SSC CGL 2017 · 2017-08-09 · Shift 3

In the case of two dices, we’ll write the face of dices in the anticlock wise direction starting from N, Dice Same face Opposite face 1 N S B 2 N T Q Hence, we can say that face ‘Q’ will be opposite to face ‘B’.

Let P, S, U, C, I denote the heights. The clues give \(S < P\), \(P < U\), \(U = C\), and \(P < I\). Combining: \(S < P < U = C\) and \(P < I\). So Sky is shorter than every other named tower, making it the shortest. Pearl is taller only than Sky and shorter than Unity, Cyber, and Indus, so it sits exactly one rung above Sky. Therefore the second shortest building is Pearl Tower.

Hence, answer is option 4.

Hence, the given question figure is embedded in option 4.

Check the rule on the first pair: \(5^{3}+5 = 125+5 = 130\). The relation is \(n : n^{3}+n\). Applying it to 6: \[6^{3}+6 = 216+6 = 222\] Hence the missing number is 222.

Substitute the symbols: + becomes ÷, × becomes +, ÷ becomes −, – becomes ×. The expression turns into: \[54 \div 162 \times 18 + 12 - 6\] Apply BODMAS (division and multiplication left to right, then addition and subtraction): \[\tfrac{54}{162} \times 18 = \tfrac{1}{3} \times 18 = 6\] \[6 + 12 - 6 = 12\] So the value is 12.

Compare alphabet positions of JPC and GMZ: J(10)→G(7), P(16)→M(13), C(3)→Z(26). Each letter shifts 3 positions backward, with C wrapping around to Z (3 − 3 → 26). Apply the same −3 shift to PUV: P(16)→M(13), U(21)→R(18), V(22)→S(19). Hence the answer is MRS.

Check the digit sums: 234→9, 243→9, 432→9, but 345→12. Equivalently, 234, 243 and 432 are divisible by 9 (\(234=9\times 26\), \(243=9\times 27\), \(432=9\times 48\)), whereas \(345 = 9\times 38 + 3\) is not. So the odd one out is 345.

Statement 1 (All cups are plate) places the whole cup-set inside the plate-set. Statement 2 (No plate is a shop) makes the plate-set and shop-set disjoint. Conclusion I (No cup is a shop): since every cup lies inside the plate-set, and the plate-set shares nothing with the shop-set, no cup can be a shop. Follows. Conclusion II (No shop is a plate): a universal negative (“No A is B”) converts symmetrically, so “No plate is a shop” directly gives “No shop is a plate”. Follows. Hence both conclusions follow.

Quick–Fast, Lazy–Slow and Exhaust–Tired all show words with similar or closely related meaning (near-synonyms or action→state). Credible (believable) and Deceptive (misleading) are antonyms, breaking the synonym pattern. So the odd pair is Credible : Deceptive.

Within each triplet the letters skip one (C-E-G, I-K-M, O-Q-S), so the internal gap is +2, +2. The first letters jump by 6: C(3)→I(9)→O(15). The next first letter is \(15+6 = 21\), i.e. U. Continuing the +2 internal pattern from U gives U(21), W(23), Y(25). Hence the missing term is UWY.

The pattern followed here is, Figure 1: → 3 × 4 + 2 × 5 = 22 Figure 2: → 2 × 1 + 7 × 6 = 44 Same will be followed for figure 3, → 7 × 8 + 5 × 2 = 66 Hence, the missing number in the diagram is 66.

According to question, People who speak only in Italian = 7 People who speak only in French = 14 So, Total number of people = 7 + 14 = 21 Hence, 21 people can speak in Italian and French. Hence, the correct option is 1.

Hence, the unfolded figure will appear as option 2.

All words begin with G, so sort by the second letter: Ga… < Gl… < Gr…. That places Gap (4) first and Group (2) last. Among the ‘Gl’ words, compare the third letter: Glade < Glitch < Globe, giving 5, 3, 1. Overall order: Gap, Glade, Glitch, Globe, Group → 4 5 3 1 2.

An ammeter is the instrument that measures electric current, so the relation is instrument : quantity measured. Checking the options: a scale measures mass (not speed); a seismograph records seismic waves (not density); a barometer measures atmospheric pressure (not mass). Only an anemometer measures wind (speed/pressure), matching the original pattern. Hence the answer is Anemometer : Wind.

From Matrix I: S occurs at 04, 11, 23, 30, 42; T at 02, 14, 21, 33, 40; R at 01, 13, 20, 32, 44. From Matrix II: A occurs at 58, 65, 77, 89, 96. Test the option 30, 21, 77, 44: 30 lies in S’s set, 21 lies in T’s set, 77 lies in A’s set, and 44 lies in R’s set. Every code matches the required letter. Hence S-T-A-R is coded as 30, 21, 77, 44.

The rule is \(\text{next} = \text{previous}\times 2 + k\) where k decreases by 1 each step: \(7\times 2 + 5 = 19\) \(19\times 2 + 4 = 42\) \(42\times 2 + 3 = 87\) Next, with k = 2: \[87\times 2 + 2 = 174 + 2 = 176\] So the missing term is 176.

Read the pattern as: square the first number, concatenate \(@C\) as a digit, then add \(D\). Verify Case 1: \(3^2=9\); concatenate with 1 to get 91; \(91+7=98\). ✓ Verify Case 2: \(4^2=16\); concatenate with 2 to get 162; \(162+16=178\). ✓ Apply to Case 3: \(5^2=25\); concatenate with 3 to get 253; \(253+9=262\). Hence the answer is 262.

Triangles in the given figure as follow, → AGB, BFG, GFC, ABC, CGH, HEG, DEG, DGC, ECG, DGH, ADG, ABD, BCD,BGC,ACD Alternate solution: Hence, there are 15 triangles in the given figure.

Hence, the mirror image of the given figure will be as option 3.

The positional shifts applied to successive letters follow the alternating series \(+1, -2, +3, -4, +5\). Check on BOARD: B+1=C, O−2=M, A+3=D, R−4=N, D+5=I → CMDNI. ✓ Apply to PRINT: P(16)+1=Q, R(18)−2=P, I(9)+3=L, N(14)−4=J, T(20)+5=Y. Therefore PRINT is coded as QPLJY.

Letters available in LEGISLATOR: L(×2), E, G, I, S, A, T, O, R — only one E and one R. Raise (R, A, I, S, E), Gist (G, I, S, T) and Legal (L, E, G, A, L — needs two L’s, available) can all be formed. Greater requires two R’s and two E’s, but LEGISLATOR has only one of each. Hence Greater cannot be formed.

Check the gap between the two letters in each pair: CD (gap 0), ST (gap 0) and WX (gap 0) are pairs of consecutive letters. PR has one letter (Q) between P(16) and R(18), giving a gap of 1. Hence PR is the odd one out.

Step 1 — C’s present age: C turned 5 nine years ago, so C is \(5+9=14\) years now. Step 2 — B’s present age: After 8 years, B will be \(4\times 14=56\), so B is \(56-8=48\) now. Step 3 — A’s present age: A is twice B, so \(A=2\times 48=96\). Therefore A is 96 years old.

The mosque famous for its “shaking minarets” (Jhulta Minar) is the Sidi Bashir Mosque in Ahmedabad, Gujarat. Vibrating one minaret causes the other to vibrate in sympathy, a phenomenon studied but never fully explained. Kanpur, Jaipur and Ranchi are not associated with this monument; Ahmedabad’s historic Indo-Islamic architecture (the city is a UNESCO World Heritage Site) is its home.

Frequency measures the number of cycles or oscillations per second. Its SI unit is the hertz (Hz), where \(1\,\text{Hz}=1\,\text{cycle/second}\), named after Heinrich Rudolf Hertz. Newton is the unit of force, watt of power, and farad of capacitance — none measures frequency.

Among the chefs listed, Sanjeev Kapoor was conferred the Padma Shri 2017 in the Culinary category for popularising Indian cuisine globally through his television shows, cookbooks and restaurants. Vikas Khanna, Ranveer Brar and Kunal Kapur are well-known chefs but were not Padma Shri awardees in 2017.

In response to the rising frequency of North Korean missile launches, Japan launched an Information Gathering Satellite (IGS) to enhance its reconnaissance of the Korean peninsula. The IGS series is operated by Japan’s Cabinet Satellite Intelligence Center for security monitoring. South Korea, the USA and China were not the country referenced in this news item.

Under Article 53(2) of the Constitution of India, “the supreme command of the Defence Forces of the Union shall be vested in the President.” Hence the President of India is the Supreme Commander of the Indian Armed Forces. The Prime Minister, Defence Minister and Council of Ministers exercise executive and administrative control, but the constitutional supreme command rests with the President.

The World Outside My Window is a collection of essays and reflections by Ruskin Bond, the Indian author of British descent best known for his stories set in the Himalayan foothills and recipient of the Sahitya Akademi Award and Padma Shri. Emily Brontë, Jane Austen and Henry Fielding are English novelists of earlier eras and are unconnected to this title.

M-SIPS stands for Modified Special Incentive Package Scheme. Launched by the Ministry of Electronics and Information Technology, it offsets disabilities of domestic manufacturing by providing a capital subsidy (20% in SEZs, 25% in non-SEZs) for investments in the Electronics System Design and Manufacturing (ESDM) sector. The other options are not actual government schemes.

Madan Mohan Malaviya founded Banaras Hindu University (BHU) in Varanasi, established by the BHU Act of 1915 and operational from 1916. He conceived, planned, and raised funds for the institution as a centre for the revival of Indian culture and modern scientific education. Sukumar Dutt was a Buddhist scholar; Rajendra Prasad was India's first President; Motilal Nehru was a Congress leader and lawyer — none founded BHU.

Tawang is a town in Arunachal Pradesh, situated south of the McMahon Line in the eastern sector of the India–China border. China rejects the McMahon Line and claims Arunachal Pradesh (including Tawang) as 'South Tibet', making this a major land dispute with China. Pakistan's disputes lie in the western sector (J&K); India shares no direct border with Afghanistan; India–Bangladesh boundary issues were largely settled by the 2015 Land Boundary Agreement.

Blood, bone and cartilage are all classified as connective tissues — they consist of cells dispersed in an extracellular matrix (fluid plasma, mineralised matrix and semi-rigid matrix respectively). Skin is an organ, not a tissue. Its outer epidermis is epithelial tissue, while the dermis contains connective tissue. Because skin is composed of multiple tissue types, it is not itself a connective tissue.

Ozone \(\text{O}_3\) and dioxygen \(\text{O}_2\) are different structural forms of the same element (oxygen) in the same physical state, which is the definition of an allotrope. Isotopes differ in neutron number within one element; isobars are atoms of different elements with the same mass number; isotones are atoms of different elements with the same neutron number — none describe two molecular forms of one element.

Argon belongs to Group 18 (noble gases) and has a completely filled valence shell, making it chemically inert under standard conditions. It is widely used as a shielding gas in welding and inside incandescent bulbs. Hydrogen, nitrogen and oxygen all have incomplete valence shells and readily form compounds (water, ammonia, oxides, etc.), so they are reactive, not inert.

By mass, oxygen (~46.6%) and silicon (~27.7%) are the most abundant elements in Earth's crust, but they are non-metals. Among metals, Aluminium is the most abundant at about 8.1%, followed by iron (~5.0%), calcium, sodium, potassium and magnesium. Iron is the second-most abundant metal; magnesium is around 2.1%; copper is a trace metal (~0.0068%). Hence Aluminium tops the list.

The term Pedalfer is formed from Ped (soil) + Al (aluminium) + Fer (iron), and refers to soils of humid regions where heavy leaching removes soluble bases and leaves aluminium and iron oxides accumulated in the lower horizons. Chernozem is the fertile black soil of temperate grasslands rich in humus; podzol is an acidic, ash-grey forest soil; meadow soil is a general grassland soil — none are defined by Al/Fe-oxide enrichment the way pedalfer is.

A market with exactly one seller and one buyer is a bilateral monopoly — the seller behaves as a monopolist while the buyer behaves as a monopsonist, and price and quantity are settled through bargaining rather than competitive supply and demand. Public monopoly and franchised monopoly each involve one seller but many buyers; monopsony is one buyer with many sellers. Only bilateral monopoly captures both 'one buyer' and 'one seller'.

Clarence Birdseye, an American inventor, founded the modern frozen-food industry. While working as a fur trader in Labrador (1912–1916) he observed that fish frozen rapidly at very low temperatures retained their texture and flavour, and he later commercialised this 'quick-freezing' process in the 1920s. Alfred Nobel invented dynamite; Frank Whittle invented the turbojet engine; Ives McGaffey patented an early manual vacuum cleaner — none worked on frozen foods.

A convex mirror forms virtual, erect, diminished images and gives a much wider field of view than a plane mirror of the same size. These properties make it ideal as a vehicle rear-view mirror, letting the driver monitor a large area of traffic behind. Solar cookers and headlight reflectors need to converge light, so they use concave (parabolic) mirrors; an ophthalmoscope uses a concave mirror with a small aperture to focus light onto the retina.

Polio is caused by the poliovirus and chicken pox by the varicella-zoster virus — both are members of the virus group of micro-organisms, which can replicate only inside host cells. Bacteria cause diseases such as tuberculosis and cholera; protozoa cause malaria and amoebic dysentery; algae are generally photosynthetic and are not typical human pathogens.

The Red Data Book, maintained by the IUCN, documents the conservation status of species that are at risk of extinction — recording population, distribution, threats and required conservation measures. Of the choices given, 'all endangered species' best describes its focus. It does not list every plant or every animal species — only those evaluated as threatened — and although extinct species are noted, its dynamic content centres on currently endangered species needing protection.

Regional Rural Banks (RRBs) were set up under the RRB Act, 1976 on the recommendations of the Narasimham Working Group, and each RRB is sponsored by a Scheduled Commercial Bank (commonly called a National Commercial Bank). The capital is shared in the ratio Central Government 50%, Sponsor Bank 35%, State Government 15%. The sponsor bank provides managerial, financial, and training support. The RBI only regulates RRBs and NABARD supervises them, so neither the RBI, foreign banks, nor co-operative banks sponsor them. Hence the correct answer is National Commercial Banks.

The Second Battle of Tarain (1192 AD) was fought between Mohammed Ghori and Prithviraj Chauhan at Tarain (modern Taraori, Haryana). Ghori, defeated by Prithviraj a year earlier in the First Battle of Tarain (1191), returned with a better-organised cavalry and decisively defeated and captured Prithviraj. The other pairs belong to different battles: Alexander vs Porus fought the Battle of Hydaspes (326 BC), Jai Chand vs Ghori at Chandawar (1194), and Akbar vs Hemu at the Second Battle of Panipat (1556). Ghori's victory paved the way for the Delhi Sultanate.

Red rot is a fungal disease of sugarcane, caused by Colletotrichum falcatum (perfect stage Glomerella tucumanensis). It attacks the stalk, producing characteristic red patches interrupted by white cross-bands inside the cane, along with leaf yellowing and a sour, alcoholic smell. Paddy is affected by blast and bacterial blight; mustard by white rust and Alternaria blight; wheat by rusts and smuts — none of them suffer from red rot. The disease spreads chiefly through infected setts, which is why disease-free planting material and resistant varieties are the standard control measures.

A modifier key is a key that, when held with another key, changes the second key's normal action rather than typing a character on its own. Ctrl alters keys to trigger shortcuts (Ctrl+C, Ctrl+V); Shift changes letter case and gives the upper symbols on number keys; Alt produces shortcuts like Alt+F4 and Alt+Tab. Since Ctrl, Shift, and Alt all behave this way, all options are correct. Other typical modifier keys are the Windows key, Command (on macOS), and Fn.

Birdie is a Golf term — finishing a hole one stroke under par — so 1–c. Volley, hitting the ball before it bounces, is a fundamental Tennis stroke, so 2–a. Hit Wicket is a mode of dismissal in Cricket where the batsman dislodges his own stumps while playing a shot or starting a run, so 3–b. The matching sequence is therefore 1–c, 2–a, 3–b.

The Anti-defection law was inserted by the 52nd Constitutional Amendment Act, 1985, and is contained in the Tenth Schedule of the Indian Constitution. It lays down the grounds on which a member of Parliament or a State Legislature can be disqualified for defection — voluntarily giving up party membership, voting against a party whip without permission, an independent joining a party, or a nominated member joining a party after six months. The Second Schedule deals with salaries of constitutional posts, the Third with oaths and affirmations, and the Fourth with allocation of Rajya Sabha seats — none of these contain the anti-defection provisions.

Multiply numerator and denominator by the conjugate and use the identity \(\sec^2 A - \tan^2 A = 1\): \[\frac{1}{\sec A + \tan A} = \frac{\sec A - \tan A}{\sec^2 A - \tan^2 A} = \sec A - \tan A\] Squaring and converting to sine and cosine: \[(\sec A - \tan A)^2 = \left(\frac{1 - \sin A}{\cos A}\right)^2 = \frac{(1-\sin A)^2}{\cos^2 A}\] Using \(\cos^2 A = 1 - \sin^2 A = (1-\sin A)(1+\sin A)\) and cancelling one factor of \((1-\sin A)\): \[= \frac{1 - \sin A}{1 + \sin A}\] Therefore the simplified value is \(\dfrac{1-\sin A}{1+\sin A}\).

Step 1 — Relative speed: Trains move in the same direction, so \[v_{rel} = 51 - 43 = 8 \text{ km/h} = 8 \times \frac{5}{18} = \frac{20}{9}\text{ m/s}\] Step 2 — Length of faster train: Crossing a man means the distance equals the train's own length: \[L = v_{rel} \times t = \frac{20}{9} \times 72 = 160 \text{ m}\] Therefore the faster train is 160 metres long.

Step 1 — Angle in \(\triangle ABP\): Since BP ⊥ AC, \(\angle APB = 90^\circ\). With \(\angle BAP = 50^\circ\): \[\angle ABP = 180^\circ - 90^\circ - 50^\circ = 40^\circ\] Step 2 — Use \(\angle ABC = 90^\circ\): \[\angle PBC = \angle ABC - \angle ABP = 90^\circ - 40^\circ = 50^\circ\] Therefore \(\angle PBC = 50^\circ\). (Equivalently, the altitude on the hypotenuse gives \(\angle PBC = \angle BAC\).)

Step 1 — Volume of cone: \[V_{cone} = \tfrac{1}{3}\pi r^2 h = \tfrac{1}{3}\pi (8)^2 (24) = 512\pi \text{ cm}^3\] Step 2 — Volume of cylinder: \[V_{cyl} = \pi r^2 h = \pi (6)^2 (6) = 216\pi \text{ cm}^3\] Step 3 — Percent wasted: \[\frac{V_{cone} - V_{cyl}}{V_{cone}} \times 100 = \frac{512\pi - 216\pi}{512\pi}\times 100 = \frac{296}{512}\times 100 \approx 57.8\%\] Therefore about 57.8% of the material is wasted.

For second show, Number of audience in screen 3 = 7 × 100 = 700 ……..(i) Number of audience in screen 1 = 3 × 100 = 300 ……..(ii) ⇒ required value = (i) – (ii) = 700 – 300 = 400 ∴ the correct option is 3)

Step 1 — Andy's share of work: \[1 - \tfrac{8}{13} = \tfrac{5}{13}\] Step 2 — Wages are paid in the ratio of work done, so Andy's share is: \[\tfrac{5}{13}\times 2600 = 5\times 200 = \text{Rs } 1000\] Therefore Andy receives Rs 1000.

Since \(x^2 - 9 = (x-3)(x+3)\), both \(x = 3\) and \(x = -3\) are roots of \(P(x) = px^3 - 2x^2 - qx + 18\). Step 1 — Apply \(P(3)=0\): \[27p - 18 - 3q + 18 = 0 \implies 27p = 3q \implies q = 9p\] Step 2 — Check with \(P(-3)=0\): gives \(-27p + 3q = 0\), the same relation. Hence \(\dfrac{p}{q} = \dfrac{1}{9}\), so p : q = 1 : 9.

Each digit struck equals one keystroke, so count the total digits used to write 121 to 1346. Step 1 — 3-digit numbers (121 to 999): \((999-121+1)\times 3 = 879\times 3 = 2637\) Step 2 — 4-digit numbers (1000 to 1346): \((1346-1000+1)\times 4 = 347\times 4 = 1388\) Step 3 — Total keystrokes: \(2637+1388 = 4025\) Therefore the keys must be pressed 4025 times.

In ∆BCE ⇒ ∠CBE + ∠BEC + ∠ECB = 180° ⇒ ∠ECB = 180° – 2(84°) [ISOSCELES ∆] ⇒ ∠ECB = 12° Now, we know that ⇒ ∠ADC + ∠DCB = 180° [ANGLES BETWEEN PARALLEL LINES] ⇒ ∠DCB = 180° - 78° ⇒ ∠DCB = 102° So, ∠DCE = ∠ECB + ∠DCB ⇒ ∠DCE = 12° + 102° ⇒ ∠DCE = 114° Since, BC = CE = DC [SIDES OF RHOMBUS ARE EQUAL] In ∆DCE ⇒ ∠DCE + ∠CED + ∠EDC = 180° ⇒ ∠CED + ∠EDC = 180° - 114° ⇒ 2(∠DEC) = 66° ⇒ ∠DEC = 33° ∴ the correct option is 3)

Use the identity \(\operatorname{cosec}^2 A - \cot^2 A = 1\). Step 1 — Factor the first bracket: \(\operatorname{cosec}^4 A - \cot^4 A = (\operatorname{cosec}^2 A - \cot^2 A)(\operatorname{cosec}^2 A + \cot^2 A) = \operatorname{cosec}^2 A + \cot^2 A\) Step 2 — Substitute back into the expression: \((\operatorname{cosec}^4 A - \cot^2 A) - (\cot^4 A + \operatorname{cosec}^2 A) = (\operatorname{cosec}^4 A - \cot^4 A) - (\operatorname{cosec}^2 A + \cot^2 A)\) \(= (\operatorname{cosec}^2 A + \cot^2 A) - (\operatorname{cosec}^2 A + \cot^2 A) = 0\) Therefore the simplified value is 0.

Total number of people in second show = (3 + 4.5 + 7) × 100 = 14.5 × 100 = 1450 Total number of people in third show = (6 + 4 + 7.5) × 100 = 17.5 × 100 = 1750 Percentage increase = (1750 – 1450)/1450 ⇒ 300/1450 = 20.69 ∴ the correct option is 1)

Number of audience in Screen 1 from second show = 3 × 100 = 300 Number of audience in Screen 1 from third show = 6 × 100 = 600 Percentage increase = [(600 – 300) / 300] × 100 = 100% ∴ the correct option is 2)

When every number in a set is multiplied by a constant \(k\), the average is also multiplied by \(k\). \[\text{New average} = 2 \times 7 = 14\] Therefore the new average is 14.

Factor the divisor: \(x^2 - x - 6 = (x+2)(x-3)\). Let \(P(x) = px^3 - qx^2 - 7x - 6\). Then \(P(-2) = 0\) and \(P(3) = 0\). Step 1 — Use \(P(-2)=0\): \(-8p - 4q + 14 - 6 = 0 \implies 2p + q = 2\) Step 2 — Use \(P(3)=0\): \(27p - 9q - 21 - 6 = 0 \implies 3p - q = 3\) Step 3 — Add the equations: \(5p = 5 \implies p = 1,\ q = 0\) Therefore \((p,q) = (1, 0)\).

Let original CP = \(x\). Original SP = \(1.2x\). Step 1 — New CP and SP: \(\text{New CP} = 0.4x,\quad \text{New SP} = 1.2x - 90\) Step 2 — Apply 50% gain on new CP: \(1.2x - 90 = 1.5 \times 0.4x = 0.6x\) Step 3 — Solve: \(0.6x = 90 \implies x = 150\) Therefore the original cost price is Rs 150.

Join OA where OA = 10 cm Here, AO is perpendicular to AB ⇒ Area of ∆ABC = Area of ∆OAB + Area of ∆AOC ⇒ Area of ∆ABC = 1/2(OA)(AB) + 1/2(OC)(OA)sin(∠AOC) ⇒ Area of ∆ABC = 1/2(10)(24) + 1/2(10)(10) sin(∠AOC) ⇒ Area of ∆ABC = 120 + 50 sin(∠AOC) In right angled ∆OAB ⇒ tan(∠AOB) = 24/10 = 12/5 ⇒ ∠AOB = 67.38° So, ∠AOC = 180° – 67.38° = 112.62° Hence, Area of ∆ABC = 120 + 50 (0.93) = 120 + 46.15 = 166.15 ∴ The area (in cm 2) of triangle ABC is 166.15. Alternate Method In the triangle Δ OAB, Δ OAB is right angled triangle OA is perpendicular to the AB ⇒ SinB = OA/OB = 10/26 ⇒ 5/13 In triangle Δ ABC ⇒ (1/2)× AB × BC SinB ⇒ (1/2)× 24 × 36 × (5/13) ⇒ 166.15 ∴ The area (in cm 2) of triangle ABC is 166.15.

Rewrite both sides with base 4 using \(256 = 4^4\). Step 1 — From \(4^{x+y} = 256 = 4^4\): \(x + y = 4\) Step 2 — From \(256^{x-y} = 4 \implies 4^{4(x-y)} = 4^1\): \(x - y = \tfrac{1}{4}\) Step 3 — Add and subtract: \(2x = 4 + \tfrac{1}{4} = \tfrac{17}{4} \implies x = \tfrac{17}{8}\) \(y = 4 - \tfrac{17}{8} = \tfrac{15}{8}\) Therefore \((x, y) = \left(\tfrac{17}{8}, \tfrac{15}{8}\right)\).

Use the identity \(\left(x^2 + \tfrac{1}{x^2}\right)\left(x^3 + \tfrac{1}{x^3}\right) = \left(x^5 + \tfrac{1}{x^5}\right) + \left(x + \tfrac{1}{x}\right)\). Step 1 — Compute \(x^2 + \tfrac{1}{x^2}\): \(\left(x+\tfrac{1}{x}\right)^2 - 2 = 25 - 2 = 23\) Step 2 — Compute \(x^3 + \tfrac{1}{x^3}\): \(\left(x+\tfrac{1}{x}\right)^3 - 3\left(x+\tfrac{1}{x}\right) = 125 - 15 = 110\) Step 3 — Combine: \(x^5 + \tfrac{1}{x^5} = 23 \times 110 - 5 = 2530 - 5 = 2525\) Therefore the value is 2525.

Under simple interest the yearly interest is constant, so the difference of amounts gives the interest for the time gap. Step 1 — SI for 1.5 years: \(969 - 918 = 51\) Rs Step 2 — SI per year and principal: \(\text{SI/year} = \tfrac{51}{1.5} = 34\) Rs; \(P = 918 - 2\times 34 = 850\) Rs Step 3 — Rate: \(R = \dfrac{34 \times 100}{850 \times 1} = 4\) Therefore the rate of interest is 4%.

Number of audience in screen 1 = (5 + 3 + 6) × 100 = 1400 Number of audience in screen 2 = (6 + 4.5 + 4) × 100 = 1450 Number of audience in screen 3 = (6.5 + 7 + 7.5) × 100 = 2100 Total revenue of screen 1 = 350 × 1400 = Rs. 490000 Total revenue of screen 2 = 300 × 1450 = Rs. 435000 Total revenue of screen 3 = 250 × 2100 = Rs. 525000 ⇒ Maximum total revenue is of screen 3 ∴ the correct option is 4)

Step 1 — Combine the denominator: \[\cot\tfrac{A}{2}+\tan\tfrac{A}{2}=\frac{\cos\tfrac{A}{2}}{\sin\tfrac{A}{2}}+\frac{\sin\tfrac{A}{2}}{\cos\tfrac{A}{2}}=\frac{\cos^2\tfrac{A}{2}+\sin^2\tfrac{A}{2}}{\sin\tfrac{A}{2}\cos\tfrac{A}{2}}=\frac{1}{\sin\tfrac{A}{2}\cos\tfrac{A}{2}}\] Step 2 — Substitute and apply the double-angle identity: \[\frac{2}{\cot\tfrac{A}{2}+\tan\tfrac{A}{2}}=2\sin\tfrac{A}{2}\cos\tfrac{A}{2}=\sin A\] Therefore the simplified value is sin A.

Find the mixture's cost price first, then apply the rule of alligation. Step 1 — CP of mixture from SP and 20% profit: \(\text{CP} = \dfrac{42}{1.2} = 35\) Rs/kg Step 2 — Alligation between Rs 30 and Rs 45: \[\dfrac{\text{Qty at }30}{\text{Qty at }45} = \dfrac{45-35}{35-30} = \dfrac{10}{5} = \dfrac{2}{1}\] Therefore the required ratio is 2 : 1.

For two successive discounts of \(a\%\) and \(b\%\), the net discount is \(\left(a + b - \dfrac{ab}{100}\right)\%\). \[20 + 30 - \dfrac{20\times 30}{100} = 50 - 6 = 44\] Therefore the net discount is 44%.

Let Amit's income be \(I\). Step 1 — After the 20% donation: remainder \(=0.80\,I\). Step 2 — After depositing 20% of the remainder in the bank: what is left \(=0.80\,I\times(1-0.20)=0.80\times0.80\,I=0.64\,I\). Step 3 — Equate to Rs 12800: \[0.64\,I=12800\implies I=\frac{12800}{0.64}=20000\] Therefore Amit's income is Rs 20,000.

When the bisectors of the two exterior angles at Q and R meet at O, the angle formed at O relates to the third interior angle P by the standard result: \[\angle QOR = 90^\circ - \tfrac{1}{2}\angle QPR\] Substituting \(\angle QOR = 50^\circ\): \[50^\circ = 90^\circ - \tfrac{1}{2}\angle QPR \implies \tfrac{1}{2}\angle QPR = 40^\circ\] Therefore \(\angle QPR = 80^\circ\).

Nemesis means a deserved and inescapable punishment or retribution for one's wrongdoing — exactly matching the phrase "just punishment for wrongdoing". "Dandy" denotes a man obsessed with his appearance, "prodigy" denotes an exceptionally talented person, and "wagon" is a vehicle — none relate to punishment.

Lethargy means sluggishness, drowsiness, or lack of energy. Drowsy — meaning sleepy and sluggish — captures the same state of reduced energy. "Activity" is the opposite of lethargy; "modest" (humble) and "pleasure" (enjoyment) are unrelated. Hence the synonym is Drowsy.

The sentence is in past continuous active voice (were + laughing). The passive form follows the pattern: object + was/were + being + V3 + by + subject. Since "laugh at" is a phrasal verb, the preposition at must be retained. So "The kids were laughing at the old lady" becomes "The old lady was being laughed at by the kids." Option 3 drops "at" (wrong); option 4 shifts to simple past ("was laughed at"), losing the continuous aspect.

An independent judiciary requires executive interference in judge appointments to be as low as possible. Minimal (very small in amount) fits this need precisely. "Maximum" implies heavy interference (opposite of independence); "negotiable" and "reasonable" still permit significant interference. Hence the correct word is minimal.

The preceding context establishes that reducing executive interference strengthens judicial independence — a positive development for a free country. Such a change would naturally be greeted favourably, i.e. welcomed. "Adhered" doesn't fit grammatically; "neglected" and "rejected" imply disapproval, contradicting the passage's pro-independence tone.

The passage moves from withdrawing from social feedback to its long-term effect on identity. Q opens by introducing the "social mirror" and feedback. S follows with "this social feedback" becoming a comfort zone. R begins with "And", extending S — we avoid self-examination. P closes with "In that frame of mind", referring back to R's state of reverie. Hence the order is QSRP.

The idiom "an axe to grind" means having a private, often selfish motive or hidden personal agenda behind one's words or actions. "To act bravely", "to act like a fool", and "to take risk" describe manner of action, not motive. Hence the correct meaning is To have a selfish motive.

Trepidation means fear, anxiety, or nervous apprehension. Its antonym is therefore a state free of agitation — Calm (peaceful, untroubled). "Fear" is actually a synonym, not an antonym; "bawdy" (indecent) and "violent" (using force) are unrelated to emotional state.

Since an independent judiciary is the hallmark of a free country, the process appointing its judges must be essential — i.e. of vital importance (absolutely necessary). "Mere" downplays importance (opposite sense); "mourn" is a verb of grief (ungrammatical here); "social" is too vague for the critical role described.

The idiom "kick the bucket" is an informal euphemism meaning to die. "Lose temper" relates to anger, "to delay a little longer" to postponement, and "to meet with an accident" to mishaps — none capture the idiom's specific meaning of dying.

Spelling Word Identification The task is to identify the word that contains a spelling mistake from the given list. We need to check the spelling of each word provided in the options. Analyzing the Spelling of Given Words Secondary: This word is correctly spelt. It refers to something that is less important or comes after something else in order or importance. Sizeable: This word is correctly spelt. It means fairly large or considerable in size. Succumb: This word is correctly spelt. It means to fail to resist pressure, temptation, or some other negative force. Sustanence: This word is incorrectly spelt. Identifying the Incorrect Spelling Upon review, the word "Sustanence" is not spelt correctly. The correct spelling for this word is Sustenance. Sustenance refers to the maintaining of someone or something, or the condition of having food or drink required to live. The error in the provided word "Sustanence" is the omission of the second letter 'n'. Therefore, the incorrectly spelt word is "Sustanence".

An independent judiciary — protecting rights, upholding the rule of law, and checking executive/legislative power — is a defining feature of a democratic country, where power rests with the people and separation of powers prevails. "Autocratic" rule concentrates power and lacks judicial independence; "liberal" describes an ideology rather than the political system; "participative" refers to citizen involvement, not the governmental structure where judicial independence is the hallmark.

For a yes/no direct question, the reported clause must use 'if' or 'whether' with statement word order, and the present tense backshifts to past. So "Do you want" becomes "whether I wanted". Option 4 — "My cousin asked me whether I wanted some more chocolates" — uses the correct reporting verb (asked), conjunction (whether), pronoun shift (you to I), and backshifted tense (want to wanted). Option 1 fails the tense backshift; option 2 wrongly uses "said to" with 'if'; option 3 uses 'that', reserved for statements.

Hoodwink means to deceive or trick someone, often by misleading them. Among the options, Defraud — to cheat or deceive someone (typically for gain) — shares the core meaning of deception, making it the correct synonym. Illicit means forbidden by law (an adjective, not a verb of deception); Secret refers to hidden information; Stare means to gaze fixedly. Only Defraud captures the act of deceiving.

The noun hindrance takes the preposition 'to' to indicate what is being obstructed — "a hindrance to progress / development / growth". "Hindrance of" describes the nature of the obstruction itself, not its target; "over" and "upon" are not idiomatic with this noun. Hence the correct sentence is: "Corruption is a standing hindrance to the nation's development."

The error lies in part (2). The phrasal verb 'pass away' means 'to die' and cannot be used with 'the time'. The correct idiom is 'pass the time', meaning to occupy oneself so a period seems shorter. Parts (1) and (3) are grammatically sound. The corrected sentence reads: "My brother finds it difficult to pass the time at our grandparent's house."

The sentence needs a negative conditional: hard work is a necessary condition for success. 'Unless' means 'if not', so "Unless you work hard, you cannot succeed" = "If you do not work hard, you cannot succeed" — the intended meaning. 'If' would wrongly imply hard work causes failure. 'Till' and 'Until' express time ('up to the moment that') rather than a conditional necessity, and pairing them with "cannot succeed" sounds unidiomatic here. Hence Unless is correct.

Multifaceted means having many aspects, sides, or features — i.e., complex or many-sided. Its direct opposite is Simple, meaning uncomplicated, with few aspects. Adroit (skilful) and Handy (useful) relate to ability, not complexity; Pliable (flexible, easily bent) relates to adaptability. Only Simple negates the idea of having many facets.

The phrasal verb 'look forward to' means to anticipate something with pleasure. Here 'to' is a preposition (not an infinitive marker) and must be followed by a noun, pronoun, or gerund. So "looking forward for" is wrong; the correct improvement is "are looking forward to", giving "We are looking forward to a positive response from you." Options using 'at' are not idiomatic with 'look forward'.

The error is in part (3). The construction 'No sooner ... than' is a fixed correlative pair: "No sooner had he finished his morning walk than it began to rain." Parts (1) and (2) correctly use inversion after 'No sooner'. The conjunction 'when' is used with Hardly / Scarcely / Barely, not with 'No sooner'. Replacing 'when' with 'than' makes the sentence correct.

Q is the topic sentence — "Comfort is now one of the causes of its own spread" — introducing the central idea. S follows with the pronoun 'It' referring back to comfort, explaining how it spreads ("a physical habit, a fashion, an ideal"). R then states a consequence of this widespread pursuit — the more comfort spreads, the more it is valued. P concludes by noting the flip side: for those habituated to valued comfort, discomfort feels like torture. Hence the logical order is QSRP.

The blank refers to the executive's function in judicial appointments, which a Supreme Court advisory opinion would clarify or limit. The correct word is role — i.e., the executive's part or function in appointing judges, of which 'interference' is a specific aspect. 'Career' and 'future' don't fit a discussion of the executive as a branch in a process; 'plight' (a difficult situation) does not pair naturally with "and its interference". Hence: "the role of the executive and its interference in the appointment of judges".

Glamoros is misspelt. The correct spelling is Glamorous — the adjectival suffix is '-ous', the standard ending for adjectives like famous, dangerous, and marvellous. Continuous, Meticulous, and Vicious are all correctly spelt.

The verb 'promise' is followed by an infinitive (to + base verb) when the subject commits to an action: "He promised to mend his ways." This is grammatically correct and idiomatic. Option 1 ("had a promised to mending") is ungrammatical; option 2 ("promised for mending") uses a wrong preposition + gerund; option 3 ("was promised of mending") shifts to passive and uses a non-standard structure. Hence No improvement is needed.

Vindictive means having a strong or unreasoning desire for revenge against someone who has wronged you — exactly matching the phrase "one who is determined to take full revenge". The distractors do not fit: enmity is a state of hostility (not a person), pedantic describes someone fussy about minor details, and the other option is an offensive slur unrelated to revenge.