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

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.

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:
D
`because 10!=2(8)*3^(4)*5^(2)*7^(1)`
`therefore`Total number of divisors
`=(8+1)(4+1)(2+1)(1+1)=270`
hence, statement-1 is false and statement-2 is true.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|17 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Permutations and Combinations Exercise 5: Matching Type Questions|1 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

if 10!=2^(p)3^(q)5^(r)7^(s) then

The number of odd proper divisors of 3^(p)*6^(q)*15^(r),AA p,q,r, in N , is

The number of proper divisors of 2^(p)*6^(q)*21^(r),AA p,q,r in N , is

The number of proper divisors of apbic'ds where a,b,c,d are primes &p,q,r,s in N is

Statement 1: If p ,q ,

The statement (p^^(p to q) ^^ (q to r)) to r is

If p,q,r,s are natural numbers such that p>=q>=r If 2^(p)+2^(q)+2^(r)=2^(s) then

If p, q are r are three logical statements, then the truth value of the statement (p^^q)vv (~q rarr r) , where p is true, is

If 10!=2^(p).3^(q).5^(r).7^(s) then (A)2q=p(B)pqrs=64(C) number of divisors of 10! is 280(D) number of ways of putting 10! as a product of two natural numbers is 135

Given that the divisors of n=3^(p)*5^(q)*7^(r) are of of the form 4lamda+1,lamdage0 . Then,