SSC CGL 2018 · 2019-06-13 · Shift 3

The relationship is letter-by-letter reversal: ACCIDENT → TNEDICCA. Applying the same reversal to PASSENGER (P-A-S-S-E-N-G-E-R) gives REGNESSAP, which matches option 2.

The terms form a geographical containment hierarchy from smallest to largest: city → state → region → country → continent. Mapping: Jaipur (3, city) → Rajasthan (1, state) → North India (4, region) → India (2, country) → Asia (5, continent). Hence the order is 3, 1, 4, 2, 5.

The code is twice the sum of the positional values of the letters. Check: J = 10, so \(2 \times 10 = 20\). For BAT, \(2 \times (2+1+20) = 2 \times 23 = 46\). For CRICKET: \(3+18+9+3+11+5+20 = 69\). Therefore code \(= 2 \times 69 = \mathbf{138}\).

Swap ÷ and ×. The equation becomes \(20 \times 20 + 20 - 25 \div 25\). Applying BODMAS: \(20 \times 20 = 400\) and \(25 \div 25 = 1\), giving \(400 + 20 - 1 = 419\), which matches the RHS. The other swaps yield 606, −604 and 476 respectively, so option 4 is correct.

Each term equals \(n^3 - 1\) where n is the position: \(1^3-1=0,\ 2^3-1=7,\ 3^3-1=26,\ \dots,\ 9^3-1=728\). For the 10th term: \(10^3 - 1 = 1000 - 1 = \mathbf{999}\).

Hence, “15” is the correct answer.

Decode from the inside out: “the wife of my husband” is Veena herself; “the son of the wife of my husband” is Veena's son; therefore the “sister of the son of the wife of my husband” is Veena's daughter. So Kavi is Veena's daughter, which makes Veena Kavi's mother.

Here, the arrow moves two places and three places in clockwise direction alternatively. Hence, the above figure will come next in the given series.

In each pair, the first number should equal the square of the second: \(14^2=196,\ 12^2=144,\ 15^2=225\). But \(11^2 = 121 \neq 123\), so 123 : 11 breaks the pattern and is the odd one out.

The first differences are 2, 4, 6, 8, 10, 12, 14, 16 — an arithmetic progression with common difference 2. The next difference is \(16 + 2 = 18\), so the next term is \(83 + 18 = \mathbf{101}\).

The cipher alternates +1, −1 on successive letters: F→G, R→Q, I→J, E→D, N→O, D→C gives GQJDOC. Applying the same to PEACE: P(+1)→Q, E(−1)→D, A(+1)→B, C(−1)→B, E(+1)→F — i.e. QDBBF.

Apple comes in the category of Fruit. But there is no relation between Fruit and vegetable. Hence, “Option 4” is the correct answer.

Count occurrences of the digit 7 by place value. Units place: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97 — 10 occurrences. Tens place: 70, 71, 72, …, 79 — 10 occurrences. The two lists count the two 7s of 77 separately, so the total is \(10 + 10 = \mathbf{20}\).

Cutting a painted cube into 27 equal pieces means \(n = 3\) along each edge. The cubes painted on exactly one face are the centre cubes of each face of the original cube. Using the standard formula \(6(n-2)^2\): \[6(3-2)^2 = 6 \times 1 = 6\] Therefore 6 small cubes are painted on one face only.

Each letter in the first cluster shifts forward by one position to give the second: A→B, F→G, K→L, P→Q (AFKP → BGLQ). Applying +1 to each letter of GLQV: G→H, L→M, Q→R, V→W, giving HMRW.

If we look closely, figure is hidden in option figure 1 as shown below. Hence, “Option 3” is the correct answer.

Hence, the above figure will be the final figure.

Each term follows the rule \(n^2 + 1\), where \(n\) is the position of the term: \(1^2+1=2,\ 2^2+1=5,\ 3^2+1=10,\ 4^2+1=17,\ 5^2+1=26,\ 6^2+1=37\). The missing term is the 7th, so \(7^2+1=49+1=\mathbf{50}\). This is confirmed by the next terms: \(8^2+1=65,\ 9^2+1=82,\ 10^2+1=101\).

Pedology (study of soils), Cardiology (study of the heart), and Seismology (study of earthquakes) are all scientific disciplines that study a specific natural or biological subject. Terminology, however, is the set of terms used in a specialised field — it deals with vocabulary, not a physical or natural phenomenon. Hence Terminology is the odd one out.

The relationship is \((n+1)^2\): \((19+1)^2 = 20^2 = 400\). Applying the same rule to 24: \((24+1)^2 = 25^2 = \mathbf{625}\).

From "All flowers are trees", every flower is a tree, so Some trees are flowers — Conclusion I follows. The premises fix no relation between trees and grasses: trees that are not flowers may or may not be grasses. So neither II (Some trees are grasses) nor III (No tree is a grass) follows individually. But they are contradictory — exactly one must be true — giving an either II or III case. Hence Conclusion I follows, and either II or III follows.

The series has 18 positions with 6 blanks at positions 1, 3, 6, 11, 14, 17. Testing each option by inserting its letters sequentially into the blanks yields no recognisable repeating block, cyclic, or progressive pattern in any case. Since none of acbcad, cdcbad, or bdbcba produces a coherent series, the answer is None of these.

The word is flipped horizontally Hence, “Option 1” is the correct answer.

The vowels in the English alphabet are A, E, I, O, U. Among the given letters, E, U, and I are vowels, while V is a consonant. Therefore V is the odd one out.

The pair School : Student links an institution to the person who goes there to receive its primary service (education). Similarly, a patient goes to a Hospital to receive its primary service (treatment). In the other pairs, the second word is a service-provider (judge, teacher, chef), not the recipient. Hence the matching pair is Hospital : Patient.

Following Operation Vijay (18 December 1961), the Portuguese Governor-General of Goa, Manuel António Vassalo e Silva, signed the Instrument of Surrender on 19 December 1961, ending roughly 450 years of Portuguese rule over Goa, Daman and Diu. 15 August 1947 marks India's independence from British rule, and 26 January 1948 has no relevance here — neither concerns the Portuguese territories.

In 1608, the Mughal throne was held by Jahangir (reigned 1605–1627), as Akbar had died in 1605. Captain William Hawkins arrived at Surat aboard the Hector and travelled to Agra, where Jahangir received him cordially — partly because Hawkins spoke Turki. Shah Jahan (from 1628) and Humayun (16th century) reigned outside this date, so Jahangir is the answer.

Vidarbha won the Ranji Trophy 2018-19, defeating Saurashtra in the final held at Nagpur. It was Vidarbha's second consecutive title, having also won the 2017-18 edition. Saurashtra were runners-up that season; Kerala were eliminated in the semi-finals and Karnataka in the quarter-finals.

The Khadi and Village Industries Commission Act was passed in 1956. It established KVIC as a statutory body under the Ministry of MSME, replacing the All India Khadi and Village Industries Board that had been set up in 1953. KVIC plans and promotes Khadi and village industries in rural areas through training, raw material supply, marketing, and financial assistance.

Mahe, an enclave of the Union Territory of Puducherry surrounded by Kerala on the west coast, is the smallest district in India by area — about \(9\ \text{km}^2\). Hailakandi (Assam, ~1,327 km²), Alirajpur (Madhya Pradesh, ~3,180 km²), and Guntur (Andhra Pradesh, ~11,391 km²) are far larger.

The Bardoli Satyagraha (1928) was a no-tax campaign by farmers of Bardoli taluka in Gujarat protesting a 22% hike in land revenue imposed by the Bombay Presidency despite poor crop conditions. Vallabhbhai Patel organised and led the movement, directing farmers to refuse the revised tax and enforcing a social boycott of collaborators. A government inquiry later struck down the hike. The women of Bardoli conferred on him the title 'Sardar' for his leadership. Nehru and Shastri were not involved, and Tilak had died in 1920.

Sushmita Sen was crowned Miss Universe 1994 in Manila, becoming the first Indian to win the title. Reita Faria was the first Indian to win Miss World (1966) — a different pageant. Madhu Sapre finished 2nd runner-up at Miss Universe 1992, and Persis Khambatta won Femina Miss India 1965 but did not place at Miss Universe.

An adult human skeleton has 206 bones — 80 in the axial skeleton (skull, vertebral column, ribs, sternum) and 126 in the appendicular skeleton (limbs and girdles). Newborns are born with about 300 bones, many of which fuse during growth — hence option 300 refers to infants, not adults.

According to FAO and NDDB data, India produced about 176 million tonnes of milk in 2017-18, contributing roughly 19% of global milk output, making it the world's largest milk producer. This dominance is driven by a large bovine population, smallholder dairy farming, and the cooperative movement launched under Operation Flood (the White Revolution) led by Dr Verghese Kurien.

Venus is the hottest planet, with a mean surface temperature of about 465°C — hotter than Mercury despite being farther from the Sun. Its atmosphere is roughly 96.5% carbon dioxide and exerts about 92 times Earth's surface pressure, producing a runaway greenhouse effect that traps solar radiation. Mercury, lacking a meaningful atmosphere, cools sharply on its night side, so its average temperature is far lower than Venus's.

The Chota Char Dham of North India lies entirely in Uttarakhand and comprises Yamunotri, Gangotri, Kedarnath and Badrinath. Vaishno Devi, in the Trikuta hills near Katra, Jammu & Kashmir, is a major Shakti Peetha pilgrimage but is not part of the Char Dham circuit. Hence it is the odd one out.

The Sun's diameter is about \(1{,}392{,}000\) km and Earth's about \(12{,}742\) km. \[\frac{1{,}392{,}000}{12{,}742}\approx 109.2\] So the Sun's diameter is approximately 109 times Earth's. Volumetrically, that means about \(109^{3}\approx 1.3\) million Earths could fit inside the Sun.

Kolkata Port (now Syama Prasad Mookerjee Port) on the Hooghly River is the oldest operating port built by the British East India Company. It was developed from Job Charnock's 1690 settlement at Sutanati and formally commissioned as a port in 1870, and continues to operate today. Madras (Chennai) and Bombay (Mumbai) ports were developed later as modern harbours, while Visakhapatnam Port opened only in 1933.

Guwahati, the largest city of Assam, was historically known as Pragjyotishpur — the 'City of Eastern Light/Astrology' — and served as the capital of the ancient kingdom of Pragjyotisha-Kamarupa mentioned in the Mahabharata and the Puranas, ruled by kings such as Naraka and Bhagadatta. Machilipatnam is in Andhra Pradesh, Bhagyanagara is an older name for Hyderabad, and Purushapura is ancient Peshawar.

The Pradhan Mantri Shram Yogi Maandhan (PM-SYM) pension scheme, launched in 2019 for unorganised-sector workers, has an entry-age window of 18 to 40 years. Anyone above 40 at the time of enrolment is ineligible. The figure 60 is the age at which beneficiaries start receiving the assured pension of Rs 3,000 per month — not the enrolment cut-off.

Indore (Madhya Pradesh) was ranked India's cleanest city in Swachh Survekshan 2019, conducted by the Ministry of Housing and Urban Affairs. It was Indore's third consecutive top rank (2017, 2018, 2019), driven by 100% door-to-door waste collection and effective source segregation. Mysuru topped the very first survey (2016); Surat and Ujjain were strong performers but did not win the top rank in 2019.

The Micro, Small and Medium Enterprises Development (MSMED) Act was enacted by Parliament in 2006 and came into force on 2 October 2006. It provided the first statutory definition and classification of micro, small and medium enterprises in both manufacturing and services, and set up Facilitation Councils to address delayed payments to MSMEs.

Diksha Dagar is the hearing-impaired Indian golfer who turned professional at 18 and won the South African Open in March 2019, becoming the second Indian (after Aditi Ashok) to win on the Ladies European Tour. She uses cochlear implants and has since become an inspirational figure in Indian women's golf. Aditi Ashok was the first Indian on the LET (2016), not the second; Gursimar Badwal and Vani Kapoor have not won on the LET.

The Pradhan Mantri Shram Yogi Maan-Dhan (PM-SYM) scheme, launched in 2019, provides an assured pension of Rs. 3,000 per month after the age of 60 to unorganised-sector workers whose monthly income is Rs. 15,000 or less. Eligibility also requires entry age between 18 and 40 years and non-coverage under EPFO, ESIC or NPS. Hence the prescribed income ceiling is Rs. 15,000.

The Ayushman Bharat - Pradhan Mantri Jan Arogya Yojana (PM-JAY), launched in September 2018, offers cashless secondary and tertiary hospitalisation cover of up to Rs. 5 lakh per family per year at empanelled hospitals. It is the world's largest government-funded health assurance scheme, targeting poor and vulnerable families identified through SECC 2011 data. The defined benefit ceiling is therefore Rs. 5 lakh.

Microlattice, unveiled by Boeing and HRL Laboratories in 2015, is a 3D open-cellular metallic structure of interconnected hollow nickel-phosphorus tubes. It is roughly 99.99% air, giving it an extremely low density, yet its lattice geometry yields a very high strength-to-weight ratio - hence the marketing description "lighter than air, stronger than steel". Molybdenum, titanium and iridium are dense conventional metals and do not match this description.

The Sao Joao festival, celebrated in Goa on 24 June in honour of St. John the Baptist, falls in the heart of the monsoon. To mark the season's bounty, Goans traditionally exchange fruits - especially mangoes, jackfruits and pineapples - with neighbours and relatives. Revellers also wear flower-and-leaf crowns called "kopel" and jump into wells, but the customary gift between households is fruit, not flowers, beer or fish.

Wilson's disease is an autosomal recessive disorder caused by mutations in the ATP7B gene, which codes for a copper-transporting protein in the liver. The defect prevents biliary excretion of excess copper, so it builds up first in the liver and then in the brain, eyes (Kayser-Fleischer rings), kidneys and joints, causing hepatic and neurological damage. Iron overload corresponds to haemochromatosis; calcium and sodium imbalances are unrelated to this disease.

Sukumar Sen, an ICS officer, was the first Chief Election Commissioner of India, serving from 21 March 1950 to 19 December 1958. He oversaw India's first two general elections (1951-52 and 1957) - an enormous logistical exercise involving over 170 million voters, most of them illiterate. T. N. Seshan (10th, 1990-96), M. S. Gill (11th, 1996-2001) and Sunil Arora (23rd, 2018-21) all held the office much later.

The westernmost point of the Indian mainland is the village of Guhar Moti in the Lakhpat taluka of Kutch district, Gujarat, located close to the Sir Creek area on the India-Pakistan border at roughly \(23.71^\circ\) N, \(68.03^\circ\) E. Dahod lies in eastern Gujarat, while Bharuch (south Gujarat) and Amreli (Saurashtra) are well inland of Kutch.

Identity: Cubing \(x+\tfrac{1}{x}\) gives \[\left(x+\tfrac{1}{x}\right)^3 = x^3+\tfrac{1}{x^3}+3\left(x+\tfrac{1}{x}\right)\] so \(x^3+\tfrac{1}{x^3}=k^3-3k\) where \(k=x+\tfrac{1}{x}\). Substitute \(k=5\): \[x^3+\tfrac{1}{x^3}=5^3-3(5)=125-15=110\] Therefore 110.

Identity: If \(a+b+c=0\), then \(a^3+b^3+c^3=3abc\). Step 1 - Match the form: Let \(a=x-5,\;b=x-6,\;c=x-7\). The given equation is exactly \(a^3+b^3+c^3=3abc\). Since \(a,b,c\) have different constants they cannot be equal, so the identity forces: \[(x-5)+(x-6)+(x-7)=0\] Step 2 - Solve: \[3x-18=0 \implies x=6\] Therefore x = 6.

Step 1 - List the interest values (Lakh Rs.): 23.4, 32.5, 41.6, 36.4, 49.4 for the years 1998-2002. Step 2 - Sum: \[23.4+32.5+41.6+36.4+49.4=183.3\] Step 3 - Average over 5 years: \[\text{Average}=\dfrac{183.3}{5}=36.66\] Therefore the average interest paid is Rs. 36.66 Lakh.

Step 1 - Convert mixed numbers: \(9\tfrac{3}{4}=\tfrac{39}{4},\;2\tfrac{1}{6}=\tfrac{13}{6},\;4\tfrac{1}{3}=\tfrac{13}{3},\;2\tfrac{1}{2}=\tfrac{5}{2}\). Step 2 - Innermost bracket: \[\tfrac{5}{2}+\tfrac{3}{4}=\tfrac{10+3}{4}=\tfrac{13}{4}\] Step 3 - Braces: \[\tfrac{13}{3}-\tfrac{13}{4}=\tfrac{52-39}{12}=\tfrac{13}{12}\] Step 4 - Square bracket: \[\tfrac{13}{6}\div\tfrac{13}{12}=\tfrac{13}{6}\times\tfrac{12}{13}=2\] Step 5 - Outer division: \[\tfrac{39}{4}\div 2=\tfrac{39}{8}\] Therefore the value is \(\tfrac{39}{8}\).

From the table, Printing = 20% and Royalty = 15%. The difference in percentage points is \(20-15=5\). The question asks how much less royalty is compared to printing, so printing is the base: \[\frac{20-15}{20}\times 100=\frac{5}{20}\times 100=25\%\] Therefore royalty expenditure is 25% less than printing expenditure.

Add the sales (in thousands) of branches B1, B3, B6 across both years: \[\underbrace{(80+105)}_{B1}+\underbrace{(95+110)}_{B3}+\underbrace{(70+80)}_{B6}=185+205+150\] \[=540\text{ thousand}\] Therefore the total is 540 thousand.

Step 1 — Use the cyclic quadrilateral property: Opposite angles are supplementary, so \(\angle ABC=180^\circ-\angle ADC=180^\circ-129^\circ=51^\circ\). Step 2 — Angle in a semicircle: Since AB is the diameter, \(\angle ACB=90^\circ\) (angle in a semicircle). Step 3 — Apply the triangle angle sum in ▵ABC: \[\angle BAC=180^\circ-90^\circ-51^\circ=39^\circ\] Therefore ∠BAC = 39°.

Step 1 — Head start of A: In 4 hours A covers \(4\times 4=16\) km. Step 2 — Relative speed: B gains on A at \(10-4=6\) kmph. Time to close the 16 km gap: \[t=\frac{16}{6}=\frac{8}{3}\text{ hours}\] Step 3 — Distance from start: Distance B travels in this time: \[10\times\frac{8}{3}=\frac{80}{3}\approx 26.67\text{ km}\] Therefore B catches A 26.67 km from the starting point.

The amount at the end of year 5 is the year-4 amount grown by one year's interest. Dividing the two amounts eliminates the principal: \[\frac{A_5}{A_4}=1+\frac{R}{100}=\frac{2409}{2190}\] Compute the increase: \(\frac{2409-2190}{2190}=\frac{219}{2190}=\frac{1}{10}\). So \(\frac{R}{100}=\frac{1}{10}\), giving R = 10%.

Daily wages: A earns \(180\times 7=1260\) per day; B earns \(160\times 5=800\) per day. Ratio: \[\frac{1260}{800}=\frac{63}{40}\] Therefore the ratio of wages of A to B is 63 : 40.

Single discount: 30% of 2000 = Rs. 600, leaving Rs. 1400. Successive discounts: After 25%, price is \(2000\times 0.75=1500\). After a further 5%, price is \(1500\times 0.95=1425\). Equivalent single rate \(=25+5-\dfrac{25\times 5}{100}=28.75\%\), less than 30%. Difference in final prices = \(1425-1400=\) Rs. 25.

When O is the intersection of the bisectors of the two exterior angles at B and C of ▵ABC, the standard result is: \[\angle BOC=90^\circ-\tfrac{1}{2}\angle A\] Derivation: Exterior angles satisfy \(\angle CBD=\angle A+\angle C\) and \(\angle BCE=\angle A+\angle B\). In ▵BOC, \(\angle OBC+\angle OCB=\tfrac{1}{2}(\angle CBD+\angle BCE)=\angle A+\tfrac{1}{2}(\angle B+\angle C)=\angle A+\tfrac{1}{2}(180^\circ-\angle A)=90^\circ+\tfrac{1}{2}\angle A\). Hence \(\angle BOC=180^\circ-(90^\circ+\tfrac{1}{2}\angle A)=90^\circ-\tfrac{1}{2}\angle A\). With \(\angle A=50^\circ\): \(\angle BOC=90^\circ-25^\circ=\) 65°.

Use \(\cot\theta=\tan(90^\circ-\theta)\) on the RHS: \[\cot(45^\circ+2x)=\tan(45^\circ-2x)\] The equation becomes \(\tan x=\tan(45^\circ-2x)\), giving \(x=45^\circ-2x\), hence \(3x=45^\circ\). Therefore x = 15°.

First term: Since \(66^\circ=90^\circ-24^\circ\), we have \(\sin 66^\circ=\cos 24^\circ\) and \(\cos 66^\circ=\sin 24^\circ\). So numerator and denominator both equal \(\sin^2 24^\circ+\cos^2 24^\circ=1\), making the fraction \(=1\). Second part: \(\sin 29^\circ=\cos 61^\circ\), so \(\cos 61^\circ\sin 29^\circ=\cos^2 61^\circ\). Then \(\sin^2 61^\circ+\cos^2 61^\circ=1\). Total \(=1+1=\) 2.

Let the number be \(x\). Then: \[0.85x+75=x\implies 75=0.15x\implies x=\frac{75}{0.15}=500\] Check: 85% of 500 = 425, and \(425+75=500\). Therefore the number is 500.

Step 1 — Equivalent work units: Take 1 man's daily work as \(M\). Then 1 woman = \(3M\) and 1 boy = \(\tfrac{M}{2}\). Step 2 — Group rate per day: \[3M+4(3M)+6\left(\tfrac{M}{2}\right)=3M+12M+3M=18M\] Step 3 — Total work: Total = \(18M\times 6=108M\) man-days. Step 4 — Women needed in 4 days: One woman does \(3M\) per day, so in 4 days she does \(12M\). Number of women = \(\dfrac{108M}{12M}=9\). Therefore 9 women are required.

Step 1 — Angle at centre: A radius is perpendicular to the tangent at the point of contact, so \(\angle OAP = \angle OBP = 90^\circ\). In quadrilateral PAOB the angles sum to \(360^\circ\): \[\angle AOB = 360^\circ - 90^\circ - 90^\circ - 40^\circ = 140^\circ\] Step 2 — Base angle of isosceles ΔOAB: Since \(OA = OB\) (radii), \(\angle OAB = \angle OBA\). Using the angle sum of the triangle: \[\angle OAB = \frac{180^\circ - 140^\circ}{2} = 20^\circ\] Therefore \(\angle OAB = 20^\circ\).

Average \(= 0\) implies the sum of all 27 numbers is \(0 \times 27 = 0\). To maximise positives, keep just one number negative and let it offset the rest. For example, 26 numbers equal to \(1\) and one number equal to \(-26\) give a total of \(26 + (-26) = 0\). All 27 cannot be positive, since their sum would then be strictly positive. Hence at most 26 numbers can be greater than zero.

In an equilateral triangle the centroid, circumcentre and incentre coincide, and the centroid divides every median in the ratio \(2:1\) from vertex to opposite side. The longer segment is the circumradius \(R\) and the shorter segment is the inradius \(r\), giving the standard relation: \[R = 2r \implies r = \frac{R}{2} = \frac{8}{2} = 4 \text{ cm}\] Therefore the inradius is 4 cm.

When an integer n is divided by 8, then remainder is 3 Let the value of n be 11 which satisfied the condition. According to the question ⇒ (6n – 1) ÷ 8 ⇒ (6 × 11 – 1) ÷ 8 ⇒ (66 – 1) ÷ 8 ⇒ 65 ÷ 8 Remainder will be 1

Step 1 — Convert percentages to actual marks (max = 120): A: \(108\), B: \(96\), C: \(84\), D: \(96\), E: \(102\), F: \(78\), G: \(60\). Step 2 — Sum: \[108+96+84+96+102+78+60 = 624\] Step 3 — Average over 7 students: \[\frac{624}{7} \approx 89.142857 \approx 89.14\] Therefore the average is 89.14.

Volume is conserved when a solid is melted and recast. The number of small spheres equals the volume ratio, and the \(\frac{4}{3}\pi\) factor cancels: \[n = \frac{R^3}{r^3} = \frac{6^3}{2^3} = \frac{216}{8} = 27\] Therefore 27 spheres can be made.

Given \(40 \cdot SP = 50 \cdot CP\), the per-article ratio is: \[\frac{SP}{CP} = \frac{50}{40} = \frac{5}{4}\] Since \(SP > CP\), there is a gain. Taking \(CP = 4\) and \(SP = 5\): \[\text{Gain \%} = \frac{SP - CP}{CP} \times 100 = \frac{1}{4} \times 100 = 25\%\] Therefore the transaction is a 25% gain.

The expression should be read as \(3\cos^2 A + 7\sin^2 A = 4\). Replace \(\cos^2 A = 1 - \sin^2 A\): \[3(1-\sin^2 A) + 7\sin^2 A = 4 \implies 3 + 4\sin^2 A = 4\] \[\sin^2 A = \frac{1}{4} \implies \sin A = \frac{1}{2}\] For an acute angle this gives \(A = 30^\circ\), so: \[\cot A = \cot 30^\circ = \sqrt{3}\] Therefore \(\cot A = \sqrt{3}\).

Use the identity \(a^3 - b^3 = (a-b)(a^2 + ab + b^2)\). Substituting the given values: \[208 = 4(a^2 + ab + b^2) \implies a^2 + ab + b^2 = 52\] Expand the target expression: \[(a+b)^2 - ab = a^2 + 2ab + b^2 - ab = a^2 + ab + b^2\] Therefore \((a+b)^2 - ab = \mathbf{52}\).

To illuminate means to light up or make bright. Its direct opposite is darken, meaning to make dark or dim. "Light" is a synonym, not an antonym; "add" and "erase" are unrelated to brightness. Hence the antonym is darken.

The contraction he's stands for he is, and at dinner time the tusker receives the food rather than giving it. The passive construction "is + past participle" is required, so the past participle fed fits: "he's fed balls made of steamed ragi flour". "Feeding" would make him the one giving food; "feed" and "feeds" cannot follow "is". Hence the answer is fed.

The standard spelling of the verb meaning to select from alternatives is choose (double o, ending in se). "Chooj", "chuse" and "chooze" are all non-standard misspellings. Therefore the correctly spelt word is choose.

"Done" is the past participle of do and needs an auxiliary such as have/has/had. For a completed action in the simple past, the correct form is did: "I did a lot of work today." The other segments — "a lot of", "work today" and "she said" — are grammatically fine. The error therefore lies in "I done".

The sentence lists energising effects of colours: energize, make you active, and the blank. The required word must continue that positive, energising theme. Invigorate means to fill with life, energy, or vitality, which fits perfectly alongside energize and active. Involve (engage) and interest (arouse curiosity) do not convey physical energy; enrage (anger) is negative and contradicts the tone. Hence the blank is filled by Invigorate.

scramble is the only word spelt correctly. The others should be: defnition → definition (missing i after def), jewlri → jewellery / jewelry, and acceptence → acceptance (ends in -ance, not -ence).

The idiom suit you, when said of clothing or accessories like glasses, means the item flatters the wearer's appearance — it looks very good on your face. Make you look weird is the opposite meaning; need to be worn with a suit mistakes the noun suit for the verb; not suitable for your work shifts the meaning to task-suitability, not appearance.

Sentence C opens the scene (the bus inching through evening traffic that keeps growing). D follows as the direct result — no space on the road anymore. A then describes the consequence for the cyclist, who is forced onto the pavement. B closes with the mishap when he tries to return to the road (the pronoun he clearly refers back to the man in A). Hence the correct order is CDAB.

The active sentence is in the simple present tense (Ananya plucks). The passive form is: Object + is/am/are + past participle + by + subject. With the plural object fresh flowers as the new subject, the auxiliary is are and the past participle is plucked: Fresh flowers are plucked by Ananya from the garden every day. Have been plucked (present perfect) and were plucked (simple past) shift the tense; option 3 garbles the subject and object.

The phrase is balls made of steamed ragi flour mixed ___ some rice, green gram, salt and jaggery. To list ingredients that are combined together, English uses with after mixed — e.g. flour mixed with water. From indicates origin, by introduces an agent, and of is not idiomatic with mixed when listing components. Hence the blank takes with.

Two grammar points apply. First, when Scarcely begins a sentence, the clause is inverted: auxiliary before subject (had he gone out). Second, the correlative pair is Scarcely … when (than goes with No sooner, not with Scarcely). Only option 3, had he gone out when, preserves the inversion and uses the correct conjunction. The full sentence reads: Scarcely had he gone out when a client came to meet him.

The clause ___ are half-a-dozen Forest Department [officials] around needs an introductory word that asserts the existence of people in the vicinity. The standard existential construction in English is There + be (There are six people in the room). Nowhere would negate their presence, contradicting around; Everywhere wrongly implies omnipresence; Here is possible but less natural for a descriptive passage about a distant scene. Hence the blank is filled by There.

The rule: use between for two parties and among for three or more. Since the sentence mentions exactly two families, among is wrong; the correct preposition is between. Option 1 keeps among and shifts to the future tense; option 2 has the ungrammatical has exist; option 4 leaves the error in place. Only option 3, exists between the two families, fixes the preposition while keeping the present tense.

Attribute (noun) means a characteristic or feature belonging to a person or thing — e.g. patience is one of her finest attributes. The closest match among the options is quality, which likewise denotes an inherent characteristic. Speech refers to talking, praise is an expression of approval, and respect is a feeling of admiration — none of these denote an inherent trait.

The phrase is Field Director ___ ATR, linking a designation to the organisation it heads. English uses of to show this affiliation — President of India, CEO of the company, Field Director of ATR. Among needs a group, on suits surfaces or topics, and between needs two entities — none fit a title-organisation link. Hence the blank takes of.

Deficit denotes a shortfall — the amount by which something (especially money) falls short of what is required. Its direct opposite is surplus, meaning an excess beyond what is needed (e.g. budget deficit vs budget surplus). Adhere (stick to) and remove (take away) are unrelated; credit is the accounting counterpart of debit, not of deficit.

As a verb, fuse means to join, blend, or merge two or more things into one whole (often by melting). The closest synonym among the options is combine, which similarly means to unite or merge into a single entity. "Unused" and "correct" are unrelated to joining, while "break" is the antonym of fuse.

Sentence B introduces the topic by stating that opening a bank account can seem intimidating. D follows with the reassuring counterpoint signalled by "Fortunately", pointing to a standardised process. C then elaborates what that process involves (providing details and funding the account). A concludes with the outcome once formalities are complete. Hence the order is BDCA.

The judiciary is the branch of government comprising the courts; it interprets laws, administers justice, and runs the legal system. The legislature makes laws, the executive implements them, and the police are an enforcement wing of the executive — none of these is responsible for the legal system itself.

The idiom "to one's heart's content" means doing something as much or as long as one wishes, until fully satisfied. Applied to the sentence, the dog played in the pond as much as he wanted to. The other options wrongly imply a physical limit, caution, or harmful excess, none of which the idiom carries.

A barometer is the instrument used to measure atmospheric pressure, typically via a column of mercury or an aneroid cell. A thermometer measures temperature, an ammeter measures electric current, and an altimeter measures altitude (though it may infer height from pressure changes).

The blank needs a verb meaning to take part in a contest. Compete fits precisely: women in ancient Greece were barred from competing in the Olympic Games. Comply means to obey rules, cope means to manage difficulty, and collide means to crash — none describes participation in a sporting event.

The opening participial phrase "Entering the hall" must logically be performed by the subject of the main clause. Here the subject is "the show", but a show cannot enter a hall — making this a dangling modifier. The error therefore lies in the segment "Entering", which heads the misattached phrase. A correct version would be: "Entering the hall, I found that the show had started."

To convert from passive to active, the agent (his grandmother) becomes the subject, the original subject (Dinesh) becomes the object (him), and the passive verb was looked after reverts to the simple past looked after. The subordinate clause stays unchanged. This gives: "Dinesh's grandmother looked after him when his parents went abroad." Option 1 wrongly uses present tense; Option 3 reverses the roles; Option 4 shifts to past continuous.

The blank follows "half-a-dozen Forest Department ____ around", requiring a plural noun denoting authorised staff. Officials fits — it collocates naturally with Forest Department and matches the presence of senior personnel like the Field Director. Person is singular and ungrammatical here; ministers are political heads, unlikely at a routine camp scene; employee is singular and too generic.