read 33 as 3 ,sorry for the mistake

31st Since there are six faces, you can form 6*4=24 right-angled triangles on the faces. and 24 diagonally so total right anled triangles formed=48 ...

33 We start choosing by the lowest number, and will not choose any number before that number and I proceed by choosing only in increasing order. So, w...

for first cube: 5 black (B1) faces and 1 white (W1) probability of getting black on top= P (B1)=5/6 probability getting white on top= P(W1)=1/6 For s...

sample space should be 4!

45th total 4 digit no. formed =4! it will be divisible by 4 only when the last two digits will be 28,24,48,32,84 total no. formed when it ends with...

48th Assuming the seating assignments are fixed, the problem is tantamount to arranging 17 blue chairs and 33 green chairs in a circle so that no two ...

41st No of groups = 4Towns in each group = 3For towns belonging to the same group.Lets say a1, a2, a3.Each requires 3 connections with other town in s...

47th Number of ways of selecting 3 different letters:=4C3=4 ways Number of ways to select 2 similar and 1different letter:=4C1×3C2=12 ways Number of ...

The center of the coin is at least one coin radius from any grid line.You can then shade the area of a grid square where the coin center cannot fall -...

30th part (iii) three cases will be formed with atleast 2 girls (2G,2B) (3G,1B) (4G,0B) 5C2*4C2 +5C3*4C1 +5C2*4C0 10*6+10*4+5=105 WAYS

Treat commission as the discount he will give and apply mp/cp= (100+profit)/(100-discount) In first case p=8.08 and commission is 36 Mp/cp= 108.8/64 ...

Answer is 49.6 ?

Alternate apporach cp=100 ,sp=100(1+p/100) [p is profit] new cp= 118 , new sp=118(1+p/100) 118(1+p/100) - 100(1+p/100) =9 18p/...