Q1. Number of triangles that can be formed with 10 points as vertices, n of them being collinear, is 110. Then n is Q2. If N be an element of the set A = { 1, 2, 3, 5, 6, 10, 15, 30} and P, Q and R integers such that PQR = N, then the number of positive integral solutions of PQR = N, is Q3. Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points? Q4. How many different words can be formed by using all the letters of the word "WEDNESDAY", so that neither the two E’s nor the two D’s are together? Q5. The number of positive integral solutions of xyz = 42 is Q6. A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? Q7. If all possible four-digit numbers are formed using the digits 1, 2, 3, 4 without repetition and arranged in ascending order of magnitude, then the position of the number 3241 is __________________
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Q4. How many different words can be formed by using all the letters of the word "WEDNESDAY", so that neither the two E’s nor the two D’s are together?
a. [9! /(2!)^2 ] – 8!
b. 5! 6!/(2!)^3
c. 8!
d. 7!(11)
e. 7!(55)
ans:
d. 7!(11)
Soln.
10C3 - nC3=110
=>nC3=60
=>n!/3!(n-3)!=60
By tryin wd d options we get (c)5 is d correct one...
Giv ur best to d word.
Nd d best will cm back to u....
Regards,
Dipanjan...
n/a
Soln.:Me getting 42 as nswer...
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan...
n/a
Soln.:Suppose we are drawing d triangles taking vertices at d next line which consists of 11 points...
So, (1+2+..+10) x 10=55x10=550...
Regards,
Dipanjan.....
n/a
Soln.:
2 x 3 x 7 ->3!
1 x 2 x 21 ->3!
1 x 3 x 14 ->3!
6 x 7 x 1 ->3!
1 x 1 x 42,42 x 1 x1,1 x 42 x1->3
Geting 27 as nswer.....
So option (b) is correct.....
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
n/a
Soln.:
2x3x7->3!
1x2x21->3!
1x3x14->3!
6x7x1->3!
1x1x42->3
So total 27 no.s r possible....
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
n/a
Soln.:
1XXX->3!
2XXX->3!
32XX->2!
3214
3241
Position:16
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
n/a
Q6. A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?
a. 320
b. 160
c. 80
d. 200
ans is 160
because, 5c3*4c0+5c3*4c1+5c3*4c2+5c3*4c3+5c3*4c4
=10+40+60+40+10
=160
Little Star
n/a
Q2. If N be an element of the set A = { 1, 2, 3, 5, 6, 10, 15, 30} and P, Q and R integers such that PQR = N, then the number of positive integral solutions of PQR = N, is
a. 32
b. 64
c. 96
d. 128
ans is 64
pqr=1 then 1 slolution
pqr=2 then 3 slolution
pqr=3 then 3 slolution
pqr=5 then 3 slolution
pqr=6 then 9 slolution(116-3 solution,123-6 solution)
pqr=10 then 9 slolution(1110-3 solution,125-6 solution)
pqr=15 then 9 slolution(1115-3solutin,135-6 solution)
pqr=30 then 27 slolution(1130-3solution,1103-6 solution,235-6 solution,165-6solution,1215-6 solution)
Little Star
n/a
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