SSC CGL 2018 · 2019-06-19 · Shift None · Re-exam

Figure 1 has 2 sides; figure 2 has 3 sides; figure 3 has 4 sides. Therefore, figure 4 must have 5 sides. Hence, the figure in option 1 is the correct answer.

The natural hierarchy from smallest to largest geographical unit is: City → State → Country → Continent → World. Substituting the labels (City=3, State=5, Country=2, Continent=4, World=1) gives the sequence 3, 5, 2, 4, 1, which matches option 4.

The differences between consecutive terms form the sequence of consecutive odd numbers: \(100-99=1,\ 99-96=3,\ 96-91=5,\ 91-84=7,\ 84-75=9,\ 75-64=11\) The next subtraction is \(13\), so the missing term is: \(64-13=51\) Therefore the answer is 51.

Check the relation between 4 and 67. Since \(4^3=64\) and \(64+3=67\), the rule is \(n \to n^3+3\). Applying it to 8: \(8^3+3=512+3=515\) Therefore the missing number is 515.

Pattern: each letter shifts +4 positions. CDF (3,4,6) → GHJ (7,8,10). Apply to KLN (11,12,14): \(11+4=15\,(O),\ 12+4=16\,(P),\ 14+4=18\,(R)\). Therefore the answer is OPR.

A cube has 6 faces in 3 pairs of opposite faces. Opposite faces are not adjacent, so each opposite pair can share one colour. Assign one colour to each of the 3 opposite-face pairs: top–bottom, front–back, left–right. Every adjacency lies between faces from different pairs, so no two adjacent faces share a colour. Two colours fail because the four side faces around a top face are mutually adjacent and cannot all take the single remaining colour. Hence the minimum is 3.

Consecutive differences are \(3,5,7,9,11,13,15,17\) — successive odd numbers. The next difference is \(19\), so the next term is \(83+19=102\). Therefore the answer is 102.

The least possible Venn diagram is: Hence, the figure in option 4 is the correct answer.

Pattern from PICTURE → RHESWQG: alternating shifts of \(+2,-1,+2,-1,+2,-1,+2\) on letter positions. Apply to MOUNTAIN: M\((+2)\)=O, O\((-1)\)=N, U\((+2)\)=W, N\((-1)\)=M, T\((+2)\)=V, A\((-1)\)=Z, I\((+2)\)=K, N\((-1)\)=M. Therefore MOUNTAIN is coded as ONWMVZKM.

Hence, the minimum number of straight lines required to construct the given figure are 13.

When folded given figure will appear as shown below:

A right-side mirror reverses letter order and laterally flips each letter. MINT reversed is TNIM. Letters T, I, M are laterally symmetric and look unchanged; N flips to its mirrored form (shown as И in the options). Therefore the mirror image is TИIM.

Rule: \(n \to n+\sqrt{n}\). Check: \(961+\sqrt{961}=961+31=992\). Apply to 841: \(\sqrt{841}=29\), so \(841+29=870\). Therefore the answer is 870.

Diabetes results from a deficiency or dysfunction of insulin, the hormone that regulates blood glucose. The analogy is disease : substance whose deficiency causes it. Iron-deficiency anaemia, the most common form of anaemia, is caused by a lack of iron, which is needed to synthesise haemoglobin in red blood cells. Blood is the tissue affected, not the deficient substance; water and "harmon" do not fit. Therefore the answer is Iron.

China : Beijing is a country : capital pair. Iraq is a country and Baghdad is its capital, matching exactly. Japan : Yen is country : currency; Sweden : Madrid is wrong (Stockholm is Sweden’s capital); Dollar : USA reverses the order to currency : country. Therefore the answer is Iraq : Baghdad.

Similarly, Hence, ‘TCASRO’ is the correct answer.

Code = sum of alphabetical positions (A=1 … Z=26). Check: PROPERTY = \(16+18+15+16+5+18+20+25=133\); ESTATE = \(5+19+20+1+20+5=70\). DEVELOPMENT = \(4+5+22+5+12+15+16+13+5+14+20=131\). Therefore the answer is 131.

Hence, the figure in option 3 is the correct answer.

Consecutive differences are constant: \(180-162=198-180=216-198=234-216=288-270=18\). The series is an AP with common difference 18. The missing term is \(234+18=252\), and \(252+18=270\) confirms the next term. Therefore the answer is 252.

To divide a roll into 11 pieces requires \(11-1=10\) cuts. Reading the rate as 50 cuts per minute, total cuts in 25 minutes are \(50\times 25=1250\). Number of rolls = \(\dfrac{1250}{10}=125\). Therefore the answer is 125 rolls.

Check the ratio of first to second in each pair: \(90/18=5,\ 150/30=5,\ 60/12=5\), but \(100/25=4\). Three pairs follow the rule “first = 5 × second”; only (100, 25) breaks it. Therefore the odd pair is 100, 25.

Conclusion III follows by immediate conversion of "Some rabbits are ducks": a particular affirmative converts to "Some ducks are rabbits." Conclusion I ("No horse is a duck") does not follow. "No dog is a horse" only separates dogs from horses; ducks that are not dogs could still be horses. Conclusion II ("No dog is a rabbit") does not follow. The ducks that are dogs may or may not overlap with the ducks that are rabbits, so a dog being a rabbit is possible. Hence only Conclusion III follows.

Check the gaps between consecutive letters: EGIK gives +2, +2, +2; SUWY gives +2, +2, +2; PRTV gives +2, +2, +2. LNPQ gives L(12) → N(14) → P(16) → Q(17), i.e. +2, +2, +1. Three clusters follow a constant gap of two, while LNPQ breaks the pattern at the last step.

Vikram states "I have no brother and sister," so "my father's son" must be Vikram himself. Therefore "the wife of my father's son" is Vikram's wife. Kumar's mother is Vikram's wife, which makes Vikram Kumar's father. Hence Kumar is Vikram's son.

Two letters are "opposite" in the alphabet when their positions sum to 27 (A+Z, B+Y, ...). Check each pair: PK → 16+11 = 27, HS → 8+19 = 27, CX → 3+24 = 27. LQ → 12+17 = 29. Three clusters are opposite-letter pairs; LQ is not, so it is the odd one out.

Dr. B. R. Ambedkar served as independent India's first Law Minister in Jawaharlal Nehru's cabinet from 1947 to 1951, alongside chairing the Drafting Committee of the Constituent Assembly. For reference, R. K. Shanmukham Chetty was the first Finance Minister, Jagjivan Ram the first Labour Minister and Baldev Singh the first Defence Minister.

Amylase breaks down complex carbohydrates such as starch into simpler sugars like maltose and glucose. Digestion begins in the mouth with salivary amylase (ptyalin) and continues in the small intestine with pancreatic amylase. Protease and peptidase act on proteins and peptides, while lipase digests fats, so they do not target carbohydrates.

Raja Todar Mal was Akbar's Finance Minister (Diwan-i-Ashraf). He introduced the Dahsala (Zabt) revenue system, which fixed the state's share based on the average produce and prices of crops over the preceding ten years. His reforms standardised land measurement and revenue assessment, forming the financial backbone of Akbar's administration.

Football is the official state sport of Goa. The game took root during Portuguese rule and remains the most widely played and followed sport in the state, which has produced numerous national-level players and clubs such as Salgaocar, Dempo and Churchill Brothers. Kabaddi is the state sport of Punjab and Tamil Nadu, not Goa.

A battery stores energy in its electrolyte and electrode materials. When the circuit is closed, a redox reaction transfers electrons from anode to cathode, releasing the energy held in chemical bonds as electrical energy. Hence a battery converts chemical energy into electrical energy. Solar cells use light, generators use mechanical energy, and thermoelectric devices use heat.

India's first lunar probe was Chandrayaan-1, launched by ISRO on 22 October 2008 aboard a PSLV-XL from Sriharikota. It orbited the Moon until August 2009 and confirmed the presence of water molecules on the lunar surface. Bhaskara-1 was an Earth-observation satellite, while Surya-1 and Chandragupta 1 are not ISRO missions.

Coorg (Kodagu) in Karnataka is known as the "Scotland of India" because of its rolling Western Ghats hills, mist-covered valleys, dense forests and sprawling coffee and spice plantations that resemble the Scottish Highlands. Darjeeling and Shimla are popularly called the "Queen of the Hills," not the Scotland of India.

SEBI was first set up as a non-statutory body in 1988. It was given statutory status through the SEBI Act, 1992, which made it the independent regulator of India's securities market under the Ministry of Finance. Since the question concerns its formal establishment as a statutory authority, the correct year is 1992.

Bhanu Athaiya won the Academy Award for Best Costume Design at the 55th Academy Awards for her work on Richard Attenborough's Gandhi (1982). She was the first Indian to win an Oscar in any category. Ritu Kumar, Nita Lulla and Ritu Beri are noted Indian fashion/costume designers but none has received an Academy Award.

Pramod Sawant became Chief Minister of Goa in March 2019 after the death of Manohar Parrikar. He represents the Sanquelim constituency in North Goa, which he has held since 2012. Calangute, Poriem and Navelim are other Goa Assembly seats, but none of them is Sawant's constituency.

The ritual described is Saka (also spelt Shaka) — the final do-or-die charge made by Rajput warriors when defeat in a siege was certain. The men donned saffron robes and rode out to fight to the death, while the women performed Jauhar (self-immolation) inside the fort. Famous instances occurred at Chittorgarh, Ranthambore and Jaisalmer. The Maratha, Sikh and Mughal traditions did not follow this specific ritual.

Under Odisha's KALIA (Krushak Assistance for Livelihood and Income Augmentation) scheme, eligible farmers could avail short-term crop loans of up to Rs 50,000 at 0% interest for the Kharif 2019 season. The scheme also provides direct income support of Rs 25,000 over five seasons to small and marginal farmers, but the 0% interest crop-loan ceiling was Rs 50,000.

Sikandar Lodi, the Lodi Sultan, founded the city of Agra in 1504 and shifted his capital from Delhi to Agra in 1506 to better control the rebellious Rajput chiefs of the region. Humayun, Jahangir and Shah Jahan all used Agra during their reigns, but they inherited it as an existing capital — Shah Jahan in fact later moved the capital to Shahjahanabad (Delhi).

The Blue Umbrella is a 1980 novella by Ruskin Bond, set in a Himachal village and centred on a girl named Binya who trades her lucky leopard-claw pendant for a blue umbrella. It was adapted into a National Award-winning film by Vishal Bhardwaj in 2005. Jhumpa Lahiri (Interpreter of Maladies), Aravind Adiga (The White Tiger) and R K Narayan (Malgudi Days) are unrelated to this work.

Viswanathan Anand, the chess Grandmaster and multiple-time World Champion, was conferred the Padma Vibhushan in 2007 — making him the first sportsperson in India to receive the country's second-highest civilian honour. Sachin Tendulkar received the Padma Vibhushan in 2008 (and later the Bharat Ratna in 2014). Pankaj Advani and Michael Ferreira are Padma Bhushan/Padma Shri awardees but have not received the Padma Vibhushan.

India's first Lokpal, constituted in March 2019, was chaired by Justice Pinaki Chandra Ghose with four judicial and four non-judicial members. Archana Ramasundaram — a former IPS officer and ex-Director General of the Sashastra Seema Bal — was one of the four non-judicial members. Justice Abhilasha Kumari, Justice Dilip B. Bhosale and Justice P. K. Mohanty served as judicial members of the same body.

India's Position in the World Bank Doing Business Report 2019 The World Bank's Doing Business Report (DBR) is an annual publication that provides objective measures of business regulations and their enforcement in 190 economies. It covers various aspects that impact the ease of doing business, such as starting a business, obtaining credit, paying taxes, trading internationally, and enforcing contracts. Details of India's 2019 Doing Business Report Rank The Doing Business Report 2019 evaluated the business environments of countries based on several key indicators. For the year 2019: India's Rank: India was ranked 77th among the 190 economies assessed in the report. Context: This position represented an improvement compared to previous years, reflecting efforts made by the Indian government to streamline business regulations and enhance the operational landscape for businesses operating within the country. Understanding India's rank in reports like the Doing Business Report is crucial for evaluating economic reforms and their impact on the business ecosystem.

Limestone is a sedimentary rock composed primarily of calcium carbonate \(\left(\text{CaCO}_3\right)\), mostly in the mineral form of calcite. It forms either organically, from accumulated shells and skeletons of marine organisms such as corals, molluscs and foraminifera, or inorganically by direct precipitation from calcium-rich water. Sodium chloride forms rock salt (halite), sodium bicarbonate is baking soda, and nitrogen oxides are gaseous pollutants — none of these forms limestone.

The Chandela Rajput dynasty (9th–13th centuries CE) ruled Bundelkhand in Central India and established their religious capital at Khajuraho, where they built the famous group of Hindu and Jain temples between roughly 950 and 1050 CE. The Mauryas (Pataliputra), Guptas (Pataliputra/Ujjain) and Cholas (Thanjavur, in South India) have no association with Khajuraho.

Nagpur is called the 'Zero Mile City' because the British Great Trigonometrical Survey installed the Zero Mile Stone there in 1907, treating it as the geographical centre of undivided British India and the reference point from which distances to other cities were measured. Delhi, Hyderabad and Ahmedabad have no such marker; Nagpur is also famous as the 'Orange City' and the winter capital of Maharashtra.

A grasshopper hears through a pair of tympanal organs — thin membranes located on the sides of the first abdominal segment, right where the hind legs join the body. Sound waves vibrate these membranes, which are connected to sensory neurons. The wings, stomach and antennae carry no hearing organs in grasshoppers; the antennae handle touch and smell, not sound.

Makar Sankranti is the pan-Indian harvest festival marking the sun's transit into Capricorn (Makara), celebrated around 14 January. It carries different regional names: Khichdi in Uttar Pradesh and Bihar (after the rice-and-lentil dish offered), Uttarayan in Gujarat and Rajasthan (referring to the sun's northward journey, marked by kite flying), and Lohri in Punjab and Haryana (the bonfire celebration on the eve). Holi (colours, spring), Dussehra (Vijayadashami, autumn) and Ganesh Chaturthi (Bhadrapada) are unrelated to these names.

The Koshi (Kosi) river is called the 'Sorrow of Bihar' because of its devastating annual floods and frequent course shifts across north Bihar. Rising in Nepal and joining the Ganga, it carries one of the highest silt loads in the world, which raises its bed, breaches embankments and inundates lakhs of hectares each monsoon. Mahanadi is the 'Sorrow of Odisha', Damodar was the 'Sorrow of Bengal', and Chambal and Narmada do not flow through Bihar.

The Treaty of Mangalore was signed on 11 March 1784 between the British East India Company and Tipu Sultan of Mysore, ending the Second Anglo-Mysore War (1780–1784). Tipu had succeeded his father Hyder Ali (who died in 1782 during the war) and negotiated the treaty, which essentially restored the pre-war status quo with mutual return of captured territories and prisoners. The Nizam, Baji Rao II and the Nawab of Arcot were not signatories to this treaty.

In banking parlance, ADF stands for Automated Data Flow. It is an RBI initiative (launched in 2010-11) requiring banks to submit accurate, regulatory and supervisory returns directly from their source systems to the RBI without any manual intervention. The framework eliminates manual data preparation, reduces errors, and ensures consistency, timeliness and integrity of data sent to the regulator. The other options (All Day Finance, Automated Digital Flow, Actual Data Flow) are not standard banking abbreviations.

Step 1 — Radius perpendicular to tangent: \(\angle OAP = \angle OBP = 90^\circ\). Step 2 — Find \(\angle AOB\) from quadrilateral OAPB: \[\angle AOB = 360^\circ - (90^\circ + 90^\circ + 30^\circ) = 150^\circ\] Step 3 — Use isosceles \(\triangle OAB\): Since \(OA = OB\) (radii), \(\angle OAB = \angle OBA\). Hence \[\angle OAB = \frac{180^\circ - 150^\circ}{2} = 15^\circ\] Therefore \(\angle OAB = 15^\circ\).

Average = 0 means the sum of all 39 numbers is 0. If all 39 were positive, the sum would be positive — impossible. So at least one number must be non-positive. Taking 38 positives and just one negative is enough to balance the sum. Example: thirty-eight 1's and one \(-38\) give \(38(1) + (-38) = 0\), average \(0\). Hence at most 38 numbers can be greater than zero.

Step 1 — Extract sales (thousands): B1: 80 + 105 = 185; B2: 75 + 65 = 140; B5: 75 + 95 = 170. Step 2 — Add the three branch totals: \[185 + 140 + 170 = 495\] Therefore the combined sales of B1, B2 and B5 across 2000 and 2001 is 495 thousand.

Step 1 — Split the price (Max marks 40,000): First portion = 62.5% of 40,000 = \(25{,}000\); remaining = \(15{,}000\). Step 2 — Discount on each portion: \[0.10 \times 25{,}000 = 2{,}500;\quad 0.04 \times 15{,}000 = 600\] Step 3 — Total discount and percentage: \[\text{Total} = 2{,}500 + 600 = 3{,}100\] \[\text{Overall \%} = \frac{3{,}100}{40{,}000}\times 100 = 7.75\%\] Therefore the overall percentage discount is 7.75%.

Step 1 — Convert percentages to actual marks (max = 150): A: 135, B: 150, C: 135, D: 120, E: 120, F: 105, G: 97.5. Step 2 — Sum: \[135+150+135+120+120+105+97.5 = 862.5\] Step 3 — Average over 7 students: \[\frac{862.5}{7} \approx 123.21\] Therefore the average marks in Mathematics is 123.21.

Step 1 — Sum tax for 1998–2002 (Lakh Rs.): \[83 + 108 + 74 + 88 + 98 = 451\] Step 2 — Divide by 5 years: \[\frac{451}{5} = 90.2\] Therefore the average annual tax paid is Rs. 90.2 Lakh.

Under compound interest, if a sum becomes \(k\) times in \(t\) years, it becomes \(k^n\) times in \(nt\) years at the same rate. Given \(k = 3,\ t = 4\). Since \(27 = 3^3\), we need \(n = 3\). \[\text{Time} = 3 \times 4 = 12 \text{ years}\] Therefore the sum becomes 27 times in 12 years.

Step 1 — Set up speeds: Let going speed = \(v\); return speed = \(4v\) (given going is \(\tfrac{1}{4}\) of return). Step 2 — Apply harmonic mean for equal distances: \[\text{Avg speed} = \frac{2 v_1 v_2}{v_1 + v_2} = \frac{2 \cdot v \cdot 4v}{v + 4v} = \frac{8v}{5}\] Step 3 — Solve for \(v\): \[\frac{8v}{5} = 15 \implies v = \frac{75}{8} \text{ km/h}\] Therefore the going speed is \(\dfrac{75}{8}\) km/h.

Use the identity \(\left(x+\tfrac{1}{x}\right)^3 = x^3+\tfrac{1}{x^3} + 3\left(x+\tfrac{1}{x}\right)\), which gives \(x^3+\tfrac{1}{x^3} = \left(x+\tfrac{1}{x}\right)^3 - 3\left(x+\tfrac{1}{x}\right)\). Substitute \(x+\tfrac{1}{x}=4\): \[x^3+\tfrac{1}{x^3} = 4^3 - 3(4) = 64 - 12 = 52\] Therefore the value is 52.

Paper expenditure is 25% and Promotion is 10%, so Promotion is 25 - 10 = 15 percentage points lower. The phrase "less than Paper by" requires expressing this difference relative to the Paper value (the base): \[\text{Percent less} = \frac{25-10}{25}\times 100 = \frac{15}{25}\times 100 = 60\%\] Hence Promotion is 60% less than Paper.

Step 1 — Cube the given: Using \(\left(a-\tfrac{1}{a}\right)^3 = a^3-\tfrac{1}{a^3} - 3\left(a-\tfrac{1}{a}\right)\): \[a^3-\tfrac{1}{a^3} = 3^3 + 3(3) = 27+9 = 36\] Step 2 — Square the result: Using \(\left(a^3-\tfrac{1}{a^3}\right)^2 = a^6+\tfrac{1}{a^6} - 2\): \[a^6+\tfrac{1}{a^6} = 36^2 + 2 = 1296 + 2 = 1298\] Therefore 1298.

By volume conservation, the number of small spheres equals the ratio of volumes. Since the \(\tfrac{4}{3}\pi\) factor cancels: \[n = \frac{r_1^3}{r_2^3} = \frac{5^3}{2^3} = \frac{125}{8} = 15.625\] Only complete spheres count, so take the floor: 15 complete spheres (with leftover material insufficient for a 16th).

First term: Since \(\sin 65^\circ = \cos 25^\circ\) and \(\cos 66^\circ = \sin 24^\circ\), both numerator and denominator become \(\sin^2\theta+\cos^2\theta = 1\), giving \(\tfrac{1}{1}=1\). Last two terms: Since \(\sin 29^\circ = \cos 61^\circ\), \(\cos 61^\circ \sin 29^\circ = \cos^2 61^\circ\). So \(\sin^2 61^\circ + \cos^2 61^\circ = 1\). Total \(= 1+1 = \mathbf{2}\).

Apply the difference-of-cubes identity \(a^3-b^3 = (a-b)(a^2+ab+b^2)\). Substituting the given values: \[210 = 5\,(a^2+ab+b^2) \implies a^2+ab+b^2 = \frac{210}{5} = 42\] The required expression \((a^2+b^2)+ab\) is the same as \(a^2+ab+b^2\), so the value is 42.

In a cyclic quadrilateral, opposite angles are supplementary, so \(\angle ABC = 180^\circ - \angle ADC = 180^\circ - 150^\circ = 30^\circ\). Since AB is the diameter, the angle in the semicircle gives \(\angle ACB = 90^\circ\). In \(\triangle ABC\), the angles sum to \(180^\circ\): \[\angle BAC = 180^\circ - 90^\circ - 30^\circ = 60^\circ\] Hence \(\angle BAC = \mathbf{60^\circ}\).

Step 1 — Innermost bracket: \(2\tfrac{1}{2}+\tfrac{3}{4} = \tfrac{10}{4}+\tfrac{3}{4} = \tfrac{13}{4}\). Step 2 — Curly braces: \(4\tfrac{1}{3}-\tfrac{13}{4} = \tfrac{13}{3}-\tfrac{13}{4} = \tfrac{52-39}{12} = \tfrac{13}{12}\). Step 3 — Square bracket (division): \(\tfrac{13}{6} \div \tfrac{13}{12} = \tfrac{13}{6}\times\tfrac{12}{13} = 2\). Step 4 — Final addition: \(9\tfrac{3}{4}+2 = \tfrac{39}{4}+\tfrac{8}{4} = \tfrac{47}{4}\). Therefore the value is \(\mathbf{\tfrac{47}{4}}\).

The identity \(a^3+b^3+c^3 = 3abc\) holds when \(a+b+c=0\) (or \(a=b=c\)). Here \(a=x-4,\ b=x-5,\ c=x-3\); the equality \(a=b=c\) is impossible since the constants differ. So set the sum to zero: \[(x-4)+(x-5)+(x-3)=0 \implies 3x-12=0 \implies x=4\] Therefore \(x = \mathbf{4}\).

Let the required number of women be x. A woman does double the work a man does in a day ⇒ W = 2M ----(1) A boy does half the work a man does in a day ⇒ M = 2B ----(2) Now, using the formula M 1D 1/W 1= M 2D 2/W 2 ⇒ (3M + 4W + 6B) × 5 = x × W × 7 ⇒ (3M + 8M + 3M) × 5 = x × 2M × 7 ⇒ 14M × 5 = 14M × x ⇒ x = 5 W

For similar triangles, the ratio of areas equals the square of the ratio of corresponding sides. From \(\triangle ABC\sim\triangle QPR\), side BC corresponds to PR. \[\left(\frac{BC}{PR}\right)^2 = \frac{9}{16} \implies \frac{BC}{PR} = \frac{3}{4}\] With \(BC=6\): \(\tfrac{6}{PR}=\tfrac{3}{4} \implies PR = \tfrac{6\times 4}{3} = 8\) cm. Therefore \(PR = \mathbf{8}\) cm.

Daily wage = hourly rate × hours per day. A: \(80\times 8 = 640\) Rs. B: \(60\times 6 = 360\) Rs. Ratio \(= 640:360\). Dividing both by 40 (their GCD): \(\tfrac{640}{40}:\tfrac{360}{40} = 16:9\). Therefore A : B = 16 : 9.

Substituting \(\sec\theta = \tfrac{1}{\cos\theta}\) and letting \(c=\cos\theta\) gives \(c+\tfrac{1}{c}=2\), i.e. \(c^2-2c+1=0\), so \((c-1)^2=0\) and \(\cos\theta=1\). Hence \(\theta\) is a multiple of \(2\pi\), making \(\cos 117\theta = 1\) and \(\sec 117\theta = 1\). Therefore \(\cos^{117}\theta + \sec^{117}\theta = 1^{117}+1^{117} = \mathbf{2}\). (Same result whether the exponent is on the function or the angle, since \(\cos\theta=1\).)

Let the number be \(x\). The condition gives: \[0.5x + 75 = x\] \[75 = 0.5x \implies x = 150\] Check: 50% of 150 = 75, and \(75 + 75 = 150\). Therefore the number is 150.

For successive discounts of \(d_1, d_2, d_3\), the equivalent single discount is: \[D = \left[1 - \left(1-\tfrac{d_1}{100}\right)\left(1-\tfrac{d_2}{100}\right)\left(1-\tfrac{d_3}{100}\right)\right]\times 100\] \[D = [1 - (0.80)(0.90)(0.85)]\times 100 = [1 - 0.612]\times 100 = 38.8\%\] Therefore the equivalent single discount is 38.8%.

Given \(n \equiv 3 \pmod{7}\). Multiplying both sides by 6: \[6n \equiv 18 \pmod{7}\] Since \(18 = 2\times 7 + 4\), we get \(18 \equiv 4 \pmod{7}\). Therefore \(6n \equiv 4 \pmod{7}\), so the remainder is 4.

3cos 2A + 7sin 2A = 3 ⇒ 3cos 2A + 3sin 2A + 4sin 2A = 3 ⇒ 3 + 4sin 2A = 3 ⇒ 4sin 2A = 0 ⇒ sin A = 0 = sin 0° ⇒ A = 0°

BRUTAL means savagely cruel, violent, and lacking compassion. Its opposite is a word denoting kindness and compassion. Humane means showing compassion and benevolence — the direct antonym. Fierce and savage are near-synonyms (both imply violence/cruelty), and sane relates to mental soundness, not cruelty. Hence the antonym is Humane.

Fragile literally means easily broken or damaged (e.g., fragile glass), which exactly matches the phrase. Pliable means easily bent, ductile means able to be drawn into wire, and malleable means able to be hammered into shape — all three describe deformation without breaking, the opposite of the required sense. Hence the one-word substitution is fragile.

Austere means stern, severe, or strict in manner; it can also mean plain or without luxury. Among the options, strict directly captures the 'severe/stern' sense. Generous is an antonym (in the 'lacking luxury' sense), while unwilling and careless are unrelated. Hence the synonym is strict.

The blank links Bagheera's gaining strength to his subsequent escape — a time/condition relationship meaning 'as soon as'. Once means 'as soon as / after' and fits perfectly: "Once he was strong enough, he broke the lock..." Unless (= if not) reverses the meaning; But introduces contrast (illogical here); Only does not connect a clause this way. Hence the answer is Once.

The intended sense is exclusivity — the committee dealt with no important question except this one. The standard idiom is "no other ... but ..." (or 'than'); pairing "no other" with "only" is ungrammatical. Option 1, "with no other important question but this", uses the correct construction. "Other this" (option 3) and "one other ... either this" (option 2) are ungrammatical, and the original needs correction, so "No improvement" is wrong. Hence the answer is with no other important question but this.

As a verb, converse means to engage in conversation — to speak with someone. Talk carries exactly this meaning and is the closest synonym. Oppose means to resist, display means to show, and agree means to share an opinion — none denotes the act of speaking with someone. Hence the synonym is talk.

The idiom 'sit on the fence' means to avoid taking sides or making a decision — to stay neutral or undecided. The sentence's tail "without committing themselves" confirms this sense. Option 1, remain undecided and unsure, matches exactly. Options 2 and 3 describe laziness/inaction, and option 4 takes the phrase literally — idioms are figurative. Hence the meaning is remain undecided and unsure.

The standard English spelling is certificate — from Medieval Latin certificatum, beginning with 'cert-' and ending with '-ficate'. The other options misspell either the opening ('sert-', 'cart-', 'sart-') or the suffix ('-fikate'). Only option 2 has the correct letters in the correct order. Hence the correctly spelt word is certificate.

Sentence A introduces the topic ("When you begin to house train your puppy, follow these steps") and must lead. D then gives the first concrete step — taking the puppy out in the morning and every thirty minutes. C follows with the related feeding-schedule rule, and B closes with "Also, always take her outside after meals or when she wakes from a nap" — the connector 'Also' and the reference to meals/naps mark it as the supplement to C. Hence the correct order is ADCB.

The blank describes how Bagheera, a strong panther, got out of a locked cage. A captive animal does not turn a key, so "opened" is unnatural; "bent" and "loosened" suggest partial damage that would not release the door. "Broke" conveys forcefully shattering the lock, which fits a powerful panther escaping captivity. The completed clause reads: "he broke the lock of his cage and ... into the jungle."

The clause "into the jungle" follows the action of breaking the cage lock, so the verb must describe gaining freedom from confinement. "Marched" suggests formal walking, "jumped" and "climbed" describe specific physical motions that do not collocate naturally with "into the jungle" after breaking a lock. Escaped precisely means breaking free from captivity, matching the cage-to-jungle movement. The sentence reads: "he broke the lock of his cage and escaped into the jungle."

With the correlative pair neither...nor, the verb agrees with the subject closer to it. Here the nearer subject is Jaya, which is singular, so the verb must be singular. The segment "are responsible" uses the plural "are" and violates this rule; it should be "is responsible." Corrected: "neither Juhi nor Jaya is responsible for breaking the vase."

The outermost layer of any celestial body — planet, moon, or asteroid — is called its surface. NASA's OSIRIS-REx mission detected hydrated clay minerals on the outer layer of Bennu, which is precisely what this term denotes. "Ground" and "soil" are Earth-specific (and "soil" implies biological/organic content), while "earth" names our planet, not an asteroid. Hence surface is the standard and correct term.

Stationary means fixed in one place, not moving. An antonym must therefore convey motion or change of position. "Motionless" and "still" are synonyms of stationary, not antonyms. "Tired" is unrelated to movement. "Shifting" means moving or changing position, which is the direct opposite of being stationary.

The sentence "He regularly _____ in the stories of Mowgli" needs a verb describing a character's recurring presence in a narrative. "Involves" and "invites" require an object (one involves/invites someone or something) and are ungrammatical here. "Rises" implies upward motion or growth in stature, not narrative presence. "Appears in the stories" is the standard collocation for a character featuring in a work, so it fits perfectly.

The pronoun each is always singular, even when followed by "of + plural noun." It therefore takes a singular verb. "Each of the guests were given" violates this rule and must become "was given." Option 3 keeps the plural verb, and option 4 wrongly pluralises the noun after "each" (it should be "each guest," not "each guests"). Hence "Each of the guests was given" is correct.

Friction is an uncountable (singular) noun, so in the simple present tense it must take a verb ending in -s. The segment "Friction reduce" pairs this singular subject with the bare plural-form verb "reduce," breaking subject-verb agreement. The correct form is "Friction reduces the efficiency of machines..." The other segments are grammatically fine.

Sentence C introduces the subject Swami and his intention to disrupt classes — a natural opener. A follows as the direct consequence: those disruptions annoy his teachers. B adds a parallel teacher-reaction (they are baffled by his questions), expanding on "his teachers" from A. D concludes with the escalation — teachers writing notes to summon his parents. The cause-effect progression confirms the order CABD.

For an imperative sentence, the passive is formed as Object + should/must + be + past participle. The object "the glass table" becomes the subject, and "rub" becomes "be rubbed." Option 1 wrongly swaps subject and instrument. Option 2 keeps the verb active ("must rub"). Option 4 uses "have" with a singular subject (should be "has"). Only option 3, "The glass table should be rubbed with a soft cloth to make it shine," is grammatically and structurally correct.

The idiom foot the bill means to pay for something, especially for a group or an unexpected expense. In the sentence, Raju was shocked because he had to cover the cost of his friends. Options about "preparing," "picking up from the floor," or "kicking away" are literal misreadings. The correct meaning is "pay for everything."

A menagerie is a collection of wild animals kept confined for exhibition, so being born in one means being born in a state of confinement. "Park," "jungle," and "cave" name physical locations and do not describe this condition; "jungle" is in fact the opposite (the wild he later escapes to). "Captivity" precisely names the state of confinement that fits the menagerie context.

The prefix bi- means "two" and -lingual relates to languages, so bilingual precisely denotes a person who speaks two languages fluently. "Monolingual" means speaking only one language. A "linguist" studies the science of language, not necessarily speaks multiple. A "lexicologist" studies words and dictionaries.

Adventurous is the correctly spelt word, meaning willing to take risks or full of excitement. The other options are misspelt: "advertizment" should be advertisement, "advantegious" should be advantageous, and "adversery" should be adversary.

The idiomatic collocation "on the occasion of" is used to mark a specific day or event being commemorated — here, World Sparrow Day. It fits both grammatically and contextually. "Festivity," "event," and "project" do not collocate with "on the ___ of [a named day]"; "on the event of" is redundant since a cyclothon is itself an event, and "project" describes a planned task rather than a date.

The given sentence is in future simple passive ("will be known"). To convert to active voice, the agent "us" becomes the subject "We", the verb becomes the active future simple "will know", and "the results" becomes the object. This yields: We will know the results by the end of the next month. Options 2 (present perfect), 3 (present continuous), and 4 (present simple) all use the wrong tense.