EASY

JEE Main/Advance

IMPORTANT

Earn 100

Find the total number of ways of selecting two numbers from the set of first $100$ natural numbers such that difference of their square is divisible by $3$ .

Important Questions on Permutation and Combination

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 45

A four digit number plate of a car is said to be lucky if sum of first two digit is equal to sum of last two digit. Then find the total number of such lucky plate. (Assume

0000, 0011, 0111, \dots \dots \dots .

all are four digit number)

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 46

Let each side of the smallest square of a chessboard is one unit in length.

(i)

Find the total number of squares of side length equal to

3

and whose side is parallel to the side of the chessboard.

(ii)

Find the sum of the area of all possible squares whose side is parallel to the side of chessboard.

(iii)

Find the total number of rectangles (including squares) whose side parallel to side of chess board.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 47

A person is to walk from $A$ to $B$ . However, he is restricted to walk only to the right of $A$ or upwards of $A$ , but not necessarily in the order shown in the figure. Then find the number of paths from $A$ to $B$ .

Question Image

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 48

The number of signals that can be made with

3

flags each of different colour by hoisting

1

2

3

above the other, is

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 49

8

chairs are numbered from

1

8

. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked

1

4,

then the men select the chairs from among the remaining. The number of possible arrangements is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 50

Number of words that can be made with the letters of the word

" GENIUS "

if each word neither begins with

G

nor ends in

S,

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 51

The number of words that can be formed by using the letters of the word

^{'} {MATHEMATICS}^{'}

that start as well as end with

T,

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 52

5

boys &

3

girls are sitting in a row of

8

seats. Number of ways in which they can be seated so that not all the girls sit side by side, is

Find the total number of ways of selecting two numbers from the set of first 100 natural numbers such that difference of their square is divisible by 3.

Important Questions on Permutation and Combination

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Find the total number of ways of selecting two numbers from the set of first $100$ natural numbers such that difference of their square is divisible by $3$ .