Find the mode from the given data.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2 , 3, 4, 1, 2, 3, 4, 1 ,2 , 3, 4, 5, 5, 1, 5, 5, 5, 3, 5, 1, 2, 4, 5, 6, 1, 2, 4, 2, 1

Q. Following are the margins of victory in the football matches of a league.
$1,3,2,5,1,4,6,2,5,2,2,2,4,1,2,3,1,1,2,3,2,6,4,2,1,1,4,2,1,5,3,3,2,3,2,4,2,1,2,3$, find the mode of this data.

Q.

(1) 4² + 2⁴ − 3²

(2) 3³ − 2² + 2⁰

(3) 5³ − 2² + 4⁰

(4) 6¹ + 5⁰ − 4¹

(5) (−2)² + 1² − 2²

Q.

Gopi spun the spinner 30 times and got the following results:

2, 1, 4, 2, 4, 5, 1, 4, 1, 5, 3, 1, 4, 2, 3, 1, 5, 4, 4, 2, 3, 3, 5, 4, 2, 2, 5, 3, 1, 4

What is the frequency of 4?

Q. Observe the following pattern
$\left(1\times 2\right)+\left(2\times 3\right)=\frac{2\times 3\times 4}{3}$
$\left(1\times 2\right)+\left(2\times 3\right)+\left(3\times 4\right)=\frac{3\times 4\times 5}{3}$
$\left(1\times 2\right)+\left(2\times 3\right)+\left(3\times 4\right)+\left(4\times 5\right)=\frac{4\times 5\times 6}{3}$
and find the value of
(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)

Q.

Question 4(d) :

Look at the figures and write ‘<’ or ‘>’ between the given pairs of fractions:

$\frac{6}{6}\square \frac{3}{3}$