Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 6

EASY

CAT

IMPORTANT

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If $m, n, p$ are in A.P. and $m^{n} = p^{m} = n! + p; m, n, p \in N$ , then the value of $m . n . p$ is, where $2 < m, n < p < 10$ :

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Important Questions on Number System

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 7

The value of

(n!)^{n}

if

n + (n - 1) + (n - 2) = n (n - 1) (n - 2)

, where

n^{3} > 9

, a positive number:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 8

If $(n)^{3} - (n)^{2} - n = n$ , then the number of values of $n$ that satisfy the given relation is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 10

The given relation

n^{(n - 1)} + n^{(n + 1)} = {(n^{2} + 1)}^{2} - (n^{2} + 1)

is valid for every

n \in N

if

n

equals to:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 11

The smallest possible number that can be expressed as the sum of cube of two natural numbers in two different combinations:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 12

8^{6} - 5^{6}

is individually divisible by:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 13

Total number of factors of a number is

24

and the sum of its.

3

prime factors out of four is

25

. The product of all

4

prime factors of this number is

1365

. Then such a greatest possible number can be:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 14

If p be any odd natural number greater than

3

, then which digit will never appear as the last digit in the product of

(p^{2} - 1) (p^{2} + 1)

?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 19

A six digit number of the form abcabc is written where

a, b, c \in I^{+}

, then which statement is true about this number?