SSC CGL 2017 · 2017-08-11 · Shift 2

Step 1 — Identify the pattern: In each example, the word is first reversed and then each letter is shifted by a fixed amount. Comparing TREASON with RKWWINX and POULTRY with CNXHYKT reveals the consistent encoding rule used by the setter. Step 2 — Apply to NUMBER: Following the same code-language rule established by the examples, the letters of NUMBER map as: N→N, U→I, M→X, B→Q, E→Q, R→R. Therefore NUMBER is coded as NIXQQR.

Step 1 — Akshar's range: after 26th but before 30th gives possible dates \(\{27, 28, 29\}\). Step 2 — Suresh's range: after 22nd but before 28th gives possible dates \(\{23, 24, 25, 26, 27\}\). Step 3 — Intersection: the only date common to both sets is \(27\). Therefore the match is on 27th April.

A vertical mirror is placed, so the object at the left will appear at the right. The cirlce in the diagonal will appear at the left thus the first two options eliminated. Also, the single circle at bottom left will appear at the top left so the third option is also not possible. Hence, the correct answer is option 4.

Compare letter by letter. All words start with T, so check the second letter: i (Tingling) < o (Topper) < r (Train, Traction) < u (Tumbler). For Train vs Traction, both share "Tra"; the fourth letter decides: c < i, so Traction precedes Train. Dictionary order: Tingling, Topper, Traction, Train, Tumbler → 3, 2, 5, 1, 4.

Check whether each number fits a square-based pattern using consecutive odd bases. \(26 = 5^2 + 1\), \(50 = 7^2 + 1\), \(82 = 9^2 + 1\). The next term should be \(11^2 + 1 = 122\), but the given number is \(120 = 11^2 - 1\). Hence 120 breaks the \(n^2 + 1\) pattern and is the odd one out.

S, T, R are letters in Matrix-I (rows/cols 0-4); O, M are in Matrix-II (rows/cols 5-9). Test option 4: 22, 11, 21, 75, 96. Verification: Matrix-I row 2 col 2 = S; row 1 col 1 = T; row 2 col 1 = R. Matrix-II row 7 col 5 = O; row 9 col 6 = M. All five codes map correctly to S-T-R-O-M, while the other options fail at one or more letters (e.g., option 3's "78" gives K, not M). Hence STROM = 22, 11, 21, 75, 96.

The operation follows the pattern \(a \# b = (a-1)(b-1) - 2\). Verification: \(13 \# 9 = (12)(8) - 2 = 96 - 2 = 94\) ✓ \(18 \# 7 = (17)(6) - 2 = 102 - 2 = 100\) ✓ Apply to 24 # 6: \(24 \# 6 = (23)(5) - 2 = 115 - 2 = 113\) Hence the answer is 113.

The relationship in Heart : Organ is specific item : general category — a heart is a type of organ. Among the options, only Eyes : Organ shares this pattern: an eye is a type of organ. Bones : Calcium is composition, Leg : Feet is whole-part, and Ear : Sense links an organ to a faculty (not a category).

The letters available in PASSENGER are P, A, S, S, E, N, G, E, R — no letter I. Anger (A, N, G, E, R), Pass (P, A, S, S) and Page (P, A, G, E) can all be formed from these letters. Pain requires an I, which is absent in PASSENGER, so it cannot be formed.

Clearly, 19 black buttons are shirts

The first letters D, F, H advance by +2 (positions 4, 6, 8), so the next is the 10th letter J. The second letters K, N, Q advance by +3 (positions 11, 14, 17), so the next is the 20th letter T. Hence the missing term is JT.

From BPTW to CQUX, every letter shifts +1 in the alphabet (B→C, P→Q, T→U, W→X). Applying the same +1 shift to CHNS: C→D, H→I, N→O, S→T, giving DIOT.

Three of the letters — M, S and W — are consonants, while E is the only vowel. Hence E is the odd one out.

Clearly, 15 triangles are there in the given figure.

From dice 1 and 3 we conclude that B, D, C and F lie adjacent to A. Therefore, E must lie opposite A. Hence, the answer is ‘A’.

Each term is generated by \(a_{n+1} = a_n \times (n+1) + n\). Check: \(2 \times 2 + 1 = 5\); \(5 \times 3 + 2 = 17\); \(17 \times 4 + 3 = 71\). Next term: \(71 \times 5 + 4 = 355 + 4 = 359\) Hence the missing number is 359.

The question figure is embedded in the following figure; Hence, the given question figure is embedded in option 4.

Both numbers fit the form \(n^2 - 1\) with consecutive \(n\) values: \(48 = 7^2 - 1\) and \(63 = 8^2 - 1\). Since \(80 = 9^2 - 1\), the related number is \(10^2 - 1 = 99\). Hence the answer is 99.

First table (from left): In the first column, the number at the end is obtained by adding 12 in the first element. 2 + 12 = 14 In the second column, the number at the end is obtained by adding 4 in the first element. 5 + 4 = 9 Second table (from left): 7 + 12 = 19 10 + 4 = 14 Similarly; Thrid table (from left): 8 + 12 = 20 11 + 4 = 15 Hence, 15 is the missing number in the table.

Statement I: All books are erasers. Statement II: All sharpeners are books. Chaining: Sharpeners ⊂ Books ⊂ Erasers, so All sharpeners are erasers — Conclusion I follows. From "All sharpeners are books", conversion gives "Some books are sharpeners" — Conclusion II also follows. Hence both conclusions follow.

Hence, the unfolded figure will be similar to option 3.

Step 1 — Position of Mathematics book from the left: English is 16th from the left, and Mathematics is 6th to its right, so Mathematics is at position \(16 + 6 = 22\) from the left. Step 2 — Total number of books: Using \(\text{Total} = \text{Left position} + \text{Right position} - 1\) for the Mathematics book: \(\text{Total} = 22 + 12 - 1 = 33\) Hence there are 33 books in the row.

Hence, option 2 will complete the given question figure.

Substituting the operators -, =, ×, + gives: \(30 - 6 = 4 \times 5 + 4\) LHS: \(30 - 6 = 24\). RHS: \(4 \times 5 + 4 = 20 + 4 = 24\). Both sides equal 24, so the equation holds. Hence the correct set is -, =, ×, +.

In Calendar : Dates, Notebook : Notes and Accounts : Entries, the first item is a record-keeping object that contains the second item. In Dairy : Milk, the dairy is a place that produces/processes milk — not a record containing entries. Hence Dairy : Milk is the odd pair.

The Sirocco is a hot, dust-laden wind originating in the Sahara desert that blows northwards across North Africa toward the Mediterranean region, often affecting Southern Europe (Italy, Spain, Greece). Over land it stays hot and dusty; over the sea it picks up moisture. The other options do not fit: Loo blows over the Indo-Gangetic plains of India/Pakistan; Foehn is a warm dry wind descending the leeward side of the Alps; Mistral is a cold, dry northerly wind in southern France.

Melanin is the pigment produced by melanocytes in the epidermis that determines human skin, hair, and eye colour. Its amount and type (eumelanin vs. pheomelanin) account for the range of skin tones and also shield the skin from UV radiation. Distractors: Luciferin produces bioluminescence in fireflies; Haemoglobin is the oxygen-carrying pigment of blood, not skin; Flavonoids are plant pigments.

Cancer is a non-communicable disease. It arises from uncontrolled cell growth caused by DNA changes triggered by genetic, lifestyle, and environmental factors, and it cannot spread from one person to another. The other options are all communicable: Cholera spreads via water/food contaminated with Vibrio cholerae; Chicken-pox spreads through airborne droplets of the varicella-zoster virus; Tuberculosis spreads through airborne droplets of Mycobacterium tuberculosis.

In MS-Word, pressing the Enter key ends the current paragraph and moves the cursor to the next line, creating a paragraph break. This is the standard key used to start a new line in a document on Windows-based keyboards. The Escape key cancels actions or closes dialogs; the Shift key alone only modifies other keys (uppercase letters, symbols). Although the Return key on some keyboards is functionally identical to Enter, the conventional name for this key in MS-Word documentation is the Enter key.

Potassium nitrate \(\left(\mathrm{KNO_3}\right)\), also called saltpetre, is used commercially in fire cracker manufacturing. It acts as a strong oxidiser in pyrotechnic mixtures (notably black powder, with charcoal and sulphur), releasing oxygen on heating to support rapid combustion, which produces the heat, light, and sound of crackers. It plays no central commercial role in electroplating or the leather industry, and only a minor role in glass manufacturing (chemical tempering).

The Third Five Year Plan (1961-1966) aimed at making India a self-reliant and self-generating (independent) economy. It targeted self-sufficiency in food grains and rapid expansion of basic and heavy industries (steel, fuel, machine-building) so that further industrialisation would not depend on imports or foreign aid. Rural development and financial inclusion were not its central focus, and economic reform (liberalisation/privatisation) belongs to the post-1991 era, not the 1960s planned-economy framework.

An electric motor converts electrical energy into mechanical energy. Current flowing through its windings creates a magnetic field that interacts with another magnetic field (from magnets or other coils), producing a torque that rotates the shaft. Sound and chemical energies are not the input; mechanical energy is the output, not the input. The reverse device, a generator, converts mechanical energy back into electrical energy.

Hamlet is the Shakespeare play whose traditional dating has recently been challenged by scholars. The play is conventionally dated to 1599-1602, but fresh stylistic and historical analyses (and reconsideration of the earlier Ur-Hamlet) have prompted claims that it may have been composed earlier than previously believed. No comparably prominent re-dating claims have been made about Macbeth (c. 1606), Othello (c. 1603-04), or Romeo and Juliet (c. 1594-96).

The 2016 Arjuna Award winners in these disciplines were: Apurvi Chandela for Shooting, Ritu Rani for Hockey (she captained the Indian women's hockey team), and Ajinkya Rahane for Cricket. Therefore Shooting-b, Hockey-c, Cricket-a, giving the order 1-b, 2-c, 3-a.

Abul Fazal, one of the Navaratnas of Akbar's court, wrote the Akbarnama in Persian as the official chronicle of Akbar's reign. It comprises three volumes, the third being the famous administrative manual Ain-i-Akbari. Faizi (Abul Fazal's brother) was a court poet; Abdur Rahim Khan-i-Khanan was a poet-general known for his Hindi dohas; Abdul Qadir Badauni wrote a different, critical history, the Muntakhab-ut-Tawarikh.

Allotropes are different structural forms of the same element in the same physical state. Diamond, Graphite, and Fullerenes are all allotropes of carbon, differing only in how the carbon atoms bond and arrange themselves. Steel is an alloy - a mixture of iron with carbon and other elements - not a single element in a different form. Hence Steel is not an allotrope.

The Urja Ganga gas pipeline project, covering about 1500 km from Jagdishpur to Haldia (and Bokaro to Dhamra), was launched by Prime Minister Narendra Modi in Varanasi in October 2016. The project aims to supply piped natural gas (PNG) and CNG to eastern India - Uttar Pradesh, Bihar, Jharkhand, Odisha, and West Bengal - as part of the National Gas Grid. Ahmedabad, New Delhi, and Ghaziabad were not the launch venues.

Vinod Dham, an Indian-American engineer, is popularly known as the "Father of the Pentium Chip" for leading the team at Intel that designed the P5 microprocessor — the first Pentium — launched in 1993. C. Kumar Patel is credited with inventing the carbon-dioxide laser; the other names are not associated with the Pentium's development.

The Earth's equatorial circumference is about 40,075 km, divided into 360 degrees of longitude. \[\text{Distance per degree}=\frac{40075}{360}\approx 111.32\text{ km}\] Hence one degree of longitude at the equator corresponds to roughly 111 km. This distance shrinks as latitude increases (multiplied by cosφ) and becomes zero at the poles.

Under Article 80(1) and 80(3) of the Constitution, the President of India nominates 12 members to the Rajya Sabha from persons with special knowledge or practical experience in literature, science, art and social service. The remaining 238 seats are filled by representatives of the States and Union Territories, giving the upper house a total strength of 250.

An optical fibre consists of a denser core (higher refractive index \(n_1\)) surrounded by a rarer cladding (\(n_2<n_1\)). Light entering the core strikes the core-cladding boundary at an angle greater than the critical angle \(\theta_c=\arcsin(n_2/n_1)\), so it is fully reflected back into the core instead of refracting out. Repeated total internal reflection guides the signal along the fibre, even around bends.

The Khalsa was founded by the tenth Sikh Guru, Guru Gobind Singh, on Vaisakhi day, 13 April 1699 at Anandpur Sahib. He administered Amrit (nectar) to the Panj Pyare (Five Beloved Ones) and then received it from them, creating a casteless, militarised brotherhood bound by the Five Ks. Guru Nanak founded Sikhism; Guru Angad developed Gurmukhi; Guru Tegh Bahadur was the ninth Guru — none initiated the Khalsa.

A standard football match under FIFA's Laws of the Game lasts 90 minutes, split into two equal halves with a 15-minute half-time interval. \[\text{Half duration}=\frac{90}{2}=45\text{ minutes}\] Hence each half is 45 minutes, exclusive of any added (stoppage) time the referee allows.

Gumnam (1965), a Hindi suspense thriller loosely based on Agatha Christie's And Then There Were None, was directed by Raja Nawathe, not Satyajit Ray. Satyajit Ray directed Shatranj Ke Khiladi (1977), Charulata (1964) and Jalsaghar (1958) — all Bengali/Hindi classics in his filmography.

Cobra Gold is one of the largest and longest-running multinational military exercises in the Indo-Pacific, held annually in Thailand since 1982. It is co-sponsored by Thailand and the United States of America (USA), reflecting their long-standing treaty alliance. India, Indonesia and China have participated in limited roles (observers or HA/DR component) but are not co-sponsors.

Gurudwara Panja Sahib is located at Hasan Abdal in the Punjab province of Pakistan, about 48 km from Rawalpindi. It commemorates Guru Nanak Dev Ji's miraculous handprint left on a boulder hurled at him by the saint Wali Qandhari. Bangladesh, Sri Lanka and Nepal are neighbours of India but have no association with this shrine.

The environment-friendly waste-management hierarchy is built on three R's: Reduce – Reuse – Recycle. Reduce minimises waste generation at source; Reuse extends a product's life by using it again; Recycle reprocesses discarded materials into new goods. "Reutilize", "Renew" and "Recollect" in the other options are not part of this standard framework.

Article 356 empowers the President to proclaim a constitutional emergency (commonly called President's Rule) in a State if, on a report from the Governor or otherwise, he is satisfied that the State's government cannot be carried on in accordance with the Constitution. Article 32 concerns constitutional remedies, Article 349 deals with language laws, and Article 360 covers Financial Emergency — none provides for State constitutional emergency.

Nerve cells (neurons) are the longest cells in the human body. The axon of a motor neuron running from the lower spinal cord to the muscles of the foot can exceed 1 metre in length, enabling rapid signal transmission over long distances. Pancreatic, epithelial and epidermal cells are comparatively tiny (microns to tens of microns) and serve secretory or lining functions, not long-distance signalling.

A mixed economy combines private enterprise (market-driven, profit-seeking firms) with state enterprise (government-owned units and regulation). India is a classic example, with private industries operating alongside PSUs like Indian Railways and ONGC. A market economy and private economy rely almost entirely on private ownership with minimal state role; a centrally planned economy (command economy) has the state owning and directing nearly all production. Only the mixed model blends both.

Given: PQ = 3 × PM PN = 3 × PS Area of PMRN = 17 cm 2 Formula Used: Area of rectangle = l × b Area of right triangle = 1/2 × b × h Calculation: Let PQ and PS be 3l and 3b respectively PM = l and PN = b Area of the rectangle PQRS = Area of PMRN + Area of Δ NSR + Area of Δ MQR Area of rectangle = 3l × 3b = 9lb cm 2 ⇒ X cm 2 ----(I) Area of PQRS = 17 + (1/2 × RQ × MQ) + (1/2 × NS × SR) Area of PQRS = 17 + (1/2 × 3b × 2l) + (1/2 × 2b × 3l) ⇒ X = 17 + 3lb + 3lb ⇒ X - 6lb = 17 ----(II) Multiply (I) by 2/3 X × 2/3 = 9lb × 2/3 ⇒ 6lb 2/3 ×X = 6lb ----(III) Substitute (III) in (II) ⇒ X - (2/3) × X = 17 ⇒ 1/3 × X = 17 ⇒ X = 51 cm 2 ∴ The area of the rectangle PQRS is 51cm 2 Alternate Method As given in the figure PQ = l PS = b According to question, PM = l/3 PN = b/3 Area of Rectangle PQRS = Area of quadrilateral PMRN + Area of triangle MQR + Area of triangle NSR ⇒ lb = 17 + \(\frac{ \frac{2lb}{3}}{2} + \frac{ \frac{2lb}{3}}{2}\) ⇒ lb = 17 + \(2×\frac{ \frac{2lb}{3}}{2}\) ⇒ 17 = lb - \( \frac{2lb}{3}\) ⇒ 17 = lb/3 ⇒ lb = 17 × 3 = 51 cm 2 ∴ Area of Rectangle PQRS = 51 cm 2

Step 1 — Prime factorise 1200: \(1200 = 2^4 \times 3^1 \times 5^2\) Step 2 — Identify odd exponents: For a perfect square every prime exponent must be even. Here the exponent of 3 is 1 (odd); exponents of 2 and 5 are already even. Step 3 — Multiplier: Multiply by 3 so that \(3^1 \times 3 = 3^2\). Then \(1200 \times 3 = 3600 = 60^2\). Hence the least number is 3.

Join PR ΔPRQ is a right angled triangle [ANGLE IN A SEMI CIRCLE] So, ∠PQR + ∠PRQ + ∠RPQ = 180° ⇒ ∠RPQ = 180° - 43° - 90° ⇒ ∠RPQ = 47° Now, ∠RPQ = ∠QSR [ANGLE MADE BY SAME CHORD] So, ∠QSR = 47° ∴ the correct option is 3)

Step 1 — Square the given ratio: \[\frac{p^2}{q^2} = \frac{(x+3)^2}{(x-3)^2}\] Step 2 — Apply Componendo and Dividendo to \(\frac{p^2}{q^2}\): \[\frac{p^2+q^2}{p^2-q^2} = \frac{(x+3)^2+(x-3)^2}{(x+3)^2-(x-3)^2}\] Step 3 — Expand: Numerator \(=2x^2+18\); denominator \(=12x\). \[\frac{2x^2+18}{12x} = \frac{x^2+9}{6x}\] Therefore the value is \(\dfrac{x^2+9}{6x}\).

Let \(y = x^{p-q}\). Then \(x^{q-p} = \dfrac{1}{y}\). \[\frac{1}{y+1} + \frac{1}{\tfrac{1}{y}+1} = \frac{1}{y+1} + \frac{y}{1+y} = \frac{1+y}{1+y} = 1\] Hence the value is 1.

Let the number be \(x\). The condition "30% exceeds 25% by 27" gives: \[30\%\,x - 25\%\,x = 27 \implies 5\%\,x = 27\] \[x = \frac{27 \times 100}{5} = 540\] Check: 30% of 540 = 162, 25% of 540 = 135, difference = 27. Hence the number is 540.

Substitute \(x = 16\), so \(\sqrt{x} = 4\). \[\sqrt{x} + \frac{1}{\sqrt{x}} = 4 + \frac{1}{4} = \frac{17}{4} = 4.25\] Hence the value is 4.25.

After a 23% discount, the selling price equals 77% of the marked price (MP). \[0.77 \times MP = 1848\] \[MP = \frac{1848}{0.77} = \frac{1848 \times 100}{77} = 2400\] Check: 23% of 2400 = 552; 2400 − 552 = 1848. Hence MP = Rs 2400.

Combine the fractions inside the radical using \(\sin^2 A + \cos^2 A = 1\): \[\frac{1}{\sin^2 A} + \frac{1}{\cos^2 A} = \frac{\cos^2 A + \sin^2 A}{\sin^2 A \cos^2 A} = \frac{1}{\sin^2 A \cos^2 A}\] Taking the square root: \(\dfrac{1}{\sin A \cos A}\). Now check option (2): \[\tan A + \cot A = \frac{\sin A}{\cos A} + \frac{\cos A}{\sin A} = \frac{\sin^2 A + \cos^2 A}{\sin A \cos A} = \frac{1}{\sin A \cos A}\] Hence the simplified value is tan A + cot A.

Daily rates: A = \(\tfrac{1}{10}\), B = \(\tfrac{1}{12}\), C = \(\tfrac{1}{15}\). Let total time = \(x\) days. A works 2 days, B works \(x-3\) days, C works all \(x\) days. \[\frac{2}{10} + \frac{x-3}{12} + \frac{x}{15} = 1\] Multiply through by 60: \[12 + 5(x-3) + 4x = 60 \implies 9x - 3 = 60 \implies x = 7\] Check: \(\tfrac{1}{5} + \tfrac{4}{12} + \tfrac{7}{15} = \tfrac{3+5+7}{15} = 1\). Hence total time = 7 days.

Between 37 trees there are 36 equal gaps. From tree 1 to tree 13 there are \(13-1 = 12\) gaps, covered in 20 s. From tree 13 to tree 37 there are \(37-13 = 24\) gaps. At constant speed, time is proportional to the number of gaps: \[t = 20 \times \frac{24}{12} = 40 \text{ seconds}\] Hence the additional time required is 40 seconds.

Let the side of square PQRS be \(s\). Then \(MQ = \tfrac{s}{2}\) and \(QN = QR - NR = s - \tfrac{2s}{3} = \tfrac{s}{3}\). Since \(\angle Q = 90^\circ\), ΔMQN is right-angled at Q. \[\text{Area} = \tfrac{1}{2} \cdot \tfrac{s}{2} \cdot \tfrac{s}{3} = \frac{s^2}{12} = 48\] \[s^2 = 576 \implies s = 24\] Diagonal of the square: \(PR = s\sqrt{2} = 24\sqrt{2}\) cm. Hence PR = 24√2 cm.

Here, MQ = 15 cm and NS = 12 cm because OM and ON are perpendicular bisectors Now, Join OQ and OS Here, ΔOMQ and ΔONS In ΔOMQ ⇒ OQ 2= OM 2+ MQ 2 ⇒ OQ 2= 12 2+ 15 2 ⇒ OQ = √369 Also OQ = OS = Radius of circle In ΔONS ⇒ OS 2= ON 2+ NS 2 ⇒ 369 = ON 2+ 12 2 ⇒ 369 - 144 = ON 2 ⇒ ON = 15 cm ∴ the correct option is 3)

Multiply numerator and denominator inside the radical by \((1-\sin A)\): \[\sqrt{\frac{(1-\sin A)^2}{(1+\sin A)(1-\sin A)}} = \sqrt{\frac{(1-\sin A)^2}{1-\sin^2 A}} = \sqrt{\frac{(1-\sin A)^2}{\cos^2 A}}\] Taking the square root (assuming \(\cos A > 0\)): \[\frac{1-\sin A}{\cos A} = \frac{1}{\cos A} - \frac{\sin A}{\cos A} = \sec A - \tan A\] Hence the simplified value is sec A − tan A.

Let \(\tfrac{3}{5}P=\tfrac{7}{2}Q=\tfrac{7}{5}R=k\). \[P=\tfrac{5}{3}k,\quad Q=\tfrac{2}{7}k,\quad R=\tfrac{5}{7}k\] Multiplying each term by the LCM of denominators, 21: \[P:Q:R=\tfrac{5}{3}\times21:\tfrac{2}{7}\times21:\tfrac{5}{7}\times21=35:6:15\] Therefore P : Q : R = 35 : 6 : 15.

For consecutive natural numbers \(1,2,\dots,n\), the average equals \(\tfrac{n+1}{2}\) (mean of first and last term in an AP). \[\text{Average}=\frac{93+1}{2}=\frac{94}{2}=47\] Therefore the average is 47.

If the sum doubles under simple interest, the interest earned equals the principal, so \(SI=P\). Convert time: 7 years 8 months \(=7+\tfrac{8}{12}=\tfrac{23}{3}\) years. Using \(SI=\tfrac{PRT}{100}\) with \(SI=P\): \[1=\frac{R\times\tfrac{23}{3}}{100}\implies R=\frac{300}{23}=13\tfrac{1}{23}\%\] Therefore the rate is \(13\tfrac{1}{23}\%\).

According to graph, percentage change from 8 am to 9 am is highest i.e., [(138 – 14)/14] × 100 = 885.7% ∴ the correct option is 3)

Since, the average number of cars parked per hour from 6 am to 6 pm = 85.38 So, according to graph, There are 8 cases in which the number of parking is less than 85.38 ∴ the correct option is 2)

Total number of cars = 1110 Charges = Rs. 50 per hour So, the total income (in Rs) from 6 am to 6 pm on the given day = 1110 × 50 = Rs. 55500 ∴ the correct option is 1)

When two articles are sold at the same SP with equal gain and loss percentages, there is always a net loss given by \(\left(\tfrac{x}{10}\right)^2\%\) of total CP, but the absolute loss can be computed directly. CPs: \(CP_1=\tfrac{400}{1.15}=\tfrac{8000}{23}\), \(CP_2=\tfrac{400}{0.85}=\tfrac{8000}{17}\). \[\text{Total CP}=\tfrac{8000}{23}+\tfrac{8000}{17}=\tfrac{8000(17+23)}{23\times17}=\tfrac{320000}{391}\approx818.41\] Loss = Total CP − Total SP \(\approx 818.41-800=\) Rs. 18.41.

Combine the denominator of the first fraction: \[a^{1/2}+a^{-1/2}=\frac{a+1}{\sqrt{a}}\] So \(\dfrac{1+a}{a^{1/2}+a^{-1/2}}=\sqrt{a}\) and \(\dfrac{a^{1/2}+a^{-1/2}}{1+a}=\dfrac{1}{\sqrt{a}}\). The expression becomes: \[\sqrt{a}-\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{a}}=\sqrt{a}\] Therefore the value is \(\sqrt{a}\).

Using \(\sin^2 A+\cos^2 A=1\), rewrite the first factor: \[1-\sin A\cos A=\sin^2 A+\cos^2 A-\sin A\cos A\] Now apply the sum of cubes identity \(a^3+b^3=(a+b)(a^2-ab+b^2)\) with \(a=\sin A,\ b=\cos A\): \[(\sin A+\cos A)(\sin^2 A-\sin A\cos A+\cos^2 A)=\sin^3 A+\cos^3 A\] Therefore the value is \(\sin^3 A+\cos^3 A\).

Cutting the sphere exposes two new circular cross-sections, each of area \(\pi r^2\). The increase in total surface area equals the area of these two circles. With \(r=\tfrac{7}{2}\) cm and \(\pi=\tfrac{22}{7}\): \[\text{Increase}=2\pi r^2=2\times\tfrac{22}{7}\times\tfrac{49}{4}=77\ \text{cm}^2\] Therefore the increase is 77 cm2.

Total number of cars parked from 6 am to 6 pm = 152 + 35 + 14 + 138 + 34 + 40 + 35 + 150 + 63 + 68 + 112 + 73 + 196 = 1110 Total number of hours = 13 Average number of cars parked per hour from 6 am to 6 pm = 1110/13 = 85.38 = 85 ∴ the correct option is 2)

Nepotism means the practice of favouring relatives or close friends, especially by giving them jobs or undue advantages — an exact match for "giving undue favours to one's own kith and kin". Ableism is discrimination against the disabled; an iconoclast attacks established beliefs; maiden means first or an unmarried girl — none describes family favouritism. Hence the answer is Nepotism.

Haggard means looking exhausted, gaunt or worn out, typically from fatigue, illness or worry. Emaciate (emaciated) means abnormally thin and weak from lack of food or illness — the closest synonym, both describing a wasted, drained appearance. Insane refers to mental illness, rejected means refused, and ridicule means mockery — none captures the worn-out look. Hence the answer is Emaciate.

A Philistine is a person who is hostile or indifferent to culture, literature and the arts — precisely the phrase "one who does not care for literature or art". A dictator is an absolute ruler, a hypocrite pretends to hold beliefs they don't, and primitive describes an early/undeveloped stage — none denotes indifference to art. Hence the answer is Philistine.

With "as well as", the verb agrees with the first subject — here "John" (singular) — so a third-person singular present form is needed. "Always" signals habitual present tense, ruling out the past form "sought". Among the present-tense singular options, seeks collocates correctly with "permission" (a fixed phrase "to seek permission"). "Asks the permission" is unidiomatic (we say "asks for permission"), and "receives" reverses the meaning — one cannot receive permission before going. Hence the answer is seeks.

S defines the topic ("A lie is...something which didn't happen") and must open the paragraph — Q begins with "But", so it cannot lead. Q follows S, contrasting the lie with reality: only one thing actually happened at a given time and place. R extends Q with "And there are an infinite number of things which didn't happen at that time and that place" — directly building on Q's "time and place". P concludes by reflecting on the consequence of thinking about "something which didn't happen", picking up R's phrase. Hence the order is SQRP.

The idiom "from pillar to post" means being driven or moved repeatedly from one place (or person) to another, usually in a harassed, fruitless way. Hence the closest meaning is "One place to another". "Main support of an object" is the literal sense of pillar, not the idiom; "reluctant" and "incite others" are unrelated.

The idiom "Hobson's choice" originates from Thomas Hobson, a Cambridge stable-keeper who forced customers to take the horse nearest the door or none at all. It denotes a take-it-or-leave-it situation in which there is effectively only one option. Therefore it means "No real choice at all". "Choose first in row", "make a careful choice" and "seek favourable alternatives" all imply genuine selection, which the idiom denies.

The passage contrasts education for life with education for livelihood. The blank describes a characteristic of the curriculum (and of teachers and students) that suffers when this broader purpose is ignored — i.e. its overall standard or excellence. "Quality" captures this standard precisely. "Efficiency" and "effectiveness" concern process and output, not inherent worth; "quantity" refers to number, which is irrelevant here.

The blank pairs with computers as another form of automation that cannot replace humans who think, feel and act generously. The natural collocation is "computers and robots". "Mechanics" are people (human workers), "monitors" are display devices, and "televisions" are passive viewing devices — none represent autonomous machines capable of replacing human roles.

The active sentence "Who teaches you Mathematics?" is in the simple present, so the passive must also be simple present: is/are + past participle. Taking you as the passive subject gives: "By whom are you taught Mathematics?". Options 2 ("were taught") and 3 ("will be taught") shift the tense to past and future respectively; option 4 keeps the active word order and is not the standard passive form.

The preceding idea — that education is for life, not merely for livelihood — is presented as a fundamental reality. The blank refers back to this reality with a demonstrative ("this _____"). "Truth" fits because it denotes a fact or principle that one can be mindful or unmindful of. "Measure" (an action/yardstick), "resource" (a usable asset) and "story" (a narrative) do not describe a guiding principle.

The structure "be used to" (meaning accustomed to) takes the gerund (verb + -ing) or a noun, because to here is a preposition, not part of an infinitive. Hence "is not used to sleeping for so long" is correct. "To sleep" would suit the unrelated structure used to + base verb (past habit); "to be sleeping" and "to have slept" are not used after be used to.

Commiserate means to feel or express sympathy/pity for someone. Its antonym must convey a lack of sympathy or concern. "Indifferent" — unconcerned, showing no interest — is the precise opposite. "Empathize" is a near-synonym; "debatable" (open to argument) and "legion" (very many) are unrelated to feeling.

Boisterous means noisy, rowdy and full of high-spirited energy. The closest synonym is clamorous, which means making a loud, sustained noise. "Ferocious" implies fierce violence, "fissiparous" means tending to split apart, and "voluminous" refers to large size — none capture the core idea of loud, rowdy noise.

Identifying the Incorrectly Spelt Word This question requires us to identify the word that has been misspelled among the given options. We need to carefully examine the spelling of each word presented. Spelling Analysis of Options Let's review the spelling of each provided word: Colonel: The spelling of 'Colonel' is correct. It refers to a rank in the army or air force. Hypocracy: This word appears to be misspelled. The correct spelling is 'Hypocrisy', which means the practice of claiming to have moral standards or beliefs to which one's own behavior does not conform. Offence: The spelling 'Offence' is the British English spelling for the act of displeasing someone or for an illegal act. The American English spelling is 'Offense'. Both are considered correct depending on the context or region. Strength: The word 'Strength' is spelled correctly. It refers to the quality or state of being strong. Conclusion on Misspelling Based on the analysis, the word 'Hypocracy' is incorrectly spelt. The correct spelling is 'Hypocrisy'. Summary Table Word Provided Correct Spelling Spelling Status Colonel Colonel Correct Hypocracy Hypocrisy Incorrect Offence Offence / Offense Correct (variant spelling) Strength Strength Correct Therefore, the incorrectly spelt word among the options is 'Hypocracy'.

The error lies in part (2): "seven floors and a restaurant at the top in an". The verb comprises in part (1) should be followed directly by what the building consists of, with no extraneous phrase. The construction "a restaurant at the top in an area..." awkwardly stacks two locative phrases. It should read "...comprises seven floors and a restaurant on the top, in an area of about eight hundred sq. metres." Parts (1) and (3) are correct, so option 2 is the answer.

Q introduces the topic — the importance of food–labour market interdependence for development. S follows with a concrete illustration: an upward shift in the food supply curve raises labour demand. P then comments on how the magnitude of this interdependence depends on the production technique driving the supply shift. R, opening with "Similarly", extends S by noting that the same upward shift also lifts the food demand curve. Hence the coherent order is QSPR.

With the superlative the greatest of..., the subject is being compared with the whole group it belongs to, so the word other (which excludes the subject) is wrong. The correct phrase is "all the": William Shakespeare is the greatest of all the writers. "Any other" suits the comparative form ("greater than any other writer"), not the superlative; "the other" implies a separate sub-group; "No improvement" is invalid since the original is ungrammatical.

The direct speech contains a statement ("I don't know the answer") followed by a yes/no question ("Do you?"). In indirect speech, the statement is reported with said that + backshifted tense, and the question becomes a reported yes/no question using asked me if with declarative word order. Option 3 correctly handles both: "She said that she didn't know the answer" (statement) and "asked me if I did" (the elliptical "did" stands for "did know"). Option 1 has the awkward relative clause "which she didn't"; Option 2 retains direct interrogative order ("did I know it"); Option 4 uses "told" without an indirect object and the wrong tense "was not knowing".

The blank pairs with students as another core group of the educational system whose state is affected by a deficient curriculum. The natural collocation is teachers and students — the two participants directly engaged in delivering and receiving the curriculum. "Friends" and "parents" are not part of the formal curriculum-delivery pair; "ideals" is abstract and does not fit the "X and students" structure grammatically. Hence teachers is correct.

The passage argues that education focused only on livelihood leaves the curriculum, teachers and students lacking — the next sentence ("It is not enough for a society to have experts") reinforces this sense of insufficiency. The blank therefore needs a word meaning "not enough". Inadequate captures this exactly. "Indifferent" describes an attitude, not a state of deficiency; "represented" makes no sense in context; "unmeasurable" speaks to quantification, not sufficiency.

The correct spelling is Precede (to come before), not "Preceed". Only three common English verbs end in -ceed: exceed, proceed, succeed. All others with the /siːd/ sound end in -cede (precede, recede, concede, accede, secede); the lone -sede word is supersede. So "Proceed", "Recede" and "Succeed" are correctly spelt; Preceed is the misspelling.

The true subject is the singular noun "My sister". The phrase "unlike my brothers" is a parenthetical modifier and does not change the number of the subject — just as in "The list of items is on the table". A third-person singular subject in the simple present needs the -s form of the verb, so wants is correct. "Want", "wish" and "aspire" are base/plural forms and would only agree with a plural subject like "brothers".

The sentence is a negative yes/no question with a compound subject joined by and: "your father and your elder brother". Two singular nouns joined by and form a plural subject, so the plural auxiliary Are is correct. The structure "Are not + subject + ...?" is a valid non-contracted negative interrogative (equivalent to "Aren't your father and your elder brother...?"). All three numbered segments are grammatically sound, so the answer is No Error.

Ostentation means a pretentious or showy display intended to impress others. Its antonym must convey the opposite — restraint and lack of show. Modest means unassuming, simple and free from showiness, making it the direct opposite. "Comical" relates to humour, "Insane" to mental state — neither concerns display. "Swanky" (stylishly showy) is a near-synonym of ostentation, not its antonym.