SSC CGL 2017 · 2017-08-06 · Shift 1

The letters available in SANCTION are S, A, N, N, C, T, I, O (no E). Checking each option: STOIC (S, T, O, I, C) - all present. TACOS (T, A, C, O, S) - all present. SONIC (S, O, N, I, C) - all present. STONE (S, T, O, N, E) - requires E, which is not in SANCTION. Hence STONE cannot be formed.

The operation '$' between two numbers A and B equals the digit-sum of A minus the digit-sum of B. Verify with examples: \(75\$26:(7+5)-(2+6)=12-8=4\) ✓ \(69\$53:(6+9)-(5+3)=15-8=7\) ✓ Apply to 82$46: \((8+2)-(4+6)=10-10=0\) Therefore the value is 0.

The relation pairs each letter with its opposite letter in the alphabet (positions summing to 27), and reverses the order: I↔R, J↔Q, K↔P, so IJK → RQP. Applying the same rule to TUV: T(20)↔G(7), U(21)↔F(6), V(22)↔E(5). Reversed, this gives GFE.

Take East and North as positive. After walking West, a left turn faces South. East-West displacement: \(+150-70=+80\) m (East). North-South displacement: \(+180-180=0\) m. The woman ends up 80 m East of her starting position.

From "All wild are lions" and "Some wild are carnivores", the wild carnivores are also lions, so some lions are carnivores — Conclusion II follows. Conclusion I ("All carnivores are lions") fails because carnivores that are not wild are unconstrained and may lie outside lions. Hence only Conclusion II follows.

The series is the 4-letter block abca repeated five times: abca | abca | abca | abca | abca. Reading off the six blanks at positions 2, 7, 9, 15, 17, 19 from this template gives b, c, a, c, a, c — i.e. bcacac.

Decode the operators: × → ÷, ÷ → −, + → ×. The expression becomes: \[12 \div 6 - 5 \times 4\] Applying BODMAS: \(=2-20=-18\) Therefore the answer is -18.

Sister, Daughter and Aunt are all female family relations. Nephew is the only male relation in the list, so it is the odd one out.

Each term is the previous term multiplied by \(-2\): \(0.05\times(-2)=-0.1\), then \(-0.1\times(-2)=0.2\), then \(0.2\times(-2)=-0.4\), then \(-0.4\times(-2)=0.8\). The missing term is 0.2.

Step 1 — Count days from 27 April to 20 October: \(3\text{ (Apr)}+31+30+31+31+30+20=176\) days. Step 2 — Reduce modulo 7: \(176\bmod 7 = 1\) (odd day). Step 3 — Shift the weekday: Thursday + 1 day = Friday.

The pattern is \(a\,\theta\,b\,\delta\,c=(a\times b)-c^{2}\). Verify: \((8\times 12)-6^{2}=96-36=60\) and \((13\times 15)-11^{2}=195-121=74\) ✓ Apply to 18 θ 21 δ 15: \((18\times 21)-15^{2}=378-225=153\) Therefore the answer is 153.

The pattern relates each word's length to the number of letters in the English spelling of its position. Position 1 "One" (3) + 2 = 5 = Smart; Position 2 "Two" (3) + 3 = 6 = Aspire; Position 3 "Three" (5) + 1 = 6 = Castle; Position 4 "Four" (4) + 3 = 7 = Abysmal; Position 5 "Five" (4) + 2 = 6 = Accost. The added differences cycle 2, 3, 1, 3, 2, 3... For Position 6: "Six" (3) + 3 = 6 letters. Among the options only Duties (6 letters) matches.

The source word INFORMATION uses the letters I, N, F, O, R, M, A, T — note that E is absent. NATION, INFRA and RATION are all built from the available letters. MATER requires an E, which INFORMATION does not contain, so MATER cannot be formed.

Compute consecutive differences of the series 9, 10, 13, 22, 49: \(1,\ 3,\ 9,\ 27\) — each difference is the previous one multiplied by 3 (powers of 3). The next difference is \(27\times 3 = 81\). Therefore the missing term is \(49 + 81 = \mathbf{130}\).

Each term is three consecutive letters. The gap between the last letter of one term and the first letter of the next increases by 1: D→E (+1), G→I (+2), K→N (+3), P→T (+4), so V→? is +5. V is the 22nd letter; \(22+5=27\), which wraps to position 1 = A. The triplet of consecutive letters starting at A is ABC.

Check the step pattern within each triplet. FED, JIH and RQP all follow (−1, −1) — three consecutive letters in reverse order. MLN goes M→L (−1) but then L→N (+2), which breaks the pattern. Hence MLN is the odd one out.

Both numbers in the first pair lie symmetrically around 100: \(95 = 100-5\) and \(105 = 100+5\). So the rule is: pair x with \(200-x\). Applying to 89: \(200 - 89 = \mathbf{111}\).

The full sum of all four boxes is \(80+60+90+70 = 300\). Any combination total equals 300 minus the sum of the omitted boxes. Check each option as 300 − (omitted boxes): 300 = all four boxes. 230 = 300 − 70 (= 80+60+90). 220 = 300 − 80 (= 60+90+70). For 290, we would need an omitted subset summing to 10, but the smallest box weighs 60 kg. Hence 290 kg is impossible.

Treat the three letter-positions independently. First letters P, R, T, ?, X step by +2, so the missing first letter is \(T+2 = V\). Second letters N, Q, T, ?, Z step by +3, giving \(T+3 = W\). Third letters R, V, Z, ?, H step by +4 with wrap-around, giving \(Z+4 = D\) (position 30 − 26 = 4). The missing term is VWD.

Compare positions: C(3)→Z(26), H(8)→E(5), A(1)→X(24), N(14)→K(11), T(20)→Q(17), E(5)→B(2), D(4)→A(1). Every letter shifts −3 positions with wrap-around past A. Apply to MAY: M(13)→J(10), A(1)→X (wrap: A→Z→Y→X), Y(25)→V(22). Code is JXV.

Yellow is the characteristic colour of a lemon. The analogy needs an object characteristically purple. Apples are typically red/green; mangoes yellow/green/orange; onions usually white/red. Brinjal (eggplant) is the standard example of a purple vegetable. Hence Brinjal.

Test each for perfect-square status: \(1600 = 40^2,\ 2500 = 50^2,\ 3600 = 60^2\), all perfect squares. \(\sqrt{4000} = 20\sqrt{10}\), which is not an integer. Therefore 4000 is the odd number.

Step 1 — Place A and B: A is at position 1; with 6 boys strictly between A and B, B is at position \(1+6+1 = 8\). Step 2 — Place C: With 3 boys between B and C, C is at position \(8+3+1 = 12\). Step 3 — Add boys after C: 12 boys follow C, so the total is \(12 + 12 = \mathbf{24}\).

Step 1 — Set up: Let present ages be \(P\) (Parvez) and \(M\) (Manish). "Six years ago Parvez = present Manish" gives \(P-6 = M\). "P is one-fourth more than M" gives \(P = \tfrac{5}{4}M\). Step 2 — Solve: Substitute \(P = M+6\) into \(P = \tfrac{5}{4}M\): \(M+6 = \tfrac{5}{4}M \Rightarrow M = 24,\ P = 30\). Step 3 — Future condition: Need \(P + x = 2M\), i.e. \(30 + x = 48 \Rightarrow x = \mathbf{18}\) years.

Check the rule on the examples. For 14 (16) 18: \(|14-18|^2 = 4^2 = 16\). For 33 (64) 25: \(|33-25|^2 = 8^2 = 64\). So the middle number equals the square of the difference of the outer two. For 25 (49) A: \(|25-A|^2 = 49 \Rightarrow |25-A| = 7\), giving \(A = 18\) or \(A = 32\). Hence 32 or 18.

The Communist Party of India (Marxist), CPI(M), was founded in 1964 following a split in the original Communist Party of India (CPI) over ideological differences linked to the Sino-Indian War (1962) and the Sino-Soviet rift. The dissenting faction held the Tenali Convention (Andhra Pradesh) in July 1964 and formalised the new party at its first congress in Calcutta in October–November 1964. Distractors: 1885 is the founding year of the INC; 1980 is the founding year of the BJP.

Red litmus turns blue in the presence of a base. Metallic oxides are generally basic, while non-metallic oxides are acidic. Magnesium is a metal; its oxide MgO reacts with water to form Mg(OH)2, a base that turns red litmus blue. Oxides of phosphorus (P2O5), sulphur (SO2/SO3) and carbon (CO2) are acidic and turn blue litmus red, so they fail this test. Hence the answer is Magnesium.

In most flowering plants, the diploid megaspore mother cell undergoes meiosis to produce four haploid megaspores arranged in a linear tetrad. Of these, only the megaspore towards the chalazal end remains functional and develops into the embryo sac, while the other three degenerate. This monosporic (Polygonum-type) development gives a functional : degenerate ratio of 1 : 3.

Compressibility depends on the spacing between particles. In solids and liquids the particles are already closely packed with negligible inter-particle space, so their volumes barely change under pressure. In a gas the particles are very far apart with large empty space between them, and intermolecular forces are negligible. Applied pressure pushes the particles much closer together, producing a large decrease in volume. Hence gases are highly compressible.

Rukmini Devi Arundale (1904–1986) was a renowned exponent and choreographer of Bharatnatyam. She is credited with reviving the classical form from its earlier devadasi tradition and giving it respectability on the modern stage, founding the Kalakshetra Foundation at Adyar, Chennai in 1936. Lavani (Maharashtra) and Dandiya (Gujarat) are folk forms, and opera is a Western form — none associated with her.

A monopoly is defined as a market structure in which there is exactly one seller of a product that has no close substitutes, protected by high barriers to entry. Being the sole supplier, the monopolist is a price-maker. Two sellers is a duopoly, and a few sellers form an oligopoly — neither qualifies as a monopoly.

The Right against Exploitation (Articles 23 and 24 of the Indian Constitution) directly covers all three prohibitions in the question. Article 23 bans traffic in human beings, begar and other forms of forced labour; Article 24 prohibits the employment of children below 14 years in factories, mines or any hazardous occupation. The Right to Equality, Right to Freedom and Right to Freedom of Religion deal with non-discrimination, civil liberties and religious freedom respectively, not exploitation.

The body of all complex animals is built from only 4 basic tissue types: Epithelial (covers and lines surfaces, secretion/absorption), Connective (supports and binds — bone, cartilage, blood, adipose), Muscular (contraction — skeletal, smooth, cardiac) and Nervous (receives stimuli and transmits impulses). These four combine in different proportions to form all organs and organ systems.

After the First Battle of Panipat (1526) and the Battle of Khanwa against Rana Sanga (1527), Babur turned on Medini Rai, the Rajput chief of Malwa holding the fort of Chanderi. In the Battle of Chanderi (1528) Babur's superior artillery overcame the defenders; the Rajputs performed jauhar and saka and Babur captured the fort. Humayun's reign began only in 1530, Akbar's in 1556 and Jahangir's in 1605, ruling them out.

Bluetooth, the short-range wireless standard operating in the 2.4 GHz ISM band, was invented by Dr. Jaap Haartsen while working at Ericsson in the Netherlands in 1994. He developed the core radio specification later adopted by the Bluetooth SIG. Kirkpatrick Macmillan invented the pedal bicycle, Benjamin Franklin the lightning rod, and Charles Babbage designed early mechanical computers — none linked to Bluetooth.

Check each statement: A — 'The Corrections' (2001) is by Jonathan Franzen. Correct. B — 'A Visit from the Goon Squad' (2010 Pulitzer) is by Jennifer Egan, not Edward P. Jones (who wrote 'The Known World'). Incorrect. C — 'Forty Thieves' (2012) is by Thomas Perry. Correct. Only A and C are correct, so the answer is A and C.

The WHO-coordinated pilot of the world's first malaria vaccine, RTS,S (Mosquirix), was announced for launch in 2018 in three sub-Saharan African countries — Ghana, Kenya and Malawi — the region carrying roughly 90% of the global malaria burden. India, Italy and the United Kingdom are not high-transmission zones for P. falciparum malaria, so the pilot site was Africa.

In April 2017, Punjab Chief Minister Captain Amarinder Singh directed that the names of Ministers and MLAs no longer be inscribed on plaques and foundation stones of state government projects. The move aimed to curb self-promotion and emphasise the public-service nature of state schemes. Among the options, Maharashtra (Devendra Fadnavis), Himachal Pradesh (Virbhadra Singh) and Uttar Pradesh (Yogi Adityanath) had different Chief Ministers in April 2017. Hence the correct answer is Punjab.

The Earth is structured in concentric layers. The outermost solid shell on which we live is the Crust, made mainly of silicate rocks. Beneath it lies the mantle, and at the centre is the core (outer liquid, inner solid). The exosphere is the outermost layer of the atmosphere, not of the Earth's solid surface. Therefore the uppermost layer over the Earth's surface is the Crust.

The horizontal sum of individual demand curves of all consumers in a market at each price level gives the Market Demand curve. It shows the total quantity demanded by all buyers together at different prices. A monotonic curve is a general mathematical property; an indifference curve shows equal-utility combinations of two goods; "diminishing" relates to marginal utility, not aggregate demand. Hence the answer is Market demand.

Whole Disk Encryption (WDE) is the technology in which the entire contents of a storage volume — operating system, applications and user data — are encrypted before being written to disk and decrypted on the fly after authentication. It protects data at rest if the device is lost or stolen. "Half", "Double" and "Triple" are not standard disk-encryption terms. Hence the correct fill-in is Whole.

The Earth's total surface area is about 510 million sq km. Of this, oceans and other water bodies cover roughly 71%, leaving about 29% as land (continents and islands). 20% understates and 35%/40% overstate the land share. Hence the correct answer is 29%.

Bhutan shares its Indian border with four states: Sikkim (west), West Bengal and Assam (south), and Arunachal Pradesh (east). Meghalaya lies south of Assam, bordering Bangladesh, and is separated from Bhutan by Assam. Hence the state that does not share a border with Bhutan is Meghalaya.

Under the system of binomial nomenclature introduced by Carolus Linnaeus, every species is named by genus followed by species. Modern humans belong to the genus Homo and species sapiens, giving the scientific name Homo sapiens (meaning "wise man"). "Melongena" is the eggplant genus, "Tigris" is the tiger's species name, and "Homo nigrum" is not a valid taxon. Hence the answer is Homo Sapiens.

An odometer is the instrument on a vehicle's dashboard that records the cumulative distance the vehicle has travelled, often with a resettable trip meter. A speedometer shows instantaneous speed, a thermometer measures temperature, and "kilometre" is a unit of distance rather than a measuring instrument. Hence the correct answer is Odometer.

Pressure is defined as force per unit area, \(P=\dfrac{F}{A}\). In SI, force is measured in newtons and area in square metres, so the derived unit is \(\text{N/m}^2\), which is given the special name pascal (Pa). Newton is the SI unit of force, weber of magnetic flux and henry of inductance. Hence the SI unit of pressure is Pascal.

Gases in the atmosphere that absorb the long-wave (infrared) radiation emitted by the Earth's surface and re-radiate part of it back downwards are collectively called greenhouse gases. This trapping of heat produces the greenhouse effect. Methane, carbon dioxide and ozone are specific examples of greenhouse gases, but the general category asked for in the blank is Greenhouse.

The 2015 ICC Men's Cricket World Cup was co-hosted by Australia and New Zealand. In the final played at the Melbourne Cricket Ground on 29 March 2015, Australia defeated New Zealand by 7 wickets to lift their fifth World Cup title. India, West Indies and Pakistan were eliminated before the final. Hence the winner was Australia.

At the Feroz Shah Kotla meeting in September 1928, the Hindustan Republican Association was reorganised as the Hindustan Socialist Republican Association/Army (HSRA). Chandra Shekhar Azad became its commander-in-chief while Bhagat Singh served as the chief ideologue, both leading its major actions (Saunders' killing, 1929 Assembly bombing). Khudiram Bose was executed in 1908, two decades before the HSRA was formed. Hence the correct answer is Both 2 and 3.

Lynn Nottage won the 2017 Pulitzer Prize for Drama for Sweat, a play depicting factory workers in Reading, Pennsylvania facing deindustrialisation and racial tension. This was her second Drama Pulitzer after Ruined (2009), making her the first woman to win the Drama Pulitzer twice. The other 2017 laureates won in different categories: Colson Whitehead (Fiction, The Underground Railroad), Hisham Matar (Biography, The Return), and Heather Ann Thompson (History, Blood in the Water).

The diagonal of a rectangle and its two sides form a right triangle, so by the Pythagorean theorem: \[w^2 = d^2 - l^2 = 25^2 - 24^2 = 625 - 576 = 49\] Hence \(w = 7\) cm (a 7-24-25 Pythagorean triple). Area \(= l \times w = 24 \times 7 = 168\) sq cm.

Pair the complementary angles: \(6^\circ + 84^\circ = 90^\circ\) and \(36^\circ + 54^\circ = 90^\circ\). Using \(\tan(90^\circ - \theta) = \cot\theta\): \[\tan 84^\circ = \cot 6^\circ,\quad \tan 54^\circ = \cot 36^\circ\] The product becomes \((\tan 6^\circ \cot 6^\circ)(\tan 36^\circ \cot 36^\circ)\tan 45^\circ = 1 \cdot 1 \cdot 1 = 1\).

Equate CP and SP for the same quantity. Take LCM(6,3)=6 bananas. CP of 6 bananas = Rs. 25. SP of 6 bananas \(= 2 \times 20 = \) Rs. 40. Profit % \(= \dfrac{40 - 25}{25} \times 100 = \dfrac{15}{25} \times 100 = 60\%\).

Let B's pay be \(B\). Then A = 160% of B = \(1.6B\). \[A + B = 1.6B + B = 2.6B = 650\] \[B = \dfrac{650}{2.6} = 250\] Therefore B is paid Rs. 250 (and A gets Rs. 400, summing to 650).

For centroid \(G(\bar x,\bar y)\) of triangle with vertices \((x_i,y_i)\): \[\bar x = \dfrac{x_1+x_2+x_3}{3},\quad \bar y = \dfrac{y_1+y_2+y_3}{3}\] x-coordinate: \(1 = \dfrac{3+0+x_3}{3} \Rightarrow x_3 = 0\). y-coordinate: \(-4 = \dfrac{-4+5+y_3}{3} \Rightarrow y_3 = -13\). Hence C = (0, -13).

Multiply through by 60 (LCM of 3, 4, 5, 6) to clear fractions: \[60 \cdot \dfrac{2(\tfrac{4x}{5}-\tfrac{3}{4})}{3} - 60 \cdot \dfrac{5}{3} = 60 \cdot \left(-\dfrac{1}{6}\right)\] \[40\left(\dfrac{4x}{5}-\dfrac{3}{4}\right) - 100 = -10\] \[32x - 30 - 100 = -10 \Rightarrow 32x = 120\] Therefore \(x = \dfrac{120}{32} = \dfrac{15}{4}\).

Let the number added be \(x\). For continued proportion \(\dfrac{55+x}{100+x} = \dfrac{65+x}{116+x}\). Cross-multiplying: \[(55+x)(116+x) = (100+x)(65+x)\] \[6380 + 171x + x^2 = 6500 + 165x + x^2\] \[6x = 120 \Rightarrow x = 20\] Check: 75, 120, 85, 136 give \(\tfrac{75}{120} = \tfrac{85}{136} = \tfrac{5}{8}\). Hence 20.

For a line in standard form \(Ax + By = C\), the slope is \(m = -\dfrac{A}{B}\). Here \(A = a\), \(B = 5\): \[-\dfrac{a}{5} = -\dfrac{4}{3} \Rightarrow a = \dfrac{4 \times 5}{3} = \dfrac{20}{3}\]

Let Bashir's one-day work be \(R\). Asif works twice as fast, so his rate is \(2R\). Combined rate \(= 3R\). Total work \(= 3R \times 30 = 90R\). Time for Asif alone \(= \dfrac{90R}{2R} = 45\) days.

Reflection across a vertical line \(x = a\) keeps the y-coordinate fixed and maps \(x_0 \to 2a - x_0\). With \(a = -4\) and point \((-1, 3)\): \[x' = 2(-4) - (-1) = -8 + 1 = -7,\quad y' = 3\] Image: (-7, 3). (Check: original is 3 units right of \(x=-4\); image is 3 units left.)

Let the average after 9 matches be \(A\). Total runs after 10 matches \(= 9A + 111\), and the new average is \(A + 5\): \[\dfrac{9A + 111}{10} = A + 5\] \[9A + 111 = 10A + 50 \Rightarrow A = 61\] Therefore the average after the 10th match is \(61 + 5 = 66\).

Performing long division of 7251 by 66: \(66 \times 109 = 7194\) and \(7251 - 7194 = 57\). So \(7251 = 66 \times 109 + 57\), giving quotient 109 and remainder 57.

Standard values: \(\cot 45^\circ = 1\) and \(\operatorname{cosec} 60^\circ = \dfrac{2}{\sqrt{3}}\). \[\cot 45^\circ - \tfrac{1}{\sqrt{3}} \cdot \operatorname{cosec} 60^\circ = 1 - \tfrac{1}{\sqrt{3}} \cdot \tfrac{2}{\sqrt{3}} = 1 - \tfrac{2}{3} = \tfrac{1}{3}\] Therefore the value is 1/3.

Simplify using \(\cot F = \dfrac{\cos F}{\sin F}\): \[2\sin F \cdot \cot F = 2\sin F \cdot \dfrac{\cos F}{\sin F} = 2\cos F\] With \(F = 45^\circ\), \(\cos 45^\circ = \dfrac{1}{\sqrt{2}}\), so \(2\cos 45^\circ = \dfrac{2}{\sqrt{2}} = \sqrt{2}\). Therefore the value is \(\sqrt{2}\).

Using the identity \(\operatorname{cosec}^2 \theta = 1 + \cot^2 \theta\): \[\operatorname{cosec}^2 \theta = 1 + \left(\tfrac{21}{20}\right)^2 = \tfrac{400 + 441}{400} = \tfrac{841}{400}\] Taking the positive square root: \(\operatorname{cosec} \theta = \dfrac{29}{20}\). Therefore the value is 29/20.

Since R, O, S are collinear (ROS passes through centre O) and OR = OQ = radius \(r\), given QS = OR = \(r\). Step 1 — Triangle OQS (isosceles, OQ = QS): Angles opposite equal sides are equal: \(\angle QOS = \angle QSO = 30^\circ\). Step 2 — Exterior angle at Q: In \(\triangle OQS\), \(\angle OQP\) (exterior, since P-Q-S collinear) equals the sum of remote interior angles: \(\angle OQP = 30^\circ + 30^\circ = 60^\circ\). Step 3 — Triangle OPQ (isosceles, OP = OQ): \(\angle OPQ = \angle OQP = 60^\circ\), so \(\angle POQ = 180^\circ - 120^\circ = 60^\circ\). Step 4 — Angle POR: Since R-O-S is a straight line, \(\angle POR + \angle POS = 180^\circ\), and \(\angle POS = \angle POQ + \angle QOS = 60^\circ + 30^\circ = 90^\circ\). Therefore \(\angle POR = 180^\circ - 90^\circ = \mathbf{90^\circ}\).

Step 1 — Marked Price: \(MP = 1600 \times 1.60 = 2560\) Step 2 — Apply 25% discount: \(SP = 2560 \times (1 - 0.25) = 2560 \times 0.75 = 1920\) Therefore the selling price is Rs. 1920.

Let the fraction be \(x\). Then \(x + \dfrac{3}{x} = \dfrac{73}{20}\). Multiplying by \(20x\): \[20x^2 - 73x + 60 = 0\] Factoring: \((4x - 5)(5x - 12) = 0\), giving \(x = \dfrac{5}{4}\) or \(x = \dfrac{12}{5}\). Among the options, only 5/4 appears. Check: \(\dfrac{5}{4} + 3 \cdot \dfrac{4}{5} = \dfrac{25}{20} + \dfrac{48}{20} = \dfrac{73}{20}\). ✓

A sum of real squares equals zero only when each square is zero. So \(x - 2 = 0\), \(y + 3 = 0\), \(z - 15 = 0\), giving \(x = 2,\ y = -3,\ z = 15\). Therefore \(x + y + z - 5 = 2 - 3 + 15 - 5 = \mathbf{9}\).

Using the identity \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\): \[(a+b)^3 = 35 + 3(6)(a+b) = 35 + 18(a+b)\] Let \(s = a+b\): \(s^3 - 18s - 35 = 0\). Testing \(s = 5\): \(125 - 90 - 35 = 0\). ✓ Verification: with \(a+b=5\) and \(ab=6\), \((a,b) = (2,3)\), and \(2^3 + 3^3 = 8 + 27 = 35\). Therefore \(a+b = \mathbf{5}\).

Step 1 — Drop altitude to the base of 30 cm: The altitude bisects the base, forming a right triangle with hypotenuse 20 and one leg 15. \[h = \sqrt{20^2 - 15^2} = \sqrt{400 - 225} = \sqrt{175} = 5\sqrt{7}\] Step 2 — Area: \[\text{Area} = \tfrac{1}{2} \times 30 \times 5\sqrt{7} = 75\sqrt{7}\ \text{cm}^2\] Therefore the area is \(75\sqrt{7}\) cm².

Let foot distance be \(d\) km; cycle distance is \(60 - d\). Total time: \[\dfrac{d}{6} + \dfrac{60-d}{12} = 7\] Multiplying by 12: \(2d + 60 - d = 84 \implies d = 24\). Check: \(24/6 + 36/12 = 4 + 3 = 7\) hours. ✓ Therefore foot distance is 24 km.

For 2 years at 12% p.a., the multiplier is \((1.12)^2 = 1.2544\), so CI factor is \(0.2544\). \[P \times 0.2544 = 10176 \implies P = \dfrac{10176}{0.2544} = 40000\] Therefore the sum invested is Rs. 40000.

Step 1 — Set up equations: Using \(a_n = a_1 + (n-1)d\): \[a_1 + 3d = 11,\quad a_1 + 6d = -4\] Step 2 — Solve: Subtracting gives \(3d = -15\), so \(d = -5\) and \(a_1 = 26\). Step 3 — Sum of 11 terms: \[S_{11} = \tfrac{11}{2}\bigl(2(26) + 10(-5)\bigr) = \tfrac{11}{2}(52 - 50) = \tfrac{11}{2}\cdot 2 = 11\] Therefore S11 = 11.

Since DE is parallel to BC, \(\triangle ADE \sim \triangle ABC\) by AA similarity. Step 1 — Side ratio: With AD : DB = 2 : 5, we get \(\dfrac{AD}{AB} = \dfrac{2}{2+5} = \dfrac{2}{7}\). Step 2 — Area ratio: Areas of similar triangles scale as the square of side ratio: \[\dfrac{[\triangle ADE]}{[\triangle ABC]} = \left(\dfrac{2}{7}\right)^2 = \dfrac{4}{49}\] Step 3 — Compute: \([\triangle ADE] = \tfrac{4}{49}\times 98 = 8\) cm². Therefore area of BDEC \(= 98 - 8 = \mathbf{90}\) cm².

Transcend means to go beyond, surpass, or rise above a limit. Eclipse, beyond the astronomical sense, also means to surpass or outshine — matching the core idea of transcending. "Fizzle" (fail weakly), "abort" (stop early), and "blunder" (mistake) all suggest failure or error, the opposite direction. Hence the synonym is Eclipse.

Each segment is grammatically sound: "Chilika Lake is the" (subject + verb + article before the superlative), "largest brackish water" (superlative with compound modifier), and "lagoon in Asia" (noun + prepositional phrase). Subject-verb agreement, article use, and word order are all correct. Hence the sentence is free from error — No Error (4).

The phrase "a sense of ___" requires a noun to complete the noun phrase. Among the options, only familiarity is a noun; "familiar" is an adjective, "familiarly" an adverb, and "familiarise" a verb — none of which can follow "a sense of." The completed sentence "Repetition bred a sense of familiarity with the characters" is idiomatic and meaningful.

After an imperative joined by "and", the second verb takes the bare base form to express a parallel command or its expected outcome (e.g., "Come and see"). "Will see" breaks this parallel; "saw" (past) and "seeing" (participle) are ungrammatical here. Replacing the bracketed phrase with see yields the correct sentence: "Take out your binoculars and see the Andromeda galaxy."

Denature means to take away or alter the natural qualities of a substance (commonly used for proteins or alcohol). "Unadulterated" means pure (the opposite), "authentic" means genuine, and "limpid" means clear or transparent — none describes the act of altering natural qualities. Hence the correct substitute is Denature.

The active sentence is in the simple past: subject "The homeowners", verb "remodelled", object "the house". The passive structure for simple past is Object + was/were + past participle + by + Subject. Since "the house" is singular, the auxiliary is "was", and the infinitive purpose clause "to help it sell" carries over unchanged. The correct passive is "The house was remodelled by the homeowners to help it sell." Option 2 wrongly uses present "is"; options 3 and 4 mangle the purpose clause.

Fragment Z ("in comparison with the solar") needs a following noun, supplied by Y ("system is the tight packing of the"), which in turn requires X ("seven planets around the star") to complete the prepositional object. Reading ZYX with the lead-in gives: "Another major difference in comparison with the solar system is the tight packing of the seven planets around the star." This is the only order that yields a grammatical, meaningful sentence.

Sentience is the capacity to feel, perceive, and be aware. Its opposite must denote a lack of feeling or awareness. "Consciousness" and "perception" are near-synonyms, and "appreciation" implies positive awareness — none qualifies as an antonym. Disregard, meaning a lack of attention or concern, conveys the absence of awareness and is therefore the opposite of sentience.

For converting a 'Wh' question to indirect speech: drop the quotation marks, use the wh-word as connector, change the structure from interrogative to assertive, and shift tense back since the reporting verb "asked" is in the past. Present continuous "is worrying" becomes past continuous "was worrying", and "you" (Ravi) becomes "him". This yields "She asked Ravi what was worrying him." Options 1 and 3 fail to back-shift the tense; option 2 also wrongly changes "asked" to "asks".

The passage explicitly links the author's struggle with sciatica to having recovered from a herniated disc and its lingering effects (useless left leg, limp). Of the four options — a type of animal, a real place, an imaginary place, or a herniated disc — only the last refers to the medical condition described in the passage. The author's reference to sciatica as a "creature" is metaphorical, not literal; no place by that name is mentioned. Hence the answer is a herniated disc.

The passage states: "my parents moved to Mundakotukurussi, our ancestral village." An ancestral village is the place where one's forefathers lived, so Mundakotukurussi is the correct answer. Chalavara is described only as a nearby, better-developed village; Bengaluru and "Out of India" are not mentioned in the passage at all.

The error lies in part (1): "The climb upside". The preposition "upside" is not used to indicate upward movement along something; the correct preposition with "climb" is "up". The phrase should read "The climb up the mountain". Parts (2) "the mountain" and (3) "was not easy" are grammatically sound, so option 1 is correct.

Incensed means extremely angry or enraged. Among the options, Exasperated (intensely irritated/frustrated, bordering on anger) is the closest synonym. Ecstatic and Elated mean overwhelmingly happy — opposite in tone — while Blithe means cheerfully indifferent. Hence option 2 is correct.

To putrefy means to decay or rot, especially organic matter, producing a foul (fetid) smell — an exact definitional match for the given phrase. Crisp (firm and brittle), Neoteric (modern/new) and Virgin (untouched/pure) have no connection to decomposition, so option 1 is correct.

Read as a single thought: "we deny that a mental image can occupy any portion of space, we need not think of it as losing its parts and shrivelling to a point." Z ("we deny that a mental image can") introduces the claim; Y ("occupy any portion of space, we need not") completes the denial and pivots to a consequence; X ("think of it as losing its parts and shrivelling to a point") supplies that consequence. Hence the order is ZYX.

The passage states: "when I recovered from a herniated disc, it was to discover that I had a useless left leg." The disability is therefore a useless left leg. Depression, memory loss and poor visibility are not mentioned as consequences of the herniated disc.

The passage explicitly says Chalavara was "a superior grade of a village as compared to Mundakotukurussi, with a high school, a fine library, ATMs and several shops." These civic amenities are what make Chalavara better, so option 1 is correct. Mundakotukurussi (not Chalavara) is the ancestral village; the passage says nothing about the writer's schooling or childhood walks there.

The correctly spelt word is bereaving — the present participle of "bereave", meaning to deprive someone of a loved one through death. The other options misspell it: "bereving" drops the 'a', while "bareaving" and "bareving" begin with the wrong vowel "bare-". Hence option 2 is correct.

The idiom rat race refers to a way of life dominated by an exhausting, fiercely competitive struggle for wealth, status or power — the image being rats endlessly chasing one another in a maze. This matches option 3 exactly. The other options describe cruelty, oppression or manipulation, none of which capture the self-driven competitive pursuit central to the idiom.

To spin one's wheels draws on the image of a stuck vehicle whose wheels turn rapidly without the vehicle moving — that is, lots of effort but no forward progress. It therefore means to expend much effort for little or no gain, matching option 3. Bragging, trying one's luck and starting a journey have no link to the futility-of-effort idea.

The subject "A small makeshift stage" is singular and the action is in the past passive (the stage receives the action of building). Passive past for a singular subject takes was + past participle, so "was construct" must become was constructed. "Are constructed" (present plural) and "were constructed" (past plural) fail subject-verb agreement, and "No improvement" ignores the missing -ed. Option 2 is correct.

Incapacitate means to disable or make unable to function. Its opposite is Facilitate, which means to make a process easier or to enable — option 2. Cripple, Maim and Immobilize all describe disabling someone or something, so they are synonyms, not antonyms, of incapacitate.

The word required is the superlative of the adjective frothy. When an adjective ends in a consonant + y, the y changes to i before adding -est (happy → happiest, easy → easiest). Applying the rule: frothy → frothiest. The other options retain the y or insert spurious vowels, violating the rule.

The passage explicitly states that the author "stored the unknown road in my head under 'One Day I Will'." The phrase therefore functions as the author's mental label for that unknown road he intended to explore. The villages, tourist places and famous paths mentioned elsewhere are not what the phrase tags; it is tied directly to the road.

The blank precedes the noun understandings, so an adjective is required. "Tactfully" and "tacitly" are adverbs and are ruled out. "Taciturn" (reserved in speech) describes people, not understandings. Tacit means understood or implied without being stated — exactly the kind of shared, unspoken knowledge that rituals reinforce in a society.