Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 36

EASY

CAT

IMPORTANT

Earn 100

The remainder when $1^{3} + 2^{3} + 3^{3} + \dots + 999^{3} + 1000^{3}$ is divided by $13$ is:

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Important Questions on Number System

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 37

If

22^{3} + 23^{3} + 24^{3} + \dots + 87^{3} + 88^{3}

is divided by

110

then the remainder wil be:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 38

The sum of the n terms of a series is

n! + n^{2}

then the

6 th

term is, if

n \in N

:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 39

A smallest possible number which is divisible by either

3, 5

or

7

when represented by only two digits either

0

or

1

, then the minimum number of digits required to represent it:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 40

The sum of first n odd numbers (i.e.,

1 + 3 + 5 + 7 + \dots + 2 n - 1

) is divisible by

11111

then the value of n is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 41

Anjuli bought some chocolates from Nestle's exclusive shop, and she gave Amit one less than half of what she had bought initially. Then she gave

3

chocolates to Bablu and then half of the chocolates which she had given to Charles. Thus, finally she gave one chocolate to Deepak and the remaining one she ate herself. The number of chocolates she had purchased.

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 42

If

{(a_{1} b_{1} c_{1})}^{100} + {(a_{2} b_{2} c_{2})}^{100} + {(a_{3} b_{3} c_{3})}^{100} + \dots {(a_{100} b_{100} c_{100})}^{100}

, where

a_{i} b_{i} c_{i}

is a three-digit positive number and in the expression, all the

100

numbers are any consecutive

3

digit numbers. The last digit is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 46

Which of the following is/are true?

(i) $43^{3} - 1$ is divisible by $11$

(ii) $56^{2} + 1$ is divisible by $19$

(iii) $50^{2} - 1$ is divisible by $17$

(iv) $(729)^{5} - 729$ is divisible by $5$

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 47

Capt. Manoj Pandey once decided to distribute

180

bullets among his

36

soldiers. But he gave n bullets to a soldier of nth row and there were same number of soldiers in each row. Thus he distributed all his

180

bullets among his soldiers. The number of soldiers in

(n - 1) th

row was: