SSC CGL 2017 · 2017-08-09 · Shift 1

The relationship is larger unit : 1000 × smaller unit of the same quantity. \(1\ \text{km}=1000\ \text{m}\), so for mass we need a unit such that \(1\ \text{tonne}=1000\ \text{?}\). Since \(1\ \text{tonne}=1000\ \text{kg}\), the answer is Kilogram. Litre (volume), Hours (time) and Weight (not a unit) do not fit.

Each letter shifts +8 positions in the alphabet: A(1)→I(9), G(7)→O(15), N(14)→V(22). Applying +8 to BLM: B(2)→J(10), L(12)→T(20), M(13)→U(21). Hence BLM → JTU.

The pattern links the two numbers by the sum of their digits, which increases by 10: \(9+1+4+3=17\) and \(9+9+6+3=27\), a jump of 10. For 6731, digit-sum \(=6+7+3+1=17\), so the answer must have digit-sum 27. Checking options: 1368→18, 5666→23, 8964→27, 9694→28. Hence the answer is 8964.

Chennai (Tamil Nadu), Raipur (Chhattisgarh) and Dispur (Assam) are capitals of Indian states. Daman, however, is a capital of the Union Territory of Dadra and Nagar Haveli and Daman and Diu. Hence Daman is the odd one out.

Letters B, D and P each contain a curved stroke in their structure. W is built from straight lines only, with no curves. Hence W is the odd letter.

Check divisibility by 5 (last digit 0 or 5): 425, 925 and 1035 all end in 5 and are divisible by 5. 313 ends in 3 and is not. Hence 313 is the odd number.

All five words share the prefix "Bal". Comparing the 4th letter, "Bala..." (a) precedes "Ball..." (l), so words 4, 2, 5 come before 1 and 3. Within the Bala-group, after "Balanc" the next letters are e(Balance), e→d(Balanced), i(Balancing): Balance(4) → Balanced(2) → Balancing(5). Within the Ball-group, Ball(1) precedes Balls(3) as the shorter word. Final order: 4-2-5-1-3.

Each term advances both letters by +11 positions (mod 26) in the alphabet. First letters: A(1) \(\to\) L(12) \(\to\) W(23) \(\to\) H(34\(\equiv\)8) \(\to\) S(19). Second letters: G(7) \(\to\) R(18) \(\to\) C(29\(\equiv\)3) \(\to\) N(14) \(\to\) Y(25). Hence the missing term is SY.

The series alternates addition and subtraction of consecutive odd numbers starting from 3. 13 \(\xrightarrow{+3}\) 16 \(\xrightarrow{-5}\) 11 \(\xrightarrow{+7}\) 18 \(\xrightarrow{-9}\) 9 \(\xrightarrow{+11}\) 20 \(\xrightarrow{-13}\) ? \(20-13=7\). Hence the missing term is 7.

"Your father's wife" is the lady's mother; her sister is the lady's maternal aunt. This maternal aunt is also Punit's aunt, so Punit's mother and the lady's mother are sisters. Therefore the lady and Punit are children of two sisters, i.e. cousins. Since the lady is female, she is Punit's cousin sister.

Using the standard ranking formula: \[\text{Rank from Left}=\text{Total}-\text{Rank from Right}+1\] \[=45-20+1=26\] Hence the lemon tree is 26th from the left end.

Understanding the Word Formation Puzzle The question asks us to find which of the given words cannot be formed using only the letters available in the word "UNIFORMITY". To solve this, we first need to list the letters present in the word "UNIFORMITY" and their counts. Letters in UNIFORMITY The letters in the word "UNIFORMITY" are: U: 1 N: 1 I: 2 F: 1 O: 1 R: 1 M: 1 T: 1 Y: 1 So, we have one of each letter U, N, F, O, R, M, T, Y, and two occurrences of the letter I. Analyzing the Options for Word Formation Now, let's examine each option to see if it can be formed using the letters from "UNIFORMITY". We will check if all required letters for each option are present in our list of available letters and if their counts are sufficient. Option 1: ANNUITY Let's look at the letters needed to form the word "ANNUITY": A: 1 N: 2 U: 1 I: 1 T: 1 Y: 1 Comparing these required letters with the available letters in "UNIFORMITY": We need 'A', but there is no 'A' in "UNIFORMITY". We need two 'N's, but there is only one 'N' in "UNIFORMITY". Since the word "ANNUITY" requires letters ('A' and a second 'N') that are not available in "UNIFORMITY", this word cannot be formed. Option 2: FORUM Let's look at the letters needed to form the word "FORUM": F: 1 O: 1 R: 1 U: 1 M: 1 Comparing these required letters with the available letters in "UNIFORMITY": We need 'F', and there is one 'F' in "UNIFORMITY". We need 'O', and there is one 'O' in "UNIFORMITY". We need 'R', and there is one 'R' in "UNIFORMITY". We need 'U', and there is one 'U' in "UNIFORMITY". We need 'M', and there is one 'M' in "UNIFORMITY". All required letters for "FORUM" are available in "UNIFORMITY" with sufficient counts. Therefore, this word can be formed. Option 3: MINT Let's look at the letters needed to form the word "MINT": M: 1 I: 1 N: 1 T: 1 Comparing these required letters with the available letters in "UNIFORMITY": We need 'M', and there is one 'M' in "UNIFORMITY". We need 'I', and there are two 'I's in "UNIFORMITY" (one is sufficient). We need 'N', and there is one 'N' in "UNIFORMITY". We need 'T', and there is one 'T' in "UNIFORMITY". All required letters for "MINT" are available in "UNIFORMITY" with sufficient counts. Therefore, this word can be formed. Option 4: UNIFORM Let's look at the letters needed to form the word "UNIFORM": U: 1 N: 1 I: 1 F: 1 O: 1 R: 1 M: 1 Comparing these required letters with the available letters in "UNIFORMITY": We need 'U', and there is one 'U' in "UNIFORMITY". We need 'N', and there is one 'N' in "UNIFORMITY". We need 'I', and there are two 'I's in "UNIFORMITY" (one is sufficient). We need 'F', and there is one 'F' in "UNIFORMITY". We need 'O', and there is one 'O' in "UNIFORMITY". We need 'R', and there is one 'R' in "UNIFORMITY". We need 'M', and there is one 'M' in "UNIFORMITY". All required letters for "UNIFORM" are available in "UNIFORMITY" with sufficient counts. Therefore, this word can be formed. Conclusion Based on our analysis, the word "ANNUITY" cannot be formed using the letters from "UNIFORMITY" because it requires the letter 'A' and two 'N's, neither of which are available in the required quantity (or at all for 'A') in "UNIFORMITY". The other options, FORUM, MINT, and UNIFORM, can all be formed using the letters from "UNIFORMITY". Revision Table: Word Formation from UNIFORMITY Word Letters Required Available in UNIFORMITY? Can be Formed? ANNUITY A (1), N (2), U (1), I (1), T (1), Y (1) No 'A', Only one 'N' (Needs 2) No FORUM F (1), O (1), R (1), U (1), M (1) Yes (F:1, O:1, R:1, U:1, M:1 available) Yes MINT M (1), I (1), N (1), T (1) Yes (M:1, I:2, N:1, T:1 available) Yes UNIFORM U (1), N (1), I (1), F (1), O (1), R (1), M (1) Yes (U:1, N:1, I:2, F:1, O:1, R:1, M:1 available) Yes Additional Information: Letter Puzzles and Word Games Word formation puzzles, like the one above, are common in verbal ability and reasoning tests. They assess your attention to detail and vocabulary. The key is to carefully check the count of each letter needed for the potential word against the count of available letters in the source word. Variations might involve checking if letters are used more times than they appear in the source word, or if letters not present in the source word are used. Understanding how to break down words into their constituent letters and compare lists is a fundamental skill in solving these types of letter-based puzzles.

The code equals the sum of the alphabetical positions of the letters in the word. Check: TIRED = \(20+9+18+5+4=56\); BRAIN = \(2+18+1+9+14=44\). For LAZY: \(12+1+26+25=64\). Hence the code is 64.

Substitute the operators from each option and apply BODMAS. Option 2 (\(\div, \times, =\)): \(18\div 6\times 9 = 3\times 9 = 27\), which equals 27. True. The other options give \(12\), \(117\), and \(15\) respectively — none equal 27. Hence the correct set is \(\div, \times\) and \(=\).

The bracketed number equals the product of the two outer numbers divided by 6. Check: \(\dfrac{18\times 3}{6}=9\); \(\dfrac{36\times 5}{6}=30\). Pattern confirmed. Applying to 19 (A) 18: \(A=\dfrac{19\times 18}{6}=19\times 3=57\). Hence A = 57.

1512 ÷ 168 = 9 504 ÷ 56 = 9 Hence 56 is the correct answer.

The given figure has 17 triangles in total.

Statements: Some pens are pencils (\(P \cap C \neq \varnothing\)); All pencils are erasers (\(C \subseteq E\)). Conclusion I — Some pencils are not pens: A possibility diagram where the whole set of pencils sits inside pens (\(C \subseteq P\)) still satisfies both statements. In that case every pencil is a pen, so "some pencils are not pens" need not be true. Hence I does not follow. Conclusion II — Some erasers are not pens: Nothing forces any eraser to lie outside pens. A diagram in which all erasers are pens (\(E \subseteq P\)) with \(C \subseteq E\) still satisfies both premises. Hence II does not follow either. Therefore neither conclusion follows, matching option 3.

The four sides adjacent to face containing ‘4’ are faces containing ‘5’, ‘2’, ‘6’, and ‘3’. Thus the side opposite to ‘4’ is ‘1’.

Piano and Guitar are two types of music instruments. Thus, option figure 2 is correct.

The final pattern will be as shown in below, Thus image 3) completes the given pattern.

On close observation, we find that fig. 1 is embedded in question figure as shown below: Hence, Image of option 1) is correct answer.

The paper cutting folding image is given below: Hence, the correct answer is option 4.

The archived key marks Option 2 as correct; a worked explanation is not included in this transcription.

Locate each letter in the matrices (row, column). S in Matrix-I: 00, 11, 23, 32, 44. C in Matrix-I: 04, 12, 21, 33, 40. A in Matrix-II: 57, 68, 78, 86, 95. M in Matrix-II: 59, 66, 75, 87, 99. Option 2 gives S=11, C=04, A=86, M=59 — all valid. The other options contain at least one invalid code. Hence the code for SCAM is 11, 04, 86, 59.

The General Equilibrium Theory was formulated by the French economist Leon Walras in his work Éléments d'économie politique pure (1874). He modelled the economy as a system of simultaneous equations showing that all markets can clear together at one set of prices. Adam Smith and David Ricardo are classical economists who predate the theory, and J. M. Keynes is associated with macroeconomic aggregate-demand analysis.

A Demand Draft is a pre-paid banker's instrument: the bank collects the full amount upfront and then issues the draft, so payment is guaranteed by the bank itself. Hence it cannot be dishonoured for lack of funds — the funds are already with the bank. The other statements are true: a DD is a negotiable instrument, is a banker's cheque, and is issued only by a bank.

Under Article 60 of the Constitution of India, the oath of office to the President is administered by the Chief Justice of India; in his absence, the senior-most available Judge of the Supreme Court administers it. The Governor General's office ended in 1950, while the Prime Minister and Vice President have no constitutional role in the President's oath.

John Austin, the 19th-century British jurist, propounded the monistic (or legal/absolute) theory of sovereignty. He held that sovereignty resides in a determinate human superior who is habitually obeyed by the bulk of society and is not himself obedient to any higher authority; law is simply the command of this sovereign backed by sanctions. Darwin (biologist), Aristotle (political philosophy of the polis, not sovereignty), and Marx (class-struggle theory of the state) are not associated with the monistic theory.

Match each event to its year: III. Poona Pact — 1932; I. Quit India Movement — 1942; II. Shimla Conference — 1945; IV. Cabinet Mission — 1946. Arranging chronologically (earliest to latest): 1932 → 1942 → 1945 → 1946, which corresponds to III, I, II, IV.

In 1917, Mahatma Gandhi launched the Champaran Satyagraha in Bihar to support indigo cultivators oppressed by the British tinkathia system, under which peasants were forced to grow indigo on 3/20th of their land on unfair terms. It was Gandhi's first application of Satyagraha (truth-force, non-violent resistance) on Indian soil. The Non-Cooperation Movement (1920), Quit India Movement (1942) and Swadeshi Movement (1905, post-Bengal Partition) all came later and from different locations.

Tropical cyclones in the Northwest Pacific Ocean, including the China Sea, Japan and the Philippines, are called Typhoons. Hurricanes are the equivalent storms in the North Atlantic and Northeast Pacific; tornadoes (also called twisters) are violently rotating land-based air columns, much smaller in scale than tropical cyclones and unrelated to the China Sea naming convention.

Scandinavia, in its standard definition, comprises the three kingdoms of Denmark, Norway and Sweden — countries that share the closely related North Germanic languages (Danish, Norwegian, Swedish) and a common historical-cultural heritage. Finland is part of the broader Nordic group but is excluded from Scandinavia proper because Finnish is a Uralic language unrelated to the North Germanic family, and Finland's political history is distinct. Hence Finland is the odd one out.

Cattle are ruminants with a four-chambered stomach (rumen, reticulum, omasum, abomasum). They swallow grass quickly with minimal chewing and store it in the largest first chamber, the rumen, where microbial fermentation breaks down cellulose. The partly digested mass (cud) is later regurgitated, re-chewed and re-swallowed. The oesophagus is only a passageway; the small intestine handles absorption after full digestion; salivary glands secrete saliva but store nothing.

Red blood cells (erythrocytes) carry oxygen throughout the body. They contain haemoglobin, an iron-containing protein that binds oxygen in the lungs (where partial pressure is high) and releases it to tissues (where partial pressure is low). White blood cells are immune cells; plasma is mostly a transport medium for nutrients, hormones and wastes (only a tiny fraction of oxygen dissolves in it); nerves transmit electrical signals, not gases.

The kidneys perform excretion — they filter blood to remove metabolic wastes such as urea, creatinine, excess salts and water, eliminating them as urine. They also help regulate blood pressure, electrolyte and water balance. Respiration (gas exchange) is performed by the lungs; digestion by the alimentary canal and accessory glands; transportation by the circulatory system. None of these are primary kidney functions.

The bending or spreading of light around the edges of an obstacle or through a narrow slit is called diffraction. It is a characteristic wave phenomenon and becomes appreciable when the size of the slit or obstacle is comparable to the wavelength \(\lambda\) of light. Reflection is bouncing off a surface; refraction is bending while changing media; total internal reflection is complete reflection inside a denser medium beyond the critical angle — none describe bending around a corner or slit.

In a desert, the ground heats the air just above it, creating a stack of air layers whose density (and refractive index) increases with height. Light from the sky travelling downward repeatedly bends away from the normal as it enters successively rarer (hotter) layers — this is continuous refraction. Eventually the angle of incidence exceeds the critical angle \(\theta_c\), where \(\sin\theta_c = \dfrac{n_2}{n_1}\), and the ray undergoes total internal reflection, curving back up to the observer's eye. The brain projects it straight, producing the watery image on the sand. Hence a mirage involves both refraction and total internal reflection of light.

FORTRAN (FORmula TRANslation), developed by IBM in the 1950s, was purpose-built for scientific and mathematical computation — numerical analysis, simulations, weather forecasting, engineering calculations — so statement (II) describes a core use. It has no native graphics capability and is not designed for drawing pictures, making statement (I) the task FORTRAN is not used for. Therefore the correct choice is Only (I).

Bond strength is measured by the energy needed to break the bond. Covalent single, double and triple bonds are intramolecular and very strong — typical C–C, C=C and C≡C bond energies are roughly \(347,\ 614\ \text{and}\ 839\ \text{kJ/mol}\) respectively. A hydrogen bond is an intermolecular attraction between an H bonded to a highly electronegative atom (N, O, F) and another electronegative atom. Its energy is only about \(10\text{–}40\ \text{kJ/mol}\) — an order of magnitude weaker than any covalent bond listed. Hence the hydrogen bond is the weakest.

A neutralisation reaction follows the general pattern: Acid + Base → Salt + Water. The \(H^+\) from the acid combines with \(OH^-\) from the base to give water, while the remaining cation of the base and anion of the acid form a salt. Example: \(HCl + NaOH \rightarrow NaCl + H_2O\). Hence the blank is Salt. Carbon dioxide forms only when acids react with carbonates; hydrogen gas evolves with active metals, not bases.

The Bishnoi movement is rooted in the protection of trees, particularly the sacred Khejri tree. In 1730, at Khejarli village near Jodhpur, 363 Bishnois led by Amrita Devi sacrificed their lives hugging trees to stop the Maharaja of Marwar's soldiers from felling them for a new palace. The movement was therefore primarily started against the cutting of trees. While Bishnoi principles also forbid killing animals, the defining historical trigger was tree-felling, not hunting or pollution.

The Pradhan Mantri Ujjwala Yojana (PMUY), launched on 1 May 2016 by the Ministry of Petroleum & Natural Gas, aims to provide free LPG connections to women from BPL households. Its goal is to replace polluting traditional fuels (firewood, dung) with clean cooking gas, improving women's health and reducing indoor air pollution. Electricity falls under Saubhagya Yojana, LED bulbs under UJALA, and village roads under PMGSY — none relate to Ujjwala.

John Logie Baird, a Scottish engineer, gave the first public demonstration of a working television system in London in 1926, transmitting moving silhouette images using a mechanical Nipkow disk. He is widely credited as the inventor of television. Faraday and Joseph Henry are associated with electromagnetic induction, and Giovanni Caselli built the pantelegraph (an early fax), not television.

In standard indoor volleyball, each team fields 6 players on the court at a time — three in the front row and three in the back row — as per FIVB rules. Substitutes sit on the bench but are not on court simultaneously. Basketball uses 5, kabaddi uses 7; the volleyball figure is 6. Beach volleyball (a variant) has 2 per side, but the standard format referenced here is 6.

Matching each temple with its presiding deity: 1. Lingaraja Temple, Bhubaneswar (Odisha) — dedicated to Lord Shiva (as Harihara) → c. 2. Tijara Mandir, Alwar (Rajasthan) — a Digambar Jain temple of Chandraprabha, associated with the Jain tradition of Lord Mahavira → a. 3. Venkateswara Temple, Tirupati — dedicated to Lord Venkateswara, a form of Lord Vishnu → b. Hence the correct combination is 1–c, 2–a, 3–b.

Among the listed names, author Preeti Shenoy — one of India's bestselling English-language fiction writers — was recognised with the 'Indian of the Year' honour by a leading media platform for her literary contributions. Sunita Rani is an athlete, while Dhiraj Singh and Abhishek Kumar are not linked to this award.

Selection Day (2016) is a novel by Aravind Adiga, the Booker-winning author of The White Tiger. Set in Mumbai, it follows two brothers groomed to be cricket prodigies and explores class, ambition and modern Indian society. It was later adapted into a Netflix series. Anil Menon writes science fiction, Krishna Sobti was a Hindi novelist, and Arunava Sinha is a Bengali-to-English translator — none of them wrote Selection Day.

BRICS originally stood for Brazil, Russia, India, China and South Africa (added in 2010). Brazil, Russia and China are all founding members. Iceland is a Nordic European country and has never been part of BRICS, making it the odd one out.

The Kalapani region lies at the tri-junction of India, Nepal and China in Uttarakhand's Pithoragarh district. India administers it, but Nepal claims it as part of Darchula district. The dispute arises from differing interpretations of the source of the Kali River, the boundary fixed by the 1816 Treaty of Sugauli. Hence Kalapani is a territorial dispute between India and Nepal. Bangladesh, Pakistan and Sri Lanka are unrelated to this particular issue.

Step 1 — Take LCM of indices: The roots are 3, 4, 6, 12. LCM = 12. Raise every term to the 12th power to compare. \((\sqrt[3]{5})^{12}=5^{4}=625\) \((\sqrt[4]{6})^{12}=6^{3}=216\) \((\sqrt[6]{12})^{12}=12^{2}=144\) \((\sqrt[{12}]{276})^{12}=276\) Step 2 — Compare: 625 > 276 > 216 > 144. The largest is 625, corresponding to \(\sqrt[3]{5}\). Therefore \(\sqrt[3]{5}\) is the largest.

Step 1 — Find C's share: A + B did 60%, so C did \(100\%-60\%=40\%\). Step 2 — Find A's share: B + C did 70%, so A did \(100\%-70\%=30\%\). Step 3 — Find B's share: \(B = 60\%-30\% = 30\%\). Step 4 — Compare: A = 30%, B = 30%, C = 40%. Since all worked for the same duration, efficiency is proportional to work done. Therefore C is the most efficient.

Step 1 — New sphere radius (volume conserved): \[r_{new}^3 = 3^3+4^3+5^3 = 27+64+125 = 216 \implies r_{new}=6 \text{ cm}\] Step 2 — Surface areas: Initial total \(=4\pi(3^2+4^2+5^2)=4\pi(50)=200\pi\) cm2. Final \(=4\pi(6^2)=144\pi\) cm2. Step 3 — Percentage decrease: \[\frac{200\pi-144\pi}{200\pi}\times 100=\frac{56}{200}\times 100=28\%\] Therefore the surface area decreases by 28%.

Step 1 — Price after first 10% discount: \[4800\times(1-0.10)=4800\times 0.9=4320\] Step 2 — Second discount amount: \(4320-3672=648\). Step 3 — Second discount percentage (on 4320): \[\frac{648}{4320}\times 100=\frac{3}{20}\times 100=15\%\] Therefore the second discount is 15%.

For exactly 1 year with annual compounding, CI equals SI, so interest \(=\dfrac{P\cdot R}{100}\), i.e. proportional to \(P\times R\). Take principals as 3, 4, 5 and rates 20, 15, 10: \(3\times 20 : 4\times 15 : 5\times 10 = 60:60:50 = 6:6:5\) Therefore the ratio of interests is 6 : 6 : 5.

Step 1 — Total ages: Initial: \(120\times 60.7=7284\). After addition: \(150\times 56.3=8445\). Step 2 — Sum of ages of 30 new members: \[8445-7284=1161\] Step 3 — Average of new members: \[\frac{1161}{30}=38.7 \text{ years}\] Therefore the average age of the new members is 38.7 years.

Let SP and CP be per pineapple. Gain on 175 pineapples \(=175\,SP-175\,CP\), and this equals \(50\,SP\). \[175\,SP-175\,CP=50\,SP \implies 125\,SP=175\,CP \implies \frac{SP}{CP}=\frac{7}{5}\] Gain on one item \(=SP-CP=\tfrac{2}{5}CP\), so \[\text{Gain }\%=\frac{2/5\,CP}{CP}\times 100=40\%\] Therefore the gain percentage is 40%.

Let B = 100. Then A \(=100+20=120\). Percentage by which B is less than A (base = A): \[\frac{A-B}{A}\times 100=\frac{20}{120}\times 100=\frac{100}{6}\approx 16.66\%\] Therefore B's marks are 16.66% less than A's. Equivalently, using \(\frac{x}{100+x}\times 100=\frac{20}{120}\times 100\).

Let distance be \(D\). Speeds: \(S_1=D/6\) (Delhi→Jaipur), \(S_2=D/5\) (Jaipur→Delhi). Step 1 — Gap at 12 p.m.: Train 1 has run 2 hours, covering \(2\cdot D/6=D/3\). Remaining gap \(=2D/3\). Step 2 — Relative speed (opposite directions): \[S_1+S_2=\frac{D}{6}+\frac{D}{5}=\frac{11D}{30}\] Step 3 — Time to meet after 12 p.m.: \[t=\frac{2D/3}{11D/30}=\frac{20}{11}\text{ hr}=1\text{ hr }\tfrac{540}{11}\text{ min}\approx 1\text{ hr }49\text{ min}\] Therefore they meet at approximately 1:49 p.m.

For half-yearly compounding at 8% p.a. for 1 year, rate per period = 4%, periods = 2. Step 1 — Express CI and SI: \[CI=P\left[\left(1+\tfrac{4}{100}\right)^2-1\right]=P\cdot\tfrac{51}{625},\quad SI=\tfrac{P\cdot 8\cdot 1}{100}=\tfrac{50P}{625}\] Step 2 — Apply the difference: \[CI-SI=\frac{51P-50P}{625}=\frac{P}{625}=64\] \[P=64\times 625=40000\] Therefore the sum is Rs 40,000.

If \((x-2)\) and \((x+3)\) are factors of the monic quadratic, then \[(x-2)(x+3)=x^2+x-6\] Comparing with \(x^2+k_1 x+k_2=0\): \(k_1=1\) and \(k_2=-6\). Therefore \(k_1=1,\ k_2=-6\).

Let \(A=x-15\) and \(B=y-8\). Then \[A-B=(x-15)-(y-8)=(x-y)-7=7-7=0\] So \(A=B\), which gives \(A^3-B^3=0\). Therefore \((x-15)^3-(y-8)^3=\mathbf{0}\).

Given: x – y = –1 + √18 ----(i) ⇒ x + y = 1 + 3√2 ----(ii) Multiplying (i) and (ii) . We get ⇒ x 2 – y 2= (–1 + √18) (1 + 3√2) ⇒ x 2 – y 2= -1 + 18 = 17 Now, from (i) and (ii) ⇒ x = 3√2 and y = 1 So, 12xy = 12(3√2) = 36√2 ∴ Required value = 12xy(x 2 – y 2) = (36√2) (17) = 612√2

Since \(\dfrac{p}{q}=\dfrac{r}{s}=\dfrac{t}{u}=\sqrt{5}\), squaring gives \(p^2=5q^2,\ r^2=5s^2,\ t^2=5u^2\). Substitute into the numerator: \[3p^2+4r^2+5t^2=5\bigl(3q^2+4s^2+5u^2\bigr)\] \[\therefore\ \frac{3p^2+4r^2+5t^2}{3q^2+4s^2+5u^2}=\mathbf{5}\]

AD is a common altitude of both triangles ABD and ADC, with bases BD and DC on the same line. Step 1 — Find BD: \(BD=BC-DC=9-3=6\) cm. Step 2 — Equal heights, so areas in ratio of bases: \[\frac{[\triangle ABD]}{[\triangle ADC]}=\frac{BD}{DC}=\frac{6}{3}=\frac{2}{1}\] Therefore the ratio is 2 : 1.

Step 1 — Find hypotenuse PQ: \(PQ=\sqrt{PR^2+RQ^2}=\sqrt{9+16}=5\) cm. Step 2 — Equate two area expressions: Area \(=\tfrac{1}{2}\cdot PR\cdot RQ=\tfrac{1}{2}\cdot PQ\cdot RS\). \[\tfrac{1}{2}\cdot 3\cdot 4=\tfrac{1}{2}\cdot 5\cdot RS\implies RS=\dfrac{12}{5}\text{ cm}\] Therefore RS = 12/5 cm.

For the incentre B, the standard result is \(\angle PBR=90^\circ+\tfrac{1}{2}\angle Q\). For the orthocentre A, \(\angle PAR=180^\circ-\angle Q\). Step 1 — Find ∠Q: \(105^\circ=90^\circ+\tfrac{1}{2}\angle Q\implies \angle Q=30^\circ\). Step 2 — Apply orthocentre formula: \(\angle PAR=180^\circ-30^\circ=150^\circ\). Therefore ∠PAR = 150°.

The maximum number of intersection points for 4 lines (no two parallel, no three concurrent) is \(\binom{4}{2}=6\). Achievable counts are 0 (all parallel), 1 (all concurrent), 3 (three parallel + one transversal), 4 (two pairs of parallels, or three concurrent + one separate), 5 (two parallel + two intersecting them and each other), and 6 (general position). Since 7 exceeds the maximum 6, 7 cannot occur.

Rewrite using sine and cosine: \[\operatorname{cosec}2A+\cot 2A=\dfrac{1+\cos 2A}{\sin 2A}\] Apply \(1+\cos 2A=2\cos^2 A\) and \(\sin 2A=2\sin A\cos A\): \[\dfrac{2\cos^2 A}{2\sin A\cos A}=\dfrac{\cos A}{\sin A}=\cot A\] Therefore the expression simplifies to cot A.

The exponent 3 denotes a power applied to the trig value, not a triple angle. So evaluate \(\sin^3 A+\cos^3 B+\tan^3 C-3\sin A\cos B\tan C\). With \(\sin 30^\circ=\tfrac{1}{2}\), \(\cos 60^\circ=\tfrac{1}{2}\), \(\tan 135^\circ=-1\): \[\left(\tfrac{1}{2}\right)^3+\left(\tfrac{1}{2}\right)^3+(-1)^3-3\cdot\tfrac{1}{2}\cdot\tfrac{1}{2}\cdot(-1)=\tfrac{1}{8}+\tfrac{1}{8}-1+\tfrac{3}{4}=0\] The identity \(a^3+b^3+c^3-3abc=(a+b+c)(\dots)\) with \(a+b+c=\tfrac{1}{2}+\tfrac{1}{2}-1=0\) confirms the value is 0.

Group using identities. By Pythagoras: \(\sin^2\theta+\cos^2\theta=1\). By AM-GM with \(\tan^2\theta\cdot\cot^2\theta=1\): \(\tan^2\theta+\cot^2\theta\ge 2\). Using \(\sec^2\theta=1+\tan^2\theta\) and \(\operatorname{cosec}^2\theta=1+\cot^2\theta\): \[\sec^2\theta+\operatorname{cosec}^2\theta=2+\tan^2\theta+\cot^2\theta\ge 4\] All three minima are reached together at \(\theta=45^\circ\), giving total \(1+2+4=\mathbf{7}\).

Number of hours dedicated to algebra = (9/100) x 500 = 45 hours Number of hours dedicated to modern maths = (4/100) x 500 = 20 hours ∴ difference in number of hours of teaching algebra and modern Maths = 45 – 20 = 25 hours.

Number of hours dedicated to geometry = 36 hours Since, 36 hours is 6% of the total hours taught ⇒ 1% of total hours = 36/6 = 6 hours ⇒ Total hours = 6 x 100 = 600 hours Number of hours dedicated to arithmetic = (46/100) (600) = 276 hours ∴ Number of hours dedicated to ratio = 276/4 = 69 hours

% of time dedicated to Data Interpretation and Modern Maths = 8 + 4 = 12% ⇒ Given : 12% of total hours = 96 hours ⇒ 1% of total hours = 96/12 = 8hours Hence, total hours = 8 x 100 = 800 hours ⇒ % time dedicated to Number system and Geometry taught = 23 + 6 = 29% So, total hours dedicated to Number system and Geometry = 800 x (29/100) = 232 hrs ∴ answer is 232 hours

% left after removing arithmetic = 100 – 46 = 54% ⇒ 10% of the left percentage is dedicated to problem solving ⇒ % dedicated to problem solving = (10/100) x 54 = 5.4% ∴ the central angle = (5.4/100) x 360° = 19.44°

The 'if' clause uses past perfect ("If you had told me earlier"), which sets up the third conditional. The main clause must therefore take "would have + past participle", not the simple future "will help". The error lies in part (3) "I will help you"; the correct form is "I would have helped you."

Adjective-preposition collocations differ here: "angry" pairs with with (a person), while "indifferent" pairs with to. The sentence forces both adjectives to share "to me", which is wrong for "angry". The fix is "angry with and indifferent to me." Hence the error sits in part (2) "angry and", where the preposition "with" is missing.

"Loiter" collocates with around to mean lingering aimlessly in or about a place. "Off" and "of" are grammatically wrong with "loiter", and "at" would point to a single spot rather than the length of the corridor. The correct sentence is "Don't loiter around the corridor."

When the main clause is in the simple future ("I will scold him"), a subordinate clause introduced by the temporal conjunction "when" takes the simple present, not "will". Therefore the correct completion is "he comes": "I will scold him when he comes." "He will come", "he would come" and "he had come" all violate this sequence-of-tenses rule.

Mellifluous means sweet-sounding, smooth and pleasing to the ear (from Latin mel, honey + fluere, to flow). Dulcet means sweet and soothing, especially of a sound or voice — an exact match. "Shiver" (tremble), "Frank" (candid) and "Immoral" (unethical) bear no relation to sound quality.

Dodge means to evade something by a quick movement or by cunning — essentially, to avoid. "He dodged the question" = "He avoided the question." "Soften" (make less harsh), "Order" (command/arrangement) and "Chaotic" (disordered) carry unrelated meanings, so Avoid is the correct synonym.

Meretricious means apparently attractive but lacking real value — gaudy, showy, or artificially flashy. Its antonym must convey genuineness and lack of artificiality. Natural means unaffected, genuine, and not artificial — the direct opposite of falsely showy. Hence the answer is Natural. Gaudy is a synonym, not an antonym. Brazen (bold, shameless) and Exemplary (model-worthy) describe unrelated qualities.

Nebulous means vague, hazy, or ill-defined. Its antonym must convey clarity and precision. Definite means clearly defined, distinct, and not vague — a direct opposite. Hence the answer is Definite. Inchoate (just begun, undeveloped) is closer to a synonym than an antonym. Dismal and Sullen describe gloomy moods, unrelated to clarity.

The idiom Spick and Span describes something perfectly tidy and clean, free of dirt or clutter. The phrase that matches this meaning is Neat and clean. High and low means everywhere; Dark and light refers to illumination; Happy and sad refers to emotions — none relate to cleanliness.

The idiom To draw the longbow means to tell an improbable story or stretch the truth — i.e. to exaggerate. Hence the correct substitute is To exaggerate. To nullify (make void), To underrate (the opposite of exaggerate) and To demarcate (set boundaries) do not fit the figurative sense of overstatement.

The idiom "add another feather to one's cap" means to gain a fresh honour or credit for a notable achievement. Rescuing a child from fire is exactly such an achievement, so the bracketed phrase fits the context perfectly. Option 1 contradicts the heroic act; Option 2 ("gifted with precious thing") misreads the idiom as receiving a gift; Option 3 ("crowned and rewarded") is too literal. Hence No improvement is required.

The phrasal verb take up means to begin or undertake an activity or task — exactly what the government is doing with the construction project. The original sentence is grammatically correct and contextually apt. Take off (leave the ground / succeed) and take in (understand / deceive) do not fit. While take on is also acceptable, it is not required as an improvement. Hence No improvement.

The phrase describes a person lacking kindness and sympathy — i.e. emotionally hardened and insensitive to others' suffering. Callous precisely means insensitive and unsympathetic, making it the correct substitute. Credulous and Gullible both mean easily deceived, and Bohemian denotes an unconventional lifestyle — none relate to absence of sympathy.

A Glutton is a person who eats excessively or is greedy in eating — the exact match for the given phrase. Impostor means one who pretends to be someone else; Hypochondriac means one excessively anxious about health; Intestate refers to someone who dies without making a will. None relate to overeating.

Checking each option: Forfeit, Gorilla, and Corrupt are spelt correctly. Blissfull is incorrect. The suffix -ful (meaning "full of") always carries a single l when added to a noun. The correct form is Blissful.

Afforestation, Foreigner, and Achievement are all spelt correctly. Translusent is incorrect. The word meaning "allowing light to pass through diffusely" derives from Latin lucere (to shine) and is correctly spelt Translucent — with a c, not an s.

Q is the opening — it introduces the topic by stressing the need for clarity about the goals of higher education in the context of national development. R follows naturally with "No doubt, one of the important aims…", specifying creation of trained manpower as a key aim drawn from Q's broader goals. S then explains the mechanism — the educational apparatus must be geared progressively to fulfil sectoral requirements identified in R. P concludes by stating the ultimate aim: avoiding both paucity and surfeit of trained manpower. Hence the order is QRSP.

Q opens by introducing the first internal problem — arrogant managers who misjudge performance and learn slowly. S extends this with a parallel problem: inwardly focused employees who miss external threats and opportunities, complementing Q's manager-level failure. P broadens the picture to organisational culture — bureaucratic cultures smother those who try to respond, providing the structural backdrop for Q and S. R concludes with "And the lack of leadership…", where "the morass" refers to the combined problems above. Hence the order is QSPR.

The active sentence "She teaches us English" is in the Simple Present tense with two objects: indirect ("us") and direct ("English"). Either object can become the passive subject. Taking the indirect object "us" as the new subject gives "We are taught English by her." The structure is Subject + is/am/are + past participle + by + agent, which matches Simple Present passive. Option 1 uses present continuous ("is being taught"); Option 3 uses present perfect ("have been taught"); Option 4 uses past perfect ("had been taught"). Only Option 2 preserves the Simple Present tense.

For a yes/no interrogative in direct speech, the reporting verb "said to" becomes "asked", the conjunction "if" (or "whether") joins the clauses, and the sentence becomes assertive in order. Since the reporting verb is past tense, "will" shifts to "would". Pronouns change: "you" (Swati) becomes "she", "me/my" (Nisha) become "her". The time marker "just now" shifts to "just then". This yields: "Nisha asked Swati if she would help her in her project just then." Options 1, 3, and 4 fail on reporting verb, conjunction, tense, or time-shift rules.

The sentence states a core duty of democracy toward individual dignity. "Ensure" means to guarantee or make certain, which captures democracy's active commitment to protect dignity. "Built" is wrong because dignity is inherent, not constructed. "Keep" is weak and intransitive in this context. "Support" is too passive for a guaranteed obligation. Hence the correct word is ensure.

The blank is part of the well-known utilitarian principle "the greatest good of the greatest number", associated with Bentham and Mill and often cited as a democratic ideal. "Smallest" contradicts the aim of collective welfare. "Largest" does not collocate naturally with "good". "Heaviest" is irrelevant. Only greatest completes the standard phrase.

The blank completes the standard utilitarian phrase "the greatest good of the greatest number", signifying maximum benefit to the largest section of society. "People" is grammatically possible but breaks the fixed idiom. "Digit" is meaningless here. "Individual" contradicts the collective sense of "greatest". Therefore number is correct.

An opposition party's defining role is to challenge and resist the ruling government's flawed plans, policies, and decisions. The verb that conveys this is "oppose". "Rely on" implies dependence — the opposite role. "Against" is a preposition, not a verb, so it fails grammatically. "Support" would mean endorsing wrong actions, contradicting the opposition's function. Hence oppose fits.

A government strengthens its position by addressing the real, fundamental requirements of citizens — basic necessities, safety, and services. The word for such real needs is "genuine". "Mere" trivialises needs. "Emotional" is too narrow to make a government's position solid. "Luxurious" denotes non-essential comforts, which would alienate the public rather than build support. Hence genuine is correct.