Home
Class 12
MATHS
Statement-1: the number of even divisors...

Statement-1: the number of even divisors of the number N=12600 is 54.
Statement-2: 0,2,4,6,8, . . . Are even integers.

A

Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1

B

Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1

C

Statement-1 is true, statement-2 is false

D

Statement-1 is false, statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
`becauseN=12600=2^(3)*3^(2)*5^(2)*7^(1)`
`therefore`Numbe of even divisors`=3*(2+1)*(2+1)*(1+1)=54`
both statement are true but statement-2 is not a correct exaplanation for statement-1.
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of even proper divisors of 1008

Consider the number N=2016 . Q. Sum of the even divivisors of the number N is

Statement-1: The number of divisors of 10! Is 280. Statement-2: 10!= 2^(p)*3^(q)*5^(r)*7^(s) , where p,q,r,s in N.

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Statement-1: the highest power of 3 in .^(50)C_(10) is 4. Statement-2: If p is any prime number, then power of p in n! is equal to [n/p]+[n/p^(2)]+[n/p^(3)] + . . ., where [*] denotes the greatest integer function.

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.

Statement-1: Number of permutations of 'n' dissimilar things taken 'n' at a time is n!. Statement-2: If n(A)=n(B)=n, then the total number of functions from A to B are n!.

Statement-1: Number of rectangles on a chessboard is .^(8)C_(2)xx.^(8)C_(2) . Statement-2: To form a rectangle, we have to select any two of the horizontal lines and any two of the vertical lines.

Statement-1: A number of four different digits is formed with the help of the digits 1,2,3,4,5,6,7 in all possible ways. The number of ways which are exactly divisible by 4 is 200. Statement-2: A number divisible by 4, if units place digit is also divisible by 4.

Translate the following statements into symbolic form: x and y are even integers.