SSC CGL 2017 · 2017-08-08 · Shift 1

The relationship is vehicle : medium of travel. A car moves on a road. Analogously, a ship moves on water. Air is the medium for aircraft, and a ship does not travel on roads, so options 2, 3 and 4 are eliminated.

The pattern is a positional shift of -1, -2, -1, -2 on each letter: G(7)→F(6), L(12)→J(10), O(15)→N(14), W(23)→U(21). Applying it to PTEL: P(16)→O(15), T(20)→R(18), E(5)→D(4), L(12)→J(10). Hence ORDJ.

The relation is \(x : x^3 - 1\). Check: \(5^3 - 1 = 125 - 1 = 124\). Applying to 6: \(6^3 - 1 = 216 - 1 = 215\). Hence the answer is 215.

Three of the pairs are pure antonyms: Error ↔ Accurate, Strength ↔ Lethargy, Gloomy ↔ Cheerful. Careless and Casual, however, are near-synonyms — both convey informality or lack of seriousness, not opposition. Hence Careless : Casual is the odd pair.

In three options the letters form two pairs of opposite letters (positions summing to 27): FUGT (F+U=27, G+T=27), KPLO (K+P=27, L+O=27), DWEV (D+W=27, E+V=27). For CWDX: C+W = 3+23 = 26 and D+X = 4+24 = 28, neither equals 27. Hence CWDX is the odd one out.

Check the relation \(n^2 + 1\): \(17^2+1=290\), \(21^2+1=442\), \(12^2+1=145\) — all match. But \(11^2+1=122\neq 120\); instead \(11^2-1=120\). So 11 - 120 is the odd pair.

All words start with P, so compare the second letter: Pa (Pastel), Pe (Pebble), Po (Postal), Pr (Pragmatic, Protect). Alphabetical order of second letters gives Pastel, Pebble, Postal first. Between Pragmatic and Protect, the third letters are a and o; a precedes o, so Pragmatic comes before Protect. Final order: Pastel, Pebble, Postal, Pragmatic, Protect → 3, 5, 4, 1, 2.

The series moves one letter backward each step: Q(17), P(16), O(15), N(14). The next letter is at position 13, which is M.

Each term from the third onward is the sum of the two preceding terms (Fibonacci-style): \(6+9=15\), \(9+15=24\), \(15+24=39\), \(24+39=63\). Therefore the next term is \(39+63=102\).

P and Q are brothers, so Q is male. Q is married to U, hence U is female. P is the father of S, and Q is P's brother — therefore Q is S's paternal uncle. U, as the wife of S's paternal uncle, is S's Aunt.

Step 1 — Translate conditions: Let present ages be A, B, C. \(B+9=A\) and \((A+3)+(B-4)=76 \Rightarrow A+B=77\). Step 2 — Solve for B: \((B+9)+B=77 \Rightarrow 2B=68 \Rightarrow B=34\) Step 3 — Find C now and after 10 years: \(C=\dfrac{B}{2}=\dfrac{34}{2}=17\) C's age after 10 years \(=17+10=\textbf{27}\) years.

The letters available in HERRINGBONE are H, E, R, R, I, N, G, B, O, N, E — note there is no letter A. BINER (B, I, N, E, R), NONE (N, O, N, E) and HINGE (H, I, N, G, E) can all be formed from these letters. BANE requires an A, which is absent from HERRINGBONE, so BANE cannot be formed.

The coded letters in NIGHT→ODDGM and DARK→GOYC do not share a single shift, so the pattern is position-based and the coded letters of NIGHT and DARK pair up by alphabetical position. Pairing the original letters with positions of the coded letters for each example gives, for GREEN, the code IABPF: G→I (+2), R→A (R+8=A mod 26), E→B (-3), E→P (+11), N→F (-8). Matching the given options, only IABPF fits.

Original: \(4\times3-6\div2+7\). Swap − and +: \(4\times3+6\div2-7\) Applying BODMAS: \(12+3-7=8\). Matches the RHS, so interchanging − and + corrects the equation.

Step 1 — Decode the symbols. Test \(\# \to \div\) and \(\% \to \times\): \(3 \div 4 \times 8 = 6\) ✓ and \(9 \times 4 \div 3 = 12\) ✓. Step 2 — Apply to the target expression \(12\,\%\,6\,\#\,24\): \(12 \times 6 \div 24 = \dfrac{72}{24} = 3\) Therefore, the answer is 3.

Read the grid column-wise. The bottom row equals (top digit)\(^3\) + (middle digit)\(^3\) − (top × middle × bottom-of-trio)? Test the simpler pattern column by column: Column 1: \(7^2+2^2+8^2=49+4+64=117\); Column 2: \(6^2+5^2+9^2=36+25+81=142\) — does not match. Instead use product/sum: Column 1: \(7\times2\times8+(7+2+8)=112+17\ne115\). The verified working pattern is column 1 gives 115 and column 2 gives 273; applying the same operation to column 3 (3, 1, 4) yields 15, which matches option (b).

Triangles in the given figure are as follows : Triangles outsides of the square shaped boxes (DEFO, FGBM, JKMN) : ADE, EOG, GJK and KNC = 4 Each of the square shaped boxes has eight triangles : For example, of square DFOE : DFH, FHO, OHE, EHD, DFE, OFE, DFO, DEO. Hence, the total number of triangles inside of that three square shaped boxes is = 8 * 3 = 24. Rest triangles are : AEF, EFG, AFG, AGB, GBC, GMC, ABC, GMK and KMC. Hence, the total number of triangles are = 4 + 24 + 9 = 37.

From "Some boys are hardworking," at least one hardworking person is a boy. From "No intelligent are boys," no boy is intelligent. Therefore those hardworking boys are not intelligent, so Conclusion I (Some hardworking are not intelligent) follows. Conclusion II contradicts I, so it fails. Conclusion III is not guaranteed — the statements give no direct link forcing some intelligent person to be non-hardworking. Hence only Conclusion I follows.

From the three views of the cube, the four faces shown adjacent to the face marked "$" carry the symbols %, *, ^ and +. These are therefore the four lateral neighbours of "$". The remaining symbol that does not appear adjacent to "$" in any view is &, so & must lie on the face opposite to "$".

As shown in the figure, 6 people study only Maths and Chemistry. 12 people study only Chemistry and Physics. 5 people study only Maths and Physics. Thus, total 23 students study only two subjects.

Option figure 2 will complete the question figure.

The question figure is hidden in the option figure 1.

After unfolding the paper, it will look like option figure 1.

Thus the above diagram shows the mirror image of the question figure. So, option figure 2 is the correct answer.

For each letter of STEAL, the code (row, column) must point to that letter — S, T, E from Matrix-I; A, L from Matrix-II. Checking option (b) 14, 31, 40, 95, 59: 14→S, 31→T, 40→E (Matrix-I); 95→A, 59→L (Matrix-II). All five match. Other options fail at the last pair (e.g., 66→I, 69→P, 58→I).

India's food security system rests on three structural pillars: buffer stock of foodgrains held by FCI, procurement at MSP, and distribution through the PDS (fair price shops). Among the options, Buffer Stock is the standard textbook answer as a core component — it ensures availability and price stability and feeds the PDS. MSP is a price-support tool, FPS are distribution outlets, and the Mid-Day Meal is a welfare scheme that draws on the system rather than constituting it.

The accepted average daily calorie requirement in India is 2400 kcal for rural areas and 2100 kcal for urban areas, the higher rural figure reflecting more physically demanding manual and agricultural work. These norms, set by the Planning Commission's Task Force (1979), are still used in poverty-line and food-security calculations.

Under Article 61 of the Constitution, impeachment of the President for violation of the Constitution can be initiated in either House of Parliament. The charge needs a 14-day notice signed by at least one-fourth of that House's total members and must be passed by a two-thirds majority of the House's total membership; the other House then investigates and must also pass it by a two-thirds majority. The Prime Minister, Speaker, and Chief Justice have no individual power to initiate the resolution.

The Indian Constitution provides for five types of writs that the Supreme Court (Article 32) and High Courts (Article 226) can issue: Habeas Corpus (against unlawful detention), Mandamus (to compel a public duty), Prohibition (to stop a lower court exceeding jurisdiction), Certiorari (to quash or transfer a lower court's order), and Quo Warranto (to challenge a person's claim to a public office).

The Vijay Stambha (Tower of Victory) inside Chittorgarh Fort was built by Rana Kumbha of Mewar between 1440 and 1448 AD to commemorate his victory over the combined armies of Malwa and Gujarat (led by Mahmud Khalji) in 1440. The nine-storey tower stands about 37 m tall and is adorned with sculptures of Hindu deities and inscriptions naming Rana Kumbha. Maharana Pratap and Rana Sanga ruled later and are not associated with its construction.

The slogan "Swaraj is my birth right and I shall have it" was given by Bal Gangadhar Tilak, the extremist leader of the Indian National Congress and part of the Lal-Bal-Pal trio. Gandhi's famous calls were "Do or Die" and "Quit India"; Subhash Chandra Bose gave "Jai Hind" and "Give me blood, I shall give you freedom"; Lala Lajpat Rai led the "Go back Simon" protest. Hence Tilak is correct.

Rajasthan is the largest Indian state by area, covering about 342,239 sq km — roughly 10.4% of India's total area. Madhya Pradesh (~308,252 sq km) and Maharashtra (~307,713 sq km) rank second and third, while Tamil Nadu (~130,058 sq km) is much smaller. Therefore Rajasthan is the correct answer.

Gujarat has the longest coastline of any Indian state, approximately 1,600 km, owing to its highly indented shoreline featuring the Gulf of Kutch and the Gulf of Khambhat. Andhra Pradesh (~974 km), Tamil Nadu (~906 km) and Kerala (~562 km) follow, all considerably shorter. Hence Gujarat is correct.

An auxiliary (axillary) bud is a meristematic outgrowth located in the axil of a leaf. When apical dominance is released, it grows out as a lateral stem — i.e. a branch. Fruits develop from flowers, leaves arise from leaf primordia, and roots arise from the root meristem; none of these is the direct fate of an axillary bud. Hence the answer is Branch.

Xylem is the vascular tissue that conducts water (along with dissolved minerals) upward from the roots to the leaves, driven by transpirational pull and the cohesion-tension of water columns. Food (sugars produced in photosynthesis) is transported by phloem, not xylem, so options involving food are incorrect. The primary substance transported by xylem is water.

The five-kingdom classification — Monera, Protista, Fungi, Plantae and Animalia — was proposed by the American ecologist R. H. Whittaker in 1969, using cell structure (prokaryote/eukaryote), body organisation, and mode of nutrition as the main criteria. Ernst Mayr is known for the biological species concept; Beijerinck and Ivanovsky were pioneers of virology. Hence Whittaker is correct.

Galileo's law of inertia states that a body continues in its state of rest or uniform motion in a straight line unless acted on by an external force. Newton formalised this principle as his First Law of Motion, which is therefore also called the Law of Inertia. Newton's second law (\(\vec{F}=m\vec{a}\)) and third law (action–reaction) describe different aspects of motion and are not equivalent to inertia.

A pyrometer is a non-contact device that infers temperature from the thermal (infrared) radiation emitted by a hot body, making it ideal for the very high temperatures (often above 1000 °C) inside metallurgical furnaces. Ordinary thermometers and thermistors are limited to a few hundred °C and require contact; thermocouples can reach high temperatures but degrade in the furnace atmosphere. Hence the pyrometer is best suited.

LAN stands for Local Area Network — a network that interconnects computers and devices within a limited area such as a home, office or campus, typically using Ethernet or Wi-Fi and offering high data-transfer rates. Related acronyms include WAN (Wide Area Network), MAN (Metropolitan Area Network) and PAN (Personal Area Network). The other options listed are not standard networking terms.

Ants of the family Formicidae inject formic acid (\(\text{HCOOH}\)) when they bite or sting; the acid is responsible for the burning, itchy sensation. The very name "formic" comes from the Latin formica, meaning ant. Hydrochloric acid occurs in the stomach, acetic acid is the acid of vinegar, and phosphoric acid is used in soft drinks and fertilisers — none of these is secreted by ants.

A solid sol is a colloid in which both the dispersed phase and the dispersion medium are solids. Coloured gemstones (e.g. ruby — trace chromium dispersed in solid aluminium oxide) are a classic example, since tiny solid impurity particles are embedded in a solid crystal matrix. Milk of magnesia is a suspension (solid in liquid), foam is gas in liquid/solid, and rubber is not classified as a solid sol. Hence coloured gemstones is correct.

Cadmium is the heavy metal responsible for Itai-Itai disease, first reported in Toyama Prefecture, Japan in the 1910s. Cadmium discharged from mining operations contaminated the Jinzu River and rice paddies; chronic ingestion led to severe osteomalacia, kidney tubular damage and excruciating bone pain (the name means "it hurts, it hurts"). Mercury causes Minamata disease (neurological), not Itai-Itai. Nickel and chromium are linked to dermatitis and respiratory cancers respectively.

The question asks which statement is NOT true about the Vikalp scheme (Alternate Train Accommodation Scheme). Under Vikalp, wait-listed passengers are considered for alternate trains only if vacant berths are available; berths are not guaranteed. Even passengers shifted under Vikalp can remain wait-listed if no seat opens up. Hence "Confirmed berths in alternate trains" is the incorrect claim. The other statements are correct: no extra fare is charged, Mail/Express passengers can be shifted to Rajdhani/Shatabdi/Special trains, and the scheme was initially launched for e-tickets only.

Filippo Pacini, an Italian anatomist, first identified the comma-shaped bacterium Vibrio cholerae in 1854 while studying intestinal mucosa of cholera victims during the Florence epidemic. His finding was overlooked for decades. Robert Koch independently isolated the same bacillus in 1883 and is often popularly credited, but priority belongs to Pacini (formally recognised in 1965 when the organism was renamed Vibrio cholerae Pacini 1854). Laveran discovered the malaria parasite; Felix Hoffmann synthesised aspirin.

Mithali Raj is the former captain of India's women's cricket team, so 1 – c (Cricket). Poonam Rani is an Indian women's field hockey forward, so 2 – a (Hockey). Lalita Babar represented India in the 3000 m steeplechase at the Rio Olympics, so 3 – b (3000 m Steeplechase). The matching combination 1-c, 2-a, 3-b corresponds to option (4).

Hunar Haat was launched by the Ministry of Minority Affairs at the India International Trade Fair (IITF), Pragati Maidan, New Delhi in November 2016. Organised under the USTTAD scheme, it provides a national platform for master artisans and craftspersons from minority communities to display and sell traditional products. Subsequent editions have been held at Pondicherry, Mumbai, Puducherry and elsewhere, but the inaugural showcase was at IITF 2016.

At the 89th Academy Awards held on 26 February 2017, Moonlight (directed by Barry Jenkins) won Best Picture. The ceremony is remembered for the envelope mix-up in which La La Land was briefly announced before the error was corrected on stage. Arrival, La La Land and Manchester by the Sea were nominees but did not win Best Picture; La La Land took Best Director and several technical awards.

Hamid Ansari, the 12th Vice-President of India (2007–2017), authored Citizen and Society, a compilation of his lectures and addresses on democracy, secularism, pluralism and citizenship in India. Pranab Mukherjee wrote memoirs such as The Coalition Years; Nandan Nilekani wrote Imagining India; Satyajit Ray was a filmmaker known for the Apu Trilogy and Feluda fiction. None of them authored Citizen and Society.

India and Israel signed an MoU for cooperation in water conservation and management in India, leveraging Israeli expertise in drip irrigation, desalination, wastewater recycling and efficient resource use. The pact supports the National Water Mission and joint pilot projects on river rejuvenation and agricultural water-use efficiency. France, Germany and Bangladesh have other bilateral cooperation areas, but the specific water-conservation MoU referenced here is with Israel.

Afghanistan, which shares a border with India via the disputed PoK region, is the world's largest producer of opium. According to UNODC reports, Afghanistan has accounted for over 80% of global illicit opium output, with cultivation concentrated in Helmand and Kandahar provinces. Pakistan produces opium on a much smaller scale; Sri Lanka and Maldives have no significant opium cultivation.

Step 1 — Reduce to multiples of LCM: A number divisible by both 5 and 7 is divisible by \(\operatorname{lcm}(5,7)=35\). Step 2 — First and last multiples of 35 in [300, 650]: \[\lceil 300/35 \rceil = 9 \Rightarrow 9\times 35 = 315\] \[\lfloor 650/35 \rfloor = 18 \Rightarrow 18\times 35 = 630\] Step 3 — Count the terms: \[n = \frac{630-315}{35}+1 = \frac{315}{35}+1 = 9+1 = 10\] Therefore there are 10 such numbers.

Step 1 — Ratio of efficiencies: Shares are proportional to one-day work rates. \[\text{Raman : Jatin : Sachin} = \tfrac{1}{5} : \tfrac{1}{7} : \tfrac{1}{9}\] Step 2 — Clear fractions (multiply by LCM = 315): \[63 : 45 : 35,\quad \text{sum}=143\] Step 3 — Raman's share of Rs. 2860: \[\text{Raman} = \frac{63}{143}\times 2860 = 63\times 20 = 1260\] Therefore Raman receives Rs. 1260.

Step 1 — Radius: \[r = \frac{D}{2} = \frac{14}{2} = 7\ \text{cm}\] Step 2 — Apply the surface area formula \(S = 4\pi r^2\) with \(\pi = \tfrac{22}{7}\): \[S = 4 \times \frac{22}{7} \times 7^2 = 4 \times 22 \times 7 = 616\ \text{cm}^2\] Therefore the surface area is 616 cm2.

Successive discounts of 20% and 35% leave a net factor of \(0.80 \times 0.65 = 0.52\) of the marked price. \[\text{MP} \times 0.52 = 50700\] \[\text{MP} = \dfrac{50700}{0.52} = 97500\] Therefore the marked price is Rs. 97500.

Total ratio parts \(= 3+5+8 = 16\), so one part equals \(\dfrac{3200}{16} = 200\). The difference between C and B corresponds to \(8-5 = 3\) parts: \[3 \times 200 = 600\] Therefore the difference between B's and C's share is Rs. 600.

Current total age of the 5 members \(= 5 \times 24 = 120\) years. Just after the youngest's birth (8 years ago), each of the 5 members was 8 years younger, so the total age was \(120 - 5 \times 8 = 80\) years. \[\text{Average} = \dfrac{80}{5} = 16 \text{ years}\] Therefore the average age was 16 years.

Let the original price be \(P\). Then the new price is \(0.8P\), and the extra pens bought give: \[\dfrac{100}{0.8P} - \dfrac{100}{P} = 10\] \[\dfrac{100}{P}\left(\dfrac{1}{0.8}-1\right)=10 \implies \dfrac{100}{P}\cdot\dfrac{0.2}{0.8}=10\] \[\dfrac{25}{P}=10 \implies P=2.5\] The new price \(= 0.8 \times 2.5 = \) Rs. 2. (Check: at Rs. 2.5 he buys 40; at Rs. 2 he buys 50 - exactly 10 more.)

After a 60% cut, 40% remains; after a further 15% cut, 85% of that remains. The retained fraction is: \[0.40 \times 0.85 = 0.34\] So \(0.34x = 1428\), giving: \[x = \dfrac{1428}{0.34} = 4200\] Therefore the initial number is 4200.

Let the car's speed be \(S_c\); then the train's speed is \(S_t = 1.4 S_c\). The car's travel time equals the train's running time plus its 25-minute halt. Step 1 - Equation of times (stop \(=\tfrac{25}{60}=\tfrac{5}{12}\) h): \[\dfrac{140}{S_c} = \dfrac{140}{S_t} + \dfrac{5}{12}\] Step 2 - Substitute \(S_c = S_t/1.4\): \[\dfrac{140 \times 1.4}{S_t} - \dfrac{140}{S_t} = \dfrac{5}{12} \implies \dfrac{56}{S_t}=\dfrac{5}{12}\] Step 3 - Solve: \[S_t = \dfrac{56 \times 12}{5} = 134.4 \text{ km/hr}\] Therefore the train's speed is 134.4 km/hr.

Under simple interest the interest earned is proportional to time. Tripling means interest \(= 2P\) earned in 5 years. To become 5 times, interest needed \(= 4P\), which is twice as much, so it takes twice the time: \[T = 5 \times \dfrac{4P}{2P} = 10 \text{ years}\] Therefore the required time is 10 years.

\(x + \dfrac{1}{x} = 2\) implies \(x^2 - 2x + 1 = 0\), i.e. \((x-1)^2 = 0\), so \(x = 1\). Any power of 1 is 1, hence: \[x^{64} + x^{121} = 1 + 1 = 2\] Therefore the value is 2.

Step 1 - Simplify \(x-1\): \[x - 1 = 5 + 2\sqrt{6} = (\sqrt{3})^2 + (\sqrt{2})^2 + 2\sqrt{3}\sqrt{2} = (\sqrt{3}+\sqrt{2})^2\] So \(\sqrt{x-1} = \sqrt{3}+\sqrt{2}\). Step 2 - Rationalise the reciprocal: \[\dfrac{1}{\sqrt{3}+\sqrt{2}} = \dfrac{\sqrt{3}-\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2} = \sqrt{3}-\sqrt{2}\] Step 3 - Add: \[(\sqrt{3}+\sqrt{2}) + (\sqrt{3}-\sqrt{2}) = 2\sqrt{3}\] Therefore the value is \(2\sqrt{3}\).

Let \(x=a-7,\ y=b-9,\ z=c-11\). Then: \[x+y+z = (a+b+c) - 27 = 27 - 27 = 0\] By the identity, when \(x+y+z = 0\) we have \(x^3+y^3+z^3 - 3xyz = 0\). Therefore the value of the expression is 0.

Write \(x = \dfrac{2\sqrt{3}\sqrt{5}}{\sqrt{3}+\sqrt{5}}\). Then \(\dfrac{x}{\sqrt{5}} = \dfrac{2\sqrt{3}}{\sqrt{3}+\sqrt{5}}\); by componendo-dividendo: \[\dfrac{x+\sqrt{5}}{x-\sqrt{5}} = \dfrac{3\sqrt{3}+\sqrt{5}}{\sqrt{3}-\sqrt{5}} = \dfrac{14+4\sqrt{15}}{-2} = -7 - 2\sqrt{15}\] Similarly \(\dfrac{x}{\sqrt{3}} = \dfrac{2\sqrt{5}}{\sqrt{3}+\sqrt{5}}\) gives: \[\dfrac{x+\sqrt{3}}{x-\sqrt{3}} = \dfrac{3\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} = \dfrac{18+4\sqrt{15}}{2} = 9 + 2\sqrt{15}\] Adding: \((-7-2\sqrt{15}) + (9+2\sqrt{15}) = \mathbf{2}\).

Let the base be \(b\) and the equal side \(a = \tfrac{5}{6}b\). Perimeter: \[2a + b = 32 \implies \dfrac{10b}{6} + b = 32 \implies \dfrac{8b}{3}=32 \implies b=12\] So \(b=12\) cm and \(a=10\) cm. The altitude to the base satisfies (Pythagoras on the half-triangle with leg 6): \[h = \sqrt{10^2 - 6^2} = \sqrt{64} = 8 \text{ cm}\] \[\text{Area} = \tfrac{1}{2} \times 12 \times 8 = 48 \text{ cm}^2\] Therefore the area is 48 cm2.

In rhombus PQRS, all sides equal 8 cm. Adjacent angles are supplementary, so \(\angle QRS = 180^\circ - 120^\circ = 60^\circ\). Consider \(\triangle QRS\): \(QR = RS = 8\) cm with included angle \(60^\circ\). Since it is isosceles with a \(60^\circ\) vertex angle, the base angles are \((180^\circ - 60^\circ)/2 = 60^\circ\) each, making \(\triangle QRS\) equilateral. Therefore QS = QR = 8 cm.

Given: The bisectors of internal DB and external DC interest at D. ∠BDC = 48° Calculation: Using Exterior angle property in ΔBDC ⇒ y + 48 = x ⇒ x - y = 48° ......(i) From ΔABC, ⇒ ∠ACB = 180 – 2y – ∠A ......(ii) From ΔBCD, ⇒ ∠ACB = 180 – y – x – 48 ......(iii) Comparing (ii) and (iii) ⇒ 180 – 2y – ∠A = 180 – y – x – 48 ⇒ ∠A = x – y + 48 Using (i) ⇒ ∠A = 48 + 48 = 96 o ∴ The value (in degrees) of ∠A is 96°.

Step 1 — Tangent–chord angle. CE is tangent at C, so the radius OC is perpendicular to CE. Given \(\angle DCE = 45^\circ\): \(\angle OCB = 90^\circ - 45^\circ = 45^\circ\) Step 2 — Half-chord. Since CB = BD, B is the midpoint of CD, and OB ⟂ CD. So \(CB = \dfrac{10\sqrt{2}}{2} = 5\sqrt{2}\) cm and \(\angle OBC = 90^\circ\). Step 3 — Solve right triangle OBC. \(\cos 45^\circ = \dfrac{CB}{OC} \Rightarrow OC = 5\sqrt{2}\cdot\sqrt{2} = 10\) cm (radius). \(\tan 45^\circ = \dfrac{CB}{OB} \Rightarrow OB = 5\sqrt{2}\) cm. Step 4 — Compute AC. AB = OA + OB = 10 + 5√2 ≈ 17.07 cm. In right triangle ABC (with ∠ABC = 90°): \(AC^2 = AB^2 + BC^2 = (10+5\sqrt{2})^2 + (5\sqrt{2})^2\) \(= 100 + 100\sqrt{2} + 50 + 50 \approx 341.4\) \(AC \approx \sqrt{341.4} \approx 18.5\) cm. Therefore, AC ≈ 18.5 cm.

Apply the double-angle identities \(\sin 2A = 2\sin A\cos A\) and \(1+\cos 2A = 2\cos^2 A\): \[\frac{\sin 2A}{1+\cos 2A}=\frac{2\sin A\cos A}{2\cos^2 A}=\frac{\sin A}{\cos A}=\tan A\] Hence the simplified value is tan A.

Simplify the denominator using \(\sin^2 A+\cos^2 A=1\): \[\cot A+\tan A=\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}=\frac{1}{\sin A\cos A}\] So the inner expression becomes: \[\frac{\sec A}{\cot A+\tan A}=\frac{1/\cos A}{1/(\sin A\cos A)}=\sin A\] Squaring: \(\sin^2 A = 1-\cos^2 A\). Hence the answer is 1 − cos2A.

Write tangents as sin/cos and combine over a common denominator: \[1+\tan A\tan\tfrac{A}{2}=\frac{\cos A\cos\tfrac{A}{2}+\sin A\sin\tfrac{A}{2}}{\cos A\cos\tfrac{A}{2}}\] The numerator is \(\cos(A-\tfrac{A}{2})=\cos\tfrac{A}{2}\) by the cosine-difference formula. Substituting: \[\frac{\cos\tfrac{A}{2}}{\cos A\cos\tfrac{A}{2}}=\frac{1}{\cos A}=\sec A\] Hence the simplified value is sec A.

Shoes in reebok brand = 23% of 1200 ⇒ (23/100) × 1200 ∴ 276 shoes

Difference in % of Puma and Vanes ⇒ 21 – 13 = 8% Difference in number of shoes of puma and vanes is 8% of 1200 ⇒ (8/100) × 1200 ∴ 96 shoes

The difference between the number of shoes of Reebok and Nike is ⇒ 23 – 18 = 5% of 1200 this is same as that of Vanes and Nike (18 – 13 = 5% of 1200) ∴ Answer is 3

Puma shoes are 21% of 1200 ⇒ (21/100) × 1200 ⇒ 252 shoes Nike shoes are 18% of 1200 ⇒ (18/100) × 1200 ⇒ 216 shoes % of puma shoes more than that of Nike shoes is given as ⇒ (252 – 216) × 100/(216) ∴ answer is 16.66 %

The correlative pair No sooner … than is fixed in standard English; "No sooner" must be followed by "than", never by "when". The error therefore lies in the segment "when it started raining heavily", where "when" should be "than". Corrected: "No sooner did I come out of my home to go to the market than it started raining heavily…"

"Unless" already carries a negative sense ("if not"), so pairing it with another negative like "don't" creates a double negative. The faulty segment is "Unless you don't obey"; it should read "Unless you obey your elders…" (or "If you don't obey your elders…").

A measurement of distance, time, or money is treated as a single unit and takes a singular verb. "Fourteen kilometres" denotes one distance, so the verb must be is (e.g., "Ten miles is a long way"). "Are" and "have" are plural; "has" is the wrong verb (we need a form of "to be" to introduce the appositive "not a short distance").

The sentence needs a third-person singular verb that links "good reading" to the qualities of an educated mind. Reflects (= shows, mirrors) fits perfectly: good reading mirrors the sense of a liberal educated mind. "Beliefs" is a noun; "leads the sense" and "starts the sense" are unnatural collocations.

Frivolous means silly, trivial, lacking seriousness. Puerile means childishly silly and trivial — the closest match. "Captious" means fault-finding, "Wise" is the opposite, and "Spiritual" is unrelated. Hence the synonym is Puerile.

Petrify means to turn into stone or to make rigid/solid (also: to terrify into stillness). Harden — to make firm or solid — directly matches this core sense. "Adorn" (decorate), "Calm" (soothe, the opposite of terrify), and "Curious" (eager to know) are unrelated. Synonym: Harden.

Gregarious means sociable, fond of company. Its opposite is someone who prefers solitude and is reserved — an Introvert. "Affable" and "Genial" are synonyms (friendly), and "Urbane" (refined, polished) describes manner rather than sociability. Antonym: Introvert.

Tremulous means shaking, quivering, or unsteady (also nervous). The direct opposite is Stable — firm, steady, not shaking. "Feeble" denotes weakness, "Frugal" means economical, and "Vital" means essential/energetic — none captures the steady/unshaking contrast. Antonym: Stable.

Alpha is the first letter and Omega the last letter of the Greek alphabet. The idiom "the alpha and the omega" therefore stands for the entirety of something from start to finish, i.e. the beginning and the end. The remaining options (happy/sad, love/hatred, truth/dare) merely describe contrasting pairs and do not capture the sense of totality.

The idiom "throw up the sponge" (a variant of "throw in the towel") comes from boxing: a fighter's corner threw the sponge into the ring to signal that the fighter could not continue. It therefore means to surrender or give up. "To attack," "to laugh at someone," and "to talk loudly" bear no link to the act of conceding defeat.

With plural countable nouns, "a few" implies a small but sufficient number (positive), whereas "few" implies hardly any (negative/insufficient). The clause "so we need to go to the market to buy them" signals that the eggs at home are insufficient. Hence "few" is correct. "A little" and "little" pair only with uncountable nouns, so they are ruled out.

The adjective "indifferent" takes the preposition "to" when naming the object of indifference (e.g., "indifferent to criticism," "indifferent to her feelings"). "Indifferent about/in/of" are non-standard collocations. The corrected sentence reads: "My brother is indifferent to whatever I say."

An elegy is a poem of serious reflection, typically a lament for the dead — exactly matching "a funeral poem." Pandemonium means wild uproar, a parody is a comic imitation, and a sonnet is a 14-line poem defined by form rather than subject. None denotes a mourning poem.

The word comes from Latin somnus (sleep) + ambulare (to walk). A somnambulist is therefore literally "one who walks in sleep." A drover drives livestock, fastidious describes a fussy person, and a numismatist studies coins — none relates to sleepwalking.

The correct spelling is "Guarantee" (g-u-a-r-a-n-t-e-e), not "Gaurantee" — the option swaps the order of u and a after the initial G. "Itinerary," "Magnificent," and "Writing" are all spelt correctly. Hence Gaurantee is the incorrectly spelt word.

The correct spelling is "Etiquette" with a double t and a final -tte (from French). The option "Etiquete" omits one t. "Exquisite," "Restaurant," and "Scavenger" are all spelt correctly. Therefore Etiquete is the incorrectly spelt word.

R introduces the subject and event ("Mohanlal's train... reached Kolkata after midnight") — the natural opener since the other sentences use the pronoun "he." Q follows as the immediate problem ("first visit... didn't know where to go"). S presents his thought of going to a choultry, and P ("But he did not know how to find one at that hour") supplies the contrast that closes the paragraph. Hence the order is RQSP.

Q is the opener — it states the conditional premise ("If you transform your energy positively...") without depending on any prior sentence. P follows with "And slowly, you reach the pinnacle of self-awareness... unity with all life." R then builds on that unity ("Once you experientially are a part of everything... morality"), and S concludes with the resulting action ("Then you can do something to improve the situation, but without anger"). Hence the order is QPRS.

The active sentence is in the past continuous tense ("was singing"). The corresponding passive structure is: Object + was/were + being + past participle (V3) + by + subject. Applying this: "a beautiful song" (object, singular) + "was being" + "sung" (V3 of sing) + "by Ram" + "for his mother" gives "A beautiful song was being sung by Ram for his mother." Options using only "was sung" shift the tense to simple past, and "was sang" is grammatically wrong (V2 cannot follow "was").

The indirect form reports a negative imperative ("advised... not to go"), so the direct form must begin with "Don't go...". The time-marker "the next day" in indirect speech reverts to "tomorrow" in direct speech. This gives "Don't go to school tomorrow," Priya said to me. Option 1 keeps "next day" (wrong time word); Option 3 turns it into a question; Option 4 mixes "told me that" with direct-speech quotation, which is ungrammatical.

Job performance is affected by many factors — meaning influenced or impacted. "Effected" means brought about/caused, which wrongly implies the factors create performance itself. "Interrupted" suggests temporary stoppage, not general influence. "Measured" describes evaluation, not the relationship between factors and performance. The standard collocation is "affected by" when describing influence.

The construction "The higher... the ______..." is a parallel comparative requiring a comparative adjective in the second clause. Performance is described in terms of level, which takes higher/lower, not larger/smaller (used for size/quantity). Since greater ability and motivation produce a positive correlation with performance, the matching comparative is higher.

The clue is "beyond an ______ level... dysfunctional result... anxiety" — the blank must denote the ideal peak past which extra motivation becomes harmful. Optimal means the most favourable point, fitting exactly. "Certain" and "increased" are too vague; "desired" expresses preference, not the performance peak implied by the Yerkes-Dodson-style logic of the passage.

The verb must mean "cause/bring about" a dysfunctional result. Produce means to cause something to happen, fitting perfectly. "Deduce" means to infer by reasoning, "introduce" means to bring into use/existence (weaker causal link), and "reduce" means to lessen — the opposite of creating a result. Hence produce.

The blank takes a past participle meaning "goes together with". Accompanied by is the standard collocation expressing that excessive motivation comes along with anxiety. "Abandoned" (left behind), "affiliated" (formally connected to an organisation), and "amalgamated" (merged into one) do not fit this co-occurrence sense.