ఏపీపీఎస్సీ గ్రూప్-1 ప్రిలిమ్స్ 2024

378 ప్రశ్నలు, ప్రతిదానికి అధికారిక సమాధానం మరియు వివరణ.

ఒకే ప్రశ్న పలు సంవత్సరాల్లో వస్తే, మొదటిసారి అడిగిన సంవత్సరం కింద చూపిస్తాం.

281. Q281Ratio, percentage and commercial arithmetic

     (Directions for questions 12 - 15) Read the following instructions carefully and answer the questions given below : Nandu and Mohan decided to sell their Apple 6 Series watches each at ₹ 42,000 to Karthik and Ganesh respectively. In each case the selling price of ₹ 42,000 was arrived at by increasing the cost price by 25%. While Nandu gives a discount of 10% on the first ₹ 12,000, 8% on the next ₹ 16,000 and 5% on the rest to the buyer Karthik, Mohan gives a discount of 8% on the first ₹ 16,000, 7% on the next ₹ 8,000 and 5% on the rest to his buyer Ganesh. These discounts were however subject to the condition, that the buyers make the payment on time, failing which the discount gets reduced by 1% for every delay of a week. 12. If Nandu and Mohan got all the payments on time, what is the approximate percentage of profit of the person getting the higher profit ?

     • a14%
     • b21%
     • c17%సరైన సమాధానం
     • d9%

     వివరణ త్వరలో.

282. Q282Ratio, percentage and commercial arithmetic

     If Ganesh defaults in each payment by 2 weeks, what would be the profit of Mohan on the sale of a watch ?

     • a₹ 5,400
     • b₹ 6,200
     • c₹ 6,500సరైన సమాధానం
     • d₹ 6,800

     వివరణ త్వరలో.

283. Q283Ratio, percentage and commercial arithmetic

     Directions for questions 12 to 15: Read the following information carefully and answer the questions given below. Nandu and Mohan decided to sell their Apple 6 series watches for Rs. 42,000 each to Karthik and Ganesh. The selling price of Rs. 42,000 was arrived at by increasing the cost price by 25%. Nandu gave his buyer Karthik a discount of 10% on the first Rs. 12,000, 8% on the next Rs. 16,000 and 5% on the remainder, while Mohan gave his buyer Ganesh a discount of 8% on the first Rs. 16,000, 7% on the next Rs. 8,000 and 5% on the remainder. These discounts are conditional: if a buyer fails to make a payment on time, the discount is reduced by 1% for every week of delay. If Nandu and Mohan receive all payments on time, what is the approximate profit percentage of the person who earns more profit between the two?

     • a14%
     • b21%
     • c17%సరైన సమాధానం
     • d9%

     వివరణ త్వరలో.

284. Q284Ratio, percentage and commercial arithmetic

     Directions for questions 12 to 15: Read the following information carefully and answer the questions given below. Nandu and Mohan decided to sell their Apple 6 series watches for Rs. 42,000 each to Karthik and Ganesh. The selling price of Rs. 42,000 was arrived at by increasing the cost price by 25%. Nandu gave his buyer Karthik a discount of 10% on the first Rs. 12,000, 8% on the next Rs. 16,000 and 5% on the remainder, while Mohan gave his buyer Ganesh a discount of 8% on the first Rs. 16,000, 7% on the next Rs. 8,000 and 5% on the remainder. These discounts are conditional: if a buyer fails to make a payment on time, the discount is reduced by 1% for every week of delay. If Karthik fails to make the second and third payments for 1 and 2 weeks respectively, what is the profit Nandu made from the watch sale?

     • aRs. 5,480
     • bRs. 5,545
     • cRs. 5,660సరైన సమాధానం
     • dRs. 5,740

     వివరణ త్వరలో.

285. Q285Ratio, percentage and commercial arithmetic

     Directions for questions 12 to 15: Read the following information carefully and answer the questions given below. Nandu and Mohan decided to sell their Apple 6 series watches for Rs. 42,000 each to Karthik and Ganesh. The selling price of Rs. 42,000 was arrived at by increasing the cost price by 25%. Nandu gave his buyer Karthik a discount of 10% on the first Rs. 12,000, 8% on the next Rs. 16,000 and 5% on the remainder, while Mohan gave his buyer Ganesh a discount of 8% on the first Rs. 16,000, 7% on the next Rs. 8,000 and 5% on the remainder. These discounts are conditional: if a buyer fails to make a payment on time, the discount is reduced by 1% for every week of delay. If Ganesh fails to make each payment for 2 weeks, what is the profit Mohan made from the watch sale?

     • aRs. 5,400
     • bRs. 6,200
     • cRs. 6,500సరైన సమాధానం
     • dRs. 6,800

     వివరణ త్వరలో.

286. Q286Ratio, percentage and commercial arithmetic

     Directions for questions 12 to 15: Read the following information carefully and answer the questions given below. Nandu and Mohan decided to sell their Apple 6 series watches for Rs. 42,000 each to Karthik and Ganesh. The selling price of Rs. 42,000 was arrived at by increasing the cost price by 25%. Nandu gave his buyer Karthik a discount of 10% on the first Rs. 12,000, 8% on the next Rs. 16,000 and 5% on the remainder, while Mohan gave his buyer Ganesh a discount of 8% on the first Rs. 16,000, 7% on the next Rs. 8,000 and 5% on the remainder. These discounts are conditional: if a buyer fails to make a payment on time, the discount is reduced by 1% for every week of delay. If both buyers fail to make each payment for one week, what is the difference in profits between Nandu and Mohan?

     • aRs. 440సరైన సమాధానం
     • bRs. 464
     • cRs. 488
     • dRs. 520

     వివరణ త్వరలో.

287. Q287Ratio, percentage and commercial arithmetic

     Krishna, Suresh, and Raghava started a business with initial investments of Rs. 15,000, Rs. 18,000, and Rs. 20,000 respectively. After one year, Krishna and Suresh increased their investments by Rs. 5,000 and Rs. 2,000 respectively, while Raghava withdrew Rs. 5,000. After another year, Krishna, Suresh, and Raghava increased their investments by 20%, 25%, and 40% respectively. It was decided that Raghava would receive 20% of the total profit for his additional work, and the remaining profit would be distributed according to their investments. After 3 years, the total profit they received was Rs. 53,400. If the additional profit received by Raghava is excluded, find the ratio of the profit shares of Krishna, Suresh, and Raghava:

     • a56 : 63 : 53
     • b53 : 63 : 56
     • c59 : 63 : 56సరైన సమాధానం
     • d69 : 63 : 56
     ›వివరణ

     Option C is correct because the profit is distributed strictly in proportion to the total product of capital and duration for each partner over the three years. Krishna total capital-years = (15000 * 1) + (20000 * 1) + (24000 * 1) = 59000 Suresh total capital-years = (18000 * 1) + (20000 * 1) + (25000 * 1) = 63000 Raghava total capital-years = (20000 * 1) + (15000 * 1) + (21000 * 1) = 56000 Ratio of profit shares = 59000 : 63000 : 56000 = 59 : 63 : 56 Option A: 56 : 63 : 53 miscalculates the third-year additions and withdrawals for Krishna and Raghava. Option B: 53 : 63 : 56 transposes the final values of Krishna and Raghava while miscomputing the additions. Option D: 69 : 63 : 56 adds an extra 10000 to Krishna total capital instead of the calculated values.

288. Q288Ratio, percentage and commercial arithmetic

     Krishna, Suresh and Raghava together started a business with the initial investments of ₹ 15,000, ₹ 18,000 and ₹ 20,000 respectively. After a year, Krishna and Suresh increased their investments by ₹ 5,000 and ₹ 2,000 respectively, while Raghava withdrew ₹ 5,000. After one more year, Krishna, Suresh and Raghava increased their investments by 20%, 25% and 40% respectively. It was decided that Raghava would receive 20% of the total profit received by them for his extra work and the rest of the profit would be distributed according to their investments. After 3 years, the total profit received by them was ₹ 53,400. If the extra profit received by Raghava was excluded, then find the ratio of profit shares of Krishna, Suresh and Raghava :

     • a56 : 63 : 53
     • b53 : 63 : 56
     • c59 : 63 : 56సరైన సమాధానం
     • d69 : 63 : 56

     వివరణ త్వరలో.

289. Q289Ratio, percentage and commercial arithmetic

     Ganesh donated 50% of his saving of ₹ 1,26,588 to Ayodhya Trust and he invested the rest of the amount at 10% compound interest per annum, separately for his children Krishna and Veda in such a way that when they attain the age of 18 years, they would receive the same amount. The age of Krishna is 13 years and that of Veda is 11 years. Then the amount invested for Veda must be :

     • a₹ 28,204
     • b₹ 28,640సరైన సమాధానం
     • c₹ 26,840
     • d₹ 28,460

     వివరణ త్వరలో.

290. Q290Ratio, percentage and commercial arithmetic

     సందీప్ Reliance Infra Private Limited లో ఒక నిర్దిష్ట మొత్తాన్ని పెట్టుబడిగా పెట్టాడు, ఇది సంవత్సరానికి 5% చొప్పున చక్రవడ్డీని (వార్షికంగా లెక్కించబడుతుంది) అందిస్తుంది మరియు ఆ మొత్తంలో 50%కి సమానమైన మొత్తాన్ని Reliance Jio లో పెట్టుబడిగా పెట్టాడు, ఇది సంవత్సరానికి 10% చొప్పున చక్రవడ్డీని (వార్షికంగా లెక్కించబడుతుంది) అందిస్తుంది. రెండు కంపెనీలలో పెట్టుబడి వ్యవధి 2 సంవత్సరాలు. రెండు కంపెనీల నుండి పొందిన మొత్తం మధ్య వ్యత్యాసం ₹ 6,965 అయితే, రెండు కంపెనీలలో పెట్టుబడి పెట్టిన మొత్తాల మధ్య వ్యత్యాసం ఎంత?

     • a₹ 7,000సరైన సమాధానం
     • b₹ 8,400
     • c₹ 7,900
     • d₹ 6,600
     ›వివరణ

     Option A సరైనది ఎందుకంటే రెండు చక్రవడ్డీ మొత్తాల మధ్య బీజగణిత వ్యత్యాసం మొదటి కంపెనీలో పెట్టుబడి పెట్టిన అసలును కనుగొనడానికి అనుమతిస్తుంది, దాని నుండి రెండు పెట్టుబడుల మధ్య వ్యత్యాసం నిర్ణయించబడుతుంది. Reliance Infra లోని మొత్తం P అనుకుందాం; Reliance Jio లోని మొత్తం 0.5 * P అవుతుంది Reliance Infra నుండి వచ్చే మొత్తం = P * (1 + 0.05)^2 = 1.1025 * P Reliance Jio నుండి వచ్చే మొత్తం = 0.5 * P * (1 + 0.10)^2 = 0.6050 * P మొత్తాల మధ్య వ్యత్యాసం = 1.1025 * P - 0.6050 * P = 0.4975 * P = 6965 P = 6965 / 0.4975 = Rs 14000 పెట్టుబడి పెట్టిన మొత్తాల మధ్య వ్యత్యాసం = P - 0.5 * P = 0.5 * 14000 = Rs 7000 Option B: ₹ 8,400 అనేది అవసరమైన 50% వ్యత్యాసానికి బదులుగా అసలులో 60% తీసుకోవడం వల్ల వస్తుంది. Option C: ₹ 7,900 అనేది సరిగా లేని దశాంశ తీసివేత వల్ల ఉత్పన్నమయ్యే అంకగణిత లోపం. Option D: ₹ 6,600 అనేది రెండవ సంవత్సరం చక్రవడ్డీ గుణకాన్ని తప్పుగా లెక్కించడం వల్ల వస్తుంది.

291. Q291Ratio, percentage and commercial arithmetic

     Sandeep invested a certain amount in Reliance Infra Pvt Ltd, which offers 5% p.a. compound interest (compounded annually). And he invested an amount equal to 50% of that amount in Reliance Jio, which offers 10% p.a. compound interest (compounded annually). The investment period for both companies is 2 years. If the difference between the amounts received from the two companies is Rs. 6,965. What is the difference between the capital invested in the two companies?

     • aRs. 7,000సరైన సమాధానం
     • bRs. 8,400
     • cRs. 7,900
     • dRs. 6,600
     ›వివరణ

     Option A is correct because the difference between the initial capitals corresponds to the variable solved from the maturity difference, which is Rs. 7,000. Let the capital in Reliance Jio be P, so Reliance Infra is 2P Amount from Reliance Infra = 2P * (1.05)^2 = 2.205 P Amount from Reliance Jio = P * (1.10)^2 = 1.210 P Difference between amounts = 2.205 P - 1.210 P = 0.995 P 0.995 P = 6,965 P = 7,000 Difference in capital invested = 2P - P = P = Rs. 7,000 Option B: Rs. 8,400 wrongly applies simple interest instead of compound interest. Option C: Rs. 7,900 is obtained if 10% interest is calculated for only one year. Option D: Rs. 6,600 is an incorrect value resulting from rounding errors in the compound interest multipliers.

292. Q292Ratio, percentage and commercial arithmetic

     Ganesh donated 50% of his income of Rs. 1,26,588 to traffic and invested the remaining amount at 10% compound interest per annum, separately for his children Krishna and Veda. After they turn 18 years old, both of them receive the same amount. Krishna's age is 13 years and Veda's age is 11 years. Then the amount that must have been invested for Veda is:

     • aRs. 28,204
     • bRs. 28,640సరైన సమాధానం
     • cRs. 26,840
     • dRs. 28,460
     ›వివరణ

     Option B is correct because dividing the remaining amount according to the compound interest formula gives Rs. 28,640 for Veda. Remaining amount = 1,26,588 / 2 = Rs. 63,294 Time for Krishna to reach 18 years = 18 - 13 = 5 years Time for Veda to reach 18 years = 18 - 11 = 7 years Equal maturity amount condition: K * (1.1)^5 = V * (1.1)^7 K = V * (1.1)^2 = 1.21 V K + V = 63,294 2.21 V = 63,294 V = Rs. 28,640 Option A: Rs. 28,204 is incorrect due to a miscalculation in the ratio 1.21 to 1. Option C: Rs. 26,840 is an incorrect transposition of digits. Option D: Rs. 28,460 results from an arithmetic error when dividing 63,294 by 2.21.

293. Q293Ratio, percentage and commercial arithmetic

     It takes Madhu 2t minutes to complete Form-A which has k questions and 3t minutes to complete Form-B which has k/2 questions. If Madhu answers all the questions, how much more time does he take on an average to answer a Form-B question than he takes to answer a Form-A question ?

     • a2tk
     • b8t/k
     • c4t/kసరైన సమాధానం
     • dt/k

     వివరణ త్వరలో.

294. Q294Ratio, percentage and commercial arithmetic

     Madhu takes 2t minutes to complete Form-A which has k questions, and 3t minutes to complete Form-B which has k/2 questions. If Madhu answers all questions, how much more time on average does he take to answer a Form-B question than the average time he takes to answer a Form-A question?

     • a2 tk
     • b8 tk
     • c4 tkసరైన సమాధానం
     • dt/k

     వివరణ త్వరలో.

295. Q295Time, work, speed and distance

     A, B and C are hired for a painting job. Working together, A and B can do a job in 12 days, B and C can do the same job in 8 days, while A and C can do it in 16 days. Then how long will it take, if all of them work together to complete the job?

     • a3 7/13 days
     • b7 7/13 days
     • c3 7/12 days
     • d7 5/13 daysసరైన సమాధానం

     వివరణ త్వరలో.

296. Q296Time, work, speed and distance

     Pipe 'N' can fill a tank in 1/4 hour, and another pipe 'M' can fill it in 1/6 hour. Both pipes were opened to fill an empty tank, but after 1/15 hour, a leak developed in the tank. This leak alone can empty the full tank in 1/12 hour. If both pipes were opened at 9 PM, at what time will the tank be empty?

     • a9:20 pmసరైన సమాధానం
     • b9:30 pm
     • c9:25 pm
     • d9:40 pm

     వివరణ త్వరలో.

297. Q297Time, work, speed and distance

     A, B, and C were chosen for a painting job. If A and B work together, they can do the work in 12 days, B and C can do the same work in 8 days, and A and C can do it in 16 days. In that case, if all of them work together to complete the work, how long will it take?

     • a3 7/13 days
     • b7 7/13 days
     • c3 7/12 days
     • d7 5/13 daysసరైన సమాధానం
     ›వివరణ

     Option D is correct because summing the pairwise daily work rates gives twice the combined daily work rate of all three persons. Combined pairwise daily work = 1/12 + 1/8 + 1/16 = (4 + 6 + 3)/48 = 13/48 Twice the joint work rate = 2(A + B + C) = 13/48 Joint daily work rate of A, B, and C = 13/96 Time taken working together = 96/13 = 7 5/13 days Option A: 3 7/13 days is 46/13, which is an arithmetic error. Option B: 7 7/13 days incorrectly evaluates 96/13 as having a remainder of 7 instead of 5. Option C: 3 7/12 days miscalculates both the denominator and the quotient.

298. Q298Time, work, speed and distance

     అమిత్ వరుసగా మూడు రోజులలో 66 km, 88 km మరియు 110 km దూరాలను ప్రయాణించాలి. అతను మూడు రోజులలో సాధ్యమైనంత ఎక్కువ స్థిరమైన వేగంతో (km/hrలో) ప్రయాణిస్తాడు, తద్వారా అతను ప్రతి రోజు సంబంధిత దూరాలను పూర్ణాంక గంటలలో పూర్తి చేస్తాడు. ప్రయాణాన్ని పూర్తి చేయడానికి అతనికి ఎన్ని గంటలు పడుతుంది?

     • a8 hours
     • b12 hoursసరైన సమాధానం
     • c22 hours
     • d24 hours
     ›వివరణ

     ప్రతి రోజు పూర్ణాంక సంఖ్యలో గంటలను అనుమతించే అత్యధిక వేగం ఆ మూడు దూరాల గరిష్ట సామాన్య భాగాహారం (గ.సా.భా) కావడం వల్ల మరియు మొత్తం ప్రయాణ సమయం ప్రతి రోజు పట్టిన గంటల మొత్తం కాబట్టి Option B సరైనది. గరిష్ట వేగం = HCF(66, 88, 110) = 22 km/hr 1వ రోజు సమయం = 66 / 22 = 3 గంటలు 2వ రోజు సమయం = 88 / 22 = 4 గంటలు 3వ రోజు సమయం = 110 / 22 = 5 గంటలు మొత్తం సమయం = 3 + 4 + 5 = 12 hours Option A: 8 hours గంటలను తప్పుగా తీసివేయడం లేదా చెల్లని వేగాన్ని ఉపయోగించడం వల్ల వస్తుంది. Option C: 22 hours సమయానికి బదులుగా km/hr లో వేగం యొక్క సంఖ్యా విలువను పొరపాటున ఇస్తుంది. Option D: 24 hours సాధ్యమైనంత ఎక్కువ వేగానికి బదులుగా 11 km/hr అనే తప్పుడు భాజకాన్ని ఉపయోగించడం వల్ల వస్తుంది.

299. Q299Time, work, speed and distance

     Amit traveled distances of 66 km, 88 km, and 110 km on three consecutive days. If he traveled at the highest possible constant speed (in km/hr) over the three days, he would cover the respective distances each day in an integer number of hours. How many hours will it take him to complete the journey?

     • a8 hours
     • b12 hoursసరైన సమాధానం
     • c22 hours
     • d24 hours
     ›వివరణ

     Option B is correct because the highest possible constant speed is the greatest common divisor of the three distances, and the total time is the sum of times taken on each day. Highest possible speed = HCF(66, 88, 110) = 22 km/hr Time on Day 1 = 66 / 22 = 3 hours Time on Day 2 = 88 / 22 = 4 hours Time on Day 3 = 110 / 22 = 5 hours Total time = 3 + 4 + 5 = 12 hours Option A: It underestimates the total hours needed to cover 264 km at 22 km/hr. Option C: It confuses the value of the highest speed (22 km/hr) with the number of hours. Option D: It doubles the correct total time.

300. Q300Time, work, speed and distance

     Vande Bharat Express travelling at 63 kmph can cross a platform of Visakhapatnam railway station which is 199.5 m long in 21 seconds. How much time would Vande Bharat Express take to completely cross (from the moment they meet) Duronto Express 157 m long and travelling at 54 kmph in the opposite direction to it ?

     • a8 seconds
     • b10 secondsసరైన సమాధానం
     • c12 seconds
     • d16 seconds

     వివరణ త్వరలో.

301. Q301Time, work, speed and distance

     Vande Bharat Express, traveling at a speed of 63 km/hr, can cross Visakhapatnam Railway Station platform, which is 199.5 meters long, in 21 seconds. How much time will it take for Vande Bharat Express to completely cross (from the moment they meet) Duronto Express, which is 157 meters long and traveling at 54 km/hr in the opposite direction to Vande Bharat Express?

     • a1) 8 seconds
     • b2) 10 secondsసరైన సమాధానం
     • c3) 12 seconds
     • d4) 16 seconds
     ›వివరణ

     Option B is correct because the length of Vande Bharat Express is first determined using the platform data, after which the time to cross Duronto Express is calculated using their combined lengths and relative speed. Vande Bharat speed = 63 * (5/18) = 17.5 m/s Vande Bharat length = (17.5 * 21) - 199.5 = 367.5 - 199.5 = 168 m Total distance to cross Duronto = 168 + 157 = 325 m Relative speed = (63 + 54) * (5/18) = 117 * (5/18) = 32.5 m/s Time taken = 325 / 32.5 = 10 seconds Option A: 1) 8 seconds underestimates the time by miscalculating the length of Vande Bharat Express. Option C: 3) 12 seconds uses an incorrect relative speed in the denominator. Option D: 4) 16 seconds incorrectly calculates crossing time without accounting for the relative speed of the moving train.

302. Q302Mensuration and geometry

     చుట్టుకొలత 2p గల n భుజాలున్న బహుభుజి యొక్క అన్ని భుజాలను తాకే వృత్తం యొక్క వ్యాసార్థం r అయితే, బహుభుజి వైశాల్యం:

     • ap + n 2r
     • b(p – n)r
     • c(2p – n)r
     • dprసరైన సమాధానం
     ›వివరణ

     Option D సరైనది, ఎందుకంటే వృత్తం చుట్టూ పరిలిఖించబడిన ఏ బహుభుజినైనా, బహుభుజి భుజాలకు సమానమైన భూములు మరియు అంతర్వ్యాసార్థానికి సమానమైన ఎత్తులు కలిగిన త్రిభుజాలుగా విభజించవచ్చు. ప్రతి త్రిభుజ వైశాల్యం = (1/2) x భుజం x r మొత్తం వైశాల్యం = (1/2) x (అన్ని భుజాల మొత్తం) x r అన్ని భుజాల మొత్తం = చుట్టుకొలత = 2p మొత్తం వైశాల్యం = (1/2) x 2p x r = pr Option A: p + n 2r అనేది వైశాల్యంతో పరిమాణాత్మకంగా పొసగదు మరియు అంతర్వ్యాసార్థ సూత్రాన్ని తప్పుగా వర్తింపజేస్తుంది. Option B: (p – n)r అనేది అర్ధ చుట్టుకొలత నుండి భుజాల సంఖ్యను పొరపాటుగా తీసివేస్తుంది. Option C: (2p – n)r అనేది మొత్తం చుట్టుకొలతను భుజాల సంఖ్యతో పొరపాటుగా కలుపుతుంది.

303. Q303Mensuration and geometry

     If a circle with radius r touches all n sides of a polygon with perimeter 2p, then what is the area of that polygon:

     • a1) p+n / 2r
     • b2) (p - n)r
     • c3) (2p - n)r
     • d4) prసరైన సమాధానం
     ›వివరణ

     Option D is correct because the area of any polygon enclosing an inscribed circle is equal to half the perimeter multiplied by the radius. Perimeter of polygon = 2p Semiperimeter of polygon = p Radius of inscribed circle = r Area of polygon = (1/2) x Perimeter x r = (1/2) x 2p x r = pr Option A: 1) p+n / 2r is dimensionally incorrect for area and improperly introduces the side count n. Option B: 2) (p - n)r incorrectly subtracts the number of sides from the semiperimeter. Option C: 3) (2p - n)r subtracts the number of vertices from the perimeter before multiplying by r.

304. Q304Mensuration and geometry

     Consider the following statements : I. An equilateral triangle in a circle will have the maximum area compared to other triangles inside the same circle. II. If the height of an equilateral triangle is 10 cm, its area will be equal to 100√3/3 cm². III. If three sides of a triangle are 5, 12 and 13 cm, then the circumradius of the triangle is 2.5 cm. IV. Scalene triangle is a triangle with none of the sides equal to any other sides. Which among the above given statements are correct ?

     • aI, II and III only
     • bI, II and IV onlyసరైన సమాధానం
     • cII, III and IV only
     • dAll the above

     వివరణ త్వరలో.

305. Q305Mensuration and geometry

     Consider the following statements : I. A Parallelogram having all the sides equal is a Rhombus. II. All the Rhombuses are Parallelograms, but the reverse is not true. III. A Rhombus may or may not be a Square, but all Squares are Rhombuses. Which among the above given statements are correct ?

     • aI and II only
     • bII and III only
     • cI and III only
     • dAll the aboveసరైన సమాధానం

     వివరణ త్వరలో.

306. Q306Mensuration and geometry

     Consider the following statements: I. An equilateral triangle inscribed in a circle has the maximum area compared to other triangles in the same circle. II. If the height of an equilateral triangle is 10 cm, its area will be 100√3/3 cm². III. If the three sides of a triangle are 5, 12, and 13 cm, the circumradius of the triangle is 2.5 cm. IV. In a Scalene triangle, no sides are equal to other sides. Which of the above statements is/are correct?

     • aI, II and III only
     • bI, II and IV onlyసరైన సమాధానం
     • cII, III and IV only
     • dAll of the above
     ›వివరణ

     Option B is correct because statements I, II, and IV are geometrically accurate, while statement III provides an incorrect circumradius for the given right triangle. Statement I: An equilateral triangle maximises area among all inscribed triangles in a circle. Statement II: Area = h^2 / sqrt(3) = 100 / sqrt(3) = 100sqrt(3)/3 cm². Statement III: The sides 5, 12, and 13 form a right triangle, so the circumradius is half the hypotenuse, which is 13 / 2 = 6.5 cm, not 2.5 cm. Statement IV: A scalene triangle by definition has all three sides of unequal length. Option A: Excludes the correct statement IV and includes the false statement III. Option C: Omits statement I and includes the false statement III. Option D: Incorrectly marks statement III as true.

307. Q307Mensuration and geometry

     Consider the following statements: I. A parallelogram with all sides equal is a rhombus. II. All rhombuses are parallelograms, but not all parallelograms are rhombuses. III. A rhombus may or may not be a square, but all squares are rhombuses. Which of the statements given above are correct?

     • aI and II only
     • bII and III only
     • cI and III only
     • dAll of the aboveసరైన సమాధానం
     ›వివరణ

     Option D is correct because all three statements accurately reflect standard geometric definitions and subset relationships among quadrilaterals. Option A: I and II only ignores statement III, which is correct because every square satisfies the definition of a rhombus. Option B: II and III only ignores statement I, which is the standard definition of a rhombus. Option C: I and III only ignores statement II, which correctly notes that rhombuses form a strict subset of parallelograms.

308. Q308Data interpretation and probability

     Study the following bar chart and answer the question given below. The chart shows the number of students who appeared for and passed the B.Tech. exam from various IITs in 2024. Number of students who appeared for and passed the B.Tech. exam from various IITs in India ☐ Appeared ⬛ Passed. What percentage (in decimal order) is the number of students who passed the exam from IIT Kanpur and IIT Pune of the average number of students who appeared for the exam from IIT Madras, IIT Tirupati and IIT Bombay?

     
     • a1) 60% and 85%
     • b2) 64% and 90%సరైన సమాధానం
     • c3) 65% and 70%
     • d4) 62% and 90%

     వివరణ త్వరలో.

309. Q309Data interpretation and probability

     Study the following bar chart and answer the question that is given below. The chart shows the number of students that appeared for and passed B.Tech. examination from different IITs in 2024. Number of students who appeared for and passed B.Tech. exam from different IITs in India IIT Kanpur IIT Madras IIT Pune IIT Tirupati IIT Bombay ☐ Appeared ⬛ Passed The number of students who passed the examination from IIT Kanpur and IIT Pune is what percentage of the average number of students who appeared for the examination from IIT Madras, IIT Tirupati and IIT Bombay respectively?

     • a60% and 85%
     • b64% and 90%సరైన సమాధానం
     • c65% and 75%
     • d62% and 90%

     వివరణ త్వరలో.

310. Q310Data interpretation and probability

     The letters of the word 'ENTRANCE' are arranged in such a way that all vowels are always written together. How many such ways of writing the word is possible?

     • a1080సరైన సమాధానం
     • b1440
     • c1384
     • d1526

     వివరణ త్వరలో.

311. Q311Data interpretation and probability

     The letters in the word 'ENTRANCE' are arranged such that all vowels always come together. Then how many ways are possible to write such a word?

     • a1080సరైన సమాధానం
     • b1440
     • c1384
     • d1526
     ›వివరణ

     Option A is correct because treating the vowels as a single entity yields six units to arrange with two identical consonants, multiplied by the arrangements of the vowels themselves. Letters in ENTRANCE are E, N, T, R, A, N, C, E (8 letters with 2 E's and 2 N's) Consonants are N, T, R, N, C (5 letters with two N's) Vowels are E, A, E (3 letters with two E's) Arrangements of 6 items (5 consonants + 1 vowel group) = 6! / 2! = 360 Internal arrangements of the vowel group (E, A, E) = 3! / 2! = 3 Total arrangements = 360 * 3 = 1080 Option B: 1440 forgets to divide by 2! for the repeated letter N or E. Option C: 1384 is an arbitrary arithmetic error. Option D: 1526 incorrectly accounts for the permutations of repeated letters.

312. Q312Data interpretation and probability

     Find the median of the following data (correct to two decimal places): | Variables | Frequency | |---|---| | 15-25 | 4 | | 25-35 | 11 | | 35-45 | 19 | | 45-55 | 14 | | 55-65 | 0 | | 65-75 | 2 |

     
     • a39.26
     • b40.26సరైన సమాధానం
     • c41.56
     • d42.65
     ›వివరణ

     Option B is correct because applying the median formula for grouped frequency distributions places the median in the 35-45 class at 40.26. Total frequency N = 50 Median position N / 2 = 25, which lies in class 35-45 Lower boundary L = 35 Cumulative frequency before median class cf = 15 Frequency of median class f = 19 Class width h = 10 Median = 35 + ((25 - 15) / 19) * 10 = 35 + (100 / 19) = 35 + 5.263 = 40.26 Option A: 39.26 underestimates the interpolation inside the median class. Option C: 41.56 results from using an incorrect cumulative frequency. Option D: 42.65 adds an excessively large fraction to the lower class boundary.

313. Q313Psychological abilities

     మీరు 2024 సార్వత్రిక ఎన్నికలకు ఒక పోలింగ్ స్టేషన్ యొక్క పోలింగ్ అధికారి అని మరియు పోలింగ్ బూత్ మావోయిస్టుల ప్రాబల్యం ఎక్కువగా ఉన్న ప్రాంతంలో ఉందని అనుకుందాం. పోలింగ్ రోజున ఒక మావోయిస్టుల బృందం వచ్చి ఓటర్లను భయపెట్టి, తుపాకులతో కాల్పులు జరిపి కార్యకలాపాలకు అంతరాయం కలిగించడానికి ప్రయత్నిస్తుంది. మీరు ఏమి చేస్తారు?

     • aవెంటనే పోలింగ్‌ను నిలిపివేసి, సంఘటన గురించి మీ ఉన్నతాధికారులకు తెలియజేయండి.
     • bఅదనపు బలగాలను తెప్పించి మావోయిస్టులను ప్రతిఘటించమని పోలీసులను అడగండి.
     • cఅక్కడ మోహరించిన పోలీసు బలగాలకు తెలియజేసి, ముఖ్యమైన పత్రాలు మరియు EVMల భద్రతను నిర్ధారించమని వారిని అడగండి.సరైన సమాధానం
     • dమీ అధీనంలో ఉన్నవారిని మరియు ఓటర్లను మావోయిస్టులకు వ్యతిరేకంగా తిరుగుబాటు చేయమని అడగండి.
     ›వివరణ

     Option C సరైనది ఎందుకంటే సాయుధ అంతరాయం సమయంలో పోలింగ్ అధికారి యొక్క ప్రాథమిక కార్యాచరణ బాధ్యత ఏమిటంటే, ప్రాణాలను, EVMలను మరియు చట్టబద్ధమైన ఎన్నికల పత్రాలను రక్షించడానికి బూత్‌లో అప్పటికే మోహరించిన భద్రతా సిబ్బందితో సమన్వయం చేసుకోవడం. Option A: స్థానిక భద్రతా దళాలను అప్రమత్తం చేయకుండా వెంటనే పోలింగ్‌ను నిలిపివేయడం తక్షణ ముప్పును ఎదుర్కోవడంలో విఫలమవుతుంది మరియు సిబ్బందిని, ఓటింగ్ సామగ్రిని ప్రమాదంలో పడేస్తుంది. Option B: అదనపు బలగాలను ఏర్పాటు చేయడం అనేది పోలీసు కమ్యూనికేషన్ గ్రిడ్ ద్వారా నిర్వహించబడే కార్యాచరణ పోలీసు కమాండ్ విధి, పోలింగ్ అధికారి ద్వారా నేరుగా కాదు. Option D: సాయుధ తిరుగుబాటుదారులతో పోరాడమని నిరాయుధులైన పౌరులను మరియు అధీన సిబ్బందిని కోరడం నిర్లక్ష్యపూరితమైనది మరియు మానవ ప్రాణాలను ప్రమాదంలో పడేస్తుంది.

314. Q314Psychological abilities

     Assume you are a polling officer at a polling station in the General Elections 2024, and that polling booth is in a Maoist-dominated area. On polling day, a group of Maoists arrived, intimidated voters, fired guns, and tried to disrupt the activities. What would you do then?

     • a1) Immediately stop the polling and inform your superiors about the incident.సరైన సమాధానం
     • b2) Ask the police forces to gather and resist the Maoists present there.
     • c3) Ask the police forces present there to retreat and ensure the safety of important documents and EVMs.
     • d4) Ask your subordinate officers and voters to revolt against the Maoists.
     ›వివరణ

     Option A is correct because the safety of voters and election personnel is paramount, and standard statutory polling procedures require the immediate suspension of polling and reporting to superior election authorities when armed disruption occurs. Option B: It is beyond the authority of a civil polling officer to direct tactical armed combat against insurgents during an ongoing attack. Option C: It inappropriately usurps command over security personnel to order retreats, when standard protocol requires pausing the poll and reporting to superiors. Option D: It endangers civilian lives and subordinates by inciting unequipped people to physically confront armed militants.

315. Q315People: appointments, honours and passings

     Who among the following eminent personalities are recipients of 58th Jnanpith Award ? I. Sampooran Singh Kalra II. Jagadguru Rambhadracharyaji III. Damodar Mauzo Select the correct answer using the codes given below :

     • aI and II onlyసరైన సమాధానం
     • bII and III only
     • cII only
     • dI and III only

     వివరణ త్వరలో.

316. Q316People: appointments, honours and passings

     Identify the incorrect pair regarding persons and their field of activity who were conferred with the Sangeet Natak Akademi Awards 2023:

     • aLV Gangadhara Sastry – Music
     • bJagdish Gangani – Dance
     • cParikshit Mahato – Tribal Danceసరైన సమాధానం
     • dHelen Giri – Folk and Traditional Music

     వివరణ త్వరలో.

317. Q317People: appointments, honours and passings

     Who among the following prominent personalities are the recipients of the 58th Jnanpith Award? I. Sampooran Singh Kalra II. Jagadguru Rambhadracharya III. Damodar Mauzo Choose the correct answer using the codes given below:

     • aI and II onlyసరైన సమాధానం
     • bII and III only
     • cII only
     • dI and III only
     ›వివరణ

     Option A is correct because the 58th Jnanpith Award for 2023 was jointly conferred on eminent Urdu poet and lyricist Gulzar, whose original name is Sampooran Singh Kalra, and renowned Sanskrit scholar Jagadguru Rambhadracharya. Sampooran Singh Kalra: Conferred the 58th Jnanpith Award for Urdu Jagadguru Rambhadracharya: Conferred the 58th Jnanpith Award for Sanskrit Damodar Mauzo: Conferred the preceding 57th Jnanpith Award for Konkani Option B: It erroneously includes Damodar Mauzo, who won the 57th Jnanpith Award, and omits Sampooran Singh Kalra. Option C: It fails to recognise Sampooran Singh Kalra, who was a joint recipient along with Jagadguru Rambhadracharya. Option D: It incorrectly includes Damodar Mauzo instead of Jagadguru Rambhadracharya.

318. Q318People: appointments, honours and passings

     Identify the incorrect pair among the following individuals who received Sangeet Natak Akademi Awards 2023 and their respective fields:

     • aVizzi Gangadhara Sastry - Music
     • bJagadeesh Gangani - Dance
     • cSatish Kumar - Tribal Danceసరైన సమాధానం
     • dParas Giri - Folk and Traditional Music
     ›వివరణ

     Option C is correct because the pair is incorrect; Satish Kumar (P. Satish Kumar) received the award for Carnatic Instrumental Music (Mridangam), not for Tribal Dance. Option A: Vizzi Gangadhara Sastry is correctly matched with the Music field for Harikatha. Option B: Jagadeesh Gangani is correctly matched with Dance for his contribution to Kathak. Option D: Paras Giri is correctly matched with Folk and Traditional Music of Uttarakhand.

319. Q319Sports

     Which of the following state topped the Khelo India Para Games 2023 medal table ?

     • aHaryanaసరైన సమాధానం
     • bUttar Pradesh
     • cTamil Nadu
     • dGujarat

     వివరణ త్వరలో.

320. Q320Sports

     ఖేలో ఇండియా పారా గేమ్స్ 2024 పతకాల పట్టికలో కింది రాష్ట్రాలలో ఏది అగ్రస్థానంలో నిలిచింది?

     • a1. హర్యానాసరైన సమాధానం
     • b2. తమిళనాడు
     • c3. గుజరాత్
     • d4. జమ్మూ & కాశ్మీర్
     ›వివరణ

     Option A సరైనది, ఎందుకంటే ప్రారంభ ఖేలో ఇండియా పారా గేమ్స్‌లో 40 స్వర్ణాలు, 39 రజతాలు మరియు 26 కాంస్య పతకాలతో సహా మొత్తం 105 పతకాలతో హర్యానా పతకాల పట్టికలో అగ్రస్థానంలో నిలిచింది. పతకాల స్థానాల ప్రకారం అగ్ర రాష్ట్రాలు: 40 స్వర్ణ పతకాలతో హర్యానా 25 స్వర్ణ పతకాలతో ఉత్తరప్రదేశ్ 20 స్వర్ణ పతకాలతో తమిళనాడు Option B: మొత్తం స్థానాల్లో హర్యానా మరియు ఉత్తరప్రదేశ్ తర్వాత తమిళనాడు మూడవ స్థానంలో నిలిచింది. Option C: గుజరాత్ పతకాల పట్టికలో మొదటి ఐదు స్థానాల వెలుపల నిలిచింది. Option D: జమ్మూ & కాశ్మీర్ పట్టికలో అగ్రస్థానంలో నిలవడానికి సరిపడా పతకాలను సాధించలేదు.