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intermediate(ipc)course (no) (1460 Points)

08 September 2011

1).the no. of ways of forming a comittee consisting 4 men & 6 women such that there must be atleast 2 men & at least twice the women as men would be.

ans:94.

2).if the sum of first n terms of an A.P is 2n^2+n then the difference of its tenth & first term is

ans:36.

3).in how many ways can 15 people be seated at two round tables with 7 seats & 8 seats respectively.

ans:15C8*6!*7!

4).how many 3 digits even numbers can be formed with no repeated digit by using the digits 0,1,2,3,4 & 5?

ans:52.

5).if simple interest on a sum at 6% for 7 years is equal to the simple interest on another sum of money for 9 years at 10%.then the two sums in the ratio

ans:15:7.

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6 Replies

(Guest)

1) Combination of 2 men and 4 women in 4C2 x 6C4 ways = 90.

Combination of 3 men and 6 women in 4C3 x 6C6 ways = 4.

Total 94.

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(Guest)

2) Sum of n terms = n/2(2a +nd -d) which is the standard form.

Given expression of sum of n terms is 2n^2+n. Expressing it in standard form we get, n(2n+1) i.e. n/2(4n+2).

Comparing nth term in both the standard form and modified expression, we find that for the only n term within brackets is 4n, equating it to nd, we get d=4.

Now, difference of tenth and first term is a+9d-a i.e. 9d =36.

(Guest)

3) 8 people can be selected out of 15 to sit in one round table in 15C8 ways. Remaining 7 people will go to the other table automatically.

Now, 8 persons can arrange amongst themselves in (8-1)! ways on one table and 7 persons can arrange amongst themselves on the other table in (7-1)! ways.

So total number of ways are 15C8*7!*6!.

(Guest)

4) Units digit can be filled up only by 0, 2 or 4.

Now, fixing zero in unit's place, remaining 2 digits can be selected in 5P2 ways i.e. 20 ways.

Now, fixing 2 in unit's place, remaining 2 digits can be selected in 5P2 ways subtracted by cases in which zero are in the hundreth's place which can be selected in 4P1 ways giving (5P2-4P1) i.e. 16 ways.

So total = 52.