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Science & Math for K6 - K12 Students

Exercises-VI ,V & VI
Exercise-IV
1. If 2x + 4y = 28 and find x
 Sol: 8y = 24x y = 3x 2x + 4y = 28 2x + 4(3x) = 28 14x = 28 x = 2 Grid form is

2. If find x
 Sol: = 10(x – 2) = 6(x + 2) 10x – 20 = 6x + 12 4x = 32 x = 8 Grid form is

3. 42 drums contain a total of 17640 litres of water. If each bottle contains the same amount of water, how many litres of water are in each drum
 Sol: 42 drums contains 17640 litres of water 1 drum contains ? litres of water = 420 litres of water 1 drum contains 420 litres Grid form is

4. A Philharmonic orchestra will choose 5 wow singers from its apprentice program. The apprentice program is made of 8 women and 4 men. If 4 women and 1 man are to be chosen from the singer, how many different groupings are possible?
 Sol: There are 8 women total to choose from and the company needs 4, so you would do 8 × 7 × 6 × 5 = 1180 However because order doesn't matter to get rid of duplicates. Mathematically this is done by dividing your answer by the factorial of spaces you need to fill Because we need 4, we divide by 4! or 24 which leaves us with 70 (1680 24 = 70). Now on, to the men. There are 4 men to choose and we need only 1. so there are 4 ways to choose that. Now that we have to count (70) women and our men are 4 Remember in probability that and means multiply 70 × 4 = 280, which is the answer Grid form is

5. The estimated population of snow leapords in a certain region is given by the function p(t) = xt + 200 where t is an integer which represents the number of years after the snow leapord population was counted 0 ≤ t ≤ 20, and 'x' is a constant. If there were 600 snow leapords after 4 yrs the population was first counted, how many snow leapords will there be 12 years after the population was first counted?
 Sol: p(t) = xt + 200 (put t = 4 , p(t) = 600) 600 = x × 4 + 200 600 – 200 = 4x 4x = 400 x = 100 leapords p(t) = xt + 200 (put t = 12 , x = 100) p(12) = 12(100) + 200 = 1400

6.
x , y , z are the radius of circles where x = 2y = 6y. If perimeter of the shaded region is 70 πcm. Find the length of AF
 Sol: πr1 + πr2 + πr3 = 70π Where r1 = x = 42cm , r2 = 2y = 42cm → y = 21cm , r3 = 6z = 42cm → z = 7cm AF = 2z + 2y + 2x + 2y + 2z = 4y + 4z + 2x = 4 × 21 + 4 × 7 + 2 × 42 = 84 + 28 + 84 = 196cm Grid form is

7. There are some birds in a bird sanctuary. of the birds are flight less. of the flight less birds have white wings. What % is the percentage of birds which do not have white wings.(The birds which can fly have no white wings)
 Sol: Let the number of birds be 500 Number of flight less birds = = 300 Number of flight less birds which have white wings = = 75 Number of birds which do not have white wings = 300 – 75 = 225 % of birds which do not have white wings = = 45% Grid form is

8. 139 persons have for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is
 Sol: Required number of matches will be = 139 – 1 = 138 Grid form is
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