Explanation

601

If the word started with the latter A then the remaining 5 positions can be filled in 5! ways.

Similarly, for the other letters

No. of word starts with A = 5!

No. of word starts with C =5!

No. of word starts with H = 5!

No. of word starts with I = 5!

No. of word starts with N = 5!

Total words = 5! + 5! + 5! + 5! + 5! = 5(5!) = 600

Next when words starting with S appears, SACHIN itself will be the 1st word as ACHIN are all in dictionary order, 

Now add the rank of SACHIN.

so rank is 600 + 1 = 601 

Explanation

The expression p ∨ ¬p (read as "p or not p") is a tautology.

A tautology is a logical statement that is always true regardless of the truth value of its components.

 p ∨ ¬p is always true because either p is true or ¬p (not p) is true.

Explanation

The calculation is done as follows:

3 × 4 = 12
12 + 2 = 14

So, 3 × 4 + 2 = 14.

Explanation

In the fraction 3/5, the numerator is 3 (the top number), and the denominator is 5 (the bottom number).

Explanation

99 x 4 = 396

Explanation

Y% of Z = 2 (X% of Y)

=>YZ/100 = 2xy/100

=> Z = 2x

Explanation

756

Select 3 men from a group of 7 (7C3) and select 2 women from a group of 6 (6C2) to form a committee of 5  and increase these combinations. Do the same for the other two cases and add all these values ​​to get  the answer you need. Therefore, the total number of ways to form a five-member committee is 756.

Explanation

Let  ? = X

(2567/17) × 3 = X + 180

151 × 3 = X + 180

453 = X + 180

X = 453 – 180

X = 273

Explanation

Let quantity of water to be added further be x litres.

Then, milk : water =                       40                           .

20 + x

Now,                     40                           =             1

20 + x    2

 20 + x = 80

 x = 60.

Quantity of water to be added = 60 litres.

Explanation

Let the original money be Rs.100,

then money spent on machinery = Rs. 35

Money spent on raw material = Rs. 40

Money spent on staff = Rs. 10

Money left = 100 - 85 = Rs. 15

If money left is Rs. 15, original money = 100

If money left is 60000, original money =10015×60000=400000

Hence the total money spent on machinery and raw material =400000×75%=Rs.300000