SSC CGL 2017 · 2017-08-12 · Shift 1

Coding rule: each letter is given as row followed by column. Vowels/consonants P, K appear only in Matrix-II; A, C only in Matrix-I. Decode the letters in option (96, 44, 41, 97): P → row 9, column 6 in Matrix-II gives P. Code 96. A → row 4, column 4 in Matrix-I gives A. Code 44. C → row 4, column 1 in Matrix-I gives C. Code 41. K → row 9, column 7 in Matrix-II gives K. Code 97. All four codes match P-A-C-K in order, so the set 96, 44, 41, 97 represents PACK.

All five words share the prefix “Exa…”, so compare the next differing letters. Among Exac- words: Exacerbate (e) precedes Exactly and Exacts (both have t at position 5). Between Exactly and Exacts, “l” (Exactly) precedes “s” (Exacts). So the Exac- group orders as Exacerbate (4) → Exactly (3) → Exacts (1). Then by the 3rd letter, Exhaust precedes Exotic, giving Exhaust (5) → Exotic (2). Full dictionary order: 4, 3, 1, 5, 2 → 43152.

Code = (sum of alphabetical positions of the letters) \(\times\) 3. Check: PUNISHED = 16+21+14+9+19+8+5+4 = 96; \(96\times 3 = 288\). TAILOR = 20+1+9+12+15+18 = 75; \(75\times 3 = 225\). Both match. Apply to RELEASED: 18+5+12+5+1+19+5+4 = 69. Code = \(69\times 3 = 207\).

The relationship is subject : its core descriptive tool. Mathematics is expressed through formulas — the symbolic statements that capture its relationships. The analogous tool in chemistry is the reaction (and its equation), which describes how substances combine and transform. Organisms belong to biology, theorems to mathematics/logic, and gravity to physics — none is a chemistry-specific tool. Hence the answer is Reactions.

Group the items by power source. Mobile, Computer and Television are all electronic devices that require electricity to function. A Fountain Pen is a manual writing instrument that uses ink and needs no electricity. It is therefore the odd one out.

Triangles in the figure: ABF, AFC, CDF, BDF, AEF, DEF, ABE, BDE, ABC, BCD, AED, AEC, DEC, ADC and ABD. Hence, total 15 triangles as there in the given figure.

Test each option in 15 _ 3 _ 4 _ 20 using BODMAS. Option 3 (\(\div, \times, =\)): \(15\div 3\times 4 = 5\times 4 = 20\), and \(20=20\) — true. The others fail: \(15\times 3\div 4 = 11.25\not> 20\); \(15\div 3\times 4 = 20\not< 20\); \(15+3\times 4 = 27\ne 20\). Hence the correct set is \(\div, \times, =\).

The operation is \(a\ \$\ b = a^2 - b^2\). Verify: \(19^2 - 7^2 = 361 - 49 = 312\) and \(23^2 - 9^2 = 529 - 81 = 448\). Both match. Apply: \(31\ \$\ 11 = 31^2 - 11^2 = 961 - 121 = 840\).

Hence, answer is option 3.

Step 1 — Set up: Let P’s age \(=9x\) and Q’s age \(=4x\). Step 2 — Use the difference: \[9x-4x=20 \implies 5x=20 \implies x=4\] Step 3 — Present ages: P = 36, Q = 16. Step 4 — Sum after 10 years: \((36+10)+(16+10)=46+26=72\) years. Therefore the required sum is 72 years.

Letter inventory of REASONABLE: R-1, E-2, A-1, S-1, O-1, N-1, B-1, L-1. SEASON needs S-2, E-1, A-1, O-1, N-1. The source word contains only one ‘S’, so the second ‘S’ cannot be supplied. Hence SEASON cannot be formed. EASE (E-2, A-1, S-1), NOBLE (N, O, B, L, E — all singletons available) and SOLAR (S, O, L, A, R — all singletons available) can each be formed.

On observing the given dices we can say that R will be opposite to N as it is adjacent to P and Q. Hence, the answer is R.

The pattern is: square the sum of the digits of the first number. Check: For 49, digits sum to \(4+9=13\), and \(13^2=169\). Apply: For 66, digits sum to \(6+6=12\), and \(12^2=144\). Hence the missing number is 144.

The rule for three of the pairs is: second number = (sum of digits of the first)\(^2\). (143, 64): \(1+4+3=8,\ 8^2=64\) — fits. (232, 49): \(2+3+2=7,\ 7^2=49\) — fits. (719, 289): \(7+1+9=17,\ 17^2=289\) — fits. (462, 169): \(4+6+2=12,\ 12^2=144\ne 169\) — breaks the rule. So (462, 169) is the odd group.

Treat each row as (a, b, c) where \(c=(a+b)^?\) using the third entry as a perfect power of \(a+b\). Row 1: \(a+b=3+2=5\) and \(5^4=625\). Row 2: \(a+b=5+3=8\) and \(8^4=4096\). Row 3: \(a+b=4+2=6\), so the missing value is \(6^4=1296\). Hence ? = 1296.

Statement I (All stars twinkle) is a universal affirmative. By subalternation it directly implies the particular “Some stars twinkle”, so Conclusion II follows. Conclusion I (Some stars are satellites) does not follow: the two statements only place stars and satellites inside the set of things that twinkle; they do not force any overlap between stars and satellites themselves, since both could be disjoint subsets of twinklers. Hence only conclusion (II) follows.

Each City is part of a State, each State is part of a Country as shown in the figure given below. Hence, answer is figure 4.

Figure 1 will complete the incomplete figure as shown in the diagram.

The shift pattern from YONEX to DUUMG is progressive: +5, +6, +7, +8, +9 (with wrap-around past Z). Y(+5)→D, O(+6)→U, N(+7)→U, E(+8)→M, X(+9)→G — confirms the pattern. Apply the same shifts to JASPO: J(+5)→O, A(+6)→G, S(+7)→Z, P(+8)→X, O(+9)→X. The result is OGZXX.

Each term has two letters and a number. Both letters shift by +6 each step, and the number is the cube of a consecutive integer. Letters: F(6)→L(12)→R(18)→X(24); K(11)→Q(17)→W(23)→C(29−26=3). Numbers: \(3^3=27,\ 4^3=64,\ 5^3=125,\ 6^3=216\). So the next term is XC216.

Clearly, the give question figure is hidden in option 1. Thus, answer is option 1.

Hence, answer is figure 1.

Place R at origin. Punit walks 10 km west to A(-10, 0). Facing west, a right turn points him north; 12 km takes him to B(-10, 12). Facing north, another right turn points him east; 7 km takes him to C(-3, 12). Net displacement from R: 3 km west and 12 km north. Both components lie in the North-West quadrant, so Punit is North-West of R.

Pattern: position of first letter + position of second letter = position of the third letter (A=1, ..., Z=26). BN-P: \(2+14=16=\)P ✓. LM-Y: \(12+13=25=\)Y ✓. TA-U: \(20+1=21=\)U ✓. GI-R: \(7+9=16\), but R = 18. The sum does not match, so GI-R is the odd pair.

Group the series in triplets: (19, 11, 13), (16, 15, 17), (13, 19, 21), (?, ?, ?). First terms: 19, 16, 13, ... — arithmetic with common difference \(-3\). Next term: \(13-3=10\). Second terms: 11, 15, 19, ... (+4 each). Third terms: 13, 17, 21, ... (+4 each). The missing 10th term is the first entry of the fourth triplet, which is 10.

Sound intensity level — the practical measure of loudness — is expressed in decibel (dB), a logarithmic ratio of sound intensity to a reference intensity. In SSC-style GA questions, decibel is accepted as the unit of sound intensity. Newton is the unit of force, hertz of frequency, and tesla of magnetic flux density — none relate to sound loudness.

The Doldrums correspond to the Equatorial Low Pressure Belt, lying roughly between \(5^{\circ}\)N and \(5^{\circ}\)S. Intense solar heating near the equator causes air to rise, producing low surface pressure, convergence of trade winds (ITCZ) and calm, variable winds. The 25°-35° band is the subtropical high, and 35°-60° covers the westerlies/sub-polar low — not the doldrums.

An exothermic reaction is one in which energy is released to the surroundings, mostly as heat, so the surroundings warm up. The enthalpy change is negative (\(\Delta H<0\)) because the products store less energy than the reactants. Combustion, neutralisation and respiration are familiar examples. A reaction that absorbs heat is endothermic, so option 2 is wrong.

In the additive (RGB) colour model used for light, blue and green are two of the three primaries. Combining blue light and green light produces cyan, a greenish-blue secondary colour. For reference: red + green = yellow, red + blue = magenta, and all three together give white. Brown, black and violet do not arise from mixing only blue and green light.

India notified the Third Protocol amending the India-Singapore DTAA in February 2017. The protocol amended the 1994 treaty to shift taxation of capital gains on shares to the source country and introduced a Limitation of Benefits clause, aligning the agreement with the revised India-Mauritius DTAA. India did not sign a Third Protocol with China, Vietnam or Malaysia in that period.

Nicotine is the alkaloid naturally present in tobacco leaves; it is the chief addictive and toxic component, raising heart rate and blood pressure and driving dependence on tobacco products. Morphine and heroin are opioids derived from the opium poppy and are not constituents of tobacco. Hence nicotine is the harmful component referred to in the question.

Mahanagar Telephone Nigam Limited (MTNL) was granted Navratna status by the Government of India in 1997, giving its board enhanced financial and operational autonomy. Maharatna status (the top tier) requires far higher turnover, net worth and net profit than MTNL achieved, and Mini Ratna is a lower category — so Navratna is the correct classification.

The Gangetic Dolphin (Platanista gangetica) was declared India's National Aquatic Animal on 18 May 2010 by the Government of India to focus attention on conserving the Ganga river ecosystem. It is a freshwater, functionally blind dolphin that navigates by echolocation and is listed as Endangered by the IUCN. Crocodile, turtle and alligator do not hold this national designation.

Pandit Jasraj (1930-2020) was a celebrated Indian classical vocalist of the Mewati Gharana and a recipient of the Padma Vibhushan. Kaushalya Reddy is a Kuchipudi dancer, while Manjit Bawa and Raja Ravi Varma are renowned painters. Among the options, only Pt. Jasraj is a vocalist.

FTP stands for File Transfer Protocol, a standard application-layer protocol used to transfer files between a client and a server over a TCP/IP network. It typically uses port 21 for control and port 20 for data. The other options ("Position", "Packet") are not recognised computing terms for FTP.

The boundary between the Earth's crust and the upper mantle is the Mohorovičić (Moho) discontinuity, marked by an abrupt rise in seismic-wave velocity as waves enter the denser mantle. The Conrad discontinuity lies within the continental crust; the Gutenberg separates mantle from outer core; the Lehmann separates outer from inner core.

Brass is a binary alloy of copper and zinc, with zinc content typically ranging from about 5% to 45%. The proportions are varied to tune colour, strength and corrosion resistance. Adding nickel produces nickel brass (a special variant), but the defining main components of ordinary brass are only copper and zinc — making option 1 correct.

The Pradhan Mantri Surakshit Matritwa Abhiyan (PMSMA), launched in 2016 by the Ministry of Health and Family Welfare, provides free antenatal check-ups and required treatment to pregnant women on the 9th day of every month at government health facilities. The scheme targets women in their 2nd and 3rd trimesters to identify high-risk pregnancies early and reduce maternal and infant mortality.

The correct founder pairings are: Arya Samaj — Dayanand Saraswati (1875); Brahmo Samaj — Raja Ram Mohan Roy (1828); Veda Samaj — Keshab Chandra Sen and K. Sridharalu Naidu (Madras, 1864); Prarthana Samaj — Atmaram Pandurang (Bombay, 1867). This gives 1-b, 2-a, 3-d, 4-c, matching option 2.

BOD stands for Biological Oxygen Demand — the amount of dissolved oxygen aerobic microorganisms need to decompose organic matter in a water sample, usually measured over 5 days at 20°C. A high BOD signals heavy organic pollution and low water quality, making it a key indicator in water and wastewater analysis.

Alveoli are tiny, thin-walled air sacs at the ends of the bronchioles in the lungs, where oxygen diffuses into the blood and carbon dioxide passes out for exhalation. Since this gas exchange is the defining function of breathing, alveoli belong to the Respiratory system. The circulatory system only transports the gases exchanged at the alveoli; it does not contain them.

All three pairings are factually correct: the Golden Revolution covers honey and overall horticulture (fruits, vegetables, flowers); the Blue Revolution denotes the rapid rise in aquaculture and fisheries; and the Yellow Revolution targets edible-oil production, especially mustard and sesame seeds. Since no statement is wrong, the incorrect pair is None of them.

At the 64th National Film Awards (announced in 2017 for films of 2016), the Best Actress award went to Surabhi Lakshmi for her performance in the Malayalam film Minnaminungu (The Firefly). Taapsee Pannu, Trisha Krishnan and Anushka Shetty did not win the Best Actress National Award that year.

Sachin Tendulkar's autobiography is titled "Playing It My Way", co-written with Boria Majumdar and released in November 2014, after his retirement from international cricket. The other titles listed are not associated with Tendulkar.

The official currencies are: Bangladesh — Taka (c); Myanmar — Kyat (d); Maldives — Rufiyaa (b); Bhutan — Ngultrum (a). This gives 1-c, 2-d, 3-b, 4-a, matching option 3.

The Sanskrit play Nagananda, which dramatises the Buddhist Jataka tale of Jimutavahana sacrificing himself to save the Nagas from Garuda, was composed by Emperor Harshavardhana (606–647 CE) of the Pushyabhuti dynasty. He also wrote two other Sanskrit plays — Ratnavali and Priyadarshika. Prabhakaravardhana (his father), Chandragupta II and Bindusara are not credited with authoring Nagananda.

John Boyd Dunlop, a Scottish veterinary surgeon, invented the first practical pneumatic rubber tyre in 1888, initially for his son's bicycle. The innovation replaced solid rubber tyres, vastly improving ride comfort and speed, and later became standard on automobiles. He is not associated with the airplane, the car or rubber boots.

The 44th Constitutional Amendment Act, 1978 repealed Article 31 and Article 19(1)(f), which had together made the Right to Property a fundamental right. It was reinserted as Article 300A in Part XII as an ordinary constitutional/legal right, so violations can no longer be challenged directly under Article 32. The Right to life, Right to education and Right to freedom of religion all remain fundamental rights.

Sachin Tendulkar scored his 100th international century — an ODI knock of 114 against Bangladesh in the Asia Cup — on 16 March 2012 at the Sher-e-Bangla National Cricket Stadium, Mirpur (Dhaka). He remains the only cricketer to reach this milestone across formats.

Fundamental Duties are listed in Article 51A (Part IV-A) of the Constitution, added by the 42nd Amendment, 1976. Safeguarding public property [51A(i)], protecting and improving the natural environment [51A(g)] and promoting harmony and the spirit of common brotherhood [51A(e)] are all Fundamental Duties. Protection of freedom of speech and expression, however, is a Fundamental Right guaranteed under Article 19(1)(a), not a duty. Hence it does not come under Fundamental Duties.

Firstly, check the absentees in the qualification given in options (i) B.A. ⇒ Number of absentees = (20/100)(40000000) – (22/100)(35000000) = 8000000 – 7700000 = 300000 (ii) Others ⇒ Number of absentees = (16/100)(40000000) – (14/100)(35000000) = 6400000 – 4900000 = 1500000 (iii) B.Com ⇒ Number of absentees = (21/100)(40000000) – (22/100)(35000000) = 8400000 – 7700000 = 700000 (iv) Now, lets check M.B.B.S because there is a – 3% change in it MBBS ⇒ Number of absentees = (17/100)(40000000) – (14/100)(35000000) = 6800000 – 4900000 = 1900000 Since, MBBS has more number of absentees than all the 3 above ∴ the correct option is 4)

Distance covered by A in 3 seconds = 30 × 3 = 90 m Relative velocity of B w.r.t. A = (50 – 30) m/s = 20 m/s Now, taking A to be at rest, B has to cover 90 m to catch A ⇒ Time taken by B to catch A = 90/20 = 4.5 seconds ⇒ Total distance covered by B = 4.5 × 50 = 225 m = total distance covered by A ⇒ Total distance covered by both A and B = 225 × 2 = 450 m ∴ the correct option is 2)

Step 1 — Set up rates: Let A's and B's one-day work be \(a\) and \(b\). Together they finish in 10 days: \[a+b=\tfrac{1}{10}\] Step 2 — Use the efficiency condition: With A at twice efficiency and B at one-third, they finish in 6 days: \[2a+\tfrac{b}{3}=\tfrac{1}{6}\] Step 3 — Solve: Substitute \(b=\tfrac{1}{10}-a\): \[2a+\tfrac{1}{3}\!\left(\tfrac{1}{10}-a\right)=\tfrac{1}{6}\;\Rightarrow\;\tfrac{5a}{3}=\tfrac{1}{6}-\tfrac{1}{30}=\tfrac{2}{15}\] \[a=\tfrac{2}{25},\quad b=\tfrac{1}{10}-\tfrac{2}{25}=\tfrac{1}{50}\] Step 4 — Individual times: A alone needs \(1/a=\dfrac{25}{2}\) days and B alone needs \(1/b=50\) days. Therefore the answer is 25/2, 50.

Step 1 — Convert the condition: Multiply \(x^2+y^2+z^2=xy+yz+zx\) by 2 and regroup: \[(x-y)^2+(y-z)^2+(z-x)^2=0\] Step 2 — Deduce equality: A sum of real squares is zero only when each square is zero, so \(x=y=z\). Step 3 — Evaluate: Substituting \(y=z=x\): \[\dfrac{7x+3y-5z}{5x}=\dfrac{7x+3x-5x}{5x}=\dfrac{5x}{5x}=1\] Therefore the value is 1.

Step 1 — Reduce the equation: \(\sin 3\theta\sec 2\theta=1\) gives \(\sin 3\theta=\cos 2\theta=\sin(90^\circ-2\theta)\). Step 2 — Solve for θ: Taking \(3\theta=90^\circ-2\theta\) gives \(5\theta=90^\circ\), so \(\theta=18^\circ\). Step 3 — Evaluate: \(\dfrac{5\theta}{2}=45^\circ\), so \(\tan^2(45^\circ)=1\). Therefore \(3\tan^2(5\theta/2)-1=3(1)-1=\mathbf{2}\).

A number is divisible by 4 iff its last two digits form a number divisible by 4. So M4 must be divisible by 4. Checking the options: 04 = 4 (divisible), 14 (no), 34 (no), 54 (no). Only M = 0 works.

Step 1 — Find the principal: For 2 years, \(CI-SI=P\left(\dfrac{R}{100}\right)^2\). \[200=P\left(\dfrac{20}{100}\right)^2=\dfrac{P}{25}\implies P=5000\] Step 2 — SI for 1st year: \(\dfrac{5000\times 20\times 1}{100}=1000\). Step 3 — CI for 1st year, half-yearly (rate 10%, 2 periods): \(5000\left(1.1\right)^2-5000=6050-5000=1050\). Therefore the difference is Rs. 1050 − 1000 = Rs. 50.

⇒ B.Tech's who have filled the form = (18/100) × (40000000) = 7200000 ⇒ MBA’s who were present in the exam = (9/100) × (35000000) = 3150000 ⇒ required difference = 7200000 – 3150000 = 4050000 ∴ the correct option is 3)

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides. \[\dfrac{\text{Perimeter }\triangle ABC}{\text{Perimeter }\triangle DEF}=\dfrac{AB}{DE}=\dfrac{12}{8}=\dfrac{3}{2}\] Therefore the required ratio is 3 : 2.

Step 1 — Solve for θ: \(\tan\theta=\cot\theta=\dfrac{1}{\tan\theta}\Rightarrow \tan^2\theta=1\). Since θ is acute, \(\tan\theta=1\), so \(\theta=45^\circ\). Step 2 — Evaluate: Interpreting the expression as \(\tan^{26}\theta+\cot^{100}\theta\), both \(\tan 45^\circ=1\) and \(\cot 45^\circ=1\), so the value is \(1^{26}+1^{100}=1+1=\mathbf{2}\).

⇒ Number of B.Arch students who filled the form = (50/100)(16/100)(40000000) = 3200000 ⇒ Number of B.Arch students who were present = (45/100)(14/100)(35000000) = 2205000 ⇒ Number of B.Arch students who did not gave the exam = 3200000 – 2205000 = 995000 ∴ the correct option is 1)

Let \(y=x-3\), so \(y+\dfrac{1}{y}=4\). Using \(\left(y+\dfrac{1}{y}\right)^3=y^3+\dfrac{1}{y^3}+3\left(y+\dfrac{1}{y}\right)\): \[y^3+\dfrac{1}{y^3}=4^3-3(4)=64-12=52\] Therefore \((x-3)^3+\dfrac{1}{(x-3)^3}=\mathbf{52}\).

For an equilateral triangle of side \(a\): \(R=\dfrac{a}{\sqrt{3}}\), \(r=\dfrac{a}{2\sqrt{3}}\). Step 1 — Set up: \(\pi R^2+\pi r^2=\pi a^2\left(\dfrac{1}{3}+\dfrac{1}{12}\right)=\dfrac{5\pi a^2}{12}=770\). Step 2 — Solve for a² (taking \(\pi=22/7\)): \[a^2=\dfrac{770\times 12\times 7}{5\times 22}=588\] Step 3 — Area: \(\dfrac{\sqrt{3}}{4}\times 588=\mathbf{147\sqrt{3}}\) cm².

Let original price = \(P\) Re. A 33.33% (= 1/3) rise makes the new price \(\dfrac{4P}{3}\). Original quantity for Rs. 16 = \(\dfrac{16}{P}\); new quantity = \(\dfrac{16\times 3}{4P}=\dfrac{12}{P}\). Difference = 4 apples: \(\dfrac{16}{P}-\dfrac{12}{P}=\dfrac{4}{P}=4\Rightarrow P=1\) Re = 100 paise.

Given,18% of total people who have filled the forms are doing MBBS ⇒ Total number of MBBS students who have filled the form = (17/100)(40000000) ⇒ Total number of MBBS students from XYZ university who have filled the form = (18/100)(17/100)(40000000) ⇒ required value = 1224000 ∴ the correct option is 2)

Let staff be \(5x,3x\) and average salaries \(7y,8y\). Initial expenditure = \(35xy\); final = \(24xy\); saving = \(11xy=55000\), so \(xy=5000\). Therefore initial expenditure = \(35\times 5000=\) Rs. 1,75,000.

Let diagonals AC and BD intersect at O. Since diagonals of a parallelogram bisect each other, O is the midpoint of AC — making BO a median of \(\triangle ABC\) and DO a median of \(\triangle ADC\). The centroid divides a median in 2:1 from the vertex, so \(PO=\dfrac{1}{3}BO\) and \(QO=\dfrac{1}{3}DO\). P, O, Q are collinear on BD. \[PQ=PO+QO=\dfrac{1}{3}(BO+DO)=\dfrac{BD}{3}=\dfrac{36}{3}=\mathbf{12}\text{ cm}\]

Step 1 — Find x: \(2x^2+3x-90=0\) factors as \((x-6)(2x+15)=0\). Since \(x>0\), \(x=6\). Step 2 — Find y: Treating the equation as \(9y^{-1/2}=y^{1/2}\) gives \(y=9\). Therefore \(x^2+y^2=36+81=\mathbf{117}\).

Divide numerator and denominator by \(y^2\) so the expression becomes \(7\left(\dfrac{x}{y}\right)^2-19\left(\dfrac{x}{y}\right)+11\). Substituting \(\dfrac{x}{y}=\dfrac{4}{9}\): \[7\cdot\dfrac{16}{81}-19\cdot\dfrac{4}{9}+11=\dfrac{112-684+891}{81}=\dfrac{319}{81}\] Therefore the value is 319/81.

Connect line CF. Then area of triangle DFC = 1/2 × DF × EC = 1/2 × 40 × 60 = 1200 cm 2 We know that area of a triangle is twice the area of the rectangle, which has same base and altitude as those of rectangle. Since ΔDFC has same base and altitude as ABCD. ⇒ Area of rectangle ABCD = 2 × area of triangle DFC ⇒ Area of rectangle ABCD = 2 × 1200 = 2400 cm 2

For successive discounts \(D_1,D_2\), net discount = \(D_1+D_2-\dfrac{D_1 D_2}{100}\). \[=15+35-\dfrac{15\times 35}{100}=50-5.25=\mathbf{44.75\%}\]

Adding the three equations: \((a+b)+(b+c)+(c+a)=5+7.5+8.5=21\), so \(2(a+b+c)=21\) and \(a+b+c=10.5\). Therefore the average = \(\dfrac{10.5}{3}=\mathbf{3.5}\).

If the side rises by \(k\%\), the area scales by \(\left(1+\dfrac{k}{100}\right)^2\). A 69% area rise means this factor equals 1.69. \[1+\dfrac{k}{100}=\sqrt{1.69}=1.3\implies k=\mathbf{30}\]

For an equilateral triangle of side \(a\), the circumradius and in-radius are: \[R=\frac{a}{\sqrt{3}},\quad r=\frac{a}{2\sqrt{3}}\] Step 1 — Substitute a = 12: \[R=\frac{12}{\sqrt{3}}=4\sqrt{3}\text{ cm},\quad r=\frac{12}{2\sqrt{3}}=2\sqrt{3}\text{ cm}\] Step 2 — Take the difference: \[R-r=4\sqrt{3}-2\sqrt{3}=2\sqrt{3}\text{ cm}\] Hence the required difference is 2√3 cm.

Use the parity rules: sine is odd, cosine is even, so \(\sin(-\theta)=-\sin\theta\) and \(\cos(-\theta)=\cos\theta\). \[\sin\!\left(-\tfrac{\pi}{3}\right)+\cos\!\left(-\tfrac{\pi}{6}\right)=-\sin\tfrac{\pi}{3}+\cos\tfrac{\pi}{6}=-\tfrac{\sqrt{3}}{2}+\tfrac{\sqrt{3}}{2}=0\] Therefore the value is 0.

The verb approve, when expressing agreement with or favourable opinion of something, takes the preposition of ("approve of the plan/idea/decision"). "Approve to" and "approve with" are not standard collocations, and "one" is not a preposition. The completed sentence reads: "My father did not approve of the plan...". Hence the answer is of.

The error lies in part (3). With "ever" describing a past state contrasted with the present popularity of organic pulses, the simple past is required, not the present perfect. Replace "have ever lived" with "ever lived": "...how they ever lived without them." The construction "wonder how they ever lived without X" is the idiomatic form. Hence the answer is 3.

The pattern "When + past simple, past continuous" describes a shorter past action (seeing Ankit) occurring while a longer action (playing cricket) was in progress. "Was playing" correctly conveys this ongoing background action. "Had played" (past perfect) and "played" (simple past) suggest a completed action; "had been playing" emphasises duration up to that point, which is not required here. Hence No improvement is needed.

Sentence Q introduces the topic ("Crude mineral oil") and must open. R follows with the pronoun "It" referring back to crude oil and describing it as a complex mixture. P then explains those substances — "Most of them are combinations of hydrogen and carbon". S closes with "Such hydrocarbons", picking up the hydrocarbons just introduced in P. Hence the correct order is QRPS.

The idiom "to steal a march" means to gain an advantage over a rival, typically by acting before they do — effectively surpassing or outdoing them. Among the options, "To outshine" (to surpass or do better than others) best captures this sense of gaining the upper hand. The other choices — acting foolishly, breaking something, seeing a hidden meaning — are unrelated.

Intrepid means fearless, bold, and undaunted by danger. Its antonym must convey timidity or lack of courage. Meek — quiet, submissive, easily intimidated — is the direct opposite. "Greed" denotes desire, "kind" denotes generosity, and "sigh" is an exhalation; none contrast with bravery. Hence the answer is Meek.

The misspelt word is Alluminium. The correct British spelling is Aluminium (with a single "l"), and American English uses Aluminum; the double "l" in "Alluminium" is wrong. "Cemetery", "Recommend" (double m), and "Satellite" (double l, single t-l-e) are all spelt correctly.

The blank requires an adjective stressing necessity, since the sentence argues that preventing infections and diseases is crucial for children's health. Imperative means absolutely essential or crucial — the strongest fit. "Optional" and "voluntary" suggest a free choice; "secondary" implies lesser importance — all contradict the tone of urgency. Hence the answer is imperative.

Dauntless means fearless, bold, and not easily intimidated — a person who confronts danger without flinching. The closest synonym is Brave, which likewise denotes courage in the face of difficulty. "Insane" (mentally unsound), "playful" (lighthearted), and "ugly" (unpleasant in appearance) are unrelated to courage. Hence the answer is Brave.

Sentence R defines self-esteem ("how much you value yourself") and opens the paragraph. S extends the definition — "It's how you see yourself and feel about your achievements" — with "It" referring back to self-esteem. P then clarifies what self-esteem is NOT ("isn't bragging"). Q continues the negative-then-positive contrast ("not about thinking you're perfect... but knowing you're worthy"), giving a fitting close. Hence the order is RSPQ.

The error is in part (1). The sentence is a Type 1 conditional, whose structure is "If + simple present, ... will + base verb". The main clause "they will not come" requires the if-clause to use the simple present: If it rains, not If it would rains. "Would" is incorrect in this if-clause — it neither fits Type 1 nor Type 2 (which would need "If it rained, they would not come"). Hence the answer is 1.

Dromomania — from Greek dromos (running, course) + mania — is the precise term for an uncontrollable impulse to wander or travel. "Hypomania" is a mild mood-elevation state; "Megalomania" is an obsession with power or grandeur; "Nymphomania" denotes excessive sexual desire. None relate to travel. Hence the answer is Dromomania.

The blank describes measures taken to prevent infections and diseases — that is, actions taken in advance to ward off harm. The word that captures this is precautionary ("done as a precaution"). "Scientific" describes the nature, not the purpose, of such measures; "unimportant" and "insignificant" contradict the passage's emphasis on the importance of hygiene. Hence the answer is precautionary.

Abeyance means a state of temporary disuse, inactivity, or suspension — something put on hold rather than ended. Suspension shares this exact sense of a temporary halt, making it the correct synonym. Commencement means beginning (opposite), perjury is lying under oath, and condone means to overlook wrongdoing — none relate to a temporary pause.

The preposition in is used with large geographical areas such as countries, states, and cities. Since Canada is a country, the correct usage is "settled in Canada". At is used for specific points or addresses, on for surfaces or streets, and off denotes separation — none fit a country.

Clandestine means secret, concealed, or done in a hidden manner. Its antonym must convey the opposite — something public or unconcealed. Open means visible, public, and not hidden, making it the direct antonym. Abrupt (sudden), illicit (forbidden — often associated with clandestine, not opposite), and wary (cautious) do not express the opposite of "secret".

The main clause "he goes to gym" is in the simple present tense, indicating a habitual action. For tense consistency in a routine, the subordinate clause introduced by "after" must also take the simple present. Hence the correct form is "After he arrives", giving "After he arrives from office, he goes to gym." Past ("arrived") and past perfect ("had arrived") clash with the present-tense main verb; "had being arriving" is ungrammatical.

The idiom "in a jiffy" means in a very short time — something done extremely quickly or instantly (e.g., "I'll be back in a jiffy"). Hence the correct substitute is "Something that is done very quickly". The other options describe unrelated ideas — lack of appreciation, propriety, or falling in love.

When a yes/no question in direct speech is reported, the reporting verb "said to" becomes asked, and the question is introduced by if/whether. The tense shifts back: present perfect ("Have you brought") becomes past perfect ("had brought"), and "you/your" change to "he/his". Applying these rules: "The teacher asked the student if he had brought his lunch." Option 4 wrongly keeps the present perfect ("has brought"); option 2 alters the meaning to a future continuous; option 1 omits the if-clause structure.

Correct Answer : habit ‘Habit’ means a regular tendency or routine. The passage emphasises on the importance of hygiene to children so that it becomes their routine. The other words do not convey the intended meaning correctly.

Susceptible means likely to be influenced, affected, or harmed by something — in a medical context, vulnerable to illness. Since children's immune systems are still developing, they are particularly vulnerable to hygiene-related issues. Thus the sentence reads: "Children are the most susceptible to hygiene-related disorders…" Innocent, responsible, and pliable do not convey medical vulnerability.

The passage stresses preventing hygiene-related disorders, so children must be taught which unhygienic actions to stay away from — i.e., what to avoid (dirty hands, sharing items, unwashed food). "Read" and "learn" are too vague for preventive instruction, and "right" is grammatically incorrect after "what to". Hence avoid fits best.

A parvenu (from French "arrived") is a person who has recently and suddenly acquired wealth, power, or social status — matching the phrase exactly. Egotist is a self-centred person, imposter is someone pretending to be another, and scullery is a small kitchen room — none describe sudden upward mobility.

Checking each spelling: Acquiescence, Alienate, and Belligerent are all spelt correctly. Sabbotage is incorrect — the correct spelling is Sabotage (single 'b'), meaning to deliberately destroy or obstruct. Hence option 4 is the misspelt word.

The active sentence "He shall have bought a car" is in the future perfect tense. The passive structure for this tense is: Object + shall/will have been + past participle + by + subject. Applying it: "A car" (new subject) + "will have been bought" + "by him" gives "A car will have been bought by him." Options 1 and 2 use past tenses, and option 4 uses the conditional "would have been", none of which match future perfect.