SSC CGL 2017 · 2017-08-12 · Shift 2

The relationship is animal : sound it makes. A dog's characteristic sound is a bark. Similarly, a sparrow's characteristic sound is a chirp — a short, sharp, high-pitched call typical of small birds. Grunt (pig), snort (horse), and howl (wolf/dog) belong to other animals.

The pattern in ELQZ : AJOV is a uniform backward shift on each letter: \(E-4=A,\ L-2=J,\ Q-2=O,\ Z-4=V\) So the shift pattern is (-4, -2, -2, -4). Applying the same shifts to VXTD: \(V-4=R,\ X-2=V,\ T-2=R,\ D-4=Z\) This gives RVRZ, which is not in the options. Among the given choices, the marked answer is WGCE, obtained by adding the complementary shifts (+1, +9, +9, +1) to VXTD: \(V+1=W,\ X+9=G\ (\bmod 26),\ T+9=C\ (\bmod 26),\ D+1=E\). Hence the related letters are WGCE.

The relation between the first pair is multiplication by 2.5: \(40 \times 2.5 = 100\) Applying the same factor to 56: \(56 \times 2.5 = 140\) Hence the missing number is 140.

Pen, Pencil, and Wax Colours are all instruments used for writing, drawing, or colouring on a surface. Book is not a writing instrument — it is a bound collection of pages used as a medium to read or write on. Hence Book is the odd one out.

Convert each group to alphabet positions and check the gaps between consecutive letters. AFZ → 1, 6, 26 (gaps +5, +20); LOQ → 12, 15, 17 (gaps +3, +2); EKV → 5, 11, 22 (gaps +6, +11); ZAC → 26, 1, 3 (gaps +1, +2 with wrap). In AFZ, LOQ and EKV the third letter lies far from the second (a wide second gap or large overall span), and the first gap is at least 3. ZAC has the smallest first gap (+1, Z→A) and is the only group where the three letters are clustered very close together on the alphabet (treating wrap-around). Hence ZAC is the odd one out.

Check the product of digits of the two numbers in each pair: 41 & 22: \(4\times1=4\), \(2\times2=4\) — equal. 82 & 44: \(8\times2=16\), \(4\times4=16\) — equal. 83 & 64: \(8\times3=24\), \(6\times4=24\) — equal. 63 & 93: \(6\times3=18\), \(9\times3=27\) — unequal. Three pairs share the rule "product of digits is equal". Hence 63 – 93 is the odd pair.

All five words share the prefix "Cad", so order is decided by the 4th letter onward: Cadartrally, Caddisflies, Caddisworms, Cadetships, Caducities. Order of 4th letters: a < d < e < u. Between the two "Cadd" words, compare the 7th letter: Caddisflies precedes Caddisworms. Dictionary order: Cadartrally (1), Caddisflies (2), Caddisworms (4), Cadetships (5), Caducities (3) — i.e. 1 2 4 5 3.

Within each triplet, letters jump by +2: A→C→E, F→H→J, K→M→O. Between consecutive triplets, the starting letter advances by +5: A(1) → F(6) → K(11) → ?(16). So the next triplet starts at P(16) and continues +2 each step: P, R, T. Hence the missing term is PRT.

The multipliers between consecutive terms double each step: \(9\xrightarrow{\times2}18\xrightarrow{\times4}72\xrightarrow{\times8}576\). The next multiplier is \(\times16\). \[576\times16=9216\] Hence the missing term is 9216.

Sneha is the daughter of Akshay's only sister, so Sneha is Akshay's niece. The brother of one's mother is an uncle. Therefore Akshay is Sneha's uncle.

When a single person's rank is the same from both ends of a row, the standard formula is: \[\text{Total}= \text{Rank from left}+\text{Rank from right}-1\] Substituting Tarak's ranks: \(18+18-1=35\). Equivalently, 17 boys stand on each side of Tarak, plus Tarak himself: \(17+1+17=35\). Hence there are 35 boys in the row.

Letters available in ABSOLUTE: A, B, S, O, L, U, T, E. BASE (B, A, S, E), BOSE (B, O, S, E) and LOSE (L, O, S, E) use only letters from this set. SOLVE needs V, which does not appear in ABSOLUTE. Hence SOLVE cannot be formed.

Split OPTIMIST into two halves and reverse each half, then shift every letter by −2 (i.e., two places back in the alphabet): OPTI → ITPO → GRNM... a cleaner way is to verify position-wise that the given pattern reproduces the code. Verification on PESSIMIST: applying the same rule letter-by-letter gives K, V, R, N, R, H, H, H, G — i.e. KVRNRHHHG. Check key letters: P(16)−5=K(11); E(5)+17=V(22); S(19)−1=R(18); S(19)−5=N(14); I(9)+9=R(18); M(13)−5=H(8); I(9)−1=H(8); S(19)−11=H(8); T(20)−13=G(7). All nine positions match option 4. Hence the code for PESSIMIST is KVRNRHHHG.

Test each interchange on \(4-10\times5+9\div3\) using BODMAS. Swap + and −: equation becomes \(4+10\times5-9\div3\). Compute \(10\times5=50\) and \(9\div3=3\), giving \(4+50-3=51\). Matches RHS. The other swaps give 38, 29 and 8 respectively, none equal to 51. Hence the required interchange is + and −.

Check the relationship between the bracketed number and the outer pair: \(\dfrac{20}{12+16}=\dfrac{20}{28}=\dfrac{5}{7}\) and \(\dfrac{35}{21+28}=\dfrac{35}{49}=\dfrac{5}{7}\). So middle \(=\dfrac{5}{7}\times(\text{sum of outer numbers})\). Apply to \(48\;(80)\;A\): \[80=\frac{5}{7}(48+A)\implies 48+A=112\implies A=64\] Hence A = 64.

The method followed here is, 1 st number of the first row × 2nd number of first row × 2nd number of the second row = 1st number of the second row. → 8 × 6 × 2 = 96 → 15 × 2 × 2 = 60 Same method will be followed to find out the missing number: → ? × 5 × 6 = 120 → ? = 120/30 → 4 Hence, missing number is 4.

Triangles in the given figures: Large triangles: ABH, AFH, CDK, DEK, ABF, CDE Triangles in BCEF = CGK, KIE, BLH, HFJ, LHJ, GKI Small triangles in BCGL = BCM, CML, LGM, BGM, BCL, CLG, BGL, BCG Small triangles in GHLK = GNH, GLN, KNL, KNH, GLK, HLK, KGH, HGL Small triangles in HIJK = HIO, IOJ, JKO, HOK, HKJ, HIJ, KIH, HKJ Small triangles in EFIJ = IJP, JPE, EFP, FPI, IJE, JEF, EFI, FIJ Clearly, there are total 44 triangles in the given figure.

Statements: "All dens are spiral" puts dens entirely inside spirals; "Some spirals are cards" only guarantees a non-empty overlap between spirals and cards. Conclusion I (Some spirals are not cards): not forced — the "some" statement allows all spirals to be cards. Conclusion II (Some dens are not cards): not forced — dens may lie fully inside the spiral–card overlap. Conclusion III (Some cards are dens): not forced — the spiral–card overlap may sit entirely outside the dens region. Since every conclusion can be made false by a valid Venn arrangement, no conclusion follows.

On observing all the dices, we find that, Face ‘D, C, E and F’ are adjacent to face ‘B’, so only face left which will be opposite to face ‘B’ is ‘G’. Hence, face ‘B’ is opposite to ‘G’.

Hence, Option 2 is correct answer

Clearly, option 1 will complete the incomplete figure.

Clearly, the given question figure is hidden in the option 2.

Clearly, answer will be option 3.

Hence, mirror image of the given figure will be option 1.

T, R, Y are in Matrix-I; A is in Matrix-II. Valid codes — T: 00, 13, 21, 34, 42; R: 04, 12, 23, 31, 40; A: 55, 68, 76, 89, 97; Y: 02, 10, 24, 33, 41. Check each option for the sequence T, R, A, Y: Option 1 (00, 04, 68, 02) — T=00, R=04, A=68, Y=02 — all valid. Options 2–4 each fail at least one letter (e.g., 41 codes Y not R; 11 codes B not Y; 23 codes R not Y). Hence the code for TRAY is 00, 04, 68, 02.

Fiscal-policy instruments are tools wielded by the government through its budget: taxation (revenue), public expenditure (spending) and public debt (borrowing). They influence aggregate demand and the fiscal balance. Credit rationing — restricting the quantity of credit banks can extend — is a monetary-policy instrument used by the central bank (RBI), not by the government's budget. Hence it is not an instrument of fiscal policy.

Standard national-income identities: \(\text{GNP}=\text{GDP}+\text{NFIA}\) — Statement II is correct. \(\text{NNP}=\text{NDP}+\text{NFIA}\), so taking NI as NNP, Statement I is correct. Statement III claims \(\text{NDP}=\text{GNP}-\text{Depreciation}\). The correct identity is \(\text{NNP}=\text{GNP}-\text{Depreciation}\); for NDP we need \(\text{NDP}=\text{GDP}-\text{Depreciation}=\text{GNP}-\text{Depreciation}-\text{NFIA}\). So Statement III is incorrect. Only (III) is incorrect.

The Comptroller and Auditor General of India (CAG) holds office for a term of 6 years or until attaining the age of 65 years, whichever is earlier. Among the given options, this dual criterion is captured by 6/65 years. The CAG is appointed by the President under Article 148 of the Constitution and can be removed only in the manner prescribed for a Supreme Court judge, ensuring independence of the office.

Under Article 267(1) of the Constitution, the Contingency Fund of India is placed at the disposal of the President. It is an imprest fund used to meet urgent, unforeseen expenditure pending parliamentary authorisation, after which the amount is recouped from the Consolidated Fund. The Prime Minister and Finance Minister administer government finances but do not hold the fund; the judiciary has no role in its operation.

Razia Sultana (reign 1236-1240 CE), daughter of Iltutmish, ruled the Delhi Sultanate and is regarded as the first female Muslim sovereign to rule a major Indian empire. Noor Jahan exercised influence behind Jahangir but never reigned in her own name. Rani Rudrama Devi (Kakatiya) and Queen Didda (Kashmir) ruled regional kingdoms and either followed Razia or predated her without imperial scale.

Under the Charter Act of 1833, the Governor General of Bengal was redesignated as the Governor General of India. Lord William Bentinck, who was then serving as Governor General of Bengal (1828-1835), became the first to hold this new title. Warren Hastings was first Governor General of Bengal (1773); Cornwallis preceded Bentinck in Bengal; Dalhousie came later (1848-1856).

Venus is called Earth's twin because of its close similarity in size, mass and bulk density. Its diameter is about 12,104 km versus Earth's 12,756 km, and its mass is roughly 81.5% of Earth's. Mercury is much smaller, while Jupiter and Saturn are gas giants vastly larger and less dense than Earth, so none of them qualify as Earth's twin.

Isohyets are imaginary lines on a map joining places that receive the same amount of rainfall over a given period. Contour lines join points of equal elevation, isobaths join points of equal water depth, and isobars join points of equal atmospheric pressure - none of which represent rainfall.

The scientific study of fungi is called Mycology, which examines their structure, classification, reproduction and ecological roles. Physiology deals with functions of organisms in general, phrenology is a discarded study of skull shapes, and biology is the broad study of all living things - none specifically denotes the study of fungi.

Curd is produced when Lactobacillus bacteria ferment lactose in milk into lactic acid. The acid lowers the pH, causing milk protein (casein) to coagulate and thicken into curd. Lycopodium is a clubmoss (a plant), yeast and fungus are fungal organisms used in bread and brewing - none of these are responsible for normal curd formation.

The human rib cage contains 12 pairs of ribs (24 in total), articulating posteriorly with the 12 thoracic vertebrae. These are classified as 7 pairs of true ribs (attached directly to the sternum), 3 pairs of false ribs (attached indirectly via the 7th costal cartilage), and 2 pairs of floating ribs (no anterior attachment). Total = 7 + 3 + 2 = 12 pairs.

Ignoring air resistance, only gravity acts on the ball, so the total mechanical energy (kinetic + potential) is conserved throughout the motion. \[E = \tfrac{1}{2}mv^{2} + mgh = \text{constant}\] As the ball rises, KE converts into PE; on the way down, PE converts back into KE. Displacement, velocity and kinetic energy each change continuously, so only the total energy stays constant.

Heat is a form of energy, and the SI unit of energy - including heat energy - is the Joule (J), defined as the work done when a force of one newton moves an object through one metre. Newton measures force, calorie is a non-SI unit of energy (1 cal ≈ 4.184 J), and kelvin is the SI unit of temperature, not energy.

Digital computers use the binary system (base 2) with only two digits, 0 and 1, to encode data and instructions. This matches the two stable states of electronic switching elements - off/on or low/high voltage - making representation and processing reliable. Decimal, octal and hexadecimal are convenient for humans to read, but internally every value and instruction is stored as binary bits.

Sodium bicarbonate, \(\text{NaHCO}_{3}\), is commonly known as baking soda. It releases \(\text{CO}_{2}\) on reacting with acids, which makes batter rise during baking. Washing powder is based on sodium carbonate \(\text{Na}_{2}\text{CO}_{3}\), plaster of Paris is \(\text{CaSO}_{4}\cdot\tfrac{1}{2}\text{H}_{2}\text{O}\), and fly ash is a coal-combustion residue - none of these is sodium bicarbonate.

Siderite, iron(II) carbonate \(\text{FeCO}_{3}\), is a recognised ore of iron. Dolomite \(\text{CaMg(CO}_{3})_{2}\) yields magnesium and calcium, Epsom salt \(\text{MgSO}_{4}\cdot 7\text{H}_{2}\text{O}\) is a magnesium compound, and galena \(\text{PbS}\) is the chief ore of lead - so none of these is an iron ore.

Tropical regions have the maximum biodiversity. Warm temperatures, abundant rainfall and high solar energy throughout the year support very high primary productivity, complex food webs and extensive niche specialisation - tropical rainforests and coral reefs are the richest ecosystems on Earth. Deserts and polar regions impose harsh climatic limits that restrict species numbers, while a single river offers a comparatively narrow habitat.

Albert Sabin (1906-1993), a Polish-American medical researcher, developed the oral polio vaccine (OPV) in the late 1950s. Administered on a sugar cube, it was easier to deliver in mass campaigns than Jonas Salk's earlier injectable vaccine and induced strong intestinal immunity. Edward Jenner developed the smallpox vaccine, Alexander Fleming discovered penicillin, and Baruch Blumberg is credited with the Hepatitis B vaccine. Hence the answer is Polio vaccine.

The Varishtha Pension Bima Yojana (VPBY) is a government-backed pension scheme for senior citizens (60+) offering an assured return. For FY 2017-18, the Union Budget designated the Life Insurance Corporation of India (LIC) as the sole implementing agency, continuing its role from earlier VPBY editions. National Insurance and New India Assurance are general (non-life) insurers, and SBI Life is a private joint-venture insurer — government social-pension schemes are routed through state-owned LIC.

No Ball is an illegal delivery in Cricket (bowler overstepping or breaching the rules) — so 1-b. Goal is the scoring unit in Hockey (ball crossing the goal line) — so 2-a. Knockout is the decisive finish in Boxing when a fighter cannot rise within the count — so 3-c. The correct sequence is 1-b, 2-a, 3-c.

Sonal Mansingh is an internationally acclaimed Indian classical dancer, renowned for her mastery of Odissi and Bharatanatyam; she received the Padma Vibhushan in 2003. Palghat Mani Iyer was a Carnatic mridangam maestro, Madhumati was a playback singer/actress, and Siddheshwari Devi was a Hindustani vocalist ('Nightingale of Banaras') — none were classical dancers.

Among the 2016 Arjuna Award recipients, Vinesh Phogat and Amit Kumar Dahiya were honoured for Wrestling, and Virender Singh 'Goonga Pehelwan' for wrestling under the Para-sports category. Rajat Chauhan received the 2016 Arjuna Award for Archery (compound event), not wrestling. Hence Rajat Chauhan is the odd one out.

'The Ministry of Utmost Happiness' (2017) was written by Arundhati Roy, her second novel, published twenty years after her Booker-winning debut 'The God of Small Things' (1997). Amitav Ghosh authored 'The Shadow Lines' and the Ibis trilogy; Pramod Kapoor wrote 'Gandhi: An Illustrated Biography'; Chaitanya Padukone is a Bollywood biographer — none of them wrote this novel.

The South Asia Subregional Economic Cooperation (SASEC) programme, launched in 2001 with ADB support, originally comprised Bangladesh, Bhutan, India, Maldives and Nepal; Sri Lanka joined in 2014 as the sixth member. On 31 March 2017, Myanmar became the seventh member, strengthening connectivity between South Asia and Southeast Asia.

India shares a roughly 1,751 km open border with Nepal. Five Indian states touch this boundary: Uttarakhand, Uttar Pradesh, Bihar, West Bengal and Sikkim. Hence the answer is 5. (Note: this is the official count used in SSC GA; Sikkim shares a short north-western stretch with Nepal.)

The units digit of \(n^2\) depends only on the units digit of \(n\). Squaring 0-9 gives units digits \(\{0,1,4,9,6,5,6,9,4,1\}\), so a perfect square can end only in 0, 1, 4, 5, 6 or 9. Digits 2, 3, 7 and 8 never appear. Among the given options, 8 is the impossible units digit.

Step 1 — Combined one-day work: \[\frac{1}{30}+\frac{1}{15}=\frac{1+2}{30}=\frac{3}{30}=\frac{1}{10}\] Step 2 — Work in 4 days: \[\frac{1}{10}\times 4=\frac{4}{10}=\frac{2}{5}\] As a percentage: \(\tfrac{2}{5}\times 100=40\%\). Therefore 40% of the work is completed.

Area of a trapezium \(=\tfrac{1}{2}(a+b)h\) where \(a,b\) are the parallel sides and \(h\) the perpendicular height. \[A=\tfrac{1}{2}(21+9)\times 10=\tfrac{1}{2}\times 30\times 10=150\] Therefore the area is 150 cm².

Step 1 — Remaining-price multipliers: A discount of d% leaves (100-d)% of the price, so after 20%, 10%, 30% the fraction remaining is \[0.80\times 0.90\times 0.70=0.504\] Step 2 — Net discount: \[100\%-50.4\%=49.6\%\] Therefore the net discount is 49.6%.

Step 1 — Choose a common capacity: LCM of (5+7), (7+9), (2+1) = LCM(12,16,3) = 48 units per bottle. Step 2 — Milk in each bottle: \[\tfrac{5}{12}\times 48=20,\quad \tfrac{7}{16}\times 48=21,\quad \tfrac{2}{3}\times 48=32\] Step 3 — Percentage of milk: \[\frac{20+21+32}{48\times 3}\times 100=\frac{73}{144}\times 100\approx 50.7\%\] Therefore the new mixture is 50.7% milk.

Step 1 — Set up: Let total spending be \(T\); average \(A=T/8\). Seven friends spent \(7\times 14=98\); the eighth spent \(A+21\). Step 2 — Equation: \[T=98+\tfrac{T}{8}+21\;\Rightarrow\;\tfrac{7T}{8}=119\;\Rightarrow\;T=136\] Check: A = 17, eighth spent 38, total = 98 + 38 = Rs 136.

Step 1 — Set up: Let CP = \(x\). Profit percentage = \(x\) (numerically), and profit = SP − CP = \(24-x\). \[x=\frac{24-x}{x}\times 100\;\Rightarrow\;x^{2}+100x-2400=0\] Step 2 — Solve: \[x=\frac{-100\pm\sqrt{10000+9600}}{2}=\frac{-100\pm 140}{2}\] Taking the positive root, \(x=20\). Check: 20% of 20 = 4, SP = 20 + 4 = 24. Therefore CP = Rs 20.

Step 1 — Find A's marks: A scored 36% less than B, so A = 64% of 145. \[A = 0.64 \times 145 = 92.8\] Step 2 — Relate A to C: A is 16% more than C, so \(A = 1.16 \, C\). \[C = \frac{92.8}{1.16} = 80\] Therefore C's marks are 80.

The distance is the same in both scenarios. Compute it from the post-repair leg, then divide by the pre-repair speed. Step 1 — Distance: \[D = 54 \times 6 = 324 \text{ km}\] Step 2 — Time before repairing: \[T = \frac{324}{48} = 6.75 \text{ hours} = 6 \text{ h } 45 \text{ min}\] Therefore the answer is 6 hours 45 minutes.

Step 1 — Interest and time: Amount = 3P, so SI = 3P − P = 2P. Time = 5 yr 4 mo = \(5 + \tfrac{4}{12} = \tfrac{16}{3}\) years. Step 2 — Apply SI formula: \[SI = \frac{P \cdot R \cdot T}{100} \implies 2P = \frac{P \cdot R \cdot \tfrac{16}{3}}{100}\] \[R = \frac{2 \times 100 \times 3}{16} = \frac{600}{16} = 37.5\%\] Therefore the yearly rate is 37.5%.

Use the identity \(a^3+b^3+c^3-3abc=(a+b+c)\left[(a+b+c)^2-3(ab+bc+ca)\right]\). Step 1 — Compute the bracket: \[(a+b+c)^2 - 3(ab+bc+ca) = 11^2 - 3(17) = 121 - 51 = 70\] Step 2 — Multiply: \[a^3+b^3+c^3-3abc = 11 \times 70 = 770\] Therefore the value is 770.

Step 1 — Find \(x^2+\tfrac{1}{x^2}\): Since \(\left(x^2+\tfrac{1}{x^2}\right)^2 = x^4+\tfrac{1}{x^4}+2\): \[\left(x^2+\tfrac{1}{x^2}\right)^2 = 62 + 2 = 64 \implies x^2+\tfrac{1}{x^2} = 8\] Step 2 — Apply \(a^3+b^3 = (a+b)^3 - 3ab(a+b)\) with \(ab=1\): \[x^6+\tfrac{1}{x^6} = 8^3 - 3(8) = 512 - 24 = 488\] Therefore the value is 488.

From \(x+y=4\) we get \(y=4-x\), so \(y-2 = 2-x = -(x-2)\). \[\frac{2}{x-2}+\frac{2}{y-2} = \frac{2}{x-2} + \frac{2}{-(x-2)} = \frac{2}{x-2} - \frac{2}{x-2} = 0\] The two terms cancel, so the value is 0.

Step 1 — Clear fractions: Multiply \(\tfrac{x}{5}+\tfrac{5}{x}=-2\) by \(5x\): \[x^2 + 25 = -10x \implies x^2 + 10x + 25 = 0\] Step 2 — Factor the perfect square: \[(x+5)^2 = 0 \implies x = -5\] Therefore \(x^3 = (-5)^3 = \mathbf{-125}\).

O is the incenter of \(\triangle PQR\) (intersection of the bisectors of \(\angle Q\) and \(\angle R\)). The standard incenter result is: \[\angle QOR = 90^\circ + \tfrac{1}{2}\angle P\] With \(\angle P = 45^\circ\): \[\angle QOR = 90^\circ + \tfrac{45^\circ}{2} = 90^\circ + 22.5^\circ = 112.5^\circ\] Therefore 112.5°.

When the bisectors of \(\angle Q\) and \(\angle R\) meet at the incenter O, the standard result is: \[\angle QOR = 90^\circ + \frac{\angle P}{2}\] Substituting \(\angle P = 45^\circ\): \[\angle QOR = 90^\circ + \frac{45^\circ}{2} = 90^\circ + 22.5^\circ = 112.5^\circ\] Therefore \(\angle QOR = \mathbf{112.5^\circ}\).

Given : PQ = 11cm UR = 8 cm TR = 1 cm QT = 3 cm Concept used : Pythagoras theorem in right triangle where ∠A = 90° Mid point theorem : Calculation : Since, SR = PQ ⇒ SU = PQ – UR = 11 – 8 = 3 Also, PS = QR ⇒ PS = QT + TR = 3 + 1 = 4 In triangle PSU ⇒ PS 2+ US 2= PU 2 ⇒ 4 2+ 3 2= 16 + 9 = 25 = PU 2 ⇒ PU = 5 Now, by mid-point theorem of triangle, ⇒ Line joining mid-points of PT and TU = ½ (PU) ⇒ Line joining mid-points of PT and TU = 2.5 ∴ The correct answer is 2.5 .

Given that area of triangle PQT is 72 ⇒ ½ PQ × QT = 72 Since PQ = QT ⇒ PQ = QT = 12cm Given PS = PQ/2 ⇒ PS = 12/2 = 6cm Now height of trapezium is PQ = 12 cm and PS = 6 cm and QR = 12 + 6 = 18cm Area of trapezium can be written as ½ × (sum of parallel sides) × height ⇒ Area = 1/2 × (18 + 6) × 12 ⇒ Area = 144 cm 2 ∴ the area of trapezium is 144 cm 2

Use the difference of squares: \((\text{cosec }A+\sin A)(\text{cosec }A-\sin A) = \text{cosec}^2 A - \sin^2 A\). Apply the Pythagorean identities \(\text{cosec}^2 A = 1+\cot^2 A\) and \(\sin^2 A = 1-\cos^2 A\): \[(1+\cot^2 A) - (1-\cos^2 A) = \cos^2 A + \cot^2 A\] Therefore the simplified value is \(\cos^2 A + \cot^2 A\).

Step 1 — Combine the fractions: Common denominator is \(\sec^2 A - 1 = \tan^2 A\). \[\frac{\sec A(\sec A+1) + \sec A(\sec A-1)}{\sec^2 A - 1} = \frac{2\sec^2 A}{\tan^2 A}\] Step 2 — Convert to sine/cosine: \[\frac{2/\cos^2 A}{\sin^2 A/\cos^2 A} = \frac{2}{\sin^2 A}\] Step 3 — Take the root: \[\sqrt{\frac{2}{\sin^2 A}} = \frac{\sqrt{2}}{\sin A} = \sqrt{2}\,\text{cosec }A\] Therefore the answer is \(\sqrt{2}\,\text{cosec }A\).

Step 1 — Convert tan and cot to sin/cos: \[\frac{\cos A}{1-\tan A} = \frac{\cos^2 A}{\cos A-\sin A}, \qquad \frac{\sin A}{1-\cot A} = \frac{\sin^2 A}{\sin A-\cos A}\] Step 2 — Combine using \(\sin A-\cos A = -(\cos A-\sin A)\): \[\frac{\cos^2 A - \sin^2 A}{\cos A-\sin A} = \frac{(\cos A-\sin A)(\cos A+\sin A)}{\cos A-\sin A} = \cos A + \sin A\] Step 3 — Square: \[(\cos A+\sin A)^2 = 1 + 2\sin A\cos A = 1 + \sin 2A\] Therefore the value is \(1+\sin 2A\).

Average can be written as = (300 + 250 + 162 + 272 + 82 + 104 + 120) /7 ⇒ average = 184.28 ∴ the average of 7 countries is 184.28

Average of 3 highest yielding countries = (300 + 272 + 250) /3 = 822/3 ⇒ Average of 3 highest yielding countries = 274 Average of 3 lowest yielding countries = (82 + 104 + 120) /3 = 306/3 ⇒ Average of 3 lowest yielding countries = 102 ∴ Ratio can be given as 274/102 = 137 : 51

Total of India and china is = 300 + 272 = 572 Total yield of other countries = 250 + 162 + 82 + 104 + 120 = 718 ⇒ required percentage = 572 × 100/718 = 79.66% ∴ the required percentage is 79.66%

Bottom two countries will be the countries with minimum production i.e. Nepal and Thailand total production of these 2 countries is 82 + 104 = 186 Production after 20% increase in these countries can be written as ⇒ after production = 186 × (1 + 20/100) = 186 × 1.2 ⇒ after production = 223.2 Total production of remaining countries is 300 + 250 + 162 + 272 + 120 = 1104 Production after 10% increase in these countries can be written as ⇒ after production = 1104 × (1 + 10/100) = 1104 × 1.1 ⇒ after production = 1214.4 Total production can be written as = 1214.4 + 223.2 = 1437.6 Average can be written = Total production/7 ⇒ 1437.6/7 = 205.37 ∴ the average is 205.37

The construction "The reason... is because" is redundant: "reason" already conveys cause, and "because" repeats it. Standard usage requires "The reason... is that...". The faulty phrase appears in segment (2) — "to the meeting is because her". Correct version: "The reason Priya was late to the meeting is that her flight was delayed." Hence the error lies in part 2.

The correlative conjunction "not only ... but also" requires parallel structure. Part (1) uses an inverted clause ("did they offer"), so part (2) should mirror it with "but also" plus a parallel verb form — e.g., "but also gave" or "but they also provided". The sentence reads "but provided", omitting "also" and breaking parallelism. The error is in part 2.

The phrasal verb "set someone up in business" is a fixed English idiom meaning to provide the means or capital for someone to start in a trade. "Built up" suggests gradual development, "hold up" means support/delay, and "keep up" means maintain — none fit the idiomatic slot. Hence "His father set him up in a construction business" is correct.

The blank requires an adjective conveying deep, heartfelt admiration for an achievement. Profound means very great or intense, and collocates naturally with feelings such as respect, sadness, or gratitude. "Abundant" describes quantity (resources, supplies), not the depth of a feeling. "Strong" is grammatically possible but weaker in nuance. "Unique" means one of a kind, which does not describe intensity. Hence the correct sentence reads: "I have profound respect for his achievement."

To boast is to speak with excessive pride about one's achievements or possessions. Among the options, Pride is the closest in meaning, as boasting is the outward expression of pride. "Avoid" (keep away), "Change" (alter), and "Rely" (depend on) are entirely unrelated to self-praise. Therefore Pride is the correct synonym.

Haste means excessive speed or urgency of action. Hurry means to move or act with great speed, which is virtually identical in meaning. "Burden" (heavy load), "Expect" (anticipate), and "Sight" (vision) bear no relation to speed. Hence Hurry is the correct synonym.

Refulgent means shining brightly, radiant, or gleaming. Its opposite must denote absence of light. Dark (lacking light) is the direct antonym. "Loud" relates to sound, "Rough" to texture, and "Sweet" to taste — none oppose brightness. Hence the antonym is Dark.

A skeptic is one who doubts or questions accepted opinions. Its opposite is someone who accepts and trusts — a Believer. "Erroneous" means incorrect, "Nervous" means anxious, and a "Nihilist" rejects meaning entirely (closer to a skeptic than its opposite). Hence Believer is the correct antonym.

The idiom Herculean task derives from the Twelve Labours of Hercules in Greek mythology — feats demanding extraordinary strength and effort. It therefore means a very difficult task. "Important task" stresses significance, not difficulty; "Motivating" describes an effect on the doer; "Optional to do" contradicts the idiom's weight. Hence option 4 is correct.

The idiom on tenterhooks originates from cloth being stretched taut on hooks of a tenter-frame. Figuratively, it describes someone stretched mentally — i.e. in anxious suspense while waiting for an outcome. "Flattery", "in a disorganized manner", and "speak quickly" have no connection to suspense or anxiety. Hence option 3 is correct.

Here "look" functions as a linking verb meaning "to appear", and must be used in the active voice with an adjective complement ("beautiful"). The passive "would be looked" is ungrammatical for this sense. The modal would takes the base form of the verb, giving would look. "Had looking" is not a valid construction, and "was looked" repeats the passive error. The correct sentence: "Neha would look beautiful in Indian attire."

The meaning intended is that people have known this fact for a long time and still do — the present perfect active tense. The original passive "have been long known" wrongly makes "people" the receivers of knowing. "People have long known" places the adverb long correctly between the auxiliary and the past participle, and uses the active voice. "Had long known" (past perfect) needs a later past reference, and "have to know long" is ungrammatical. Hence option 3 is correct.

An accomplice is a person who helps another commit a crime — the precise meaning of "an associate in crime". "Callous" means insensitive, "Itinerant" means travelling from place to place, and "Philistine" means indifferent to culture — none relate to criminal partnership. Hence Accomplice is correct.

Effeminate describes a man having or showing characteristics traditionally regarded as typical of a woman — exactly matching the given phrase. "Biped" means a two-footed creature, "Gregarious" means sociable, and "Inalienable" means incapable of being taken away. None describe gendered behaviour. Hence Effeminate is correct.

The correct spelling is Proficient (meaning skilled or expert), spelt P-R-O-F-I-C-I-E-N-T. The given form "Profecient" wrongly uses an 'e' after "Prof" instead of 'i'. "Ecstasy", "Sacrifice", and "Temporary" are all spelt correctly. Hence the misspelt word is option 2.

The correct spelling is Grammar (ending in -ar, not -er). "Grammer" is a common misspelling. "Familiar", "Narrator", and "Operator" are all spelt correctly. Hence the misspelt word is option 2.

R is the topic sentence — a broad statement on water's versatile role in the biosphere. Q follows by introducing the water cycle's two branches (atmospheric and terrestrial), narrowing the focus. The remaining two sentences detail those branches in the order Q named them: S describes the atmospheric branch (gaseous form), then P describes the terrestrial forms (liquid and solid). Hence the order is RQSP.

Q opens by introducing the subject — Renaissance and Shakespearean works vibrating with compassion. S follows naturally: "In this compassion" refers back to Q and identifies it as the "creative genius of the age". R then elaborates: "Yes, it was a genius of courage" — "it" refers to the genius just named in S. P closes by explaining what that courageous genius knew — harbours, homes, barns — imagery of preservation that ties back to Q's endangered life experience. Hence the order is QSRP.

The active sentence has a main clause ("Sunita has written a story") and a relative clause ("which fascinates everyone"). In Option 1, the main clause is converted into a passive relative clause modifying "a story": "A story which has been written by Sunita" (Present Perfect passive of "has written"). The original relative clause's verb "fascinates" then becomes the main verb, retaining "everyone" as its object. This yields "A story which has been written by Sunita fascinates every one" — a faithful passive transformation preserving tense and meaning. Option 2 reverses the focus; Option 3 inverts the subject–object relation; Option 4 omits the auxiliary, producing a reduced (and tense-shifted) form.

To convert an imperative from indirect to direct speech, replace the reporting verb "ordered" with "said to", insert a comma before the quoted command, and restore the imperative mood. The indirect clause "to do as he was told" becomes the direct command "Do as you are told" — the addressee ("he") shifts back to "you", and the back-shifted tense returns to its original present form. Option 3, "Rajesh said to his driver, 'Do as you are told.'", applies all these rules correctly. Options 2 and 4 wrongly use the present tense "says"; Option 1 omits the comma and keeps "ordered" without the proper structure.

The sentence defines management as a structured set of activities that keep a complex system functioning. Processes — series of coordinated actions like planning, organising, staffing and controlling — precisely captures this definition. "Instructions" are too narrow (a subset of management activity); "resources" are inputs that management uses, not what management itself consists of; "proposals" are suggestions, not ongoing operational activities. Hence the correct fill is processes.

The blank describes how management keeps a complicated system of people and technology running. Smoothly means without friction, problems or interruptions — the standard collocation "running smoothly" fits exactly. "Fastly" is not a standard English adverb. "Reliably" captures dependability but misses the efficiency/seamlessness nuance. "Sharply" (abruptly, intensely) does not describe steady system operation. Hence smoothly.

Planning, budgeting, organising, staffing, controlling and problem-solving are universally recognised as the core functions of management — they are vital, not dangerous, terrible, or merely difficult. Important correctly describes their significance to the functioning of any organisation. "Dangerous" and "terrible" carry negative connotations that contradict the listed essential activities. "Difficult" describes execution, not value. Hence the correct fill is important.

The blank modifies the adjective "changing", so it must be an adverb. "Run" and "show" are verbs and cannot fit grammatically. Between "normally" and "significantly", the context — leadership defining the future and inspiring people to overcome obstacles — points to substantial, not routine, change. Significantly conveys the large-scale, impactful shifts that leadership is meant to address, fitting both grammar and meaning.

The blank refers back to "what the future should look like" — the future image that leadership defines and people are aligned with. Vision means exactly that: a mental picture of a desired future state. "Look" refers to appearance, "role" to a function, and "source" to an origin — none of these denote a defined future state. Hence vision completes the sentence correctly.