CAT Questions

---

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

Let the required number be 'p'.

From the given data,

p + 12 = 160 x 1/p

=> p + 12 = 160/p

=> p(p + 12) = 160

=> P^2 + 12p - 160 = 0

=> p^2 + 20p - 8p - 160 = 0

=> P(p + 20) - 8(p + 20) = 0

=> (p + 20)(p - 8) = 0

=> p = -20 or p = 8

As, given the number is a natural number, so it can't be negative.

Hence, the required number p = 8.

STARTLING is a required 9 letter English word is still a word each time you remove a letter from the word. And how it is shown below: 

1. Remove the L, and the word becomes: STARTING

2. Remove one T, and the word becomes: STARING

3. Remove the A, and the word becomes: STRING

4. Remove the R, and the word becomes: STING

5. Remove the other T, and the word becomes: SING

6. Remove the G, and the word becomes: SIN

7. Remove the S, and the word becomes: IN

8. Remove the N, and the word becomes: I

The gram formula mass of a compound is nothing but the molar mass.

The molar mass of K2CO3 (Potassium Carbonate) is given by

Atomic weights of individual elements are

K (Potassium) = 39 g

C (Carbon) = 12 g

O (Oxygen) = 16 g

Hence, that of K2CO3 = 39(2) + 12 + 16(3)

= 78 + 12 + 48

= 138.

An excise or excise tax or excise duty is a type of tax charged on goods produced within the country (as opposed to customs duties, charged on goods from outside the country). It is a tax on the production of a good. This tax is now known as the Central Value Added Tax (CENVAT).

Lt. Gen. Sanjeev Kumar Shrivastava took over as the 25th Director General of the Border Roads (DGBR). He has replaced Lt. Gen. Suresh Sharma. Prior to it, he was holding the appointment of Director General Combat Engineers at Integrated Headquarters of Ministry of Defence(Army).

The religious guru of Shivaji was Ram Das.