AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let $N = 24500, then find$ :-

(i) The number of ways by which N can be resolved into two factors.

(ii) The number of ways by which 5N can be resolved into two factors.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(i) N = 23; (ii) 5 N = 56

(i) N = 18; (ii) 5 N = 56

(i) N = 18; (ii) 5 N = 23

None of these

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept- We will first find the factors of the given number, then we will compare the factors with

N = x^{a} y^{b} z^{c}

, we will get the value of

a, b, c

then we will substitute the values of

a, b, c

in,

N = \frac{1}{2} (a + 1) (b + 1) (c + 1)

, formula to get the number of ways.
(i) Factors of

24500 = 2^{2} {\times 5}^{3} {\times 7}^{2}

On comparing this

N = x^{a} y^{b} z^{c}

, we get,

a = 2, b = 3, c = 2,

N = 24500

Using formula:-

N = \frac{1}{2} (a + 1) (b + 1) (c + 1)

N = \frac{1}{2} (2 + 1) (3 + 1) (2 + 1)

N = 18

(ii) Given

5 N,

which becomes

5 \times 24500

5 N = 5 \times 24500

Factors of

5 \times 24500 = 2^{2} {\times 5}^{4} {\times 7}^{2}

On comparing this

N = x^{a} y^{b} z^{c}

, we get,

a = 2, b = 4, c = 2,

N = 5 \times 24500

Using formula:-

N = \frac{1}{2} [(a + 1) (b + 1) (c + 1) + 1]

N = \frac{1}{2} [(2 + 1) (4 + 1) (2 + 1) + 1]

N = 23

Hence, the correct answer is option 3.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!