Advertisements
Advertisements
प्रश्न
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
If the number of digits formed is taken to be n, the number of segments required to
form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to form 5, 10, 100 digits of the kind −
Advertisements
उत्तर
It is given that the number of segments required to form n digits of the kind
is (5n + 1)
Number of segments required to form 5 digits = (5 × 5 + 1)
= 25 + 1 = 26
Number of segments required to form 10 digits = (5 × 10 + 1)
= 50 + 1 = 51
Number of segments required to form 100 digits = (5 × 100 + 1)
= 500 + 1 = 501
APPEARS IN
संबंधित प्रश्न
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to form 5, 10, 100 digits of the kind −
Use the given algebraic expression to complete the table of number patterns.
| S. No |
Expression |
Terms | |||||||||
| 1st | 2nd | 3rd | 4th | 5th | ... | 10th | ... | 100th | ... | ||
| 1 | 2n - 1 | 1 | 3 | 5 | 7 | 9 | - | 19 | - | - | - |
| 2 | 3n + 2 | 5 | 8 | 11 | 14 | - | - | - | - | - | - |
| 3 | 4n + 1 | 5 | 9 | 13 | 17 | - | - | - | - | - | - |
| 4 | 7n + 20 | 27 | 34 | 41 | 48 | - | - | - | - | - | - |
| 5 | n2 + 1 | 2 | 5 | 10 | 17 | - | - | - | - | 10001 | - |
Write down the following in the product form: x2y4
Write down the following in the product form: 9xy2z
If 11 is subtracted from 4 times a number, the result is 89. Find the number.
If a number is tripled and the result is increased by 5, we get 50. Find the number.
One out of two numbers is thrice the other. If their sum is 124, find the numbers.
Deepak is twice as old as his brother Vikas. If the difference between their ages is 11 years, find their present ages.
Mrs. Goel is 27 years older than her daughter Rekha. After 8 years she will be twice as old as Rekha. Find their present ages.
The side of a regular hexagon is denoted by l. Express the perimeter of the hexagon using l.
(Hint: A regular hexagon has all its six sides equal in length.)
The side length of the top of square table is x. The expression for perimeter is ______.
The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
The speed of car is 55 km/hrs. The distance covered in y hours is ______.
A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:
- How much wire is left?
- If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.
The sum of squares of first n natural numbers is given by `1/6n(n + 1)(2n + 1)` or `1/6(2n^3 + 3n^2 + n)`. Find the sum of squares of the first 10 natural numbers.
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 19.
Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?
