SSC CGL 2017 · 2017-08-17 · Shift 3

Each term is obtained by multiplying the previous term by \(-0.2\): \(100\times(-0.2)=-20\); \(-20\times(-0.2)=4\). The missing term is \(4\times(-0.2)=-0.8\). Check: \(-0.8\times(-0.2)=0.16\) and \(0.16\times(-0.2)=-0.032\). The answer is -0.8.

Letters available in ORDINALS: O, R, D, I, N, A, L, S. DINAR (D, I, N, A, R), ADORN (A, D, O, R, N) and SALON (S, A, L, O, N) use only these letters. IDEAL needs the letter E, which is not present in ORDINALS. Hence IDEAL cannot be formed.

Apply the substitutions: \(\times\to\div,\ \div\to-,\ +\to\times,\ -\to+\). The expression \(42\times 7\div 7+9-62\) becomes \(42\div 7-7\times 9+62\). Using BODMAS: \(42\div 7=6\) and \(7\times 9=63\), giving \(6-63+62=5\). The answer is 5.

Statement I: "Some clever are intelligent" — by conversion, "Some intelligent are clever" also holds. So Conclusion I follows. Statement II: "No intelligent is smart" tells us intelligent and smart are disjoint. It says nothing about the overlap between smart and clever, so "Some smart are clever" is not established. Conclusion II does not follow. Hence Only Conclusion I follows.

Count the letters in each word: Pension (7), Aptitude (8), Captain (7), Tropical (8), Survive (7). The pattern alternates 7, 8, 7, 8, 7, so the next word must have 8 letters. Among the options, only Tetrapod (8 letters) fits. Parrot (6), Apply (5) and Trap (4) do not.

Cube 2 cannot be formed as crossed side figure and hexagon side figure cannot be adjacent to each other. Option 2 is the correct answer.

Find valid (row, column) codes for each letter of PURE: P (Matrix-II): 89. U: 58, 66, 96, 98. R: 59, 86. E (Matrix-I): 13. The required pattern is (P)(U)(R)(E). Option 1 — 89, 96, 86, 13 — matches: 89=P, 96=U, 86=R, 13=E. The other options start with codes for K, L or E, not P. Hence the answer is 89, 96, 86, 13.

Wool (from sheep), Silk (from silkworms) and Cotton (from the cotton plant) are all natural fibres. Nylon is a man-made synthetic polymer. Hence Nylon is the odd one out.

Total days from June 1 (exclusive) to December 3 (inclusive): June 29 + July 31 + Aug 31 + Sept 30 + Oct 31 + Nov 30 + Dec 3 = \(185\) days. Odd days: \(185\bmod 7=3\). Starting from Thursday and moving 3 days forward: Fri, Sat, Sunday. So December 3 is a Sunday.

Compare alphabet positions of QUICKLY → OSGAIJW: Q(17)→O(15), U(21)→S(19), I(9)→G(7), C(3)→A(1), K(11)→I(9), L(12)→J(10), Y(25)→W(23). Each letter shifts −2. Apply to HUE: H(8)→F(6), U(21)→S(19), E(5)→C(3). Hence HUE is coded as FSC.

Test the rule \(A@B=\dfrac{A-B}{2}\) on the examples: \(\tfrac{17-1}{2}=8\), \(\tfrac{9-1}{2}=4\), \(\tfrac{6-4}{2}=1\) — all match. Therefore \(8@2=\dfrac{8-2}{2}=\dfrac{6}{2}=\mathbf{3}\).

Compare alphabet positions: F(6)→L(12), D(4)→J(10), H(8)→N(14). Each letter shifts +6. Apply to RPT: R(18)→X(24), P(16)→V(22), T(20)→Z(26). Hence the answer is XVZ.

Check the gap between consecutive letters in each triplet: GDA: 7,4,1 — gap −3. NKH: 14,11,8 — gap −3. URO: 21,18,15 — gap −3. ZXV: 26,24,22 — gap −2. ZXV breaks the pattern, so ZXV is the odd one.

Find the ratio: \(\dfrac{52}{39}=\dfrac{4}{3}\), i.e. the second term is \(\tfrac{4}{3}\) times the first. Apply to 51: \(51\times\dfrac{4}{3}=17\times 4=68\). Hence the answer is 68.

Box weights: 20, 30, 40, 50 kg. Each box may be used at most once. Check each option as a subset sum: 140 = 20 + 30 + 40 + 50 (all four boxes). Achievable. 120 = 30 + 40 + 50. Achievable. 90 = 40 + 50 (or 20 + 30 + 40). Achievable. 130: needs sum 130. The two largest are 40 + 50 = 90; adding 30 gives 120, adding 20 gives 110; all four give 140. No subset reaches 130. Therefore 130 kg cannot be formed.

The relationship is organ : sense. The tongue is the sense organ for taste. Correspondingly, the nose is the sense organ for smell (olfaction). 'Face' and 'Chin' are anatomical regions, not senses; 'Touch' is associated with the skin, not the nose.

Read the 3×3 grid column-wise: each column's top entry equals the product of the two entries below it. Column 1: \(45 \times 68 \ne 23\), but reading digits: \(45 \rightarrow 4+5=9,\ 68 \rightarrow 6+8=14\); sum digits of 23 = 5. Instead, use sum-of-digits pattern across the column: \((2+3)+(4+5)+(6+8)=5+9+14=28\). The reliable pattern is column digit-sum: column 1 sums to \(28\), column 2 to \((1+1+4)+(2+5)+(8+9)=6+7+17=30\). For column 3 with 204, 36 and ?, digit sums \((2+0+4)+(3+6)+s=6+9+s\). Matching the option set, 168 gives \(1+6+8=15\), total 30, matching column 2's total. Hence the missing number is 168.

Option 3 is the correct answer.

Option 1 is the correct answer.

Square → Dietitians Triangle → Botanists Circle → Psychologists Rectangle → Indians In order to get the letters which represents Psychologists who are not Botanists, the letters should be in circle but not in triangle. ABC satisfy the given condition.

Option 4 is the correct answer.

Check divisibility by 20: \(20=20\times1,\ 40=20\times2,\ 60=20\times3\) are all multiples of 20, while 15 is not. Equivalently, 15 is the only odd number; the other three are even multiples of 10. Hence 15 is the odd one out.

Within each triplet, letters 1 and 2 are consecutive and letter 3 is the letter just before letter 1 (e.g. DEC: D, E, C where C = D−1). Between triplets, every position advances by +4: D→H→L→P→T→X; E→I→M→Q→U→Y; C→G→K→O→S→W. Therefore the next term is XYW.

Hence, option 4 is the correct answer.

Track displacement along the N-S and E-W axes. Step 1 — Directions after each turn: 36 km N, 9 km W, 50 km S, then a left turn while facing South means turning to face East, so 9 km E. Step 2 — Net displacement: \[\text{N-S}: 36 - 50 = -14 \text{ km (i.e. 14 km South)}\] \[\text{E-W}: -9 + 9 = 0 \text{ km}\] The truck ends up 14 km South of its starting position.

Statement 1 is correct: 'Half of a Yellow Sun' (2006) was written by Nigerian author Chimamanda Ngozi Adichie. Statement 2 is correct: 'Middlesex' (2002), winner of the Pulitzer Prize for Fiction, was written by Jeffrey Eugenides. Statement 3 is incorrect: the novella 'Missile Gap' (2006) was written by Charles Stross, not China Mieville. Hence only statements 1 and 2 are correct.

The Right to Constitutional Remedies (Article 32) empowers citizens to move the Supreme Court directly to enforce any Fundamental Right violated by the State. Dr. B. R. Ambedkar called Article 32 the ‘heart and soul’ of the Constitution because it makes the other Fundamental Rights enforceable through writs such as habeas corpus, mandamus, prohibition, certiorari and quo warranto. The other listed rights (Cultural and Educational, Against Exploitation, Freedom of Religion) protect specific substantive freedoms but do not themselves grant the remedy to approach the court.

In physics, a force is defined as a push or a pull acting on an object. Forces can start, stop, speed up, slow down, redirect or deform a body, and are measured in newtons (N). 'Pick', 'Lift' and 'Shut' describe specific actions or outcomes, not the general scientific term for a push or pull.

The human larynx (voice box) contains two true vocal cords — paired folds of mucous membrane stretched across the larynx. Air pushed from the lungs vibrates these two folds to produce sound; tension and length adjustments change pitch. Above them lie a second pair called the false vocal cords (vestibular folds), which do not normally produce voice.

At the 89th Academy Awards (held 26 February 2017), the Best Picture Oscar was won by Moonlight, directed by Barry Jenkins. Although La La Land was mistakenly announced first due to an envelope mix-up, the award was corrected on stage and presented to Moonlight. Arrival and Fences were nominated but did not win Best Picture.

The Satluj (Sutlej) rises in Lake Rakshastal in Tibet, enters India in Himachal Pradesh, crosses Punjab and then flows into Pakistan, where it joins the Chenab. The Ghaghra is a tributary of the Ganga (entirely in India and Nepal); the Betwa joins the Yamuna within India; and the Tapi flows westward into the Arabian Sea through Gujarat. Hence only the Satluj flows from India into Pakistan.

In a market economy, decentralized decisions of buyers and sellers are coordinated through price signals. Rising prices signal scarcity, prompting producers to supply more and consumers to economize; falling prices do the opposite. Through this signalling, prices answer the central questions of what and how much to produce. Supply and demand are the underlying forces, but it is the resulting price that conveys information across the economy; the stock market is only one specific market, not the general coordinating mechanism.

The HTML attribute cellspacing sets the distance, in pixels, between the borders of adjacent cells in a <table>. cellpadding instead controls the space between a cell's content and its border; width and height set the dimensions of the table or cells, not the gap between them.

The Constituent Assembly of India was constituted under the Cabinet Mission Plan of 1946. Elections to the Assembly were held in July–August 1946, and its first meeting took place on 9 December 1946, with Dr. Sachchidananda Sinha as temporary chairman. 1940 refers to the August Offer, 1947 to Indian independence, and 1950 to the Constitution coming into force — none of these is the year the Assembly was founded.

In adults, haematopoiesis (blood cell formation) occurs in the red bone marrow, which contains hematopoietic stem cells that differentiate into RBCs, WBCs, and platelets. RBC production specifically is called erythropoiesis and is stimulated by erythropoietin from the kidneys. Yellow bone marrow is fatty and inactive in normal RBC production. "Blue", "white", and "black" bone marrow are not recognised classifications. Active red marrow in adults is found in the sternum, ribs, vertebrae, pelvis, and ends of long bones.

Primary xylem develops sequentially from the procambium. The first-formed elements are protoxylem (narrow, with annular/spiral wall thickenings, formed during elongation). The later (second) formed elements are metaxylem — wider vessels with reticulate, scalariform, or pitted thickenings that mature after elongation ceases. Xylem parenchyma (storage cells) and xylem fibres (sclerenchyma for support) are accessory components of xylem tissue, not the conducting elements classified by time of formation.

The Patkai hills lie on India's north-eastern border with Myanmar and form part of the Purvanchal Range (Eastern Highlands), together with the Naga, Manipur, Mizo (Lushai), and Tripura hills. These ranges are offshoots of the Eastern Himalayas that bend southward along the Indo-Myanmar boundary. Himachal refers to the Lesser Himalayan range in the north-west; Himgiri is a general term for snowy Himalayan peaks; the Hindu Kush lies in Afghanistan/Pakistan — none of these include the Patkai hills.

The four diagnostic features of Phylum Chordata are: a notochord, a dorsal hollow nerve cord, pharyngeal gill slits, and a post-anal tail — all present at some stage of life. Crucially, the chordate heart (when present) is ventral, not dorsal. A dorsal heart is characteristic of non-chordates such as annelids and arthropods. Hence the statement "Heart is dorsal (if present)" does not hold true for chordates. The other three options correctly state chordate features.

Soap is produced by saponification — the hydrolysis of fats or oils (triglycerides) with a strong alkali to yield the sodium/potassium salt of a fatty acid (soap) and glycerol. Hard bar soaps use sodium hydroxide (NaOH), the only strong alkali among the choices. Silicon dioxide (SiO2) is an acidic oxide (sand), calcium hydroxide gives insoluble "scum" soaps unsuitable for washing, and ammonium hydroxide is too weak and volatile for saponification. Hence the base in soap is NaOH.

The Bal Swachhta Mission was launched by the Central Government on 14 November 2014 (Children's Day) as part of the Swachh Bharat Abhiyan, specifically to create cleanliness and hygiene awareness among children — covering clean schools, anganwadis, drinking water, toilets, handwashing, and clean play areas. Sukanya Samriddhi Yojana is a girl-child savings scheme; Pradhan Mantri Jan Dhan Yojana targets financial inclusion; Beti Bachao Beti Padhao addresses the girl child's survival and education — none focus on children's cleanliness.

Microsoft acquired LinkedIn for USD 26.2 billion in an all-cash deal announced on 13 June 2016 and closed in December 2016. It remains one of Microsoft's largest acquisitions and was intended to integrate LinkedIn's professional network with Office 365, Dynamics CRM, and LinkedIn Learning. Apple, Facebook (Meta), and IBM were not involved in this deal.

Scottish physicist James Clerk Maxwell produced the first durable colour photograph in 1861, using the principle of additive colour mixing. He photographed a tartan ribbon three times through red, green, and blue filters and then projected the three black-and-white plates simultaneously through matching filters; the superimposed images formed a full-colour picture. Robert Noyce (integrated circuit), Enrico Fermi (nuclear reactor), and John Logie Baird (television) worked in unrelated fields.

Brazil hosted the 2014 FIFA World Cup from 12 June to 13 July 2014 — the second time Brazil hosted the tournament (the first being 1950). Germany won the title by defeating Argentina 1–0 in extra time in the final at the Maracanã, Rio de Janeiro. Argentina were the runners-up but not hosts; Germany were the champions; the Netherlands finished third.

The Law of Variable Proportions states that as units of a variable input are added to fixed inputs in the short run, the marginal product first rises (increasing returns, due to better utilisation of the fixed factor), then falls after a certain point (diminishing returns, as the fixed factor becomes scarce), and may eventually turn negative. This exactly matches the question's description. The Law of Diminishing Marginal Product covers only the falling phase. "Short run" and "long run" are time periods, not laws.

The Red Fort (Lal Qila) was built by the Mughal emperor Shah Jahan between 1639 and 1648 as the palace-fortress of his new capital Shahjahanabad. From its completion in 1648 until 1857, it served as the principal residence of the Mughal emperors — placing it squarely in the 17th century under Mughal occupation. The Khalji (1290–1320) and Tughluq (1320–1413) dynasties ruled centuries before the fort existed; Rajputs were not the central rulers of Delhi in that era.

During British rule, Punjab was developed as the empire's granary. The British built an extensive canal colonies network (Upper Bari Doab, Sirhind, Lower Chenab, Lower Jhelum canals) that transformed arid tracts into irrigated farmland, and cultivators were persuaded or coerced into growing wheat — a commercial cash crop exported to Britain and used to feed the army and administration. Jute belonged to Bengal, tea to Assam and the southern hills, and sugarcane was not the British focus in Punjab.

India's total land boundary is approximately 15,200 km, shared with seven neighbours: Bangladesh (~4,096 km, longest), China (~3,488 km), Pakistan (~3,323 km), Nepal (~1,751 km), Myanmar (~1,643 km), Bhutan (~699 km), and Afghanistan (~106 km). The mainland coastline is about 6,100 km (7,516.6 km including islands) — clearly distinct from the land boundary. Hence 15,200 km is correct.

Pollution is defined as any undesirable change in the physical, chemical, or biological characteristics of air, water, land, or soil caused by contaminants (pollutants). It is broadly classified as air, water, soil, noise, and thermal pollution. The greenhouse effect is a natural warming process (only one consequence, not the general definition); solid wastes are a type of pollutant, not the change itself; deforestation is the removal of forest cover, a specific action rather than the umbrella term.

The Jama Masjid of Delhi (Masjid-i Jehân-Numâ) was built by the Mughal emperor Shah Jahan between 1644 and 1656 in his new capital Shahjahanabad. Constructed in red sandstone and white marble, it is one of the largest mosques in India and can accommodate over 25,000 worshippers. Shah Jahan also built the Taj Mahal and the Red Fort. Babar founded the empire, Humayun's reign is marked by his tomb (built posthumously), and Akbar built Fatehpur Sikri — none built Delhi's Jama Masjid.

Ants belong to the family Formicidae, and their sting injects formic acid (HCOOH, also called methanoic acid) — the simplest carboxylic acid. The name itself derives from the Latin formica meaning ant. Acetic acid is found in vinegar, citric acid in citrus fruits, and lactic acid in sour milk and fatigued muscle tissue — none are associated with ant stings.

Tickets sold by airlines A = 5000 And Tickets sold by airlines E = 6000 Required % = (6000 - 5000) /5000 × 100 = 20% Airline E sold how 20% more tickets than Airline A

Step 1 — Combined one-day work: \[\frac{1}{12}+\frac{1}{8}+\frac{1}{24}=\frac{2+3+1}{24}=\frac{6}{24}=\frac{1}{4}\] Step 2 — Total days: reciprocal of the combined rate. \[T=\frac{1}{1/4}=4\text{ days}\] Therefore working together they finish the job in 4 days.

Step 1 — Set up the profit relation: profit on 21 items equals SP of 1 item. \[21\,\text{SP}-21\,\text{CP}=\text{SP}\] Step 2 — Simplify: \[20\,\text{SP}=21\,\text{CP}\] Step 3 — Profit % on cost: \[\text{Profit\%}=\frac{\text{SP}}{21\,\text{CP}}\times100=\frac{\text{SP}}{20\,\text{SP}}\times100=5\%\] Therefore the profit percentage is 5%.

Step 1 — Use the identity: \[a^{3}+b^{3}=(a+b)^{3}-3ab(a+b)\] Step 2 — Substitute given values \(a+b=1\) and \(a^{3}+b^{3}=19\): \[19=1^{3}-3ab(1)=1-3ab\] Step 3 — Solve for ab: \[3ab=1-19=-18 \implies ab=-6\] Therefore ab = -6.

Step 1 — Speed in km/h: \[\text{Speed}=\frac{144}{3.2}=45\text{ km/h}\] Step 2 — Convert to m/s by multiplying by \(\dfrac{5}{18}\): \[45\times\frac{5}{18}=\frac{225}{18}=12.5\text{ m/s}\] Therefore the required average speed is 12.5 m/s.

Use standard values: \(\cot 45^{\circ}=1\) and \(\operatorname{cosec}60^{\circ}=\dfrac{2}{\sqrt{3}}\). \[\frac{1}{\sqrt{2}}\cdot 1+\frac{1}{\sqrt{3}}\cdot\frac{2}{\sqrt{3}}=\frac{1}{\sqrt{2}}+\frac{2}{3}\] Common denominator \(3\sqrt{2}\): \[\frac{3}{3\sqrt{2}}+\frac{2\sqrt{2}}{3\sqrt{2}}=\frac{3+2\sqrt{2}}{3\sqrt{2}}\] Therefore the value is \(\dfrac{3+2\sqrt{2}}{3\sqrt{2}}\).

By the midpoint formula, if P is the midpoint of AB with B = (5, -4) and P = (3, 1): \[\left(\frac{x_A+5}{2},\frac{y_A-4}{2}\right)=(3,1)\] Step 1 — x-coordinate: \(x_A+5=6 \implies x_A=1\). Step 2 — y-coordinate: \(y_A-4=2 \implies y_A=6\). Therefore A = (1, 6).

Step 1 — Find the rate. Principal grows 18% in 2 years at SI, so \[R=\frac{18}{2}=9\%\text{ per annum}\] Step 2 — Compound amount on Rs 7000 for 3 years at 9%: \[A=7000\left(1.09\right)^{3}=7000\times1.295029=9065.20\] Step 3 — Compound interest: \[\text{CI}=9065.20-7000=2065.20\] Therefore CI = Rs 2065.2.

Step 1 — Convert averages to sums: \[P+Q+R=3\times45=135\] \[P+Q=2\times36.5=73,\quad Q+R=2\times52=104\] Step 2 — Add the pair sums: \[(P+Q)+(Q+R)=73+104=177=(P+Q+R)+Q\] Step 3 — Isolate Q: \[Q=177-135=42\text{ kg}\] Therefore Q weighs 42 kg.

Step 1 — Simplify the bracket. Common denominator 15: \[\frac{7x}{5}-\frac{4}{3}=\frac{21x-20}{15}\] Step 2 — Multiply by \(\tfrac{5}{2}\): \[\frac{5}{2}\cdot\frac{21x-20}{15}=\frac{21x-20}{6}\] Step 3 — Multiply the whole equation by 6: \[2x-(21x-20)=-x \implies -19x+20=-x\] Step 4 — Solve: \[20=18x \implies x=\frac{10}{9}\] Therefore \(x=\dfrac{10}{9}\).

Step 1 — Slope of given line through (-5, 1) and (-2, 0): \[m=\frac{0-1}{-2-(-5)}=\frac{-1}{3}\] Step 2 — Perpendicular slope is the negative reciprocal: \[m_{\perp}=-\frac{1}{m}=-\frac{1}{-1/3}=3\] Therefore the required slope is 3.

Total ratio parts = \(11+7+5=23\). Step 1 — Value of one part: \[\frac{103500}{23}=4500\] Step 2 — B's share = 7 parts: \[7\times4500=31500\] Therefore B receives Rs 31,500.

Step 1 — 150% of 400: \[1.5\times400=600\] Step 2 — 10% of 600: \[0.1\times600=60\] Therefore the value is 60.

Angles sum to 180°: with \(\angle B=90^{\circ}\) and \(\angle A=60^{\circ}\), we get \(\angle C=30^{\circ}\). Standard values: \(\sec 30^{\circ}=\dfrac{2}{\sqrt{3}}\) and \(\sin 60^{\circ}=\dfrac{\sqrt{3}}{2}\). \[\sec C\cdot\sin A=\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{2}=1\] Therefore the value is 1.

Area of an equilateral triangle of side \(s\): \[A=\frac{\sqrt{3}}{4}s^{2}\] Substituting \(s=14\): \[A=\frac{\sqrt{3}}{4}\times196=49\sqrt{3}\text{ sq cm}\] Therefore the area is \(49\sqrt{3}\) sq cm.

For two successive discounts \(d_1\) and \(d_2\), the effective discount is: \[d_{\text{eff}} = d_1 + d_2 - \frac{d_1 d_2}{100}\] Substituting \(d_1 = 20\) and \(d_2 = 10\): \[d_{\text{eff}} = 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%\] Therefore the effective discount is 28%.

Through observations, we can clearly say that the E sold the second highest number of tickets.

For reflection of a point \((x, y)\) in a vertical line \(x = c\), the image is \((2c - x,\ y)\) — the y-coordinate is unchanged and the line acts as the perpendicular bisector of the x-distance. With \((x, y) = (-2, 5)\) and \(c = -1\): \[x' = 2(-1) - (-2) = -2 + 2 = 0,\quad y' = 5\] Therefore the reflected point is (0, 5).

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides: \[\frac{AB}{PQ} = \frac{\text{Perimeter of }\triangle ABC}{\text{Perimeter of }\triangle PQR} = \frac{5}{9}\] With \(PQ = 45\) cm: \[AB = \frac{5}{9} \times 45 = 25 \text{ cm}\] Therefore AB = 25 cm.

Divide 4131 by 19 to find the remainder: \[4131 = 19 \times 217 + 8\] So the remainder is 8. To reach the next multiple of 19, add \(19 - 8 = 11\). Check: \(4131 + 11 = 4142 = 19 \times 218\). Therefore the least number to add is 11.

Sum of an AP given the first term \(a\), last term \(l\), and number of terms \(n\): \[S_n = \frac{n}{2}(a + l)\] Substitute \(n = 12\), \(a = -19\), \(l = 36\): \[S_{12} = \frac{12}{2}(-19 + 36) = 6 \times 17 = 102\] Therefore the sum is 102.

Tickets sold by Airlines A and D = 5000 + 3000 = 8000 Tickets sold by airlines E = 6000 ∴ Required ratio = 8000/6000 = 4/3

The price of a ticket is Rs. 7000 Revenue from sale of tickets of Airline B = 11,000 × 7,000 = Rs. 77,000,000 Revenue from sale of tickets of Airline E = 6,000 × 7,000 = Rs. 42,000,000 The sale of tickets of Airline B is greater than that of Airline E = 77,000,000 - 42,000,000 = 35,000,000 ∴ Monthly Revenue (in Rs. Millions) from sale of tickets of Airline B is greater than that of Airline E = Rs. 35 millions

Test the marked option \(x = \dfrac{11}{7}\). Its reciprocal is \(\dfrac{7}{11}\). \[x - \frac{1}{x} = \frac{11}{7} - \frac{7}{11} = \frac{121 - 49}{77} = \frac{72}{77}\] This matches the given difference, so the fraction is 11/7. (The other option 7/11 gives \(-72/77\), i.e. it is smaller than its reciprocal.)

Use the identity \(\sec^2\theta = 1 + \tan^2\theta\). \[\sec^2\theta = 1 + \left(\frac{7}{24}\right)^2 = 1 + \frac{49}{576} = \frac{625}{576}\] \[\sec\theta = \frac{25}{24}\] Taking the positive root (consistent with a right-triangle interpretation where hypotenuse \(= \sqrt{7^2 + 24^2} = 25\) and adjacent \(= 24\)), sec θ = 25/24.

A fallacy is a mistaken belief or unsound argument, often arising from prejudiced or distorted reasoning. Among the options, Bias — a prejudice that produces flawed judgement — is closest in meaning. "Conformity" means following norms, "Surety" means certainty, and "Evidence" means supporting proof — all unrelated to faulty reasoning.

The subject All here refers to people (everyone) and takes a plural verb. The intended sense is that everyone experienced surprise on finding he was not with them, which requires the past-participle adjective surprised (the -ed form describes the feeler; the -ing form would describe the cause). The plural past-tense of "to be" is were, giving were surprised. "Was surprised" fails subject-verb agreement; "is surprised" is wrong tense.

The preposition along describes movement or position beside a line (along a river, along a road), not distribution within an area. For events happening within a city, the correct preposition is in, throughout, or across. Hence "along the city" in part (3) is wrong — the sentence should read "...broke out in the city." Parts (1) and (2) are grammatically fine, so the error is in part (3).

Literal thin ice can crack at any step, so the idiom on thin ice means being in an unstable, risky position where one slip leads to trouble. Option 4, "In a precarious or risky situation," captures this exactly. The other options describe repeated failure, surviving winter, or remaining calm — none of which match the idiom's sense of imminent risk.

“On thin ice” literally evokes a surface that could break at any moment; idiomatically it means being in an unstable, risky position where one wrong move brings trouble. This matches “In a precarious or risky situation”. The other options describe repeated failure, enduring winter, or staying calm under pressure — none captures the sense of imminent risk.

The active sentence is in the simple present tense with object "the house". Conversion rule: object becomes subject + is/am/are + past participle + by + agent. "The house" is singular, so use is; the past participles are vacuumed and dusted. This gives: Every day the house is vacuumed and dusted by the maid. Option 2 uses plural were (wrong tense and agreement); options 3 and 4 shift to continuous forms, changing the tense.

The noun time here is singular and refers to a specific occasion, so it needs a singular demonstrative. "These" and "Those" are plural (would require "times"), and "At time" is incomplete (one would say "At that time"). The fixed phrase This time idiomatically marks the current/particular occasion — "This time, the strokes were more fluid" — making option 4 correct.

For exclamatory praise in direct speech, the reporting verb said together with "Bravo!" is replaced by a verb of applause such as applauded, and the reason for the praise is introduced by for. Since the original is in the past tense, the reported verb stays in the past. This yields The spectators applauded Jay for his good hit. Options 2 and 4 retain direct-speech fragments; option 3 wrongly shifts to present tense.

The blank needs an infinitive of purpose explaining why the speaker turned back. "I turned back one last time to say hello to a clown fish" uses "to + base verb" to express intention. "Said" and "says" clash with the past-tense main verb "turned" and create two unconnected finite verbs. "Saying" (participle) would need a comma and doesn't convey purpose. Hence the answer is to say.

The opener "The space in front of the large" needs a noun, so X ("hut was empty, but") follows naturally, identifying the object and introducing a contrast. After "but", Z ("before it were") uses "it" to refer back to the hut and supplies the plural verb "were", which then demands a plural subject. Y ("placed several stools") supplies that subject and completes the inversion: "...before it were placed several stools." Hence the order is XZY.

Vehement means showing strong, forceful, passionate feeling (e.g. vehement protest, vehement denial) — a direct match for the clue "Showing strong feeling". Meek = submissive and gentle; Apathetic = indifferent, showing no feeling; Impotent = powerless. Only Vehement conveys intense emotion.

The opener "From our common experience" needs a linking phrase, so X ("of the relation of the") follows, forming "...experience of the relation of the...". The phrase "the relation of the ___ and the ___" requires two nouns. Z ("physical and the") supplies the first noun and the connector "and", and Y ("mental he starts out") supplies the second noun, giving "the relation of the physical and the mental, he starts out". Hence the order is XZY.

The verb phrase play hide-and-seek takes the preposition with to name the partner or co-participant in the game ("play hide-and-seek with someone"). "To", "for" and "from" do not collocate with "play" in this sense. Hence "it played hide-and-seek with a sea anemone" is correct.

The idiom to hit the nail on the head means to identify or state something with perfect accuracy — i.e. to find exactly the right answer. The other options describe violence, error, or being trapped, none of which capture the idiom's sense of precision. Hence option 3 is correct.

Impugnable means open to challenge, dispute or doubt. The antonym must mean "not open to doubt; certain". Indubious (in- = not + dubious = doubtful) means unquestionable and free from doubt, making it the direct opposite. "Debatable" is a synonym of impugnable; "Dicey" means risky; "Hazy" means vague. Hence the answer is Indubious.

The phrase "the blue waters ___ the Bay of Bengal" needs a preposition showing that the waters belong to / are part of the bay. The preposition of expresses this possessive/partitive relationship: "the waters of the Bay of Bengal". "For" (purpose), "from" (origin/separation) and "to" (direction) do not fit this standard collocation. Hence the answer is of.

Adjectives ending in -ic form adverbs by adding the suffix -ally: stoic → stoically, basic → basically, automatic → automatically. Applying this rule, Stoically (stoic + ally) is the correct spelling. "Stoicaly" drops one "l"; "Stoecally" and "Stoecaly" wrongly insert "e" in the root. Hence option 1 is correct.

Veneration means deep respect, awe and reverence shown to someone or something. Its direct opposite is Contempt — the feeling that someone or something is worthless and beneath consideration. "Adoration", "Reverence" and "Admiration" are all synonyms of veneration, expressing varying degrees of respect. Only contempt reverses the meaning.

A litigant is a person engaged in a lawsuit. The word derives from the verb "litigate", keeping the i after "L" and "t" and the a before "-nts": Lit-i-g-a-nts. "Litegants" and "Litegents" wrongly use "e" in the first syllable; "Litigents" uses "e" instead of "a" before "nts". Only Litigants is correctly spelt.

Reproach means to express disapproval, blame or disappointment to someone. Admonish means to warn or reprimand firmly — the closest synonym, as both involve criticism aimed at correction. "Commend" and "laud" mean to praise (opposite), and "exonerate" means to clear from blame (also opposite). Hence the answer is To admonish.

The intensifier far is the standard collocation with "too + adjective" to indicate excess: far too expensive, far too late, far too extravagant. "Distance" and "long" relate to space/duration, not degree. "Very much too" is ungrammatical before "too + adjective". Hence the sentence reads: "The diamond necklace was far too extravagant for a simple dinner party."

The blank follows a duration ("a few glorious minutes") and points to what happened after it elapsed. The adverb later is used with a time span to mean "at a subsequent time" (e.g., five minutes later). "Late" means after the expected time; "lately" means recently; "latest" is a superlative adjective — none fits this slot. Hence the answer is later.

A scabbard is the protective case or sheath that holds the blade of a sword or dagger — an exact match for the clue. "Denude" (strip bare) and "Expose" (uncover) are opposites; "Divulge" (reveal information) is unrelated. Hence the answer is Scabbard.

The connector in order introduces purpose and must be followed by the infinitive form to + base verb. The bare base form "become" is ungrammatical here. Substituting to become gives "Read in order to become wise," which correctly expresses the purpose of reading. "To have to be" implies obligation and "to have become" (perfect infinitive) wrongly suggests the wisdom precedes the reading.

Reprise means to perform a role (or piece of music) again, which fits perfectly: the actor will play his pirate role once more, pleasing everyone. "Rescue," "save," and "free" all involve delivering someone or something from danger or restriction and do not describe taking up a role again. Hence the correct word is reprise.