AIEEE Questions

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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.

A bristle is a part of a brush; a key is a part of a piano.

Given number series is 5  19  49  101  181  295 ?

Here the series follows pattern that

5   19   49   101   181   295  ?

  14   30   52    80     114   (difference)

      16  22   28     34 (difference)

         6     6     6  (Common difference)

Therefore, the missing number in the series is ? = 295 + 115 + 34 + 6 = 449.

The next number in the series is

143 143 136 110

      0    7      26 (Differences)

 $$\begin{gathered} 13 - 1 , 23 - 1, 33 - 1, 43 - 1,... \\ Now the next number is given by \\ 110 - (43 - 1) = 110 - 63 = 47. \end{gathered}$$

Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135)/2= Rs.130.50

So, Now the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say Rs. 'x' per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find 'x'.

Cost of 1 kg tea of 1st kind         Cost of 1 kg tea of 2nd kind 

x-153/22.50 = 1  => x - 153 = 22.50  => x=175.50.

 Hence, price of the third variety = Rs.175.50 per kg.

The pattern followed is +3 , +6 , +12 , +24 , +48

Vaunt - Vaunt means to boast or to praise about something excessively.

Flaunt - Flaunt also means to boast about something or to praise something.

Flaunt is the synonym of the word Vaunt.

Disparate - Disparate means essentially different in its kind or unlike or not able to be compared.

Then the required word is the synonym of Disparate.

Here in the given options, Contrast is the only word which is similar in meaning of Disparate.

Hence, Vaunt : Flaunt :: Disparate : Contrast.