Let, 1 + x + x 2 9 = α 0 + α 1 x + … + α 18 x 18 , then which of the following is true?

α 0 + α 2 + … + α 18 is even.

α 0 + α 2 + … + α 18 = α 1 + α 3 + … + α 17

α 0 + α 2 + … + α 18 is divisible by 9

α 0 + α 2 + … + α 18 is divisible by 3 but not by 9

E M B I B E

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 25

HARD

CAT

IMPORTANT

Earn 100

If the number of ways of selecting $k$ coupons out of an unlimited number of coupons bearing the letters $A, T$ , and $C$ so that they cannot be used to spell the word $CAT$ is $93$ , then what is the value of $k$ ?

50% studentsanswered this correctly

Important Questions on X+2 Maths

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 26

In a test of

10

multiple choice questions of one correct answer, each having

4

alternative answers, then the number of ways to put ticks at random for the answers to all the questions is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 27

The streets of a city are arranged like the lines of a chessboard. There are

m

streets running north-south and

n

streets running in east-west direction. What is the number of ways in which a man can travel on these streets from the north-west to the south-east corner, going by the shortest possible distance?

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 28

Let,

{(1 + x + x^{2})}^{9} = α_{0} + α_{1} x + \dots + α_{18} x^{18}

, then which of the following is true?

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 29

If

N

be an element of the set

A = {1, 2, 3, 5, 6, 10, 15, 30}

, and

P, Q

and

R

are integers, such that

PQR = N

, then the number of positive integral solutions of

PQR = N

is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 30

In how many ways can one arrange letters the in the word 'INSTITUTION' such that no two same letters comes together along with the following conditions:

(A) There is no ' $T$ ' which is immediately preceded as well as followed by ' $N$ '.

(B) There is no ' $T$ ' which is immediately preceded as well as followed by ' $T$ '.

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 31

How many positive integers less than

1000

are

6

times the sum of their digits?

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 32

Six 'X's have to be placed in the square of the figure such that each row contains at least one X. In how many different ways can this be done

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