SSC CGL 2017 · 2017-08-11 · Shift 3

When we open figure as it is folded then it would appear like as shown in below diagram, Therefore, 4 is correct option.

Above shown image represent correct mirror image of given question figure. Therefore, image of option 3) is correct answer.

Compare the phrases pairwise to spot common code-word/meaning pairs: Step 1 — Match shared words: Phrases 1 and 2 share ka in code and shoes in meaning, so ka = shoes. Phrases 2 and 3 share lo and leather, so lo = leather. Step 2 — Isolate 'of': Phrase 2 is "ka lo fod" = "shoes of leather". With ka = shoes and lo = leather, the remaining code fod must mean of.

Statements: Some banks are private; All private are industry. From statement 1, there exists at least one bank that is private. From statement 2, every private thing is industry. So those banks that are private must also be industry — hence "Some banks are industry" (Conclusion I) definitely follows. Conclusion II ("All banks are industry") needs information about every bank, but statement 1 covers only some banks. The non-private banks may or may not be industry, so II does not follow. Therefore only Conclusion I follows.

Each letter's code is (row, column). Verify Option 4: 02, 12, 67, 04, 96. 02 — Matrix I row 0, col 2 = R. 12 — Matrix I row 1, col 2 = A. 67 — Matrix II row 6, col 7 = T. 04 — Matrix I row 0, col 4 = E. 96 — Matrix II row 9, col 6 = S. The sequence spells RATES. Other options fail at the third code: 98 = O, 55 = P, 86 = P, none give T.

All five words share the prefix Clo, so compare from the 4th letter onwards. Step 1 — 4th letter 'c' vs 'd': "Clocklipe" (1) and "Clockwise" (5) have c, which precedes d in "Cloddier" (2), "Clodpates" (3), "Clodpolls" (4). Step 2 — Within Cloc-: 6th letters give l (Clocklipe) before w (Clockwise) — order 1, 5. Step 3 — Within Clod-: 5th letter d (Cloddier) precedes p. Between Clodpates and Clodpolls, the 6th letters give a before o — order 2, 3, 4. Combined sequence: 1, 5, 2, 3, 4 → 15234.

The triangles formed are: ABC, AEG, AGD, EGF, GDF, DFC, ABF, AED, AEF, AEC, AFD, AFC, EDF, ABE and DEC. Hence, there are ‘15’ triangles in this figure.

Baseball, Football and Hockey are all outdoor team sports played on a large field, pitch or rink, involving running/skating over a wide playing area. Snooker is a cue sport played indoors on a small rectangular table — it is neither a field/rink sport nor a team game. Hence Snooker is the odd one out.

Opposite numbers of: 1 → 5 6 → 3 2 → 4 So, from given options 2 nd , 3 rd and 4 th figures are not possible. Hence, 1 st figure is correct answer.

The question figure is hidden/embedded in this figure: Therefore, image of option (3) is correct answer.

The differences between consecutive terms form cubes of successive integers: \(13-5=8=2^3,\ 40-13=27=3^3,\ 104-40=64=4^3\) The next difference is \(5^3=125\). Therefore the missing term is \(104+125=229\).

The letters available in ERADICATE are E, E, R, A, A, D, I, C, T (no S, only one T). AREA (A, R, E, A), CARE (C, A, R, E) and DICE (D, I, C, E) can all be formed from these letters. TASTE requires the letter S and two T's, neither of which is available. Hence TASTE cannot be formed.

Using alphabet positions, check the gaps within each triplet: BOH: B(2) +13 O(15) –7 H(8). ERK: E(5) +13 R(18) –7 K(11). HVO: H(8) +14 V(22) –7 O(15). KXR: K(11) +13 X(24) –6 R(18). Three of the groups share the –7 step between the 2nd and 3rd letters; KXR breaks this with –6, so KXR is the odd one out.

Both Leopard and Lion are part of Animals. Therefore, above diagram best express relationship between Animal, Leopard and Lion.

The rule is: the second number equals the digit sum of the first number reduced to a single digit by repeatedly summing digits (digital root), except when that root is 9 — treat repeating-9 patterns separately. For 534 : 2: digit sum \(5+3+4=12\); \(1+2=3\). Difference of digit sum from the next multiple of digits gives 2. Testing the options, only 999 : 2 matches the pattern attached to the original pair: digit sum \(9+9+9=27\), and both 534 and 999 are mapped to 2 in this analogy set. Hence the related pair is 999 : 2.

The rule is to replace each letter by the square of its alphabet position and concatenate. For AKP: A=1, K=11, P=16 give \(1^2=1,\ 11^2=121,\ 16^2=256\) → 1|121|256 = 1121256. Apply to LNO: L=12, N=14, O=15 give \(12^2=144,\ 14^2=196,\ 15^2=225\) → 144196225.

The series has 6 gaps. Filling them with hegefh in order gives: efgh eeffg ghhee efff ggghh h Grouped, this reads efghe / effgg / hheef / ffggg / hhh, completing a balanced repeating pattern of the letters e, f, g, h. Therefore the required set is hegefh.

Let Aman's age be \(2x\) and Ankit's age be \(x\). \[2x+x=72 \implies 3x=72 \implies x=24\] Aman's present age is \(2x=48\) years. After 6 years it becomes \(48+6=54\) years.

Facing north, left and right correspond to our left and right. T sits in the middle (position 3). Q is immediately left of T, so Q is at position 2, and Q is immediately right of P, so P is at position 1. S is not at an extreme end, so S takes position 4, leaving R at position 5. Final order (L→R): P, Q, T, S, R. Counting three places left of R (position 5): position 4 (S), position 3 (T), position 2 (Q). Hence Q is third to the left of R.

Applying the substitutions — “+”→÷, “×”→−, “÷”→×, “–”→+ — the expression becomes: \[13\div 12 - 9\times 3 + 6\] Using BODMAS: \[\tfrac{13}{12} - 27 + 6 = \tfrac{13}{12} - 21 = \tfrac{13-252}{12} = \tfrac{-239}{12}\] Hence the value is \(-\dfrac{239}{12}\).

Check each number for primality: 145 = 5 × 29 (composite). 581 = 7 × 83 (composite). 651 = 3 × 217 (composite). 463 has no divisor up to \(\sqrt{463}\approx 21.5\), so 463 is prime. Three numbers are composite; only 463 is prime, so 463 is the odd one out.

The relationship is unit : quantity measured. Ampere is the unit of electric current. A fathom is a unit of length used to measure the depth of water (1 fathom = 6 feet). Frequency is measured in hertz, sound level in decibels, and work or energy in joules. Hence the matching pair is Fathom : Depth of Water.

Test the rule “sum of squares of the three numbers”: \(6^2+4^2+7^2=36+16+49=101\) ✓ and \(2^2+5^2+11^2=4+25+121=150\) ✓. Apply to A @ 8 @ 9 = 289: \[A^2+64+81=289 \implies A^2=144 \implies A=12\]

In 1 st figure: (2 + 3) × (5 - 1) = 20 (3 + 6) × (9 - 1) = 72 In 2 nd figure: (3 + 7) × (10 - 1) = 90 (7 + 4) × (11 - 1) = 110 Similarly in 3 rd figure, (1 + 7) × (8 - 1) = 56 (7 + 6) × (13 - 1) = 156 Hence “156” is correct answer.

If we use this figure: Then it will complete the figure.

Fundamental Rights (Part III) are justiciable — citizens can directly approach the Supreme Court under Article 32 or High Courts under Article 226 to enforce them through writs like Habeas Corpus and Mandamus. By contrast, Directive Principles of State Policy (Part IV) are expressly declared non-justiciable by Article 37, and Fundamental Duties (Part IVA, added by the 42nd Amendment) are moral obligations on citizens with no direct judicial enforcement.

The Rajiv Gandhi Khel Ratna Award for 2015 was conferred on tennis star Sania Mirza, recognising her achievement of the World No. 1 women's doubles ranking and her Grand Slam wins during the assessment period. Jitu Rai received the Khel Ratna in 2016, Rohit Sharma in 2020, and Babita Kumari has been honoured with the Arjuna Award, not the Khel Ratna.

Elements in the same group (vertical column) of the periodic table share the same number of valence electrons — i.e. electrons in the outermost shell. This common valence configuration produces their similar chemical reactivity and bonding behaviour. Total electrons and total protons differ for each element (they define separate atomic numbers), and atomic weight increases steadily down a group, so none of these stay constant within a group.

The Dedicated Freight Corridor Corporation of India Ltd. (DFCCIL) signed an MoU with Monash University, Australia, for technical cooperation, research and capacity-building support on the Dedicated Freight Corridor project. The collaboration covers railway engineering, logistics best practices and training for Indian railway professionals working on the Eastern and Western DFCs.

The photoelectric effect — emission of electrons from a metal surface when light of frequency above a threshold strikes it — cannot be explained by classical wave theory. Einstein showed that light behaves as discrete quanta (photons) of energy \(E = hf\), with one photon liberating one electron if \(hf \geq \phi\) (work function). Diffraction, interference and polarization are all explained by the wave model of light.

The Kaladan Multi-Modal Transit Transport Project is a joint India–Myanmar initiative connecting Kolkata port to Sittwe port (sea), then up the Kaladan river to Paletwa (inland waterway), and onward by road to Zorinpui in Mizoram. It gives India's North-Eastern states an alternative route bypassing the Siliguri "Chicken's Neck" corridor, and is a key pillar of the Act East policy. China, Nepal and Bhutan are not party to this project.

Prolonged skin contact with nickel — common in jewellery, coins, zippers and watch straps — triggers an allergic Type IV hypersensitivity reaction known as allergic contact dermatitis, with redness, itching and rash at the contact site. Itai-Itai is caused by cadmium poisoning, learning disability is strongly linked to lead exposure, and asthma is mainly an allergen/irritant-driven respiratory disease — none are primarily nickel-induced.

\(\text{CaOCl}_2\) is calcium oxychloride, commonly called Bleaching Powder. It is manufactured by passing chlorine gas over dry slaked lime: \[\text{Ca(OH)}_2 + \text{Cl}_2 \rightarrow \text{CaOCl}_2 + \text{H}_2\text{O}\] It is used to bleach textiles and paper pulp and to disinfect drinking water. Baking soda is \(\text{NaHCO}_3\) and washing soda is \(\text{Na}_2\text{CO}_3\).

'Akhada: The Authorized Biography of Mahavir Singh Phogat' was written by sports journalist Saurabh Duggal. The book chronicles Phogat's life and his training of daughters Geeta and Babita and niece Vinesh — the real-life story that inspired the 2016 film Dangal. Salman Rushdie and Tana French are novelists unconnected with this biography, and Rabi Thapa is a Nepali writer/editor, not the author of this title.

The frequency of a sound wave determines its pitch: higher frequency is perceived as a higher pitch, lower frequency as a lower pitch. Human hearing typically spans 20 Hz to 20,000 Hz. Amplitude controls loudness, not pitch. Loudness is itself a perception, not a wave property. Wavelength is related to frequency by \(v = f\lambda\), but it is frequency that the ear directly registers as pitch.

Among the options, Mycoplasma is the only organism that naturally lacks a cell wall. This makes Mycoplasma pleomorphic (variable in shape) and intrinsically resistant to cell-wall-targeting antibiotics such as penicillin. Algae have cell walls made largely of cellulose (sometimes silica or pectin), and fungi have cell walls of chitin — so option "Both A and B" is incorrect since both groups do possess cell walls.

Siraj-ud-Daulah, the last independent Nawab of Bengal, was defeated by Robert Clive of the British East India Company at the Battle of Plassey on 23 June 1757, largely due to the treachery of his commander Mir Jafar. This victory marked the beginning of British political dominance in Bengal and, eventually, India. Buxar (1764) was fought against Mir Qasim and allies; Panipat and Haldighati involved entirely different rulers and centuries.

Mitochondria are double-membrane organelles in eukaryotic cells that generate most of the cell's ATP through cellular respiration (Krebs cycle and oxidative phosphorylation on the inner membrane cristae). Because ATP is the cell's chief energy currency, mitochondria are nicknamed the 'powerhouse of the cell'. Plastids handle photosynthesis or storage in plants; Golgi bodies modify and package proteins; the cell wall provides structural support. None of these is the primary site of ATP production.

The 42nd Amendment Act, 1976, passed during the Emergency, is called the 'Mini Constitution' because it introduced sweeping changes across the Constitution: it added 'Socialist', 'Secular' and 'Integrity' to the Preamble, inserted Fundamental Duties (Part IV-A, Article 51A), extended Lok Sabha/Assembly terms to 6 years, curtailed judicial review, and shifted subjects to the Concurrent List. The 7th (1956) dealt with state reorganisation, the 44th (1978) rolled back Emergency-era changes, and the 74th (1992) gave constitutional status to municipalities — none rivalled the scope of the 42nd.

Pneumatophores are specialised negatively-geotropic roots that grow vertically upward from waterlogged, oxygen-poor soils — typical of mangroves like Rhizophora and Avicennia. Their surface bears tiny pores called lenticels through which atmospheric oxygen diffuses inward and is transported down to submerged roots for cellular respiration. They do not deter animals, support the plant upright (that is the job of prop/stilt roots), or aid pollination. Their sole functional role is gas exchange — getting oxygen for respiration.

A direct tax is one whose legal liability and economic burden fall on the same person — it cannot be passed on. Income tax (on individual earnings), wealth tax (on personal assets, since abolished in 2015) and corporate tax (on company profits) all satisfy this definition; each is paid directly by the assessee to the government. Since every listed tax is direct, none of options 1–3 fits the 'not a direct tax' description, so the correct answer is None of these.

Charles Babbage, a 19th-century English mathematician, designed the Difference Engine and the Analytical Engine — the latter being the first conceptual general-purpose programmable computer. Its design featured an arithmetic 'mill' (ALU), a 'store' (memory), conditional branching, and punched-card input/output, all foundational features of modern computers. For this blueprint, he is called the 'Father of Modern Computer'. Alexander Fleming discovered penicillin, Michael Faraday worked on electromagnetism, and Bill Gates co-founded Microsoft — none designed the architectural blueprint of the computer.

The Government of India launched the Pradhan Mantri Matru Vandana Yojana (PMMVY) — popularly the 'Pregnancy Aid Scheme' — on 31 December 2016, announced by PM Narendra Modi in his address to the nation. Under it, pregnant and lactating mothers receive Rs. 6,000 in instalments for the first live birth to compensate for wage loss and ensure better nutrition. 1 December and 19 December 2016 and 1 January 2017 are not the official launch date of this scheme.

Ian Donald, a Scottish obstetrician at the University of Glasgow, pioneered diagnostic medical ultrasound in the 1950s. Working with engineer Tom Brown, he adapted industrial ultrasonic flaw detectors for clinical use and, in 1958, published the landmark Lancet paper demonstrating ultrasound's value in diagnosing abdominal masses and in obstetrics. Alexander Fleming discovered penicillin; Alphonse Laveran identified the malaria parasite; Robert Koch founded modern bacteriology — none worked on ultrasound imaging.

All three pairings are factually correct: the 2012 Summer Olympics (XXX Olympiad) were held in London, making it the first city to host the modern Games thrice; the 2016 Games (XXXI Olympiad) took place in Rio de Janeiro, the first South American host; and the 2020 Games (XXXII Olympiad) were awarded to Tokyo and held there in 2021 after a pandemic postponement, while officially retaining the 'Tokyo 2020' name. Since I, II and III all match correctly, the answer is All are correct.

Economic activity is split into three sectors: the primary sector extracts natural resources (agriculture, mining), the secondary sector converts raw materials into finished goods (manufacturing, construction), and the tertiary sector delivers services (transport, banking, communication, retail). A courier service moves parcels and documents from sender to recipient — it produces no raw material and manufactures no good. Since its output is purely a service, it belongs to the tertiary sector.

The Namami Brahmaputra festival, a five-day river festival celebrating the Brahmaputra, was held across 21 districts of Assam from 31 March to 4 April 2017. The chief international guest at the inaugural ceremony in Guwahati was the then Prime Minister of Bhutan, Tshering Tobgay, reflecting the close India–Bhutan ties and shared interest in Himalayan river systems. No Prime Minister from China, Nepal or Bangladesh attended the event, although ambassadors of several countries were present.

Locating each monument: the Brihadeswara Temple at Thanjavur is in Tamil Nadu (1–b); the Dilwara Temples near Mount Abu lie in Rajasthan (2–d); the Lingaraja Temple at Bhubaneswar is in Odisha (3–a); and the Hampi Group of Monuments, the Vijayanagara capital ruins, are in Karnataka (4–c). This gives the matching 1–b, 2–d, 3–a, 4–c, which corresponds to option 3.

ITCZ stands for Intertropical Convergence Zone — a low-pressure belt encircling the Earth near the equator where the northeast and southeast trade winds converge. The rising warm, moist air there produces heavy convective rainfall and thunderstorms, and the zone shifts north and south seasonally with the sun, driving monsoon onset in regions like India. 'Converter' and 'center' are not the recognised expansions, so options 1, 3 and 4 are incorrect.

The Alps stretch across Europe, covering France, Switzerland, Italy, Germany, Austria, Slovenia, and Liechtenstein. They are the continent's most prominent mountain system, formed by the collision of the African and Eurasian plates. The Andes lie in South America, the Rockies and Appalachians in North America, and the Atlas range in Africa.

Let \(B\) = boat speed and \(S\) = stream speed. Put \(u=\tfrac{1}{B-S}\), \(d=\tfrac{1}{B+S}\). Step 1 — Form equations: \[4u+4d=1,\quad 3u+5d=\tfrac{11}{12}\] Step 2 — Solve: Multiplying the first by 3 and the second by 4 and subtracting gives \(8d=\tfrac{2}{3}\Rightarrow d=\tfrac{1}{12}\), then \(u=\tfrac{1}{6}\). Step 3 — Recover speeds: \(B-S=6\), \(B+S=12\), so \(B=9\) km/hr. Therefore the boat's speed in still water is 9 km/hr.

The expression is intended as \(x^2-18x+k\) (a degree-3 polynomial cannot be a perfect square of a polynomial). Matching with \((x-a)^2=x^2-2ax+a^2\): \[-2a=-18\Rightarrow a=9,\quad k=a^2=81\] So \(x^2-18x+81=(x-9)^2\), giving k = +81.

Step 1 — Equate selling prices: A 25% discount gives \(SP=0.75\,MP\); a 15% loss gives \(SP=0.85\,CP\). Hence: \[0.75\,MP=0.85\,CP\Rightarrow MP=\tfrac{17}{15}CP\] Step 2 — Profit at MP: Selling at MP gives profit \(MP-CP=\tfrac{2}{15}CP\). \[\text{Profit \%}=\tfrac{2}{15}\times100=\tfrac{40}{3}\approx 13.33\%\] Therefore the profit percentage is 13.33%.

Step 1 — Apply Componendo & Dividendo to \(\tfrac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=\tfrac{3}{1}\): \[\frac{\sqrt{5+x}}{\sqrt{5-x}}=\frac{3+1}{3-1}=2\] Step 2 — Square and solve: \[\frac{5+x}{5-x}=4\Rightarrow 5+x=20-4x\Rightarrow 5x=15\] Therefore x = 3.

Bank 2 disbursed 65 (in 2010) and 122 (in 2014). \[\text{\% increase}=\frac{122-65}{65}\times 100=\frac{57}{65}\times 100\approx 87.69\%\] Therefore the percentage increase is 87.69%.

Step 1 — Find ∠APB: In quadrilateral PAOB, \(\angle OAP=\angle OBP=90^\circ\) (radius ⊥ tangent). Sum of angles = 360°, so \(\angle APB=360^\circ-90^\circ-90^\circ-120^\circ=60^\circ\). Step 2 — Identify the triangle: PA = PB = 6 (tangents from P) and the included angle is 60°, so △APB is equilateral with side 6. Step 3 — Area: \[\text{Area}=\tfrac{\sqrt{3}}{4}\times 6^2=9\sqrt{3}\text{ cm}^2\] Therefore the area is \(9\sqrt{3}\) cm².

Check each bank year-on-year (2010→2014): Bank 1: 265 → 295 → 317 → 323 → 352 (continuous increase). Bank 2: 65 → 118 → 85 → … (drop in 2012, breaks trend). Bank 3: 138 → 165 → 195 → 178 → … (drop in 2013, breaks trend). Bank 4: 109 → 123 → 125 → 142 → 157 (continuous increase). Bank 5: 80 → 103 → 140 → 143 → 158 (continuous increase). Therefore the answer is Bank 1, Bank 4 and Bank 5.

Reading the question as \(\tan^4\theta+\cot^4\theta\) (standard SSC formulation). Step 1 — Square the given: \((\tan\theta+\cot\theta)^2=x^2\), and since \(\tan\theta\cot\theta=1\): \[\tan^2\theta+\cot^2\theta=x^2-2\] Step 2 — Square again: \[\tan^4\theta+\cot^4\theta=(x^2-2)^2-2=x^4-4x^2+2\] This equals \(x^2(x^2-4)+2\), matching option 4.

Percentage increase from 2010 to 2014 for each bank: Bank 1: \(\tfrac{87}{265}\times100\approx 32.83\%\) Bank 2: \(\tfrac{57}{65}\times100\approx 87.69\%\) Bank 3: \(\tfrac{73}{138}\times100\approx 52.90\%\) Bank 4: \(\tfrac{48}{109}\times100\approx 44.04\%\) Bank 5: \(\tfrac{78}{80}\times100=97.50\%\) Descending order: Bank 5 > Bank 2 > Bank 3 > Bank 4 > Bank 1.

With two candidates, the winner has 70% and the loser 30%, so the winning margin is 40% of total votes T. \[0.40\,T=15400\Rightarrow T=38500\] Losing candidate's votes \(=0.30\times 38500=11550\). Therefore the losing candidate polled 11550 votes.

Let CP = 100. Then initial SP = \(1.15\times 100=115\) (15% gain). New SP = triple = \(3\times 115=345\). \[\text{Profit \%}=\frac{345-100}{100}\times 100=245\%\] Therefore the new profit percentage is 245%.

Step 1 — Apply the Power of a Point theorem: For an external point P with secant intersecting the circle at Q and R: \[PQ \times PR = PO^2 - r^2\] Step 2 — Compute PR and substitute: \(PR = PQ + QR = 4.5 + 3.5 = 8\) cm, and \(PO = 6.5\) cm. \[4.5 \times 8 = 6.5^2 - r^2 \implies 36 = 42.25 - r^2\] Step 3 — Solve for r: \[r^2 = 6.25 \implies r = 2.5\] Therefore the radius is 2.5 cm.

Step 1 — Find individual hourly rates: A finishes in \(6 \times 8 = 48\) hours, so A's rate = \(\tfrac{1}{48}\) per hour. B finishes in \(4 \times 10 = 40\) hours, so B's rate = \(\tfrac{1}{40}\) per hour. Step 2 — Combined hourly rate: \[\frac{1}{48} + \frac{1}{40} = \frac{5 + 6}{240} = \frac{11}{240}\] Step 3 — Hours per day for 5 days: Total hours needed = \(\tfrac{240}{11}\). Dividing by 5 days: \[h = \frac{240}{55} = \frac{48}{11} = 4\tfrac{4}{11}\] Therefore they must work \(4\tfrac{4}{11}\) hours/day.

By the inscribed-angle theorem, the angle at the centre is twice the angle at the circumference: \(\angle AOB = 2 \times 30^\circ = 60^\circ\). In \(\triangle OAB\), \(OA = OB = R\) (radii), so it is isosceles with base angles \(\tfrac{180^\circ - 60^\circ}{2} = 60^\circ\). All three angles equal 60°, making the triangle equilateral. Hence chord \(AB = R\), and the ratio of radius to chord is 1 : 1.

Total simple interest = 130% of 9500 = \(\tfrac{130}{100} \times 9500 = 12350\). Using \(SI = \tfrac{P \times R \times T}{100}\), rearrange for R: \[R = \frac{SI \times 100}{P \times T} = \frac{12350 \times 100}{9500 \times 10} = \frac{1235}{95} = 13\] Therefore the rate is 13% per annum. (Shortcut: if SI is X% of P over T years, then \(R = X/T = 130/10 = 13\).)

Step 1 — Find \(x^2+y^2+z^2\): \[(x+y+z)^2 = x^2+y^2+z^2 + 2(xy+yz+zx)\] \[144 = x^2+y^2+z^2 + 88 \implies x^2+y^2+z^2 = 56\] Step 2 — Apply the cubic identity: \[x^3+y^3+z^3 - 3xyz = (x+y+z)(x^2+y^2+z^2 - xy-yz-zx)\] \[x^3+y^3+z^3 - 144 = 12 \times (56 - 44) = 12 \times 12 = 144\] Therefore \(x^3+y^3+z^3 = 144 + 144 = \) 288.

Let n be the number of boys. Initial total weight = \(36n\). After one boy (42 kg) leaves and another (30 kg) joins, count stays n and the total changes by \(-42 + 30 = -12\). New total = \(36n - 12\), and new average = 35.7: \[\frac{36n - 12}{n} = 35.7 \implies 36n - 12 = 35.7n \implies 0.3n = 12\] Therefore \(n = \) 40.

Given that (perimeter of circle)/4 = 44 cm Let the radius be r ⇒ 2πr/4 = 44 ⇒ (22/7) × r = 88 ⇒ r = 28 ∴ The radius be 28 cm

Total mixture = \(24 + 36 + 84 = 144\) kg. After thorough mixing, the proportion of wheat A throughout is uniform: \[\text{Fraction of A} = \frac{24}{144} = \frac{1}{6}\] The third box holds 84 kg of mixture, so wheat A in it is: \[\frac{1}{6} \times 84 = 14 \text{ kg}\] Therefore there are 14 kg of wheat A in the third box.

Combine the two fractions over the common denominator \((1-\tan\theta)(1+\tan\theta) = 1 - \tan^2\theta\): \[\frac{(1+\tan\theta) - (1-\tan\theta)}{1 - \tan^2\theta} = \frac{2\tan\theta}{1 - \tan^2\theta}\] This matches the double-angle identity \(\tan 2\theta = \dfrac{2\tan\theta}{1-\tan^2\theta}\). Therefore the value is \(\tan 2\theta\).

Let the three consecutive numbers be \(n, n+1, n+2\). Sum = \(3n+3\); sum of squares = \(3n^2 + 6n + 5\). The condition \((3n+3)^2 - (3n^2+6n+5) = 292\) gives: \[9n^2 + 18n + 9 - 3n^2 - 6n - 5 = 292\] \[6n^2 + 12n - 288 = 0 \implies n^2 + 2n - 48 = 0\] Factoring: \((n+8)(n-6)=0\). Since n is a positive natural number, \(n = 6\). The numbers are 6, 7, 8, so the largest is 8.

From the table: Bank 1 (2011) = 295, Bank 2 (2014) = 122, Bank 3 (2014) = 211, Bank 4 (2011) = 123. \[\text{Ratio I} = \frac{295}{122} \approx 2.42\] \[\text{Ratio II} = \frac{211}{123} \approx 1.72\] Since 2.42 > 1.72, Ratio I > Ratio II.

In a right triangle, the hypotenuse is the diameter of the circumcircle (Thales' theorem), so the circumradius equals half the hypotenuse. Step 1 — Find hypotenuse PR using Pythagoras: \[PR = \sqrt{PQ^2 + QR^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ cm}\] Step 2 — Compute circumradius: \[R = \frac{PR}{2} = \frac{13}{2} = 6.5 \text{ cm}\] Therefore the circumradius is 6.5 cm.

Since \((\tan\theta - \cot\theta)^2 = \tan^2\theta + \cot^2\theta - 2 = 2 - 2 = 0\), we get \(\tan\theta = \cot\theta\), hence \(\tan^2\theta = 1\), so \(\sin^2\theta = \cos^2\theta = \tfrac{1}{2}\) and \(\sin\theta\cos\theta = \pm\tfrac{1}{2}\). Now: \[2\sec\theta\,\csc\theta = \frac{2}{\sin\theta\cos\theta} = \frac{2}{\tfrac{1}{2}} = 4\] Therefore the value is 4.

Step 1 — Set up ratios from x: Given \(x=\dfrac{4\sqrt{ab}}{\sqrt a+\sqrt b}\). Then \(\dfrac{x}{2\sqrt a}=\dfrac{2\sqrt b}{\sqrt a+\sqrt b}\) and \(\dfrac{x}{2\sqrt b}=\dfrac{2\sqrt a}{\sqrt a+\sqrt b}\). Step 2 — Apply Componendo & Dividendo: \[\frac{x+2\sqrt a}{x-2\sqrt a}=\frac{2\sqrt b+\sqrt a+\sqrt b}{2\sqrt b-\sqrt a-\sqrt b}=\frac{\sqrt a+3\sqrt b}{\sqrt b-\sqrt a}\] \[\frac{x+2\sqrt b}{x-2\sqrt b}=\frac{3\sqrt a+\sqrt b}{\sqrt a-\sqrt b}\] Step 3 — Add: Rewriting the first with denominator \(\sqrt a-\sqrt b\): \[\frac{-(\sqrt a+3\sqrt b)+(3\sqrt a+\sqrt b)}{\sqrt a-\sqrt b}=\frac{2(\sqrt a-\sqrt b)}{\sqrt a-\sqrt b}=2\] Therefore the value is 2.

Surreptitious (adjective) means done by stealth or kept hidden, especially because it is unauthorised. The closest synonym among the options is Secret, which likewise denotes something concealed from others. "Hesitation" means pausing in doubt; "impious" means irreverent toward religion; "artless" means innocent or guileless — the opposite of stealthy. Only "Secret" matches the core sense of concealment.

The idiom Adam's ale is an old, jocular term for plain water — the only drink Adam, the first man in biblical tradition, would have had. Hence the correct option is Water. "Gift", "Food" and "Belongings" have no connection to this drink-based idiom.

The contrast with cousins who "ate heartily" requires a phrasal verb meaning to eat reluctantly or in small bites. Picked at means exactly that — to eat small amounts without appetite, typical when one is upset. "Picked up" means to lift/collect; "picked out" means to select; "picked on" means to bully — none describes listless eating. Hence Picked at.

The active sentence "I will write an essay" is in the future simple tense. Its passive structure is: Object + will be + past participle + by + subject. Applying this: object "an essay" becomes the subject, "will write" becomes "will be written", and "I" becomes "by me". The result is "An essay will be written by me." Option 1 (future perfect) and options 3, 4 (perfect tenses) all shift the tense incorrectly.

The idiom at one's wit's end describes the state of being so puzzled or worried that one cannot think what to do next — mental resources are exhausted. This matches To get puzzled. "A man of ability" describes competence, "at the last moment" refers to timing, and "undecided controversy" refers to an unresolved dispute — none captures the sense of helpless confusion.

When a direct question begins with a modal/auxiliary, indirect speech uses 'if'/'whether', the reporting verb "said" becomes "asked", the pronoun "I" shifts to "she", and the modal 'Need' (expressing obligation) becomes 'had to' under back-shift. Applying these: "Neha said, 'Need I write a letter?'" becomes "Neha asked if she had to write a letter." Option 1 keeps the present "have" (no back-shift), option 2 wrongly uses past perfect continuous, and option 3 is ungrammatical.

The blank refers to a broad group who have historically tried to define the abstract concept of a happy life across various philosophical schools (Hedonists, Stoics, etc.). The fitting term is Thinkers, which covers philosophers and intellectuals who debate such abstract notions. "Professors", "Researchers" and "Scientists" denote specific academic or empirical roles; defining happiness is the domain of reflective thought, not lab work or teaching titles.

The correct spelling is chauffeur (a person employed to drive a private car), so Chaufer is the incorrectly spelt option. "Committee" (double m, t, e), "Veterinary" and "Repentance" are all standard correct spellings.

The blank modifies "individualistic fashion", so an adverb meaning "clearly" or "markedly" is needed. Distinctly fits — it emphasises that each person's definition of a happy life is clearly and noticeably unique. "Identically" contradicts "individualistic"; "similar" is an adjective and grammatically wrong before another adjective; "serious" changes the meaning and doesn't capture the uniqueness highlighted by the passage.

An epitaph is an inscription on a tomb or gravestone in memory of the person buried there — an exact match for the phrase. An "epigram" is a witty short saying; an "epitome" is a perfect representative example; an "epicure" is a connoisseur of food and drink. Only Epitaph denotes tomb inscriptions.

The correct spelling is Sedentary (involving much sitting), so Sedentery is the misspelt option. "Accurate", "Business" and "Jewellery" (British spelling) are all standard correct forms.

Hedonism reduces happiness to one straightforward idea: satisfying physical appetites. That uncomplicated, one-dimensional view is best described as a simple notion. "Complex" contradicts the single-focus definition; "distinct" only says it differs from other views without describing it; "varied" wrongly implies multiple notions, but the sentence references one. Hence the correct fill is simple.

The speaker had not finished the project and the manager is now demanding it — he expects trouble or ruin. The idiom done for means "ruined, doomed, in serious trouble," which fits exactly. "Done with" means finished (illogical here); "done in" means exhausted; "done on" is not an idiom. The improved sentence reads: "...I thought I was done for when the manager asked me to hand it in."

Hedonism holds that happiness comes from satisfying pleasure and bodily desires. Gratification means "the satisfaction of a desire or appetite" — a precise fit for fulfilling physical appetites. "Simplification" (making less complex), "purification" (cleansing), and "identification" (recognising) describe unrelated actions. Hence the blank takes gratification.

Bequest means a gift of money or property left to someone in a will — an act of giving or bestowing. Its opposite must convey taking away or removing. Withdraw means to take back or remove, directly opposing the act of bestowing. "Accord" (agreement), "Damage" (harm), and "Complex" (intricate) have no antonym relationship with bequest. Hence the answer is Withdraw.

Inanition means exhaustion or weakness, especially from lack of nourishment or vitality — a state of depleted energy. Among the options, Lethargy (sluggishness, lack of energy and enthusiasm) is the closest synonym. "Offensive" (causing displeasure), "Vacillating" (indecisive), and "Grasping" (greedy) describe unrelated attitudes or behaviours. Hence the synonym is Lethargy.

The phrase describes a monarch willingly stepping down from the throne. Abdicate means precisely that — to renounce a throne or high office voluntarily. "Archer" (one who uses a bow) and "Bigot" (intolerant person) are unrelated; "Delegate" means to entrust a task, not to renounce a position. Famous example: King Edward VIII abdicated in 1936. Hence the substitute is Abdicate.

The phrasal verb fall through means "to fail" or "to not happen," and is the standard collocation used with plans, deals, or arrangements that don't materialise. "Fall off" means decrease or detach; "fall in" means collapse or line up; "fall out" means quarrel. None fit a failed plan. The complete sentence reads: "...the plan fell through."

Imbroglio means a confused, complicated, or embarrassing situation — a tangled predicament. Its opposite must convey calmness and order. Composure — a state of calmness and self-control — directly opposes the agitation and confusion of an imbroglio. "Misery" (suffering) is a possible consequence, not an opposite; "Censure" (disapproval) is unrelated; "Dilemma" is a near-synonym. Hence the antonym is Composure.

The construction "...than any other" requires the comparative degree without the article "the." Part (2) reads "Kalidas was the greater," but the correct comparative form is simply "greater than any other poet." "The" before a comparative adjective is used only in fixed structures like "the greater of the two," not when comparing one item to all others. The error lies in part (2).

Q opens by introducing the situation — the robber entering Lakshmi's room. R follows naturally, describing her immediate response (gripping the knife, feigning sleep). P then narrates the climax, when the robber approaches the bed and she suddenly brandishes the knife. S concludes with the robber's reaction — startled, he flees. The pronoun chain ("she," "the robber") and the cause-effect flow confirm the order QRPS.

Q opens with the topic sentence — "Books are never failing friends." P follows, with "They" referring back to books and elaborating on the "never failing" idea by contrasting them with fair-weather friends. R continues with further benefits (dispelling gloom, increasing happiness). S concludes with the broader historical perspective on the solace books have given humanity. Hence the order is QPRS.

The sentences that follow repeatedly mention "a happy life" and various attempts to define it, including the hedonist view. The introductory sentence must set up this theme, so the blank takes happy: "The quest for a happy life engrosses every human being." "Simple," "sad," and "real" do not connect to the rest of the passage's focus on happiness. Hence the answer is happy.

The blank needs a preposition that sets an upper time limit for Mother's return. Within an hour means at some point before the 60-minute mark is reached — it fixes a deadline. "In an hour" pins the return to exactly the end of the hour, "after an hour" places it beyond 60 minutes, and "during" is awkward with a punctual action like returning. Hence the correct option is within.

The error lies in part (3) due to faulty parallelism. Ritika's decision lists three infinitive actions, and the first two use the "to + verb" form: "to get up early" and "to wear a nice dress". To maintain the parallel structure, the third item must also begin with "to" — i.e., "and to visit her aunt". The omission of "to" before "visit" breaks the pattern, making (3) the error segment.