SSC CGL 2017 · 2017-08-10 · Shift 1

Check each number against perfect cubes: \(216 = 6^3,\ 125 = 5^3,\ 343 = 7^3\) However, \(510\) lies between \(7^3 = 343\) and \(8^3 = 512\), so it is not a perfect cube. Therefore 510 is the odd one out.

Split each pair: the first letters K, L, M move +1 forward, while the second letters V, U, T move -1 backward. Next first letter: M + 1 = N. Next second letter: T - 1 = S. Hence the missing term is NS.

From "All stars are white" and "All white are moon", we get All stars are moon; combined with "No moon is blue", we also get No star is blue, and from St II + III, No white is blue. Conclusion I (Some moon are stars): Converse of "All stars are moon" — follows. Conclusion II (No blue is stars): Converse of "No stars are blue" — follows. Conclusion III (Some white are stars): Converse of "All stars are white" — follows. Conclusion IV (Some blue are white): Contradicts "No white is blue" — does not follow. Therefore only I, II, and III follow.

Clearly, fig.4 will complete the pattern when placed in the blank space of question figure as shown below: Option figure 4 will complete the question figure as shown in above diagram.

Square, Rectangle and Triangle are all two-dimensional polygons (flat shapes bounded by straight sides). A Cylinder is a three-dimensional solid with two circular bases and a curved surface — it has volume, unlike the others. Hence Cylinder is the odd one out.

Each letter in the first group shifts +2 positions forward to give the second group: J(10) → L(12), Q(17) → S(19), X(24) → Z(26), E(5) → G(7). Applying +2 to MTNL: M(13) → O(15), T(20) → V(22), N(14) → P(16), L(12) → N(14). Hence the answer is OVPN.

Compare letter by letter. All five words start with D, so look at the second letter: Deviate (De-) < Dormont (Do-) < the three "Dr-" words. Among the Dr- words, the third letter decides: Draculla, Dragon, Drapery all share "Dra"; the fourth letters c < g < p give the order Draculla < Dragon < Drapery. Final order: Deviate (5), Dormont (3), Draculla (2), Dragon (1), Drapery (4) → 53214.

Each 2×2 grid has cells that sum to a constant. Grid 1: \(3 + 17 + 11 + 4 = 35\). Grid 2: \(2 + 16 + 10 + 7 = 35\). Grid 3: \(6 + 13 + 15 + ? = 35 \implies ? = 35 - 34 = 1\). Hence the missing number is 1.

List the letters available in SUPERCONDUCTORS: S, U, P, E, R, C, O, N, D, T (with repeats of S, R, C, O). Check each option: Sports (S, P, O, R, T), Spunt (S, P, U, N, T) and Stern (S, T, E, R, N) use only these letters. Spectrum needs the letter M, which does not appear in SUPERCONDUCTORS. Hence Spectrum cannot be formed.

Use alphabet positions (A=1 … Z=26) and take the difference of the sums of the two words. PEN-TAN: \((16+5+14) - (20+1+14) = 35 - 35 = 0\). Matches the given code. DEN-COB: \((4+5+14) - (3+15+2) = 23 - 20 = 3\). Hence the code is 3.

The four adjacent sides to face containing ‘5’ are ‘3’, ‘6’, ‘4’ and ‘2’. Therefore the opposite side to ‘5’ should be faced containing ‘1’. Trick: How to easily find the opposite faces: Choose any 2 dices which have only one number in common. As in, I and II only 5 is common. Now move clockwise as per the dice. In I, 5 - 3 - 6 In II, 5 - 2 - 4 So, we can observe that 3 is opposite to 2 and 6 is opposite to 4. Now only 5 is left, which will be opposite to 1.

When we open the punched folded paper then it will appear as it is shown in the below figure. Hence, “Image of option 2)” shows correct answer.

Read # as multiplication and @ as addition, evaluated with normal precedence (multiply first, then add). Check example 1: \(5\#9@7 = 5\times 9 + 7 = 45 + 7 = 52\). Matches. Apply to the question: \(7\#6@9 = 7\times 6 + 9 = 42 + 9 = 51\). The marked option 67 does not match this rule (it would correspond to \(7\times 9 + 6 - 2 = 67\) or similar contrived adjustments), but among the four given choices the option keyed by the test is 67.

Therefore above image represent mirror image of given question figure. Therefore, option 4) is the correct answer.

The relationship is Country : Capital — Ottawa is the capital of Canada. Applying the same relation, Cairo is the capital of Egypt. The other pairs are wrong capitals — Havana is Cuba's (Norway's is Oslo), Rome is Italy's (France's is Paris), and Tehran is Iran's (Kenya's is Nairobi).

Hence, only 7 open flats are rough.

Let Anil's present age be \(4x\) and Aakash's be \(5x\). Three years later, the ratio condition gives: \[\frac{4x+3}{5x+3}=\frac{7}{8}\] Cross-multiplying: \(8(4x+3)=7(5x+3)\), i.e. \(32x+24=35x+21\), so \(3x=3\) and \(x=1\). Therefore Anil's present age is \(4x=\mathbf{4}\) years. Check: after 3 years the ages are 7 and 8, ratio 7 : 8.

There are total of 15 triangles in the given figure.

The series interleaves three sub-sequences at positions (1,4,7,10,13...), (2,5,8,11,14...) and (3,6,9,12,15...). Sub-series A (positions 1,4,7,10,13): 3, 4, 6, 9, 13 — successive differences 1, 2, 3, 4. Sub-series B (positions 2,5,8,11,14): 4, 9, 16, 25, 36 — consecutive squares \(2^2,3^2,4^2,5^2,6^2\). Sub-series C (positions 3,6,9,12,15): 5, 10, 15, 20, ? — arithmetic with common difference 5. The 15th term belongs to sub-series C, so it is \(20+5=\mathbf{25}\).

The pattern is \(n \to n^2-1\): \(7^2-1=49-1=48\). Applying it to 11: \(11^2-1=121-1=\mathbf{120}\).

Karan's condition "not after 18th August" allows dates \(\le 18\). Mother's condition "after 17th and before 20th" allows only {18, 19}. The single date common to both sets is 18. Hence the sister's birthday is on the 18th of August.

Decoding each pair as (row, column) from the appropriate matrix: 20 → Matrix I, row 2 col 0 = P. 04 → Matrix I, row 0 col 4 = A. 79 → Matrix II, row 7 col 9 = L. 87 → Matrix II, row 8 col 7 = E. The set encodes PALE, so option (20, 04, 79, 87) is correct.

Replace the symbols per the code: ÷→×, +→–, –→+, ×→÷. Option 4: \(18 \times 6 \div 8 - 12 = 36\) becomes \(18 \div 6 \times 8 + 12\). Evaluating with BODMAS: \((18 \div 6)\times 8 + 12 = 3 \times 8 + 12 = 24+12 = 36\). LHS = RHS, so option 4 is the true equation. The other options yield \(422/21\), \(-67/6\) and \(-34\) respectively, none matching their RHS.

A, U and I are vowels of the English alphabet, while S is a consonant. Hence S is the odd one out.

The question figure is embedded in the following figure: Hence, question figure is embedded in option 2) figure.

Akbar, the third Mughal emperor, is historically recorded as illiterate — unable to read or write — yet he was an exceptional patron of learning who kept a vast library and had books read aloud to him daily. Jahangir authored the memoir Tuzuk-i-Jahangiri, Shah Jahan was schooled in Arabic and Persian, and Aurangzeb was a scholar of Islamic theology, so all three were literate.

"Certiorari" comes from the Latin certiorare, meaning "to be certified" or "to be informed". The writ is issued by a higher court to a lower court or tribunal to call up records and review the legality of its decision. The other literal meanings belong to different writs: "we command" (Mandamus), "to have the body of" (Habeas Corpus) and "to forbid" (Prohibition).

The Strait of Malacca is a narrow shipping channel between the Malay Peninsula (Malaysia/Singapore) on the northeast and the Indonesian island of Sumatra on the southwest. It links the Andaman Sea (Indian Ocean) with the South China Sea (Pacific Ocean) and is one of the world's busiest trade routes. Africa and Europe are separated by the Strait of Gibraltar, India and Sri Lanka by the Palk Strait.

On 23 January 2017, President Donald Trump signed an executive order withdrawing the United States from the Trans-Pacific Partnership shortly after taking office. The US exit effectively halted the original 12-nation deal; the remaining 11 countries later signed the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP) in 2018. Japan, Mexico and Brunei stayed on as signatories.

Thyroxin is a hormone secreted by the thyroid gland in animals; it regulates basal metabolism, growth and development, and is not produced by plants. Gibberellins (stem elongation, seed-dormancy breaking), auxins (cell elongation, apical dominance) and cytokinins (cell division, delayed senescence) are all phytohormones. Hence thyroxin is the odd one out.

The Azad Hind Fauj (Indian National Army) was founded in Singapore in 1942 by Rash Behari Bose, drawing recruits from Indian prisoners of war captured by Japan in Malaya and Singapore. It was later revitalised and led by Netaji Subhas Chandra Bose from 1943, with Singapore continuing as its principal base. Its motto was Ittehad, Etemad, Qurbani (Unity, Faith, Sacrifice).

Under Article 155 of the Constitution, the Governor of a State is appointed by the President of India by warrant under his hand and seal. The President acts on the aid and advice of the Union Council of Ministers, but the formal appointing authority is the President — not the Prime Minister, the Council of Ministers, or any judge of the Supreme Court. The Governor holds office during the pleasure of the President (Article 156).

The Balance of Payments is conventionally divided into the Current Account (goods, services, income, current transfers including unilateral payments) and the Capital Account (capital transfers and financial flows, including official reserves). The Official Reserves Account is not a separate standalone account of the BoP — changes in official reserves are recorded within the Capital/Financial Account as a balancing item that finances the overall surplus or deficit. Hence it is the option that is not an account under BoP.

Chhattisgarh was the first state to implement the Saur Sujala Yojana, launched on 1 November 2016 (state foundation day) by then PM Narendra Modi in Raipur. The scheme provides subsidised solar-powered irrigation pumps (3 HP and 5 HP) to farmers in areas with weak grid connectivity, reducing dependence on diesel pumps and improving irrigation access.

The biography Rekha: The Untold Story (2016) was authored by Yasser Usman, a journalist known for unauthorised celebrity biographies of Bollywood stars including Rajesh Khanna and Sanjay Dutt. Anand Neelakantan writes mythological fiction; Ram Kamal Mukherjee authored a biography of Hema Malini; K. Vijay Kumar is associated with policing/security writing — none wrote this book.

Nandalal Bose (1882–1966) was a pioneering Indian painter of the Bengal School, famous for illustrating the original manuscript of the Constitution of India. He had no association with the flute, so the pair Nandalal Bose – Flute is incorrect. Muthuswami Dikshitar (Carnatic Trinity composer), Parveen Sultana (Hindustani classical singer), and M.S. Gopalakrishnan (Carnatic/Hindustani violinist) are all correctly paired.

A neutral atom has equal numbers of protons and electrons. When it gains one or more electrons, it acquires a net negative charge and becomes an anion. For example, \(\text{Cl} + e^- \rightarrow \text{Cl}^-\). Losing electrons forms cations; gaining or losing neutrons only changes the mass number, producing isotopes, not ions.

The speed of light in a medium is \(v = c/n\), where \(n\) is the refractive index. A vacuum contains no particles with which light can interact, so its refractive index is exactly 1 — the lowest possible value. All material media (gases, liquids, solids) have \(n > 1\) and therefore slow light below \(c = 299{,}792{,}458\) m/s. Hence light travels fastest in a vacuum.

Acid rain is caused mainly by emissions of sulphur dioxide \((\text{SO}_2)\) and nitrogen oxides \((\text{NO}_x)\) from burning fossil fuels in power plants, vehicles, and industries. In the atmosphere these gases react with water and oxygen to form sulphuric acid \((\text{H}_2\text{SO}_4)\) and nitric acid \((\text{HNO}_3)\), which fall as acid rain. Carbon dioxide produces only weak carbonic acid; carbon monoxide and oxygen are not acid-rain precursors.

Globalisation is the interaction and integration among people, companies and governments of different nations — matches b. Privatisation is the transfer of a business, industry or service from public to private ownership and control — matches c. Liberalisation is the reduction or removal of restrictions on international trade — matches a. Hence the correct matching is 1-b, 2-c, 3-a.

Sir Tim Berners-Lee, a British computer scientist at CERN, invented the World Wide Web in 1989–1990. He designed the foundational standards — HTML, HTTP, and URLs — and built the first web browser and server; the first website went live in August 1991. Martin Cooper pioneered the handheld mobile phone, James Clerk Maxwell formulated electromagnetic theory, and S.A. Forbes was a biologist — none are linked to the WWW.

The nephron is the structural and functional unit of the kidney. Each kidney contains roughly one million nephrons, which filter blood, reabsorb useful substances, and form urine through filtration, reabsorption, and secretion. Since the kidneys (along with ureters, bladder, and urethra) constitute the excretory system, the nephron belongs to this system. It is not part of the circulatory, reproductive, or respiratory systems.

The veteran Indian actor Om Puri was posthumously honoured with the Outstanding Achievement in Cinema award at the 7th Asian Awards (2017). He passed away in January 2017, and the award recognised his decades-long body of work across Indian, British and Hollywood films, including Ardh Satya, East is East and The Hundred-Foot Journey. The Asian Awards, founded by Paul Sagoo in 2010, celebrate outstanding achievements of people of pan-Asian origin in cinema, sport, philanthropy and business.

An IPv4 address is written as four octets separated by dots (e.g. 192.168.1.1). Each octet is 8 bits, so the total length is \(4 \times 8 = 32\) bits, giving \(2^{32} \approx 4.29\) billion unique addresses. The newer IPv6 address is 128 bits, but unqualified references to "an IP address" in SSC-level questions point to IPv4. Hence the answer is 32 bits.

The SI base unit of electric current is the ampere (A), named after Andre-Marie Ampere. One ampere equals a flow of one coulomb of charge per second: \(1\,\text{A}=1\,\text{C/s}\). Newton is the unit of force, joule of energy/work, and watt of power (\(P=VI\)) — none of these measure current itself.

Vitamin D (cholecalciferol) is the "sunshine vitamin". When UV-B rays strike the skin, 7-dehydrocholesterol is converted into previtamin D3, which is then processed in the liver and kidneys into active vitamin D. It is essential for calcium absorption and bone health. Vitamin A (carrots, liver), Vitamin C (citrus) and Vitamin K (leafy greens) are obtained only from diet — they are not synthesised via sunlight.

Sikkim lies roughly between \(27^\circ\text{N}\) and \(28^\circ\text{N}\) latitude. Rajasthan extends from about \(23^\circ\text{N}\) to \(30^\circ\text{N}\), so the parallels passing through Sikkim also cross Rajasthan. Punjab (about 29-32°N) and Himachal Pradesh (about 30-33°N) lie entirely north of Sikkim's band, and Uttarakhand (about 28-31°N) only marginally touches its upper edge.

B. Sai Praneeth is an Indian professional badminton player. He won the men's singles title at the 2017 Singapore Open Super Series and a bronze medal at the 2019 BWF World Championships — the first Indian male shuttler to do so in 36 years. Hockey, chess and boxing are unrelated to his career.

The Padmanabhaswamy Temple is located in Thiruvananthapuram, Kerala (India) — not in Sri Lanka. Hence the pair "Sri Lanka - Padmanabhaswamy Temple" is mismatched. The other pairings are correct: the Great Wall is in China, Paro Taktsang (Tiger's Nest) is in Bhutan, and Pashupatinath Temple stands on the Bagmati in Kathmandu, Nepal.

Oxidation is defined as the loss of electrons by a species; the substance's oxidation state increases. For example, \(\text{Na}\to\text{Na}^{+}+e^{-}\) shows sodium being oxidised. Reduction is the opposite — a gain of electrons. Radiation is the emission of energy, not an electron-transfer process. Hence the process of losing electrons is oxidation.

A number that is both a perfect square and a perfect cube must be a perfect sixth power, since its prime-factor exponents must be multiples of \(\operatorname{lcm}(2,3)=6\). Step 1 — List sixth powers: \(3^6=729,\ 4^6=4096,\ 5^6=15625\) Step 2 — Apply the range 2000-7000: Only \(4^6=4096\) lies between 2000 and 7000 (note \(4096=64^2=16^3\)). Therefore exactly 1 such number exists.

Step 1 — Equalise the bases: Using \(\tfrac{y}{x}=\left(\tfrac{x}{y}\right)^{-1}\), the equation becomes \[\left(\tfrac{x}{y}\right)^{a-4}=\left(\tfrac{x}{y}\right)^{-(2a-5)}=\left(\tfrac{x}{y}\right)^{5-2a}\] Step 2 — The relation must hold for every \(a\): Equating exponents gives \(a-4=5-2a\Rightarrow a=3\), a specific value — not a relation between \(x\) and \(y\). For the identity to hold independently of \(a\), the base itself must equal 1, i.e. \(\tfrac{x}{y}=1\). Therefore \(x=y\).

Step 1 — Total runs of 7 players: \(7\times 53=371\) Step 2 — Sum of the 6 known scores: \(121+40+26+56+37+48=328\) Step 3 — 7th player's runs: \(371-328=43\) Therefore the 7th player scored 43 runs.

Step 1 — Effective cost price: Purchase + repairs = \(2700+500=3200\). Step 2 — Profit: \(\text{SP}-\text{CP}=3520-3200=320\). Step 3 — Profit %: \[\text{Profit \%}=\frac{320}{3200}\times 100=10\%\] Therefore Mohit's profit is 10%.

Step 1 — Combine cotA + tanA: \[\cot A+\tan A=\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}=\frac{\cos^2 A+\sin^2 A}{\sin A\cos A}=\frac{1}{\sin A\cos A}\] Step 2 — Multiply by (cosA + sinA): \[(\cos A+\sin A)\cdot\frac{1}{\sin A\cos A}=\frac{\cos A}{\sin A\cos A}+\frac{\sin A}{\sin A\cos A}=\frac{1}{\sin A}+\frac{1}{\cos A}\] Therefore the expression equals cosec A + sec A = sec A + cosec A, matching option 1.

Step 1 — Rate from Case 1: SI = 882 − 720 = 162 on P = 720 for T = 1.5 yr. \[R=\frac{SI\times 100}{P\times T}=\frac{162\times 100}{720\times 1.5}=15\%\] Step 2 — Time for Case 2: SI = 1040 − 800 = 240 on P = 800 at R = 15%. \[T=\frac{SI\times 100}{P\times R}=\frac{240\times 100}{800\times 15}=2\text{ years}\] Therefore the answer is 2 years (option 4).

Step 1 — Isolate sinθ: \(\sin\theta=2-2\cos\theta\). Step 2 — Apply \(\sin^2\theta+\cos^2\theta=1\): \[(2-2\cos\theta)^2+\cos^2\theta=1\] \[5\cos^2\theta-8\cos\theta+3=0\] Step 3 — Factor: \((5\cos\theta-3)(\cos\theta-1)=0\), giving \(\cos\theta=\tfrac{3}{5}\) or \(\cos\theta=1\). Therefore cos θ = 1 or 3/5 (option 1).

Step 1 — Exports of Year 1: Ratio 10:9, total trade 5700. \[E_1=\frac{10}{19}\times 5700=3000\text{ crore }\$\] Step 2 — Total trade Year 5: \(\tfrac{5700}{2}=2850\). Step 3 — Exports of Year 5: Ratio 12:13. \[E_5=\frac{12}{25}\times 2850=1368\text{ crore }\$\] Step 4 — Difference: 3000 − 1368 = 1632 crore dollars (option 2).

Let \(a=x+\sqrt{x^2-1}\). Since \((x+\sqrt{x^2-1})(x-\sqrt{x^2-1})=1\), we get \(x-\sqrt{x^2-1}=\tfrac{1}{a}\). Step 1 — Rewrite the equation: The given sum becomes \[\frac{a}{1/a}+\frac{1/a}{a}=a^2+\frac{1}{a^2}=194\] Step 2 — Find a + 1/a: \(\left(a+\tfrac{1}{a}\right)^2=a^2+\tfrac{1}{a^2}+2=196\), so \(a+\tfrac{1}{a}=14\). Step 3 — Recover x: \(a+\tfrac{1}{a}=(x+\sqrt{x^2-1})+(x-\sqrt{x^2-1})=2x\). Therefore \(2x=14\Rightarrow x=7\) (option 3).

Here, ΔPRM and ΔMRN are isosceles triangles Also, in ΔRPN ⇒ ∠RPM + ∠RNP = 102° ….(i) [EXTERIOR ANGLE PROPERTY] ⇒ ∠MRN = ∠MNR ⇒ ∠MRN + ∠MNR = ∠RMP …(ii) [EXTERIOR ANGLE PROPERTY ⇒ 2∠RNP = ∠RMP = ∠RPM By (i) and (ii), we get ⇒ 3/2(∠RPM) = 102° ⇒ ∠RPM = 68° ∴ the correct option is 2)

Step 1 — Simplify the given equation: Divide by 3: \[a-\frac{1}{a}=1\] Step 2 — Find \(a^2+\tfrac{1}{a^2}\): Square both sides. \[a^2-2+\frac{1}{a^2}=1\Rightarrow a^2+\frac{1}{a^2}=3\] Step 3 — Apply \(a^3-\tfrac{1}{a^3}=(a-\tfrac{1}{a})(a^2+\tfrac{1}{a^2}+1)\): \[a^3-\frac{1}{a^3}=1\times(3+1)=4\] Therefore \(a^3-\tfrac{1}{a^3}+2=4+2=\mathbf{6}\) (option 4).

Selling price after successive discounts of 20% and 12% relates to the marked price as: \[SP=MP\times\left(1-\frac{20}{100}\right)\left(1-\frac{12}{100}\right)=MP\times 0.80\times 0.88=0.704\,MP\] Solve for MP: \[MP=\frac{16896}{0.704}=24000\] Therefore the marked price is Rs 24000 (option 4).

For a fixed distance, time is inversely proportional to speed: \(T\propto\tfrac{1}{S}\). With speeds in ratio 3 : 4 : 6, times are in ratio \[\frac{1}{3}:\frac{1}{4}:\frac{1}{6}\] Multiplying each term by LCM(3,4,6) = 12 gives 4 : 3 : 2 (option 3).

Step 1 — Third angle of ΔABC: \(\angle ABC=180^\circ-(75^\circ+80^\circ)=25^\circ\). Step 2 — Central angle: The angle subtended by arc AC at centre O is twice that at B: \[\angle AOC=2\angle ABC=50^\circ\] Step 3 — Use isosceles ΔOAC (OA = OC): \(\angle OAC=\angle OCA\), so \[\angle OAC=\frac{180^\circ-50^\circ}{2}=65^\circ\] Therefore \(\angle OAC=\mathbf{65^\circ}\) (option 2).

Step 1 — Find \(x^2+\tfrac{1}{x^2}\): Square \(x+\tfrac{1}{x}=3\): \[x^2+\frac{1}{x^2}=9-2=7\] Step 2 — Divide numerator and denominator by \(x^2\): \[\frac{x^4+5x^3+3x^2+5x+1}{x^4+1}=\frac{\left(x^2+\tfrac{1}{x^2}\right)+5\left(x+\tfrac{1}{x}\right)+3}{x^2+\tfrac{1}{x^2}}\] Step 3 — Substitute: \[=\frac{7+5(3)+3}{7}=\frac{25}{7}\] Therefore the value is 25/7 (option 1).

Step 1 — Equivalence: Since 3 men and 4 women each finish in 120 days, 3M = 4W, i.e. 4 women ≡ 3 men. Step 2 — Convert the new group to men: 16 women ≡ \(\tfrac{16}{4}\times 3=12\) men. So 12 men + 16 women ≡ 24 men. Step 3 — Time: 3 men take 120 days, so 24 men take \[\frac{3\times 120}{24}=15\text{ days}\] Therefore the job is completed in 15 days (option 3).

Let car speed be \(V_c\) and train speed \(V_t=1.2\,V_c\). Step 1 — Equate total times (train stop = 0.5 hr): \(\frac{180}{V_c}=\frac{180}{V_t}+0.5\) Step 2 — Substitute \(V_c=V_t/1.2\): \(\frac{180\times 1.2}{V_t}-\frac{180}{V_t}=0.5\Rightarrow\frac{36}{V_t}=0.5\) Step 3 — Solve: \(V_t=\tfrac{36}{0.5}=72\) km/hr. Therefore the train's speed is 72 km/hr (option 3).

For constant expenditure, \(P_1 C_1 = P_2 C_2\), so \(\dfrac{C_2}{C_1}=\dfrac{P_1}{P_2}=\dfrac{24}{36}=\dfrac{2}{3}\). Percentage decrease in consumption \(=\left(1-\dfrac{2}{3}\right)\times 100=\dfrac{100}{3}\approx 33.33\%\). Therefore the household must reduce consumption by 33.33%.

AD is the median, so \(BD=DC=\tfrac{1}{2}BC\). Given \(AD=\tfrac{1}{2}BC\), hence \(AD=BD=DC\). Step 1 — Isosceles ΔACD: Since \(AD=DC\), \(\angle DAC=\angle ACD=40^\circ\). Step 2 — Isosceles ΔABD: Since \(AD=BD\), let \(\angle DAB=\angle ABD=x\). Step 3 — Angle sum in ΔABC: \((x+40)+x+40=180 \Rightarrow 2x=100\). Therefore \(\angle DAB=\mathbf{50^\circ}\). (The condition implies ∠BAC = 90°, a known right-angle median property.)

Radius \(r=\dfrac{21}{2}\) cm. Volume of a hemisphere \(=\dfrac{2}{3}\pi r^3\). \[V=\dfrac{2}{3}\times\dfrac{22}{7}\times\left(\dfrac{21}{2}\right)^3=\dfrac{2}{3}\times\dfrac{22}{7}\times\dfrac{9261}{8}=\dfrac{4851}{2}=2425.5\text{ cm}^3\] Therefore the volume is 2425.5 cm³.

In a rhombus the diagonals bisect at right angles, so each side, \(d_1/2\) and \(d_2/2\) form a right triangle: \(a^2=(d_1/2)^2+(d_2/2)^2\). With \(a=4\) and smaller diagonal \(d_1=4\): \(16=4+(d_2/2)^2 \Rightarrow d_2/2=2\sqrt{3} \Rightarrow d_2=4\sqrt{3}\) cm (the bigger diagonal). Area of an equilateral triangle of side \(s=4\sqrt{3}\): \[A=\dfrac{\sqrt{3}}{4}s^2=\dfrac{\sqrt{3}}{4}\times 48=12\sqrt{3}\text{ cm}^2\] Therefore the area is \(12\sqrt{3}\) cm².

Combine the fractions over the common denominator \((\csc A-1)(\csc A+1)=\csc^2 A-1\): \[\dfrac{\csc A(\csc A+1)+\csc A(\csc A-1)}{\csc^2 A-1}=\dfrac{2\csc^2 A}{\csc^2 A-1}\] Using \(\csc^2 A-1=\cot^2 A\) and writing in sin/cos: \(\dfrac{2/\sin^2 A}{\cos^2 A/\sin^2 A}=\dfrac{2}{\cos^2 A}=2\sec^2 A\). Taking the square root gives \(\sqrt{2\sec^2 A}=\sqrt{2}\,\sec A\). Therefore the answer is \(\sqrt{2}\sec A\).

Year 3 ratio of Exports : Imports is 4 : 3, so total trade corresponds to \(4+3=7\) parts. With total trade = 1183, one part \(=\dfrac{1183}{7}=169\) crore dollars. Difference = (Exports − Imports) parts × one part \(=(4-3)\times 169=169\) crore dollars. Therefore the difference is 169 crore dollars.

Step 1 — Year 4 values: Ratio 5 : 8 with Exports = 315 gives one part \(=315/5=63\), so Imports = \(8\times 63=504\). Total Trade (Year 4) \(=315+504=819\). Step 2 — Year 2 total: Year 2 total = Year 4 total = 819. Step 3 — Year 2 imports: Year 2 ratio 11 : 7, total parts \(=18\). One part \(=819/18=45.5\), so Imports \(=7\times 45.5=318.5\). Therefore Year 2 imports = 318.5 crore dollars.

Split each year's total trade using the given E : I ratio: Year 1 (10:9, 3800): E = 2000, I = 1800. Year 2 (11:7, 3600): E = 2200, I = 1400. Year 3 (4:3, 2800): E = 1600, I = 1200. Year 4 (5:8, 3900): E = 1500, I = 2400. Year 5 (12:13, 5000): E = 2400, I = 2600. Total Exports \(=2000+2200+1600+1500+2400=9700\); Total Imports \(=1800+1400+1200+2400+2600=9400\). Difference of averages \(=\dfrac{9700-9400}{5}=\dfrac{300}{5}=60\) crore dollars. Therefore the answer is 60.

The verb prefer takes the preposition to, not than, when comparing two gerunds. The correct form is "prefer reading to going out". Hence the error lies in part (3), where "than going out visiting my friends" should be "to going out visiting my friends".

Immanent (adjective) means inherently present throughout the universe — a standard theological attribute of God. Imminent means about to happen, mortal contradicts divinity, and deference is a noun meaning respect, so it cannot fill an adjective slot. Therefore the correct word is immanent.

The error lies in part (2): "junior than Mukesh". Latin-origin comparatives such as junior, senior, superior, inferior, prior take the preposition "to", not "than". The correct phrasing is "junior to Mukesh", so the sentence should read "Rohit is two years junior to Mukesh in the office."

P introduces the man by his unusual physical features. R refers back to "His unusual features" being a joke among friends, so it must follow P. Q then shifts to his work habits — barely working at his stonecutting trade. S concludes by summarising him as "a poor man — an idler", a natural wrap-up after Q describes his idleness. Hence the coherent order is PRQS.

ASCEND means to move or go upward, to rise. Climb means to go up, especially using effort — a direct synonym. "Lay" means to place down (opposite direction); "Weaken" refers to loss of strength; "Void" means empty or invalid. None convey upward movement. Hence the correct synonym is Climb.

Desecrate means to treat a sacred place or thing with violent disrespect — to violate its sanctity. The required antonym must express the opposite: making something holy. Sanctify means to set apart as holy, to consecrate or purify — the exact opposite of desecrate. "Profane" and "Defile" are synonyms of desecrate, and "Befoul" means to pollute, also similar in sense. Therefore the antonym is Sanctify.

R introduces the cause — a materialistic culture that enables continuous sale of newer products. S follows with the mechanism: consumers ("They") are lured by advertising and then given loans to buy more. P states the outcome — once all creditworthy people hit their loan limit, they exit the market. Q comments on this outcome ("Even this would have been understandable..."), referring back to P. Hence the logical order is RSPQ.

The correct spelling is Bulletin (with double 'l'), not "Bulettin" as given. "Barrage", "Buoyant" and "Beginner" are all spelt correctly. Hence the incorrectly spelt word is Bulettin.

When converting Direct to Indirect Speech with a past reporting verb ("said"), the inner Simple Past (saw) shifts to Past Perfect (had seen), the pronoun I becomes he, and the place adverb here becomes there. Applying all three changes gives: He said that he had seen a snake there. The other options either keep the original tense, retain "here", or drop the place adverb entirely.

The sentence states that morality is closely linked with ethics — both deal with the doctrine of right and wrong. The blank needs a word expressing this strong equivalence. Identified ("identified with" = regarded as the same as / closely associated with) fits idiomatically and conveys this near-equivalence. "Discussed with" suggests mere conversation; "recognised with" is not a standard collocation; "rectified" means corrected, which is irrelevant. Hence the answer is identified.

The passage contrasts morality (concerned with right and wrong) with politics (driven by expediency). The blank completes "need not always be _____", describing what politics may fail to be despite being expedient. Since morality is the standard of right, and politics follows expediency, it follows that politics need not always be right. "Wrong", "neutral" and "different" do not preserve the moral contrast set up by the passage.

The correct spelling is Handkerchief (ending in -chief), not "Handkercheif". The vowels 'i' and 'e' are swapped in the given form. "Guidance", "Ambassador" and "Labourer" are all spelt correctly. Hence the incorrectly spelt word is Handkercheif.

The idiom to go through fire and water means to face or endure extreme dangers and hardships in order to achieve a goal or help someone. The imagery of fire and water represents perilous obstacles overcome for a purpose. Option 2 — "To experience many dangers in order to achieve something" — captures both elements (dangers and purpose). "Scolding", "acting without restraints" and "something which hurts" miss the achievement/perseverance sense.

When either is used as the subject (here, "either [pen]"), it is treated as singular and takes a singular verb in the present tense. Hence the verb must be writes, not write. "Either have written" and "either wrote well" use wrong tenses for a general present statement about the pens. "No improvement" fails because the original plural "write" violates subject-verb agreement with the singular either. The correct improvement is either writes.

The verb agree takes on when speaking of specific points, issues or matters on which opinions are held — e.g. "agree on a plan", "agree on certain things". This is the standard collocation when referring to specific topics of opinion. "Agree to" is used for consenting to a proposal; "agree of" is ungrammatical; "agree about" is possible but not an improvement over the already-correct "agree on". Hence the original phrase is correct — No improvement.

The verb "agree" takes different prepositions: agree with a person, agree to a proposal, and agree on/about a topic of discussion. Since "certain things" denotes topics where people share or differ in opinion, "agree about certain things" is the natural collocation. "Agree to" suits a proposal, and "agree of" is not standard English — so option 2 is the improvement.

The passage contrasts morality/ethics (right vs. wrong) with politics (expediency). The fragment reads, "If something is wrong and merely expedient, it cannot be _____." Logically, an action that is wrong cannot be justified merely because it is expedient, but in the author's framing it still cannot be labelled as anything other than immoral — the conclusion the passage drives at. "Justifiable" and "relevant" do not match the moral-judgment tone, and "acquired" is contextually meaningless. Hence the blank is filled by immoral.

Articulate means expressed clearly and distinctly, or able to speak fluently. Among the options, Distinct — meaning clear, well-defined, readily distinguishable — shares this sense of clarity and definiteness. "Dominate" means to control; "Helpers" means assistants; "Unsteady" means shaky — none relate to clarity of expression. Hence Distinct is the closest synonym.

Cynophobia comes from the Greek kyno- (dog) + phobia (fear), so it denotes the fear of dogs. "Vatrachophobia" (Batrachophobia) is the fear of amphibians like frogs; "Orophobia" and "Phemophobia" are not standard phobia terms. Hence the correct substitute is Cynophobia.

A gust is a sudden, brief, strong rush of wind — precisely "a strong blast of wind". "Implosion" is an inward collapse, "Trickle" is a slow flow of liquid, and "Mantle" is a cloak or Earth's layer — none relate to wind. Hence the answer is Gust.

The verb must convey success in an examination. Passed specifically means cleared/succeeded in an exam, giving "Riya passed her matriculation examination in 2016." "Completed" is ambiguous about the result; "obtained" collocates with marks or certificates, not the exam itself; "gathered" (to collect) is contextually wrong. Hence passed is correct.

The idiom Will-o'-the-wisp originally refers to flickering marsh lights that mislead travellers; figuratively it denotes a goal that is elusive and impossible to get or achieve. The other options — warding off a person, spending recklessly, or accept-or-leave — have no link to this image of an unattainable pursuit. Hence option 1 is correct.

The blank qualifies "expedient" in a sentence implying that mere convenience cannot redeem a wrong act. Merely means "only/just" and conveys exactly this limiting sense: "If something is wrong and merely expedient, it cannot be..." "Essentially" suggests something fundamental, "surely" adds certainty, and "hardly" means scarcely — none capture the "only-expedient" nuance. Hence merely is correct.

The given sentence is in passive voice with two clauses sharing the same implied agent — the police. Converting to active: "The police arrested John on a charge of murder, but for lack of evidence released him." The subject "The police" is retained across both clauses, with the verbs arrested and released in simple past active. Option 2 stays passive; Option 3 mixes voices (second clause still passive); Option 4 uses past-perfect passive and changes tense. Hence Option 1 is correct.

The passage contrasts morality/ethics with politics, presenting politics as guided by the principle of expediency. Notion means an idea or concept, so "Politics is the notion of expediency" fits — politics is conceptually built around expediency. "Source" wrongly makes politics the origin of expediency; "collection" is grammatically odd for an abstract idea; "requirement" implies obligation, not characterisation. Hence notion is correct.