9 June Maths Iv

Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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(1+3+5+… 3983)/1992? • • • • • • • • •

This is an example of AP. Sum of AP = n/2(1st + last) N=1991+1 =1992 1992/2(1+3983) =996*3984=3968064 Divide it by 1992 =1992 Or 1992*1992 / 1992 =1992 Ans.

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Sue of 1 + ¾ + 9/16 .. .. To infinite? • • • • •

This is an example of infinite series. Sum of an infinite series = a/ (1-r) A = 1, R = ¾ 1 / (1-3/4) = 1/(1/4) = 4 Ans.

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.3111… +.6666.. + .02222..?

• These can be written as • (31-3)/90 +6/9 + 2/90 • Rule: deduct the number which is not repeated and divide by 10 for this number. Divide by 9 for the number which is repeated. • =28/90+60/90+2/90 • =90/90 • =1 ans. www.afterschoool.tk

Find the greatest number of three digits, which when divided by 6,9,12 gives remainder of 3 in each case?

• Now first find LCM of 6,9,12, the LCM is 36. Now find the greatest number of 3 digits divisible by 36. Let us divide 1000 by 36. the remainder is 28. Deduct 28 from 1000 = 972. Now add 3 in this = 975 • Ans. = 975 www.afterschoool.tk

(1^3 + 2^3 + 3^3 … 15^3) – (1+2+3…..15) ? • • • • • • •

The sum of the first series is: (N+1)^2*N^2 / 4 =(15+1)^2 *15*15 / 4 =256*225/4 = 14400. The sum of the next series is : n *(n+1) /2 =15*16/2 = 120 Answer = 14400 - 120 = 14280 ans. www.afterschoool.tk

K-2, 2K+1, 6K+3 are in GP, what is K? • In GP, the square of middle (2nd ) term is equal to multiple of first and 3rd term. • (K-2)*( 6K+3 ) = (2k+1)^2 • 6k^2 -9K – 6 = 4k^2 +4k+1 • 2k^2-13k-7 = 0 • 2k^2 -14k + k -7 =0 • 2K(k-7)+1(k-7) = 0 • K = 7 or -1/2 • Ans.

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.06^2 + .47^2 + .079^2 / .006^2 + .047^2 + .0079^2 ? • Taking common values and cutting these, we are left with: • (10/1)^2=100 Ans.

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A garrison of 2000 men had enough food to last for 30 days. After 10 days 500 more men joined then how long will the food last?

• Total food = 2000*30 = 60000 • Food now left: 2000*20 = 40000 • Number of persons now = 2000+500 = 2500 • No, of days left: 40000 / 2500 = 16 ans

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A contractor undertook to complete a work in 120 days. He employed 200 men in 72 days. Only half of the work was done. How many more men should be employed to complete the remaining work in time?

• Half of the work is 200*72 = 14400 • This work is to be done in (120-72) =48 days. • No. of persons requred 14400/48 • =300 • The contractor has to employ (300200) 100 more workers. Ans. www.afterschoool.tk

20 men can complete a work in 40 days. When should 4 men leave so that the work is completed in 48 days?

16 people will work for all 48 days. 16*48 = 768 Remaining work = 800 – 768 = 32 No. of days when 4 workers will work = 32/4 = 8 • They will leave after 8 days. Ans. • • • •

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A & B can do a work in 30 days, B+C can do it in 24 days, A + C can do it in 20 days. They all work for 12 days. B +C leave. How much more time will be required? • One days work =(1/30+1/24+1/20)*1/2 • =15/240, = 1/16 • 12 days work (12*15) = 180/240 = 3/4 • Remaining work is = ¼ • A’s one days work is 1/16-1/24 = 1/48 • 48*1/4 = 12 • Remaining work will be done by A in 12 days. Ans. www.afterschoool.tk

A man goes to a garden and runs in the following way: from start, 25 m. west, then 60 m north, 80 m. east and finally 12 m. south. What is the distance between starting and finishing points? • • • • •

Difference of east and west = 80-25 = 55 East Difference of north and south= 60-12 = 48 north Applying pythogorus rule = 55^2 +48^2 = =3025+ 2304 = 5329 Square root of 5329 = 73 ans. www.afterschoool.tk

Median of a triangle passes through the point which divides each median in the ratio?

• 2:1 ans.

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What is the point called which is at equal perpendicular distance from the sides of the triangle?

• Incentre – it has equal distance from sides.

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A 25 m. ladder against wall has its foot 7 m. far from foot of wall. If top of ladder slides by 4m downwards, how much will the foot slide? ladder Assume the height of ladder = x X^2 +7^2 = 625 X= square root of 576 = 24. Now height is reduced by 4, new height is 20. • 625-400 = 225, square root of 225 is 15. thus the ladder has slided by 15-7 = 8 m. ans.

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