Exams

It is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.

Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.

Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.

Hence, number of ways in which we can select the black balls

= 4C1 + 4C2 + 4C3 + 4C4
= 24-1 ........(A)

Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.

Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red balls

Hence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
=23-1........(B)

Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.

Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + … + 5C5
= 25..............(C)

From (A), (B) and (C), required number of ways
=  2524-123-1

The State game of Madhya Pradesh is Mallakhamba.

The work to be done = Capacity of reservoir  = 30 litres.

 1^st Minute ---> inlet pipe opened ---> 5 lit filled

 2^nd minute ---> inlet pipe closed; outlet pipe opened ---> 4 lit emptied

In 2 minutes (5 litres - 4 litres = 1lit) is filled into the reservoir.

It takes 2 minutes to fill 1lit ---> it takes 50 minutes to fill 25 litres into the reservoir.  

In the 51^st minute inlet pipe is opened and the reservoir is filled.

Let us consider Karthik as K1 and Kalyan as K2.

Given k18+k1 and K2 - (K1 + 5) = 3 

K2 - K1 = 8

K2 = 8 + K1

Now, 

k18+k1= 45

=> K1 = 32 years

Therefore K2 = 40 years.

K1 + K2 = 72 years.

we interchange the positions of the letters as shown below:

The new letter sequence is CENSSEYRA.
Clearly, the seventh letter from the left is Y.

Given word is TIRADES
Now the consonants T, R, D, S are replaced by S, Q, C, R
And Vowels are I, A, E are replaced by J, B and F
They are arranged alphabetically
New word is BCFJQRS

The fourth letter from the right end is J.

The Coffee Board of India is an organisation managed by the Ministry of Commerce and Industry of the government of India to promote coffee production in India. The headquarters of the coffee board of India is located in Bangalore, Karnataka.

The Coffee Board of India was established by an act of Parliament in 1942.

Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.