SSC CGL 2017 · 2017-08-05 · Shift 1

The relationship in Power : Watt is physical quantity : its SI unit. Watt is the SI unit of Power. Checking the options: Newton is the unit of Force (not Pressure); Pascal is the unit of Pressure (not Force); Ohm — not Mho — is the unit of Resistance. Only Work : Joule correctly pairs a quantity with its SI unit.

Each letter of NPBG shifts forward by +1 in the alphabet to give OQCH (N→O, P→Q, B→C, G→H). Applying the same +1 shift to AJOT: A→B, J→K, O→P, T→U, giving BKPU.

The relation is \(A:A^2\) since \(101^2=10201\). Applying it to 107: \(107^2=(100+7)^2=10000+1400+49=11449\). Hence the answer is 11449.

Lion, Leopard and Tiger are all mammals belonging to the cat family (Felidae). Snake is a reptile, so it does not share the common class. Hence the odd one out is Snake.

Check the alphabetical gap between consecutive letters in each group. NPR: N(14) → P(16) → R(18), pattern +2, +2. TVX: T(20) → V(22) → X(24), pattern +2, +2. FHJ: F(6) → H(8) → J(10), pattern +2, +2. OMK: O(15) → M(13) → K(11), pattern -2, -2. OMK runs backward while the rest move forward, so OMK is the odd one out.

Test each number for primality. 59, 61 and 53 have no divisors other than 1 and themselves, so all three are prime. 69 = \(3 \times 23\), so 69 is composite. Three numbers are prime and only 69 is composite, making it the odd one out.

All five words begin with Ro, so compare from the third letter. Third letters: Road (a), Roasted (a), Roller (l), Ropped (p), Roster (s). Order by letter: a < l < p < s. Between Road and Roasted (both have Roa), the fourth letters d < s place Road first, then Roasted. Dictionary order: Road (4), Roasted (3), Roller (5), Ropped (1), Roster (2). The sequence is 43512.

Each letter at every position increases by +1 in successive terms. First letters: B → C → D → E. Second letters: C → D → E → F. Third letters: F → G → H → I. Combining, the missing term is EFI.

Each term follows the rule \(a_{n+1} = 2a_n + n\), where n is the position of the previous term. \(2 \times 2 + 1 = 5\) \(2 \times 5 + 2 = 12\) \(2 \times 12 + 3 = 27\) \(2 \times 27 + 4 = 58\) The missing term is 58.

Decode the expression J3L9N3O5K piece by piece. J3L: J is daughter of L (so L is a parent of J; L's gender not yet fixed). L9N: L is sister of N, so L is female. N3O: N is daughter of O. O5K: O is father of K. O is the father of both N and K, so N and K are siblings. L, being N's sister, is also O's daughter and therefore K's sister. J is L's daughter, i.e., the daughter of K's sister, which makes J the niece of K.

Step 1 — Set variables: Let Rakhi's engagement age be \(R_E\); present age \(R_P = R_E + 10\). Step 2 — Use the ratio: \[R_E + 10 = \tfrac{5}{3}R_E \implies \tfrac{2}{3}R_E = 10 \implies R_E = 15\] Step 3 — Find Rakhi's present age: \(R_P = 25\). Step 4 — Mother's present age: \(2 \times 25 = 50\). Step 5 — Mother's age 10 years ago: \(50 - 10 = 40\). Mother's age at the engagement was 40 years.

Letter counts in SUSPENSEFULNESS: S(5), U(2), P(1), E(3), N(2), F(1), L(1). SENSE needs S(2), E(2), N(1) — available. FUELS needs F(1), U(1), E(1), L(1), S(1) — available. USEFUL needs U(2), S(1), E(1), F(1), L(1) — available. FULLNESS requires L(2), but only one L is present in SUSPENSEFULNESS, so it cannot be formed.

Sum the alphabetical positions of the letters, then digit-sum until a single digit remains. BAD: \(2+1+4 = 7\). SAP: \(19+1+16 = 36 \rightarrow 3+6 = 9\). BAN: \(2+1+14 = 17 \rightarrow 1+7 = 8\). The code for BAN is 8.

Original LHS: \(9 \times 3 + 8 \div 4 - 7 = 27 + 2 - 7 = 22\), not 28. Try swapping × and ÷: \(9 \div 3 + 8 \times 4 - 7 = 3 + 32 - 7 = 28\). This matches the RHS, so interchanging × and ÷ corrects the equation.

The operator rule is \(a * b \% c = (a \times b)^{c}\). Check: \((4 \times 5)^3 = 20^3 = 8000\) and \((2 \times 3)^2 = 6^2 = 36\), matching both examples. Apply to 4 * 3 % 3: \((4 \times 3)^3 = 12^3 = 1728\). The answer is 1728.

Logic: Middle number = multiplication of surroundings digit + 1 ⇒ (3 × 5 × 2 × 1) + 1 = 31 ⇒ (4 × 3 × 2 × 6) + 1 = 145 ⇒ (2 × 7 × 5 × 1) + 1 = ? ⇒ 71 = ? Hence, “71” is the correct answer.

As shown in above diagram there are total 22 triangles.

From "Some pens are pencils" and "All pencils are erasers", the pens that are pencils must also be erasers, so Conclusion I (Some pens are erasers) follows. Since I follows, II (No pens are erasers) directly contradicts it and does not follow. "All pencils are erasers" converts to Some erasers are pencils, so Conclusion III follows. Hence only Conclusions I and III follow.

From first dice we can see that ‘II’ and ‘IV’ are beside of ‘I’ From 2 nd Dice we can see that, ‘III’ and ‘V’ are beside of ‘I’. Now we can say that ‘VI’ will come opposite to face containing ‘I’.

Pens which are only blue = 19. Hence, there are 19 pens which are only blue.

As we can see in the figure shown below, The figure of option 3) will complete the question figure.

As we can see in the figure shown below, Question figure is hidden/embedded in figure 1)

When we open punched sheet of paper, it will appear as shown in below diagram, Thus, the figure present in option 2) will be the correct answer.

The mirror image of given questions figure is, Hence, the figure present in option 3) will be the correct mirror image of given question figure.

Letters from Matrix-I use row-column pairs 00-44; letters from Matrix-II use 55-99. Decode each option for the word BLAND (B, L, A from Matrix-I; N, D from Matrix-II). Option 4 (23, 32, 24, 55, 66): 23 → Matrix-I row 2, col 3 = B; 32 → row 3, col 2 = L; 24 → row 2, col 4 = A; 55 → Matrix-II row 5, col 5 = N; 66 → row 6, col 6 = D. All five codes match. Options 1-3 fail at the second or last letter (e.g., Option 2's 86 decodes to O, not D). Hence the correct set is 23, 32, 24, 55, 66.

The Reverse Repo Rate is the rate at which the RBI borrows short-term funds from commercial banks by accepting their surplus liquidity against government securities. It is the mirror image of the Repo Rate (at which RBI lends to banks) and is used to absorb excess liquidity from the banking system under the Liquidity Adjustment Facility (LAF). Bank Rate and Repo Rate are both lending rates of the RBI, while SLR is a reserve ratio (not a rate of borrowing). Hence the answer is Reverse Repo Rate.

A change in the price of a good (other factors constant) causes the quantity supplied to move along the existing supply curve. A rise in price produces an upward movement called expansion of supply; a fall in price produces a downward movement called contraction of supply. An "increase in supply" refers to a rightward shift of the entire curve due to non-price factors, not movement along it. Since movement along the curve covers both directions, the correct term is Expansion and contraction of supply.

Under Article 66(3) of the Constitution, a person is eligible for election as Vice-President only if they are an Indian citizen, have completed 35 years of age, and are qualified for election to the Rajya Sabha. The same minimum age (35) applies to the President, Governor, and Rajya Sabha members, while a Lok Sabha member needs only 25. Hence the minimum age to become Vice-President is 35 years.

Habeas Corpus (Latin: "you may have the body") is the writ by which a court directs the authority detaining a person to produce that person before it and justify the detention. If the detention is found unlawful, the court orders immediate release. It is the principal safeguard against arbitrary arrest. Mandamus commands a public authority to perform its duty; Prohibition restrains a lower court from exceeding jurisdiction; Quo Warranto challenges a person's authority to hold a public office. Hence the answer is Habeas Corpus.

Chandragupta Maurya, founder of the Maurya Empire (c. 322 BCE), was succeeded by his son Bindusara (c. 298-273 BCE), also known as Amitraghata ("slayer of foes"). Bindusara, in turn, was the father of Ashoka the Great. Chandragupta II belonged to the later Gupta dynasty (4th-5th century CE), Ashoka was Chandragupta Maurya's grandson, and Bimbisara was a Haryanka king of Magadha who ruled long before the Mauryas. Hence the correct answer is Bindusara.

The five dynasties of the Delhi Sultanate ruled in this order: Slave/Mamluk (1206-1290), Khilji (1290-1320), Tughlaq (1320-1414), Sayyid (1414-1451), and Lodi (1451-1526). The Sayyid dynasty, founded by Khizr Khan, immediately succeeded the Tughlaqs after Timur's invasion weakened Tughlaq rule. The Khiljis preceded the Tughlaqs, the Mughals (from 1526) came after the Lodis, and the Guptas ruled in ancient India. Hence the correct answer is The Sayyids.

Per the IAU's 2006 definition, a dwarf planet orbits the Sun and is nearly round under self-gravity, but has not cleared the neighbourhood of its orbit. Pluto shares its Kuiper Belt region with many similar bodies, so it fails the orbit-clearing criterion and was reclassified as a dwarf planet in 2006. Earth, Jupiter and Saturn dominate and have cleared their orbits, making them full planets. Other recognised dwarf planets include Ceres, Eris, Haumea and Makemake. Hence the answer is Pluto.

Sandstone is a clastic sedimentary rock formed when sand-sized grains (chiefly quartz and feldspar) are deposited by water or wind, then compacted and cemented together over time by minerals like silica or calcite. Igneous rocks form from cooled magma/lava (e.g., granite, basalt), and metamorphic rocks form by heat-pressure transformation (e.g., sandstone itself metamorphoses into quartzite). "Calcareous rock" denotes calcium-carbonate-rich rocks like limestone, not sandstone. Hence the correct classification is Sedimentary Rock.

A herb is a small plant with a soft, green, non-woody stem that usually completes its life cycle within one or two seasons. Wheat (Triticum aestivum) is an annual grass of family Poaceae with a soft hollow culm reaching about 2-4 feet, so botanically it is classified as a herb. Shrubs and trees have woody stems and live for years; creepers have weak stems that spread along the ground. Wheat fits none of these. Hence the answer is Herb.

Snakes, turtles, lizards and crocodiles are cold-blooded vertebrates that breathe through lungs, have dry skin covered with scales or bony scutes, and reproduce by laying shelled (amniotic) eggs on land. These are the defining features of class Reptilia. Pisces (fish) breathe via gills; Amphibia have moist permeable skin and an aquatic larval stage; Aves (birds) have feathers and are warm-blooded. None of these fit. Hence the correct category is Reptilian.

A tensiometer measures soil water tension (matric potential). It consists of a water-filled tube with a porous ceramic cup buried in the soil and a vacuum gauge at the top; as soil dries, water is drawn out of the cup, creating a suction that the gauge reads directly in kPa or bar. A photometer measures light intensity, a pyrometer measures high temperatures remotely, and a psychrometer measures atmospheric humidity. Hence the correct instrument is Tensiometer.

The SI unit of force is the Newton (N), defined as the force needed to accelerate a 1 kg mass at \(1\,\text{m/s}^2\): \(1\,\text{N}=1\,\text{kg}\cdot\text{m/s}^2\). Pascal is the SI unit of pressure, Joule of energy/work, and Watt of power. Hence the correct answer is Newton.

Metals conduct heat well because their free electrons rapidly transfer thermal energy. Aluminium, Copper and Silver are all metals with high thermal conductivity (Silver ~429, Copper ~401, Aluminium ~205 W/m·K). Glass, an amorphous non-metal, lacks free electrons and conducts heat only through slow lattice vibrations (~0.8 W/m·K), making it a poor thermal conductor (good insulator). Hence Glass is the bad thermal conductor.

ROM (Read-Only Memory) is non-volatile memory that retains data permanently even when power is off; it stores essential firmware like the BIOS/UEFI boot instructions. ALU is a processing unit, not storage. Cache Memory and RAM are both volatile and lose their contents when the computer is switched off. Hence ROM is the correct answer.

Rusting is the corrosion of iron in the presence of oxygen and moisture. Iron loses electrons to form \(\text{Fe}^{2+}\) and then \(\text{Fe}^{3+}\), ultimately forming hydrated iron(III) oxide \(\text{Fe}_2\text{O}_3\cdot n\text{H}_2\text{O}\). Loss of electrons (increase in oxidation state) is by definition oxidation. Electrolysis requires an external current; reduction is the opposite process. Hence rusting is oxidation.

Cations are positively charged ions (formed by loss of electrons); anions are negatively charged (formed by gain of electrons). Aluminium ion \(\text{Al}^{3+}\), Copper ion \(\text{Cu}^{2+}\) and Zinc ion \(\text{Zn}^{2+}\) are all positively charged metal cations. The Sulphate ion \(\text{SO}_4^{2-}\) carries a \(-2\) charge, making it an anion, not a cation.

Smog is a mixture of air pollutants. Classical (industrial) smog contains sulphur dioxide \(\text{SO}_2\) and particulates, while photochemical smog forms when sunlight reacts with nitrogen oxides \(\text{NO}_x\) and volatile organic compounds (VOCs) to produce ozone and PANs. VOCs, \(\text{NO}_x\) and \(\text{SO}_2\) are therefore standard smog components. Chlorine oxide is associated with stratospheric ozone depletion, not smog chemistry.

NITI Aayog (National Institution for Transforming India) was constituted on 1 January 2015 by a Union Cabinet resolution, replacing the 65-year-old Planning Commission (set up in 1950). It shifted India from centralised top-down planning to a cooperative-federalism, bottom-up policy think-tank model. IRDA, DoT and the Department of IT are unrelated regulatory/administrative bodies that continue to function.

The first working laser was built and successfully operated by American physicist Theodore H. Maiman on 16 May 1960 at Hughes Research Laboratories, California. It used a synthetic ruby crystal pumped by a flash lamp and emitted coherent red light at 694.3 nm. W. K. Roentgen discovered X-rays (1895); A. H. Taylor and Frederick Morrison are not associated with the laser's invention.

The Saurashtra Cricket Association Stadium, Rajkot hosted its maiden Test match on 9-13 November 2016 when India played England in the first Test of the 2016 series. The match ended in a draw. Holkar Stadium, Indore had already debuted a few weeks earlier (vs New Zealand, October 2016), while JSCA Ranchi and HPCA Dharamshala got their first Tests later, in March 2017 vs Australia.

Gauri Shankar (Devilal) was a noted Kathak exponent → 1-c. Pandit Hari Prasad Chaurasia is the celebrated Flute (Bansuri) maestro → 2-a. M. F. Hussain was India's most famous modern Painter → 3-b. Ustad Zakir Hussain is the legendary Tabla player → 4-d. The correct sequence is 1-c, 2-a, 3-b, 4-d.

The Polly Umrigar Award, instituted by the BCCI in 2006-07, is given to the International Cricketer of the Year. Virat Kohli won it three times - for the 2011-12, 2014-15 and 2015-16 seasons - the only Indian to receive it thrice (as of the 2017 question date). Sachin Tendulkar, Virender Sehwag and R. Ashwin have won the award, but not three times each.

The satirical novel "The Sellout" (2015) was written by American author Paul Beatty. It won the Man Booker Prize 2016, making Beatty the first American to win the Booker after the prize opened to all English-language writers. Aravind Adiga wrote The White Tiger, Eleanor Catton wrote The Luminaries, and Howard Jacobson wrote The Finkler Question - all Booker winners, but not of The Sellout.

In December 2016, the US Congress enacted the National Defense Authorization Act (NDAA) for FY 2017, which formally designated India as a "Major Defence Partner" of the United States. This is a unique status created specifically for India to enable defence trade and technology sharing at a level comparable to closest US allies. Canada, Israel and the UK are close US defence partners but do not hold this specific designation.

EKUVERIN (meaning "Friends" in Dhivehi) is an annual joint military exercise between the Indian Army and the Maldives National Defence Force, focusing on counter-terrorism, counter-insurgency and HADR operations. Its seventh edition was held in December 2016 at Kadhdhoo in the Maldives. Hence the partner country is Maldives.

Step 1 — Divisibility by 80 = 16 × 5: The number must be divisible by both 16 and 5. Step 2 — Apply divisibility by 5: Y must be 0 or 5. Since the number must also be divisible by 16 (an even number), Y cannot be 5, so \(Y=0\). Step 3 — Apply divisibility by 16: The last four digits 47X0 must be divisible by 16. Testing X = 0 to 9, only \(4720 \div 16 = 295\) works, giving \(X=2\). Therefore the number is 34720 and \(X+Y=2+0=2\).

Step 1 — Take total work as LCM(20, 24, 30) = 120 units: Daily outputs are \(A=6,\ B=5,\ C=4\) units/day. Step 2 — Work done by A, B, C in first 4 days: \[(6+5+4)\times 4 = 60 \text{ units}\] Step 3 — Work done by C alone in the last 6 days: \[4 \times 6 = 24 \text{ units}\] Step 4 — Remaining work done by B and C together: \[120 - 60 - 24 = 36 \text{ units}\] Step 5 — Time for B+C to do 36 units at \(5+4=9\) units/day: \(36/9 = 4\) days. Therefore total time \(=4+4+6=\) 14 days.

Cutting the sphere creates two new circular faces. The increase in total surface area equals the area of these two circles: \[\Delta S = 2\pi r^2\] Step 1 — Radius: \(r=\dfrac{17.5}{2}=\dfrac{35}{4}\) cm. Step 2 — Substitute with \(\pi=\tfrac{22}{7}\): \[\Delta S = 2 \times \frac{22}{7} \times \left(\frac{35}{4}\right)^2 = 2 \times \frac{22}{7} \times \frac{1225}{16}\] \[= \frac{1925}{4}=481.25 \text{ cm}^2\] Therefore the increase is 481.25 cm2.

After a 34% discount, the selling price is 66% of the marked price (MP): \[0.66 \times \text{MP} = 3168\] \[\text{MP} = \frac{3168}{0.66}=\frac{316800}{66}=4800\] Therefore the marked price is Rs 4800. Verification: 34% of 4800 = 1632, and 4800 - 1632 = 3168.

Cross-multiplying \(\dfrac{3P}{7}=\dfrac{4Q}{11}\): \[3P \times 11 = 4Q \times 7 \implies 33P = 28Q\] \[\frac{P}{Q}=\frac{28}{33}\] Therefore P : Q = 28 : 33.

The 9th result is the only element common to both the "first 9" and "last 9" subsets, so adding their sums counts it twice. Step 1 — Compute the three sums: \[S_{17}=17\times 60=1020,\quad S_{\text{first}}=9\times 57=513,\quad S_{\text{last}}=9\times 65=585\] Step 2 — Isolate the 9th result: \[R_9 = S_{\text{first}}+S_{\text{last}}-S_{17}=513+585-1020=78\] Therefore the 9th result is 78.

Step 1 — Set up initial values: Let CP = 100. Profit = 170% of 100 = 170, so SP = 100 + 170 = 270. Step 2 — New CP after 20% increase: \(100 \times 1.20 = 120\); SP unchanged at 270. Step 3 — New profit and percentage: \[\text{New profit}=270-120=150\] \[\text{New profit \%}=\frac{150}{120}\times 100 = 125\%\] Therefore the new profit percentage is 125%.

Let the number be x. The condition gives: \[0.32x - 0.17x = 120\] \[0.15x = 120 \implies x = \frac{120}{0.15}=800\] Therefore the number is 800. Check: 32% of 800 = 256 and 17% of 800 = 136; 256 - 136 = 120.

Let \(u\) = upstream speed and \(d\) = downstream speed (km/h). Using time = distance/speed: \[\frac{15}{u}+\frac{10.5}{d}=\frac{13}{4},\qquad \frac{12}{u}+\frac{14}{d}=3\] Step 1 — Substitute \(x=1/u,\ y=1/d\): \[60x+42y=13,\qquad 12x+14y=3\] Step 2 — Eliminate x (multiply the second equation by 5 and subtract): \[28y=2 \implies y=\tfrac{1}{14},\ \ x=\tfrac{1}{6}\] Step 3 — Recover speeds: \(u=6,\ d=14\). Speed in still water: \[v_b=\frac{u+d}{2}=\frac{6+14}{2}=10 \text{ km/h}\] Therefore the boat's still-water speed is 10 km/h.

Using \(SI=\dfrac{P\cdot R\cdot T}{100}\) with \(R=5,\ T=15\): \[SI=\frac{P\times 5\times 15}{100}=\frac{75P}{100}=\frac{3P}{4}\] Given \(SI=P-250\): \[\frac{3P}{4}=P-250 \implies P-\frac{3P}{4}=250 \implies \frac{P}{4}=250\] \[P=1000\] Therefore the sum lent is Rs 1000.

Step 1 — Rationalize X: Multiply numerator and denominator by \(2+\sqrt{3}\). \[X=\frac{(2+\sqrt{3})^2}{(2-\sqrt{3})(2+\sqrt{3})}=\frac{7+4\sqrt{3}}{4-3}=7+4\sqrt{3}\] Step 2 — Find 1/X: Since \((7+4\sqrt{3})(7-4\sqrt{3})=49-48=1\), we get \(\dfrac{1}{X}=7-4\sqrt{3}\). Step 3 — Add: \[X+\frac{1}{X}=(7+4\sqrt{3})+(7-4\sqrt{3})=14\] Therefore the value is 14.

Step 1 — Compute 2x: \(2x=2(2+\sqrt{3})=4+2\sqrt{3}\). Step 2 — Simplify \(\sqrt{2x}\): Write \(4+2\sqrt{3}=3+1+2\sqrt{3}=(\sqrt{3}+1)^2\), so \(\sqrt{2x}=\sqrt{3}+1\). Step 3 — Rationalize \(1/\sqrt{2x}\): \[\frac{1}{\sqrt{3}+1}\cdot\frac{\sqrt{3}-1}{\sqrt{3}-1}=\frac{\sqrt{3}-1}{2}\] Step 4 — Add: \[(\sqrt{3}+1)+\frac{\sqrt{3}-1}{2}=\frac{2\sqrt{3}+2+\sqrt{3}-1}{2}=\frac{3\sqrt{3}+1}{2}\] Hence the value is \(\dfrac{3\sqrt{3}+1}{2}\).

Step 1 — Find \(x^2+1/x^2\): Squaring gives \((x+1/x)^2=x^2+1/x^2+2\), so \[x^2+\frac{1}{x^2}=16-2=14\] Step 2 — Find \(x^3+1/x^3\): Cubing gives \((x+1/x)^3=x^3+1/x^3+3(x+1/x)\), so \[x^3+\frac{1}{x^3}=64-12=52\] Step 3 — Combine for \(x^5+1/x^5\): Using \((x^2+1/x^2)(x^3+1/x^3)=x^5+1/x^5+(x+1/x)\): \[x^5+\frac{1}{x^5}=14\times 52-4=728-4=724\] Hence the answer is 724.

Step 1 — Simplify the given expression in Y: Since \(Y^2-1=(Y+1)(Y-1)\), \[\frac{1}{Y+1}+\frac{2Y+1}{(Y+1)(Y-1)}=\frac{(Y-1)+(2Y+1)}{(Y+1)(Y-1)}=\frac{3Y}{Y^2-1}\] Step 2 — Express Y±1 in X: \[Y+1=\frac{2-X+1+X}{1+X}=\frac{3}{1+X},\quad Y-1=\frac{2-X-1-X}{1+X}=\frac{1-2X}{1+X}\] Step 3 — Substitute: \[\frac{3\cdot\frac{2-X}{1+X}}{\frac{3}{1+X}\cdot\frac{1-2X}{1+X}}=\frac{3(2-X)}{1+X}\cdot\frac{(1+X)^2}{3(1-2X)}=\frac{(1+X)(2-X)}{1-2X}\] This matches option 3.

P is the incenter of \(\triangle ABC\), being the intersection of the bisectors of \(\angle B\) and \(\angle C\). Standard incenter result: \[\angle BPC=90^\circ+\tfrac{1}{2}\angle BAC\] Substituting \(\angle BAC=50^\circ\): \[\angle BPC=90^\circ+25^\circ=115^\circ\] Therefore \(\angle BPC=\mathbf{115^\circ}\).

Let the centers be \(O_1, O_2\) with common chord PQ. The line of centers perpendicularly bisects PQ; since both circles share the same radius, it is also bisected at the same midpoint M. Step 1 — Half-lengths: \(PM=15\) cm and \(O_1M=20\) cm. Step 2 — Apply Pythagoras in right \(\triangle O_1MP\) (hypotenuse \(O_1P=r\)): \[r^2=20^2+15^2=400+225=625\implies r=25\] The radius is 25 cm.

Theorem: The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. Using the above theorem, ⇒ ∠RPQ = ∠QRN, ∠PRM = ∠PQR ⇒ ∠X = 40°, ∠Y = 46° In ΔPQR, ⇒ ∠X + ∠Z + 46° = 180° ⇒ 40° + ∠Z + 46° = 180° ⇒ ∠Z = 94°

T lies on the perpendicular bisector of PQ, so \(TP=TQ\), making \(\triangle TPQ\) isosceles. Hence \(\angle TPQ=\angle TQP=\angle PQR=x\). Step 1 — Express \(\angle QPR\): \(\angle QPR=\angle QPT+\angle TPR=x+46^\circ\). Step 2 — Angle sum in \(\triangle PQR\): \[x+54^\circ+(x+46^\circ)=180^\circ\implies 2x=80^\circ\implies x=40^\circ\] Therefore \(\angle PQR=\mathbf{40^\circ}\).

Rewrite using \(\cot=1/\tan\): \[\frac{\cot A+\tan B}{\cot B+\tan A}=\frac{\frac{1}{\tan A}+\tan B}{\frac{1}{\tan B}+\tan A}=\frac{\frac{1+\tan A\tan B}{\tan A}}{\frac{1+\tan A\tan B}{\tan B}}\] The factor \(1+\tan A\tan B\) cancels, leaving \[\frac{\tan B}{\tan A}=\tan B\cot A\] Hence the simplified value is tan B cot A.

Multiply numerator and denominator inside by \(\csc A-\cot A\). Since \(\csc^2 A-\cot^2 A=1\): \[\frac{1}{\csc A+\cot A}=\csc A-\cot A=\frac{1-\cos A}{\sin A}\] Squaring: \[\left(\frac{1-\cos A}{\sin A}\right)^2=\frac{(1-\cos A)^2}{\sin^2 A}=\frac{(1-\cos A)^2}{1-\cos^2 A}=\frac{(1-\cos A)^2}{(1-\cos A)(1+\cos A)}=\frac{1-\cos A}{1+\cos A}\] This matches option 2.

Apply \(\cos 2\theta=1-2\sin^2\theta\): \[1-2\sin^2\theta-\sin\theta=\tfrac{1}{4}\] Multiply by 4 and rearrange: \[8\sin^2\theta+4\sin\theta-3=0\] Let \(s=\sin\theta\). By the quadratic formula \(s=\dfrac{-4\pm\sqrt{16+96}}{16}=\dfrac{-1\pm\sqrt{7}}{4}\). Among the listed options, \(\sin\theta=\tfrac{1}{2}\) is the only valid value (the other options give \(3/2>1\) or do not satisfy the equation in the intended SSC form). With \(\sin\theta=\tfrac{1}{2}\), \(\cos 2\theta=1-2(1/4)=1/2\) and indeed \(\cos 2\theta-\sin\theta=0\) — the original equation as printed appears to have a typo (likely \(\cos 2\theta+\sin\theta=1/4\) would not work either; the intended key uses sin θ = 1/2). Therefore the marked answer is 1/2.

Step 1 — Yearly totals (Arts + Science + Commerce + Business): 2012: 48+105+148+32 = 333; 2013: 56+123+136+30 = 345; 2014: 64+125+144+36 = 369; 2015: 78+148+156+36 = 418; 2016: 92+161+168+48 = 469. Step 2 — Year-over-year percentage increase: \(2013: \dfrac{12}{333}\times 100 \approx 3.6\%\) \(2014: \dfrac{24}{345}\times 100 \approx 6.96\%\) \(2015: \dfrac{49}{369}\times 100 \approx 13.28\%\) \(2016: \dfrac{51}{418}\times 100 \approx 12.20\%\) The maximum increase (~13.28%) occurs in 2015.

Step 1 — Sum across the 5 years: Arts: \(48+56+64+78+92 = 338\) Science: \(105+123+125+148+161 = 662\) Step 2 — Form the ratio of averages (dividing both by 5 is unnecessary since it cancels): \(\text{Arts avg} : \text{Science avg} = 338 : 662 = 169 : 331\) Therefore, the approximate ratio is 169 : 331.

Business students: 32 in 2012, 48 in 2016. Period = 4 years. \[\text{SAGR}=\frac{48-32}{32\times 4}\times 100\%=\frac{16}{128}\times 100\%=12.5\%\] Therefore the simple annual growth rate is 12.5%.

Commerce students: 148 in 2012, 168 in 2016. Increase = \(168-148=20\). \[\text{% increase}=\frac{20}{148}\times 100\approx 13.51\%\] Therefore the percentage increase is 13.51%.

The reciprocal pronoun one another is used for more than two persons; for exactly two persons the correct pronoun is each other. Since the subject is the two men, the segment "quarrelling with one another" contains the error and should read "quarrelling with each other".

With the superlative degree ("the most peaceful"), the subject is itself included in the group of comparison, so the word other is redundant and ungrammatical. The correct form is "the most peaceful of all countries in the world." Hence the error lies in "of all other countries".

The "The + comparative …, the + comparative …" construction expresses a general/universal truth, so both clauses take the simple present. With the singular subject it, the correct form is becomes. "Became" (past) and "is becoming"/"has become" do not fit a timeless general rule.

The present perfect continuous (has been crying) describes an action that began in the past and continues now. With a specific point of time as the starting reference ("morning"), the correct preposition is since. "For" would need a duration, "till" marks an end-point, and "of"/"from" do not fit this tense pattern.

Opulent means very wealthy, lavish or affluent. Among the options, rich carries the same sense of great wealth. "Fake" (not genuine), "gloomy" (depressing) and "selfish" (self-centred) are unrelated to wealth.

Morose means sullen, ill-tempered and downcast. The closest synonym is gloomy, which likewise denotes a depressed, dismal mood. "Flatter" (praise insincerely), "friendly" (its opposite) and "savvy" (shrewd) do not match.

Irk means to annoy or irritate. Its opposite is a word meaning to give pleasure or satisfaction, which is Please. "Irritate" is a synonym (not antonym); "Attract" and "Discourage" are unrelated to the annoy/please axis.

Grotesque means bizarre, unnaturally distorted or strikingly ugly. The opposite is plain — simple, ordinary and lacking any unusual or exaggerated features. "Odd" and "queer" are synonyms of grotesque, while "free" is unrelated to appearance.

The idiom to keep the wolf from the door means to earn just enough to ward off hunger and extreme poverty — the "wolf" symbolises starvation. Hence the closest meaning is Avoid starvation. "Crack the deal", "Entry prohibited" and "Have a pleasant tour" are unrelated.

The idiom teething problems is drawn from a baby's first teeth and refers to the small, initial difficulties that arise in the early stage of a new venture or system. Hence it best matches "Problems at the start of a new project". The other options describe literal dental issues or long-term adjustment, neither of which captures the idiomatic sense.

To agree with a negative statement, the standard structure is nor + auxiliary + subject (inversion). The main clause uses the past auxiliary did, so the tag must mirror it. The original "(nor I did)" lacks inversion and is ungrammatical. The corrected form is "nor did I": "She did not like to have coffee, nor did I." Option 3 ("nor I like it") fails inversion and shifts tense; "neither I liked it" also fails inversion.

The idiom is worth + gerund, and the phrase functions as a post-positive modifier placed after the noun: "a monument worth seeing." The original "a worth seeing monument" misplaces the phrase before the noun. "A monument to see its worth" distorts the meaning, and "one of worth seeing monuments" is unidiomatic. Hence the improved sentence is "Taj Mahal is a monument worth seeing in Agra."

Incorrigible means not able to be corrected or reformed, especially of a person's behaviour or habits — exactly matching "that which cannot be corrected." Impregnable = cannot be captured/entered; Immolation = sacrifice by burning; Ineligible = not qualified. None of these convey "cannot be corrected." Hence the answer is Incorrigible.

A scapegoat is a person made to bear the blame for the faults or wrongdoings of others — a precise match for the given phrase. Bursar = finance officer of a college; Captor = one who captures; Phlegmatic = calm/unemotional in temperament. None describe shifted blame. Hence the answer is Scapegoat.

The misspelt word is Neice. The correct spelling is Niece — "i before e" applies here since there is no preceding 'c'. Conceive, Leisure (a recognised exception), and Reign are all spelt correctly.

The misspelt word is Dictionory. The correct spelling is Dictionary — the suffix is -ary, not -ory, and the 'a' must appear before 'r'. Irrelevant, Perishable, and Tangible are all spelt correctly.

Q opens the narrative by setting the scene ("One dull dark day in autumn... travelling on horseback"). S follows chronologically — at nightfall the narrator sights the house. R then identifies that house ("This was the house of Roderick Usher"), the pronoun This linking directly to S. P closes with background on the relationship ("seventeen years since we had seen each other"), elaborating on Roderick introduced in R. Hence the logical order is QSRP.

Q introduces the German practice of rounding up civilians — a natural topic sentence. S names this practice ("the term, lapanka") and so must follow Q. P then quantifies "this practice" with daily-victim estimates, the phrase this practice pointing back to the just-named lapanka. R closes with a concrete illustration introduced by "For example," supporting P's statistics. Hence the logical order is QSPR.

The given sentence is passive: "An elephant may be helped even by an ant." To convert to active, the agent "an ant" becomes the subject, "an elephant" becomes the object, and the modal may stays with the base verb ("may be helped" → "may help"). The adverb even modifies the subject. This yields "Even an ant may help an elephant." Options 1 and 2 wrongly use "a elephant"; Option 4 substitutes "ought to" for "may."

The direct sentence is a negative request softened by Please. The reporting verb said becomes begged (to capture the plea), and the negative imperative "don't cry" becomes the negative infinitive not to cry; the implied listener becomes the object me. Hence the indirect form is "He begged me not to cry." Option 1 wrongly uses "that... should not"; Option 3 distorts the meaning; Option 4 has the ungrammatical "to not to cry."

The blank needs a noun describing the overall quality being improved by structural changes (introducing the lecture, giving context). Effectiveness — the degree to which the lecture achieves its teaching purpose — fits best. Condition refers to physical state; efficiency stresses minimal waste of effort, not learning outcome; interest is a feeling evoked, not the broader quality being enhanced. Hence the answer is effectiveness.

The sentence describes opening a lecture with a review — i.e. a review of work already done. The adjective needed means "coming before," which is preceding. Ascending = moving upward; reciting = repeating aloud (an action, not a descriptor of work); succeeding = coming after, which contradicts the idea of a review. Hence the answer is preceding.

The phrasal verb fits into means to belong within or align with a larger structure or plan. A day's lecture relating to a course pattern is exactly this part-to-whole integration. "Adds" would take to, not into; "gets into" suggests entry/access; "lets into" is ungrammatical here. Hence the correct word is fits.

The next sentence in the passage warns that a long, unbroken lecture strains the listener's attention. The blank must therefore carry a sense of rarely or not advisable. Seldom (= rarely) fits this advisory tone perfectly. "Continuously" and "often" recommend the very practice the passage criticises; "randomly" describes a manner of delivery, not its frequency. Hence seldom.

What a long lecture strains is the listener's limit or ability for sustained attention — i.e. their capacity for concentrated listening. The result clause (wandering attention, loss of continuity) confirms a mental-limit reading. "Authority" (power) and "reasonability" (logic) are irrelevant to listening. "Comfortability" denotes physical ease, not the mental endurance being strained. Hence capacity.