This PYQ is from

UGC-NET-Paper1

Maths

UGC-NET-Paper1 PYQs

Year-wise PYQs

Section-wise PYQs

Read the Question carefully and choose the correct option.

If the arithmetic mean of x and 1/x is K, then the arithmetic mean of x^2 and 1/(x^2) is:

1. K^2-1
2. 2(K^2 - 1)
3. 2K^2 - 1
4. 2K^2 + 1

यदि x और 1/x का समांतर माध्य K है, तब x^2 और 1/(x^2) कि का समान्तर माध्य होगा:

1. K^2-1
2. 2(K^2 - 1)
3. 2K^2 - 1
4. 2K^2 + 1

This Question came in

UGC-NET-Linguistics-10-January-2025-Shift-2-Q41

UGC-NET Paper 1 Full Course

To-the-point Video Lectures

Topic-wise PYQs

24x7 Doubt Solving

Detailed Explanation & Answer

Given,
Mean of x + 1/x = K
x + 1/x = 2K

Square the given equation
=> (x + 1/x)² = (2K)²

Here lets say x = a and 1/x = b
Then (a + b)² = a² + b² + 2ab
(ek extra 2ab aya ki nahi aya...)

Then,
x² + 1/x² + 2 = 4K²
=> x² + 1/x² = 4K² - 2

Now, get the mean of x² + 1/x²
=> (x² + 1/x²)/2 = (4K² - 2)/2
=> (x² + 1/x²)/2 = 2K² - 1

दिया गया है,
x + 1/x का माध्य = K
x + 1/x = 2K

दिए गए समीकरण का वर्ग करें
=> (x + 1/x)² = (2K)²

यहाँ मान लें कि x = a और 1/x = b
तो (a + b)² = a² + b² + 2ab
(एक एक्स्ट्रा 2ab आया कि नहीं आया...)

तो,
x² + 1/x² + 2 = 4K²
=> x² + 1/x² = 4K² - 2

अब, x² + 1/x² का माध्य निकालें
=> (x² + 1/x²)/2 = (4K² - 2)/2
=> (x² + 1/x²)/2 = 2K² - 1

The Correct Answer is 3

Free PYQ Test Series

Join Telegram for Free PYQ Test Series of UGC-NET-Paper1

Join Telegram