Number System
- How many digits in all are required to write numbers from 1 to 50?
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Number of digits from 1 to 9 = 9
Number of digits used in writing from 10 to 50
= 41 × 2 = 82
∴ Total digits = 82 + 9 = 91Correct Option: C
Number of digits from 1 to 9 = 9
Number of digits used in writing from 10 to 50
= 41 × 2 = 82
∴ Total digits = 82 + 9 = 91
- The numbers 2, 4, 6, 8 ...., 98, 100 are multiplied together. The number of zeros at the end of the product must be :
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A product gets 0 at its end when
(i) a multiple of 5 is multiplied by an even number or
(ii) a multiple of 10 is multiplied by any number.
All the given numbers are even and do not contain any multiple of 5. So, zeros at the end of the product will come only on multiplications by multiples of 10.
Multiples of 10 that lie in the given range from 2 to 100 are 10, 20, 30, 40,50, 60, 70, 80, 90 and 100. Each of these multiples will yield one zero except 100 which will yield two zeros at the end of the product.
∴ Total no. of zeros at the product = 9 + 2 = 11Correct Option: C
A product gets 0 at its end when
(i) a multiple of 5 is multiplied by an even number or
(ii) a multiple of 10 is multiplied by any number.
All the given numbers are even and do not contain any multiple of 5. So, zeros at the end of the product will come only on multiplications by multiples of 10.
Multiples of 10 that lie in the given range from 2 to 100 are 10, 20, 30, 40,50, 60, 70, 80, 90 and 100. Each of these multiples will yield one zero except 100 which will yield two zeros at the end of the product.
∴ Total no. of zeros at the product = 9 + 2 = 11
- 800 chocolates were distributed among the students of a class. East student got twice as many chocolates as the number of students in the class. The number of students in the class was :
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Let the number of students be n.
So, each of n students got 2n chocolates
Total no. of chocolates
= (2n) × n = 800
⇒ 2n2 = 800
⇒ n2 = 400 ⇒ n = 20Correct Option: D
Let the number of students be n.
So, each of n students got 2n chocolates
Total no. of chocolates
= (2n) × n = 800
⇒ 2n2 = 800
⇒ n2 = 400 ⇒ n = 20
- If the sum of two numbers is 3 and the sum of their squares is 12,then their product is equal to :
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Let two numbers be x and y.
x + y = 3
x2 + y2 = 12
⇒ (x + y)2 = (3)2
⇒ x2 + y2 + 2xy = 9
⇒ 12 + 2xy = 9
⇒ 2xy = − 3⇒ xy = − 3 2 Correct Option: C
Let two numbers be x and y.
x + y = 3
x2 + y2 = 12
⇒ (x + y)2 = (3)2
⇒ x2 + y2 + 2xy = 9
⇒ 12 + 2xy = 9
⇒ 2xy = − 3⇒ xy = − 3 2
- The sum and product of two numbers are 12 and 35 respectively. What will be the sum of their reciprocals?
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Let the two numbers be x and y.
∴ x + y = 12 and xy = 351 + 1 = y + x = 12 x y xy 35
Correct Option: C
Let the two numbers be x and y.
∴ x + y = 12 and xy = 351 + 1 = y + x = 12 x y xy 35
