13 and so on.
So the difference between the two consecutive no's in the series is 3. When 13 is already completed, the next no in the series should be 13+3=16.
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7. If there are 30 cans out of them one is poisoned. If a person tastes very little of this he will die within 14 hours so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can?
Answer:
Explanation:The mice will die within 24 hours not exactly on the 24th hour.
For example, if there are 7 cans,
1st Can's solution is given to mice A. 2nd Can's solution is given to mice B. 3rd Can's solution is given to mice C. 4th Can's solution is given to A and B. 5th Can's solution is given to B and C. 6th Can's solution is given to C and A. 7th Can's solution is given to A, B and C.
Then within 24 hours if A alone dies, Can 1 is poisoned. If B alone dies, Can 2 is poisoned.
If C alone dies, Can 3 is poisoned.
A and B dies if Can 4 is poisoned, B and C dies if Can 5 is poisoned, C and A dies if Can 6 is poisoned & if all A, B, C dies then Can 7 is poisoned.
From this we can tell that to check 23-1 = 7 Cans we need 3 mouse.
Therefore we can tell that in order to check 30 Cans (25-1 = 31 maximum) we need 5 mouse.
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8. The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 6) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
Answer:
Explanation:In decimal system total no. of 3's from 1 to 1000 are 100*3 = 300 In base 6, value of 300 = 3*(6^2) + 0*(6^1) + 0*(6^0) = 108.
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9. When 40! Is expressed in base 8 form, what is the last non-zero digit in the base 8 expansion?
Answer:
Explanation:We need to find the largest power of 8 that divides 40!.
We need to find the largest power of 2 that divides 40! This is given by (40/2) and then successive division by 2. = 20 + 10 + 5 + 2 + 1 = 38
So, 238 divide 40! Or, (23)12 × 22 divides 40! (23)12 divides the number or the base 8
representation ends with 12 zeroes. Now, the base 8
representation of this number will be some (abcd…n)8
× (1000000000000)8. Now, (abcd…n)8 does not end in 0 and is a multiple of 22. The last digit has to be 4.
The last non-zero digit is 4.
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10. The IT giant Tirnop has recently crossed a head count of 150000 and earning of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate Suppose 16 such programmers take 16 minutes to write 16 lines of code in total. How many lines of code can be written by 96 programmers in 96 minutes? The IT giant Tirnop has recently crossed a head count of 150000 and earning of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate Suppose 16 such programmers take 16 minutes to write 16 lines of code in total. How many lines of code can be written by 96 programmers in 96 minutes?
Answer:
Explanation:(16 men)*(16 min)/ (16 lines) = (96 men) (96 min)/x (lines)
Hence x=576
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