SSC CGL 2017 · 2017-08-18 · Shift 1

Check divisibility by 11: \(44=11\times4\), \(66=11\times6\), \(77=11\times7\) are all multiples of 11. \(111=3\times37\) is not divisible by 11 (\(111\div11=10\) remainder 1). Therefore 111 is the odd one out.

Football, Hockey and Cricket are all outdoor team sports played on a large field with running-based physical activity. Carrom is an indoor board game played while seated, using a striker on a wooden board. It does not belong to the same category, making it the odd one out.

The operator follows the rule \(a\,@\,b = 2(a-b)\). Check: \(2(9-3)=12\), \(2(15-4)=22\), \(2(16-14)=4\) — all match. Applying to 6 @ 2: \(2(6-2)=2\times4=8\). Therefore the answer is 8.

Here square shape cube is opposite to dotted shape cube. Line check cube is opposite to circle shape cube. The Hexagon shape cube is opposite to cross cube. As we know the figure opposite to any shown figure can’t be on the adjacent face. As, the dotted shape cube can’t be on the adjacent face with square shape cube. Therefore, the figure in option 1 cannot be made based on the unfolded cube given in the question.

Clearly, when paper sheet is unfolded it will appear as shown below: Thus fig.3 is the correct answer.

Step 1 — Apply substitutions: ×→÷, +→×, ÷→−, −→+. The expression becomes: \[60\div5\times3-24+6\] Step 2 — Evaluate using BODMAS: \[60\div5=12,\quad 12\times3=36\] \[36-24+6=18\] Therefore the value is 18.

Letters available in THUMBING: T, H, U, M, B, I, N, G. THING (T,H,I,N,G), MIGHT (M,I,G,H,T) and THUMB (T,H,U,M,B) use only these letters. HAUNT requires the letter A, which is not present in THUMBING. Hence HAUNT cannot be formed.

Use the rule \((\text{col1}+\text{col2})\times\text{col3}=\text{col4}\). Row 1: \((3+4)\times2=14\). Row 2: \((6+5)\times4=44\). Row 3: \((5+2)\times7=7\times7=49\). Therefore the missing number is 49.

Count the letters in each word: tub (3), size (4), latin (5), formal (6). The length increases by 1 each time. The next word needs 7 letters. Among the options, only capital has 7 letters (smooth = 6, idle = 4, scramble = 8).

Decode each pair using the matrices for S-H-O-W in order. 76 → Matrix-II row 7, col 6 = S. 12 → Matrix-I row 1, col 2 = H. 87 → Matrix-II row 8, col 7 = O. 97 → Matrix-II row 9, col 7 = W. All four match, so the correct set is 76, 12, 87, 97.

Clearly, fig.1 shows the correct mirror image of question figure. Hence, figure 1 is the correct answer.

Convert each triplet to alphabet positions and check the gap. ACE: 1, 3, 5 (gap +2). FHJ: 6, 8, 10 (gap +2). KMO: 11, 13, 15 (gap +2). QTW: 17, 20, 23 (gap +3). The gap differs, so QTW is the odd one out.

The relationship in the first pair is \(101 = 99 + 2\) — add 2 to the first number. Applying the same rule: \(100 + 2 = 102\). Therefore the answer is 102.

Step 1 — Trace P: Start at (0, 0). 11 km west → (-11, 0). 16 km south → (-11, -16). Facing south, right turn is west; 14 km west → \((-25,-16)\). Step 2 — Trace Q: Start at (0, 0). 30 km south → (0, -30). Facing south, right turn is west; 25 km west → \((-25,-30)\). Step 3 — Compare: Same x-coordinate; Q is \(|-30-(-16)|=14\) km further south. Therefore Q is 14 km South of P.

Compare each letter's alphabet position with its coded letter. H(8)→J(10), U(21)→W(23), M(13)→O(15), B(2)→D(4), L(12)→N(14), E(5)→G(7), D(4)→F(6). Each letter shifts by +2. Applying +2 to WAX: W(23)→Y(25), A(1)→C(3), X(24)→Z(26). Therefore WAX is coded as YCZ.

Step 1 — Count days from May 21 to Nov 14: 10 (May) + 30 (Jun) + 31 (Jul) + 31 (Aug) + 30 (Sep) + 31 (Oct) + 14 (Nov) = \(177\) days. Step 2 — Find odd days: \(177 = 7\times25 + 2\), so 2 odd days. Step 3 — Shift weekday: Sunday + 2 days = Tuesday.

Refer the diagram shown below: Clearly, the set of letters E and G represents Psychologists and actors who are also fathers.

Clearly, fig.4 will complete the pattern when placed in the blank space of question figure as shown below: Thus, figure 4 is the correct answer.

List all subset sums of {40, 50, 70, 80} using each box at most once. Singles: 40, 50, 70, 80. Pairs: 40+50=90, 40+70=110, 40+80=120, 50+70=120, 50+80=130, 70+80=150. Triples: 40+50+70=160, 40+50+80=170, 40+70+80=190, 50+70+80=200. All four: 40+50+70+80=240. Possible totals: 40, 50, 70, 80, 90, 110, 120, 130, 150, 160, 170, 190, 200, 240. Checking the options, 240, 160, and 200 all appear, but 220 does not. Therefore 220 kg cannot be formed.

Each term has four consecutive letters in reverse alphabetical order, and the first-letter positions decrease by 5: Y(25), T(20), O(15), j(10), E(5). The next first letter is at position \(5-5=0\equiv 26\), i.e. Z. So the next block of consecutive descending letters is ZYXW. The position of the lowercase letter cycles 4th, 3rd, 2nd, 1st, 4th, so the next term has its lowercase letter in the 3rd position. Applying this to ZYXW gives ZYxW, matching option 2.

Argument I cites environmental and dietary advice on eating local fruit. That preference is loosely connected to lifestyle, not to the economic question of whether banning exports would actually lower domestic mango prices, so it is weak. Argument II points out that exports earn valuable foreign exchange — a concrete, significant economic consequence of any ban. This directly engages with the policy proposal and is strong. Hence only Argument II is strong.

Compare letter positions: I(9)→F(6), L(12)→I(9), N(14)→K(11). Each letter shifts back by 3 positions. Apply the same shift to RUW: R(18)→O(15), U(21)→R(18), W(23)→T(20). The result is ORT, matching option 1.

The analogy pairs a regular polygon with the measure of each of its interior angles. A square has interior angles of 90°. An equilateral triangle has three equal angles summing to 180°, so each angle is \(\dfrac{180^\circ}{3}=60^\circ\). Hence the answer is 60°.

The terms follow \(a_n = n^2+1\): \(1^2+1=2,\;2^2+1=5,\;3^2+1=10,\;4^2+1=17\), and \(6^2+1=37\). The missing 5th term is \(5^2+1=26\). Equivalently, the successive differences are 3, 5, 7, 9, 11 — consecutive odd numbers — giving \(17+9=26\).

On close observation, we find that question figure is embedded in fig.1, as shown below: Thus, figure 1 is the correct answer.

The charge that flows through the ballistic galvanometer equals the charge that was stored on the capacitor. Step 1 — Charge from the throw: \[Q = k\theta = (1\,\mu\text{C/deg})(22.5^\circ)=22.5\,\mu\text{C}\] Step 2 — Capacitance from Q = CV: \[C=\dfrac{Q}{V}=\dfrac{22.5\,\mu\text{C}}{15\,\text{V}}=1.5\,\mu\text{F}\] Therefore C = 1.5 μF.

The Soil Health Card scheme, launched by the Government of India in 2015, issues every farmer a card carrying soil-test results (N, P, K, secondary nutrients, micronutrients, pH, EC, organic carbon) together with crop-wise recommendations for nutrient and fertiliser doses. This matches the description in the question exactly. PMFBY is a crop-insurance scheme, while the Shyama Prasad Mukherji Rurban Mission and National Rurban Mission target rural-urban cluster development — none of these issue soil cards.

Mughal painting reached its peak under Jahangir (1605–1627), himself a connoisseur of art. His atelier produced highly refined naturalistic portraits and detailed studies of birds, animals and plants by masters such as Ustad Mansur, Abul Hasan and Bishandas, marking the golden age of the school. Akbar established and expanded the atelier, but the artistic refinement and naturalism characteristic of the school's flowering belong to Jahangir's reign.

Bengal's fertile deltaic plains were ideal for jute, and demand for jute fibre to make sacking and packaging soared with the industrial revolution in Britain. The colonial administration pushed cultivators into growing jute through cash advances, contracts and outright coercion, often at the expense of food crops. Tea was promoted in Assam and Darjeeling, sugarcane and wheat were not the targeted Bengal cash crop. Hence the answer is Jute.

In 1219, Genghis Khan personally led the Mongol invasion of the Khwarazmian Empire, which included Transoxiana, in retaliation for the Shah's killing of Mongol envoys at Otrar. The campaign destroyed Bukhara, Samarkand and Urgench. Timur (late 14th c.), Nadir Shah (18th c.) and Ahmad Shah Abdali (18th c.) all lived centuries later and are unrelated to this event.

Amphoteric metals such as aluminium and zinc react with sodium hydroxide solution to liberate hydrogen gas, forming a soluble aluminate or zincate: \[2\text{Al}+2\text{NaOH}+2\text{H}_2\text{O}\rightarrow 2\text{NaAlO}_2+3\text{H}_2\uparrow\] \[\text{Zn}+2\text{NaOH}\rightarrow \text{Na}_2\text{ZnO}_2+\text{H}_2\uparrow\] Oxygen, elemental sodium and water are not the gaseous products. Hence the answer is hydrogen gas.

Nutrient enrichment (nitrates, phosphates) fuels the rapid multiplication of free-floating microscopic algae — the planktonic algae (phytoplankton) — which dominate the water column and discolour the water. Algal bloom is the result, eutrophication is the process, and biomagnification is unrelated to algal growth. The question asks for the type of algae, which is planktonic.

Cases that come straight to a court without first being heard by any lower court fall under its Original Jurisdiction. Under Article 131, the Supreme Court exclusively hears disputes between the Union and one or more States, or between States, as a court of first instance. Appellate jurisdiction hears appeals, writ jurisdiction (Article 32) issues writs to enforce fundamental rights, and advisory jurisdiction (Article 143) gives opinions to the President — none fit the definition given.

Lime water is a clear, saturated aqueous solution of calcium hydroxide, \(\text{Ca(OH)}_2\) (slaked lime). It is used to test for CO₂, turning milky due to insoluble CaCO₃: \[\text{Ca(OH)}_2+\text{CO}_2\rightarrow \text{CaCO}_3\downarrow+\text{H}_2\text{O}\] NaOH, Mg(OH)₂ and NH₄OH are different bases with different uses and are not present in lime water.

The Total Product (TP) is the total quantity of output produced by a firm when a variable input (e.g., labour) is changed while all other inputs (e.g., capital) are held constant. It directly maps the variable input to the output level in the short run. Average product is output per unit of variable input (TP/variable input), not the input-output relationship itself. Isoquant belongs to long-run analysis with two variable inputs. The long run treats all inputs as variable, which contradicts the condition of holding others constant.

Fyodor Pirotsky, a Russian engineer, is credited with inventing the electric tram. In 1880 at Saint Petersburg he successfully demonstrated the first passenger-carrying electric tramway by powering a tram car using current supplied through the rails. James Cook was a British explorer of the Pacific; William Harvey discovered blood circulation; Robert Boyle was a 17th-century chemist known for Boyle's Law. None are linked to electric traction.

New Zealand won the 2015 Men's Rugby World Cup, hosted by England. In the final at Twickenham Stadium on 31 October 2015, the All Blacks defeated Australia 34–17. This was New Zealand's third title (after 1987 and 2011) and made them the first team to successfully defend the Webb Ellis Cup. South Africa and England were eliminated before the final.

Verify each pairing: Statement 1: 'Forty Thieves' (2016) is indeed by Thomas Perry – correct. Statement 2: 'Half of a Yellow Sun' was written by Chimamanda Ngozi Adichie, not Jennifer Egan – incorrect. Statement 3: 'Middlesex' (Pulitzer 2003) was written by Jeffrey Eugenides, not Adichie – incorrect. Hence statements 2 and 3 are incorrect, matching option (2).

In the 2016 Human Development Report released by UNDP, the United States was ranked 10th with an HDI score of 0.920, placed in the 'Very High Human Development' category. Norway topped the index that year. Rank 1 belonged to Norway, not the USA; ranks 100 and 200 are far too low for a developed economy with high life expectancy, schooling years, and GNI per capita.

Article 32 of the Constitution confers Writ Jurisdiction on the Supreme Court, allowing any individual whose Fundamental Right is violated to move the Court directly for enforcement through writs – Habeas Corpus, Mandamus, Prohibition, Certiorari and Quo Warranto. Dr. B.R. Ambedkar called Article 32 the 'heart and soul' of the Constitution. Original jurisdiction (Art. 131) covers Centre–State disputes; appellate jurisdiction hears appeals from lower courts; advisory jurisdiction (Art. 143) is exercised only on a Presidential reference.

The Soviet Union (USSR, 1922–1991) is the textbook example of a centrally planned (command) economy through most of the 20th century. The state owned the means of production, agriculture was collectivised, and Gosplan directed output and prices through successive Five-Year Plans. The USA and Japan were market economies driven by private ownership; India adopted a mixed economy after 1947, blending public-sector planning with a sizeable private sector.

Platelets are also called Thrombocytes. They are small, anucleate cell fragments derived from bone-marrow megakaryocytes, and the prefix 'thrombo-' refers to their central role in blood clotting (haemostasis). Leucocytes are white blood cells (immune defence) and erythrocytes are red blood cells (oxygen transport); 'Platelets' restates the term in the question rather than giving the alternative name.

By number of described species, Arthropoda is the largest animal phylum and Mollusca ranks second, with roughly 85,000–100,000 living species including snails, bivalves, squids and octopuses. They are characterised by a soft body, mantle, muscular foot and (usually) a calcareous shell. Chordata ranks third; Annelida (segmented worms) is much smaller. 'Coelomates' is not a phylum but a grade of organisation covering many phyla.

When the protoxylem (first-formed) lies towards the centre and the metaxylem (later-formed) lies towards the periphery, xylem differentiation proceeds centrifugally (outwards). This pattern is termed Endarch and is characteristic of stems and leaves of angiosperms. In the opposite Exarch pattern (typical of roots), protoxylem is peripheral and metaxylem central. Xylem fibres and xylem parenchyma are component cell types, not arrangement terms.

Dangal (2016), Nitesh Tiwari's biographical sports drama on wrestler Mahavir Singh Phogat and his daughters, won Best Film at the 62nd Filmfare Awards held on 14 January 2017. It also took Best Director and Best Actor (Aamir Khan) the same night. Rustom, Airlift and Udta Punjab were 2016 releases that received other nominations but did not win the Best Film trophy.

The Time Period (T) of a pendulum is defined as the time taken to complete one full oscillation (one to-and-fro swing). For a simple pendulum of length L under gravity g, it is given by \(T = 2\pi\sqrt{\dfrac{L}{g}}\). Maximum and average speed describe how fast the bob moves, not the duration of a cycle; 'time interval' is a generic phrase, whereas 'time period' is the precise physics term for one complete oscillation.

The Himalayas are divided longitudinally by major rivers into four regional sections. The stretch between the Tista (west) and the Dihang i.e. Brahmaputra (east) is called the Assam Himalayas, covering parts of Sikkim, Bhutan and Arunachal Pradesh. Punjab/Kashmir Himalayas lie between the Indus and Sutlej; Kumaon between the Sutlej and Kali; Nepal Himalayas between the Kali and Tista.

The Delhi–Lahore bus service is officially named Sada-e-Sarhad, meaning 'Call of the Frontier' in Urdu. It was inaugurated on 19 February 1999, with PM Atal Bihari Vajpayee travelling on its first run to Lahore to meet PM Nawaz Sharif. 'Maitree' is the Kolkata–Dhaka India-Bangladesh service; 'Dosti' and 'Yaad-e-Shaheed' are not the official names of the Delhi–Lahore bus.

An Ecosystem is the life-supporting system within the biosphere where living organisms (biotic components) interact with one another and with their non-living surroundings (abiotic components) through energy flow and nutrient cycling, making them inter-related and interdependent for survival. A mountain range is a landform; a forest is one specific type of ecosystem rather than the general concept; the atmosphere is only the gaseous envelope of Earth and does not capture inter-organism dependence.

Inertia is the property by which a body resists changes to its state of rest or uniform motion. An undisturbed body — with zero net external force — continues at rest or moves with constant velocity, exactly as the question describes. This is the qualitative statement of Newton's first law of motion, often called the law of inertia. Force causes a change in motion, acceleration is the rate of that change, and friction is one specific resistive force — none of them name the tendency itself. Hence the answer is inertia.

Multiples of 6 strictly between 11 and 80 form an AP: 12, 18, 24, …, 78. Step 1 — Identify first and last terms: \(a = 12,\ l = 78\) Step 2 — Use the AP-average shortcut: For an arithmetic progression, the average equals the mean of the first and last terms. \[\text{Average} = \frac{a + l}{2} = \frac{12 + 78}{2} = \frac{90}{2} = 45\] Therefore the required average is 45.

Apply the Pythagorean identity \(\operatorname{cosec}^2\theta - \cot^2\theta = 1\). Step 1 — Substitute the given value: \[\cot^2\theta = \left(\frac{25}{7}\right)^2 - 1 = \frac{625}{49} - \frac{49}{49} = \frac{576}{49}\] Step 2 — Take the positive root (options are positive, so \(\theta\) lies in Q1): \[\cot\theta = \sqrt{\frac{576}{49}} = \frac{24}{7}\] Therefore \(\cot\theta = \dfrac{24}{7}\).

Step 1 — SI per year: Simple interest is constant each year, so the first-year SI is \(\frac{1500}{2} = 750\). Step 2 — Extra interest under CI: The CI−SI gap for 2 years equals the interest charged on the first-year interest during year 2. \[\text{CI} - \text{SI} = 1575 - 1500 = 75\] Step 3 — Solve for R: Rs. 75 is the 1-year SI on Rs. 750. \[75 = \frac{750 \times R \times 1}{100} \implies R = 10\] Therefore the rate is 10% per annum.

Given: price index at the beginning of 2015 = 200 Price index at end of 2015 = 200(1 + 2/100) = 200 × 1.02 = 204 ∴ Price index at end of 2016 = 204(1 + 5/100) = 204 × 1.05 = 214.2

Inflation% in country C in 2015 = 8% Inflation % in country A in 2015 = 4% ∴ Required ratio = 8/4 = 2 : 1

Let the fraction be \(x\). The condition gives: \[4x + \frac{6}{x} = 11\] Step 1 — Clear the denominator (multiply by \(x\)): \[4x^2 - 11x + 6 = 0\] Step 2 — Factorise: \[(4x - 3)(x - 2) = 0 \implies x = \tfrac{3}{4} \text{ or } x = 2\] Step 3 — Pick the option present: Only \(\tfrac{3}{4}\) appears. Check: \(4 \cdot \tfrac{3}{4} + 6 \cdot \tfrac{4}{3} = 3 + 8 = 11\). Therefore the fraction is \(\tfrac{3}{4}\).

Step 1 — Distance shortfall per hour: Without stoppages the bus would cover 72 km in 1 hour; with stoppages it covers only 60 km. The 12 km shortfall is the distance lost to halts. Step 2 — Convert distance lost to time at running speed: \[\text{Stoppage time} = \frac{12}{72}\text{ hour} = \frac{1}{6}\text{ hour} = 10\text{ minutes}\] Therefore the bus stops for 10 minutes every hour.

The centroid of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) is the average of the coordinates: \[G = \left(\frac{x_1+x_2+x_3}{3},\ \frac{y_1+y_2+y_3}{3}\right)\] Substituting A(1, −5), B(4, 0), C(−2, 2): \[G = \left(\frac{1+4-2}{3},\ \frac{-5+0+2}{3}\right) = \left(\frac{3}{3},\ \frac{-3}{3}\right) = (1,\ -1)\] Therefore the centroid is (1, −1).

Reflecting a point \((x_1, y_1)\) in the vertical line \(x = a\) keeps the y-coordinate unchanged and sends the x-coordinate to \(2a - x_1\). Here \(a = -3\) and the point is (5, 2): \[x' = 2(-3) - 5 = -11,\quad y' = 2\] Check: distance from (5, 2) to the line is 8, and from (−11, 2) to the line is also 8 — equal on opposite sides. Therefore the reflection is (−11, 2).

Use standard values \(\sec 45^\circ = \sqrt{2}\) and \(\tan 30^\circ = \dfrac{1}{\sqrt{3}}\). \[\sqrt{2}\,\sec 45^\circ - \tan 30^\circ = \sqrt{2}\cdot\sqrt{2} - \frac{1}{\sqrt{3}} = 2 - \frac{1}{\sqrt{3}}\] Combine over the common denominator \(\sqrt{3}\): \[2 - \frac{1}{\sqrt{3}} = \frac{2\sqrt{3} - 1}{\sqrt{3}}\] Therefore the value is \(\dfrac{2\sqrt{3} - 1}{\sqrt{3}}\).

Use the identity \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\). Let \(s = a+b\). Step 1 — Substitute given values \(a^3+b^3=19\), \(ab=-6\): \[s^3 = 19 + 3(-6)s = 19 - 18s\] \[s^3 + 18s - 19 = 0\] Step 2 — Solve: Testing \(s = 1\): \(1 + 18 - 19 = 0\). Factorising gives \((s-1)(s^2+s+19)=0\); the quadratic factor has discriminant \(1 - 76 = -75 < 0\), so no other real root exists. Therefore \(a+b = \mathbf{1}\).

By looking at the graph, change in annual inflation % A : +3 ; B : 0 ; C : -1 ; D : +5 So, lowest is -1

Step 1 — Isolate the bracket. Subtract \(\tfrac{3}{2}\) from both sides and multiply by \(\tfrac{2}{7}\): \[\frac{5x}{3} - \frac{3}{2} = \left(\frac{1}{4} - \frac{3}{2}\right)\cdot\frac{2}{7} = \left(-\frac{5}{4}\right)\cdot\frac{2}{7} = -\frac{5}{14}\] Step 2 — Solve for x: \[\frac{5x}{3} = \frac{3}{2} - \frac{5}{14} = \frac{21 - 5}{14} = \frac{16}{14} = \frac{8}{7}\] \[x = \frac{8}{7}\cdot\frac{3}{5} = \frac{24}{35}\] Therefore \(x = \dfrac{24}{35}\).

Given \(40\%\) of \(x = y\), i.e. \(y = \dfrac{40x}{100}\). Compute \(y\%\) of 40 and substitute: \[y\% \text{ of } 40 = \frac{y}{100}\cdot 40 = \frac{40y}{100} = \frac{40}{100}\cdot\frac{40x}{100} = \frac{1600x}{10000} = \frac{16x}{100}\] That is 16% of \(x\). (Equivalently, \(a\%\) of \(b = b\%\) of \(a\), so \(y\%\) of 40 = 40% of \(y\) = 40% of (40% of x) = 16% of x.)

Step 1 — Find marked price from the 10% case: SP = MP × (1 − discount). \[4500 = \text{MP}\times 0.90 \implies \text{MP} = \frac{4500}{0.9} = 5000\] Step 2 — Apply the 27.5% discount on Rs. 5000: \[\text{New SP} = 5000\times(1 - 0.275) = 5000\times 0.725 = 3625\] Therefore the new selling price is Rs. 3625.

The lateral surface area (area of 4 walls) of a cuboid is \(2(l+b)h\). Substitute \(l = 18,\ h = 8\), area = 448: \[2(18 + b)\times 8 = 448 \implies 16(18 + b) = 448\] \[18 + b = 28 \implies b = 10\] Therefore the breadth is 10 cm.

If 72, 168, 150, x are in proportion then \(\dfrac{72}{168} = \dfrac{150}{x}\). Cross-multiplying: \[x = \frac{168\times 150}{72} = \frac{25200}{72} = 350\] Check: \(\dfrac{72}{168} = \dfrac{3}{7}\) and \(\dfrac{150}{350} = \dfrac{3}{7}\). Therefore the fourth proportional is 350.

Apply alligation on the profit percentages with the mean profit 12%: \[\text{Qty at 20%} : \text{Qty at 8%} = (12-8) : (20-12) = 4 : 8 = 1 : 2\] Total parts = 3, corresponding to 960 kg, so 1 part = 320 kg. Quantity sold at 8% profit = \(2 \times 320 = 640\) kg. Hence the answer is 640.

Combined one-day work = sum of individual rates. LCM(72, 24, 36) = 72. \[\frac{1}{72}+\frac{1}{24}+\frac{1}{36}=\frac{1+3+2}{72}=\frac{6}{72}=\frac{1}{12}\] So together they complete \(\tfrac{1}{12}\) of the work per day, finishing in 12 days.

Using the slope formula for A\((x,-5)\) and B\((-5,3)\): \[m=\frac{3-(-5)}{-5-x}=\frac{8}{-5-x}=-\frac{4}{3}\] Cross-multiplying: \(-4(-5-x)=24 \implies 20+4x=24 \implies 4x=4\). Therefore x = 1.

In \(\triangle ABC\), \(\angle B = 90^\circ\) and \(\angle A = 60^\circ\), so by the angle sum property \(\angle C = 180^\circ - 90^\circ - 60^\circ = 30^\circ\). Since \(\sin 30^\circ = \tfrac{1}{2}\), \(\operatorname{cosec} 30^\circ = 2\). Thus \[\frac{1}{\sqrt{3}}\,\operatorname{cosec} C = \frac{1}{\sqrt{3}} \times 2 = \frac{2}{\sqrt{3}}\] The answer is \(\tfrac{2}{\sqrt{3}}\).

Step 1 — Find a and d: From \(a_3 = a+2d = -13\) and \(a_6 = a+5d = -4\), subtract to get \(3d = 9 \implies d = 3\), so \(a = -13 - 6 = -19\). Step 2 — Apply sum formula: \[S_{12} = \frac{12}{2}\big[2(-19) + 11(3)\big] = 6[-38+33] = 6(-5)\] Therefore \(S_{12} = \mathbf{-30}\).

Annual inflation % in 2015 in country D = 2% Annual inflation % in 2016 in country D = 5% ⇒ Required % = [(5 - 2)/2] × 100 ∴ Required % = 150%

Divide 6729 by 35: \(35 \times 192 = 6720\), and \(6729 - 6720 = 9\). Since 9 is less than the divisor 35, the remainder is 9.

Since DE is parallel to BC, \(\triangle ADE \sim \triangle ABC\) (AA similarity). Given \(AD:DB = 2:5\), we get \(\tfrac{AD}{AB}=\tfrac{2}{7}\). By the area ratio of similar triangles: \[\frac{[\triangle ADE]}{[\triangle ABC]} = \left(\frac{2}{7}\right)^2 = \frac{4}{49}\] So \([\triangle ABC] = 8 \times \tfrac{49}{4} = 98\) sq cm, and \([BDEC] = 98 - 8 = 90\) sq cm. Ratio \([\triangle ADE]:[BDEC] = 8:90 = \mathbf{4:45}\).

The reporting verb "said" is past tense, so the indirect form must also be past — eliminating options 1 ("requests") and 3 ("begs"). For a plea/request like "Let me...", the standard conversion uses requested + object + to let + him + base verb. The subordinate verb "die" must back-shift to "died" to maintain past-tense sequence, which rules out option 4 ("dies"). Only option 2 satisfies all three rules: "The accused requested the judge to let him meet his children before he died."

The sentence contrasts "the birds of the East" with "___ of the West". To avoid repeating the plural noun "birds", a plural demonstrative pronoun is required. "This" is singular; "whose" and "whom" are relative/possessive pronouns that do not fit the parallel structure. Only those is the plural demonstrative that substitutes for "the birds", giving "the birds of the East and those of the West".

Scrimp means to be very economical or stingy, using minimal resources. Its opposite is to spend wastefully and recklessly — exactly what squander means. "Skimp" is a synonym, not an antonym; "conserve" means to save (similar idea); "curtail" means to cut down or reduce. Hence the antonym is Squander.

The error lies in part (2). When two distinct parties are involved — here, the British and the Americans — the correct preposition is between, not among. "Among" is used for more than two entities considered as a group. The corrected sentence reads: "Several great battles took place between the British and the Americans." Hence the error is in part 2.

Obliterate means to destroy something completely or wipe it out. Annihilate means to destroy utterly, reducing to nothing — the closest match in meaning. "Construct" (to build) and "Revive" (to bring back) are antonyms; "Initiate" (to begin) is unrelated. Hence the synonym is Annihilate.

The blank needs a demonstrative pointing to the singular noun "mischief-maker" identified as Clark's nutcracker. "What" introduces questions, "it" is a pronoun that cannot precede a noun like an adjective, and "there" indicates place — none fit. That is the singular demonstrative determiner used to specify a particular noun, giving "and that mischief-maker, Clark's nutcracker."

“Guzzle” means to eat or drink greedily and in large amounts. Its direct opposite must denote the absence of consumption, which is “Starve” (to suffer from lack of food). Carouse, Imbibe and Quaff all describe drinking — they are synonyms or near-synonyms of guzzle, not antonyms.

The fragments combine into: "If there is a Z-change in brain activity of a certain Y-kind, there has to be a X-corresponding sensation." Z opens with "change in brain activity of a certain", which needs Y ("kind") to complete the noun phrase "a certain kind". The clause after the comma then states the consequence — a corresponding sensation (X). Hence the order is ZYX.

Sarcasm is, by definition, the use of irony to mock, ridicule, or convey contempt — typically a cutting verbal remark that says one thing while meaning the opposite. "Sanction" means official approval or a penalty; "flatter" and "compliment" denote praise, the opposite of mockery. Only Sarcasm matches the given definition.

The idiom "cannot help" (meaning "cannot stop oneself from") is always followed by a gerund (-ing form), never an infinitive or past form. Hence "to fall", "fallen" and "fell" are ruled out. The correct completion is "One cannot help falling into the speculative mood."

The blank needs a noun describing something loud that occurred between a husband and wife — i.e. a heated argument. Quarrel means exactly that. "Coral" is a marine substance, "moral" is a lesson/principle, and "laurel" is a plant or honour wreath — none can be "loud". Hence the answer is quarrel.

The main clause "She was uneasy" is in the simple past. The reason — her lack of prior plane experience — refers to a state existing before that past moment, so the past perfect (had + past participle) is required. "Never been" lacks an auxiliary; "is never been" mixes tenses. The correct improvement is "had never been": "She was uneasy because she had never been on a plane before."

"To heave a sigh of relief" describes the deep exhale of comfort one gives when a worrying or unpleasant situation is over or has been averted — i.e. to suddenly feel very happy because something unpleasant has not happened or has ended. Tiredness, sympathy for another's misfortune, and silent anger all describe different emotions and do not match the relief expressed by this idiom.

The word means general agreement. The standard English spelling uses a single 's' after each vowel: Con-sen-sus. "Conssensus", "Consenssus" and "Conssenssus" all double the 's' incorrectly. Hence the correctly spelt option is Consensus.

Parts (1) "The stream gurgled" and (2) "contentedly as it" are grammatically clean. Part (3) "slowed to rounding the bend" is faulty: after "slowed to" English requires a noun phrase ("slowed to a halt") or a base infinitive ("slowed to round the bend"), not a gerund. The error therefore lies in part (3).

The active sentence is in the Simple Past ("destroyed"). The passive form is: Object + was/were + past participle + by + Subject. Object "the whole neighbourhood" is singular, so we use was + destroyed: "The whole neighbourhood was destroyed by the fire." Options using "is", "is being", or "was being" change the tense and are therefore wrong.

The opening "As for ourselves, we" needs a finite verb next, so Z ("were contented with") must come first. "Contented with" then takes a list of items linked by "and": Y ("a good wash and") + X ("combing our hair"). The coherent sentence reads: "As for ourselves, we were contented with a good wash and combing our hair." Hence the order is ZYX.

The idiom "to be on cloud nine" describes a state of intense delight or euphoria — i.e. to be extremely happy. Feeling lucky, intoxication, and "one last attempt" are unrelated to this expression of joy. Option 1 (despite the slightly clipped phrasing "To extremely happy") conveys the intended meaning and is the correct choice.

The auxiliary "has" requires the past participle of the main verb to form the present perfect tense. The past participle of "become" is itself become (become – became – become). Hence "until he has become accustomed to his changed environment" is correct. "Became" (simple past), "becomes" (present), and "to be" (infinitive) do not follow "has".

The preposition between is used to express contrast or relationship involving two distinct groups — here "the birds of the East" and "those of the West". "Beside" (next to), "beneath" (under) and "below" (lower than) denote physical position, not comparison. Hence the correct word is between.

An alias is an assumed or false name, typically used to hide one's real identity — exactly what a criminal would adopt to elude the police. "Alternative" and "option" mean a choice in general, not a false name; "untrue" is an adjective and cannot follow "an" as a noun. Hence the correct word is alias.

"Litter" as a noun means rubbish or waste carelessly scattered about. Its closest synonym among the options is Trash, which likewise denotes discarded waste. "Order" and "system" suggest organisation — the opposite idea — and "possess" means to own. Hence the answer is Trash.

The verb escape is followed by a gerund. Here the subject is the recipient of the violent action, so a passive gerund is needed: being + past participle. The past participle of "dash" is "dashed", giving "escaped being dashed to pieces" — meaning he avoided being smashed. "Being dash" is ungrammatical, "dashed" alone cannot follow "escaped", and the original "(dash)" clearly needs improvement.

Upthrust is the upward buoyant force a fluid exerts on a body immersed or floating in it (Archimedes' principle: equal to the weight of the displaced fluid). The other options describe actions or states, not forces: plunge means to dive in; submerge means to be fully covered by liquid; capsize means to overturn. Only upthrust names a force.

The verb thrash (to beat violently) takes the present participle by simply adding -ing: thrashing. No extra 'e' is inserted before or after 'thr-' or '-sh-'. 'Threashing', 'Thrasheing', and 'Threasheing' all insert spurious 'e' letters and are non-standard spellings.