Number System
- The simplified value of
1 − 1 
1 − 1 1 − 1 ........ 1 − 1 1 − 1 3 4 5 99 100
-
View Hint View Answer Discuss in Forum
2 × 3 × 4 ×......× 98 × 98 3 4 5 99 100 = 2 = 1 100 50 Correct Option: C
2 × 3 × 4 ×......× 98 × 98 3 4 5 99 100 = 2 = 1 100 50
- The sum of the squares of two positive numbers is 100 and difference of their squares is 28. Find the sum of the numbers :
-
View Hint View Answer Discuss in Forum
According to question
x2 + y2 = 100 ...(i)
x2 − y2 = 28 ...(ii)
Adding both the equations
x2 + y2
x2 − y2
-----------
2x2 128
⇒ x2 = 64 ∴ x = 8
From the equation (i)
y2 = 100 − 64 ∴ y = 6
So, x + y = 8 + 6 = 14Correct Option: C
According to question
x2 + y2 = 100 ...(i)
x2 − y2 = 28 ...(ii)
Adding both the equations
x2 + y2
x2 − y2
-----------
2x2 128
⇒ x2 = 64 ∴ x = 8
From the equation (i)
y2 = 100 − 64 ∴ y = 6
So, x + y = 8 + 6 = 14
- The numbers 1, 3, 5,7 .., 99 and128 are multiplied together. The number of zeros at the end of the product must be :
-
View Hint View Answer Discuss in Forum
In 2m × 5n, the number of zeros
= n when m ≥ n
= m when m < n
Here, 128 = 27
In 1 × 3 × 5 × 7 × ... × 99 multiples of 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (= 510)
Clearly, 7 zeros will be found in the product.Correct Option: C
In 2m × 5n, the number of zeros
= n when m ≥ n
= m when m < n
Here, 128 = 27
In 1 × 3 × 5 × 7 × ... × 99 multiples of 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (= 510)
Clearly, 7 zeros will be found in the product.
