Future First MCQS (6m Intern + PPO) - IIIT UNA

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"Future First MCQS ## Geometry & Math **1. Circle and Chord Length** In a circle with a radius of 13 meters and its center at O(0,0), a chord PQ lies on a horizontal line passing through points A(0,5) and B(9,5). What is the length of the chord PQ? A) 12 B) 20 C) 24 D) 26 **2. Trading Cards Distribution** A collector gives half of their current stock of trading cards plus 1 more to each successive client. If they have exactly 0 cards remaining after giving cards to the 5th client, what was their initial number of trading cards? A) 30 B) 62 C) 64 D) 126 **3. Exponential Inequality** Let p_k = 2^k. Find the smallest natural number m that satisfies the inequality: (p_1)^1 × (p_2)^2 × ... × (p_18)^18 < p_19 × p_20 × ... × p_{18+m}. A) 48 B) 49 C) 50 D) 51 **4. Recurrence Relation** Given the recurrence relation d_m = d_{m+1} + (m+1) and d_1 = -2, what is the value of d_100? A) -5050 B) 5050 C) -5051 D) 5051 **5. Portfolio Valuation** The average value of Yara's and Cyrus' portfolios is ₹5 lakh. The total value of Xavier's portfolio combined with the average value of Xavier's and Cyrus' portfolios is ₹7 lakh. Assuming all portfolio values are positive integers, what is the combined value of Xavier's and Yara's portfolios? A) ₹4 lakh B) ₹8 lakh C) ₹10 lakh D) ₹12 lakh --- ## Logical Reasoning & Puzzles **6. Queue Positioning** Seven researchers (Aarav, Bilal, Chirag, Darsh, Eklavya, Fahad, and Gaurav) stand in a queue, and each submitted a distinct number of reports from 1 to 7. Chirag stood immediately behind Fahad and submitted 3 more reports than him. At least four researchers are standing in front of Gaurav, and all of them submitted more reports than him. The researcher immediately in front of Aarav submitted two fewer reports than Gaurav. The person who submitted the least number of reports is exactly two positions away from Eklavya. Darsh is not at either end of the queue but is somewhere in front of Eklavya. Who submitted the highest number of reports? A) Aarav B) Bilal C) Chirag D) Darsh **7. Circular Seating Arrangement** Six doctors (Sen, Khan, Rao, Iyer, Mehta, and Bose) sit around a circular table. Dr. Sen sits directly opposite Dr. Khan. Dr. Rao sits immediately between Dr. Sen and Dr. Iyer. Dr. Mehta sits immediately between Dr. Khan and Dr. Bose. Who sits directly opposite Dr. Rao? A) Dr. Bose B) Dr. Iyer C) Dr. Mehta D) Dr. Sen **8. Blood Relations** In a family of 8 members across 3 generations, Esha is Bhaskar's only grandchild. Deepak is one of Esha's two maternal uncles. Gita and Deepak are children of Bhaskar, and exactly one of them is male. Harish is Gita's husband. Farhan is the father of Deepak. Charu is married to one of Gita's brothers. Based on this, which of the following statements is true? A) Arun is the sister of Gita. B) Esha can be the son of Harish. C) Charu is the aunt of Esha. D) Charu is the daughter of Bhaskar. **9. Matrix Letter Coding** Using a standard two-matrix coding system where letters are identified by row and column numbers, which set of numbers correctly represents the word "JUDGE"? A) 13, 31, 96, 10, 88 B) 00, 30, 56, 31, 99 C) 42, 43, 65, 21, 55 D) 34, 01, 86, 23, 66 --- ## Data Interpretation (Charts & Graphs) *(Note: Questions 10-14 refer to a line graph showing votes for companies A, B, C, and D across different months)* **10. Vote Comparison** By what percentage is the total number of votes in favor of A and C combined in January, May, and September less than the total number of votes in favor of B and D combined in March, July, and November? A) 27% less B) 37% less C) 18% more D) None of the above **11. Percentage Decline Ratio** What is the ratio of the percentage decline in votes for Company C from January to March to the percentage decline for Company B from January to May? A) 20 : 11 B) 11 : 20 C) 39 : 25 D) 25 : 39 **12. Target Ratio Adjustment** In July, if the ratio of votes for C to D was initially 5:9, what is the percentage increase required in C's votes to make the ratio of D to C 9:5, assuming D's votes remain the same? A) 200% B) 224% C) 250% D) 274% **13. Vote Target Shortfall** In September, how many additional votes are needed for the combined votes of Company A and Company B to be 7% more than Company D's total votes? A) 14,000 B) 81,500 C) 200,000 D) 281,500 **14. Aggregate Vote Percentage** What percentage of Company A's total votes across all 6 months represents the additional votes Company A would need to equal Company D's total votes over the same period? A) 168% B) 172% C) 185% D) 201% *(Note: Questions 15-17 refer to pie charts detailing PC market share by Value and Volume for the year 2005)* **15. Lowest Average Selling Price** Based on the market share by volume and value, which PC company had the lowest average selling price per PC in 2005? A) Apple B) Commodore C) IBM D) Tandy **16. Overall Value Increase** In 2006, if IBM's market share by value increases by 50%, Apple's increases by 15%, and all other companies' sales remain the same, what is the overall percentage increase in total PC sales (value-wise)? A) 14.0% B) 15.5% C) 16.1% D) 18.2% **17. Average Unit Sale Price** If the Total Market Value was US $1,650,000 and the Total Units Sold was 1,500 units, what was the average unit sale price of an IBM PC in 2005? A) $2,850 B) $3,080 C) $3,200 D) $3,500 --- ## Speed, Time, Work & Sets **18. Train Speed and Time** A train moving in the same direction as two people walking at 2 km/h and 4 km/h crosses them in 90 seconds and 120 seconds, respectively. How long will it take for the train to cross a stationary electric post? A) 60 seconds B) 72 seconds C) 80 seconds D) 90 seconds **19. Merchant Profit Margin** A merchant buys 35 mugs and initially sets a marked price to earn a 20% profit on each. They sell 5 mugs at this marked price, 15 mugs at a 10% discount, and 5 mugs break. To achieve an overall 20% profit on the entire purchase, the merchant increases the price of the remaining 10 mugs by p% over the initial marked price. What is the value of p? A) 50 B) 55 C) 60 D) 65 **20. Three-Set Venn Diagram** Out of 260 analysts, 148 work in Equities, 125 in Commodities, and 135 in Forex. 60 work in Equities and Commodities, 27 in Commodities and Forex, and 65 in Equities and Forex. How many analysts work ONLY in Commodities? A) 27 B) 42 C) 60 D) 87 **21. Additional Manpower** A project to lay 8 km of cable in 240 days initially employs 160 technicians. After 80 days, only 2 km of cable has been laid. How many additional technicians are needed to complete the work on schedule? A) 60 B) 80 C) 160 D) 240 **22. Stars and Bars Combinatorics** In how many ways can 12 identical cupcakes, 5 identical storybooks, and 4 identical pencils be distributed among 3 distinguishable students, such that each student receives at least 3 cupcakes and at least 1 storybook? A) 600 B) 750 C) 900 D) 1050 --- ## Number Series **23. Find the Missing Term** What number replaces the question mark in the series: 4, 18, ?, 100, 180, 294, 448? A) 36 B) 42 C) 48 D) 56 **24. Find the Wrong Number** Find the wrong number in the following series: 6, 12, 20, 30, 42, 54, 72, 90, 110. A) 42 B) 54 C) 72 D) 90 --- ## Visual & Non-Verbal Reasoning **25. Cube Folding** Given a flattened net of a cube featuring a central circle, two half-shaded faces, and blank faces, which configurations can be formed by folding the sheet? A) Configuration 1 and 2 only B) Configuration 2 and 3 only C) Configurations 1, 2, and 3 D) Configurations 1, 3, and 4 **26. Mirror Image** What is the correct mirror image of the word "O B S T I N A T E" when a mirror is placed vertically to its right? A) Ǝ T A И I T Ꙅ 8 O B) E T A N I T S B O C) O 8 Ꙅ T I И A T Ǝ D) E T A И I T S B O **27. Paper Folding Pattern** A transparent square sheet has the letter 'S' printed on it. If the bottom half is folded upward over the top half along a horizontal central dotted line, what will the resulting pattern look like? A) Figure 1 B) Figure 2 C) Figure 3 (Intersecting curves resembling the Chanel logo) D) Figure 4 **28. Embedded Figure** Which alternative figure contains the given Figure (X) (a square frame with a continuous top-left to bottom-right diagonal, a lower-left triangular corner cut, and an upper-right corner diagonal notch) as an embedded part without rotation? A) Figure 1 B) Figure 2 C) Figure 3 D) Figure 4"