Which of the following statement(s) is/are true?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Options

The statement (7)⁴⁵⁰ > (9)³⁰⁰is true

Statement I :

(7)⁴⁵⁰ > (9)³⁰⁰

9 = 32

9300 = ((3)2)300 = 3600 = 31.33×450

Again it can be written as 4.31450

9300 = 4.31450

We may readily state that because the powers of 4.31 and 7 are equal and 7 is greater than 4.31.

(7)⁴⁵⁰ > (4.31)⁴⁵⁰

⇒ (7)⁴⁵⁰ > (9)³⁰⁰

Statement 1 is true

Table of content

Statement II: (2)⁹⁰⁰ > (7)⁴⁵⁰

2 = 32

2900 = (22 x 450) = (22)⁴⁵⁰ = 4450

We may readily state that because the powers of 4 and 7 are equal and 7 is greater than 4.

(7)⁴⁵⁰ > (4)⁴⁵⁰ ⇒ (7)⁴⁵⁰ > (2)⁹⁰⁰

Statement 2 is false

Only Statement 1 is true

Alternate,

(7)⁴⁵⁰> (9)³⁰⁰

(73)¹⁵⁰ > (92)¹⁵⁰

⇒ (343)¹⁵⁰ > (81)¹⁵⁰ (Right)

(2)⁹⁰⁰ > (7)⁴⁵⁰

⇒ (22)⁴⁵⁰ > (7)⁴⁵⁰

⇒ (4)⁴⁵⁰ > (7)⁴⁵⁰ (Wrong)

Summary:

Which of the following statement(s) is/are true? (A) (7)⁴⁵⁰ > (9)³⁰⁰ (B) (2)⁹⁰⁰ > (7)⁴⁵⁰ (1) Only I (2) Only II (3) Both I and II (4) Neither I nor II

The statement (7)⁴⁵⁰ > (9)³⁰⁰ is true.