How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 167

MEDIUM

CAT

IMPORTANT

Earn 100

Find the remainder when $40!$ is divided by $41$ .

100% studentsanswered this correctly

Important Questions on Number Systems

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 168

Find the remainder when

(x^{4} + 3 x^{3} + 4)

is divided by

(x + 3)

.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 169

If

X

is a prime number then for how many values of

X

,

(X^{2} + 7)

is also a prime number?

HARD

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 170

If

X = 99^{3} - 63^{3} - 36^{3}

, then the number of factors of

X

are:

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 171

if

x

is a natural number and

4 < x < 50

, then the largest

n

, such that

n!

would always divide

x (x^{2} - 1) (x^{2} - 4) (x^{2} - 9) (x + 4)

is?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 172

if

X

is a natural number and

X!

ends with

Y

zeroes then the number of zeroes at the end of

5 X!

is:

HARD

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 173

There are

90

questions in a test. Each correct answer fetches

1

mark, each wrong answer and unanswered question attract a penalty of

\frac{1}{4}

marks and

\frac{1}{8}

marks respectively. Bilbo scored

23

marks in the test. What is the minimum possible number of the questions wrongly answered by him?

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 174

If

A = {n^{2 n}}^{n}, B = n^{n^{2 n}}, C = {(n^{2 n})}^{n}, D = {(n^{n})}^{n^{2}}

when

n

is a natural number and

n \neq 1

. Then arrange them in terms of their values.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 175

How many numbers in the form of $(2^{n} - 1)$ which are less than $5000$ are prime?