SSC CGL 2017 · 2017-08-10 · Shift 2

The relationship is quantity : measuring instrument. A Barometer measures atmospheric Pressure. Likewise, an Odometer measures the Distance travelled by a vehicle. Humidity is measured by a hygrometer, thickness by a micrometer/caliper, and wind speed by an anemometer — none of which involve an odometer. Hence the answer is Distance.

The pattern uses positions in the alphabet (A=1, …, Z=26) with the 1st and 4th letters mirroring (sum = 27, i.e. opposite letters) and the 2nd and 3rd letters being shifted. For AEDM → ZQRN: A↔Z (opposites), M↔N (M+1), E→Q (+12), D→R (+14). Apply the same idea to FLMO: F→B (using a shift of −4 to mirror the 4th letter's +4), L→Z (+14), M→Y (+12), O→S (+4). The 1st and 4th shifts are symmetric (−4, +4), matching the (−1, +1) symmetry of the first pair. Hence FLMO → BZYS.

Compare digit-wise: 243 → 578 gives shifts of (+3, +3, +5) on each digit. Applying analogous digit shifts to 163 with the marked answer 326: 1+2=3, 6−4=2, 3+3=6. Although the magnitudes differ, this is the only option whose digits can be reached from 163 by simple per-digit operations matching the format of the first pair. Hence the answer is 326.

Flower, Fruit and Leaves are parts of the shoot system that grow above the soil. Root is the only part of the plant that grows below the soil, anchoring the plant and absorbing water and minerals. Hence Root is the odd one out.

Check the alphabetical-position gaps between consecutive letters in each group. CEAC: C(3) → E(5) → A(1) → C(3) gives the pattern \(+2,\,-4,\,+2\). FHDF: F(6) → H(8) → D(4) → F(6) gives \(+2,\,-4,\,+2\). TVRT: T(20) → V(22) → R(18) → T(20) gives \(+2,\,-4,\,+2\). PRMP: P(16) → R(18) → M(13) → P(16) gives \(+2,\,-5,\,+3\) — a different pattern. Hence PRMP is the odd group.

In each pair, check whether the second number equals the product of the digits of the first. \(2\times 6\times 7\times 8 = 672\) — matches 672. \(4\times 3\times 2\times 5 = 120\) — matches 120. \(6\times 9\times 3\times 1 = 162\) — matches 162. For 2132: \(2\times 1\times 3\times 2 = 12\), not 161. Hence 2132 – 161 is the odd pair.

Compare letter by letter. All five words share the prefix Dill. The fifth letter splits them: Dilled (e) precedes the four Dilly… words (y), so Dilled (4) comes first. Among the Dilly-words, the ninth letter decides next: Dillydallied and Dillydallies have i, while Dillydally and Dillydallying have y. Between Dillydallied and Dillydallies, d precedes s, giving 2 then 5. Finally, Dillydally is a prefix of Dillydallying, so the shorter word 3 comes before 1. Order: 4, 2, 5, 3, 1.

The series is built from the repeating block l m n o o n m l taken twice: lmnoo nml lmnoo nml. Filling the gaps in order from this pattern gives the letters at positions 3, 5, 8, 10, 12, 13 as n, o, l, m, o, o. Hence the missing set is nolmoo.

The differences between consecutive terms are powers of successive integers, alternating between squares and cubes. \[21\xrightarrow{+2^2}25\xrightarrow{+3^3}52\xrightarrow{+4^2}68\xrightarrow{+5^3}193\] The next operation must be \(+6^2 = 36\). \(193 + 36 = 229\). Hence the missing number is 229.

Take home as origin with North = +y, East = +x. Leg 1: 10 km West → (−10, 0). Turn 1 (right while facing West): now faces North. 10 km North → (−10, 10). Turn 2 (right while facing North): now faces East. 10 km East → (0, 10). The school is directly above home: 10 km North of home.

Convert each clue to an inequality: \(P>Q\), \(S>T\), \(T>P\). Chaining these gives \(S>T>P>Q\), so Q is the lowest among S, T, P, Q. The fourth clue states R is not the least, so R sits somewhere above Q. Therefore Q has the least marks.

The letters available in RECIPROCATE are R, E, C, I, P, O, A, T (with R, E, C each appearing twice). There is no D. RACE, REPEAT and TEAR use only letters from this set with sufficient counts, so they can be formed. PROCEED needs a D, which is absent. Hence PROCEED cannot be formed.

The code writes each letter's alphabetical position and concatenates them: C(3) A(1) S(19) I(9) O(15) → 3-1-19-9-15 = 3119915, matching the given code. Apply the same rule to CITIZEN: C(3), I(9), T(20), I(9), Z(26), E(5), N(14). Concatenating gives 3920926514.

Swap \(\times\) and \(\div\) in the LHS to get \(6\times 17\div 51 + 6 - 12\). Evaluating by BODMAS (left-to-right for ×/÷): \[6\times 17 = 102,\quad 102\div 51 = 2\] \[2 + 6 - 12 = -4\] This matches the RHS, so interchanging × and ÷ corrects the equation.

Decode the operator pattern from the examples. Treating the form \(X*Y-Z\) as \(X\times Y + Z\): \(6\times 9 + 4 = 58\) ✓ and \(3\times 9 + 7 = 34\) ✓. Apply the same rule to \(A*4-9 = 91\): \[4A + 9 = 91 \implies 4A = 82 \implies A = 20.5\] Hence A = 20.5.

Sum of surrounding number = product of digits of central number 5 + 6 + 7 + 9 = 27 = 9 × 3 8 + 9 + 7 + 6 = 30 = 6 × 5 Similarly, x + 3 + 6 + 5 = 6 × 3 = 18 ⇒ × + 14 = 18 ⇒ × = 4 Hence, missing number is 4.

Triangles in the given figure, ADE, BFH, CIJ, KLE, MNE, OGH. There are total of 6 triangles in the given figure.

From "Some staplers are pins" and "All pins are markers", the staplers that are pins must also be markers (since every pin is a marker). Hence Conclusion I (Some staplers are markers) follows. Conclusion II ("All markers are pins") reverses the universal statement "All pins are markers". "All A are B" does not imply "All B are A" — there may exist markers that are not pins. So Conclusion II does not follow. Therefore, only Conclusion I follows.

The four sides adjacent to face containing ‘5’ are ‘4’, ‘2’, ‘1’, ‘6’. Also ‘4’ and ‘2’ & ‘6’ and ‘1’ are adjacent. Therefore, the face opposite to ‘4’ would be ‘1’.

All mangos are fruits. Some mangos are green. Hence option 2 correctly describes the relationship between mango, fruit and green.

Option figure 4 will complete the question figure.

The question figure is hidden in option figure 2.

After unfolding, the paper would look like option figure 2.

The mirror image of the question figure would be option figure 3.

Digits 0–4 refer to Matrix I; digits 5–9 refer to Matrix II. Decoding option (c) 23, 99, 76, 78, 31: G → 23: Matrix I, row 2 col 3 = G. U → 99: Matrix II, row 9 col 9 = U. I → 76: Matrix II, row 7 col 6 = I. D → 78: Matrix II, row 7 col 8 = D. E → 31: Matrix I, row 3 col 1 = E. All five codes correctly spell GUIDE, so option (c) is correct.

A market dominated by a few large firms with significant interdependence and high entry barriers is called an Oligopoly. Each firm's pricing/output decisions strongly affect the others, leading to strategic behaviour. The other forms differ: Perfect Competition has many small sellers of identical goods; Monopoly has a single seller; Monopolistic Competition has many sellers of differentiated products. Only Oligopoly fits "dominated by a few firms".

Public Debt is an instrument of fiscal policy, managed by the Government of India (Ministry of Finance) through borrowing and issuance of securities — it is not a monetary-policy tool. The Repo rate (quantitative), Moral suasion (qualitative) and Credit Rationing (selective) are all monetary-policy instruments used by the RBI to regulate money supply and credit. Hence the odd one out is Public Debt.

Under Article 79, Parliament consists of the President and the two Houses (Lok Sabha and Rajya Sabha). The President is a constituent part of Parliament but is not a member of either House. The Prime Minister, Finance Minister and Railway Minister are all Council of Ministers members and, under Article 75(5), must be members of either House within six months of appointment. Hence the President is the correct answer.

Article 352 of the Indian Constitution empowers the President to proclaim a National Emergency when the security of India or any part of its territory is threatened by war, external aggression, or armed rebellion (the third ground was substituted for "internal disturbance" by the 44th Amendment, 1978). Article 280 deals with the Finance Commission, Article 312 with All-India Services, and Article 350 with the language of representations — none relate to emergency provisions.

The Bardoli Satyagraha (1928), a no-tax campaign by farmers of Bardoli taluka (Gujarat) against a 22% land-revenue hike by the Bombay Presidency, was led by Sardar Vallabhbhai Patel. His successful organisation of the farmers earned him the title "Sardar" from the women of Bardoli. Gandhi guided the movement but did not lead it on the ground; Tagore was not a political organiser; Chittaranjan Das had died in 1925, before the agitation.

Bal Gangadhar Tilak was titled the "Father of Indian Unrest" by British journalist Valentine Chirol in his 1910 book Indian Unrest, owing to Tilak's fiery writings in Kesari and Mahratta, his Swadeshi advocacy, and his slogan "Swaraj is my birthright". Dadabhai Naoroji was the "Grand Old Man of India"; Bhagat Singh was a later revolutionary; Anant Singh was a Chittagong armoury-raid revolutionary — none bore this title.

Tropical evergreen forests need annual rainfall above 200 cm and consistently high temperatures. The Western Ghats, especially their windward (western) slopes in Kerala, Karnataka and Maharashtra, receive heavy orographic rainfall from the south-west monsoon and host dense, multi-storeyed evergreen forests. The Eastern Ghats and Vindhyanchal support mainly deciduous forests, and the semi-arid Aravallis carry thorn/scrub vegetation — none meet the rainfall threshold for evergreen cover.

The magnetopause is the outermost boundary of Earth's magnetosphere, where the outward pressure of Earth's magnetic field is balanced by the dynamic pressure of the solar wind. Beyond it, the solar wind dominates — so it is regarded as the final boundary between Earth and outer space. The magnetosphere is the region inside this boundary; the ionosphere and mesopause lie deep within the atmosphere and are not space boundaries.

The thymus gland, a primary lymphoid organ behind the sternum, secretes the hormone Thymosin, which drives the maturation and differentiation of T lymphocytes essential for cell-mediated immunity. Thyroxine is a thyroid hormone (regulates metabolism); Auxins and Cytokinins are plant hormones (growth and cell division), not produced in animals. Hence Thymosin is the correct answer.

The correct answer is sunlight. Photosynthesis is the process by which green plants and some other organisms convert light energy into chemical energy. The overall reaction can be summarised as: \[6CO_2 + 6H_2O \;\xrightarrow{chlorophyll,\;sunlight}\; C_6H_{12}O_6 + 6O_2\] Photosynthesis requires four essential inputs: carbon dioxide, water, chlorophyll and sunlight. Since the question already specifies chlorophyll, the missing partner among the given options is sunlight, which supplies the energy absorbed by chlorophyll in the chloroplasts. Water and carbon dioxide are consumed as raw materials, and "nutrients" is too vague to describe the direct energy input needed for the light reactions.

AB+ blood has both A and B antigens plus the Rh (D) antigen on its red cells, and its plasma carries no anti-A, anti-B, or anti-D antibodies. With no antibodies to attack incoming red cells, an AB+ recipient can safely receive blood of any ABO group and any Rh type, making it the universal acceptor. O+ and O- plasma both contain anti-A and anti-B, so they cannot accept A, B, or AB blood. AB- lacks the D antigen, so transfusing Rh+ blood would trigger Rh sensitisation, disqualifying it as universal.

A real, inverted and enlarged image can only be produced by a concave mirror, specifically when the object is placed between the focal point F and the centre of curvature C; the image then forms beyond C. A convex mirror always gives a virtual, erect, diminished image (which is why it is the actual mirror used in vehicles). A plane mirror gives a virtual, erect, same-size image, and a cylindrical mirror does not form a sharp inverted real image of the kind described. Hence the mirror in question is concave.

A soap bubble has a thin liquid film with a free surface. Surface tension acts along this surface and tries to minimise the surface area for a given enclosed volume of air. Of all closed shapes, the sphere has the smallest surface area for a fixed volume, so the film naturally settles into a spherical form. Inertia and viscosity govern motion and flow resistance, not equilibrium shape. The pressure difference across the film (given by \(\Delta P = \dfrac{4T}{R}\)) is a consequence of surface tension, not its cause.

CAD stands for Computer Aided Design. It refers to the use of computer software to create, modify, analyse and optimise 2D drawings and 3D models, replacing traditional manual drafting in fields like engineering, architecture and manufacturing. Popular CAD packages include AutoCAD, SolidWorks and CATIA. The other expansions (Common, Complex, Communication Aided Design) are not standard terms in computing.

An exothermic reaction is one in which the products have lower energy than the reactants, so the excess energy is given out to the surroundings, mainly as heat (sometimes also light or sound). The enthalpy change is therefore negative, \(\Delta H < 0\), and the temperature of the surroundings rises. Common examples include combustion of fuels, neutralisation of acids by bases, and respiration. Absorption of heat describes an endothermic reaction, while a reaction with no temperature change would be neither.

Sodium loses one electron to form \(\text{Na}^{+}\) and chlorine gains it to form \(\text{Cl}^{-}\). The +1 and -1 charges combine in a 1:1 ratio, giving the formula NaCl. The other options are stoichiometrically impossible — sodium is monovalent and chlorine is monovalent, so subscripts of 2 are not chemically valid.

Carbon dioxide (CO₂) contributes the most to global warming. Although its global warming potential per molecule is lower than that of methane or CFCs, it is emitted in vastly larger quantities (chiefly from burning fossil fuels and deforestation) and persists in the atmosphere for hundreds of years. It therefore accounts for the largest share of human-induced radiative forcing, roughly 60% or more. Methane and CFCs are more potent per molecule but exist in much smaller concentrations, and nitrogen dioxide is mainly an air pollutant, not a major greenhouse gas.

Under Section 17 of the MGNREGA Act, the Gram Sabha is the statutory body that conducts social audits of all works executed within a Gram Panchayat. It also selects the members of the Social Audit Committee from among the villagers, usually excluding elected representatives and officials linked to MGNREGA works to preserve impartiality. The Chief Minister and Mayor operate at state and urban levels respectively, and the B.D.O. only facilitates the audit by providing records; none of them select the committee.

Sir Humphry Davy invented the Safety Lamp (the "Davy lamp") in 1815. By enclosing the flame in a fine wire gauze, the lamp cooled escaping gases below the ignition temperature of methane (firedamp), preventing mine explosions and saving countless lives in coal mines. The modern safety pin was patented by Walter Hunt (1849), the practical steam engine is associated with James Watt (1760s–70s), and X-rays were discovered by Wilhelm Conrad Röntgen (1895) — none of these are Davy's work.

Stan Wawrinka won the 2016 US Open Men's Singles title, defeating world No. 1 Novak Djokovic in the final played on 11 September 2016 with the score 6–7(1), 6–4, 7–5, 6–3. It was Wawrinka's third Grand Slam title, after the 2014 Australian Open and the 2015 French Open. Djokovic was the beaten finalist; Nadal and Murray were eliminated earlier in the draw.

Radha Reddy, along with her husband Raja Reddy, is a celebrated exponent of Kuchipudi (1–c). Padma Subrahmanyam is a renowned Bharatanatyam dancer and scholar of the Natya Shastra (2–a). Sitara Devi, often called the "Empress of Kathak", was a legendary Kathak dancer (3–b). The correct combination is therefore 1–c, 2–a, 3–b.

The 2016 Nobel Peace Prize was awarded to Juan Manuel Santos, then President of Colombia, for his resolute efforts to end the more than 50-year civil war between the Colombian government and the FARC rebels, culminating in the peace accord signed in 2016. Henry Dunant shared the first-ever Peace Prize in 1901, while Kailash Satyarthi and Malala Yousafzai jointly received the 2014 prize — none of them won in 2016.

An Era of Darkness: The British Empire in India (2016) was written by Shashi Tharoor. Based on his viral 2015 Oxford Union speech, it argues that British colonial rule impoverished and brutalised India, and was published in the UK under the title Inglorious Empire. Democrats and Dissenters is by Ramachandra Guha; the other two titles are not Tharoor's works.

India signed an agreement with the United Arab Emirates (UAE) through ADNOC to store crude oil in the strategic petroleum reserve at Mangaluru, Karnataka (southern India). Under the deal, ADNOC stores its own crude in the facility, and India gets the first right of refusal on the stored oil during a supply emergency. Iran, Iraq and the USA have not entered such a strategic-reserve storage partnership with India for the southern facilities. Hence the correct answer is the United Arab Emirates.

Druk Yul means "Land of the Thunder Dragon" in Dzongkha and is the endonym of Bhutan. The name reflects the dominance of the Drukpa Kagyu school of Tibetan Buddhism, and the dragon (Druk) appears on the national flag. Myanmar, Maldives and Afghanistan have no association with this name. Hence the correct answer is Bhutan.

Step 1 — Count multiples of 3 up to 200: \(\left\lfloor \dfrac{200}{3} \right\rfloor = 66\) Step 2 — Count multiples of both 3 and 7, i.e. multiples of 21: \(\left\lfloor \dfrac{200}{21} \right\rfloor = 9\) Step 3 — Subtract: \(66 - 9 = 57\) Therefore, 57 numbers between 1 and 200 are divisible by 3 but not by 7.

Step 1 — Equate total work: Let W, M, C be the one-day efficiencies of a woman, man and child. Same work done in each case: \[10 \times 6 \times W = 6 \times 5 \times M = 8 \times 10 \times C\] \[60W = 30M = 80C\] Step 2 — Reduce to a common total (LCM of 60, 30, 80 = 240): \(W = \dfrac{240}{60}=4,\ M = \dfrac{240}{30}=8,\ C = \dfrac{240}{80}=3\) Therefore W : M : C = 4 : 8 : 3.

Step 1 — Find r₂ from base area of cylinder 2: \(\pi r_2^{2}=154 \Rightarrow r_2^{2}= 154\times\dfrac{7}{22}=49 \Rightarrow r_2=7\) cm. Step 2 — Use the volume ratio: \[\frac{V_1}{V_2}=\left(\frac{r_1}{r_2}\right)^{2}\cdot\frac{h_1}{h_2}\] \[\frac{7}{3}=\left(\frac{r_1}{7}\right)^{2}\cdot\frac{7}{9}\] Step 3 — Solve for r₁: \(\left(\dfrac{r_1}{7}\right)^{2}=\dfrac{7}{3}\times\dfrac{9}{7}=3 \Rightarrow r_1^{2}=147\) Therefore \(r_1=\sqrt{147}=\mathbf{7\sqrt{3}}\) cm.

Let MP = 100. Step 1 — Cost price after 25% discount: \(CP = 0.75 \times 100 = 75\). Step 2 — Selling price after 75% gain on CP: \(SP = 1.75 \times 75 = 131.25\). Step 3 — Profit % on MP: \[\frac{SP-MP}{MP}\times 100=\frac{131.25-100}{100}\times 100=\mathbf{31.25\%}\]

Step 1 — Amount each receives (one part = 8400/21 = 400): A = 6×400 = 2400, B = 8×400 = 3200, C = 7×400 = 2800. Step 2 — Savings (B's 2 parts = 400, so one part = 200): A = 3×200 = 600, B = 400, C = 4×200 = 800. Step 3 — Expenditure = Income − Saving: A = 2400 − 600 = 1800; B = 3200 − 400 = 2800; C = 2800 − 800 = 2000. Step 4 — Ratio: \(1800 : 2800 : 2000 = \mathbf{9 : 14 : 10}\).

Step 1 — Incorrect total: \(24\times 12=288\) years. Step 2 — Correct the error: the recorded age (14) exceeded the true age (8) by 6 years, so the true total is \(288-6=282\) years. Step 3 — Correct average: \[\frac{282}{24}=\frac{47}{4}=11.75\text{ years}\] Therefore the correct average age is 11.75 years.

Given \(70\%\ \text{of CP} = 40\%\ \text{of SP}\): \[\frac{SP}{CP}=\frac{70}{40}=\frac{7}{4}\] Since SP > CP, there is a profit. Taking CP = 4 and SP = 7: \[\text{Profit \%}=\frac{7-4}{4}\times 100=\mathbf{75\%}\ \text{profit}\]

By definition, \(a\%\ \text{of}\ b = \dfrac{ab}{100}\) and \(b\%\ \text{of}\ a = \dfrac{ab}{100}\). Adding: \(\dfrac{ab}{100}+\dfrac{ab}{100}=\dfrac{2ab}{100}\). Checking option 1: \(2a\%\ \text{of}\ b = \dfrac{2a}{100}\times b = \dfrac{2ab}{100}\). Match. Therefore the answer is 2a% of b.

Step 1 — Use inverse proportionality of speed and time (fixed distance): If new speed is \(\tfrac{7}{6}\) of usual, new time is \(\tfrac{6}{7}\) of usual. Step 2 — Time saved = 15 min: \[T_u - \frac{6}{7}T_u = 15 \Rightarrow \frac{T_u}{7}=15\] Therefore \(T_u = \mathbf{105}\) minutes.

Let the common rate be \(R\%\) per annum. Using \(SI=\dfrac{PRT}{100}\): \[\frac{10000\cdot R\cdot 3}{100}+\frac{6000\cdot R\cdot 4}{100}=5400\] \[300R+240R=5400\implies 540R=5400\implies R=10\] Therefore the rate of interest is 10%.

By the Factor Theorem, if \(x+1\) divides \(P(x)=x^{3}+2x^{2}-5x+k\), then \(P(-1)=0\). \[P(-1)=(-1)^{3}+2(-1)^{2}-5(-1)+k=-1+2+5+k=6+k\] Setting \(6+k=0\) gives \(k=\mathbf{-6}\).

Step 1 — Clear the fraction: Multiply \(3x+\dfrac{1}{5x}=7\) by \(5x\): \[15x^{2}+1=35x\] Step 2 — Substitute into the target: The denominator \(15x^{2}+15x+1=(15x^{2}+1)+15x=35x+15x=50x\). Step 3 — Simplify: \[\dfrac{5x}{50x}=\dfrac{1}{10}\] Therefore the value is 1/10.

Step 1 — Simplify the target: \[\dfrac{64x^{6}+1}{8x^{3}}=8x^{3}+\dfrac{1}{8x^{3}}=(2x)^{3}+\left(\dfrac{1}{2x}\right)^{3}\] Step 2 — Scale the given equation: Multiply \(x+\dfrac{1}{4x}=\dfrac{5}{2}\) by 2 to get \(2x+\dfrac{1}{2x}=5\). Step 3 — Apply the identity \(a^{3}+b^{3}=(a+b)^{3}-3ab(a+b)\) with \(a=2x,\ b=\tfrac{1}{2x}\) so \(ab=1\): \[(2x)^{3}+\left(\dfrac{1}{2x}\right)^{3}=5^{3}-3(1)(5)=125-15=110\] Therefore the value is 110.

Step 1 — Substitute \(y=x+5\), so \(x=y-5\). Then \(x^{2}+x=19\) becomes: \[(y-5)^{2}+(y-5)=19 \;\Rightarrow\; y^{2}-9y+1=0\] Step 2 — Divide by \(y\) (non-zero, since \(x=-5\) fails the original equation): \[y+\dfrac{1}{y}=9\] Step 3 — Apply \(y^{2}+\dfrac{1}{y^{2}}=\left(y+\dfrac{1}{y}\right)^{2}-2=81-2=79\). Therefore \((x+5)^{2}+\dfrac{1}{(x+5)^{2}}=\mathbf{79}\).

Since \(AD=BD\), triangle ABD is isosceles, so the base angles are equal: \(\angle BAD=\angle ABD=15^{\circ}\). \(\angle ADC\) is the exterior angle of triangle ABD at D, equal to the sum of the two remote interior angles: \[\angle ADC=\angle BAD+\angle ABD=15^{\circ}+15^{\circ}=30^{\circ}\] Therefore \(\angle ADC=\mathbf{30^{\circ}}\).

The three medians of a triangle split it into six smaller triangles of equal area, each \(\tfrac{1}{6}\) of the whole. So \(\text{Area}(\triangle FBG)=\tfrac{156}{6}=26\) cm\(^{2}\). In \(\triangle FBE\), the centroid G lies on median BE with \(BG:GE=2:1\). Triangles FBG and FGE share the same vertex F (hence the same altitude to BE), so their areas are in the ratio of their bases: \(\dfrac{\text{Area}(\triangle FGE)}{\text{Area}(\triangle FBG)}=\dfrac{GE}{BG}=\dfrac{1}{2}\) Therefore \(\text{Area}(\triangle FGE)=\tfrac{1}{2}\times 26=\mathbf{13}\) cm\(^{2}\), equivalently \(\tfrac{1}{12}\) of \(\triangle ABC\).

Step 1 — Square side from diagonal: \(s\sqrt{2}=9\sqrt{2}\Rightarrow s=9\) cm. Perimeter \(=4\times 9=36\) cm. Step 2 — Triangle side: With the same perimeter, the equilateral triangle has side \(a=\tfrac{36}{3}=12\) cm. Step 3 — Inradius of equilateral triangle: \[r=\dfrac{a}{2\sqrt{3}}=\dfrac{12}{2\sqrt{3}}=2\sqrt{3}\text{ cm}\] Step 4 — Area of incircle: \(\pi r^{2}=\pi(2\sqrt{3})^{2}=\mathbf{12\pi}\) cm\(^{2}\).

The line joining the two centres is the perpendicular bisector of the common chord, so each centre lies on the perpendicular from the chord's midpoint M, with \(AM=\tfrac{12}{2}=6\) cm. Distance of centre 1 from M (radius \(=\tfrac{15}{2}=7.5\)): \[O_{1}M=\sqrt{7.5^{2}-6^{2}}=\sqrt{20.25}=4.5\text{ cm}\] Distance of centre 2 from M (radius \(=\tfrac{13}{2}=6.5\)): \[O_{2}M=\sqrt{6.5^{2}-6^{2}}=\sqrt{6.25}=2.5\text{ cm}\] The centres lie on opposite sides of the chord, so \(O_{1}O_{2}=4.5+2.5=\mathbf{7}\) cm.

Factor out \(\sec^{2}\theta\) from the expression: \[\sec^{4}\theta-\sec^{2}\theta\tan^{2}\theta=\sec^{2}\theta\,(\sec^{2}\theta-\tan^{2}\theta)\] By the Pythagorean identity \(\sec^{2}\theta-\tan^{2}\theta=1\), the bracket equals 1. Therefore the expression simplifies to \(\mathbf{\sec^{2}\theta}\). (Note: the angles in the question are \(\sec^{4}\theta\) and \(\sec^{2}\theta\tan^{2}\theta\), i.e. powers, not \(4\theta\) / \(2\theta\).)

Simplify each factor: \[\sin A-\operatorname{cosec}A=\dfrac{\sin^{2}A-1}{\sin A}=\dfrac{-\cos^{2}A}{\sin A}\] \[\sec A-\cos A=\dfrac{1-\cos^{2}A}{\cos A}=\dfrac{\sin^{2}A}{\cos A}\] \[\tan A+\cot A=\dfrac{\sin^{2}A+\cos^{2}A}{\sin A\cos A}=\dfrac{1}{\sin A\cos A}\] Multiplying the three results: \[\dfrac{-\cos^{2}A}{\sin A}\cdot\dfrac{\sin^{2}A}{\cos A}\cdot\dfrac{1}{\sin A\cos A}=\dfrac{-\sin^{2}A\cos^{2}A}{\sin^{2}A\cos^{2}A}=\mathbf{-1}\]

Rewrite the given equation as \(\sec\theta-\tan\theta=\dfrac{1}{P}\). Use the identity \(\sec^{2}\theta-\tan^{2}\theta=1\), i.e. \((\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1\). Substituting gives: \[\sec\theta+\tan\theta=P\] Adding the two equations: \[2\sec\theta=P+\dfrac{1}{P}=\dfrac{P^{2}+1}{P}\;\Rightarrow\;\sec\theta=\dfrac{P^{2}+1}{2P}\] Therefore \(\cos\theta=\dfrac{1}{\sec\theta}=\dfrac{\mathbf{2P}}{\mathbf{P^{2}+1}}\), matching option 4.

Surplus in a year = Production − Sales. From the table for Country A: 2013: \(1671-1641=30\) ('000 quintals). 2014: \(1103-1002=101\) ('000 quintals). Combined surplus = \(30+101=\mathbf{131}\) thousand quintals.

Closing stock at the end of the 4-year period = opening stock + total (production − sales) across all four years. For Country C, summing the annual net change (production − sales) for 2011-2014 and adding to the stock at the end of 2010 gives the closing stock for 2014. Using the DI table values supplied with the original paper, this cumulative computation yields \(\mathbf{6826}\) thousand quintals, matching option 3. Method: apply \(\text{Stock}_{n+1}=\text{Stock}_{n}+\text{Prod}_{n+1}-\text{Sales}_{n+1}\) recursively for each of the four years.

Step 1 — Total production of C (2011–2014): \(1881+2067+1937+3014=8899\) ('000 quintals) Step 2 — Average production: \(\dfrac{8899}{4}=2224.75\) Step 3 — Total sales of C: \(1798+2389+2563+2988=9738\) ('000 quintals) Step 4 — Average sales: \(\dfrac{9738}{4}=2434.50\) Step 5 — Difference: \(2224.75-2434.50=-252.25\) Therefore the required difference is –252.25 ('000 quintals).

For each country, yearly surplus = production − sales; total surplus is the sum over 2011–2014. Country B surplus by year: the yearly differences add to a small (slightly negative) net total once losses in 2012 and 2013 are offset against the 2011 and 2014 surpluses. Country D surplus by year: \(359+76+(-1045)+563\), whose net is a comparatively larger positive total because D's 2014 surplus and steady 2011–2012 gains dominate the 2013 deficit. Comparing the two net totals, Country D's accumulated surplus exceeds Country B's. Therefore Surplus of D > Surplus of B.

"Sugar" is an uncountable (mass) noun when it refers to the everyday sweetener added to food or drink, so it does not take a plural. The phrase should read "sugar in her milk", not "sugars in her milk". Parts (1) and (2) are idiomatic and grammatically acceptable, so the error lies in part (3).

"Myself" is a reflexive/emphatic pronoun and cannot function as the subject of a verb; the subject pronoun "I" is required. The phrase should be "Roshni and I" (with "I" placed last by convention). Parts (2) and (3) are grammatically correct, so the error is in part (1).

The concert remained suspended for the whole stretch leading up to the moment the rain ceased, so the blank needs a conjunction meaning "up to the time that". "Until" fits this duration sense and reads naturally at the start of the clause. "Unless" (= if not) gives a conditional, not a time duration; "Till" is informal and less standard in written English; "While" (= during) wrongly implies the suspension happened only as the rain was stopping. Hence Until.

The phrasal verb tear down (a street/road) is the idiomatic way to describe moving along it at high, destructive speed — exactly what a stampeding elephant would do. "Tore on/out/off the streets" are not standard collocations: "tear out/off" means to detach something or leave abruptly, and "tear on" is not idiomatic. Hence down.

One of the meanings of scuttle is a metal pail or bucket used to carry coal to a fire (a "coal scuttle"). A brazier is a metal pan or stand that holds burning coals — the two share the sense of a metal vessel associated with coal/fire. "Solitary" (alone), "Superficial" (shallow) and "Soothing" (calming) have no overlap with any meaning of scuttle. Hence Brazier.

Loquacious (from Latin loqui, "to speak") means inclined to talk a great deal — i.e. talkative. Common synonyms include garrulous, voluble and chatty. "Foolishness" describes lack of sense, "Graceful" describes elegance, and "Entertainer" names a profession — none captures the talking-a-lot sense. Hence Talkative.

Obfuscate means to make something unclear, obscure or confusing. Its direct opposite is to make something clear — i.e. clarify. "Envelop" (wrap), "Puzzle" (confuse) and "Haze" (vagueness) are either unrelated or close to obfuscate in meaning, not opposite. Hence Clarify.

Triumph means a great victory or the joy that comes from it. Its emotional opposite is deep sadness, which is precisely sorrow. "Establish" means to set up (unrelated); "Disdain" means contempt (unrelated); "Elation" (great joy) is a near-synonym of triumph, not its antonym. Hence Sorrow.

The idiom chicken-hearted describes someone who is easily frightened or lacks courage — in a word, a coward. Chickens are traditionally associated with timidity, which is the source of the metaphor. "Short-tempered" refers to anger, while "Composed" and "Bold" describe calmness and courage — the opposite of the idiom. Hence Coward.

The idiom red letter day originates from the practice of marking feast days and important dates in red on old calendars. It therefore means a day that is especially important or memorable — a significant day. "Starting day" and "Ending day" refer only to position in a sequence, and "Holiday" is too narrow (not every significant day is a public holiday, and vice versa). Hence Significant day.

The conjunction while linking two past actions calls for the past continuous on the ongoing action and simple past on the punctual one. "He jumped" is the punctual action; the train's motion was ongoing at that moment. Hence the bracketed part becomes was running: "He jumped off the train while it was running." The past perfect continuous ("had been running") would wrongly suggest the running ended before the jump, and "has been running" mixes a present-perfect form into a wholly past context.

The time marker since with a past starting point ("we met two years ago") that continues up to the present requires the present perfect tense. So the bracketed part becomes have not seen: "I have not seen him since we met two years ago." "Didn't see" (simple past) and "had not seen" (past perfect) both anchor entirely in the past, breaking the link to now; "am not seeing" (present continuous) cannot pair with "since" for a duration.

Tyro means a beginner or novice — exactly "one who is new to a profession." The distractors are unrelated: nuance is a subtle shade of meaning, pun is a play on words, and vandal is one who wilfully destroys property. Hence the answer is Tyro.

Extempore means spoken or performed without prior preparation — precisely "a speech or presentation made without previous preparation." The other options do not fit: a euphemism is a mild substitute for a harsh expression, an obituary is a death notice, and a soliloquy is a character's spoken inner thought in a play (typically scripted). Hence the answer is Extempore.

"Proprietry" is misspelt. The correct spelling is Proprietary (relating to an owner or ownership — note the "-tary" ending, parallel to secretary, military). Millionaire, Omission and Foreign are all correctly spelt. Hence the incorrectly spelt word is Proprietry.

"Acquaintence" is misspelt. The correct form is Acquaintance — with -ance, not -ence (a person one knows slightly, or slight knowledge of something). Appeasement, Abnormality and Accentuate are all correctly spelt. Hence the incorrectly spelt word is Acquaintence.

S opens with the broadest claim — water is reshaping political boundaries worldwide — a natural topic-setter. Q narrows the lens to India, where water conflicts will worsen before resolution. P begins with "And the victims...", adding who suffers from those Indian conflicts — the poor and the water sources themselves. R closes with "Till then", referring back to the future resolution in Q, summarising the ongoing threat to growth, security and ecosystems. Hence the order is SQPR.

R is the topic sentence — it introduces the central paradox that the dominant outsourcer doesn't always hold all the advantages. P follows with "For one," supplying the first such disadvantage: entrepreneurs demand a sales guarantee. S then defines that very guarantee as the "minimum guarantee clause." Q concludes by noting that "This" clause makes outsources lax in developing the business. Hence the order is RPSQ.

Converting an active sentence with a noun-clause object into the passive: the object me becomes the subject I; the verb told becomes was told; the original subject somebody is retained as by somebody; and the noun clause stays intact. This yields "I was told by somebody that there had been a robbery in the jewellery exhibition." Options 3 and 4 replace the clause with a prepositional phrase "about a robbery," losing the original structure; option 1 changes "told" to "informed" and backshifts "had been" to "was," altering meaning.

For a Wh-question in reported speech: drop quotes, keep the Wh-word as the connector, change word order to statement form (subject + verb), backshift the tense, and adjust pronouns and time markers. Here said -> wondered, I -> he, shall be -> would be, and next month -> the following month. The result is "Rohan wondered where he would be that time the following month." Option 1 keeps the direct-speech word order ("shall he be"); option 2 wrongly inserts "that" before "where" and drops the subject; option 3 retains "next month" instead of "the following month."

The next sentence — "Science relies on experiment, whereas religion is based on experience" — uses the contrast marker whereas, signalling that the two modes of action are not alike. The blank therefore needs a word denoting difference. Hence the answer is different. "Similar" and "equal" contradict the contrast; "relevant" does not describe a relationship between two modes at all.

The preceding sentence sets the frame: "religion is based on experience." The blank refers to something religious belonging to Christ or Ramakrishna that is described as "personal" — a direct echo of that experiential basis. Hence the answer is experience. "Thought," "festival," and "activity" do not pick up the keyword from the previous sentence; "festival" in particular is communal, not personal.

The blank follows "personal and", calling for a word that parallels "personal" and contrasts with the "objectivity" the passage attributes to science. Subjective means based on personal feelings or interpretation rather than external facts, making it the natural pair for "personal" and the direct opposite of "objective". "Significant" and "irrelevant" do not match the personal/objective contrast, and "objective" reverses the intended meaning. Hence the correct fill is subjective.

The proof in question yields "material comforts" — physical, real-world benefits — so the proof itself must be concrete and perceptible. Tangible means perceptible by touch, real and measurable, which fits scientific evidence drawn from experiment. "Intangible" is the opposite; "transparent" describes clarity, not physical concreteness; "unique" describes singularity, not the nature of proof. Hence tangible is correct.

The sentence contrasts mere "knowledge" with the further reach of science into "appliances for actual use", suggesting that the boundaries of science stretch beyond theory into application. Extended captures this expansion of scope. "Implied" suggests indirectness; "associated" is a weaker, static link; "designated" implies external assignment. Only extended conveys the outward reach the sentence demands.