SSC CGL 2017 · 2017-08-12 · Shift 3

The relationship is adult animal : its young one. A lamb is the young of a sheep, and similarly a calf is the young of a cow. A kitten is the young of a cat, a cub is the young of a lion/tiger/bear, and a caterpillar is the larval stage of a butterfly — none match. Hence the answer is Calf.

The pattern adds +1, +2, +3, +4 to the positions of the four letters of the first word. For PRAG → QTDK: P(16)+1=Q, R(18)+2=T, A(1)+3=D, G(7)+4=K. \(\checkmark\) Applying the same shift to STOP: \[S(19)+1=T,\ T(20)+2=V,\ O(15)+3=R,\ P(16)+4=T\] Hence the answer is TVRT.

The pattern is: the second number equals half the product of the digits of the first number. For 562: \(\frac{5\times 6\times 2}{2}=\frac{60}{2}=30\). \(\checkmark\) For 663: \(\frac{6\times 6\times 3}{2}=\frac{108}{2}=54\). Hence the answer is 54.

Carrom, Table Tennis and Chess are all indoor games, typically played on a board or table in a confined space. Cricket is an outdoor sport played on a large open field, making it the odd one out.

Convert each triplet to alphabet positions and check the gaps between consecutive letters. IMX → (9, 13, 24): gaps +4, +11. DHS → (4, 8, 19): gaps +4, +11. KOZ → (11, 15, 26): gaps +4, +11. GWK → (7, 23, 11): gaps +16, −12 — a completely different pattern. Hence GWK is the odd group.

In each pair the second number is a perfect cube \(n^3\) and the first number should equal \(n^2+1\). 122–1331: \(11^3=1331,\ 11^2+1=122\). \(\checkmark\) 197–2744: \(14^3=2744,\ 14^2+1=197\). \(\checkmark\) 290–4913: \(17^3=4913,\ 17^2+1=290\). \(\checkmark\) 173–2197: \(13^3=2197\) but \(13^2+1=170\ne 173\). Hence 173–2197 is the odd pair.

Comparing letter by letter: Xanthic (Xa…) comes first since 'a' precedes 'e' and 'y'. Among the 'Xe…' words, Xenians (Xeni…) precedes Xenons (Xeno…) because 'i' < 'o'. Among the 'Xy…' words, Xylyls (Xyl…) precedes Xyst (Xys…) because 'l' < 's'. Dictionary order: Xanthic, Xenians, Xenons, Xylyls, Xyst → 3, 4, 1, 2, 5.

Each letter advances by +7 positions (with wrap-around) from one term to the next. L(12)→S(19)→Z(26)→Z+7=33−26=7→G. O(15)→V(22)→C(3, since 22+7=29−26)→C+7=10→J. Q(17)→X(24)→E(5, since 24+7=31−26)→E+7=12→L. Hence the missing term is GJL.

Each term follows \(a_{n+1}=2a_n+n\), where the added integer increases by 1 each step: \(13\times2+1=27\), \(27\times2+2=56\), \(56\times2+3=115\). Applying the next step: \(115\times2+4=234\). Hence the missing number is 234.

Sumitra's clue (after 13th, before 16th) leaves the 14th or 15th February. Her brother's clue (after 14th, before 17th) leaves the 15th or 16th February. The only date common to both ranges is 15th February.

From the clues: Moto is the highest; Energy is greater than only Lion, so Lion is lowest and Energy is second-lowest; Bull is not more than Red, so Red > Bull. Placing Red and Bull in the remaining 2nd and 3rd ranks with Red > Bull gives the order: Moto > Red > Bull > Energy > Lion. The drink with the second-most sugar is Red.

Letter inventory of CALCULATING: C(2), A(2), L(2), U(1), T(1), I(1), N(1), G(1). GAIN, TAIL, CULT can each be formed from these letters. TANING needs two N's, but CALCULATING contains only one N. Hence the word that cannot be formed is TANING.

Take the sum of alphabetical positions (A=1...Z=26) of each letter and multiply by 11. Check: WILDHORN: \(23+9+12+4+8+15+18+14=103\), and \(103\times11=1133\). RAPTURE: \(18+1+16+20+21+18+5=99\), and \(99\times11=1089\). Apply to PORTLOUIS: \(16+15+18+20+12+15+21+9+19=145\). \(145\times11=1595\). Hence the code is 1595.

Substitute A=−, B=+, C=÷, D=× and evaluate using BODMAS. Option 3: \(13\div13-13+13\times13 = 1-13+169 = 157\), which matches the stated value. Quick check of the others: Option 1 gives \(3-12+272=263\neq163\); Option 2 gives a non-integer; Option 4 gives \(\tfrac{18}{16}\times49-27+9\approx37.125\neq200\). Hence the correct statement is Option 3.

The rule from the examples is \((a\times b)+c\): \((8\times2)+5=21\) and \((1\times4)+8=12\), both matching. Applying to 9, 2, 5: \((9\times2)+5=18+5=23\). Therefore the answer is 23.

1) 9 and 6 = 9 2+ 6 2= 81 + 36 = 117 2) 8 and 2 = 8 2+ 2 2= 64 + 04 = 68 3) 7 and 3 = 7 2+ 3 2= 49 + 09 = 58 Thus, the answer is 58.

The 4 big triangles in diagonal position. 1 triangle at the top. The top triangle further contains 3 small triangles. It means total 4. 1 triangle at the bottom. The bottom triangle further contains 3 small triangles. It means total 4. 1 triangle at the left position. The left position further contains 3 small triangles. It means total 4. 1 triangle at the right position. The right position further contains 3 small triangles. It means total 4. Thus, there are 20 triangles in the given figure.

Statement I: All LED ⊂ Bulb. Statement II: Some Bulb ∉ Tube light. The LED subset of Bulb can lie wholly inside Tube light, wholly outside it, or overlap it — all are consistent with the premises. Since a valid arrangement exists in which no LED is a tube light, Conclusion I ("Some tube lights are LED") is not guaranteed. The same counter-example shows Conclusion II ("All LED are tube lights") is not guaranteed either. Hence neither conclusion follows.

In the first and the third diagram β, ¥, θ and η are adjacent to α. Thus, the one opposite of α is δ. Hence, the correct answer is δ. Trick: How to easily find the opposite faces: Choose any 2 dices which have only one number in common. After rotating the middle one, we get, FIGURE As in, II and III only θ is common. Now move clockwise as per the dice. In II, θ - δ - β In III, θ - α - η So, we can observe that δ is opposite to α and β is opposite to η. Now the only θ is left, which will be the opposite of γ. Note: There was an ambiguity in the original question in the previous year's paper. We have modified the figure of the cube in the first position to remove this.

Dogs and cats are pet animals but not all dogs and cats are pet. Thus, the answer is option 3.

To complete the diagram, we need one vertical line and two lines in slanting position which will complete the diagram. Thus, option 2 is the correct answer.

The question figure is hidden or embedded in such a manner that in the question, the circle has an arc at the top and bottom and a vertical line in the centre. Thus, the correct answer is option 2.

Hence, answer is figure 4.

A mirror when placed on the line AB. The figure K will appear at the right hand side. The figure J will appear on the left side. The alphabets Q, K and J will get reversed. Thus, the correct answer is option 2.

Each code is (row, column). Read each pair against the matrices: 00 → M (Matrix I), 41 → A (Matrix I), 99 → Z (Matrix II), 96 → E (Matrix II). All four match M, A, Z, E in order. The other options fail at the second or third letter (e.g., 04 = C, 88 = E, 69 = T). Hence the set for MAZE is 00, 41, 99, 96.

An indifference curve plots all combinations of two goods that give a consumer the same level of total utility (satisfaction), so the consumer is indifferent between any bundles on the same curve. It is not about income, capital, business income, or savings — those belong to budget lines and national-income concepts. Hence the correct option is Satisfaction derived from two goods.

Nationalisation of major commercial banks (1969, 1980) took place under Indira Gandhi → 3. Demonetisation of ₹500 and ₹1000 notes (Nov 2016) was announced under Narendra Modi → 1. The Mandal Commission report was implemented in 1990 by V.P. Singh → 4. The 1991 Liberalisation reforms were launched by P.V. Narasimha Rao → 2. Hence the match is a-3, b-1, c-4, d-2.

The concept of Judicial Review in India is borrowed from the Constitution of the United States, where it was established in Marbury v. Madison (1803). From the UK India took parliamentary government, from Ireland the Directive Principles, and from Canada the federal scheme with a strong centre — none of these supplied judicial review. Hence the answer is United States.

Article 57 of the Constitution states that a person who holds or has held the office of President shall be eligible for re-election to that office, without specifying any upper limit on the number of terms. Unlike the US Constitution (two-term cap), the Indian Constitution places no bar on re-election. Dr. Rajendra Prasad has so far been the only President to serve two terms. Hence the correct answer is No bar.

To avenge Lala Lajpat Rai's death after the Simon Commission lathi-charge, HSRA revolutionaries planned to kill SP James Scott but mistakenly shot Assistant SP John P. Saunders outside the Lahore police headquarters on 17 December 1928. The shots were fired by Bhagat Singh and Shivaram Rajguru; Sukhdev planned the action and Chandrashekhar Azad provided cover. Among the options, only Bhagat Singh fired at Saunders. Hence the answer is Bhagat Singh. (Note: the historical date is 17 December 1928, not 1927.)

The Bardoli Satyagraha of 1928 was a peasant movement in Gujarat against a steep hike in land revenue. Sardar Vallabhbhai Patel led it to a successful conclusion, forcing the British to roll back the increase; the grateful women of Bardoli gave him the title "Sardar". The Bhoodan Movement was led by Vinoba Bhave, the Rowlatt Satyagraha by Mahatma Gandhi, and the Swadeshi Movement by the Lal-Bal-Pal trio. Hence the answer is Bardoli Satyagraha.

The correct answer is Option 2: Tundra forests. Why Tundra Forests? The Tundra biome is characterized by extremely cold temperatures, harsh winds, permafrost (permanently frozen soil), and very short growing seasons. Because of these brutal conditions, large trees cannot survive. The Vegetation: The plant life in the tundra consists mostly of low-growing vegetation like lichens, mosses, grasses, and small shrubs. Survival Mechanism: Lichens and mosses are highly resilient. They don't need deep soil to grow and can survive by absorbing moisture and nutrients directly from the air and surface water, making them perfectly suited for the frozen tundra landscape. Quick Look at the Other Options: Taiga forests (Boreal Forests): Located just south of the tundra, these forests are dominated by coniferous, evergreen trees like pines, spruces, and firs. Temperate mixed forests: These regions feature a mix of broadleaf deciduous trees (like oak and maple) and coniferous trees, found in moderate climates. Tropical evergreen forests: These are lush, dense rainforests found near the equator, featuring massive trees, a multi-layered canopy, and incredible biodiversity (like the Amazon).

Deserts exhibit the largest diurnal temperature range, often exceeding 20°C between day and night. This is caused by low humidity (little water vapour to trap outgoing radiation), clear skies (no cloud blanket), and bare sandy surfaces that heat rapidly under intense sunlight and cool just as fast after sunset. Oceans have very small ranges due to water's high heat capacity; mountains and plateaus show moderate variation. Hence the answer is Desert.

The correct answer is Option 4: Vitamin A. Why Vitamin A? Vitamin A plays a crucial role in maintaining healthy vision. It is an essential component of rhodopsin, a protein found in the retina of your eyes that allows you to see in low-light and dark conditions. The Condition: When your body lacks Vitamin A, the production of rhodopsin drops, making it very difficult for the eyes to adjust to darkness. This condition is called Night Blindness (also known medically as nyctalopia). Severe Effects: Prolonged deficiency can lead to a more severe eye condition called Xerophthalmia, where the eyes become dangerously dry, potentially leading to permanent blindness.

The right side of the heart (right atrium and right ventricle) receives deoxygenated blood returning from the body via the superior and inferior vena cava. This blood is low in oxygen and high in carbon dioxide, commonly described as impure. It is then pumped through the pulmonary artery to the lungs for oxygenation. The left side carries oxygenated (pure) blood; the chambers are separated, so mixing does not occur in a healthy heart.

The liver is the largest gland in the human body, weighing about 1.4–1.6 kg in adults. It is also the largest internal organ. It functions as an exocrine gland by secreting bile and performs over 500 functions including detoxification, protein synthesis, and glycogen storage. The thyroid (~25 g), pancreas (~80 g), and kidneys are much smaller; kidneys are primarily excretory organs, not glands.

A hydraulic lift works on Pascal's law, which states that pressure applied to an enclosed incompressible fluid is transmitted undiminished in all directions. A small force \(F_1\) on a small piston of area \(A_1\) creates pressure \(P=F_1/A_1\). This pressure acts on the larger piston of area \(A_2\), producing \(F_2=F_1\,(A_2/A_1)\), giving force multiplication. Newton's law governs motion, Archimedes' deals with buoyancy, and Joule's with heat — none explain this.

Set the common numerical value as \(x\), so \(^\circ C = {^\circ F} = x\). Using the conversion \(^\circ F = \tfrac{9}{5}\,^\circ C + 32\): \[x = \tfrac{9}{5}x + 32\] \[x - \tfrac{9}{5}x = 32 \;\Rightarrow\; -\tfrac{4}{5}x = 32\] \[x = 32\times\left(-\tfrac{5}{4}\right) = -40\] Therefore \(-40\,^\circ C = -40\,^\circ F\), so the answer is -40.

MICR stands for Magnetic Ink Character Recognition. The letter I stands for Ink. It is a technology used mainly in banking to process cheques: characters are printed in special iron-oxide-based magnetic ink in a standardised font (E-13B or CMC-7), which a MICR reader magnetises and decodes. The magnetic property makes the data machine-readable, fast to process, and resistant to forgery.

The direct conversion of a solid to a gas (skipping the liquid phase) is called sublimation. It occurs when the substance's vapour pressure exceeds atmospheric pressure below its melting point. Common examples include dry ice (solid CO2), camphor, naphthalene balls, and iodine. Evaporation is liquid to gas, condensation is gas to liquid, and distillation is a separation technique using vaporisation followed by condensation.

Bronze is an alloy composed mainly of copper and tin, typically around 88% copper and 12% tin. Adding tin to copper increases hardness, lowers the melting point, and improves corrosion resistance — useful for tools, statues, bearings, and bells. The other combinations refer to different alloys: copper + zinc is brass; zinc + nickel and aluminium + nickel are not standard named alloys of common use.

Fly ash is the fine particulate residue carried up with the flue gases when pulverised coal is burned, captured by electrostatic precipitators before the stack. It consists mainly of silica, alumina, iron oxide, and calcium oxide. Hence it is produced by coal combustion power plants. Hydroelectric and tidal plants involve no combustion, and nuclear plants generate heat by fission, producing radioactive waste rather than ash.

The Dulari Kanya scheme was launched by the Government of Arunachal Pradesh to reduce infant mortality, especially among girl children. Under it, a fixed deposit is made in the name of a girl child born in a government or accredited hospital, encouraging institutional deliveries and improving newborn survival. The other states have their own girl-child schemes (Rajasthan's Rajshri, UP's Kanya Sumangala, MP's Ladli Laxmi) but not Dulari Kanya.

The Theory of Relativity was developed by Albert Einstein — Special Relativity in 1905 (introducing \(E=mc^2\) and the constancy of the speed of light) and General Relativity in 1915 (gravity as the curvature of spacetime). Newton formulated classical mechanics and universal gravitation, Darwin proposed evolution by natural selection, and Marie Curie pioneered work on radioactivity.

The Queensberry Rules, drafted in 1865 by John Graham Chambers and endorsed by the 9th Marquess of Queensberry, form the modern code for boxing. They introduced compulsory padded gloves, three-minute rounds with one-minute rest intervals, the ten-second count for a downed fighter, weight divisions, and a ban on wrestling holds — replacing earlier bare-knuckle traditions and shaping the sport as it is practised today.

Among the four, Amrita Shergill (1913–1941) was the distinguished painter. A Hungarian-Indian artist, she is regarded as a pioneer of modern Indian art, blending Western post-impressionist techniques with Indian subjects and miniature traditions; works like Bride's Toilet and Three Girls are iconic. Uday Shankar was a modern dance pioneer, while Sonal Mansingh and Yamini Krishnamurthy are celebrated classical dancers (Bharatanatyam/Odissi/Kuchipudi).

P. R. Sreejesh, the Indian hockey team goalkeeper, was conferred the Padma Shri 2017 in the Sports – Hockey category for his outstanding contribution as custodian of the national side, including captaining India at the 2016 Rio Olympics. Sardar Singh received the Padma Shri earlier in 2015; Ramandeep Singh and Yuvraj Walmiki were not among the 2017 awardees.

The biography "Hema Malini: Beyond the Dream Girl" was written by Ram Kamal Mukherjee, a film journalist and author. It was released on 16 October 2017, on Hema Malini's 69th birthday, and chronicles her journey across cinema, Bharatanatyam, and politics. Since it is a biography (not autobiography), Hema Malini herself is the subject, not the author; Meena Iyer and Vijay Kumar are unrelated to this title.

The correct answer is Great Britain. On 10 April 2017, the first direct freight train from Yiwu, China departed on the return service to London, covering roughly 7,500 miles (about 12,000 km) through Kazakhstan, Russia, Belarus, Poland, Germany, Belgium and France via the Channel Tunnel. This made London the 15th European city linked to China by rail freight under the Belt and Road Initiative. France and Kazakhstan are only transit countries on this route, and no comparable 2017 link to Pakistan exists.

The correct answer is Pakistan. SAARC summits rotate among the eight member states in English alphabetical order. The 18th Summit was hosted by Nepal in 2014, so Pakistan was due to host the 19th Summit, scheduled for Islamabad in November 2016. The summit was postponed after India, Bangladesh, Bhutan and Afghanistan withdrew following the Uri attack. Nepal had already hosted the previous summit, while Bhutan and India were not next in the rotation.

Step 1 — Set up the equation: Let the three consecutive odd numbers be \(x-2,\ x,\ x+2\). Their product is: \[(x-2)\,x\,(x+2)=x(x^2-4)=1287\] Step 2 — Estimate the middle term: Since \(\sqrt[3]{1287}\approx 10.88\), the middle odd integer must be \(x=11\). Step 3 — Verify: \[9\times 11\times 13 = 99\times 13 = 1287\ \checkmark\] The numbers are 9, 11, 13, so the largest is 13.

Step 1 — Relate men and boys: 45 men and 60 boys do equal work in the same time, so \(45M = 60B \Rightarrow 3M = 4B\), i.e. 3 men equal 4 boys in efficiency. Step 2 — Convert the mixed group: \(15\ \text{men} = 15\times\tfrac{4}{3}=20\ \text{boys}\). So 15 men + 20 boys = 40 boys. Step 3 — Find the days: Total work = \(60\times 20 = 1200\) boy-days. Days needed = \(\dfrac{1200}{40}=30\). Therefore the work takes 30 days.

Step 1 — Volume of the hemisphere: \[V_H=\tfrac{2}{3}\pi R^3=\tfrac{2}{3}\pi(6)^3=144\pi\ \text{cm}^3\] Step 2 — Volume of one small sphere: \[V_s=\tfrac{4}{3}\pi(1)^3=\tfrac{4}{3}\pi\ \text{cm}^3\] Step 3 — Conserve volume: \[N=\dfrac{V_H}{V_s}=\dfrac{144\pi}{\tfrac{4}{3}\pi}=144\times\tfrac{3}{4}=108\] Therefore 108 balls can be made.

Discount = MP − SP = \(1280-900=380\). \[\text{Discount \%}=\dfrac{380}{1280}\times 100=29.6875\%\] Rounded to two decimals, the discount is approximately 29.68%.

Step 1 — Set initial stock: Let the cans be \(8x,\ 9x,\ 15x\). Step 2 — Cans sold: Orange: \(25\%\) of \(8x = 2x\). Pineapple: \(\tfrac{1}{3}\) of \(9x = 3x\). Mixed: \(20\%\) of \(15x = 3x\). Step 3 — Remaining cans: \(8x-2x:9x-3x:15x-3x = 6x:6x:12x = 1:1:2\). Therefore the remaining ratio is 1 : 1 : 2.

Using the ratio as weights, the combined (weighted) average weight is: \[\bar{W}=\dfrac{2(18)+3(21)}{2+3}=\dfrac{36+63}{5}=\dfrac{99}{5}\ \text{kg}\] So the average weight of the whole class is \(\dfrac{99}{5}\) kg.

Step 1 — Costs and total volume: CP of milk \(=50\times 40=\text{Rs.}\ 2000\). Water is free, so total CP = Rs. 2000. Total mixture sold = \(50+5=55\) litres. Step 2 — Selling price and profit: \[SP = 55\times 42 = \text{Rs.}\ 2310,\quad \text{Profit}=2310-2000=310\] Step 3 — Profit percent: \[\text{Profit \%}=\dfrac{310}{2000}\times 100=15.5\%\] The dealer's profit is 15.5%.

Step 1 — Relative speed: Both move in the same direction, so the gap closes at \(10-8=2\) km/hr. Step 2 — Initial lead: By 8:30 am the first runner has been moving for 2.5 hours, covering \(8\times 2.5 = 20\) km. Step 3 — Time to overtake: \[t=\dfrac{20}{2}=10\ \text{hours after 8:30 am}\] 8:30 am + 10 h = 6:30 pm.

Step 1 — Head start: Runner 1 runs alone from 6:00 am to 8:30 am, i.e. 2.5 hr at 8 km/hr. \[\text{Gap} = 8 \times 2.5 = 20 \text{ km}\] Step 2 — Relative speed: Both move in the same direction, so the gap closes at \(10 - 8 = 2\) km/hr. Step 3 — Time to overtake: \[t = \frac{20}{2} = 10 \text{ hours after 8:30 am}\] 8:30 am + 10 hr = 6:30 pm.

For annual compounding, \(A=P\left(1+\dfrac{r}{100}\right)^t\), so \(P=\dfrac{A}{(1.12)^3}\). \[(1.12)^3 = 1.404928\] \[P=\dfrac{7727.104}{1.404928}=\text{Rs.}\ 5500\] The principal is Rs. 5500.

Using the identity \(\left(x-\dfrac{1}{x}\right)^2=\left(x+\dfrac{1}{x}\right)^2-4\): \[\left(x-\dfrac{1}{x}\right)^2 = 5^2-4 = 21\] Taking square roots, \(x-\dfrac{1}{x}=\pm\sqrt{21}\). The answer is \(\pm\sqrt{21}\).

Step 1 — Rationalise x: \[x=\dfrac{\sqrt 2+1}{\sqrt 2-1}\cdot\dfrac{\sqrt 2+1}{\sqrt 2+1}=\dfrac{(\sqrt 2+1)^2}{2-1}=3+2\sqrt 2\] Its conjugate gives \(\dfrac{1}{x}=3-2\sqrt 2\), so \(x+\dfrac{1}{x}=6\). Step 2 — Simplify the expression: \[\dfrac{x^5+x^4+x^2+x}{x^3}=x^2+x+\dfrac{1}{x}+\dfrac{1}{x^2}=\left(x^2+\dfrac{1}{x^2}\right)+\left(x+\dfrac{1}{x}\right)\] Step 3 — Evaluate: \(x^2+\dfrac{1}{x^2}=\left(x+\dfrac{1}{x}\right)^2-2 = 36-2 = 34\). Total = \(34+6=\) 40.

Recognise \(5-2\sqrt 6 = 3+2-2\sqrt 3\sqrt 2 = (\sqrt 3-\sqrt 2)^2\), so \(\sqrt x=\sqrt 3-\sqrt 2\) (taking the positive root). Rationalising the reciprocal: \[\dfrac{1}{\sqrt x}=\dfrac{1}{\sqrt 3-\sqrt 2}\cdot\dfrac{\sqrt 3+\sqrt 2}{\sqrt 3+\sqrt 2}=\sqrt 3+\sqrt 2\] Adding: \(\sqrt x+\dfrac{1}{\sqrt x}=(\sqrt 3-\sqrt 2)+(\sqrt 3+\sqrt 2)=\) \(2\sqrt 3\).

Expand and combine: \[27x + 27\left(x-\tfrac{1}{3}\right) = 27x + 27x - 9 = 54x - 9\] Set equal to 99: \[54x - 9 = 99 \implies 54x = 108 \implies x = 2\] Therefore x = 2.

For an equilateral triangle, the incentre, centroid and circumcentre coincide, and the centroid divides each median in a 2:1 ratio. Hence the circumradius is twice the inradius: \[R = 2r = 2 \times 10 = 20 \text{ cm}\] Therefore R = 20 cm.

The three angle bisectors of a triangle are concurrent, and their common point is the incentre — the centre of the inscribed circle, equidistant from all three sides. Perpendicular bisectors meet at the circumcentre, medians at the centroid, and altitudes at the orthocentre. Hence the answer is Incentre.

For any triangle, the angle formed at the orthocentre by two altitudes is supplementary to the opposite vertex angle: \[\angle BPC = 180^\circ - \angle A\] In an equilateral triangle, \(\angle A = 60^\circ\), so: \[\angle BPC = 180^\circ - 60^\circ = 120^\circ\] Therefore 120°.

Step 1 — Apply the Angle Bisector Theorem: \[\frac{BD}{DC} = \frac{AB}{AC} = \frac{3}{4}\] Step 2 — Use the shared-height property: Triangles ABD and ACD share vertex A with bases on BC, so their areas are in the ratio of their bases. \[\frac{[ABD]}{[ABC]} = \frac{BD}{BD+DC} = \frac{3}{7}\] Step 3 — Compute: \[[ABD] = \tfrac{3}{7} \times 350 = 150 \text{ cm}^2\] Therefore 150 cm².

Let C be the base of the lighthouse, A the initial boat position and B the position after 10 s. Height \(CD = 20\sqrt{3}\) m. Step 1 — Find AC and BC: \[AC = \frac{20\sqrt{3}}{\tan 30^\circ} = 20\sqrt{3}\cdot\sqrt{3} = 60 \text{ m}\] \[BC = \frac{20\sqrt{3}}{\tan 60^\circ} = \frac{20\sqrt{3}}{\sqrt{3}} = 20 \text{ m}\] Step 2 — Find speed: Distance AB = 60 - 20 = 40 m covered in 10 s, so speed = 4 m/s. Step 3 — Total time from A to C: \[t = \frac{AC}{\text{speed}} = \frac{60}{4} = 15 \text{ s}\] Therefore 15 seconds.

Combine over a common denominator using \((a-b)(a+b)=a^2-b^2\): \[\frac{\sec\theta}{\sec\theta-1} + \frac{\sec\theta}{\sec\theta+1} = \frac{\sec\theta(\sec\theta+1)+\sec\theta(\sec\theta-1)}{\sec^2\theta-1} = \frac{2\sec^2\theta}{\sec^2\theta-1}\] Apply \(\sec^2\theta-1=\tan^2\theta\): \[\frac{2\sec^2\theta}{\tan^2\theta} = \frac{2/\cos^2\theta}{\sin^2\theta/\cos^2\theta} = \frac{2}{\sin^2\theta} = 2\,\mathrm{cosec}^2\theta\] Therefore 2 cosec² θ.

Let the total runs scored be a Runs scored against New Zealand and Bangladesh = [(16 + 8)/100] × a ∴ Required ratio = [24a/100]/a = 24/100 = 6/25

% runs scored by pujara against South Africa = 24% % runs scored by pujara against Bangladesh = 8% ∴ Required % = [(24 - 8)/8] × 100 = 200%

Given: total runs scored by pujara = 1875 Runs scored by Pujara against South Africa = (24/100)(1875) = 450 Runs scored by Pujara against New zealand = (16/100)(1875) = 300 ∴ Required difference = 450 - 300 = 150

% of runs scored against Australia = 32% ∴ Sectorial angle made by it = (32/100)(360) = 115.2 degrees

Given: Percentages of runs scored by pujara = 8, 16, 20, 24, 32 Now, HCF of the above numbers = 4 So, least number of runs that Pujara must have scored in total = 100/4 = 25

When the feeling of annoyance is directed at a person, the standard preposition is with, not at. "Vexed at" is used for situations or events ("vexed at the delay"), while "vexed with" is used for people. The phrase should read "I am vexed with him". Hence the error is in part (1).

The reporting verb "warned" is in the past tense, so by the sequence-of-tenses rule the verb in the reported conditional clause must also shift to the past. "Persist" (present) should become "persisted" to agree with "warned" and the past conditional "would be punished". Hence the error is in part (2).

The sentence describes two parallel traits: Daniel "seldom spoke" (taciturn) and "never spent money". The blank needs an adjective for someone extremely reluctant to spend. Miserly fits perfectly — it means hoarding money and spending as little as possible. "Wary" means cautious (of danger), "discreet" relates to speech/judgement, and "cheap" is informal and less precise than miserly for this register.

The structure "too ___ to" needs an adjective describing a state that prevents the action. Timid means lacking courage or confidence, which directly explains why he could not speak before the Boss. "Shy" describes general social discomfort, "tired" refers to fatigue (unrelated), and "coward" is a noun — "too coward" is ungrammatical (the adjective form is "cowardly").

Reiterate means to say or do something again, usually for emphasis. The clearest synonym among the options is Repeat. "Abuse" means to misuse or insult, "pretend" means to feign, and "detest" means to dislike intensely — none relate to saying again.

Nincompoop is an informal noun for a foolish or silly person. The matching synonym is Fool. "Wise" is the opposite, while "lover" and "companion" describe relationships and have no link to foolishness.

Pellucid means transparent, clear, or easily understood. Its opposite is something cloudy or unclear — Murky. "Limpid" is a synonym (also means clear), "explicit" is closer in meaning than opposite, and "torpid" (sluggish) is unrelated to clarity.

Adamant means unyielding or refusing to change one's mind. Its opposite is Flexible — willing to bend or adapt. "Rigid", "fixed" and "unshakable" are all synonyms of adamant, not antonyms.

The idiom "to wrangle over an ass's shadow" means to quarrel or argue noisily about something completely trivial or insignificant. "Wrangle" is a synonym for quarrel, and an "ass's shadow" stands for something worthless. Hence, the best meaning is to quarrel over trifles. "To waste money over trifles" misses the quarrelling element, while the other options are unrelated to the idiom's sense.

The idiom "make one's flesh creep" describes causing a feeling of intense fear, horror, or revulsion — the skin-crawling sensation you get when something terrifies you. Hence it best means to frighten someone. "Confuse," "flatter," and "abuse" do not capture the element of dread or fear central to the idiom.

The "if" clause uses the past perfect ("had informed"), so this is a Type 3 conditional. The main clause must follow the pattern "would have + past participle" in the active voice, since Father is the doer of the appreciating. "Would have been appreciated" is passive and incorrectly makes the efforts the subject. The correct active form is "would have appreciated": "Father would have appreciated your efforts if you had informed him."

The adjective "surprised" takes the preposition "at" when followed by a noun denoting the cause of surprise (a result, news, reaction, etc.). "Surprised in" is non-idiomatic; "surprised to" pairs with an infinitive verb; "surprised from" is not standard English. Hence the correct phrase is "surprised at": "Neha was surprised at her result."

Oncology is the branch of medicine that deals with the study, diagnosis, and treatment of tumours, especially cancerous ones. The prefix "onco-" comes from the Greek word for tumour or mass. Oenology is the study of wine, phrenology is the pseudoscience of skull bumps, and "upology" is not a recognised term.

Zenith denotes the highest point — either the point in the sky directly overhead or, figuratively, the peak of success or power. Tempest means a violent storm, outpost is a remote military station, and archive is a collection of historical records — none of which carry the sense of "highest point."

The misspelt word is Leakeage. The correct spelling is Leakage — formed by adding the suffix "-age" directly to "leak," with no extra "e" before it. Literary, Laudable, and Loafer are all spelt correctly.

The misspelt word is Anasthetic. The accepted spellings are Anesthetic (American English) or Anaesthetic (British English) — never "Anasthetic." Obliterate, Concurrence, and Blithesome are all spelt correctly.

Q introduces the central idea — segmenting the micro-finance industry to widen credit access for the poor. R explains how this segmentation could work (multinationals at the top, development groups and regional banks below), so R follows Q. P then offers a qualification ("Yet making loans... is hardly a Poverty Cure"), and S adds the further factors ("Property rights and the role of law matter too") that complete the argument. Hence the coherent order is QRPS.

R sets the historical context ("India earlier days gave more importance to industry"). P uses the contrast marker "But" to introduce the change in scenario, so it follows R. S begins with "This is because," giving the reason — the post-9/11 rise in terrorism — so it follows P. Q then provides the concrete evidence: a higher military budget over the last ten years. Hence the logical order is RPSQ.

To turn an active sentence with a modal into the passive, the object becomes the subject and the verb takes the form modal + be + past participle. The general agent "one" is omitted. So "One should keep one's word" becomes "A word should be kept" — generalising "one's word" to "a word" and using "should be kept." The other options either use wrong tense ("be keeping"), wrong modal ("has to"), or introduce a wrong agent ("by us").

In reported speech, "Thanks" becomes the reporting verb "thanked", the pronoun "I" shifts to "he," the modal "shall" changes to "would," and "this kindness" becomes "his kindness" (Ankit's). The assurance clause is linked with "assured him that." Hence: "The old man thanked Ankit and assured him that he would never forget his kindness." Option 1 distorts the meaning, option 3 wrongly uses passive voice, and option 4 omits the assurance entirely.

The sentence describes uniting "all the people of the nation into a single whole," so the blank needs a verb meaning "to bring together." Combining fits exactly — it means joining diverse elements into one unified whole. "Segregating" means the opposite (separating); "residing" means living in a place; "complying" means obeying — none describe the act of unification.

National integration is described as something that "binds together all people" regardless of religion, caste or language — i.e., an abstract unifying feeling. The word that captures this is sentiment, meaning a shared feeling or emotional attitude. "Resources," "essentials," and "finances" are concrete or material in nature and cannot describe what emotionally binds a nation together.

The bond is one that unites every citizen despite differences of religion, caste, language or history — so the adjective must mean "shared by all." Common fits precisely: a "common bond" is one shared equally by everyone. "Real" describes authenticity, not sharedness; "nominal" means "in name only" (the opposite of a binding force); "similar" implies likeness rather than a single shared bond.

The blank modifies "cementing force" — the adjective must convey the force's power to bind diverse people into one nation. "Strong" captures exactly this binding effectiveness. "Weakening" is the opposite of binding; "natural" describes origin, not strength; "settled" describes a state, not the force's capacity. Hence the correct word is strong.

The passage centres on national integration — diverse people uniting as one nation. The blank pairs with "peacefully" to describe their mode of coexistence, which must signify unity. "Separately" contradicts integration; "jointly" implies a shared task, not shared living; "happily" describes feeling, not togetherness. Together directly expresses the unified coexistence the passage describes.