The greatest power of $3$ , when $41!$ is expressed in prime factors:

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Important Questions on Number System

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 123

A two digit number is such that it is the product of the two distinct perfect squares. The tens digit, unit digit and the sum of these two digits are in A.P. Further if we reverse the digits mutually, the new number increases by

27

. The original number is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 126

If

4

is added to the numerator of a fraction, it becomes

\frac{1}{3}

and if

3

is added to the denominator of the same fraction it becomes

\frac{1}{6}

then the sum of the numerator and denominator is:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 127

In an opera house, there are

7777

chairs to be placed, but the organiser of the event arranged all the chairs in such a way that there were as many columns as there were rows. So he had to remove minimum 'n' chairs from the total

7777

chairs. The minimum value of n is:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 128

If $p^{r} \cdot p^{- 1} \cdot p^{s} = (\sqrt{p^{3}})^{2}$ and $p^{\frac{3}{2}} \cdot p^{r} = p^{s} \cdot p^{- \frac{1}{2}}$ , then find the value of $(r + s)^{(r + s)}$ is: