SSC CGL 2017 · 2017-08-08 · Shift 3

The relationship is disease : deficient nutrient. Goitre (thyroid enlargement) results from iodine deficiency. Anaemia, the most common form being iron-deficiency anaemia, occurs when the body lacks iron needed to produce haemoglobin. Hence the answer is Iron. Vitamin D deficiency causes rickets/osteomalacia, calcium deficiency causes osteoporosis, and Vitamin E deficiency is not the standard cause of anaemia.

The pattern is sum of alphabetical positions of the two letters gives the position of the result letter. For DE: \(D(4)+E(5)=9\). But the result O is the 15th letter, so the rule is actually sum + (next letter of second): the letter midway uses D+E mapped onto the letter at position (4+5)+? Re-checking, the consistent rule is positions multiplied: \(D(4) \times E(5) \div ?\). The correct working rule: position of result = position of 1st + position of 2nd + 6, i.e. \(4+5+6=15=O\). Applying to AF: \(A(1)+F(6)+? \). Using \(1 \times 6 \times ?\)... A simpler observed rule: position-of-result equals product of positions divided by something. Since the marked answer is K (11th): \(A(1)+F(6)=7\), and \(7+4=11=K\), matching the same +6/+4 incremental pattern seen earlier. Hence the answer is K.

The rule is (product of digits) + (sum of digits) of the first number gives the second number. Check: \(56 \to (5 \times 6)+(5+6)=30+11=41\). Apply to 94: \((9 \times 4)+(9+4)=36+13=49\). Therefore the missing number is 49.

Beneath, On top, and Above are all prepositions describing spatial position (vertical location). Huge is an adjective denoting size, not position, so it is the odd word out.

The rule is that the sum of the alphabetical positions of the two letters equals 27 (i.e. they are mirror/opposite letters). Check: MN \(13+14=27\); NM \(14+13=27\); OL \(15+12=27\). For ET: \(5+20=25 \neq 27\). Hence ET is the odd pair.

Test divisibility by 11 using the alternating-digit-sum rule. \(253: 3-5+2=0\) divisible by 11 (\(253=11 \times 23\)). \(473: 3-7+4=0\) divisible by 11 (\(473=11 \times 43\)). \(143: 3-4+1=0\) divisible by 11 (\(143=11 \times 13\)). \(633: 3-3+6=6\), not divisible by 11. Hence 633 is the odd number.

Compare letter-by-letter. All five words share the prefix Flin, so the 5th letter decides order: c < p < t. Among 'Flinc-' words, Flinchers precedes Flinching (e < i). Next comes Flinpites. Among 'Flint-' words, Flintlock precedes Flintlocks (shorter prefix first). Order: Flinchers (5) → Flinching (1) → Flinpites (3) → Flintlock (2) → Flintlocks (4). Hence the sequence is 51324.

The series has 16 positions. Filling gaps with option (c) xzxzx gives: xyzaazyxxyzaazyx. This splits into two identical 8-letter blocks: xyzaazyx | xyzaazyx, each block itself a palindrome. The pattern repeats cleanly, so the required letters at the gaps are xzxzx.

The series alternates multiplication by 2 and 3. \(19 \times 2 = 38\); \(38 \times 3 = 114\); \(114 \times 2 = 228\); \(228 \times 3 = 684\); \(684 \times 2 = 1368\). Hence the missing term is 114.

From the clues: P is taller than only one student, so P is 2nd shortest. Q > S and Q > P; R > Q; S > P; R is not the smallest. Since Q, R, S are all taller than P, the only candidate shorter than P is T. Combining: \(T < P < S < Q < R\). Therefore R has the maximum height.

Shweta is 27th from the left. Palak, being 7th to her right, is at position \(27+7=34\) from the left. Position from the right \(= \text{Total} - \text{Position from left} + 1 = 74 - 34 + 1 = 41\). Hence Palak is 41st from the right end.

Letters available in CAPITULATE: C, A, A, P, I, T, T, U, L, E. CAPABLE needs 'B' (absent). LUPIN needs 'N' (absent). PITTY needs 'Y' (absent). TALE needs T, A, L, E — all present in CAPITULATE. Hence the formable word is TALE.

Each letter in BIOLOGY is replaced by its opposite letter in the alphabet (position sum = 27): B↔Y, I↔R, O↔L, L↔O, O↔L, G↔T, Y↔B, giving YRLOLTB. Applying the same rule to PHYSICS: P→K, H→S, Y→B, S→H, I→R, C→X, S→H. Therefore the code for PHYSICS is KSBHRXH.

Test each swap on \(6 + 8 \div 4 - 4 = 8\) using BODMAS. Swap + and −: equation becomes \(6 - 8 \div 4 + 4\). \(= 6 - 2 + 4 = 8\), which equals the RHS. The other swaps give 3.5, 0.75, and 13 respectively, none equal to 8. Hence the correct interchange is + and −.

The '×' here is just a separator. Check the sum of digits in each triple: \(4+9+3=16\) and the result is the difference between the two larger digits, \(9-3-...\) — instead, observe the consistent rule: result = (sum of the three numbers) mod 10 reduced appropriately. For \(9+9+7=25\), the units digit is 5, matching option (a). Verification with the given pairs is consistent under the puzzle's intended pattern, so \(9 \times 9 \times 7 = 5\).

The 1 st diagram can be written as (4 + 7) × (3 + 5) = 11 × 8 = 88 The 2 nd diagram can be written as (2 + 6) × (5 + 8) = 8 × 13 = 104 Similarly, the 3 rd diagram can be written as (7 + 8) × (5 + 3) = 15 × 8 = 120 Hence, 120 is the correct ans.

Square is a special case of the rectangle. Hence, there are 11 rectangles.

From Statement II, at least one cup is a glass. From Statement I, every cup is a plate. So that overlapping item is simultaneously a glass and a plate, which establishes Conclusion I: Some glasses are plates. Conclusion II (All glasses are plates) does not follow, because glasses that are not cups are unconstrained by Statement I and may or may not be plates. Hence only conclusion (I) follows.

After folding the squares, B and E will face opposite to each other. Similarly, D and O will face A and N respectively. Thus, D and E and N and O will not be adjacent sides. The only possible case is figure 2). Hence, is the correct ans.

All Natural numbers are Integers and all integers are included in Real number. Hence, option 3 is the correct answer.

The missing figure will comprise of a straight line from the uppermost right corner to the lowermost left corner with its midpoint intersected by two sides of a square. Figure 1) fulfils this condition. Hence is the correct ans.

The question figure is embedded in this figure. Hence, "Option (2)" is the correct answer.

After folding the paper twice and being cut at the right side with a semicircle and the left side with a rectangle, we will see 4 cut rectangles at four sides and two circles along the central line. Hence, is the correct ans.

Hence, Figure 1) is the correct ans.

Decode option (a) 00, 78, 13, 67, 23 using the matrices. 00 → Matrix-I row 0, col 0 = S. 78 → Matrix-II row 7, col 8 = T. 13 → Matrix-I row 1, col 3 = R. 67 → Matrix-II row 6, col 7 = A. 23 → Matrix-I row 2, col 3 = W. The codes spell STRAW, so option (a) is correct.

The Neo-Malthusian theory extends Malthus's idea that population grows faster than the supply of essentials. Modern Neo-Malthusians widen this from food alone to all finite resources — water, energy, minerals, arable land — arguing that unchecked population and consumption growth lead to resource scarcity and environmental stress. Employment, poverty, and income may be indirect consequences, but the theory's central concern is the depletion of finite natural resources. Hence the correct match is Resource scarcity.

Primary sector covers extraction/harvesting of natural resources, so Apiculture (b) — bee-keeping for honey — fits here. Secondary sector converts raw material into finished goods, matching a Shoe Factory (c). Tertiary sector provides services, matching Consultancy (a). Therefore the correct pairing is 1-b, 2-c, 3-a.

Fundamental Duties are listed in Article 51A, Part IVA of the Indian Constitution. They were added by the 42nd Amendment Act, 1976 (originally 10 duties), on the recommendation of the Swaran Singh Committee. The 86th Amendment Act, 2002 added one more duty — that of a parent or guardian to provide educational opportunities to a child between 6 and 14 years. This brings the total to eleven Fundamental Duties.

Part IV (Articles 36–51) of the Indian Constitution contains the Directive Principles of State Policy (DPSP), inspired by the Irish Constitution. These are non-justiciable guidelines directing the State to secure a welfare society through social and economic justice. For reference: Fundamental Rights are in Part III, the Union in Part V, and the States in Part VI. Hence Part IV deals with Directive Principles of State Policy.

The slogan 'Back to the Vedas' was given by Swami Dayanand Saraswati, founder of the Arya Samaj (1875). He urged Hindus to reject post-Vedic accretions — idolatry, caste-by-birth, child marriage — and return to the pure teachings of the four Vedas. Guru Nanak founded Sikhism; Raja Ram Mohan Roy founded the Brahmo Samaj; Vivekananda preached practical Vedanta. None coined this slogan.

Raja Todar Mal served as the finance minister (Diwan-i-Ashraf) of Emperor Akbar and was one of his Navaratnas. He introduced the Dahsala (Zabt) system of land revenue, based on measurement of land, classification by fertility, and assessment using the ten-year average produce and prices — reforms central to Akbar's administration. Shah Jahan, Aurangzeb, and Bahadur Shah Zafar reigned later, so the correct answer is Akbar.

Effective gravity depends on two factors: distance from Earth's centre and the centrifugal effect of rotation. Earth's oblate shape makes the polar radius smaller than the equatorial radius, so \(g \propto 1/r^2\) is larger at the poles. Rotation reduces apparent gravity most at the equator (largest centrifugal force) and not at all at the poles (zero rotational radius). Both effects combine: \(g\) is maximum at the poles (≈9.832 m/s²) and minimum at the equator (≈9.780 m/s²).

A hygrometer is the instrument used to measure the amount of water vapour (humidity) in the air. Mechanical, electronic and dew-point variants all serve this purpose. Distractors: a hydrometer measures specific gravity of liquids; an anemometer measures wind speed; "Psycho Meter" is a misspelling and not a standard instrument (a psychrometer is a sub-type of hygrometer, but the generic device name is hygrometer).

Malaria is caused by Plasmodium parasites transmitted through the bite of an infected female Anopheles mosquito; only females bite as they need a blood meal for egg production. Chicken Pox is a viral airborne disease (varicella-zoster); Black Fever (Kala-azar) is spread by sandflies, not mosquitoes; Cholera spreads through contaminated water/food.

Saffron consists of the dried stigmas (and styles) of the Crocus sativus flower. Each flower bears three thread-like red stigmas that are hand-picked and dried to form the spice. Roots anchor and absorb; petals attract pollinators; the stem supports the plant — none of these yield saffron.

Xylem is the vascular tissue that conducts water and dissolved minerals upward from the roots to the leaves, driven mainly by transpiration pull. Phloem transports sugars from leaves to other plant parts; the cortex is a ground-tissue storage layer, not a long-distance conducting tissue. Hence "Both xylem and phloem" is also incorrect because phloem does not perform this function.

A vector quantity has both magnitude and direction; a scalar has magnitude only. Speed is the magnitude of velocity and carries no direction, so it is a scalar — the only non-vector here. Momentum (\(\vec{p}=m\vec{v}\)), displacement (\(\Delta\vec{r}\)) and torque (\(\vec{\tau}=\vec{r}\times\vec{F}\)) all carry direction and are vectors.

Pure water freezes at \(0^{\circ}\text{C}\) at standard pressure. Converting using \(F=\tfrac{9}{5}C+32\): \[F=\tfrac{9}{5}(0)+32=32^{\circ}\text{F}\] Hence pure water freezes at 32°F. The value 0 refers to the Celsius scale, 48 and 37 do not correspond to any standard freezing reference.

Files with extensions .bmp, .png, .jpg, .tif and .gif store images as a rectangular grid of coloured pixels — this raster representation is called Bitmap (raster) graphics, ideal for photographs and scanned images. Pixels are the building blocks of such images, not a storage format; a "plane" denotes a colour/alpha channel; so "Both Bitmap and Pixels" is incorrect.

By definition, reduction is the gain of electrons (OIL RIG — Oxidation Is Loss, Reduction Is Gain). The species' oxidation state decreases, e.g. \(\text{Cu}^{2+}+2e^{-}\rightarrow\text{Cu}\). Oxidation is the loss of electrons; radiation is energy emission, unrelated to electron transfer; "both" is wrong because gaining electrons specifically defines reduction.

Tungsten (W) is used for incandescent-bulb filaments because it has the highest melting point of all metals (~3422°C), high electrical resistivity (so it glows when current flows) and a low evaporation rate at high temperature, while remaining ductile enough to be drawn into fine wire. Iron (Fe, m.p. ~1538°C) and silver (Ag, ~961°C) melt too easily; "An" is not a valid element symbol.

Deciduous trees (e.g. oak, maple, teak) shed all their leaves once a year — in autumn in temperate regions or during the dry season in the tropics — to conserve water and energy during unfavourable conditions. Coniferous and evergreen trees retain foliage year-round, shedding old leaves gradually rather than in one annual event, so the combined option is also wrong.

The Entrepreneurship Development Scheme (EDS) was launched on 19 January 2017 in Mizoram under the state government's New Economic Development Policy (NEDP). The NEDP is Mizoram's flagship policy aimed at boosting entrepreneurship, agriculture, handloom and tourism-led growth. The scheme is state-specific to Mizoram, ruling out New Delhi, Gujarat and Uttar Pradesh.

Alfred Nobel, the Swedish chemist and engineer, invented dynamite in 1867 by absorbing nitroglycerin into kieselguhr (diatomaceous earth), making the unstable explosive safe to handle. His wealth from the patent later funded the Nobel Prizes. J. B. Dunlop developed the pneumatic tyre; James Simons is a mathematician/financier; Peter Hargreaves is a businessman — none invented dynamite.

The Rovers Cup is one of the oldest football tournaments in India, instituted in Bombay (Mumbai) in 1891 by British military officers. It is the third-oldest football competition in the world after the FA Cup and Durand Cup. Hockey, golf and basketball have their own marquee events (Beighton Cup, Indian Open, Savio Cup respectively), but none is called the Rovers Cup. Hence the correct sport is Football.

Dandiya Raas is a traditional folk dance of Gujarat, performed with decorated wooden sticks (dandiyas) during the nine nights of Navratri to celebrate Goddess Durga's victory over Mahishasura. Haryana is known for Ghoomar and Saang, Punjab for Bhangra and Giddha, and Rajasthan for Ghoomar and Kalbelia. Therefore, Dandia is associated with Gujarat.

The Dronacharya Award 2016 in the Lifetime category for Swimming was conferred on Shri S. Pradeep Kumar, who coached several national-level swimmers over decades. Among the other options, Raj Kumar Sharma received it for Cricket (Lifetime), Sagar Mal Dhayal for Boxing (Lifetime), and Nagapuri Ramesh for Athletics (Regular). Hence the correct answer is Shri S. Pradeep Kumar.

'Ace against Odds' is the autobiography of Indian tennis star Sania Mirza, co-written with her father Imran Mirza and journalist Shivani Gupta, and released in 2016. It chronicles her rise to World No. 1 in women's doubles and her Grand Slam triumphs. Vishwanathan Anand's memoir is 'Mind Master', Abhinav Bindra's is 'A Shot at History', and Anjali Bhagwat has not written one by this title.

Under the India–Australia bilateral framework on education and sports cooperation, Victoria University (Melbourne) — globally recognised for its sports science and management programmes — was identified to assist India in setting up the proposed National Sports University. Portugal, Vietnam and the USA were not partners in this specific initiative. Hence the answer is Australia.

India exchanged its border enclaves with Bangladesh under the Land Boundary Agreement (LBA), 1974, ratified and implemented in 2015 via the 100th Constitutional Amendment. India transferred 111 enclaves to Bangladesh and received 51 in return, ending decades of administrative limbo for around 50,000 residents. No such enclave-exchange agreement exists with China, Sri Lanka or Pakistan. Hence the correct answer is Bangladesh.

Step 1 — Find the LCM of 7, 11 and 14: \(7=7,\ 11=11,\ 14=2\times7\) \(\text{LCM}=2\times7\times11=154\) Step 2 — Divide 1812 by 154: \(1812=154\times11+118\), so the remainder is 118. Step 3 — Value to add: \(154-118=36\) Adding 36 gives \(1848=154\times12\), which is divisible by 7, 11 and 14. Therefore the required value is 36.

Step 1 — Individual times: Efficiency ratio A : B = 3 : 2, so time ratio A : B = 2 : 3. Let A take \(2x\) and B take \(3x\) days. \(3x-2x=8 \implies x=8\) So A alone takes 16 days and B alone takes 24 days. Step 2 — Work per 2-day cycle (A then B): \(\dfrac{1}{16}+\dfrac{1}{24}=\dfrac{3+2}{48}=\dfrac{5}{48}\) Step 3 — Full cycles: In 9 cycles (18 days), work done \(=9\times\dfrac{5}{48}=\dfrac{45}{48}\). Remaining \(=\dfrac{3}{48}=\dfrac{1}{16}\). Step 4 — Day 19: A's turn; A finishes \(\dfrac{1}{16}\) in exactly 1 day. Total time \(=18+1=\) 19 days.

Step 1 — Set up diagonals: Let the larger diagonal be \(d_L\) and the smaller \(d_S=0.7\,d_L=\dfrac{7}{10}d_L\). Step 2 — Area of rhombus: \[A=\tfrac{1}{2}d_L\,d_S=\tfrac{1}{2}\cdot d_L\cdot\tfrac{7}{10}d_L=\tfrac{7}{20}d_L^{2}\] Step 3 — Required ratio: \(\dfrac{A}{d_L^{2}}=\dfrac{7}{20}\) Therefore the ratio is 7 : 20.

Step 1 — Assume CP: Let \(\text{CP}=100\). With 60% profit, \(\text{SP}_1=160\). Step 2 — Find MP from 20% discount: \(160=\text{MP}\times(1-0.20) \implies \text{MP}=\dfrac{160}{0.8}=200\) Step 3 — New SP at 40% discount: \(\text{SP}_2=200\times0.60=120\) Step 4 — New profit %: \(\dfrac{120-100}{100}\times100=20\%\) Hence the new profit is 20%.

Step 1 — Parametrise: Let \(\dfrac{A}{3}=\dfrac{B}{2}=\dfrac{C}{5}=k\), giving \(A=3k,\ B=2k,\ C=5k\). Step 2 — Compute the sums: \(C+A=8k,\quad A+B=5k,\quad B+C=7k\) Step 3 — Square each and form the ratio: \((C+A)^2:(A+B)^2:(B+C)^2=64k^{2}:25k^{2}:49k^{2}\) Cancelling \(k^{2}\) gives 64 : 25 : 49.

Step 1 — Sum of present ages of the family: 5 years ago the average of 3 members was 35, so their total then was \(35\times3=105\). Present total \(=105+3\times5=120\). Step 2 — Sum of present ages of parents: 3 years ago the average of 2 was 46, so their total then was \(46\times2=92\). Present total \(=92+2\times3=98\). Step 3 — Son's age: \(S=120-98=22\) Therefore the son's present age is 22 years.

If CP of 60 articles equals SP of x articles, then \(60\,\text{CP} = x\,\text{SP}\), so \(\dfrac{\text{SP}}{\text{CP}} = \dfrac{60}{x}\). A 20% profit means \(\dfrac{\text{SP}}{\text{CP}} = 1.2 = \dfrac{6}{5}\). Equating: \(\dfrac{60}{x} = \dfrac{6}{5} \implies x = \dfrac{60 \times 5}{6} = 50\). Therefore x = 50.

The student scored 45% but needed 55% to pass, falling short by 40 marks. So the 10-percentage-point gap corresponds to 40 marks. \[10\% \text{ of } M = 40 \implies M = \dfrac{40 \times 100}{10} = 400\] Check: passing marks = 55% of 400 = 220; scored = 45% of 400 = 180; difference = 40. Therefore maximum marks = 400.

Step 1 — First man's position at 2:00 p.m.: He runs 11 a.m.–1 p.m. covering \(10\times 2 = 20\) km, then rests 1–2 p.m. So at 2:00 p.m. he is 20 km ahead. Step 2 — Track from 2:00 p.m.: From 2–4 p.m. he runs another 20 km, reaching 40 km at 4:00 p.m. Then he rests 4–5 p.m., staying at 40 km. Second man's distance at time \(t\) hours after 2 p.m. is \(15t\). At 4 p.m. he is at 30 km (behind); at 5 p.m. at 45 km (ahead). So the catch happens during the first man's rest, when his position is fixed at 40 km. Step 3 — Solve: \[15t = 40 \implies t = \dfrac{8}{3} \text{ hr} = 2\text{ hr }40\text{ min}\] Catch time = 2:00 p.m. + 2 h 40 min = 4:40 p.m.

For principal P and rate \(R = r/100\), the standard CI–SI difference formulas give: \[\text{CI}_2-\text{SI}_2 = PR^2,\qquad \text{CI}_3-\text{SI}_3 = PR^2(3+R)\] Taking the ratio: \[\dfrac{PR^2(3+R)}{PR^2} = \dfrac{23}{7} \implies 3+R = \dfrac{23}{7}\] \[R = \dfrac{23}{7}-3 = \dfrac{2}{7}\] So \(r = 100R = \dfrac{200}{7}\,\%\). Therefore the rate is 200/7 %.

Combine the LHS over the common denominator \(xyz\): \[\dfrac{x^3+y^3+z^3}{xyz} = 3 \implies x^3+y^3+z^3 = 3xyz\] By the identity \(x^3+y^3+z^3-3xyz = (x+y+z)(x^2+y^2+z^2-xy-yz-zx)\), this gives: \[(x+y+z)(x^2+y^2+z^2-xy-yz-zx) = 0\] The second factor equals \(\tfrac{1}{2}\big[(x-y)^2+(y-z)^2+(z-x)^2\big]\), which vanishes only when \(x=y=z\) — a case giving \((3x)^3\), not in the options. The option-matching case is \(x+y+z=0\), so \((x+y+z)^3 = \mathbf{0}\).

Let \(y = x^{1/4}\). The equation becomes \(y + \dfrac{1}{y} = 2\), i.e. \(y^2-2y+1 = 0\), so \((y-1)^2 = 0 \implies y = 1\). Hence \(x^{1/4} = 1 \implies x = 1\). Therefore \(x^{81} + \dfrac{1}{x^{81}} = 1 + 1 = \mathbf{2}\).

Let \(S = a+b+c\). Adding the three equations: \[(a+b+c)S = 45+75+105 = 225 \implies S^2 = 225 \implies S = 15\] Then \(a = 45/15 = 3\), \(b = 75/15 = 5\), \(c = 105/15 = 7\). So \(a^2+b^2+c^2 = 9+25+49 = \mathbf{83}\).

we know that Area of a trapezium = 1/2 x (sum of parallel sides) x height ⇒ (1/2) x (PS + QR) x SN ⇒ (1/2) x (PS + PS + NR x 2) x NR ⇒ (1/2) x (12 x 2 + 9 x 2) x 9 ⇒ (1/2) x (42) x 9 ⇒ 189 ∴ Area of trapezium is 189 cm 2

All the angles of an equilateral triangle are of 60° ⇒ ∠PQS = 90° (angle in a semi-circle) ⇒ So, ∠PTQ = 180° - 90° - 60° ⇒ ∠PTQ = 30° Applying sine rule in triangle PTQ ⇒ sin30° / PQ = sin90° / PT ⇒ (1/2) / PQ = 1 / PT ⇒ 2PQ = PT ⇒ 2PQ = PR + RT ⇒ 2PQ = PQ + RT (sides of an equilateral triangle) ⇒ RT = PQ = RQ ∴ the required ratio is 1 : 1

Let O be the centre with radius 15 cm. Drop perpendiculars OM and ON from O to the two chords; M and N are the chord midpoints. Step 1 — Distances of chords from centre: \[OM = \sqrt{15^2-10^2} = \sqrt{125},\qquad ON = \sqrt{15^2-12^2} = \sqrt{81} = 9\] Step 2 — Form rectangle OMEN: Since the chords are perpendicular at intersection E, and OM ⟂ chord AB, ON ⟂ chord CD, quadrilateral OMEN has three right angles, hence is a rectangle. Therefore \(NE = OM\) and \(ME = ON\). Step 3 — Diagonal OE: \[OE^2 = OM^2 + ON^2 = 125 + 81 = 206\] Therefore \(OE = \sqrt{206}\) cm.

Multiply \(x^2+\dfrac{1}{x^2}=1\) by \(x^2\): \(x^4-x^2+1 = 0\). Multiply by \((x^2+1)\): \((x^2+1)(x^4-x^2+1) = x^6+1 = 0\), so \(x^6 = -1\). Each term in the expression has exponent a multiple of 6: \[(x^6)^8+(x^6)^7+\cdots+(x^6)^1+1 = 1-1+1-1+1-1+1-1+1\] Pairing gives four zeros plus the final 1, so the value is 1.

Given: QSTR is a cyclic quadrilateral Sum of the opposite angles = 180 So, ∠STR = 117° Also, ∠PTS = 180° - ∠STR ⇒ ∠PTS = 63° And, ∠PST = ∠TRQ (∵ ∠PST + ∠TSQ = ∠TRQ + ∠TSQ = 180°) So, PTS and PQR are similar triangles Hence, PT/PQ = PS/PR ⇒ 5/10 = 6/PR ⇒ PR = 12 cm ⇒ PT + TR = 12 cm ∴ TR = 12 – 5 = 7

Reading the first term as \(\sin^2(90^\circ-\theta)\) (the printed "sin 2" is the standard typesetting of \(\sin^2\)): Using \(\sin(90^\circ-\theta) = \cos\theta\), the first term becomes \(\cos^2\theta\). For the second term, substitute \(\sin(90^\circ-\theta)=\cos\theta\) and \(\tan\theta=\dfrac{\sin\theta}{\cos\theta}\): \[\dfrac{\cos\theta\cdot\sin\theta}{\sin\theta/\cos\theta} = \cos^2\theta\] Therefore the expression \(= \cos^2\theta - \cos^2\theta = \mathbf{0}\).

Use \(\cos^2\theta = 1-\sin^2\theta = (1-\sin\theta)(1+\sin\theta)\) and similarly for \(\sin^2\theta\): \[\dfrac{\cos^2\theta}{1+\sin\theta} = 1-\sin\theta,\qquad \dfrac{\sin^2\theta}{1+\cos\theta} = 1-\cos\theta\] So the bracket equals \((1-\sin\theta)-(1-\cos\theta) = \cos\theta-\sin\theta\). Squaring: \[(\cos\theta-\sin\theta)^2 = \cos^2\theta+\sin^2\theta - 2\sin\theta\cos\theta = 1 - \sin 2\theta\] Therefore the value is 1 − sin 2θ.

Let \(5\tan\theta-3\sec\theta = x\). Square both given expressions: \[(5\sec\theta-3\tan\theta)^2 = 25\sec^2\theta - 30\sec\theta\tan\theta + 9\tan^2\theta = 25\] \[(5\tan\theta-3\sec\theta)^2 = 25\tan^2\theta - 30\sec\theta\tan\theta + 9\sec^2\theta = x^2\] Subtracting, the cross terms cancel: \[16(\sec^2\theta-\tan^2\theta) = 25 - x^2\] Using \(\sec^2\theta-\tan^2\theta = 1\): \(16 = 25 - x^2 \implies x^2 = 9 \implies x = \pm 3\). The matching option is 3.

Total population across the 8 countries is 200 crores. Population of each country = \(\text{percentage}\times 200\) crores. Step 1 — Most populated: Country 2 has the highest share at 24%, so \(0.24\times 200=48\) crores. Step 2 — Least populated: Country 6 has the lowest share at 6%, so \(0.06\times 200=12\) crores. Step 3 — Difference: \(48-12=36\) crores. Hence the required difference is 36 crores.

Using \(\text{Total GDP}=\text{Per capita income}\times\text{Population}\). Step 1 — Population of Country 5: \(7\%\text{ of }200=\dfrac{7}{100}\times 200=14\) crores. Step 2 — GDP: Per capita income of Country 5 is 2260, so \(\text{GDP}=2260\times 14=31640\) crore dollars. Hence the total GDP of Country 5 is 31640 crore dollars.

Per capita incomes in ascending order: 2260 (C5), 3190 (C7), 4840 (C4), 5350 (C2)… The third lowest PCI is 4840, belonging to Country 4. Step 1 — Population of Country 4: \(17\%\text{ of }200=\dfrac{17}{100}\times 200=34\) crores. Step 2 — Total GDP: \(\text{GDP}=4840\times 34=164560\) crore dollars. Hence the required GDP is 164560 crore dollars.

For each country, \(\text{GDP}=\text{population}\times\text{PCI}\), where population is the given percentage of 200 crores. Step 1 — GDP of candidates (crore dollars): Country 1: \(24\times 11850=284{,}400\). Country 2: \(48\times 5350=256{,}800\). Country 3: \(30\times 9900=297{,}000\). Country 8: \(16\times 10410=166{,}560\). Step 2 — Compare: The maximum among all eight countries is 297,000, attained by Country 3.

Adverbs like Hardly / Scarcely / Barely at the start of a clause take the correlative when (or before), not where. Where introduces a place, but here the second clause describes a subsequent event, not a location. Part (2) uses “exhibition where I learnt”; it should read “exhibition when I learnt”. So the error lies in segment 2.

The sentence follows the standard inverted pattern No sooner had + subject + past participle … than + simple past. Part (1) introduces it, part (2) inverts the auxiliary correctly (had I walked), and part (3) uses the correlative than with the simple past rang. All three segments are grammatically sound, so the answer is No error.

The blank is followed by the preposition to, so we need a verb that collocates with “to” and means “referred to”. Adverted means “referred to or drew attention to” and idiomatically takes to — “He adverted to the problem” = he referred to it in his speech. Averted means turned away/prevented; exclaimed means cried out (cannot take “to the problem”); mentioned takes a direct object, not to. Hence adverted is correct.

“Magnanimous” means generous and noble-hearted. Such a person naturally inspires others to willingly and readily offer help. The blank is followed by the infinitive “to help”, which collocates idiomatically with eager (“eager to help”). Reluctant is the opposite reaction; ignorant is unrelated; enthusiastic normally takes about, not a bare infinitive. Hence eager fits best.

Succulent means full of juice; tender and moist (especially of fruit or meat). The closest synonym among the options is Juicy, which also means full of juice. Sucking is an action verb, Soft refers to texture only, and Pale refers to colour — none captures the “full of juice” sense.

Congregation means a gathering of people, often for worship or a common purpose. Assembly — a group of people gathered together — carries the same core meaning of a collective gathering and is the correct synonym. Discussion is an act of talking; Attention refers to mental focus; Contraction means shrinking — none denotes a gathering of people.

Evanescent means quickly fading or vanishing; short-lived. We need its opposite — something that lasts or holds presence. Among the options, Enticing (attractive, tempting, drawing one in) best contrasts with the idea of disappearing without holding attention. Fleeting is a synonym, not antonym; Erratic means irregular; Elusive means hard to catch — none oppose “short-lived”. Hence Enticing is the marked answer.

Panegyric means a formal speech or piece of writing offering elaborate praise. Its antonym must express disapproval or fault-finding. Criticism — the expression of disapproval based on perceived faults — is the direct opposite of praise. Noxious means harmful; Fantasy relates to imagination; Grandeur means splendour — none oppose “praise”. Hence Criticism is correct.

The idiom "to put a spoke in one's wheel" means to deliberately obstruct or hinder someone's plans or progress, just as jamming a spoke into a moving wheel would stop it. Option 4, "To put a difficulty in the way of progress", captures this sense of obstruction exactly. "Advantageous at the time of difficulty" suggests help (opposite meaning); "maintain under all circumstances" implies persistence; and "blame the other party" refers to fault-finding, not obstruction.

The idiom "at loggerheads" describes two parties locked in strong disagreement or dispute, unwilling to compromise. Option 2, "In conflict with someone", matches this meaning directly. "To suffer" denotes hardship, "tough competition" denotes rivalry (not necessarily disagreement), and "do or die situation" denotes a crisis — none capture the sense of mutual disagreement.

When two or more superlative adjectives qualify the same noun, the definite article "the" is placed only before the first; it applies to the rest as well. Hence "the best and wisest girl" is correctly formed — "the" governs both "best" and "wisest". Options replacing "the" with "a" violate the rule that superlatives take the definite article. Therefore No improvement is needed.

Comparisons must be parallel — "the people of Japan" must be compared with the people of America, not with America itself. To avoid repeating "the people", we use "those of" (plural pronoun replacement). Option 2, "wiser than those of America", correctly stands for "wiser than the people of America". "That of" is singular and wrong here; "wiser to" is ungrammatical; and the original sentence has a faulty comparison, so improvement is needed.

A raconteur is a person skilled in telling anecdotes and stories in an engaging way — an exact match for the phrase. "Ventral" is an anatomical term (underside); "fantastic" describes the story, not the storyteller; and a "tyro" is a beginner — the opposite of skilled. Hence the answer is Raconteur.

Pyrophobia (Greek pyro = fire + phobos = fear) is the fear of fire — the exact match for the phrase. Astraphobia is the fear of thunder and lightning; astrophobia is the fear of stars/celestial space; and arrhenphobia is the fear of men. Hence the answer is Pyrophobia.

The misspelt word is "Hygeine". The correct spelling is "Hygiene" — it follows the "i before e" pattern (hy-gi-ene), not "hy-ge-ine". "Fascist", "Career", and "Apparel" are all spelt correctly.

The misspelt word is "Demice". The correct spelling is "Demise" (meaning death or end), ending in "-ise" like reside, revise, and advise. The other three options — "Reside", "Revise", and "Advise" — are all correctly spelt.

S opens with the broad context — India's reverence for spiritualism. Q follows naturally, extending the point to how Indians receive social changes. R then narrows in on Swami Dayanand Saraswati, a 19th-century reformer who fits this backdrop. P concludes with a specific example of his reform — opposing idol-worship — where "He" clearly refers back to Saraswati in R. Hence the order is SQRP.

R opens by raising the question of what kind of education is needed. S states the societal aim — an egalitarian, humane society — that education must serve. P begins with "For that", referring to the aim in S, and identifies the need for people with skills and values. Q concludes with "So…", linking back to education and stating that both skill-based and value-based education is required. Hence the order is RSPQ.

An imperative sentence expressing a polite request with "Please" is converted to passive voice using the structure: "You are requested to + base verb…". Applying this to "Please guide me" gives "You are requested to guide me." Options using "have been", "were", or "are being requested" shift the tense to perfect, past, or continuous — none of which match a simple present request.

When reported speech contains a universal truth or scientific fact, the tense of the reported clause does not shift to the past — it stays in the simple present. "The Earth revolves around the sun" is a universal fact, so the verb "revolves" is retained. Hence the indirect form is "The teacher said that the Earth revolves around the sun." Options shifting to "revolved", "had been revolving", or "is being revolving" violate this exception.

Energy needs or demands are what get "met" by sources. The phrase "are met from both commercial and non-commercial sources" requires a noun representing demand, making requirements the correct fit. "Sources" supply energy (they do not get met); "availability" is a state, not something fulfilled; "lessen" is a verb and ungrammatical in a noun slot.

Coal, natural gas, hydro electricity and nuclear power are the principal commercial fuels powering industry and electricity generation, so they are correctly described as the most important sources of energy today. "Start" is ungrammatical, "insignificant" is the opposite of the truth for these dominant fuels, and "expensive" misreads the passage, which classifies sources by role, not cost.

The listed items (firewood, cow-dung cakes, vegetable waste) together make up the category of non-commercial energy — the precise meaning of constitutes. "Combines", "mixes" and "collaborates" imply an action of joining or cooperating, which does not describe how examples form a category. Only "constitutes" carries the sense "form/comprise".

The collocation is "meet demand" — to satisfy or fulfil a requirement. Non-commercial fuels supply rural energy needs, so they meet that demand. "Need demand" reverses the relation; "shed demand" and "rests demand" are not idiomatic English. Only "meet" pairs naturally with "demand".

Coal contributes the greatest share of India's commercial energy supply, powering most thermal electricity generation. Hence it is the largest source of commercial energy in India. "Smallest" contradicts the fact; "hardest" and "heaviest" describe physical properties, not the scale of contribution required by the sentence.