- In how many ways can 3 roses and 4 tulips 2 jasmines can be arranged in a garland such that all roses tied together and all tulips are tied together and jasmines also tied together?
876864867912834Option B

Required number of ways = 3( 3! * 4! *2!)

=3* 3 * 2 * 4* 3 * 2 *2

=>864 ways. - In how many ways the word “ note book “ can be arranged?
56702456672056706120Option C

notebook.

There are 8 letters. o is repeated three times

So number of words formed=8!/ 3!

=6720 ways - There are two positive integers x and y .What is the probability that x+y is even?
1/21/31/41/51/6Option A

Sum of positive integers is either odd or even.

Hence the required probability= ½ - The sum of three consecutive odd number is 93.Then what will be the middle number if they arranged in descending order?
3031293335Option B

Let the three numbers be 2a +1 , 2a+3, 2a +5

Given 2a+1 + 2a+3 +2a+ 5= 93

=>6a +6 = 93

=> 6a= 84

=>a=14

Hence the numbers are = 29,31,33

So the middle number is 31. - A bag contains 6 nestle bars and 4 kitkat bars. Two bars given at random to the children.

Then what is the probability that they are of same bars?2/153/155/156/257/15Option E

Required probability = 6C2 + 4C2 / 10C2

= 30+ 12/ 90 = 42/90

=7/15 - In how many different words can be formed from word ENCYCLOPEDIA such that all vowels come together?
2015020140201602098020790Option C

NCYCLPD(all vowels)

So number of letters= 8 also c is repeated twice.

Required probability = 8!/ 2! = 20160 ways - Out of all the 2-digit integers between 1 and 50, a 2-digit number has to be selected at random.

What is the probability that the selected number is not divisible by 13?31/4032/4025/4033/4037/40Option E

There are total 40 two digit numbers, out of them 3 are divisible by 13, these are 13, 26, 39

Therefore, probability that selected number is not divisible by 13 = 1 – 3/40 = 37/40 - How many different words can be arranged with letters of the word STENCIL when vowels occupied even places?
620720360440580Option B

Vowels are 2, places are 3. So they are arranged in 6 ( 3C2 * 2! ) ways.

Consonants can be arranged in 5! = 120 ways.

Total arrangement = 720 ways( 120*6). - There are 2 red balls, 5 orange and 4 purple balls .Two balls are drawn at random.What is the probability that one is red the other is orange or purple?
12/5511/5516/5518/5517/55Option D

There are 2 red balls and 9 other color balls. So total balls= 11

2 balls drawn at random,

=> required probablity= 2C1 * 9C1/11C2

=2*9/11*10/2

=>36/110 =18/55 - There are 8 students are selected from dance school for dance competition.The total number of students are 18.

In how many ways can be the selection be made so that 2 students are always included?80085005600670079009Option A

If 2 members are always included

The total number of ways= 2C2 * 16 C 2

=8008