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1. How many numbers less than 500 will have a digit sum equal to 5 ?

1. 39

2. 72

3. 55

4. 81

2. The infinite sum 1 + 3/4 + 5/16 + 7/64 ...... equals

1.5/3

2.2

3.20/9

4.26/9

3. If a^2, b^2, c^2 are in AP, then b+c, c+a, a+b are in ?

1. AP

2. GP

3. HP

4. None of these

4. If a - b/2 , b/2 , c -b/2 are in GP , then a,b,c are in

1. GP

2. AP

3. HP

4. None of these

5. Find the sum of the first 24 terms of an AP a1,a2,a3,...., if it is known that

a1+a5+a10+a15+a20+a24 = 225

1. 900

2. 450

3. 6000

4. None of these

6. The sum of all the products of the first n positive integers taken two at a time is ?

1. 1/48(n-2)(n-1) n^2

2. 1/6 n (n+1)(n+2)(n+5)

3. 1/24(n-1)n (n+1)(3n+2)

4. 1/8(n+1)(n+2)

7.In a certain colony of rabbits, each rabbit gives to four new rabbits every year. How many new rabbits will be born form a single productive rabbit if this reproduction rate continues for 10 years and it is know that only 75% of the new rabbits are capable enough to produce the next generation of rabbits ?

1. 3^10 -1

2. 3^11 -1

3. 2(3^10 -1)

4. 2(3^9 -1)

Please provide explanations for the answers...

Thanks in Advance!

We can first distribute 1 ball to one group and then distribute 13 other to two groups

So

11|12

1211

............

167

So 6 ways

Now assign 2 balls to 1st grp and proceed

2210

239

248

257

2|66

So 5 ways

Then;

33|8

347

356

3 ways

446

4|55

2 ways

in all...6+5+3+2 = 16 ways

see 14 balls have 13 gaps between them

we just need to find 2 gaps in this 13 gaps to divide 14 balls into 3 groups

so ans would be 13c2

Correction : ok its identical so 13c2 wont be the answer...we have to calculate manually all possibilities....i dont think there is any other way

my answer 16

1,1,12

1,2,11

1,3,10

1,4,9

1,5,8

1,6,7

2,2,10

2,3,9

2,4,8

2,5,7

2,6,6

3,3,8

3,4,7

3,5,6

4,4,6

4,5,5

correct me if I am missing something

yes its correct answer! thank u !

Find the number of ways in which 14 identical and indistinguishable balls can be divided into three groups?

a)17 b)16 c)18 d)19 e)20

Hi! I am divya completed B.E ECE in 2008. Preparing for CAT!

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