Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 20

EASY

CAT

IMPORTANT

Earn 100

Winner and Loser, the two brothers are playing a game in a recreational room at Amausi Airport, Lucknow. In this game each one in turn has to pick up a number m such that $1 \leq m \leq n; m, n \in I^{+}$ . The game stops as soon as the sum of all the numbers picked so far attains the value of $2 n + 1$ 1$ or exceeds and thus the player who picked last number was loser. With which number winner starts if he were to pick up first to defeat necessarily the loser is?

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Important Questions on Number System

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 21

The sum of the last $10$ digits of the sum of the expression:

$(1^{1} \times 2^{2} \times 3^{3} \times 4^{4} \times 5^{5}) + (1^{6} \times 2^{7} \times 3^{8} \times 4^{9} \times 5^{10}) + (1^{11} \times 2^{12} \times 3^{13} \times 4^{14} \times 5^{15}) + \dots + (1^{96} \times 2^{97} \times 3^{98} \times 4^{99} \times 5^{100})$ is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 22

One day very early morning Ravishankar went to the temple to offer some flowers as a part of Pooja. He purchased some flowers, but the seller offered him that if he would give him all his

Rs . 2

, he could get all the remaining

6

Flowers and thus could gain

60

Paise per dozen. If each time the transaction is possible only in rupees, then how many flowers did Ravishankar purchase initially?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 23

Maximum number of squares possible that can be constructed using

31

pencils of equal length on the table:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 26

Recently, a small village in Tamilnadu where only male shephereds reside with four sheep each, was devastated by Tsunami waves. Therefore

8

persons and

47

sheep were found to be dead and the people, who luckily survived, left the village with one sheep each. Since

21

sheep were too injured to move so have been left on their own luck in the village. The number of sheep which were earlier in the village is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 27

The number of

3

-digit numbers which consist of the digits in A.P., strictly in increasing order using the non-zero digits of the decimal system is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 28

The sum of:

$(2^{2} + 4^{2} + 6^{2} + \dots + 100^{2}) - (1^{2} + 3^{2} + 5^{2} + \dots + 99^{2})$ is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 29

If an integer p is such that

(8 p + 1)

is prime, where

p > 2

, then

(8 p - 1)

is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 30

The remainder when

3^{0} + 3^{1} + 3^{2} + \dots + 3^{200}

is divided by

13

is: