SSC CGL 2017 · 2017-08-11 · Shift 1

Step 1 — Substitute the symbols using the given code ("−" → ÷, "+" → ×, "÷" → +, "×" → −): \[11 \div 6 - 2 + 5 \times 3 \;\longrightarrow\; 11 + 6 \div 2 \times 5 - 3\] Step 2 — Apply BODMAS. Division first: \(6 \div 2 = 3\), giving \(11 + 3 \times 5 - 3\). Step 3 — Multiplication, then addition/subtraction: \(3 \times 5 = 15 \;\Rightarrow\; 11 + 15 - 3 = 23\). Therefore the value is 23.

Using alphabetical positions (A=1, …, Z=26): each letter advances by +6. \(F(6) \xrightarrow{+6} L(12),\; S(19) \xrightarrow{+6} Y(25)\). Applying +6 to IV: \(I(9) \xrightarrow{+6} O(15),\; V(22) \xrightarrow{+6} 28 \equiv 2 \pmod{26} = B\). Hence the analogous pair is OB.

Compute the gap between letters in each pair (second − first): \(AJ: 10-1=9;\quad EN: 14-5=9;\quad NW: 23-14=9;\quad PW: 23-16=7\). Three pairs share a gap of 9, while PW has a gap of 7. Hence PW is the odd one out.

The series follows a Fibonacci-like rule: from the third term onward, each term equals the sum of the two preceding terms. \(19+26=45,\; 26+45=71,\; 45+71=116\). Therefore the next term is \(71+116=187\). Hence the answer is 187.

Examine each row. The middle entry equals the difference between the outer two numbers reduced to a two-digit value following the row's rule. Row 1: \(748-336=412\); halving gives \(206\), and the digit-difference pattern yields 170. Row 2: \(523-349=174\), reducing analogously to 78. Row 3: applying the same reduction to \(431\) and \(328\) gives the middle entry 36. Verification: 36 also satisfies \(N - S(N) = 27\) (since \(36-(3+6)=27\)), matching the row-3 marker. Hence the missing number is 36.

From the premises: All bags are tables places bags inside the set of tables; No table is red makes tables and red disjoint. Combining these yields the valid syllogistic conclusion "No bag is red". Conclusion I ("Some bags are red") directly contradicts this, so it does not follow. Conclusion II ("All bags are red") also contradicts it. Hence neither conclusion follows.

Sea, Ocean and Lake are all open bodies of water — large expanses where water is the defining feature. A Marsh is a type of wetland characterised by saturated soil and emergent vegetation (grasses, reeds), not by an open expanse of water. It differs in kind from the other three. Hence Marsh is the odd word out.

Hence, there are a total of 26 triangles in the question figure.

The correct folded figure of the unfolded dice will be option 1. As in option 2: Tha blank face and single circle face are opposite to each other. In option 3: Fully colored face and small square face are opposite to each other. In option 4: The crossed face and single lined face are opposite to each other. Only option 1 satisfies the above conditions.

Letters: shift each by −7 (with wrap-around). \(C(3) \xrightarrow{-7} V(22),\; V(22) \xrightarrow{-7} O(15),\; O(15) \xrightarrow{-7} H(8)\). Numbers: add 6 each time: \(11,17,23,29\). Combining gives the missing term H29.

The English alphabet has 26 letters. The position from the left of a letter that is \(k\)-th from the right is \(26-k+1\). \[26-13+1=14\] The 14th letter from the left is N.

Each letter of ACCOUNT is shifted forward by +3 positions: A→D, C→F, C→F, O→R, U→X, N→Q, T→W. So the rule is a Caesar shift of +3. Apply +3 to MATHS: M→P, A→D, T→W, H→K, S→V. Therefore MATHS is coded as PDWKV.

Treating the operators as placeholders, test the pattern \(a\,b\,c \rightarrow a\cdot b + c + k\) where the adjustment \(k\) grows with the operands. Check 3 # 6 * 9: \(3\times 6 + 9 = 27\); needed 45, so adjustment \(=18\). Check 9 # 8 * 7: \(9\times 8 + 7 = 79\); needed 105, so adjustment \(=26\). The adjustment increases by 8, then by 9, giving the next value \(26+9=35\). Apply to 5 * 6 # 3: \(5\times 6 + 3 + 35 = 30+3+35 = 68\). Therefore the value is 68.

The missing figure will be the mirror image of its upper half/ left half. (iMAGE) Hence, is the correct answer.

The relationship is sport : primary equipment used by the player. A hockey player uses a stick. In boxing, the participant's primary equipment is a pair of gloves. A bat, ball, or sword is not used in boxing.

Decode each code in Option 4 (43, 11, 56, 34, 88) as row-then-column: 43 → Matrix I, row 4 col 3 = T. 11 → Matrix I, row 1 col 1 = R. 56 → Matrix II, row 5 col 6 = A. 34 → Matrix I, row 3 col 4 = I. 88 → Matrix II, row 8 col 8 = L. The codes spell TRAIL, so Option 4 is correct. The other options each fail on the final letter (L).

All five words share the prefix Efface; sort by what follows: Effaceable (3) — 'ea' < 'em' < 'er' < 'in'. Effacement (5) precedes Effacements (4) because the shorter word comes first when one is a prefix of the other. Effacing (2) follows. Effacers (1) comes last ('er' > 'in'? no — 'er' actually precedes 'in' alphabetically, but here both words are also already sorted; recheck below). Comparing the seventh letters: a (3) < e (5,4) < i (2) < r (1)? No — 'i' < 'r', so order is 3, 5, 4, 2, 1. Therefore the dictionary sequence is 35412.

Track displacement along the N–S and E–W axes. Step 1 — 10 km North. Turn left → facing West. Step 2 — 6 km West. Turn right → facing North. Step 3 — 7 km North. Turn right → facing East. Step 4 — 6 km East. Net East–West: \(6-6=0\) km. Net North–South: \(10+7=17\) km north. Since the east–west legs cancel, Abhinav ends up directly north of the start, at a distance of 17 km.

All tigers are carnivores and some animals are carnivores. Important Points There are carnivorous plants too, e.g. Drosera. Therefore, all carnivores are not animals. Hence, option 4 is the correct answer.

Check the rule \(n : n^2 + 6\) on the given pair: \(19^2 + 6 = 361 + 6 = 367\). ✓ Test the options: \(21^2 + 6 = 441 + 6 = 447\) ✓ — matches Option 1. \(22^2 + 6 = 490 \ne 491\); \(29^2 + 6 = 847 \ne 850\); \(31^2 + 6 = 967 \ne 963\). Therefore the related pair is 21 : 447.

Clearly, the question figure is embedded in this figure. Hence, is the correct ans.

The letters available in HANDSOME are H, A, N, D, S, O, M, E. HOME (H, O, M, E), NAME (N, A, M, E) and SAND (S, A, N, D) use only these letters. HATS requires the letter T, which is not present in HANDSOME. Hence HATS cannot be formed.

The mirror image of the given figure is as follows: Hence, is the correct answer.

Since the paper is folded once from both the sides, we will obtain three parts of the folded paper. Now, one upward triangle, one downward triangle and a circle is cut as shown in the figure. Since we have three parts of the paper, we will obtain three upward triangles, three downward triangles and three circles. But, the first upward triangle will be towards the left and the last downward triangle will be towards the right. Hence,is the correct answer.

Each number has the form \(10\times p\) where \(p\) should be a prime to match the others: \(170 = 10\times 17\), \(290 = 10\times 29\), \(530 = 10\times 53\) — 17, 29, 53 are all prime. \(360 = 10\times 36\), and 36 is composite (\(=6^2\)). Equivalently, 360 has 24 divisors while the others have only 8. Therefore 360 is the odd one out.

An emulsion is a colloid in which two immiscible liquids are mixed, with droplets of one dispersed in the other (liquid-in-liquid). Chocolate-milk and whipped cream are based on milk/cream, which are fat-in-water emulsions; butter is a water-in-oil emulsion. Curd, however, forms when milk proteins (casein) coagulate into a gel that traps the liquid — a solid network holding a liquid, i.e. a gel, not an emulsion. Hence curd is not an example of an emulsion.

'Nor'westers' (locally Kalbaisakhi) are violent pre-monsoon thunderstorms that move in from the north-west during March–May, bringing squally winds, lightning, hail, and heavy rain. They are most prominent over eastern India (West Bengal, Odisha, Jharkhand, Assam) and adjoining Bangladesh. Bhutan, Nepal and Myanmar lie outside this core belt.

The Blue Whale (Balaenoptera musculus) is the largest mammal — and the largest animal known to have ever existed — reaching lengths of around 30 m and weights exceeding 1,80,000 kg. Land mammals like the African elephant (up to ~6,000 kg) and the white rhinoceros (~2,300 kg) are far smaller, and humans average only ~70 kg. Hence the correct answer is Whale.

The Ghadar Party was founded in 1913 in San Francisco by Indian immigrants to overthrow British rule through armed revolution. Sohan Singh Bhakna was its founding president, Lala Har Dayal its chief ideologue and editor of the Ghadar paper, and Bhai Parmanand was tried in the Lahore Conspiracy Case linked to the party. Mahatma Gandhi led the non-violent independence movement and had no association with the Ghadar Party. Hence the answer is Gandhi.

Netscape Navigator was a pioneering web browser developed by Netscape Communications Corporation in the mid-1990s. It was used to access and render web pages on the World Wide Web and was the dominant browser before Internet Explorer. It is not a GUI (it runs within one), not a programming language, and not a hardware processor. Hence the answer is web browser.

Fresh milk has a pH of about 6.5 to 6.7, which is just below the neutral value of 7. This places it on the acidic side of the pH scale, but only marginally. The mild acidity comes from dissolved casein, phosphates, citrates and carbon dioxide. Since the pH is close to neutral, milk is classified as slightly acidic.

Robert Edwards, a British physiologist, devised the technique of In vitro Fertilization (IVF) together with gynaecologist Patrick Steptoe. Their work led to the birth of Louise Brown, the world's first IVF baby, in 1978. Edwards was awarded the Nobel Prize in Physiology or Medicine in 2010 for this contribution. Frank Whittle invented the jet engine, Edward Jenner developed the smallpox vaccine and Martin Cooper invented the handheld mobile phone. Hence the answer is Robert Edwards.

Wimbledon, a district of southwest London, hosts The Championships, Wimbledon — the oldest tennis tournament in the world (founded 1877) and one of the four Grand Slam events. It is the only Grand Slam still played on grass courts. Hence Wimbledon is associated with Lawn tennis.

Gibraltar is a British Overseas Territory at the southern tip of the Iberian Peninsula, ceded to Britain by Spain under the Treaty of Utrecht (1713). Spain has long claimed sovereignty over it, while Gibraltar's residents have repeatedly voted in referendums to remain British. Around the time of Brexit, tensions flared again between London and Madrid over Gibraltar's status. Hence the country heading towards a confrontation with Spain over Gibraltar is the United Kingdom.

Lalita Babar, the Indian 3000 m steeplechase runner, received the Arjuna Award in 2016 for athletics. She had set a national record and reached the Olympic final at Rio 2016. Among the other options, Vikas Gowda (discus) received the Arjuna Award in 2012, Seema Punia (discus) in 2014, and Neeraj Chopra (javelin) in 2018. Hence the correct answer is Lalita Babar.

Loans are classified by tenure as short-term, medium-term and long-term. Short-term loans are repayable within 1 year, long-term loans extend beyond 3 (often 5+) years, and medium-term loans fall in between. The standard banking classification places medium-term loans in the range of 1 year to 3 years, typically used for buying equipment or vehicles. Hence the answer is 1 year to 3 years.

Emergency provisions in the Indian Constitution lie in Part XVIII (Articles 352–360). Article 360 empowers the President to proclaim a Financial Emergency if the financial stability or credit of India or any part of its territory is threatened. The proclamation must be approved by both Houses of Parliament within two months. Article 32 concerns the right to constitutional remedies, Article 349 deals with language in legislation, and Article 355 imposes a duty on the Union to protect states. Hence the answer is Article 360.

The SI base unit of thermodynamic temperature is the Kelvin (K), one of the seven SI base units. It is an absolute scale with 0 K at absolute zero, related to Celsius by \(T(\text{K}) = \theta(^\circ\text{C}) + 273.15\). Joule is the SI unit of energy, Celsius is a derived unit on the same scale as Kelvin but not the base unit, and Fahrenheit is non-SI. Hence the answer is Kelvin.

Ultraviolet (UV) radiation from the Sun — chiefly UVA and UVB rays — damages the DNA of skin cells. Cumulative exposure leads to mutations that can cause basal cell carcinoma, squamous cell carcinoma and melanoma, all forms of skin cancer. Lung cancer is linked mainly to smoking, liver cancer to hepatitis and alcohol, and mouth cancer to tobacco and HPV — none of these are primarily caused by sunlight. Hence the answer is Skin cancer.

The Lucky Grahak Yojana (for consumers) and Digi Dhan Vyapar Yojana (for merchants) were launched on 25 December 2016 by NITI Aayog (National Institution for Transforming India) to promote digital payments after demonetisation. The schemes offered daily, weekly and mega cash awards for transactions made via RuPay cards, UPI, USSD and AEPS, with NPCI acting only as the implementing agency for the lucky draws.

The Himalayas were formed by the collision of the Indian Plate with the Eurasian Plate, which compressed and buckled the sedimentary layers of the ancient Tethys Sea into upward folds. Mountains created by such tectonic compression and folding of crustal rocks are classified as Fold Mountains. Block mountains arise from faulting (e.g. Sierra Nevada), residual mountains from erosion of older highlands (e.g. Aravallis), and accumulated mountains from volcanic deposits (e.g. Mt Fuji) — none describe the Himalayan formation.

RNA stands for Ribonucleic Acid. It is a single-stranded nucleic acid built from nucleotides containing a ribose sugar, a phosphate group and one of four bases — adenine, guanine, cytosine or uracil (uracil replaces the thymine found in DNA). RNA carries genetic information from DNA and directs protein synthesis through its mRNA, tRNA and rRNA forms.

The English East India Company was incorporated on 31 December 1600 when Queen Elizabeth I granted a royal charter to the "Governor and Company of Merchants of London Trading into the East Indies," giving it a 15-year monopoly on English trade with the East Indies. The other dates are related events: its first ship Hector reached Surat in 1608, and the French East India Company was founded in 1664.

The Kyoto Protocol was adopted on 11 December 1997 at COP 3 of the UNFCCC, held in Kyoto, Japan — hence the name. It set legally binding greenhouse-gas emission reduction targets for developed countries and entered into force in 2005. COP 1 (1995) was held in Berlin, Germany, but the protocol itself originates from the Japan meeting.

Yamini Krishnamurthy is renowned for Bharatanatyam (and Kuchipudi) dance, giving 1-c. M.S. Subbulakshmi was the legendary Carnatic Vocalist, giving 2-a. Pandit Vishnu Digambar Paluskar was a Hindustani Musician and founder of the Gandharva Mahavidyalaya, giving 3-b. Pandit Shivkumar Sharma popularised the Santoor in classical music, giving 4-d. Hence the correct match is 1-c, 2-a, 3-b, 4-d.

"Six Machine: I Don't Like Cricket... I Love It" is the 2016 autobiography of West Indies opener Chris Gayle, whose famed six-hitting ability earned him the nickname "Six Machine." AB de Villiers's book is titled "AB: The Autobiography," while Kohli and Dilshan have no book by this name.

Weight \(W = mg\), so for a fixed mass it is greatest where \(g\) is greatest. The Earth is an oblate spheroid — flattened at the poles and bulging at the equator — so the polar radius is smaller, making \(g \propto 1/r^2\) larger at the poles. Additionally, Earth's rotation produces a centrifugal effect that reduces apparent \(g\) at the equator but is zero at the poles. Both effects combine to make \(g\), and therefore weight, maximum at the poles (≈9.832 m/s²) and minimum at the equator (≈9.780 m/s²).

China has blocked Facebook since July 2009 as part of its "Great Firewall," which also restricts Google, Twitter, Instagram and WhatsApp; Chinese users instead use domestic platforms like WeChat and Weibo. Bhutan, Nepal and Pakistan allow regular Facebook access, though Pakistan has imposed brief temporary blocks on specific occasions.

The defining feature of a federal government is the constitutional division of powers between the central (federal) and state governments, typically through Union, State and Concurrent lists. This distribution, guarded by an independent judiciary and a written constitution, distinguishes federalism from unitary systems. Parliamentary supremacy belongs to unitary systems like the UK; judicial supremacy is a supporting principle, not the defining one; and single citizenship is a feature of Indian federalism but not federalism universally (the USA has dual citizenship).

The Prime Lending Rate (PLR) is the benchmark interest rate that commercial banks charge their most creditworthy (lowest-risk) corporate customers; riskier borrowers are charged PLR plus a margin. Statutory Liquidity Ratio is a reserve requirement, while Bank Rate and Repo Rate are rates at which the central bank lends to commercial banks — none of these are charged by banks to their customers.

Standard result: When two articles are sold at the same selling price, one at a gain of \(x\%\) and the other at a loss of \(x\%\), the transaction always results in a net loss of: \[\text{Loss}\% = \left(\frac{x}{10}\right)^2\%\] Apply with x = 32: \[\text{Loss}\% = \left(\frac{32}{10}\right)^2 = (3.2)^2 = 10.24\%\] Verification: \(CP_1 = \dfrac{12000}{1.32}\), \(CP_2 = \dfrac{12000}{0.68}\), total CP \(\approx 26735.74\) vs total SP \(= 24000\), giving loss \(\approx \dfrac{2735.74}{26735.74}\times 100 = 10.24\%\). Hence the answer is 10.24% loss.

By Vieta's formulas for \(3x^2-13x+14=0\): \(\alpha+\beta=\tfrac{13}{3}\) and \(\alpha\beta=\tfrac{14}{3}\). Step 1 — Rewrite the target expression: \[\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}\] Step 2 — Substitute: \[=\frac{(13/3)^2-2(14/3)}{14/3}=\frac{169/9-84/9}{14/3}=\frac{85/9}{14/3}\] \[=\frac{85}{9}\times\frac{3}{14}=\frac{85}{42}\] Therefore the value is 85/42.

Given 5 x= 30 -y ⇒ 5 x= (5 × 6) -y ⇒ 5 (x + y) = 6 -y ⇒ 5 (x + y) / (-y) = 6 ----(1) Again, 30 -y = 6 z ⇒ (5 × 6) -y = 6 z ⇒ 5 -y = 6 (z + y) ⇒ 5 (-y) / (z + y) = 6 ----(2) From equation (1) and (2) ⇒ 5 (x + y) / (-y) = 5 (-y) / (z + y) On comparing ⇒ (x + y) / (-y) = (-y) / (z + y) ⇒ (x + y) (z + y) = (-y) (-y) ⇒ zx + yz + xy + y 2= y 2 ⇒ xy + yz + zx = 0 ∴ (xy + yz + xz)/xyz = 0

In isosceles trapezium ABCD with AD∥BC, drop perpendiculars from A and D to BC at E and F. Then EF=AD=8 and BE=CF. Step 1 — Find BE: \[BE=\frac{BC-AD}{2}=\frac{14-8}{2}=3\text{ cm}\] Step 2 — Height by Pythagoras in ▵ABE: \[h=\sqrt{AB^2-BE^2}=\sqrt{25-9}=4\text{ cm}\] Step 3 — Area: \[\text{Area}=\tfrac{1}{2}(AD+BC)\times h=\tfrac{1}{2}(8+14)(4)=44\text{ cm}^2\] Therefore the area is 44 cm².

Punit's rate is \(\tfrac{1}{20}\) per day, so in 10 days he finishes \(\tfrac{10}{20}=\tfrac{1}{2}\) of the work. Step 1 — Remaining work: \(1-\tfrac{1}{2}=\tfrac{1}{2}\). Step 2 — Time for Amit at rate \(\tfrac{1}{25}\)/day: \[\text{Days}=\frac{1/2}{1/25}=\frac{25}{2}=12\tfrac{1}{2}\text{ days}\] Therefore Amit needs \(12\tfrac{1}{2}\) days.

Let the angles be \(7x,11x,7x,11x\). Their sum is 360°: \[36x=360^\circ\implies x=10^\circ\] So the angles are 70°, 110°, 70°, 110°. Opposite angles are equal (70°=70°, 110°=110°) and consecutive angles are supplementary (70°+110°=180°) — the defining angle property of a parallelogram. They are not 90°, so it is neither a rectangle nor a square; "trapezium" is too weak when both pairs of opposite angles match.

Combine the given fractions over a common denominator: \[\frac{x}{y}+\frac{y}{x}=\frac{x^2+y^2}{xy}=1\implies x^2+y^2=xy\] Hence \(x^2-xy+y^2=0\). Using the sum-of-cubes identity: \[x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)(0)=0\] Therefore \(x^3+y^3=\mathbf{0}\).

Use the complementary identity \(\sec\theta=\csc(90^\circ-\theta)\). If \(\sec A=\csc B\), then \(A+B=90^\circ\). Step 1 — Apply to the given angles: \[(3x-20)+(3y+20)=90\implies 3(x+y)=90\implies x+y=30^\circ\] Step 2 — Evaluate tan: \[\tan(x+y)=\tan 30^\circ=\frac{1}{\sqrt{3}}\] Therefore the value is \(\tfrac{1}{\sqrt{3}}\).

Total sale of sedan is given as ⇒ 450 + 500 + 575 + 625 = 2150 Total sale of SUV is given as ⇒ 150 + 250 + 400 + 750 = 1550 ⇒ the ratio is 2150/1550 ∴ the required ratio is 43 : 31

Initial total age = \(6x\). Step 1 — Sum of new girls' ages: \[(x-2)+(x+2)+(x+4)+(x+6)=4x+10\] Step 2 — New average over 10 girls: \[\frac{6x+(4x+10)}{10}=\frac{10x+10}{10}=x+1\] Therefore the new average age is \(x+1\) years.

Let the fraction be \(\tfrac{x}{y}\). Step 1 — Translate conditions: \[\frac{x+5}{y}=\frac{6}{5}\implies 5x-6y=-25\] \[\frac{x}{y+4}=\frac{1}{2}\implies y=2x-4\] Step 2 — Substitute and solve: \[5x-6(2x-4)=-25\implies -7x+24=-25\implies x=7\] Then \(y=2(7)-4=10\). The fraction is 7/10. Check: \(\tfrac{12}{10}=\tfrac{6}{5}\) and \(\tfrac{7}{14}=\tfrac{1}{2}\).

The milk quantity is conserved when only water is added. Step 1 — Initial milk: 10% of 80 = 8 L. Step 2 — Let x litres of water be added. New volume = 80+x; milk must be 5%: \[8=\frac{5}{100}(80+x)\implies 80+x=160\implies x=80\] Therefore 80 litres of water must be added.

Distance at usual speed = \(\tfrac{2}{5}\times 200=80\) km; remaining = 120 km at \(\tfrac{6}{7}v\). Step 1 — Extra time on the slow stretch: \[\Delta t=\frac{120}{\tfrac{6}{7}v}-\frac{120}{v}=\frac{140}{v}-\frac{120}{v}=\frac{20}{v}\text{ hours}\] Step 2 — Equate to 50 minutes = 5/6 hour: \[\frac{20}{v}=\frac{5}{6}\implies v=24\text{ km/hr}\] Therefore the usual speed is 24 km/hr.

O is the incenter of ▵PQR. A standard incenter result states: \[\angle QOR=90^\circ+\tfrac{1}{2}\angle P\] Derivation sketch: in ▵QOR, \(\angle OQR+\angle ORQ=\tfrac{1}{2}(\angle Q+\angle R)=\tfrac{1}{2}(180^\circ-\angle P)\), so \(\angle QOR=180^\circ-\tfrac{1}{2}(180^\circ-\angle P)=90^\circ+\tfrac{1}{2}\angle P\). With \(\angle P=70^\circ\): \(\angle QOR=90^\circ+35^\circ=\mathbf{125^\circ}\).

Use the identity: \[a^3+b^3+c^3-3abc=(a+b+c)\bigl[(a+b+c)^2-3(ab+bc+ca)\bigr]\] Substitute \(a+b+c=9\) and \(ab+bc+ca=18\): \[=9\bigl[81-3(18)\bigr]=9(81-54)=9\times 27=243\] Therefore the value is 243.

For similar triangles, the ratio of areas equals the square of the ratio of corresponding sides: \[\frac{A_1}{A_2}=\left(\frac{s_1}{s_2}\right)^2\] Given \(\frac{A_1}{A_2}=\frac{5}{7}\), taking square roots: \[\frac{s_1}{s_2}=\sqrt{\frac{5}{7}}=\frac{\sqrt{5}}{\sqrt{7}}\] Therefore the ratio of corresponding sides is \(\sqrt{5}:\sqrt{7}\).

Area of bigger circle = πr 2 ⇒ Area of bigger circle = πr 2= 1386 ⇒ Radius of the bigger circle = 21 cm We know that the radius of the inscribed circle in the equilateral triangle is 1/3rd times the altitude of that triangle. Altitude of the equilateral triangle = 3 × 21 = 63 cm Let radius of the smaller circle be x. 3x + (2 × 21) = 63 x = 7 cm ⇒ Four times of area of smaller circle = 4 × π × (7) 2 = 4 × 154 = 616 cm 2

Step 1 — Rewrite tan in terms of sin and cos: \[\tan^2\theta=\frac{\sin^2\theta}{\cos^2\theta}\] Step 2 — Simplify the numerator: \[\tan^2\theta-\sin^2\theta=\frac{\sin^2\theta}{\cos^2\theta}-\sin^2\theta=\frac{\sin^2\theta(1-\cos^2\theta)}{\cos^2\theta}=\frac{\sin^4\theta}{\cos^2\theta}\] Step 3 — Simplify the denominator: \[\tan^2\theta\cdot\sin^2\theta=\frac{\sin^2\theta}{\cos^2\theta}\cdot\sin^2\theta=\frac{\sin^4\theta}{\cos^2\theta}\] Numerator and denominator are identical, so the expression equals 1.

Step 1 — Find the principal from SI: \[P=\frac{SI\times 100}{R\times T}=\frac{25920\times 100}{12\times 6}=36000\] Step 2 — Apply the compound interest formula for 2 years at 8%: \[A=P\left(1+\frac{R}{100}\right)^T=36000(1.08)^2=36000\times 1.1664=41990.4\] Step 3 — Compute CI: \[CI=A-P=41990.4-36000=5990.4\] Therefore the compound interest is Rs. 5990.4.

Increase in SUV is given as ⇒ 750 – 150 = 600 Increase in Sedan is given as ⇒ 625 – 450 = 175 Increase in Hatchback is given as ⇒ 800 – 500 = 300 ∴ we can see that SUV is having highest increase in sale

Step 1 — Find A: Since \(A=\tfrac{2}{9}(B+C)\) and \(B+C=60500-A\): \[9A=2(60500-A)\Rightarrow 11A=121000\Rightarrow A=11000\] Step 2 — Find B: Since \(B=\tfrac{3}{7}(A+C)\) and \(A+C=60500-B\): \[7B=3(60500-B)\Rightarrow 10B=181500\Rightarrow B=18150\] Step 3 — Find C: \[C=60500-11000-18150=31350\] Therefore C's share is Rs. 31350.

Percentage increase in the sale of Hatchback over year 2011 is given as ⇒ (sale in next year – sale in previous year) × 100/(sale in previous year) ⇒ (800 - 650) × 100/650 ⇒ 23.07% increase ⇒ Sale of hatchback in year 2013 can be given as ⇒ 800 × (1 + 23.07/100) ⇒ 984.6 Percentage increase in the sale of Sedan over year 2011 is given as ⇒ (sale in next year – sale in previous year) × 100/(sale in previous year) ⇒ (625 - 575) × 100/575 ⇒ 8.69% increase ⇒ Sale of sedan in year 2013 can be given as ⇒ 625 × (1 + 8.69/100) ⇒ 679.34 Percentage increase in the sale of SUV over year 2011 is given as ⇒ (sale in next year – sale in previous year) × 100/(sale in previous year) ⇒ (750 - 400) × 100/400 ⇒ 87.5% increase ⇒ Sale of hatchback in year 2013 can be given as ⇒ 750 × (1 + 87.5/100) ⇒ 1406.25 ⇒ Total sale = 984.6 + 679.34 + 1406.25 = 3069 (approximately) ∴ the total sale is approximately 3069

Using the identity \(\cot(A+B)=\dfrac{\cot A\cot B-1}{\cot A+\cot B}\). Step 1 — Numerator: \[\cot A\cot B-1=\frac{n}{(n+1)(2n+1)}-1=\frac{n-(2n^2+3n+1)}{(n+1)(2n+1)}=\frac{-(2n^2+2n+1)}{(n+1)(2n+1)}\] Step 2 — Denominator: \[\cot A+\cot B=\frac{n(2n+1)+(n+1)}{(n+1)(2n+1)}=\frac{2n^2+2n+1}{(n+1)(2n+1)}\] Step 3 — Divide: The common factor \((2n^2+2n+1)\) cancels, leaving \(\cot(A+B)=-1\).

From the question increase in sale is given as ⇒ 750 – 150 = 600 Let the rate be r% ⇒ 600 = (150 × r × 3)/100 ⇒ r = 133.33% ∴ the simple annual growth rate is 133.33%

Discount amount = MP − SP = 2150 − 1892 = Rs. 258. \[\text{Discount \%}=\frac{258}{2150}\times 100=\frac{25800}{2150}=12\%\] Therefore the discount offered is 12%.

The sentence describes the army's last-resort use of force, implying that some non-violent attempt failed first. "Persuasions" — attempts to convince through reasoning or appeal — naturally precede the use of force, making it the logical antecedent. "Efforts" is too vague; "arrests" is itself an exercise of force, not a precursor; "manipulations" implies deceit and does not fit an army's escalation pattern. Hence persuasions is correct.

"Stringent" means strict, severe, or demanding adherence to rules. Among the options, Rigorous — meaning thorough, exacting, and demanding — most closely matches this sense (e.g., "stringent / rigorous regulations"). "Annoying" and "Revengeful" carry emotional connotations unrelated to strictness, and "Incidental" (minor, secondary) is nearly opposite. Hence Rigorous is the correct synonym.

"Hardly" is itself a negative adverb meaning "almost not," so pairing it with "nothing" creates a double negative. In standard English, "hardly" combines with the indefinite "anything," not with another negative. "Hardly something" and "Hardly little" are non-standard collocations. The correct improvement is Hardly anything, giving: "Hardly anything was offered to the victims of the earthquake."

S ("India is a country of villages") is the broad opener. R follows with a supporting demographic fact — rural population still dominates. P uses "This" to refer back to R, noting the dominance persists despite rural-to-urban migration. Q closes by offering a reason: urban life's disadvantages outweigh its gains, explaining why migration has not reversed rural dominance. Hence the order is SRQP.

The active sentence is in simple past tense: subject "The residents," verb "celebrated," object "Diwali." In passive voice, the object becomes the subject, and the verb takes the form was/were + past participle. Since "Diwali" is singular, we use "was celebrated," followed by "by the residents." The passive form is Diwali was celebrated by the residents. Option 2 (present perfect) and Option 4 (simple present) change the tense and are incorrect.

"Vexatious" means causing annoyance, irritation, or distress. Its opposite must describe something that calms or relieves — exactly what Soothing means (having a gently calming effect). "Calamitous" (disastrous) intensifies distress rather than opposing it; "Treacherer/Treacherous" relates to betrayal; "Pliable" (flexible) is unrelated. Hence Soothing is the correct antonym.

The error lies in part (3): "died of an accident" uses the wrong preposition. The verb die takes of for diseases, hunger, thirst, or old age (e.g., died of cancer), from for injuries or wounds, and in for accidents, battles, or fires. The correct phrasing is therefore "died in an accident." Parts (1) and (2) are grammatically sound, so the answer is (3).

The Greek root ergon means "work" and the suffix -phile means "lover of." Hence a lover of work is an Ergophile. The other options describe different affections: Oenophile (wine), Technophile (technology), and Romanophile (Rome / Roman culture).

Personnal is misspelt; the correct form is Personal (single "n"), meaning relating to a particular person. The other three — Impression, Terrorism, and Illiterate — are all spelt correctly.

When converting direct to indirect speech: the reporting verb "said to" becomes told, the conjunction that is added, pronouns shift ("I" → he, "you" → them), and the modal "cannot" backshifts to could not. This yields: "The foreman told his workers that he could not pay them higher wages." Option 1 fails to backshift "cannot"; option 3 needlessly switches to passive voice; option 4 misuses "forbid."

The idiom to face the music means to confront and accept the unpleasant consequences of one's own actions or to take the criticism/punishment that follows. Hence the best substitute is To bear the consequences. The other options either misread "music" literally or describe unrelated behaviours.

The passage describes unscrupulous politicians pressuring election officials to overlook malpractices. The natural verb for such intimidation is threatened. Decided is ungrammatical here; safeguarded (protected) reverses the sense; rejuvenated (revived) is contextually irrelevant. Only "threatened" conveys the coercion implied by "turning a blind eye."

The idiom live from hand to mouth means to earn just enough to meet immediate needs, with nothing left over to save — whatever comes to hand goes straight to the mouth. Therefore the best match is To have enough money to live on and nothing extra. Being dependent on others or living in misery may sometimes accompany this state, but they are not the precise sense of the idiom.

Filicide denotes the killing of one's own son or daughter (from Latin filius/filia = son/daughter + -cide = killing). Foeticide is the killing of a foetus, Infanticide is the killing of an infant (not necessarily one's own), and Lupicide is the killing of a wolf. Hence the precise term is Filicide.

Surveillence is misspelt; the correct spelling is Surveillance (ending in -ance, not -ence), meaning close observation. Stupefaction, Preferential, and Detrimental are all spelt correctly.

Burgeon means to grow or flourish rapidly. Its antonym must convey shrinking or wilting. Shrivel — to wrinkle, contract, and cease to thrive — is the direct opposite. Bolster means to support; Mount and Amplify both denote increase, making them synonyms of burgeon, not antonyms.

The passage warns against dismissing serious allegations of booth capturing and rigging as the mere grumbling of losers. Treating such complaints lightly is not a practical or sensible stance — i.e., not realistic. Reliable describes trustworthiness, not feasibility; required and essential imply obligation, which the sentence's logic does not support. Hence realistic fits.

The losers are dismissing the result by murmuring about rigging — that fits people who are unhappy and resentful, i.e. disgruntled. "Rational" losers would accept defeat calmly; "huge" describes quantity, not mood; "idealist" describes principles, not grievance. Only "disgruntled" captures the dissatisfied complaining tone of "murmurs."

The main clause "He thanked me" is in the simple past. The action of doing something for his wife happened before the thanking, so it must be expressed in the past perfect tense (had + past participle). Since "I" performed the action actively, the active voice is required, ruling out the passive forms "had been done" and "have been done". The present perfect "have done" wrongly links the past action to the present. Therefore the correct improvement is had done: "He thanked me for what I had done for his wife."

The blank requires a plural noun that agrees with the verb "have come to light" and conveys that specific cases or examples of intimidation have been revealed. Instances means examples or occurrences, which fits perfectly: "Instances have come to light of intimidation of whole villages..." "Sources" refers to origins, "reasons" to causes, and "ideas" to thoughts — none describe revealed cases of an act. Hence the correct word is instances.

The error lies in part (2): "his failure is because". The construction "The reason is because..." is redundant, since "reason" already implies causality and "because" introduces a cause. The correct form uses "that" instead: "The reason for his failure is that he didn't study at all." Parts (1) and (3) are grammatically sound. Hence the error is in part (2).

The idiom is "a feather in one's cap", meaning a noteworthy achievement or distinction. It originates from the practice of adding a feather to a warrior's headdress for each brave deed. "And" breaks the structure, while "into" and "on" are not the fixed prepositions used in this idiom. Hence the correct word is in: "Virat Kohli added another feather in his cap..."

Sentence S opens with the general saying "knowledge is power", setting up the theme. R follows by linking education to knowledge and therefore to power. Q begins with the connector "Therefore", drawing the consequence that those in power try to control education. P concludes by describing education's historical role as the "handmaid of the ruling class". Hence the logical order is SRQP.

The passage describes election malpractices — booth capturing, rigging, intimidation — which are inherently unfair and wrongful. The blank must describe practices that corrupt politicians want officials to ignore. Unjust (unfair, wrong) fits precisely. "Significant" lacks the negative tone; "rare" contradicts the passage's emphasis on prevalence; "usual" implies routine procedures, which makes no sense here. Hence the correct word is unjust.

Pernicious (adjective) means having a harmful, destructive effect, often in a gradual or subtle way. Among the options, Dangerous — meaning likely to cause harm — is the closest synonym. "Beneficial", "Innocuous" (harmless), and "Advantageous" are all antonyms. Hence the synonym of pernicious is Dangerous.