SSC CGL 2017 · 2017-08-09 · Shift 2

All five words start with "De". Splitting by the third letter: "Dec" group — Decollete (1), Decorous (3); "Des" group — Desecrate (2), Despicable (4), Destitute (5). "Dec" precedes "Des". Within "Dec", compare the 5th letter: Decollete (l) before Decorous (r), so order is 1, 3. Within "Des", compare the 4th letter: Desecrate (e) < Despicable (p) < Destitute (t), giving 2, 4, 5. Combined dictionary order: 1, 3, 2, 4, 5.

The rule is the sum of the alphabetical positions of the letters. Step 1 — Verify with ACOUSTIC: \(1+3+15+21+19+20+9+3 = 91\) Step 2 — Apply to RENOUNCE: \(18+5+14+15+21+14+3+5 = 95\) Therefore the answer is 95.

Check the gaps between consecutive letter positions in each group. ACFJ: 1, 3, 6, 10 — gaps +2, +3, +4. RTWA: 18, 20, 23, 27(A) — gaps +2, +3, +4. HJMQ: 8, 10, 13, 17 — gaps +2, +3, +4. NPSV: 14, 16, 19, 22 — gaps +2, +3, +3. Three groups follow +2, +3, +4 but NPSV breaks the pattern, so NPSV is the odd one out.

Apply BODMAS after swapping each suggested pair and check whether the LHS equals 16. Swap 5 and 3: \(8 \times 5 \div 4 + 9 - 3\) \(= 40 \div 4 + 9 - 3 = 10 + 9 - 3 = 16\) ✓ The other swaps give 14.67, 5.5, and 2 respectively — none equal 16. Hence the correct interchange is 5 and 3.

Step 1 — Identify the rule: Test \(x^3 \div y\). For (2)#*4: \(2^3 \div 4 = 8 \div 4 = 2\) ✓ For (4)#*4: \(4^3 \div 4 = 64 \div 4 = 16\) ✓ Step 2 — Apply to (6)#*A = 18: \(\dfrac{6^3}{A} = 18 \implies \dfrac{216}{A} = 18 \implies A = \dfrac{216}{18} = 12\) Therefore A = 12.

Hence, there are 12 triangles in the given question figure.

Step 1 — Compute consecutive differences: \(3085-1357=1728=12^{3}\) \(5282-3085=2197=13^{3}\) \(8026-5282=2744=14^{3}\) Step 2 — Apply the pattern: the differences are successive cubes, so the next difference is \(15^{3}=3375\). Therefore the missing term is \(8026+3375=\mathbf{11401}\).

A calendar is the structured reference that lists dates; analogously, an index is the structured reference that lists the contents of a book. The relationship is reference-tool to the items it organises. A glossary lists term meanings (not what an index points to), the author's name is metadata, and a summary is a condensed overview — none match the relationship. Hence the answer is Content.

Step 1 — Set up ages 5 years hence: let them be \(7x\) and \(5x\). Step 2 — Use the constant age difference: \[7x-5x=4 \implies x=2\] Step 3 — Back-calculate present ages: ages in 5 years are \(14\) and \(10\), so present ages are \(14-5=9\) and \(10-5=5\). Therefore A and B are 9 and 5 years respectively.

The code is the sum of the alphabetical position values of the letters. Check: \(R+A+I+N=18+1+9+14=42\) and \(O+H+B+Q=15+8+2+17=42\). For SUMMER: \(S+U+M+M+E+R=19+21+13+13+5+18=\mathbf{89}\).

1) It cannot be formed as ‘B’ is opposite to ‘O’. 2) It can be formed. 3) It cannot be formed as ‘Y’ is opposite to ‘I’. 4) It cannot be formed as ‘G’ is opposite to ‘R’. Hence, dice (option) 2 can be formed.

The series is built from the repeating block abcd. Filling the six blanks with a, d, b, c, b, d gives \(\underline{a\,a\,b\,c}\,\underline{d\,a\,b\,b}\,\underline{c\,d\,a\,b}\,\underline{c\,c\,d\,a}\,\underline{b\,c\,d\,d}\) — the four-letter block abcd cycles cleanly through every position, with each insertion completing the next rotation. Hence the correct set is adbcbd.

First image: (1 × 2 × 5 × 3) + (1 + 2 + 5 + 3) → 30 + 11 → 41 Second image: (4 × 3 × 6 × 2) + (4 + 3 + 6 + 2) → 144 + 15 → 159 Similarly, Third image: (5 × 7 × 3 × 2) + (5 + 7 + 3 + 2) → 210 + 17 → 227 Hence, the missing number in the diagram is ‘227’.

Statements: All rackets ⊂ bats ⊂ wickets. So all rackets are wickets, which means at least some wickets are rackets — Conclusion I follows. Conclusion II ("All wickets are rackets") would require wickets ⊂ rackets, but the statements only guarantee inclusion in the opposite direction; wickets may include bats and other items that are not rackets, so II does not follow. Therefore only Conclusion I follows.

After looking at the picture, we can assume that the upper circle is the part of its diagonal circle where extra cross lines have been brought. So, the missing part will be the square where the cross line has been added. Hence, option 3 will complete the given question figure.

Hence, the unfolded figure will be similar to option 3.

Decode each pair as (row, column) from the correct matrix and check it spells C-R-E-E-P. Option 4 (42, 98, 41, 00, 34): 42 → Matrix-I (4,2) = C; 98 → Matrix-II (9,8) = R; 41 → Matrix-I (4,1) = E; 00 → Matrix-I (0,0) = E; 34 → Matrix-I (3,4) = P. All five pairs match, so the code for CREEP is 42, 98, 41, 00, 34. The other options fail at one or more letters (e.g. Option 1's 42 gives C instead of P; Option 2's 55 gives L instead of R).

Pattern: second number = first number + (product of its digits)2. Check: \(2\times4\times3=24,\ 24^{2}=576,\ 243+576=819\). Apply to 163: \(1\times6\times3=18,\ 18^{2}=324,\ 163+324=\mathbf{487}\).

Hence, the question figure is hidden in option 1.

Hence, the mirror image of the question figure will be similar to option 1.

Track the net displacement. Facing south, a right turn faces west; another right faces north; a left from north faces west. North–South: 30 m south then 30 m north cancel to 0. East–West: 20 m west + 40 m west = 60 m west. The net displacement is 60 m due west, so Lokesh is to the West of the starting point.

In each group the second number is the square of the first. Check the ratio of the third to the second: (6, 36, 90): \(90/36=2.5\); (8, 64, 160): \(160/64=2.5\); (12, 144, 360): \(360/144=2.5\). But (4, 16, 48): \(48/16=3\), not 2.5. Hence (4, 16, 48) is the odd group.

Hence, the answer is option 3.

Football, Cricket and Hockey are all outdoor field team sports played on a large ground with a ball/puck. Table Tennis is the odd one out — it is an indoor sport played on a table, not on a field.

Letters available in ENCYCLOPEDIA: A, C, C, D, E, E, E, I, L, N, O, P, Y. The letter S is not present. CONE, CYCLE and PEACE use only letters from this pool, but NOISY requires an S, which is missing. Hence NOISY cannot be formed.

Plant tissues are broadly grouped into three main types: meristematic tissue (actively dividing cells responsible for growth, found at root and shoot tips), simple permanent tissue (parenchyma, collenchyma, sclerenchyma — one cell type, used for storage, support and protection), and complex permanent tissue (xylem and phloem — multiple cell types working together for transport of water, minerals and food). Hence the correct answer is 3.

As per Article 79 of the Constitution of India, the Parliament of India consists of the President and two Houses — the Council of States (Rajya Sabha) and the House of the People (Lok Sabha). Though the President is not a member of either House, the President is an integral constituent of Parliament — summoning/proroguing sessions and giving assent to Bills. Hence all three (i), (ii) and (iii) are constituents, making (i), (ii) and (iii) the correct answer.

The Forest Research Institute (FRI) is located in Dehradun, Uttarakhand. Established in 1906 (with origins in the 1878 Forest School), it is a premier institution under the Indian Council of Forestry Research and Education (ICFRE) and a deemed university known for its colonial-era architecture and forestry museum.

In computer terminology, a bug is an error, flaw, or fault in a program that causes it to produce an incorrect result or behave in an unintended way. The process of locating and removing bugs is called debugging. A virus is malicious software, a program is a set of instructions (a bug exists within a program), and a magnetic disk is a hardware storage device — none of these define a bug. Hence an error in program is correct.

The Konark Sun Temple in Odisha was built by King Narasimhadeva I of the Eastern Ganga dynasty around 1250 CE, reportedly to commemorate his military victory over Muslim forces. Designed as a colossal chariot of the Sun God Surya with 12 pairs of wheels and 7 horses, it is a UNESCO World Heritage Site. Anantavarman Chodaganga Deva built the Jagannath Temple at Puri; Kapilendra Deva and Purushottam Dev were later Gajapati rulers. Hence Narasimhadeva I is correct.

Antonie van Leeuwenhoek, a Dutch lens-maker, was the first to observe and describe bacteria in 1676 using his self-built single-lens microscopes. He called them animalcules ("little animals") after observing them in pond water, saliva and dental plaque, and communicated his findings to the Royal Society of London — earning him the title "Father of Microbiology". Robert Brown discovered the cell nucleus, Robert Hooke coined the term "cell", and Robert Koch identified disease-causing bacteria — but none discovered bacteria.

Zacharias Jansen, a Dutch spectacle-maker from Middelburg, is credited with inventing the compound microscope around 1590–1600, working together with his father Hans Jansen. By combining multiple lenses in a tube, the device achieved much higher magnification than a simple single-lens microscope, paving the way for microbiology. The jet engine (Whittle/von Ohain), radium (Curies) and the electric lamp (Edison) all came centuries later.

The book 'Numbers Do Lie' is co-authored by Aakash Chopra (former Indian Test opener and cricket commentator) along with Impact Index founders Jaideep Varma and Jatin Thakkar. Published in 2017, it challenges popular cricket statistics by examining the context behind the numbers across 61 myths in the game. Anil Menon and Kunal Basu are fiction writers, and Ian Chappell is an Australian cricketer-commentator — none authored this book.

India shares its longest international land border with Bangladesh, stretching about 4,096.7 km across West Bengal, Assam, Meghalaya, Tripura and Mizoram. For comparison: China — about 3,488 km, Pakistan — about 3,323 km, Nepal — about 1,751 km, Myanmar — about 1,643 km, and Bhutan — about 699 km. Hence among the options, Bangladesh is correct.

The question asks which statement is NOT a property of electromagnetic (EM) waves. EM waves are transverse (oscillating \(\vec{E}\) and \(\vec{B}\) fields mutually perpendicular and perpendicular to the direction of propagation) and require no medium — they travel through vacuum at the speed of light \(c = 1/\sqrt{\mu_0 \epsilon_0}\). Statements (2), (3) and (4) are therefore true. Being waves, EM waves do exhibit interference, diffraction, reflection, refraction and polarisation — as seen in thin-film colours and Young's double-slit experiment. Hence statement (1) — that they do not show interference and diffraction — is false and is the correct answer.

Iris Mittenaere of France won the 65th Miss Universe 2016 pageant, held on 30 January 2017 in Manila, Philippines. She was crowned by her predecessor Pia Wurtzbach (Miss Universe 2015). Raquel Pelissier (Haiti) was first runner-up and Andrea Tovar (Colombia) second runner-up. Hence Iris Mittenaere is correct.

The Sahyadri Range is the other name for the Western Ghats — a mountain chain running parallel to India's western coast from Gujarat through Maharashtra, Goa, Karnataka and Kerala to Tamil Nadu. It separates the Deccan Plateau from the Arabian Sea coast, is a UNESCO World Heritage Site and one of the world's eight "hottest hotspots" of biodiversity. The Lesser Himalayas and Shivaliks belong to the Himalayan system, while the Eastern Ghats run along the Bay of Bengal coast.

Normal human blood pH is tightly maintained between \(7.35\) and \(7.45\). Since this range lies just above the neutral value of 7, blood is classified as slightly basic (alkaline). This narrow range is regulated by the bicarbonate buffer system, along with the lungs and kidneys. Values below 7.35 lead to acidosis and above 7.45 to alkalosis.

Football, Cricket and Tennis are all played with a ball (spherical football, hard cricket ball, felt-covered tennis ball respectively). Badminton is the exception — it is played with a shuttlecock (a feathered/synthetic conical projectile), not a ball. Hence the answer is Badminton.

The Regulating Act of 1773 elevated the post of Governor of Bengal to Governor-General of Bengal, with authority over the Madras and Bombay presidencies. Warren Hastings (Governor of Bengal since 1772) became the first to hold this new title, serving from 1774 to 1785. Robert Clive was only Governor of Bengal (pre-1773); Cornwallis succeeded Hastings; William Bentinck later became the first Governor-General of India under the Charter Act of 1833.

A monopoly is a market structure in which a single seller controls the entire supply of a product that has no close substitutes. The firm is the industry, faces the whole market demand curve, and acts as a price-maker due to high barriers to entry. Oligopoly has a few dominant firms, duopoly exactly two, and monopolistic competition many sellers of differentiated products — none of these is dominated by a single seller.

After each half-life, the remaining quantity halves. If three-fourths has decayed, the remaining fraction is \(\tfrac{1}{4}\) of the original. \[\left(\tfrac{1}{2}\right)^{n}=\tfrac{1}{4}\implies n=2\ \text{half-lives}\] With each half-life equal to 6 months, total time \(=2\times 6 =\) 12 months.

Gangaur is celebrated in Rajasthan in honour of Goddess Gauri (consort of Shiva). Ganesh Chaturthi is most prominently celebrated in Maharashtra. Durga Puja is the principal festival of West Bengal. So 1-b, 2-c, 3-a, matching option (a).

Disguised unemployment occurs when more workers are engaged in an activity than required, so the marginal productivity of labour is zero — common on small Indian farms. Such workers are nominally employed but contribute nothing extra to output. This is a classic form of underemployment, where labour is not fully utilised. Frictional (between-jobs), seasonal (off-season), and cyclical (recession-driven) unemployment describe entirely different situations.

By Newton's third law, every action has an equal and opposite reaction. When the hammer strikes the nail, the nail (and the frame) pushes back with an equal force on the hammer, while the frame itself receives a reaction that would normally be balanced by a support. Because the frame is freely suspended, nothing opposes this reaction, so the frame swings away instead of resisting the blow. The energy of the strike goes into moving the frame rather than driving the nail, making nailing difficult.

A tissue is a group of structurally similar cells with a common origin that work together to perform a specific function — e.g., muscle, nervous, epithelial and connective tissues in animals; xylem and phloem in plants. An organ is built from different tissues; an organ system is a group of organs; "cellular organisation" merely describes how cells are arranged. Only tissue matches the definition given.

The Deen Dayal Rasoi Yojana was launched by the Madhya Pradesh government on 6 April 2017 to provide a full meal at the subsidised price of Rs. 5 to the poor, daily-wage labourers, rickshaw pullers and other needy people. The scheme was rolled out across major cities of the state and aligns with broader food-security objectives.

The Amazon, the world's largest river by discharge, rises in the Peruvian Andes and flows eastwards across South America, draining into the Atlantic Ocean. Of the listed countries, only Brazil lies in South America and contains the major portion of the river's course and basin. The USA and Canada are in North America, and mainland France is in Europe — none is traversed by the Amazon.

India follows a parliamentary system in which the President is the constitutional head of state. Article 53 vests the executive power of the Union in the President, and all executive actions of the Government of India are formally taken in their name. The Prime Minister is the head of government (real executive); the Cabinet Secretary and Finance Secretary are senior civil servants holding purely administrative posts.

Antonio Guterres, former Prime Minister of Portugal and former UN High Commissioner for Refugees, took office as the 9th Secretary-General of the United Nations on 1 January 2017, succeeding Ban Ki-moon. Ban Ki-moon's term ended on 31 December 2016; Kofi Annan (1997-2006) and Boutros Boutros-Ghali (1992-1996) had served much earlier.

Step 1 — Combined one-day work: \[\frac{1}{20}+\frac{1}{25}=\frac{5+4}{100}=\frac{9}{100}\] Step 2 — Work in 3 days: \[\frac{9}{100}\times 3=\frac{27}{100}\] This equals 27% of the total work.

Step 1 — Distance A covers alone (9 a.m. to 11 a.m.): \[25\times 2=50\text{ km}\] Step 2 — Remaining gap at 11 a.m.: \[260-50=210\text{ km}\] Step 3 — Closing speed and meeting time: Both move towards each other at \(25+10=35\) km/h, so they meet in \(210/35=6\) hours. Meeting time = 11 a.m. + 6 h = 5:00 p.m.

Step 1 — Find A's marks: A is 18% more than B = 220. \[A=220\times 1.18=259.6\] Step 2 — Relate A and C: A is 12% less than C, so \(A=0.88\,C\). \[C=\frac{259.6}{0.88}=295\] Therefore C scored 295 marks.

Step 1 — Find \(x^2+\tfrac{1}{x^2}\): \[\left(x^2+\tfrac{1}{x^2}\right)^2=x^4+\tfrac{1}{x^4}+2=34+2=36\] So \(x^2+\tfrac{1}{x^2}=6\). Step 2 — Find \(x-\tfrac{1}{x}\): \[\left(x-\tfrac{1}{x}\right)^2=x^2+\tfrac{1}{x^2}-2=6-2=4\implies x-\tfrac{1}{x}=2\] Step 3 — Apply \(a^3-b^3=(a-b)(a^2+ab+b^2)\): \[x^3-\tfrac{1}{x^3}=\left(x-\tfrac{1}{x}\right)\left(x^2+1+\tfrac{1}{x^2}\right)=2\times(6+1)=14\] Therefore the value is 14.

Diagonals of a rhombus bisect at right angles, so each half-diagonal forms a right triangle with the side as hypotenuse. Step 1 — Find the bigger diagonal \(d_2\): \[6^2=\left(\tfrac{6}{2}\right)^2+\left(\tfrac{d_2}{2}\right)^2\implies \left(\tfrac{d_2}{2}\right)^2=27\] So \(d_2=2\sqrt{27}=6\sqrt{3}\) cm. Step 2 — Area of equilateral triangle with side \(6\sqrt{3}\): \[\text{Area}=\frac{\sqrt{3}}{4}(6\sqrt{3})^2=\frac{\sqrt{3}}{4}\times 108=27\sqrt{3}\text{ cm}^2\] Therefore the area is \(27\sqrt{3}\) cm2.

From the table, City 4 has a literacy rate of 63%. \[\text{Literate population}=\frac{63}{100}\times 600000=378000\] Hence the number of literate people in City 4 is 378,000.

Step 1 — Literate males in City 2 (85% literate, M:F = 7:4): \[0.85\times 220000=187000;\quad \tfrac{7}{11}\times 187000=119000\] Step 2 — Literate females in City 6 (58% literate, M:F = 2:3): \[0.58\times 200000=116000;\quad \tfrac{3}{5}\times 116000=69600\] Step 3 — Required ratio: \[119000:69600=1190:696=595:348\] Therefore the ratio is 595 : 348.

Compute literate population = literacy % × total population for each city: City 1: \(0.80\times 250000=200000\) City 2: \(0.85\times 200000=170000\) City 3: \(0.78\times 220000=171600\) City 4: \(0.63\times 300000=189000\) City 5: \(0.92\times 150000=138000\) City 6: \(0.58\times 400000=232000\) Descending order: 232000 > 200000 > 189000 > 171600 > 170000 > 138000, i.e. City 6 > City 1 > City 4 > City 3 > City 2 > City 5.

Apply the compound interest formula \(A=P\left(1+\tfrac{r}{100}\right)^n\) with \(P=2500,\ A=2970.25,\ n=2\): \[\left(1+\tfrac{r}{100}\right)^2=\frac{2970.25}{2500}=1.1881\] Taking the square root: \(1+\tfrac{r}{100}=1.09\), so \(r=9\). The yearly rate of interest is 9%.

Apply the difference-of-squares identity: \[(\sec A+\cos A)(\sec A-\cos A)=\sec^2 A-\cos^2 A\] Use \(\sec^2 A=1+\tan^2 A\) and \(\cos^2 A=1-\sin^2 A\): \[\sec^2 A-\cos^2 A=(1+\tan^2 A)-(1-\sin^2 A)=\sin^2 A+\tan^2 A\] Therefore the simplified value is \(\sin^2 A+\tan^2 A\).

Rewrite the two conditions: \(x+y=1\) and \(x^2+y^2=2\). Use the identity \((x+y)^2=x^2+y^2+2xy\): \[1^2=2+2xy\implies 2xy=-1\implies xy=-\tfrac{1}{2}\] Therefore \(xy=\mathbf{-\tfrac{1}{2}}\).

let us assume ST be a and SQ be y Radius = 10/2 = 5cm ⇒ taking sin(Q) in triangles QST, QOM and QPR ⇒ sin(Q) = a/y = 5/ (5 + y) = 9/ (10 + y), using last 2 equations ⇒ 50 + 5y = 45 + 9y ⇒ y = 5/4 using this in the equation a/y = 5/ (5 + y) ⇒ 4a/5 = 5/ (5 + 5/4) ⇒ a = 1 ∴ ST is 1 cm

Area of a trapezium \(=\tfrac{1}{2}\times(\text{sum of parallel sides})\times\text{height}\). \[\text{Area}=\tfrac{1}{2}\times(18+24)\times 12=\tfrac{1}{2}\times 42\times 12=252\ \text{m}^2\] Hence the area is 252 m2.

For two successive discounts \(d_1\) and \(d_2\), the equivalent single discount is: \[D=d_1+d_2-\frac{d_1 d_2}{100}\] \[D=50+10-\frac{50\times 10}{100}=60-5=55\%\] Therefore the net discount is 55%.

Step 1 — Angle in semicircle: Since PQ is the diameter, \(\angle PRQ=90^\circ\). Step 2 — Find \(\angle PQR\) in \(\triangle PQR\): \[\angle PQR=180^\circ-90^\circ-38^\circ=52^\circ\] Step 3 — Cyclic quadrilateral property: Opposite angles sum to \(180^\circ\), so \(\angle PSR+\angle PQR=180^\circ\). \[\angle PSR=180^\circ-52^\circ=128^\circ\] Therefore \(\angle PSR=128^\circ\).

Step 1 — Use the given relation: From \(x+\dfrac{1}{x+7}=0\) we get \(\dfrac{1}{x+7}=-x\). Hence: \[x-\frac{1}{x+7}=x-(-x)=2x\] Step 2 — Solve for x: Multiplying \(x+\dfrac{1}{x+7}=0\) by \((x+7)\) gives \(x^2+7x+1=0\). \[x=\frac{-7\pm\sqrt{49-4}}{2}=\frac{-7\pm 3\sqrt{5}}{2}\] Step 3 — Compute 2x: \(2x=-7\pm 3\sqrt{5}\). The value matching the options is \(3\sqrt{5}-7\).

Step 1 — Translate the first condition: \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{xy+yz+zx}{xyz}=0 \implies xy+yz+zx=0\] Step 2 — Find \(x^2+y^2+z^2\): \[(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)\] \[9^2=x^2+y^2+z^2+0 \implies x^2+y^2+z^2=81\] Step 3 — Apply the cubic identity: \[x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)\] \[=9\times(81-0)=\mathbf{729}\]

Step 1 — Total count: Numbers from 700 to 950 inclusive \(=950-700+1=251\). Step 2 — Multiples of 3 (702 to 948): \(\dfrac{948-702}{3}+1=83\). Step 3 — Multiples of 7 (700 to 945): \(\dfrac{945-700}{7}+1=36\). Step 4 — Multiples of 21 (714 to 945): \(\dfrac{945-714}{21}+1=12\). Step 5 — Inclusion–exclusion: Divisible by 3 or 7 \(=83+36-12=107\). Neither \(=251-107=\mathbf{144}\).

Step 1 — Set up CP and SP: Let CP = Rs 100. Profit = 190% of CP = Rs 190, so SP = 100 + 190 = Rs 290. Step 2 — New CP after 10% rise: New CP = \(100\times 1.10=110\). SP unchanged at 290. Step 3 — New profit and ratio to SP: \[\text{New profit}=290-110=180\] \[\frac{180}{290}\times 100\approx 62.07\%\] Hence profit is approximately 62% of the selling price.

Given AD/DB = 5/3 ⇒ DB/AD = 3/5, add 1 to both sides ⇒ (AD + DB)/AD = (5 + 3)/5 ⇒ AB/AD = 8/5 ⇒ AD/AB = 5/8 Since triangle ADC is similar to ABC [From AAA similarity] ⇒ DE/BC = AD/AB = 5/8 ∴ DE/BC = 5/8

Step 1 — Combine the first two terms: Write \(\tan A=\tfrac{\sin A}{\cos A}\), \(\cot A=\tfrac{\cos A}{\sin A}\). Then \[\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=\frac{\sin^2 A}{\cos A(\sin A-\cos A)}+\frac{\cos^2 A}{\sin A(\cos A-\sin A)}\] \[=\frac{\sin^3 A-\cos^3 A}{\sin A\cos A(\sin A-\cos A)}\] Step 2 — Apply \(a^3-b^3\) and \(\sin^2+\cos^2=1\): \[=\frac{(\sin A-\cos A)(1+\sin A\cos A)}{\sin A\cos A(\sin A-\cos A)}=\frac{1+\sin A\cos A}{\sin A\cos A}\] Step 3 — Subtract \(\tfrac{2}{\sin 2A}=\tfrac{1}{\sin A\cos A}\): \[\frac{1+\sin A\cos A}{\sin A\cos A}-\frac{1}{\sin A\cos A}=1\] The simplified value is 1.

Step 1 — Literate males: Ratio M : F = 9 : 7 with F = 259210, so \[M=\frac{9}{7}\times 259210=9\times 37030=333270\] Step 2 — Total literate: \(333270+259210=592480\). Step 3 — Apply 92% literacy: \[\text{Population}=\frac{592480}{92}\times 100=6440\times 100=644000\] Therefore the total population of City 5 is 644000.

Step 1 — Common capacity: LCM of the ratio sums 7, 7 and 9 is 63. Assume each bottle holds 63 units. Step 2 — Split each bottle: Bottle 1 (2 : 5): milk \(=\tfrac{2}{7}\times 63=18\), water \(=45\). Bottle 2 (3 : 4): milk \(=\tfrac{3}{7}\times 63=27\), water \(=36\). Bottle 3 (4 : 5): milk \(=\tfrac{4}{9}\times 63=28\), water \(=35\). Step 3 — Combine: Milk \(=18+27+28=73\); water \(=45+36+35=116\). Final ratio milk : water = 73 : 116.

Step 1 — Initial total age: \(6\times 20=120\) years. Step 2 — New average: 25% rise of 20 gives \(20+5=25\) years. Step 3 — New total with 7 members: \(7\times 25=175\) years. Step 4 — Servant's age: \(175-120=55\) years. Hence the servant is 55 years old.

Step 1 — Simplify the denominator: \[\cot A+\tan A=\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}=\frac{\cos^2 A+\sin^2 A}{\sin A\cos A}=\frac{1}{\sin A\cos A}\] Step 2 — Simplify the inner fraction: \[\frac{\operatorname{cosec} A}{\cot A+\tan A}=\frac{1/\sin A}{1/(\sin A\cos A)}=\cos A\] Step 3 — Square: \(\left(\cos A\right)^2=\cos^2 A=1-\sin^2 A\). Therefore the simplified value is \(1-\sin^2 A\).

Monotonous means dull, tedious and repetitive — lacking variety or interest. Among the options, Dull (lacking excitement or interest) is the closest synonym. "Timid" means shy, "Unfriendly" means hostile, and "Lusty" means full of vigour — none relate to repetitive boredom.

The original phrase "Being a pleasant evening" is a dangling participle — its implied subject (the evening) does not match the main-clause subject ("we"). The correction needs an absolute construction with its own subject. "It being a pleasant evening" supplies "It" as the subject of "being", giving the cause for going out and removing the dangling modifier. Hence option 2 is correct.

The error is in part (2): "many industries, that are spread". When a comma precedes the relative pronoun, the clause is non-restrictive and must use which, not that. ("That" introduces restrictive clauses with no comma.) The correct phrasing is "many industries, which are spread across the globe." Parts (1) and (3) are grammatically fine.

Colossal means extremely large or gigantic, so its antonym must mean very small. Teeny means very small/tiny — the direct opposite. "Epic" and "Vast" are synonyms (large in scale), and "Rust" is unrelated.

Circumlocution (Latin circum = around + locutio = speech) literally means "speaking around" — using many words or indirect expressions to avoid coming to the point. This precisely matches "a roundabout way of speaking". "Centipede" is an insect, "Coercion" is forcing someone, and "Concentric" describes shapes sharing a centre — none relate to speech.

Opprobrium means harsh public criticism, disgrace or scorn. Its antonym must convey praise or admiration. Adulation means excessive praise and flattery — the direct opposite. "Ignominy" is a synonym (public shame), while "Mystical" and "Preclude" are unrelated.

The passage frames English as a biased "lens" that gives a "cross-eyed view" of animals and associates them with baseness and vulgarity — clearly a skewed, inaccurate portrayal. A lens that twists or misrepresents reality is a distorting one. "Disturbing" describes emotional impact, "popular" is irrelevant, and "useful" contradicts the negative tone of the passage.

The passage argues that English has long maintained a biased ("cross-eyed") view of animals. The verb in the blank must convey causing this view to continue over time. Perpetuated means "caused to continue indefinitely" — a perfect fit. "Accompanied" implies mere co-occurrence, "exercised a view" is not idiomatic, and "undeterred" means undiscouraged.

The blank needs a verb meaning "to suggest or imply in addition to the literal meaning". Connote exactly means this — the word "animal" carries the additional implication of brutishness and sensuality. "Rectify" (correct), "trouble" (cause distress) and "understand" (perceive meaning) do not suit a word as subject implying associations.

A Spinster is an unmarried woman, typically one past the usual marrying age — matching "an old unmarried woman" exactly. "Masochist" (one who enjoys pain), "Septuagenarian" (person aged 70–79, marital status not specified) and "Sniper" (concealed marksman) do not fit.

The passage argues that English associates animals with negative human traits. The blank needs a noun about animal behaviour that language links to "baseness and vulgarity". Instincts — innate, primal drives — are commonly contrasted with refined human reasoning and so naturally carry connotations of baseness. "Breeding", "gestures" and "species" do not bear such pejorative associations in this context.

The idiom "not to mince matters" (also "not to mince words") means to speak directly and bluntly, without softening or sugar-coating the message. Hence option 4, To speak frankly, is correct. The other options — being at ease, avoiding confusion, or not interfering — describe unrelated behaviours.

The given sentence is in the passive voice ("was not told" = was + past participle). To convert it to active voice while preserving the negative meaning, the implied agent must be nobody, since "Rohan was not told" means no person performed the act of telling. Hence the active form is "Nobody told Rohan about the e-mail." Option 2 ("Somebody did not tell...") wrongly implies a specific person failed to tell while leaving open that others might have. Option 3 stays in passive voice, and Option 4 changes the meaning by introducing capability ("could tell").

The blank needs a metaphor for a medium that shapes how we view reality. A lens filters and focuses what we see without creating the image itself — exactly how language shapes perception of the world. "Resource" and "source" suggest origin or supply, not a filter for viewing. "Telescope" is too specific (distant viewing) and unidiomatic in this context. Hence lens is correct.

"Advice" is a noun; after the auxiliary "has" we need the past participle of the verb "advise", which is advised. This gives the present perfect active form: "The doctor has advised him to take proper diet." Options 2 and 3 ("had been advised", "was advised") shift to passive voice, wrongly making the doctor the recipient. "No improvement" fails because "has advice" is ungrammatical.

Elusive describes something hard to find, catch, or understand. Baffling means perplexing or hard to comprehend — both share the core sense of difficulty in grasping or pinning down. "Enticing" (attractive) and "soothing" (calming) describe pleasant qualities, not difficulty. "Directing" (guiding) is unrelated. Hence Baffling is the closest synonym.

Sentence S defines the environment and its helpful role — a natural opening. R elaborates by naming a specific benefit ("a better medium to grow and develop"). Q extends this with another benefit ("gives us all things we need"). P closes with the connector "However," pivoting from what the environment gives us to what it needs from us. Hence the order is SRQP.

Identifying the Misspelled Word This question requires us to find the word that has an incorrect spelling among the given options. We need to carefully examine each word. Analyzing the Spelling of Each Option Let's look at each word provided: Century: This word refers to a period of one hundred years. The spelling 'Century' is correct. Finance: This term relates to the management of money, banking, investments, and credit. The spelling 'Finance' is correct. Remember: This word means to keep something in or bring back into the mind. The spelling 'Remember' is correct. Sponser: This word appears to be an attempt to spell the word related to someone who pays for or supports an event, show, or person. However, the spelling 'Sponser' is incorrect. Correcting the Misspelled Word The word 'Sponser' is misspelled. The correct spelling is Sponsor. A sponsor is typically an individual or organization that provides funds for a project or activity carried out by another, often in exchange for advertising or publicity. Conclusion on Misspelling Based on the analysis, the word Sponser is the incorrectly spelt word among the choices provided. The correctly spelt version is 'Sponsor'.

The blank takes a gerund describing the effort that led to excelling. "Working very hard" is the natural collocation for sustained effort that produces academic success. "Continuing" lacks the sense of exertion; "functioning" applies to machines/systems; "learning very hard" is unidiomatic (we say "studying hard", not "learning hard"). Hence working fits best.

Sentence R opens with a broad claim — social criticism has diverse starting points and no school monopolises it. P follows with concrete examples of those starting points (a minority's experience, a progressive movement's shortfall). Q supplies the theoretical context: under postmodernism a grand unifying theory is impossible, though dialogue remains. S closes with "Nevertheless" — despite the diversity, the critique of capitalism stays central. Hence the order is RPQS.

The direct sentence is a negative imperative. The standard indirect conversion replaces "said to" with a reporting verb (told/asked/ordered) and changes "Don't + verb" to "not to + verb". Option 1 keeps the direct form "don't run" — grammatically wrong. Option 2 turns the command into a question. Option 3 ("requested") is acceptable but adds a politeness shade not in the original. Option 4 — "Ram told Rohan not to run so fast" — uses the neutral reporting verb and the correct infinitive structure, making it the best match.

Part (3) — "much late" — contains the error. "Much" modifies comparatives (much later, much better) or uncountable nouns, not a plain adverb/adjective like "late". The correct intensifier here is "very late" or "too late". Parts (1) "She has not been" (present perfect) and (2) "to the restaurant" are grammatically fine. Hence the error lies in segment 3.

Reciept is misspelt. The correct spelling is Receipt, following the rule "i before e, except after c" — since 'c' precedes the vowels, the order is 'ei', not 'ie'. "Autumn", "Desperate" and "Traffic" are all spelt correctly. Hence Option 3 is the answer.

The verb takes a direct object ("his camera"), so the required verb is transitive lay (to place), not intransitive lie (to recline). The action is completed in the past, so we need the past tense of "lay", which is laid. "Lain" is the past participle of "lie" and needs an auxiliary. "Lay" alone is either the present base (mismatched with singular "He") or the past of intransitive "lie". "Lie" cannot take an object. Hence laid is correct.

The idiom "all agog" means full of eager excitement, wonder, or anticipation — i.e. amazed. "Avoid" (to keep away from), "contentment" (satisfied calm) and "unsystematically" (without method) bear no connection to eager wonder, so option 3 is the closest match.