Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 24

EASY

CAT

IMPORTANT

Earn 100

An $n$ -digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$ -digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of $n$ for which this is possible, is

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Important Questions on X+2 Maths

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 25

Let

a_{1}, a_{2}, \dots, a_{10}

be in

AP

and

h_{1}, h_{2}, \dots, h_{10}

be in

HP

. If

a_{1} = h_{1} = 2

and

a_{10} = h_{10} = 3

, then

a_{4} h_{7}

is

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 26

If the integers

m

and

n

are chosen at random between

1

and

100

, then the probability that a number of the form

7^{m} + 7^{n}

is divisible by

5

equals

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 27

Let

S_{1}, S_{2}, \dots .

be squares such that for each

n \geq 1,

the length of a side of

S_{n}

equals the length of a diagonal of

S_{n + 1}

. If the length of a side of

S_{1}

is

10 cm,

then for which of the following values of

n

is the area of

S_{n}

less than

1 sq . cm

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 28

If

a, b, c, d

are positive real numbers such that

a + b + c + d = 2,

then

M = (a + b) (c + d)

satisfies the relation

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 29

How many different nine-digit numbers can be formed from the number

223355888

by rearranging its digits so that the odd digits occupy even positions?

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Benchmarking Test 3>Q 30

The area bounded by the curves

y = | x | - 1

and

y = - | x | + 1

is