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UGC-NET-Paper1

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Read the Question carefully and choose the correct option.

Match the column:
(Question)
A. If, x+1/x=2, then {x-1/x} = ?
B. If, x-y=1 and x²+y²=41 then x+y = ?
C. If {1-1/x}=2, then 1+1/x² = ?
D. If {x-1/x}=3 then x²+1/x² = ?

(Answer)
I. 11
II. 2
III. 0
IV. (±)9

1. A-I, B-III, C-IV, D-II
2. A-I, B-II, C-III, D-IV
3. A-II, B-III C-I, D-IV
4. A-III, B-IV, C-II, D-I

कॉलम का मिलान करें:
(प्रश्न)
A. यदि x+1/x=2 है, तो {x-1/x} = ?
B. यदि x-y=1 और x²+y²=41 है, तो x+y = ?
C. यदि {1-1/x}=2 है, तो 1+1/x² = ?
D. यदि {x-1/x}=3 है, तो x²+1/x² = ?

(उत्तर)
I. 11
II. 2
III. 0
IV. (±)9

1. A-I, B-III, C-IV, D-II
2. A-I, B-II, C-III, D-IV
3. A-II, B-III C-I, D-IV
4. A-III, B-IV, C-II, D-I

This Question came in

UGC-NET-MassCom-25-June-2025-Shift-2-Q9

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Detailed Explanation & Answer

A. If x + 1/x = 2, then x - 1/x = ?

Let’s solve x + 1/x = 2.
Try x = 1:
1 + 1/1 = 2, which works.
So x = 1 → x - 1/x = 1 - 1 = 0

So A matches with III (0)

B. If x - y = 1 and x² + y² = 41, then x + y = ?

Use the identity:
(x + y)² = x² + y² + 2xy
(x - y)² = x² + y² - 2xy

From x - y = 1 → (x - y)² = 1
Then 1 = 41 - 2xy → 2xy = 40 → xy = 20
Now (x + y)² = 41 + 40 = 81 → x + y = ±9

So B matches with IV (±9)

C. If 1 - 1/x = 2, then 1 + 1/x² = ?

1 - 1/x = 2 → 1/x = -1 → x = -1
Then 1 + 1/x² = 1 + 1 = 2

So C matches with II (2)

D. If x - 1/x = 3, then x² + 1/x² = ?

Use identity: (x - 1/x)² = x² + 1/x² - 2
So 9 = x² + 1/x² - 2 → x² + 1/x² = 11

So D matches with I (11)

A. यदि x + 1/x = 2 है, तो x - 1/x = ?

आइए x + 1/x = 2 हल करें।
x = 1 आज़माएँ:
1 + 1/1 = 2, जो सही है।
अतः x = 1 → x - 1/x = 1 - 1 = 0

अतः A, III (0) से मेल खाता है।

B. यदि x - y = 1 और x² + y² = 41 है, तो x + y = ?

सर्वसमिका का प्रयोग करें:
(x + y)² = x² + y² + 2xy
(x - y)² = x² + y² - 2xy

x - y = 1 → (x - y)² = 1
तो 1 = 41 - 2xy → 2xy = 40 → xy = 20
अब (x + y)² = 41 + 40 = 81 → x + y = ±9

अतः B, IV (±9) से मेल खाता है।

C. यदि 1 - 1/x = 2, तो 1 + 1/x² = ?

1 - 1/x = 2 → 1/x = -1 → x = -1
तो 1 + 1/x² = 1 + 1 = 2

अतः C, II (2) से मेल खाता है।

D. यदि x - 1/x = 3, तो x² + 1/x² = ?

सर्वसमिका का प्रयोग करें: (x - 1/x)² = x² + 1/x² - 2
अतः 9 = x² + 1/x² - 2 → x² + 1/x² = 11

अतः D, I (11) से मेल खाता है।

The Correct Answer is 4

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