AIEEE Questions

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n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!(2!)2×3!

18 tens 20 ones, the given stateent can be split into

18 tens = 18 x 10 = 180

20 ones = 20 x 1 = 20

Then add both => 180 + 20 = 200

Hence, 18 tens 20 ones = 200.

Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 x 5/18 = 10 m/sec.

Distance to be covered = 260 + 140 = 400 m.

Time taken = 400/10 = 40 sec.

Let the speed of boat and stream be x and y kmph respectively.

According to question

d/x+y + d/x-y = 5h 15m or 21/4 hrs ......(i)

and 2d/x-y = 7...... (ii)

From eq. (i) and (ii)

2d/x+y = 7/2

Hence, Amith will take to row 2d km distance downstream in 7/2 hrs

= 3.5 hrs

= 3 hrs 30 min.

Let the ratio amount be 'p'

7p - 3p = 2700

4p = 2700

p = 675

R's Share = 675 × 6 = Rs. 4050

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