CAT Questions

---

Here given series follows a pattern that

0.25, 8, 128, 1024, ?

0.25 x 32 = 8

8 x 16 = 128

128 x 8 = 1024

1024 x 4 = 4096

Stars are what that come out at night without being called and are lost in the day without being stolen.

Time = (100 x 81) / (450 x 4.5) = 4 years.

In India, Islamic rulers Qutb-ud-din Aibak imposed jizya on non-Muslims first time which was called kharaj-o-jizya. Jizya was abolished by the Mughal ruler Akbar in the 16th century but was re-introduced by Aurangzeb in the 17th century.

The given words to be placed in a logical sequence. Here if you want to swith on a light or fan in a room, the sequence you follow must be like

Key,

Lock ,

Door,

Room, Swith on.

Take the key and open the lock of a door in a room and then swith on.

The given puzzle follows a logic that,

2 + 10 = 24 => 2 + 10 = 12 x 2 = 24

3 + 6 = 27 => 3 + 6 = 9 x 3 = 27

7 + 2 = 63 = 7 + 2 = 9 x 7 = 63

Similarly, 5 + 3 = 40 => 5 + 3 = 8 x 5 = 40.

The cat's foot is called a paw. The horse's foot is called a hoof.

Arithmetic Series ::

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

That is given by Sn = n(a1 + an)2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + n-1d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, $$\begin{gathered} an= a1 + n - 1d \\ a36= 2 + 36 - 13 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.