[vineet.nitd]

46 >How many 4-digit positive integers have the sum of their two leftmost digits equal to the sum of their two rightmost digits?

(a) 615 (b) 485 (c) 545 (d) none of the foregoing


47 >Rahul walks down an up-escalator and counts 150 steps. Aarav walks up the same escalator and counts 75 steps. Rahul takes three times as many steps in a given time as Aarav. How many steps are visible on the escalator?

(a) 180 (b) 150 (c) 210 (d) 120

48 >How many natural numbers less than 100 are there such that n^2 does not divide n!?

(a) 24 (b) 25 (c) 26 (d) none of the foregoing

[skylark]

Originally Posted by vineet.nitd

48 >How many natural numbers less than 100 are there such that n^2 does not divide n!?

(a) 24 (b) 25 (c) 26 (d) none of the foregoing

I think it's going to be all the prime nos. less than 100... so it should be 25 - (b)

[doomsayer]

Originally Posted by vineet.nitd

46 >How many 4-digit positive integers have the sum of their two leftmost digits equal to the sum of their two rightmost digits?

(a) 615 (b) 485 (c) 545 (d) none of the foregoing


47 >Rahul walks down an up-escalator and counts 150 steps. Aarav walks up the same escalator and counts 75 steps. Rahul takes three times as many steps in a given time as Aarav. How many steps are visible on the escalator?

(a) 180 (b) 150 (c) 210 (d) 120

48 >How many natural numbers less than 100 are there such that n^2 does not divide n!?

(a) 24 (b) 25 (c) 26 (d) none of the foregoing

46) ans a ;
n*(n+1) + n^2 =
it will be 2* sigma n^2 + sigma n
=615

[skylark]

Originally Posted by vineet.nitd

46 >How many 4-digit positive integers have the sum of their two leftmost digits equal to the sum of their two rightmost digits?

(a) 615 (b) 485 (c) 545 (d) none of the foregoing

1001, 1010
1111
1212, 1221
1313, 1331
1414, 1441
1515, 1551
1616, 1661
1717, 1771
1818, 1881
1919, 1991


19 nos. for 1000-2000... so 19*9=171...





what'm i doing wrong here?!

[doomsayer]

Originally Posted by skylark

1001, 1010
1111
1212, 1221
1313, 1331
1414, 1441
1515, 1551
1616, 1661
1717, 1771
1818, 1881
1919, 1991


19 nos. for 1000-2000... so 19*9=171...





what'm i doing wrong here?!

what abt 1322,1432,1423.. ...etc?

[doomsayer]

Originally Posted by vineet.nitd

47 >Rahul walks down an up-escalator and counts 150 steps. Aarav walks up the same escalator and counts 75 steps. Rahul takes three times as many steps in a given time as Aarav. How many steps are visible on the escalator?

(a) 180 (b) 150 (c) 210 (d) 120

47) ans (d) 120
get the relation V=75 +3/2 n
150=V+n
where V is the visible steps.

solving V=120.

[doomsayer]

Originally Posted by vineet.nitd

48 >How many natural numbers less than 100 are there such that n^2 does not divide n!?

(a) 24 (b) 25 (c) 26 (d) none of the foregoing

4 ans c) 26
prime num + 4 =25+1=26

[warrior]

Originally Posted by vineet.nitd

48 >How many natural numbers less than 100 are there such that n^2 does not divide n!?

(a) 24 (b) 25 (c) 26 (d) none of the foregoing

all primes less than 100 and 4

so total 26

[warrior]

Originally Posted by vineet.nitd

47 >Rahul walks down an up-escalator and counts 150 steps. Aarav walks up the same escalator and counts 75 steps. Rahul takes three times as many steps in a given time as Aarav. How many steps are visible on the escalator?

(a) 180 (b) 150 (c) 210 (d) 120

should be 120

when rahul is coming donw he sees 150 steps

now 150 steps > the steps he would have seen when escalotor is stopped

so only ans is 120

[warrior]

Originally Posted by vineet.nitd

46 >How many 4-digit positive integers have the sum of their two leftmost digits equal to the sum of their two rightmost digits?

(a) 615 (b) 485 (c) 545 (d) none of the foregoing

I am getting 613

my method

the sum of first two digits can be anything from 2 to 18 if no digit is zero

so for 2 - 1C1
3- 2C1 ....

10-9C1
11-8C1

.

.
.

18-1C1

same goes for last two

so we have 1^1+2^2....9^2+8^2+7^2.............. = 459

if we take zero as one the digits

1- 1+0
2-2+0

and so on

and for rightmost two we have

1- 2C1
2-3C1




9-10C1

so we have = 54

total = 613

where i am missing out

:neutral: