NTA UGC NET 27 June 2025 Second Shift Reasoning Questions with Solutions

📘 NTA UGC NET – 27 जून 2025 (द्वितीय पाली)

Q.1 (Hindi)
₹10,000 की राशि 8% वार्षिक चक्रवृद्धि ब्याज पर 2.5 वर्षों के लिए निवेश की जाती है। परिपक्वता पर कुल राशि क्या होगी?
(1) ₹12520.50 (2) ₹12024.62 (3) ₹12130.56 (4) ₹11664.48

✅ Solution (Step-by-Step):

• Principal (P) = ₹10,000
• Rate (R) = 8% per annum
• Time (T) = 2.5 years
• Compounded Annually

Step 1: Calculate compound interest for 2 years:

₹10,000 × (1 + 8/100)² = ₹10,000 × (1.08)² = ₹10,000 × 1.1664 = ₹11,664

Step 2: Apply simple interest for 0.5 year on ₹11,664:

Interest = ₹11,664 × 8% × 0.5 = ₹11,664 × 0.04 = ₹466.56

Step 3: Total Maturity Amount = ₹11,664 + ₹466.56 = ₹12,130.56

✔ Final Answer: ₹12,130.56 (Option 3)

Q.2 (English)

✅ हल (Solution with Explanation)

A. Let original fraction be x/y. After increasing 25% in numerator ⇒ 1.25x After increasing 50% in denominator ⇒ 1.5y Given: 1.25x / 1.5y = 5/3 ⇒ x/y = (5/3) × (1.5 / 1.25) = (5×1.5)/(3×1.25) = 7.5 / 3.75 = 2/1 ✅ So, A → IV

B. \( 4\frac{1}{3} - 3\frac{1}{2} = \frac{13}{3} - \frac{7}{2} = \frac{26 - 21}{6} = \frac{5}{6} \) ✅ So, B → III

C. 40% = 40/100 = 2/5 ✅ So, C → II

D. Use: a² - b² = (a - b)(a + b) Denominator = 3.25×3.20 − 3.20×3.05 = 3.20(3.25 − 3.05) = 3.20 × 0.20 = 0.64 ⇒ Expression becomes: 0.064 / 0.64 = 1/10 ✅ So, D → I

✔ सही मिलान क्रम: A-IV, B-III, C-II, D-I
🎯 सही विकल्प: (4)

Q. 03

🔍 हल (Solution):

A. \( 2^x = \frac{256}{\sqrt{2}} = \frac{2^8}{2^{1/2}} = 2^{8 - 1/2} = 2^{15/2} \Rightarrow x = 15/2 \) ✅ सही

B. \( \frac{1}{3} \times 50\% \text{ of } 150 = \frac{1}{3} \times \frac{50}{100} \times 150 = \frac{1}{3} \times 75 = 25 \) और \( \sqrt{576} = 24 \Rightarrow 25 > 24 \) ✅ सही

C. Top से 5वीं रैंक है तो नीचे से रैंक = 20 - 5 + 1 = 16th लेकिन कथन में 15th लिखा है ❌ गलत

D. Total students = 30 20 students’ avg = 45 → total = 900 Let remaining 10 students' total = x Then, (900 + x)/30 = 42.5 ⇒ 900 + x = 1275 ⇒ x = 375 ⇒ 375/10 = 37.5, लेकिन कथन कहता है 40 kg ❌ गलत

✔ सही कथन: A and B only
🟢 सही विकल्प: Option (4)

📘 UGC NET: 15 Terms of Square Series – Solved

Q 04. What is the sum of the first 15 terms of the following series?
2², 3², 4², 5², …

(1) 1261 (2) 1240 (3) 1239 (4) 1259

✅ Solution:

Series: 2² + 3² + 4² + … + 16²
Because 2² is the first term and we need 15 terms, the last term is 16².

Calculate each term:

• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36
• 7² = 49
• 8² = 64
• 9² = 81
• 10² = 100
• 11² = 121
• 12² = 144
• 13² = 169
• 14² = 196
• 15² = 225
• 16² = 256 ❌ (remove this, as it becomes the 16th term)

Sum of first 15 terms:
1495 - 256 = 1239

✔ Final Answer: Option (3) 1239

प्रश्न: निम्नलिखित श्रेणी के पहले 15 पदों का योग ज्ञात कीजिए:
2², 3², 4², 5², …

(1) 1261 (2) 1240 (3) 1239 (4) 1259

We can slove the question on the formula, put of the n=15

✅ समाधान:

यह श्रेणी वर्गों की श्रेणी है:
2² से 16² तक के वर्ग लेकिन हमें केवल 15 पद चाहिए।

तो हम 16² = 256 को घटा देंगे:
कुल योग = 1495 - 256 = 1239

✔ अंतिम उत्तर: विकल्प (3) 1239

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