SSC CGL 2017 · 2017-08-08 · Shift 2

The relation is synonymy: Vacant and Empty both mean unoccupied/containing nothing. Applying the same relation, Dearth (a lack/shortage) pairs with its synonym Scarcity. "Abundant" is its antonym; "Descend" and "Squander" are unrelated verbs.

The pattern adds +1, +2, +3, +4 to the alphabetical positions of the four letters in order. Check first pair: H(8)+1=I(9), M(13)+2=O(15), P(16)+3=S(19), U(21)+4=Y(25) — gives IOSY. ✓ Apply to GMRF: G(7)+1=H(8), M(13)+2=O(15), R(18)+3=U(21), F(6)+4=J(10). Result: HOUJ.

Each pair follows \(n^2+1 : (n+1)^2+1\). Check: \(50 = 7^2+1\) and \(65 = 8^2+1\). ✓ For 122: \(122 = 11^2+1\), so the partner is \(12^2+1 = 144+1 = 145\). Therefore the answer is 145.

Each pair links a celestial body with its correct astronomical classification: Venus is a planet, the Moon is a satellite, the Sun is a star. Jupiter, however, is a planet — not a black hole — so the pairing in Jupiter : Black Hole is factually incorrect and is the odd one out.

Compute the gap between the two letters of each pair: KQ = 17−11 = \(6\), DJ = 10−4 = \(6\), RX = 24−18 = \(6\), but SZ = 26−19 = \(7\). Three pairs share a gap of 6, so SZ with a gap of 7 is the odd one out.

1) 361 → (19)2 2) 441 → (21)2 3) 784 → (28)2 4) 876 → This is not the square of any number. Therefore, '876' is an unpaired number.

All five words begin with H, so order by the second letter: Harmony (Ha-) first, then the He- words (Helm, Herbivorous), then the Ho- words (Honour, House). Within He-: Helm (Hel-) precedes Herbivorous (Her-) since l < r. Within Ho-: Honour (Hon-) precedes House (Hou-) since n < u. Final order: Harmony, Helm, Herbivorous, Honour, House → 2, 5, 1, 4, 3.

The series A, C, E, G advances by +2 positions each step (skipping one letter). After G, skipping H gives I. So the completed series is A, C, E, G, I.

Step 1 — First differences: \(4-2=2,\ 13-4=9,\ 41-13=28,\ 106-41=65\) Step 2 — Identify the pattern: these match \(n^{3}+1\) for \(n=1,2,3,4\) since \(1+1,\ 8+1,\ 27+1,\ 64+1\). Step 3 — Next difference (n=5): \(5^{3}+1=126\) Therefore the missing term is \(106+126=\mathbf{232}\).

Positions 1 (tallest) to 5 (shortest). Hitesh sits at position 3. Bharat is between Nitin and Hitesh, so in descending order the segment reads Nitin > Bharat > Hitesh, placing Bharat at 2 and Nitin at 1. The constraint that Nitin is not at the bottom is satisfied (he is at the top). Sunny and Vicky fill positions 4 and 5 in some order. Hence the tallest is Nitin.

Decode the chain P + Q * R - S: P is father of Q, Q is brother of R, R is mother of S. So R (mother of S) has a brother Q — meaning Q is the maternal brother of S's mother, i.e. S's uncle.

The letters available in ABANDONED are A, B, D, E, N, O (with A, D, N appearing twice). The letter L does not appear at all. Bland requires B, L, A, N, D — the L cannot be sourced. Bonded, Banded and Bane use only letters present in ABANDONED with sufficient frequency. Hence Bland cannot be formed.

The rule: reverse the word, then shift the letters by +N, +(N-1), …, +1 where N is the word length. Check: REMOTE reversed is ETOMER; shifts +6,+5,+4,+3,+2,+1 give K,Y,S,P,G,S = KYSPGS. BRAND reversed is DNARB; shifts +5,+4,+3,+2,+1 give I,R,D,T,C = IRDTC. Apply to MOBILE (N=6), reversed ELIBOM: \(E(+6)\to K,\ L(+5)\to Q,\ I(+4)\to M,\ B(+3)\to E,\ O(+2)\to Q,\ M(+1)\to N\) Therefore MOBILE is coded as KQMEQN.

Substitute each symbol with its new meaning: ÷→×, +→-, ×→+, -→÷. The expression \(12-6+28\times 3\div 9\) becomes: \[12\div 6 - 28 + 3\times 9\] Applying BODMAS: \(12\div 6=2\) and \(3\times 9=27\), giving \(2-28+27=1\). Therefore the value is 1.

Look at the relation between the outer numbers and the bracketed value: \((19-13)^{2}=6^{2}=36\) and \((37-28)^{2}=9^{2}=81\). The middle number equals the square of the difference of the outer numbers. Applying this to 43 (A) 38: \(A=(43-38)^{2}=5^{2}=\mathbf{25}\)

The pattern followed here is, First table: 3 × 2 × 7 × 4 → 168 Second table: 8 × 1 × 3 × 7 → 168 Similarly, Third table: 1 × 2 × 6 × ? → 168 12 × ? → 168 → 14 Hence, the missing number in the table is 14.

Triangles in the given figure: Hence, there are 28 triangles in the given figure.

Both premises are universal affirmatives that place Insects and Machines as subsets of Dangerous. From All A are B the converse All B are A does not follow, so Conclusions I and II (claiming all dangerous are insects / machines) fail. The statements give no link between Insects and Machines themselves, so Conclusion III ("Some machines are insects") is also not necessitated — the two subsets could be disjoint within Dangerous. Hence no conclusion follows.

1) Dice (option) 1 is not possible as face with ‘1’ and the face with ‘5’ are opposite to each other. 2) Dice (option) 2 is not possible as face with ‘2’ and the face with ‘4’ are opposite to each other. 3) Dice (option) 3 is possible. 4) Dice (option) 4 is not possible as face with ‘6’ and face with ‘3’ are opposite to each other. Hence, dice (option) 3 can be formed.

Mistake Points If Only two entities ask in the question then Only those two parts counted. But, If the question is asking for two entity then, you have to take all the common part which is included in that two areas. People who like cricket and tennis are 17 + 15 → 32 Hence, 32 people like both cricket and tennis both.

Hence, option 3 will complete the given question figure.

Hence, the given question figure is hidden in option 3.

Hence, the unfolded paper will be similar to option 1.

Hence, the mirror image of the given question figure will be similar to option 2.

Read each code as (row, column) in the appropriate matrix and verify the letter for the word P-O-N-D. Option 1 — 00, 04, 67, 57: Matrix-I (0,0) = P; Matrix-I (0,4) = O; Matrix-II (6,7) = N; Matrix-II (5,7) = D. All four letters match in order. The other options misalign at least one letter (e.g. 23 gives O not P, 24 gives P not O, 87 gives T not D), so the correct code set is 00, 04, 67, 57.

A Self Help Group is a small, voluntary association whose members pool regular savings into a common fund and lend internally to one another. The group is member-owned and member-managed: contribution amounts, who receives a loan, the interest rate, and repayment terms are all decided collectively in group meetings. Banks (private or RBI) and NGOs may facilitate linkage, training or external credit, but they do not control internal savings and lending decisions. Hence the correct answer is Members of group.

The Maharatna list at the time of this paper (SSC CGL 2017) included Coal India Limited, Steel Authority of India Limited (SAIL) and Bharat Heavy Electricals Limited (BHEL), along with ONGC, IOCL, NTPC and GAIL. Bharat Dynamics Limited (BDL), a defence PSU, was a Miniratna Category-I company and was not part of the Maharatna list. Hence BDL is the odd one out.

The Indian President is elected indirectly by an electoral college of elected MPs and elected MLAs through proportional representation by means of a single transferable vote with secret ballot. This indirect-election method was modelled on the Irish Constitution. Britain contributed the parliamentary system, the USA gave fundamental rights and judicial review, and Australia inspired the Concurrent List — none of these covers the presidential election method. Hence the correct source is Ireland.

"Quo-Warranto" is a Latin phrase that literally means "by what authority (or) warrant". The writ is issued by the Supreme Court (Article 32) and High Courts (Article 226) to question the legal authority by which a person holds a public office; if the holder cannot justify the claim, the court restrains them from continuing. "We command" refers to Mandamus, and "To forbid" refers to Prohibition, so options 1 and 2 are incorrect.

Muhammad Ali Jinnah was conferred the title "Ambassador of Hindu-Muslim Unity" by Sarojini Naidu for his role as the chief architect of the Lucknow Pact (December 1916), the joint session of the Indian National Congress and the All-India Muslim League that produced unified demands for self-government. Sir Sayyad Ahmad Khan predates the pact; Fazl-ul-Haq and Sharfuddin Quadri were not its architects.

Banabhatta, a 7th-century Sanskrit scholar, was the court poet (Asthana Kavi) of King Harshavardhana (606-647 CE). He authored Harshacharita, a biography of the king, and the prose romance Kadambari. Tulsidas, Surdas and Raskhan were 16th-17th century Bhakti poets, centuries after Harsha's reign, so they cannot be his court poets.

Marble is formed when limestone (a sedimentary rock) is subjected to intense heat and pressure within the Earth's crust, causing its calcite crystals to recrystallise into a denser, harder rock. Because it originates through this transformation of a pre-existing rock, marble is classified as a metamorphic rock. Igneous rocks form from cooled magma and sedimentary rocks from deposited sediments, so neither category fits marble.

Carbon dioxide is a major greenhouse gas whose molecular vibrations absorb infrared radiation strongly across several wavelength bands. It traps a significant fraction of the longwave radiation re-emitted by the Earth and also absorbs portions of the near-infrared in incoming solar radiation, making it the dominant heat absorber among the options. Nitrogen and oxygen (the bulk of the atmosphere) are nearly transparent to infrared, and carbon monoxide is present only in trace amounts.

Body segmentation (metamerism) - the division of the body into a linear series of repeating units - is the defining feature of Phylum Annelida, which includes earthworms, leeches and marine worms. The segments are visible externally as rings and contain repeated internal organs. Porifera (sponges) lack tissues, Coelenterata show radial symmetry with a sac-like body, and Mollusca have a soft unsegmented body of head, foot and visceral mass.

A synapse is the junction between two communicating nerve cells. The synaptic cleft (the "synapse gap") is the narrow space between the presynaptic terminal of one neuron and the postsynaptic membrane of the next, across which neurotransmitters diffuse to transmit the impulse. Hence the synapse gap is located between two neurons; the brain-spinal cord interface and the kidneys are not sites of synaptic clefts.

The inner lining of the small intestine is covered with millions of finger-like projections called villi, each containing blood capillaries and a lacteal. They dramatically enlarge the absorptive surface area so that digested nutrients - sugars, amino acids, fatty acids - can pass efficiently into the blood and lymph. The stomach has rugae (folds, not villi), the large intestine mainly absorbs water, and the bladder is part of the excretory system.

A vector quantity needs both magnitude and direction and must obey the laws of vector addition (e.g. parallelogram law). Acceleration, force and velocity all satisfy this. Electric current has a magnitude and an associated direction of flow, but currents combine by simple algebraic (scalar) addition at a junction (Kirchhoff's current law: \(\sum I_{in}=\sum I_{out}\)), not by the parallelogram rule. Hence current is treated as a scalar, making it the non-vector quantity here.

Raising the outer edge of a curved road above the inner edge is called banking of roads. The tilt makes the normal force on the vehicle inclined, so its horizontal component supplies (part of) the centripetal force needed for circular motion, reducing reliance on friction. The ideal banking angle satisfies \(\tan\theta=\dfrac{v^{2}}{rg}\). "Cornering", "elevation" and "tempering" do not describe this road-design technique.

C++ is a general-purpose, compiled, multi-paradigm programming language developed by Bjarne Stroustrup as an extension of C, adding object-oriented features. It is used to write programs but is not itself an operating system. "Software" is too broad - it covers any program or data, whereas "programming language" is the precise classification. Hence option 2 is the most accurate description.

Correct Answer: Option 2 – Elements with different atomic number but same mass number What are isobars? Isobars are atoms of different elements that have the same mass number but different atomic numbers. Key idea: Same mass number (A): Total number of protons + neutrons is the same Different atomic number (Z): Number of protons is different, so they are different elements Example: Argon: ₁₈⁴⁰Ar → 18 protons, mass number 40 Calcium: ₂₀⁴⁰Ca → 20 protons, mass number 40 Both have the same mass number but are different elements. Quick comparison: Isotopes: same element, different mass number Isobars: different elements, same mass number

Checking each pair: Haematite (\(Fe_{2}O_{3}\)) - Iron is correct; it is the chief iron ore. Monazite - Thorium is also correct; monazite is a key thorium-bearing phosphate mineral. Pitchblende (Uraninite, \(UO_{2}\)) is the principal ore of uranium, not copper (copper comes from chalcopyrite, chalcocite, bornite). Therefore only pair II is incorrect.

The Kyoto Protocol was adopted at Kyoto, Japan, on 11 December 1997, but it entered into force only on 16 February 2005, ninety days after Russia's ratification on 18 November 2004 met the threshold of 55 Annex-I Parties accounting for at least 55% of 1990 emissions. Hence the correct year is 2005.

The 7th Central Pay Commission retained the existing annual increment rate of 3% across all levels of the new Pay Matrix for central government employees. The figure 2.57 mentioned in the report is the uniform fitment factor used to convert pre-revised basic pay to the new structure, not the increment rate.

Charles Louis Alphonse Laveran, a French army physician, identified the malaria-causing parasite (later named Plasmodium) in the blood of patients at Constantine, Algeria, in 1880. He was awarded the Nobel Prize in Physiology or Medicine in 1907 for this discovery. Ivanovsky and Beijerinck are linked to the discovery of viruses, and Christiaan Barnard performed the first human heart transplant—none discovered the malaria germ.

Results of the 2017 F1 season: the Australian GP was won by Sebastian Vettel (Ferrari), the Russian GP by Valtteri Bottas (his maiden F1 win for Mercedes), and the Chinese GP by Lewis Hamilton (Mercedes). This gives the pairing 1–a, 2–c, 3–b.

Amjad Ali Khan is a renowned exponent of the Sarod, a plucked string instrument—not the Tabla. Hence the pair "Amjad Ali Khan – Tabla" is incorrect. The other pairings are accurate: Ustad Bismillah Khan was a master of the Shehnai, Hema Malini is a trained Bharatnatyam dancer, and Shambhu Maharaj was a celebrated Kathak guru of the Lucknow Gharana.

The 2016 Nobel Prize in Literature was awarded to American singer-songwriter Bob Dylan "for having created new poetic expressions within the great American song tradition." The other names won 2016 Nobels in different categories: Oliver Hart (Economics), Yoshinori Ohsumi (Physiology/Medicine), and J. Michael Kosterlitz (Physics).

'The Gita for Children' is written by Bengaluru-based author Roopa Pai, who retells the Bhagavad Gita's 18 chapters in an accessible narrative for young readers. She is also known for similar works such as 'The Vedas and Upanishads for Children' and 'So You Want to Know About Economics'.

Full diplomatic relations between India and Israel were established on 29 January 1992; 2017 therefore marked the silver-jubilee (25th) year of ties. PM Narendra Modi's July 2017 visit—the first by an Indian PM to Israel—commemorated the occasion. India's diplomatic ties with France, Russia (USSR) and China were all established much earlier (late 1940s–1950).

The Duge Bridge (Beipanjiang Bridge Duge), a cable-stayed road bridge connecting Yunnan and Guizhou provinces, was opened to traffic on 29 December 2016 in China. With its deck about 565 m above the Beipan River, it is the world's highest road bridge.

Pattern observation: in each fraction the denominator is roughly 8–9 times the numerator, so the largest numerator-to-denominator ratio wins. Quick decimal check: \[\tfrac{5}{113}\approx0.0442,\ \tfrac{7}{120}\approx0.0583,\ \tfrac{13}{145}\approx0.0897,\ \tfrac{17}{160}\approx0.1063\] The largest value is \(\dfrac{17}{160}\).

Step 1 — Nirmit's total time: If Nirmit does \(\tfrac{2}{3}\) of the job in 18 days, the full job takes \[18\times\tfrac{3}{2}=27\text{ days.}\] Step 2 — Apply efficiency ratio: Kashish is twice as efficient, so he needs half the time: \[\tfrac{27}{2}\text{ days.}\] Therefore Kashish finishes the job in \(\dfrac{27}{2}\) days.

Step 1 — Total volume displaced: \[V=40\times5=200\text{ m}^3.\] Step 2 — Pool base area: \[A=30\times25=750\text{ m}^2.\] Step 3 — Rise in level: \[h=\dfrac{V}{A}=\dfrac{200}{750}=\dfrac{4}{15}\text{ m}=\dfrac{400}{15}\text{ cm}\approx26.66\text{ cm.}\] Therefore the water level rises by about 26.66 cm.

Step 1 — Purchase price after successive discounts: \[2375\times 0.50\times 0.75 = 890.625\] Step 2 — Add repair cost to get CP: \[CP = 890.625 + 165 = 1055.625\] Step 3 — Apply 62.5% profit: \[SP = 1055.625\times 1.625 = 1715.390625\] Therefore the selling price is approximately Rs. 1715.39.

Step 1 — Use the ratio: let L = 19x, B = 11x, H = 13x. Step 2 — Apply L = H + 30: \[19x = 13x + 30 \implies 6x = 30 \implies x = 5\] Step 3 — Find dimensions: L = 95, B = 55, H = 65 cm. Step 4 — Volume: \[V = 95\times 55\times 65 = 339625\ \text{cm}^3\] Therefore the volume is 339625 cm³.

Step 1 — Total age of 12 players: \[12\times 23 = 276\] Step 2 — Total age with coach (new average 25, 13 people): \[13\times 25 = 325\] Step 3 — Coach's age: \[325 - 276 = 49\] Therefore the coach is 49 years old.

Successive gains multiply: \(SP = CP\times 1.30\times 1.20 = 1.56\,CP\). \[CP = \frac{31200}{1.56} = 20000\] Therefore the cost price is Rs. 20000.

Compound growth: \(A = P(1+r/100)^t\). \[A = 17640\times (1.05)^2 = 17640\times 1.1025 = 19448.1\] Therefore the approximate count after 2 years is 19450.

When two bodies start simultaneously towards each other, meet, and then take times \(t_A\) and \(t_K\) to reach the other's start, the speed ratio satisfies: \[\frac{s_A}{s_K} = \sqrt{\frac{t_K}{t_A}} = \sqrt{\frac{225}{196}} = \frac{15}{14}\] \[s_K = 30\times \frac{14}{15} = 28\ \text{km/hr}\] Therefore Kapil's speed is 28 km/hr.

Step 1 — Interest per year on principal P: Total SI for 10 years is 3130, so annual SI = \(\frac{PR}{100}=313\). Step 2 — First 5 years (principal P): \[SI_1 = 5\times 313 = 1565\] Step 3 — Next 5 years (principal 5P): \[SI_2 = 5\times 5\times 313 = 7825\] Step 4 — Total: \[1565 + 7825 = 9390\] Therefore the total interest is Rs. 9390.

Split each fraction: \(\frac{11-13x}{x} = \frac{11}{x} - 13\), and similarly for y and z. The given equation becomes: \[11\left(\tfrac{1}{x}+\tfrac{1}{y}+\tfrac{1}{z}\right) - 39 = 5\] \[11\left(\tfrac{1}{x}+\tfrac{1}{y}+\tfrac{1}{z}\right) = 44 \implies \tfrac{1}{x}+\tfrac{1}{y}+\tfrac{1}{z} = 4\] Therefore the required sum is 4.

Step 1 — Convert to quadratic: Multiply \(2x + \tfrac{9}{x} = 9\) by x: \[2x^2 - 9x + 9 = 0 \implies (x-3)(2x-3) = 0\] So \(x = 3\) or \(x = \tfrac{3}{2}\). Step 2 — Evaluate \(x^2 + \tfrac{1}{x^2}\) for each root: \[x=3:\ 9 + \tfrac{1}{9} = \tfrac{82}{9} = \tfrac{328}{36}\] \[x=\tfrac{3}{2}:\ \tfrac{9}{4} + \tfrac{4}{9} = \tfrac{81+16}{36} = \tfrac{97}{36}\] Since \(\tfrac{97}{36} < \tfrac{328}{36}\), the minimum value is \(\tfrac{97}{36}\).

Step 1 — Find relation: Cross-multiplying \(\frac{5x-y}{5x+y}=\frac{3}{7}\): \[7(5x-y) = 3(5x+y) \implies 20x = 10y \implies y = 2x\] Step 2 — Recognise perfect squares: \[4x^2 + y^2 - 4xy = (y-2x)^2,\quad 9x^2 + 16y^2 + 24xy = (3x+4y)^2\] Step 3 — Substitute y = 2x: Numerator \((2x-2x)^2 = 0\); denominator \((3x+8x)^2 = 121x^2 \neq 0\). Therefore the value is 0.

Step 1 — Expand the first equation: \[(x+y)^2 = xy+1 \implies x^2 + 2xy + y^2 = xy + 1 \implies x^2 + xy + y^2 = 1\] Step 2 — Factor the second equation: \[x^3 - y^3 = (x-y)(x^2 + xy + y^2) = 1\] Step 3 — Substitute: Since \(x^2+xy+y^2 = 1\), we get \((x-y)(1) = 1\). Therefore \(x - y = 1\).

We know that ∠QSR = ∠OSR = 90/2 = 45 Triangle STR is equilateral ⇒ ∠TRS = 60 and in triangle SOR ⇒ ∠SOR + ∠ORS + ∠RSO = 180 ⇒ ∠SOR + 60 + 45 = 180 ⇒ ∠SOR = 180 – 60 – 45 ∴ ∠SOR is 75

By the parallelogram law, the sum of squares of the four sides equals the sum of squares of the diagonals: \[2(AB^2 + BC^2) = AC^2 + BD^2\] \[2(49 + 81) = 64 + BD^2 \implies 260 = 64 + BD^2\] \[BD^2 = 196 \implies BD = 14\ \text{cm}\] Therefore the other diagonal is 14 cm.

The number of diagonals in an \(n\)-sided polygon is given by: \[D=\frac{n(n-3)}{2}\] For an octagon, \(n=8\): \[D=\frac{8(8-3)}{2}=\frac{8\times 5}{2}=20\] Therefore an octagon has 20 diagonals.

Place the quarter circle with centre \(O\) at the origin and its two radii along the positive x and y axes. The square sits with one vertex at \(O\), the two adjacent vertices \((s,0)\) and \((0,s)\) lying on the radii equidistant from \(O\), and the opposite vertex \((s,s)\) on the arc. Apply circle equation at (s, s): \[R^{2}=s^{2}+s^{2}=2s^{2}\] Substitute \(s=\sqrt{5/2}\): \[R^{2}=2\times\frac{5}{2}=5\;\Rightarrow\;R=\sqrt{5}\text{ cm}\] Therefore the radius is \(\sqrt{5}\) cm.

Given \(\sec^{2}\theta+\tan^{2}\theta=\dfrac{5}{3}\). Using the identity \(\sec^{2}\theta-\tan^{2}\theta=1\): Add the two equations: \[2\sec^{2}\theta=\frac{5}{3}+1=\frac{8}{3}\;\Rightarrow\;\sec^{2}\theta=\frac{4}{3}\] Hence \(\tan^{2}\theta=\sec^{2}\theta-1=\dfrac{1}{3}\), so \(\tan\theta=\dfrac{1}{\sqrt{3}}\). Double-angle formula: \[\tan 2\theta=\frac{2\tan\theta}{1-\tan^{2}\theta}=\frac{2/\sqrt{3}}{1-1/3}=\frac{2/\sqrt{3}}{2/3}=\frac{3}{\sqrt{3}}=\sqrt{3}\] Therefore \(\tan 2\theta=\boldsymbol{\sqrt{3}}\).

Let the tower stand at \(O\) and break at \(P\). The upper part falls so its tip touches the ground at \(Q\); point \(R\) is on the opposite side with \(QR=180\) m. Let \(OP=h_{1}\) (standing part) and \(PQ=h_{2}\) (fallen part). Step 1 — From \(\triangle OPQ\) with \(\angle OQP=60^{\circ}\): \[h_{1}=h_{2}\sin 60^{\circ}=\tfrac{\sqrt{3}}{2}h_{2},\quad OQ=h_{2}\cos 60^{\circ}=\tfrac{h_{2}}{2}\] Step 2 — From \(\triangle POR\) with \(\angle PRO=30^{\circ}\): \[h_{1}=OR\tan 30^{\circ}=\frac{OR}{\sqrt{3}},\quad OR=180-OQ=180-\tfrac{h_{2}}{2}\] Step 3 — Equate the two expressions for \(h_{1}\): \[\tfrac{\sqrt{3}}{2}h_{2}=\frac{180-h_{2}/2}{\sqrt{3}}\;\Rightarrow\;3h_{2}=360-h_{2}\;\Rightarrow\;h_{2}=90\] So \(h_{1}=45\sqrt{3}\). Total height \(=h_{1}+h_{2}=45\sqrt{3}+90=\boldsymbol{45(\sqrt{3}+2)}\) m.

Given sinθ + sin5θ = sin3θ ⇒ -sin θ = sin5θ - sin3θ Using identity in RHS sin(x) – sin(y) = 2 × cos{(x + y)/2} × sin{(x – y)/2} ⇒ – sin θ = 2 × cos(4θ) × sin(θ) ⇒ cos(4θ) = -1/2 = cos(120) ⇒ 4θ = 120 ∴ θ is 30

For Y7: Revenue = 1600, Cost = 1240, Tax rate = 33%. Profit in Y7: \[\text{Profit}=1600-1240=360\] Tax in Y7: \[\text{Tax}=33\%\times 360=0.33\times 360=118.8\] Therefore the tax paid in Y7 is Rs 118.8 ('000 crores).

Compute Profit After Tax (PAT) = Profit − Tax for each year using Profit = Revenue − Cost and Tax = rate × Profit. Y2: Profit \(=1100-850=250\); Tax \(=0.22\times 250=55\); PAT \(=195\). Y6: Profit \(=1500-1200=300\); Tax \(=0.30\times 300=90\); PAT \(=210\). Y8: Profit \(=1850-1400=450\); Tax \(=0.13\times 450=58.5\); PAT \(=391.5\). Since \(391.5>210>195\), the correct ordering is Y8 > Y6 > Y2.

Profit = Revenue − Cost for each year: Y1: 200, Y2: 250, Y3: 300, Y4: 250, Y5: 300, Y6: 300, Y7: 360, Y8: 450. The unique values are {200, 250, 300, 360, 450} — 5 distinct profits.

Compute PAT = (Revenue − Cost) × (1 − tax rate) for each year: Y1: \(200\times 0.80=160\). Y2: \(250\times 0.78=195\). Y3: \(300\times 0.78=234\). Y4: \(250\times 0.75=187.5\). Y5: \(300\times 0.70=210\). Y6: \(300\times 0.70=210\). Y7: \(360\times 0.67=241.2\). Y8: \(450\times 0.87=391.5\). Total: \[160+195+234+187.5+210+210+241.2+391.5=1829.2\] Therefore the sum is 1829.2 ('000 crores).

The error is in segment (1): "deals with". To denote trading in a commodity (here, spare parts as a business), the correct phrasal verb is "deal in". "Deal with" means to handle or cope with a person or situation, not to trade goods. The corrected sentence reads: "My elder son deals in spare parts and manages his bread and butter."

The error lies in segment (1): "for her husband's murder". The verb accuse takes the preposition of when naming the offence — "accused of [crime]" — not "for". (Compare: charged with, blamed for, guilty of.) The correct sentence is: "Sneha was accused of her husband's murder but the court found her not guilty and acquitted her."

The required phrasal verb means "to happen / take place (in a certain manner)" — that meaning belongs to pass off, as in "the event passed off smoothly". The other options don't fit: pass away = die, pass by = go past / time elapses, pass out = faint or distribute. Hence the blank is filled by off: "My sister's marriage passed off peacefully."

The clause "so you need to purchase them from the market" signals insufficiency — a negative idea. With plural countable nouns, few carries that negative sense ("hardly any"), while a few means "some, enough" (positive). A little is for uncountables, and the few needs a previously specified set. Hence the blank takes few: "There are few books on computer science in your school library..."

Atrocity means an extremely wicked or cruel act, especially one involving physical violence. Barbarity denotes savage cruelty or brutality, making it the closest synonym. The other options are unrelated: Difficulty refers to a challenge, Shy describes timidity, and Gloomy describes sadness or darkness. Hence, the correct answer is Barbarity.

Procrastinate means to postpone or put off an action, usually one that should be done promptly. Among the options, Delay conveys the same idea of making something late or postponing it. Divert means to change direction, Deceive means to mislead, and Debase means to lower in quality — none relate to postponing. Hence, Delay is the correct synonym.

Raucous means loud, harsh, and grating in sound. Its antonym must describe something soft, sweet, or soothing. Dulcet means sweet and melodious — a direct opposite. Hoarse (rough voice) and Jarring (harsh, discordant) are synonyms of raucous, not antonyms. Torrent (a strong stream) is unrelated to sound. Hence, the answer is Dulcet.

Predilection means a strong preference or liking for something. Its antonym must express dislike or hostility. Enmity means active hostility or ill will — the direct opposite of liking. Inclination is a synonym of predilection. Enduring (lasting) and Domicile (place of residence) are unrelated. Hence, the correct antonym is Enmity.

The idiom "a wild goose chase" refers to a futile pursuit — a search or effort that yields no result because the objective is unattainable or non-existent. This matches Useless search. Fruitful search is the opposite, Timely search refers to timing rather than outcome, and Wrong decision describes a choice, not the futile pursuit itself. Hence, the answer is Useless search.

The idiom "a moot point" refers to a matter that is debatable, contested, or open to argument — often one whose resolution is uncertain or no longer relevant. This matches Disputed. Agreeable is the opposite, while Unclear and Unknown describe lack of clarity or knowledge, not active debate. Hence, the correct meaning is Disputed.

Verbs like appoint, elect, name, declare, crown take the pattern: verb + object + role, with no preposition as and no article before the role naming a unique office. So "appointed her as a secretary" should become "appointed her secretary". Parallel examples: "They elected him president"; "They made her captain". Hence the correct improvement is secretary.

After "I wish" expressing a present unreal situation, the verb to be takes the subjunctive form were for all subjects (I, he, she, it). So "I wish I was a superman" should be "I wish I were a superman". Am wrongly suggests a real situation; have been is not used for present unreal wishes. Hence the correct improvement is were.

Emeritus describes a person who has retired honourably from service (often a professor, judge, or official) and retains the title as a mark of respect. Belligerent means hostile/aggressive, Truant means one who absents themselves without permission, and Mercenary means one who serves only for money — none denote an honourable discharge. Hence, the correct word is Emeritus.

A perception that occurs without any external stimulus — entirely produced by the mind — is called a Hallucination. An Illusion differs because it involves a misinterpretation of a real external stimulus (e.g., a mirage), so it does have objective reality behind it. Cynicism (distrustful attitude) and Optimism (hopefulness) are mindsets, not sensory experiences. Hence, the answer is Hallucination.

The word "Peity" is misspelt. The correct spelling is Piety (meaning deep religious devotion or reverence) — the i comes before the e. The other words — Anxiety, Believe, and Height — are all spelt correctly. Hence, the incorrectly spelt word is Peity.

The word "Admited" is misspelt. The base verb admit ends in a single consonant preceded by a short vowel, with stress on the final syllable (ad-MIT), so the final t must be doubled before -ed. The correct spelling is Admitted. The remaining words — Benefited, Married, and Offered — follow standard spelling rules correctly. Hence, the misspelt word is Admited.

R is the topic sentence: it states the central thesis that a blanket ban on defection weakens democracy. P follows with the first concession ("Granted," acknowledging defection is opportunism). S extends that concession ("Granted also," linking back to P with the same marker plus "also"). Q closes with the contrastive "Yet," highlighting the right to dissent that the current law respects. Hence the order is RPSQ.

R opens by introducing the core idea — our reaction mirrors something within us. P elaborates that recognising this inner cause is the path to forgiveness. S continues with the next step: once the issues are discovered, work on forgiving yourself. Q concludes with the outcome — "This" refers to the entire process, leading to a changed relationship and feeling better. Hence the order is RPSQ.

The active sentence has Dr. Bose as the object of both "driving" and "dropped." In passive voice, Dr. Bose becomes the subject. The participial phrase "After driving Dr. Bose" converts to "After being driven," and the main clause "he dropped him" becomes "Dr. Bose was dropped." Combining: "After being driven to the hospital Dr. Bose was dropped at his guest house." Options 2 and 3 stay in active voice; option 4 wrongly shifts to past continuous and splits the sequence.

"Let us" in direct speech expresses a suggestion that includes the speaker. The standard indirect form is: suggested (to) + object + that + we/they + should + verb. Here, "us" covers both the speaker and the friends, so the pronoun becomes "we." This gives "I suggested to my friends that we should go to a picnic for a change." Options using "asked... if/to" report a question or request, and "permitted" implies granting permission — none capture a suggestion.

The phrase "through which a person conveys his ideas" calls for a noun denoting a channel of communication. A medium is exactly that — a means through which ideas are transmitted. "Base" suggests a foundation, "source" indicates origin, and "subject" is a topic — none fit the "through which" construction. Hence literature is a medium through which ideas are conveyed.

The verb "protest" pairs with the preposition against to express opposition to something. "Protest for" implies advocacy (opposite sense), while "in" and "off" do not collocate with "protest" in this construction. Since the sentence describes opposing societal norms, the correct phrase is "protest against different norms of society."

Literature engages with questions of right and wrong, ethics, and values — i.e. moral issues. "Broad" is too vague, "insensitive" describes manner not subject matter, and "economical" narrows the scope to economics, which does not match a discussion of societal norms and dissent. A moral issue best fits the literary context of challenging societal norms.

Words in literature are composed by an author — they are written with a particular purpose. "Brought" and "founded" do not collocate with words; "represented" is awkward here because words do the representing rather than being represented. Authors deliberately write words to convey meaning, so "written with a particular purpose" is the natural fit.

The idiom "with a particular purpose in mind" means with a specific intention or goal. "In all" and "in total" denote sums, and "in hand" suggests something currently being dealt with — neither expresses intent. The completed phrase reads "written with a particular purpose in mind," capturing the deliberate authorial intent behind the words.