SSC CGL 2017 · 2017-08-18 · Shift 2

Each letter of the code is the original letter shifted forward by +2 in the alphabet: B→D, A→C, P→R, T→V, I→K, S→U, M→O. Applying +2 to TIN: T(20)→V(22), I(9)→K(11), N(14)→P(16). Hence TIN is coded as VKP.

Rewriting the decimals as fractions gives \(1, \tfrac{1}{4}, \tfrac{1}{9}, ?, \tfrac{1}{25}, \tfrac{1}{36}\). The denominators are perfect squares \(1^2, 2^2, 3^2, ?, 5^2, 6^2\), so the general term is \(\tfrac{1}{n^2}\). The missing term is \(\tfrac{1}{4^2} = \tfrac{1}{16} = 0.0625\).

Clearly, given question figure is hidden in option 3. Hence, the answer is option 3.

Each box weight (70, 50, 30, 90) ends in 0, so every possible subset sum must also be a multiple of 10. All four options satisfy that, so we list achievable sums. Three-box sums: 70+50+30=150, 70+50+90=210, 70+30+90=190, 50+30+90=170. Four-box sum: 70+50+30+90=240. The value 220 does not appear in any one-, two-, three-, or four-box combination. Therefore 220 kg cannot be formed.

Within each triplet the inner pattern is fixed: MOQ and SUW step +2, +2; the answer triplet must mirror NLJ, which steps −2, −2. That eliminates CEG (+2 pattern) and KJI (−1 pattern). Mapping the position of the first letter: in pair 1, M(13) maps to N(14); reversing gives 26−13+1 = 14. Applying the same complement to S(19): 26−19+1 = 8 = H. Continuing with the −2 step gives H, F, D. Therefore SUW : HFD.

The letters available in SHORTING are S, H, O, R, T, I, N, G (no E). THORN (T, H, O, R, N), NITRO (N, I, T, R, O), and STING (S, T, I, N, G) use only letters from this set. NOISE requires an E, which is not present in SHORTING, so it cannot be formed.

Here, dice 3 cannot be constructed as single circle face and the crosses lined face cannot be adjacent to each other.

From the examples, \(5\,\$\,125 = \tfrac{125}{5} = 25\) and \(12\,\$\,48 = \tfrac{48}{12} = 4\). So the rule is \(a\,\$\,b = \tfrac{b}{a}\). Applying it: \(4\,\$\,24 = \tfrac{24}{4} = 6\).

Wall clock, Painting, and Photo frame are all items typically displayed by hanging on a wall. A Carpet is laid on the floor, so it does not share this placement and is the odd one out.

Hence, the answer is option 2.

Hence, answer will be figure 3.

Count the days from 10 March (exclusive) to 25 September (inclusive): \(21 + 30 + 31 + 30 + 31 + 31 + 25 = 199\) days. Odd days = remainder of \(199 \div 7 = 28\) remainder 3. (February falls before March, so leap-year status is irrelevant here.) Three days after Friday is Monday, so Shlok's birthday falls on Monday.

Find each letter's (row, column) coordinates in the two matrices. R appears in Matrix-II at 62, 67, 89. U appears at 56, 96, 97, 98, 99. B appears in Matrix-I only at 40. Y appears in Matrix-II at 79, 88. Option 4 (67, 56, 40, 88) uses R=67, U=56, B=40, Y=88 — all valid. The other options begin with codes that decode to K, J, or E, not R. Therefore RUBY = 67, 56, 40, 88.

The letter counts of the words increase by one each time: yes (3), rain (4), alive (5), subtle (6), so the next word must have 7 letters. Among the options: airport (7), smoke (5), inch (4), fabulous (8). Only airport has 7 letters.

17, 13, and 31 are all odd prime numbers. 80 is even (divisible by 2) and composite, so it does not share the property and is the odd one out.

Hope and Despair are antonyms (despair is the absence of hope). Lunatic means insane or mentally unsound; its antonym is Sane (of sound mind). Honest, Hardworking, and Stylish describe unrelated traits.

Each successive group shifts every letter forward by +6 in the alphabet (wrapping after Z): Abcd → ghIJ → Mnop → stUV → Yzab. The case pattern alternates: Ulll, llUU, Ulll, llUU, Ulll, so the next term must be llUU. Shifting Yzab by +6 (with wrap): Y→e, z→f, a→G, b→H, giving efGH.

The relation is divide by 3: \(111 \div 3 = 37\). Applying the same rule: \(123 \div 3 = 41\). Hence the missing number is 41.

The pattern in each column is: (top number) × (middle number) = bottom number. Column 1: \(13 \times 17 = 221\). Column 3: \(17 \times 19 = 323\). Column 2: \(7 \times 23 = 161\). Hence the missing number is 161.

Argument I raises an ethical principle (imprisoning animals is unethical), which directly addresses the morality of running zoos and is a substantive reason for closing them — hence strong. Argument II justifies captivity merely for entertainment; entertainment is not a serious or sufficient reason to override animal welfare concerns — hence weak. Therefore, only Argument I is strong.

Here, A and G represents Cricket Players who are either Indians or Men.

Clearly, option 2 will complete the figure as it only this figure has a half oval downward.

LMN, RST and VWX are each three consecutive letters of the alphabet (positions differ by +1, +1). PPQ has the first letter repeated (P, P) before moving to Q, so it breaks the consecutive pattern. Hence the odd group is PPQ.

Letters available in SHORTING: S, H, O, R, T, I, N, G. THORN (T,H,O,R,N), NITRO (N,I,T,R,O) and STING (S,T,I,N,G) use only these letters. NOISE needs the letter E, which is not in SHORTING. Hence NOISE cannot be formed.

Apply the code substitutions to \(45 \times 5 - 24 + 3 \div 80\): ×→÷, -→+, +→×, ÷→-. The expression becomes \(45 \div 5 + 24 \times 3 - 80\). By BODMAS: \(45 \div 5 = 9\) and \(24 \times 3 = 72\), giving \(9 + 72 - 80 = 1\). Hence the answer is 1.

The correct answer is: Alluvial soil The Northern Plains of India are formed by the deposition of alluvial soil brought by rivers like the Ganga, Brahmaputra, and their tributaries over millions of years.

The 2016 Grammy for Song of the Year (58th Annual Grammy Awards) was won by "Thinking Out Loud", written by Ed Sheeran and Amy Wadge, and performed by Ed Sheeran. "Alright" (Kendrick Lamar), "Blank Space" (Taylor Swift) and "Girl Crush" (Little Big Town) were fellow nominees but did not win this category.

Checking each statement: 1. 'Dodgers' was written by Bill Beverly, not Don Winslow → incorrect. 2. 'Forty Thieves' was written by Thomas Perry, not Bill Beverly → incorrect. 3. 'The Corrections' was written by Jonathan Franzen, not Thomas Perry → incorrect. All three statements are wrong, so the answer is 1, 2 and 3.

Coelenterates (Cnidaria: jellyfish, corals), ctenophores (comb jellies) and adult echinoderms (starfish, sea urchins) all have body parts arranged around a central axis, so any plane through that axis divides the body into similar halves — i.e. radial symmetry (pentaradial in echinoderms, biradial in ctenophores). Annelida and Platyhelminthes are phyla, not body plans, and they show bilateral symmetry. Hence the answer is Radial.

Lion (Panthera leo), Leopard (Panthera pardus) and Tiger (Panthera tigris) share the species name as their second word; the first word — the genus — is Panthera. Solanum is a plant genus; Felis is the genus of smaller cats like the domestic cat; "Tigris" is the species epithet of the tiger, not a genus.

Under Article 143, the President of India may refer questions of law or fact of public importance, or matters involving constitutional interpretation, to the Supreme Court for its opinion. This power is called Advisory Jurisdiction. Original Jurisdiction (Art. 131) covers Centre-State disputes; Writ Jurisdiction (Art. 32) enforces Fundamental Rights; Appellate Jurisdiction hears appeals from lower courts — none of these involve Presidential references for advice.

An isoquant (iso = equal, quant = quantity) is a curve showing every combination of two inputs (e.g. labour and capital) that yields the same maximum output level — exactly what the blank describes. Short run and long run denote time periods (one or all inputs variable); average product is output per unit of a single input, not an input-combination curve.

Al-Biruni accompanied Mahmud of Ghazni to India in the 11th century and wrote his Arabic account of the subcontinent's geography, religion, philosophy and sciences as Kitab-ul-Hind ("Book of India"), where Kitab is Arabic for book and Al-Hind is the Arabic name for India. The other options mix Sanskrit/Hindi words (Pustak, Bharat) that would not appear in an Arabic title.

iPods, pen drives and flash disks are all hardware devices that hold data using flash memory or hard disks. Linux, however, is an open-source operating system — software that manages hardware resources — not a device that stores data. Hence Linux is not a storage device.

Understanding the Location of Dhamek Stupa The question asks about the location of the famous Dhamek Stupa in India. The options provided are Pune, Delhi, Varanasi, and Hyderabad. The Dhamek Stupa is a significant Buddhist structure. It is located in Sarnath, which is a historical site renowned for its association with Gautam Buddha. Where is Sarnath Located? Sarnath is situated just a few kilometers northeast of Varanasi, in the state of Uttar Pradesh, India. Historically and practically, Sarnath is closely linked to Varanasi, often considered part of the Greater Varanasi region or listed as a tourist attraction under Varanasi. Gautam Buddha is believed to have delivered his first sermon, known as the Dhammachakra Pravartana, at the Deer Park in Sarnath after attaining enlightenment. This makes Sarnath one of the four most important Buddhist pilgrimage sites. The Dhamek Stupa itself was built in 522 CE to replace an earlier structure commissioned by the Mauryan King Ashoka in 249 BCE. Ashoka had erected stupas to enshrine relics of the Buddha and mark significant sites related to his life. Analyzing the Options Pune: Pune is a major city in Maharashtra, far from the important Buddhist sites in Uttar Pradesh. Delhi: Delhi is the capital of India but is located significantly west of Varanasi. While Delhi has historical significance, it is not the location of the Dhamek Stupa. Varanasi: Varanasi is a historic city in Uttar Pradesh. Sarnath, where the Dhamek Stupa is located, is very close to Varanasi and is considered its satellite town. When asking for the city location of the Dhamek Stupa, Varanasi is the correct and most appropriate answer among the given options. Hyderabad: Hyderabad is a major city in Telangana, located in Southern India, very far from Uttar Pradesh and Sarnath. Therefore, based on the geographical location of Sarnath and its close association with Varanasi, Varanasi is the correct city among the given choices where the Dhamek Stupa can be said to be located or is most easily accessed from. City Location Relative to Sarnath Is Dhamek Stupa Here? Pune Far (Maharashtra) No Delhi Far (West India) No Varanasi Very Close (Uttar Pradesh) Yes (in Sarnath, near Varanasi) Hyderabad Far (Telangana) No Conclusion The Dhamek Stupa is located in Sarnath, which is situated near the city of Varanasi in Uttar Pradesh. Among the given options, Varanasi is the city closest to and associated with the location of the Dhamek Stupa. Revision Table: Key Facts about Dhamek Stupa Feature Detail Location Sarnath, near Varanasi, Uttar Pradesh, India Significance Marks the spot where Buddha gave his first sermon Type of Structure Stupa (Buddhist mound) Original Structure by King Ashoka (3rd century BCE) Present Structure from Gupta period (522 CE) Additional Information: Significance of Sarnath Sarnath holds immense importance in the Buddhist world. Besides the Dhamek Stupa, other significant structures and sites in Sarnath include: Dharmarajika Stupa: An older stupa, largely in ruins. Mulagandhakuti Vihara: The main temple, built in the 1930s, housing frescoes by a Japanese artist. Ashoka Pillar: The remains of one of the Pillars of Ashoka, whose capital (the Lion Capital of Ashoka) is now India's national emblem. Archaeological Museum: Houses many artifacts excavated from the site, including the Ashoka Lion Capital. Sarnath attracts Buddhist pilgrims and tourists from all over the world, seeking to visit the place where Buddhism first began to spread.

After Shah Jahan fell ill in 1657, a war of succession broke out among his sons. Dara Shikoh, the eldest and favoured heir, was defeated by his younger brother Aurangzeb at the decisive Battle of Samugarh (1658) and again at Ajmer (1659). He was captured, brought to Delhi and executed in 1659 on Aurangzeb's orders. Jahangir (grandfather) and Babur (founder of the dynasty) lived earlier; Shah Jahan was his father, not a rival.

GDP measures the value of goods and services produced within a country's domestic territory. Production originates in three domestic sectors: agriculture (primary), industry (secondary), and services (tertiary). The international sector is not a domestic production sector — it represents trade (exports and imports) with other countries. While net exports affect GDP via the expenditure method, the actual production happens within the three domestic sectors, not in an "international sector". Hence GDP is not derived from the International sector.

As of June 2017, India had 7 Union Territories: Andaman & Nicobar Islands, Chandigarh, Dadra & Nagar Haveli, Daman & Diu, Lakshadweep, NCT of Delhi, and Puducherry. (Later changes — bifurcation of J&K into J&K and Ladakh in 2019, and the merger of Dadra & Nagar Haveli with Daman & Diu in 2020 — postdate the question's reference period.)

Rajya Sabha seats are allotted to states roughly in proportion to population. Sikkim, being one of India's smallest states by population, is allotted only 1 Rajya Sabha seat (and 1 Lok Sabha seat). Hence the correct answer is 1.

Motion along a straight line at constant speed means equal distances are covered in equal intervals of time, and both speed and direction remain unchanged. This is the definition of uniform motion. Periodic motion repeats after fixed intervals; circular motion follows a curved path; non-uniform motion involves changing speed — none of these fit. Hence the answer is Uniform.

Magnesium loses 2 electrons to form \(\text{Mg}^{2+}\); oxygen gains 2 electrons to form \(\text{O}^{2-}\). Charges balance in a 1:1 ratio, giving the formula MgO (magnesium oxide). The balanced equation is \(2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}\). Hence the product is MgO.

Pradhan Mantri Fasal Bima Yojana (PMFBY), launched in 2016, is the Centre's flagship crop insurance scheme. "Fasal Bima" literally means "crop insurance". It compensates farmers for yield losses due to natural calamities, pests and diseases, with very low premiums (1.5% Rabi, 2% Kharif, 5% commercial/horticulture) subsidised by the government. Soil Health Card deals with soil nutrient status; the R-Urban Missions target rural cluster development — none of these are insurance schemes.

The 2017 IPL final, played on 21 May 2017 at the Rajiv Gandhi International Stadium, Hyderabad, was won by the Mumbai Indians, who beat Rising Pune Supergiant by just 1 run. This was Mumbai Indians' third IPL title (after 2013 and 2015), making them the most successful franchise at the time.

According to standard NCERT/environmental estimates, nearly 40% of forests have been lost in the tropics, compared with only about 1% in the temperate region. Tropical forest loss is driven by agricultural expansion, logging and mining, whereas temperate forests have largely stabilised through reforestation and forest management. Hence the answer is 40.

In the UNDP Human Development Report 2016, Australia secured rank 2, behind only Norway, with an HDI value of about 0.939. The HDI combines life expectancy, education and GNI per capita, and Australia consistently ranks among the top "Very High Human Development" countries. Ranks 20, 100 or 200 are inconsistent with Australia's high living standards.

The Samjhauta Express ("Agreement Express"), introduced in 1976 following the Shimla Agreement, runs between Delhi (Old Delhi/Attari) in India and Lahore in Pakistan, with a border crossing at Attari–Wagah. Karachi connects to India via the separate Thar Express; Islamabad and Quetta have no direct Indian rail link. Hence the answer is Lahore.

Force is a vector quantity having both magnitude and direction. The magnitude is the numerical measure of how strong the force is (expressed in newtons), while direction tells where it acts. Motion is the effect of a force; interaction is its origin; direction specifies orientation — none of these quantify strength. Hence the strength of a force is expressed by its magnitude.

When an acid reacts with a base, the \(\text{H}^+\) of the acid combines with the \(\text{OH}^-\) of the base to form water, while the remaining ions form a salt: \[\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}\] The acidic and basic properties cancel out, so this reaction is called Neutralisation. Desalination, crystallisation and sublimation are physical processes, not acid–base reactions.

Ernest Rutherford discovered the proton in 1919 by bombarding nitrogen gas with alpha particles, producing hydrogen nuclei. He named this positively charged subatomic particle the "proton" (Greek protos = first) in 1920. Friedrich Miescher isolated nucleic acid; Henri Becquerel discovered radioactivity; Henry Cavendish discovered hydrogen — none of these relate to the proton's discovery.

Phloem fibres are elongated sclerenchymatous cells with thick, lignified walls that provide mechanical support to phloem tissue. They are generally absent (or scarce) in primary phloem but are commonly present in secondary phloem, contributing to the bark. Commercial fibres like jute, flax and hemp are obtained from phloem fibres. Xylem fibres/parenchyma belong to xylem, and phloem parenchyma is parenchymatous (not sclerenchymatous). Hence the answer is Phloem fibres.

Step 1 — Divide the largest 4-digit number by 93: \[9999 = 93 \times 107 + 48\] Step 2 — Subtract the remainder: \[9999 - 48 = 9951\] Step 3 — Verify: \(93 \times 107 = 9951\), and the next multiple \(9951 + 93 = 10044\) is a 5-digit number. Hence the largest 4-digit number divisible by 93 is 9951.

Let the fraction be y. According to the statement of the question, ⇒ y + 3/y = 37/10 ⇒ 10y2 – 37y + 30 = 0 ⇒ (y – 5/2) (y – 6/5) = 0 ⇒ y = 5/2 or y = 6/5 Only 5/2 satisfies the necessary condition given in the question. ∴ The fraction is 5/2.

Step 1 — Distance at original speed: \(D = 90 \times \dfrac{35}{60} = 52.5 \text{ km}\) Step 2 — New speed for 21 minutes: \(S_2 = \dfrac{52.5}{21/60} = 52.5 \times \dfrac{60}{21} = 150 \text{ km/hr}\) Step 3 — Required increase: \(150 - 90 = \mathbf{60}\) km/hr.

Since \(\cot\theta = \dfrac{\text{adjacent}}{\text{opposite}} = \dfrac{24}{7}\), take adjacent \(=24\) and opposite \(=7\). By Pythagoras, hypotenuse \(=\sqrt{24^2+7^2}=\sqrt{576+49}=\sqrt{625}=25\). Therefore \(\sec\theta = \dfrac{\text{hypotenuse}}{\text{adjacent}} = \mathbf{\dfrac{25}{24}}\).

For similar triangles, the ratio of areas equals the square of the ratio of corresponding sides: \[\dfrac{\text{Area}(\Delta XYZ)}{\text{Area}(\Delta PQR)} = \left(\dfrac{XY}{PQ}\right)^2 = \left(\dfrac{5}{1}\right)^2 = 25\] Therefore \(\text{Area}(\Delta XYZ) = 25 \times 5 = \mathbf{125}\) sq cm.

From the figure, we can see that In the year 2012, 2014 and 2015 number of admission was greater than that of the previous exam

Total number of admissions till 2015 can be given as ⇒ Total number = 100 + 150 + 150 + 250 + 350 = 1000 ∴ A total of 1000 students took admission in the coaching centre since 2011

Finding the Slope of a Linear Equation The question asks for the slope of the line represented by the equation $\text{2x - 5y = 12}$. To find the slope of a linear equation given in the form $\text{Ax + By = C}$, we can convert it into the slope-intercept form, which is $\text{y = mx + c}$. In this form, 'm' represents the slope of the line, and 'c' represents the y-intercept. Steps to Find the Slope We need to rearrange the given equation $\text{2x - 5y = 12}$ to isolate the variable 'y' on one side. Start with the given equation: $\text{2x - 5y = 12}$ Subtract $\text{2x}$ from both sides of the equation to isolate the term with 'y': $\text{-5y = 12 - 2x}$ It is often helpful to write the 'x' term first, matching the slope-intercept form $\text{y = mx + c}$. $\text{-5y = -2x + 12}$ Divide both sides of the equation by $\text{-5}$ to solve for 'y': $\text{y = } \frac{\text{-2x + 12}}{\text{-5}}$ Separate the terms on the right side: $\text{y = } \frac{\text{-2x}}{\text{-5}} \text{ + } \frac{\text{12}}{\text{-5}}$ Simplify the fractions. Remember that dividing a negative by a negative results in a positive: $\text{y = } \frac{\text{2}}{\text{5}}\text{x - } \frac{\text{12}}{\text{5}}$ Identifying the Slope (m) Now the equation is in the slope-intercept form $\text{y = mx + c}$. Comparing $\text{y = } \frac{\text{2}}{\text{5}}\text{x - } \frac{\text{12}}{\text{5}}$ with $\text{y = mx + c}$, we can clearly see that: The coefficient of $\text{x}$ is $\text{m}$, which is $\frac{\text{2}}{\text{5}}$. The constant term is $\text{c}$, which is $\text{-}\frac{\text{12}}{\text{5}}$. Therefore, the slope of the line $\text{2x - 5y = 12}$ is $\frac{\text{2}}{\text{5}}$. Equation Form General Form Example Slope Slope-Intercept Form $\text{y = mx + c}$ $\text{y = 3x + 4}$ m = 3 Standard Form $\text{Ax + By = C}$ $\text{2x - 5y = 12}$ $\text{-A/B}$ (if B $\neq$ 0) Alternatively, for a linear equation in the standard form $\text{Ax + By = C}$, where B $\neq$ 0, the slope can be calculated directly using the formula $\text{Slope = -A/B}$. In the equation $\text{2x - 5y = 12}$, we have $\text{A = 2}$, $\text{B = -5}$, and $\text{C = 12}$. Using the formula: $\text{Slope = } \frac{\text{-A}}{\text{B}} \text{ = } \frac{\text{-(2)}}{\text{(-5)}} \text{ = } \frac{\text{-2}}{\text{-5}} \text{ = } \frac{\text{2}}{\text{5}}$ Both methods yield the same result. Revision Table: Key Concepts for Finding Slope Concept Description Formula/Method Slope Measure of the steepness of a line; "rise over run" $\text{m = } \frac{\Delta\text{y}}{\Delta\text{x}} \text{ = } \frac{\text{y}_{2} \text{- y}_{1}}{\text{x}_{2} \text{- x}_{1}}$ (using two points) Slope-Intercept Form Equation of a line that shows slope and y-intercept directly $\text{y = mx + c}$ (m is slope, c is y-intercept) Standard Form A common way to write linear equations $\text{Ax + By = C}$ Finding Slope from Standard Form Method to get slope without converting to slope-intercept form (if B $\neq$ 0) $\text{Slope = -A/B}$ Additional Information on Linear Equations and Slope The slope of a line is a fundamental concept in algebra and coordinate geometry. It tells us how much the y-value changes for every unit increase in the x-value. A positive slope means the line rises from left to right. A negative slope means the line falls from left to right. A slope of zero means the line is horizontal. An undefined slope means the line is vertical. Understanding how to convert between different forms of linear equations, like the standard form ($\text{Ax + By = C}$) and the slope-intercept form ($\text{y = mx + c}$), is crucial for analyzing and graphing linear relationships. The slope-intercept form is particularly useful because it immediately provides the slope (m) and the y-intercept (c).

Given \(40 = 0.05\% \times x = \dfrac{0.05}{100}\,x = 0.0005\,x\). Therefore \(x = \dfrac{40}{0.0005} = \dfrac{40 \times 10000}{5} = \mathbf{80000}\).

Step 1 — Find length from perimeter: \(P = 2(l+b) \implies 90 = 2(l+20) \implies l = 45-20 = 25\) cm. Step 2 — Compute area: \(A = l \times b = 25 \times 20 = \mathbf{500}\) sq cm.

The middle term simplifies as \(\dfrac{3(2x - 5/3)}{2} = \dfrac{6x - 5}{2}\). Equation becomes \(\dfrac{17}{3} + \dfrac{6x-5}{2} = \dfrac{1}{6}\). Multiply throughout by 6: \[34 + 3(6x-5) = 1 \implies 34 + 18x - 15 = 1 \implies 18x = -18\] Therefore \(x = \mathbf{-1}\).

Let the Y-axis (where \(x=0\)) divide the segment from \((2,3)\) to \((-2,1)\) in ratio \(k:1\). By the section formula: \[0 = \dfrac{k(-2) + 1(2)}{k+1} \implies -2k + 2 = 0 \implies k = 1\] Therefore the ratio is \(\mathbf{1:1}\).

Step 1 — Find CP from the loss: SP at 15% loss equals 85% of CP. \(170 = 0.85 \times CP \implies CP = \dfrac{170}{0.85} = 200\). Step 2 — Profit at new SP: \(\text{Profit} = 230 - 200 = 30; \quad \text{Profit \%} = \dfrac{30}{200} \times 100 = \mathbf{15\%}\).

Use the identity \(a^3+b^3 = (a+b)^3 - 3ab(a+b)\). Substitute \(a+b=5\) and \(ab=6\): \[a^3+b^3 = 5^3 - 3(6)(5) = 125 - 90 = \mathbf{35}\]

For compound interest, the interest in each successive year grows by a factor of \((1+R)\), i.e. \(CI_{n+1} = CI_n \times (1+R)\). From year 2 to year 4 the multiplier is \((1.10)^2 = 1.21\): \[CI_4 = 1200 \times 1.21 = \mathbf{1452}\]

For an AP, \(a_n = a + (n-1)d\). Given \(a_4 = 11\) and \(a_7 = -4\): \[a_7 - a_4 = 3d = -4 - 11 = -15 \implies d = -5\] Then \(a_{15} = a_4 + 11d = 11 + 11(-5) = 11 - 55 = \mathbf{-44}\).

Reflection of \((x,y)\) in the horizontal line \(y=k\) is \((x, 2k-y)\) — the x-coordinate stays, the y-coordinate is mirrored across \(y=k\). With \((x,y)=(5,-1)\) and \(k=2\): \(2k - y = 4 - (-1) = 5\). Therefore the reflection is \(\mathbf{(5,5)}\).

Admission in 2014 is 250 Admission in 2013 is 150 ⇒ Difference = 250 – 150 = 100 Required percentage = 100 × 100/150 = 66.67% ∴ The admission in 2014 grew by 66.67% as compared to previous year

Step 1 — Combined rate: \(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{60} = \dfrac{3+2+1}{60} = \dfrac{1}{10}\) job/day. Step 2 — Work left after 1 day: \(1 - \dfrac{1}{10} = \dfrac{9}{10}\). Step 3 — Time for C alone: \(\dfrac{9/10}{1/60} = \dfrac{9}{10}\times 60 = \mathbf{54}\) days.

Set \(3A = 2B = 4C = k\), giving \(A = \dfrac{k}{3}, B = \dfrac{k}{2}, C = \dfrac{k}{4}\). Multiply each by the LCM of denominators (12) to clear fractions: \[A : B : C = \dfrac{12}{3} : \dfrac{12}{2} : \dfrac{12}{4} = \mathbf{4 : 6 : 3}\]

Initial total cost \(= 5 \times 650 = 3250\). After adding an item costing Rs. 1400, the new total is \(3250 + 1400 = 4650\) over 6 items. New average \(= \dfrac{4650}{6} = 775\). Therefore the new average is Rs. 775.

After a 25% discount, SP equals 75% of MP, so \(\text{SP} = 0.75 \times \text{MP}\). \[\text{MP} = \dfrac{9750}{0.75} = 9750 \times \dfrac{4}{3} = 13000\] Therefore the marked price is Rs. 13000.

Total number of students in first 3 years can be given as Total number of students = 100 + 150 + 150 = 400 Fees collected by them = 400 × 10000 = Rs. 4000000 Total number of students in last 3 years can be given as Total number of students = 250 + 350 + 300 = 900 Fees collected by them = 900 × 12000 = Rs. 10800000 Total fee = 4000000 + 10800000 = Rs. 1.48 crore ∴ The fee to be collected is Rs. 1.48 crore

Triangle ABC is right-angled at B, with AC as the hypotenuse. Side AB is adjacent to \(\angle A = 30^\circ\). \[\cos 30^\circ = \dfrac{AB}{AC} \implies \dfrac{\sqrt{3}}{2} = \dfrac{AB}{8}\] Therefore \(AB = 8 \times \dfrac{\sqrt{3}}{2} = 4\sqrt{3}\) cm.

Since we know that Cot 60 = 1/√3 and sec 30 = 2/√3 ⇒ 1/√3 – 2/√3 ⇒ - 1/√3 ∴ Cot 60 - Sec 30 = - 1/√3

In the active sentence the singular object "that piece" becomes the passive subject, requiring the singular auxiliary is (not "are") with the past participle "enjoyed": That piece is really enjoyed by the choir. Option 1 fails subject-verb agreement; options 3 and 4 nominalise the verb instead of forming a true passive. Hence option 2 is correct.

The relative clause Z ("which buzzed") must immediately follow its antecedent Y ("at the halo of flies") — the flies are what buzzed. X ("cheerfully round my head") then describes how/where they buzzed. This gives: "...grabbing at the halo of flies which buzzed cheerfully round my head." Hence the order is YZX.

When the reporting verb is in the past tense ("said"), the reported clause backshifts: present perfect ("has gone") becomes past perfect ("had gone"). The conjunction that links the clauses; "then" is a time adverb and is not used here. Hence the correct indirect form is "Akash said that Mahesh had gone home".

The species being "peculiar to the West" is the cause; their being "new to him" is the consequence. The connector must express result, so therefore fits: "peculiar to the West, and therefore new to him." "Because" reverses cause and effect; "if" introduces an unwarranted condition; "for" is grammatically awkward in this slot.

The preposition must show that the seven species belong to the jay family. Of is the standard English preposition for membership or classification — "species of the jay household." "For" implies purpose, "to" suggests direction, and "off" implies separation — none expresses belonging.

"Rampage" means violent, uncontrolled, chaotic behaviour. Its opposite must denote peace and order. Harmony means agreement, peace, and calm — the direct antonym. "Frenzy" and "turmoil" are synonyms of rampage, and "binge" denotes excessive indulgence, not its opposite.

"Blasphemous" means showing irreverence or disrespect towards God or sacred things. Its antonym must denote religious respect and devotion. Pious means devoutly religious and reverent — the direct opposite. "Profane" and "sacrilegious" are synonyms of blasphemous, while "irreligious" denotes absence of religion, not reverence for it.

The comparative "more" requires than to introduce the second element of the comparison: "more than compensated." The idiom "more than compensated" means amply made up for. "Then" is temporal, "that" and "this" are demonstratives — none completes a comparative structure.

"Here" is an adverb of place already meaning "in/at this place," so no preposition is needed before it. The phrase "by here" is redundant and ungrammatical; the correct form is simply "doing here?" Hence the error lies in part (3).

The idiom "to have something on the brain" means to be unable to stop thinking about something — a fixation or preoccupation, i.e. to be obsessed with something. The other options describe wit (option 2), intellectual difficulty (option 3), and nostalgia (option 4), none of which conveys obsession.

"Commemorate" means to honour or mark the memory of a person or event, often through a ceremony — closest in sense to celebrate, which also means to mark or honour an occasion. "Opprobrium," "reproach," and "disrepute" all carry negative connotations of criticism or disgrace, the opposite of commemorating.

The context — she glances back to check whether anyone is watching her at that very moment — calls for the past continuous passive: was/were + being + past participle. With the singular subject "she," the correct form is wasn't being observed. "Wasn't be" is ungrammatical; "weren't being" fails subject-verb agreement; the original "wasn't to be" wrongly suggests destiny or command rather than ongoing observation.

A plebiscite is a direct vote by the eligible electorate on an important public question. A referendum carries the same sense: a direct popular vote on a specific proposal or law. Hence the two are synonyms. The other options describe forms or styles of rule: tyranny and despotism denote oppressive absolute rule, while monarchy denotes rule by a king or queen. None involves a direct popular vote, so the correct synonym is Referendum.

The blank needs a verb meaning 'to tell apart'. Distinguish means to recognise the difference between two things — exactly what a detective does between a lie and a truth. Extinguish means to put out (a fire); finish means to complete; languish means to weaken or suffer. Only distinguish fits the context.

The idiom 'not one's cup of tea' means something one does not like or prefer — i.e. it is not to one's taste or choice. Option 4, 'Not one's choice or preference', captures this exactly. The other options refer to skipping breakfast, giving up before trying, or settling for less — none relates to personal preference.

The intended word means 'to make (pain or a problem) less severe'. The standard spelling is Alleviate — double 'l' and '-iate' ending (from Latin levis, light). Alliviate, Aleviate, and Aliviate all misplace the 'l' count or the vowel sequence. Hence Alleviate is the correctly spelt option.

The phrase 'for some time' signals a duration leading up to a past reference point, which is the cue for the Past Perfect Continuous tense (had been + verb-ing). Thus the sentence reads: 'The battle had been raging for some time.' Is raging is present continuous (wrong time frame); raged (simple past) does not stress the ongoing duration; the infinitive 'to rage' is ungrammatical, so 'no improvement' is incorrect.

Part (2) contains the error. The idiom is 'beneath the dignity', not 'down the dignity' — meaning unworthy of someone's status. The correct phrasing would be 'that was beneath the dignity of the princess'. Parts (1) and (3) are otherwise acceptable, so the erroneous segment is option 2.

The opening fragment 'The investigations of the' demands a subject completion next, so Y ('physiologist and the psychologist') follows. Z ('have revealed that the brain holds a') then supplies the verb and introduces the finding, and X ('peculiar place in the economy of the body') completes the noun phrase 'a peculiar place…'. The coherent sentence is: 'The investigations of the physiologist and the psychologist have revealed that the brain holds a peculiar place in the economy of the body.' Hence the order is YZX.

Perchance is an adverb meaning 'perhaps' or 'possibly', and fits the polite enquiry: 'Do you perchance own a copy of Shakespeare's Hamlet?' Chance and chances are noun/verb forms that cannot modify 'own' here; by chances is not a standard phrase (the correct idiom is 'by chance', meaning accidentally, which does not match the sense of possibility required).

The structure 'Most ___ of all to the rambler' needs an adjective describing the thing causing interest (the fact). Interesting means 'arousing curiosity' — a property of the thing — so it fits. Interest and interests are noun/verb forms and break the 'Most + adjective + of all' frame; interested describes the person feeling curiosity, not the source of it. Hence interesting is correct.

For location within a large geographical area such as a state, the standard preposition is in: 'In Colorado you will look in vain for the common blue jay.' On is used for surfaces or streets; into and onto indicate movement, not static location. So in is the only appropriate choice.

Treason is, by definition, the crime of betraying one's country — typically by aiding its enemies or attempting to overthrow the government. Frankness means openness or honesty; fidelity and allegiance both denote loyalty — the opposite of betrayal. Hence the correct one-word substitute is Treason.

Zealotry is defined as the fanatical and uncompromising pursuit of religious, political, or other ideals — a precise match for the phrase given. Nonpartisan and neutral imply impartiality; aloof implies emotional detachment. None conveys fanatical commitment, so Zealotry is the correct substitute.

The standard English spelling derived from the verb “compose” uses the prefix com- and the noun-forming suffix -ure (compare enclose → enclosure, expose → exposure). This gives Composure. “Cumposure”, “Composore” and “Cumposore” carry an incorrect prefix, an incorrect suffix, or both.