SSC CGL 2017 · 2017-08-16 · Shift 2

Step 1 — Shrey's position from the bottom: Manu is 7th from the bottom; Shrey is 10 ranks above Manu, so Shrey is \(7+10=17\)th from the bottom. Step 2 — Total using Shrey's two ranks: Shrey is 8th from the top and 17th from the bottom. \[\text{Total}=8+17-1=24\] Therefore there are 24 people in the row.

Substitute the symbols: \(\theta=+\), \(\beta=\times\), \(\delta=\div\), \(\alpha=-\). The expression becomes: \[10+8\times 4\div 8-9\] Apply BODMAS (× and ÷ first, left to right): \[10+32\div 8-9=10+4-9=5\] Therefore the answer is 5.

On close observation, we find the question fig. is embedded in fig. (1). Hence, the answer is option 1.

Step 1 — Form equations: Let Sahil's and Nihal's present ages be \(S\) and \(N\). Then \(S-7=N\) and \((S-5)+(N+6)=58\), i.e. \(S+N=57\). Step 2 — Solve: Substituting \(N=S-7\): \[2S-7=57\implies S=32\] Step 3 — Ruchi's age in 10 years: Ruchi is 4 years older than Sahil, so Ruchi now is \(32+4=36\). After 10 years she will be \(36+10=46\). Therefore Ruchi's age after 10 years is 46.

The relationship is category: a banana is botanically a fruit. Ginger is the underground rhizome of the plant — a modified stem, not a root, since it has nodes, internodes and buds. Hence Ginger : Stem.

The differences between consecutive terms form a simple ascending pattern: \(3-1=2,\ 6-3=3,\ 10-6=4,\ 15-10=5\). So the next difference is 6. \[15+6=21\] (These are triangular numbers: \(T_n=\tfrac{n(n+1)}{2}\); \(T_6=21\).) Hence the missing number is 21.

The letters available in REPRESENTATION are R, E, P, S, N, T, A, I, O (no C). Paint (P, A, I, N, T), Senator (S, E, N, A, T, O, R) and Trees (T, R, E, E, S) can all be formed from these letters. Strict requires the letter C, which does not occur in REPRESENTATION. Hence Strict cannot be formed.

The small "2" indicates squaring. From \(7^2\,A\,2^2\,B\,1^2=49-4-1=44\) and \(9^2\,A\,4^2\,B\,3^2=81-16-9=56\), both A and B mean subtraction. Apply to the third expression: \[11^2-5^2-7^2=121-25-49=47\] Therefore the value is 47.

From "Some girls are clever" + "All clever are hardworking", those clever girls must also be hardworking. So Conclusion II (Some girls are hardworking) follows. Conclusion I (Some girls are not hardworking) is not guaranteed — the statements allow that all girls could be hardworking. Conclusion III (Some hardworking are not girls) is also not guaranteed — the statements do not rule out that every hardworking person is a girl. Hence only Conclusion II follows.

Compare positions of letters in JPSW → LQUX: J(10)→L(12) is +2; P(16)→Q(17) is +1; S(19)→U(21) is +2; W(23)→X(24) is +1. The shift pattern is +2, +1, +2, +1. Apply to MRPT: M(13)+2 = O(15); R(18)+1 = S(19); P(16)+2 = R(18); T(20)+1 = U(21). Hence the answer is OSRU.

Leaves, Flower and Stem are all parts of a plant. A tree, however, is the whole plant that contains these parts. Hence the odd one out is Trees.

Notice \(65=8^2+1\) and \(82=9^2+1\). So the rule is: if the first number is \(n^2+1\), the second is \((n+1)^2+1\). For 145: \(145=12^2+1\), so the partner is \(13^2+1=169+1=170\). Hence the answer is 170.

From the unfolded net, the opposite-face pairs on the cube are: * opposite #, % opposite >, and $ opposite I. Figures (2), (3) and (4) each show one of these opposite pairs on adjacent faces, which is impossible. Only figure (1) keeps every opposite pair non-adjacent. Therefore the cube formed is option (1).

We shall label the figure as shown below: Quadrilaterals are: 1. ABCD, 2. ADEB, 3. BDGE, 4. ABEC, 5. BDGF. 6. DGFC and 7. CEBH Therefore, total 7 Quadrilaterals as there in the given figure. Hence, the answer is 7.

The code is the Atbash cipher: each letter maps to its mirror image in the alphabet, i.e. position \(p\) becomes position \(27-p\). Verified with T↔G (20↔7), R↔I (18↔9), etc. Apply to GENIUS: G(7)→T(20), E(5)→V(22), N(14)→M(13), I(9)→R(18), U(21)→F(6), S(19)→H(8). Hence GENIUS is coded as TVMRFH.

Clearly, 1, 26, 31 represent the group of bottles which are not brown.

All five words begin with W; order by the second letter (a, i, o, r). Among the two 'Wa' words, compare third letters: Warlike vs Waste — 'r' precedes 's', so Warlike comes before Waste. Dictionary order: Warlike (5), Waste (1), Witty (3), Worcester (4), Wrong (2). Hence the sequence is 5, 1, 3, 4, 2.

Clearly, fig. (1) will be complete the pattern when placed in the blank space of question figures Hence, answer Is (1).

The rule for each row: \((\text{col 1}+\text{col 2})\times\text{col 3}+(\text{col 1}+\text{col 2})\). Row 1: \((1+7)\times 6+(1+7)=48+8=56\). Row 2: \((1+4)\times 8+(1+4)=40+5=45\). Row 3: \((2+3)\times 6+(2+3)=30+5=35\). Hence the missing number is 35.

Clearly, when the sheet is unfolded, we get two circles. Hence, fig (1) is the answer.

Clearly, (1) is the answer figure is the right image of the question figure.

The differences between consecutive letter positions alternate +2, +3, +2, +3, +2. A \(\xrightarrow{+2}\) C \(\xrightarrow{+3}\) F \(\xrightarrow{+2}\) H \(\xrightarrow{+3}\) K \(\xrightarrow{+2}\) ? K (11) + 2 = 13 = M.

Three pairs are squares of consecutive integers: \(49\text{-}64=7^2\text{-}8^2\), \(441\text{-}484=21^2\text{-}22^2\), \(100\text{-}121=10^2\text{-}11^2\). However, \(576\text{-}729=24^2\text{-}27^2\) — the bases differ by 3, not 1. Hence 576 - 729 is the odd pair.

Encoding is row then column. Decoding each pair in option 4: 78 → Matrix II, row 7 col 8 = F. 34 → Matrix I, row 3 col 4 = A. 98 → Matrix II, row 9 col 8 = T. 21 → Matrix I, row 2 col 1 = E. All four pairs decode to F-A-T-E, so the answer is 78, 34, 98, 21. (The other options each contain at least one mismatched code, e.g. 11 → I, 96 → K, 88 → B.)

Convert each group to alphabet positions and check the gaps. CEF: 3, 5, 6 → gaps +2, +1. LNO: 12, 14, 15 → +2, +1. RTU: 18, 20, 21 → +2, +1. GIK: 7, 9, 11 → +2, +2. GIK breaks the +2, +1 pattern (it is +2, +2), so GIK is the odd group.

Quicklime is the common name for calcium oxide, formula \(\text{CaO}\). It is produced by calcining limestone: \(\text{CaCO}_3 \xrightarrow{\Delta} \text{CaO}+\text{CO}_2\). \(\text{Ca}_2\text{CO}_3\) is not a real compound (calcium carbonate is \(\text{CaCO}_3\)), and \(\text{CaO}_2\) is calcium peroxide.

Diksha Basu is the author of The Windfall (2017), a satirical novel about a Delhi family adjusting to sudden wealth after moving from East Delhi to Gurgaon. Amitav Ghosh wrote The Shadow Lines and the Ibis trilogy; Arundhati Roy wrote The God of Small Things; Manmohan Singh is an economist and former Prime Minister.

Western disturbances are extra-tropical low-pressure systems that originate over the Mediterranean and travel eastward, reaching north-west India in winter (Dec-Feb). They bring rain and snow to Punjab, Haryana, Himachal Pradesh, J&K and western UP, and are vital for the Rabi (wheat) crop. Kerala and West Bengal get their rain from the south-west monsoon; Gujarat too lies outside the main path of these disturbances.

The Charter Act of 1813 abolished the East India Company's trade monopoly with India and opened Indian trade to all British merchants. The Company retained only its monopoly over the China trade and the tea trade — these were ended by the Charter Act of 1833, which terminated all its commercial activities entirely. The Regulating Act (1773) and Pitt's India Act (1784) only restructured administration; they left the trade monopoly untouched.

The 9th BRICS Summit was hosted by China in Xiamen from 3-5 September 2017, with the theme "BRICS: Stronger Partnership for a Brighter Future". India hosted the 8th summit (Goa, 2016) and South Africa hosted the 10th (Johannesburg, 2018).

The Pradhan Mantri Gramin Digital Saksharta Abhiyan (PMGDISHA), approved by the Union Cabinet in February 2017 under the Digital India programme, aimed to make 6 crore rural households digitally literate by March 2019. It targets one member per eligible household in the 14-60 age group.

The CDC 6600, designed by Seymour Cray at Control Data Corporation and released in 1964, is regarded as the world's first successful supercomputer, achieving about 3 megaFLOPS. USENET is a discussion network (1980), Commodore VIC-20 is an early home computer (1980), and PARAM-10000 is an Indian supercomputer developed by C-DAC in 1998.

The Chipko movement began in 1973 in the Mandal village of Chamoli district (then Uttar Pradesh, now Uttarakhand), where villagers hugged trees to stop contractors from felling them. Sunderlal Bahuguna, a Gandhian environmentalist, is recognised as its pioneer and chief spokesperson; his slogan "Ecology is permanent economy" carried the movement nationally. Medha Patkar led the Narmada Bachao Andolan, and Baba Amte worked on leprosy rehabilitation and later joined the Narmada movement.

Pairing each battle with its year: Battle of Buxar was fought in 1764 (1 - b); Battle of Plassey in 1757 (2 - c); Battle of Haldighati in 1576 (3 - a). Hence the correct match is 1 - b, 2 - c, 3 - a.

In December 2016, India and Bhutan signed an agreement under which India would assist Bhutan in the green and sustainable construction of infrastructure in the Himalayan Kingdom. The pact reflected the long-standing India-Bhutan development partnership and Bhutan's carbon-neutral commitments. Nepal, Afghanistan and Pakistan had no comparable agreement of this description in that month.

Indirect taxes (sales tax, GST, VAT) are levied at a uniform rate on goods and services, so every consumer pays the same percentage on a purchase regardless of income. Since poorer households spend a much larger share of their income on consumption than richer ones (who save and invest more), the same tax takes a bigger bite out of low incomes. This regressive nature places the heavier real burden on the poor. Direct taxes (income tax, property tax) are typically progressive, with rates rising with income and exemptions for low earners, so they fall more on the wealthy.

Moisture-laden south-west monsoon winds from the Arabian Sea strike the Western Ghats, are forced to rise, cool, and drop heavy orographic rainfall on the windward (western) slopes. After crossing the Ghats, the winds descend on the leeward side; descending air warms and its moisture-holding capacity rises, so very little precipitation occurs. The Deccan Plateau lies on this leeward side and therefore falls in the rain shadow of the Western Ghats. The Eastern Ghats receive rain from the retreating north-east monsoon as well, but the plateau between them stays dry.

Coal is a sedimentary rock formed from compacted plant matter; its grades, in increasing order of carbon content, are Peat → Lignite → Bituminous → Anthracite. Anthracite, Lignite and Peat are therefore all stages/types of coal. Siderite is an iron carbonate mineral (\(\text{FeCO}_3\)) — an iron ore, not a coal. Hence Siderite is the odd one out.

At the 2017 Australian Open final, Serena Williams beat sister Venus Williams 6–4, 6–4 to claim her 23rd Grand Slam singles title. This victory took her past Steffi Graf’s 22 and made her the most-decorated singles champion of the Open Era, second only to Margaret Court’s 24 overall.

The 3-day International Yoga Fest, organised by the Morarji Desai National Institute of Yoga under the Ministry of AYUSH, was held from 8–10 March 2017 at the Indira Gandhi Indoor Stadium, New Delhi. The capital hosted yoga gurus and delegates from across the world ahead of the International Day of Yoga.

A colloid in which the dispersion medium is a gas and the dispersed phase is a liquid or solid is called an aerosol. Fog and mist are tiny liquid water droplets suspended in air; clouds are droplets or ice crystals in air — all fit the liquid/solid-in-gas pattern of an aerosol. Solid sol is solid-in-solid (coloured glass); foam is gas-in-liquid (shaving cream); gel is liquid-in-solid (jelly) — none match.

Glycolysis splits glucose into pyruvic acid in the cytoplasm. In the presence of oxygen, pyruvate enters the mitochondria, where it is converted to acetyl-CoA and oxidised through the Krebs cycle (matrix) and the electron transport chain (inner membrane). These mitochondrial steps release \(\text{CO}_2\), produce \(\text{H}_2\text{O}\) via oxygen as the final electron acceptor, and generate the bulk of the ATP. Hence mitochondria — the ‘powerhouse of the cell’ — are the site of pyruvate’s complete breakdown.

The plant cell wall is chiefly built of cellulose, a polysaccharide of glucose units linked by β-1,4 glycosidic bonds. These long chains aggregate into microfibrils that give the wall its tensile strength and rigidity. Lipids form the plasma membrane, proteins serve enzymatic/structural roles in minor amounts, and vitamins are not structural at all — so cellulose is the principal constituent.

The Fifth Five-Year Plan (1974–79) was cut short in 1978 by the new Janata government. Economist D. T. Lakdawala then introduced the Rolling Plan (1978–80), which combined an annual plan with three- to five-year and longer perspective plans, revised each year. It was scrapped in 1980 when the Sixth Plan began. Hence the Rolling Plan came right after the Fifth Plan.

Under Article 368, an amendment to the Fundamental Rights (Part III) requires a special majority — a majority of the total membership of each House plus a two-thirds majority of members present and voting. By contrast, the creation of new states (Articles 3–4), abolition or creation of State Legislative Councils (Article 169) and parliamentary rules of procedure (Article 118) need only a simple majority. Hence the amendment of Fundamental Rights is the option needing a special majority.

A parsec is a unit of astronomical distance (~3.26 light-years), so I is correct. A barrel is a unit of volume, commonly used for liquids such as crude oil (1 barrel = 42 US gallons ≈ 159 L), so II is correct. A light year is the distance light travels in vacuum in one year (\(\approx 9.46\times 10^{15}\) m); despite the word ‘year’ in its name, it measures distance, not time. Hence only pair III is incorrect.

In 1796, English physician Edward Jenner observed that milkmaids who caught cowpox did not get smallpox. He inoculated 8-year-old James Phipps with cowpox material from Sarah Nelmes, and the boy remained immune when later exposed to smallpox. This was the first successful vaccine, and the word ‘vaccine’ itself comes from vacca (Latin for cow). Polio vaccines came from Salk/Sabin, rabies from Pasteur, and TB’s BCG from Calmette & Guérin.

Power is the rate of doing work: \(P=\dfrac{W}{t}\). With work in joules and time in seconds, the SI unit of power is joule per second, given the special name watt (W), where \(1\,\text{W}=1\,\text{J/s}\). Newton is the SI unit of force, pascal of pressure, and ‘Boyle’ is not an SI unit at all.

Dr. B. R. Ambedkar called Article 32 the ‘heart and soul’ of the Constitution. It guarantees the Right to Constitutional Remedies, letting any citizen move the Supreme Court directly for the enforcement of Fundamental Rights through writs of habeas corpus, mandamus, prohibition, certiorari and quo warranto. Without this enforceability the other Fundamental Rights would be mere paper guarantees, which is why Ambedkar accorded it pride of place.

At the 62nd Filmfare Awards held on 14 January 2017, the Lifetime Achievement Award was conferred on veteran actor Shatrughan Sinha for his decades-long contribution to Hindi cinema across hits such as Kalicharan, Dostana and Shaan. Yash Chopra (2006), Kamini Kaushal and Moushumi Chatterjee were honoured in different years.

A perfect square ending in 6 must have a square root ending in 4 or 6. Since \(45^2=2025\) and \(47^2=2209\), the only candidate in the range 2110–2119 is \(46^2\). \[46^2=2116\] Hence the number is 2116, giving X = 6. Checking the other options: \(2114, 2115, 2119\) are not perfect squares (none equals \(42^2, 45^2, 47^2,\) or \(48^2\)).

Calculation: Using angle sum property in triangle PQR ⇒ 3x + 2x + 4x = 180 ⇒ 9x = 180 ⇒ x = 20 Let the point where PQ intersects TS be A ∠(QAS) = ∠(RPQ) (∵ PR || TS) Using angle sum property in triangle QSA ⇒ 3x + y + 2x = 180 ⇒ Supplementary of y = 180 - y = 5x = 5 × 20 = 100 ∴ The measure of supplementary of y is 100

By the triangle inequality, the third side \(x\) must satisfy: \[|983-893| \lt x \lt 983+893 \;\Rightarrow\; 90 \lt x \lt 1876\] Since \(x\) is an integer, \(x\in\{91,92,\dots,1875\}\). Number of integer values \(=1875-91+1=\textbf{1785}\).

Runs scored against Pakistan can be given as 12% of 1600 = 12 × 1600/100 = 192 ∴ Runs scored against Pakistan are 192

Difference between the runs scored against England and Pakistan = 21% - 12% = 9% Which is same as that of Australia and New Zealand = 25% - 16% = 9% ∴ The answer is Australia and New Zealand

Use the identity: \[a^3+b^3+c^3-3abc=\tfrac{1}{2}(a+b+c)\big[(a-b)^2+(b-c)^2+(c-a)^2\big]\] Step 1 — Sum and differences: \(a+b+c=73+74+75=222\); \((a-b)^2+(b-c)^2+(c-a)^2=1+1+4=6\). Step 2 — Substitute: \[\tfrac{1}{2}(222)(6)=111\times 6=\mathbf{666}\]

Difference between the runs scored against Australia and Sri Lanka = 25% - 9% = 16% Difference between the runs scored against Australia and Sri Lanka = 16% of 1600 = 256 ∴ The difference in the runs scored against Australia and Sri Lanka is 256 runs

Total Runs scored by Australia and New Zealand = 25% + 16% = 41% Total Runs scored by Sri Lanka and Pakistan = 12% + 9% = 21% Difference Between them is 41% - 21% = 20% Angle can be given as ⇒ 20 × 360/100 = 72 ∴ The angle subtended by sector is 72

If CP of 48 articles equals SP of 32 articles, then \(48\,\text{CP}=32\,\text{SP}\), so: \[\frac{\text{SP}}{\text{CP}}=\frac{48}{32}=\frac{3}{2}\] Taking CP = 2 and SP = 3, profit = 1 and: \[\text{Profit \%}=\frac{1}{2}\times100=\mathbf{50\%}\] Shortcut: when CP of \(x\) = SP of \(y\), profit% \(=\frac{x-y}{y}\times100=\frac{16}{32}\times100=50\%\).

Let CP = Rs 100. Step 1 — Marked Price (40% above CP): \[\text{MP}=100\times 1.40=140\] Step 2 — Selling Price after 15% discount: \[\text{SP}=140\times 0.85=119\] Step 3 — Profit %: \(\text{SP}-\text{CP}=19\), so profit = 19%. Compact form: \(1.40\times 0.85=1.19\Rightarrow 19\%\) profit.

For consecutive numbers, the average equals the mean of the middle terms. The sum is: \[S=38.5\times 8=308\] Let the numbers be \(n, n+1,\dots, n+7\). Then: \[8n+28=308 \;\Rightarrow\; n=35\] So the numbers are 35, 36, ..., 42. The largest is 42.

Step 1 — Equivalence: Since 2 men \(\equiv\) 3 women, 1 man \(\equiv \tfrac{3}{2}\) women, so 6 men \(\equiv 9\) women. Total workforce \(=9+7=16\) equivalent women. Step 2 — Total work: 3 women take 96 days, so total work \(=3\times 96=288\) woman-days. Step 3 — Time required: \[T=\frac{288}{16}=\mathbf{18}\text{ days}\]

After successive deductions of 12% and 25%, the fraction left is: \[0.88\times 0.75=0.66\] So \(0.66\,S=2508\), giving: \[S=\frac{2508}{0.66}=\mathbf{3800}\] Check: 12% of 3800 = 456; remainder 3344. 25% of 3344 = 836; remainder 2508. ✔

Trains move in opposite directions, so their relative speed is the sum: \[v=(30+45)\text{ km/h}=75\times\tfrac{5}{18}=\tfrac{125}{6}\text{ m/s}\] The distance to fully cross is the sum of lengths: \(450+550=1000\) m. \[t=\frac{1000}{125/6}=1000\times\frac{6}{125}=\mathbf{48}\text{ s}\]

Step 1 — From the given: Squaring \(x-\tfrac{1}{x}=3\) gives \(x^2+\tfrac{1}{x^2}=11\). Step 2 — Divide numerator and denominator by \(x^2\): \[\frac{2x^2+\tfrac{2}{x^2}+3x-\tfrac{3}{x}+13}{3\left(x^2+\tfrac{1}{x^2}\right)}=\frac{2\left(x^2+\tfrac{1}{x^2}\right)+3\left(x-\tfrac{1}{x}\right)+13}{3\left(x^2+\tfrac{1}{x^2}\right)}\] Step 3 — Substitute: \[\frac{2(11)+3(3)+13}{3(11)}=\frac{44}{33}=\mathbf{\tfrac{4}{3}}\]

Step 1 — Find \(x+\tfrac{1}{x}\): From \(\left(x+\tfrac{1}{x}\right)^2=x^2+\tfrac{1}{x^2}+2\): \[\left(x+\tfrac{1}{x}\right)^2=\tfrac{31}{9}+2=\tfrac{49}{9}\] Since \(x>0\), \(x+\tfrac{1}{x}=\tfrac{7}{3}\). Step 2 — Apply \(a^3+b^3=(a+b)^3-3(a+b)\): \[x^3+\tfrac{1}{x^3}=\left(\tfrac{7}{3}\right)^3-3\left(\tfrac{7}{3}\right)=\tfrac{343}{27}-7=\mathbf{\tfrac{154}{27}}\]

Factor each quadratic: \(x^2-5x+6=(x-2)(x-3)\); \(x^2-3x+2=(x-1)(x-2)\); \(x^2-7x+12=(x-3)(x-4)\); \(x^2-5x+4=(x-1)(x-4)\). Rewriting division as multiplication by the reciprocal: \[\frac{(x-2)(x-3)}{(x-1)(x-2)}\times\frac{(x-1)(x-4)}{(x-3)(x-4)}=\mathbf{1}\] All factors cancel.

Let \(a=\sec^2A\), \(b=\tan^2A\). Using \(a^3-b^3=(a-b)^3+3ab(a-b)\): \[\sec^6A-\tan^6A=(\sec^2A-\tan^2A)^3+3\sec^2A\tan^2A(\sec^2A-\tan^2A)\] Since \(\sec^2A-\tan^2A=1\), this equals \(1+3\sec^2A\tan^2A\). Therefore: \[\sec^6A-\tan^6A-3\sec^2A\tan^2A=1+3\sec^2A\tan^2A-3\sec^2A\tan^2A=\mathbf{1}\]

Using \(\text{SI}=\dfrac{P\cdot R\cdot T}{100}\) with the condition SI = P + 500: \[P+500=\frac{P\times 10\times 20}{100}=2P\] Solving: \(P=\mathbf{500}\). Check: SI on Rs 500 at 10% for 20 years = Rs 1000, which is Rs 500 more than the principal. ✔

Let \(3A=2B=12C=k\). Then: \[A=\tfrac{k}{3},\quad B=\tfrac{k}{2},\quad C=\tfrac{k}{12}\] So \(A:B:C=\tfrac{1}{3}:\tfrac{1}{2}:\tfrac{1}{12}\). Multiplying through by LCM(3,2,12) = 12: \[A:B:C=\mathbf{4:6:1}\] Verification: \(3(4)=2(6)=12(1)=12\). ✔

From the property of circle we know that ⇒ TP 2= AP × (PB) ⇒ 4(x + 4) = 6 2= 36 ⇒ x = 5 ----(i) Now join TA, in triangle TAP, using Pythagoras theorem since ∠TAP is 90 ⇒ TP 2= TA 2+ PA 2 ⇒ TA = √(6 2- 4 2) ⇒ TA = 2√5 ----(ii) In triangle TAB, using Pythagoras theorem since ∠TAB is 90 ⇒ TB 2= TA 2+ BA 2Using (i) and (ii) ⇒ TB = 2 ×radius = √(2√5 2+ 5 2) = 3√5 ⇒ radius = (3√5)/2 ∴ The radius of the circle is (3√5)/2

Volume of a cylinder is \(V=\pi r^2 h\). For volume to stay constant, \(r^2 h\) must remain the same. Step 1 — New radius: \(r_2=0.8\,r_1\), so \(r_2^2=0.64\,r_1^2=\tfrac{16}{25}r_1^2\). Step 2 — Solve for new height: \[r_1^2 h_1=\tfrac{16}{25}r_1^2\,h_2 \implies h_2=\tfrac{25}{16}h_1\] Step 3 — Percentage increase: \[\frac{h_2-h_1}{h_1}\times 100=\left(\tfrac{25}{16}-1\right)\times 100=\tfrac{9}{16}\times 100=56.25\%\] Therefore the height must be increased by 56.25%.

Convert each bracket to sine and cosine using the identity \(\sin^2 A+\cos^2 A=1\). Step 1 — Simplify each bracket: \[\operatorname{cosec} A-\sin A=\frac{1-\sin^2 A}{\sin A}=\frac{\cos^2 A}{\sin A}\] \[\sec A-\cos A=\frac{1-\cos^2 A}{\cos A}=\frac{\sin^2 A}{\cos A}\] \[\tan A+\cot A=\frac{\sin^2 A+\cos^2 A}{\sin A\cos A}=\frac{1}{\sin A\cos A}\] Step 2 — Multiply: \[\frac{\cos^2 A}{\sin A}\cdot\frac{\sin^2 A}{\cos A}\cdot\frac{1}{\sin A\cos A}=\frac{\sin^2 A\cos^2 A}{\sin^2 A\cos^2 A}=1\] Therefore the simplified value is 1.

If a, b, and c are the three sides of a triangle, then the circum-radius ‘R’ is given as, R = abc/4A Where A = area of triangle = (base × height)/2 Given, height = 8 cm Let base = QR = x cm ⇒ Area of triangle = A = 8x/2 = 4x The other two sides of triangle are of lengths 24 cm and 12 cm, ∴ Circum-radius of triangle = (24 × 12 × x)/(4 × 4x) = 18 cm

Apply difference of squares to \(\cos^4 A-\sin^4 A\): \[\cos^4 A-\sin^4 A=(\cos^2 A-\sin^2 A)(\cos^2 A+\sin^2 A)\] Using \(\cos^2 A+\sin^2 A=1\) and the double-angle identity \(\cos 2A=\cos^2 A-\sin^2 A\): \[=\cos 2A\cdot 1=\cos 2A\] Therefore the simplified value is cos 2A.

Eccentric literally means "off-centre" — deviating from a central point (used both geometrically for non-circular orbits and figuratively for unconventional behaviour). This matches "away from a centre". "Eclectic" means drawn from diverse sources; "ellipsis" is the omission mark (...); "equine" relates to horses — none touch the idea of a centre.

Sentence Q is the only general opener — it introduces the Western-vs-Eastern contrast on idealism. R follows by elaborating "In much of Western thought…", developing Q. S uses "It is then usually juxtaposed with realism", where "It" refers to Western idealism just defined in R. P closes with a specific instance (Kant's epistemological idealism). Hence the order is QRSP.

The active sentence "Karnataka grows coffee" is in the simple present tense. The passive form is object + is/am/are + past participle (+ by/in agent). Object "coffee" (singular) becomes subject; "grows" becomes "is grown"; "Karnataka" (a place) takes the preposition "in". This gives "Coffee is grown in Karnataka." Option 1 is present continuous (wrong tense); option 2 is a fragment; option 4 is an imperative passive.

The reporting verb "reminded … to take" in indirect speech signals that the original direct speech was a reminder/negative imperative about not forgetting the wallet. Option 2, "Don't forget to take your wallet, Gopal," said his mother, fits exactly: the imperative converts to the infinitive "to take", "your" becomes "his", and vocative "Gopal" becomes object "him". Option 1 is a question by Gopal; option 3 is also interrogative; option 4 is a statement of fact, not a reminder.

The passage explicitly mentions later "power to influence the activities of others", echoing the first blank. The pairing "status and power" is the standard collocation for what members compete for in organizations. "Growth" and "success" are outcomes, not direct objects of competition alongside status; "money" is too narrow given the wider talk of resources, advancement and influence.

The blank takes "_____ for the resources", a verb that pairs with "for". The preceding sentence establishes the theme of members competing for status and power, so the natural continuation is that they also compete for resources. "Expand", "rely" and "run" do not collocate naturally with "for the resources" in this context.

This is a first conditional sentence: If + simple present, … will + base verb. The main clause "she will listen" already uses "will", so the if-clause must be in the simple present. "You will approach" wrongly puts "will" in the if-clause. The correct improvement is "you approach". Options 2 and 3 use continuous tenses that don't fit a general future condition.

The idiom "rise like a phoenix" comes from the myth of the phoenix — a bird that burns to ashes and is reborn from them. Figuratively, it means to recover from failure or ruin and become successful again. "Something memorable", "time to answer for one's action" and "to make people happy" do not capture the core idea of rebirth and renewed success.

A pragmatist is, by definition, a person who deals with things sensibly and realistically, guided by practical considerations rather than theory — a direct match for "one who values practicality". "Apotheosis" means the highest point or deification; "pliable" means easily bent or influenced; "realist" describes someone who accepts things as they are, but does not specifically denote valuing practicality as a guiding principle.

The blank needs a resource used "to expand their own departments". Finance (money/funding) is the resource departments most directly need to grow — to hire, equip and run projects. "Resources" is already used in the previous clause (redundant); "infrastructure" and "source" don't naturally collocate with "to expand their own departments" as the means of expansion.

Sentence R opens by stating a striking effect of thought ("violent can be made calm…"), inviting elaboration. Q follows with the familiar proverb "a person is known by the company he keeps", generalising R's idea about influence. P then explains the underlying mechanism — a sensitive mind absorbs vibrations from associates' thoughts. S closes with a confirming example: holy places give positive vibrations. Hence the order is RQPS.

The blank modifies "advancement" in the context of what employees compete for inside an organization. The standard collocation is career advancement — promotion and progress in one's professional path. "Financial", "regional" and "technological" advancement don't fit the personal-progress theme already established by competition for status, resources and power.

The correct spelling of the word meaning "not harmful or offensive" is Innocuous (with a double 'n'), derived from Latin in- (not) + nocere (to harm). "Inocuous" omits one 'n' and is therefore misspelt. Fabulous, Gorgeous, and Heterogeneous are all spelt correctly. Hence the incorrectly spelt word is Inocuous.

The blank requires a verb describing what power lets one do with others' activities. Control means to direct or regulate actions, which is exactly how power is exercised within an organisation. "Affect" is too weak and vague; "curb" narrows it to restraint only; "pursue" (to chase) is contextually unsuitable. Hence the completed phrase reads "for power to control the activities of others."

A "squib" is a small firework; when damp it fails to ignite, fizzling out instead of exploding. The idiom damp squib therefore describes something that was expected to be impressive but turned out to be a complete failure or anticlimax. "Complete knowledge", "to motivate" and "to squander money" bear no relation to the idiom's sense of disappointing outcome.

Phlegmatic means calm, unemotional, and not easily excited. Its opposite must describe strong feeling or passion. Ardent means passionate, enthusiastic, and full of fervour — the direct antonym. "Indifferent" is a near-synonym (both imply lack of feeling); "Prohibit" is a verb meaning to forbid; "Merciless" means cruel — neither contrasts with calmness. Hence the antonym is Ardent.

The sentence needs an adjective conveying that digital cameras have become outdated due to smartphone cameras. Obsolete means "no longer produced or used; out of date," precisely capturing this technological displacement. "Extinct" overstates — digital cameras still exist; "Redundancy" is a noun and grammatically wrong here; "Superfluous" (the original) means merely "extra," missing the nuance of being superseded. Hence obsolete is the correct improvement.

The correct spelling is Pedestrian (ending in -ian, meaning a person who walks). The option "Pedestrain" swaps the order to -ain, making it misspelt. Plaintiff, Potatoes, and Potassium are all spelt correctly. Hence the incorrectly spelt word is Pedestrain.

The focusing adverb "only" must sit immediately before the word or phrase it limits. The intended meaning is that the manager was the sole person involved — so "only" should modify "with his manager," giving "The CEO discussed the new venture only with his manager." As written, "The CEO only discussed" implies discussing was the sole action taken, which distorts the meaning. The error lies in part (1).

The sentence describes being physically prevented from entering a restricted area at a checkpoint. Stopped idiomatically pairs with "from + -ing" ("stopped from entering") and conveys being halted by security. "Denied" typically takes a noun object ("denied entry/permission"), not "denied from entering"; "rejected" suits applications, not physical access; "warned" describes a caution, not prevention. Hence the correct word is stopped.

Exorbitant means excessively or unreasonably high, especially in reference to a price or amount (e.g., "exorbitant fees"). Among the options, High conveys the same idea of being great in amount or value. "Clear" relates to clarity, "Dull" to lack of brightness or interest, and "Rare" to scarcity — none captures the sense of "excessively large." Hence the closest synonym is High.

Churlish means rude, ill-mannered, or surly. The opposite is someone polite and respectful — Courteous. "Belittle" (verb: to disparage) is unrelated; "Fervent" means passionate, not polite; "Uncouth" (rude, lacking refinement) is a synonym, not an antonym. Hence the antonym is Courteous.

The adjective "disgusted" takes the preposition with when the source of disgust is a person or their habit/behaviour (e.g., "disgusted with his laziness"). Since the object here is "the habit of her brother," "with" is the natural fit. "At" or "by" is used for a specific action or sight, while "of" and "on" are not standard collocations with "disgusted." Hence the correct preposition is with.

The sentence follows the third conditional structure used for hypothetical past situations: If + past perfect, … would have + past participle. Part (1) "If she had married" correctly uses the past perfect; part (2) "she would have been" correctly starts the result clause; part (3) "recognized as Mrs. Gupta" correctly completes the passive form "would have been recognized." All parts are grammatical, so the answer is No Error — option (4).

Jeopardy means danger or exposure to harm, loss, or failure (e.g., "her career is in jeopardy"). Among the options, Risk — meaning exposure to danger — carries the same sense. "Angry" describes an emotion, "Injure" denotes the act of causing harm (not the state of danger), and "Serene" (calm) is the opposite. Hence the synonym is Risk.