RRC Group D Previous Year Paper 16 (Held On: 1 Nov 2018 Shift 1)

Option 3 is correct, i.e. e-Sanad

• e-Sanad: An initiative of the Ministry of External Affairs for online attestation and Apostille.
• Digi locker is aimed at minimizing the usage of physical documents and enable the sharing of e-documents across agencies.
• UMANG provides a single platform for all Indian Citizens to access pan India e-Gov services ranging from Central to Local Government bodies and other citizen-centric services, launched by the Ministry of Electronics and Information Technology and National e-Governance Division.
• Sakshat: The Ministry of Human Resource Development has designed an education portal that caters to the needs of students, starting from elementary students to research, scholars, teachers and life long learners
• UTTAM: The Ministry of Coal and Coal India Limited (CIL) developed UTTAM, which aims to provide an App for all citizens and coal consumers to monitor the process of Third Party Sampling of coal across CIL subsidiaries.

Option 2 is the correct, i.e. 7.5%

• GDP stands for Gross Domestic Product. GDP is the total value of good and services produced in the country on an annual basis.
• It is the final value of the goods and services produced within the geographic boundaries of a country during a specified period of time, normally a year.
• According to Moody's ratings 2019 gross domestic product (GDP) growth forecast for India to 5.6 per cent, which is lower than 7.4 per cent growth in 2018.

⇒ |21 ÷ (-7) + 12| × 21 + 5

⇒ |-3 + 12| × 21 + 5

⇒ |9| × 21 + 5

⇒ 9 × 21 + 5

⇒ 189 + 5

⇒ 194

Shortcut Trick

Let N be the total number of newspapers.

Total readings by all students = Total readings of all newspapers.

480 × 5 = N × 60

N = (480 × 5) ÷ 60

N = 8 × 5 = 40

∴ The correct answer is Exactly 40.

Alternate Method

Given:

Total number of students = 480

Newspapers read by each student = 5

Number of students reading each newspaper = 60

Formula Used:

Total Student-Newspaper interactions = (Number of Students × Newspapers per Student) = (Number of Newspapers × Students per Newspaper)

Calculations:

⇒ Total readings = 480 × 5 = 2400

⇒ Let n be the number of newspapers.

⇒ 60 × n = 2400

⇒ n = 2400 ÷ 60

⇒ n = 40

∴ The correct answer is Exactly 40.

Additional Information

Double Counting Principle

This problem uses the principle of counting the same set of pairs (Student, Newspaper) in two different ways to form an equation.

Ratio and Proportion

The number of newspapers is inversely proportional to the number of students reading each newspaper when total readings are constant.

Set Theory Application

In a bipartite graph representation, the sum of degrees of student nodes equals the sum of degrees of newspaper nodes.

Option 2 is correct, i.e. Rakesh Satyal

Option 4 is correct, i.e. Nm2kg-2

Universal Gravitation: It is numerically equal to the force of attraction between two bodies each of unit mass placed unit distance apart.

Force of Gravitation can be given as:-

⇒ F = Gm1m2/r2

⇒ F = Force (Newton)

⇒ G = Universal Gravitation Constant (Nm2kg-2)

⇒ m1, m2 = Mass of an object (kg)

⇒ r = Distance between 2 objects (m)

The correct answer is  Vocal cords.

• In humans, the sound is produced by the voice box or the larynx, or the vocal chord. This part of the body is known as the voice box. It is at the upper end of the windpipe.
• Sound is a longitudinal wave. It needs a medium to travel from one place to another.
• The speed of sound in air is 343 m/s.

Additional Information

• The trachea serves as a passage for air, moistens and warms it while it passes into the lungs, and protects the respiratory surface from an accumulation of foreign particles. The trachea is lined with a moist mucous membrane layer composed of cells containing small hairlike projections called cilia.
• The mouth is an oval-shaped cavity inside the skull. The two main functions of the mouth are eating and speaking. Parts of the mouth include the lips, vestibule, mouth cavity, gums, teeth, hard and soft palate, tongue, and salivary glands. The mouth is also known as the oral cavity or the buccal cavity.
• The pharynx is the part of the digestive tract that gets the food from your mouth. Branching off the pharynx is the esophagus, which carries food to your stomach, and your trachea or windpipe, which carries air to your lungs.

Option 2 is correct, i.e. TDP

• Telugu Desam Party is a National party. For National Status, the party wins 2% of seats in the Lok Sabha (11 seats) from at least 3 different States. At a General Election to Lok Sabha or Legislative Assembly, the party polls 6% of votes in four States and in addition, it wins 4 Lok Sabha seats.
• TDP was formed in March 1982 by Late Shri Nandamuri Taraka Rama Rao.
• The current political party in Andhra Pradesh is YSR Congress.

Option 2 is correct, i.e. Fermentation

• Homologous series: A series of compounds in which the same functional group substitutes for hydrogen in a carbon chain is called a homologous series.
• Fermentation: Fermentation occurs in yeast cells and bacteria and also in the muscles of animals. It is an anaerobic pathway in which glucose is broken down.
• Isomers: Each of two or more compounds with the same formula but a different arrangement of atoms in the molecule and different properties.

As Liquid is measured in Litre.

Similarly,

Weight is measured in Kilograms.

Hence, Weight: Kilograms is the correct answer.

Concept:

Mole Concept -

• The quantity one mole of a substance signifies 6.022 × 1023 number of particles of that substance which may be atoms, molecules, or ions.
• The quantity is a universal constant like Dozen, Gross, etc., and is known as Avogadro number, denoted by NA. after the scientist Amedeo Avogadro.
• Examples- In one mole of H2, there are 6.022 × 1023 molecules of hydrogen, and the number of atoms is 2 × 6.022 × 1023, as one molecule of hydrogen contains two-atom each.
• The mass of one mole of a substance is called its Molar Mass (M) or Atomic mass expressed in grams.
• The volume occupied by a mole of gas is 22.4 L at NTP, called its Molar Volume.
• The no. of moles (n) is calculated as =

Number of particles / Avogadro’s number.

• Mole: The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12; its symbol is mol.
• ​The molecular mass of any compound is calculated by adding the masses of all the constituent atoms. It is the mass of one molecule of a substance.
• Molar mass is defined as the mass of one mole of a substance, i.e., 6.022 × 1023 number of particles of that substance.
• The mass of one unit is expressed in the atomic mass unit, a.m.u, or simply 'u'.

​Calculation:

• 1 Mole of a Substance contains atomic mass of all atoms in the same substance. O₂  has an atomic mass of 32 (16 for 1 atom of Oxygen).

⇒ 1 Mole of Oxygen has 16 × 2 = 32 grams.

⇒ $mole = {given mass \over molar mass}$

⇒ $mole = 12 / 32$

⇒ mole = 0.375 mol

Hence, the 12g of Oxygen contains .375 mol.

Important Points

• The molar mass is the mass of one mole of a substance and is expressed in grams 'g'.
• It is the same as molecular mass only expressed in grams.

• India and Vietnam held bilateral discussions regarding the South China Sea dispute and various international affairs.
• The Prime Ministers of Both countries Narendra Modi and Tran Dai Quang held several discussions.
• India expresses interest to nations to the East because of its "Act East Policy". The two countries promised to strengthen ties through maritime cooperation and accepted to explore possibilities in co-production and transfer of technology in the defence sector.

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of sides is 1 : √3 : 2.

The side opposite to 60° (Height) is √3 units = 88√3 m.

1 unit = (88√3) ÷ √3 = 88 m.

The side opposite to 30° (Distance) is 1 unit.

∴ The correct answer is 88 m.

Alternate Method

Given:

Height of the tower (AB) = 88√3 m

Angle of depression = 60° ⇒ Angle of elevation (at building foot C) = 60°

Formula Used:

tan(θ) = Perpendicular ÷ Base

Calculations:

⇒ In right triangle ABC, tan(60°) = AB ÷ BC

⇒ √3 = 88√3 ÷ BC

⇒ BC = (88√3) ÷ √3

⇒ BC = 88 m

∴ The correct answer is 88 m.

Additional Information

Angle of Depression vs Elevation

The angle of depression from an observer to an object below is numerically equal to the angle of elevation from the object to the observer due to alternate interior angles.

Standard Trigonometric Ratios

tan(30°) = 1/√3, tan(45°) = 1, and tan(60°) = √3. These are essential for solving height and distance problems.

Pythagorean Triplets in Height and Distance

For a 30°-60°-90° triangle, the sides are always in the ratio 1 : √3 : 2, where 1 is opposite 30° and √3 is opposite 60°.

Here, the second figure is a combination of figure 1 and its water image.

Hence, the figure given above will be the next figure in the sequence.

Option 3 is correct, i.e. Sulphur

Sulphur:

• It belongs to the 16th group and 3rd period. The name is derived either from the Sanskrit 'sulvere', or the Latin 'sulfurium'.
• There are several allotropes of sulfur. The most common appears as yellow crystals or powder.
• Sulfur is a naturally occurring element, often in volcanic areas. This has traditionally been a major source for human use. It is also widely found in many minerals including iron pyrites, galena, gypsum and Epsom salts.

Let the age of Navya be x and Kavya be y

Given:

x + y = 35 and x × y = 300

→ Value of x and y = 15 and 20

The present age of Navya and Kavya is 15 and 20 years.

After one year their ages will be 16 and 21 years.

Hence, the correct answer is 21 years and 16 years.

The final figure will be as follows:

Hence, the answer will be option 2.

Caterpillar are young one of butterfly.

Similarly,

Baby is the young one of Mother.

Hence, Baby is the correct answer.

Shortcut Trick

To double a sum of money, the Simple Interest earned must be exactly equal to the Principal (100%).

Shortcut formula: Time (T) = [(n − 1) × 100] ÷ Rate (R), where n is the doubling factor.

Here, n = 2 and R = 10%.

T = [(2 − 1) × 100] ÷ 10 = 100 ÷ 10 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given:

Let the Principal (P) = ₹100

The sum doubles itself, so Amount (A) = 2 × P = ₹200

Rate of Interest (R) = 10% per annum

Formula Used:

Simple Interest (SI) = Amount − Principal

SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 200 − 100 = ₹100

⇒ 100 = (100 × 10 × T) ÷ 100

⇒ 100 = 10 × T

⇒ T = 100 ÷ 10

⇒ T = 10 years

∴ The correct answer is 10 years.

Additional Information

Simple Interest Relation

Simple Interest remains constant every year on the original Principal amount. SI = (P × R × T) ÷ 100.

Sum Becoming n-times

If a sum becomes n times itself in T years, the relationship between Rate (R) and Time (T) is R × T = (n − 1) × 100.

Amount in Simple Interest

The total Amount (A) after T years is given by A = P[1 + (R × T) ÷ 100].

Option 4 is correct, i.e. Bihar

• Madhubani painting is one of the many famous Indian art forms. As it is practised in the Mithila region of Bihar and Nepal, it is called Mithila or Madhubani art.
• The colours used in Madhubani paintings are usually derived from plants and other natural sources.

⇒ Central angle of the sector = x% × 360°

⇒ Central angle of the promotion cost = 10% × 360° = (10/100) × 360° = 36°

Shortcut Trick

Difference in working time = 7 weeks − 5 weeks = 2 weeks.

Difference in cash earned = Rs. 500 − Rs. 50 = Rs. 450.

Wage for 1 week = 450 ÷ 2 = Rs. 225.

Total wage for 7 weeks = 225 × 7 = Rs. 1,575.

Value of holiday = Total wage − Cash component = 1,575 − 500 = Rs. 1,075.

∴ The correct answer is Rs. 1,075.

Alternate Method

Given:

Earnings for 7 weeks = Rs. 500 + Holiday

Earnings for 5 weeks = Rs. 50 + Holiday

Let the value of the holiday be H.

Weekly wage is constant, so:

⇒ (500 + H) ÷ 7 = (50 + H) ÷ 5

⇒ 5 × (500 + H) = 7 × (50 + H)

⇒ 2500 + 5H = 350 + 7H

⇒ 7H − 5H = 2500 − 350

⇒ 2H = 2150

⇒ H = 2150 ÷ 2

⇒ H = 1075

∴ The correct answer is Rs. 1,075.

Additional Information

Unitary Method in Wages

Total payment divided by the number of units (time) gives the rate per unit. If rate is constant, then Total Payment ∝ Time.

Variable and Fixed Components

In salary problems, if one part is fixed (like a bonus or holiday) and the other is based on time, the difference in total payment over two periods represents the variable wage for the time difference.

Ratio & Proportion Application

The ratio of earnings for two different periods of work is equal to the ratio of the time periods: E₁/T₁ = E₂/T₂.

Shortcut Trick

Profit ratio is Investment × Time.

Ratio of A : B : C = (320,000 × 12) : (400,000 × 12) : (120,000 × 8).

Simplify ratio: (32 × 12) : (40 × 12) : (12 × 8) ⇒ 384 : 480 : 96.

Dividing by 96: 4 : 5 : 1.

Total units = 4 + 5 + 1 = 10 units = 51,840. So, 1 unit = 5,184.

A = 4 × 5,184 = 20,736; B = 5 × 5,184 = 25,920; C = 1 × 5,184 = 5,184.

∴ The correct answer is 20736, 25920, 5184.

Alternate Method

Given → A's investment = 3,20,000 for 12 months; B's investment = 4,00,000 for 12 months; C's investment = 1,20,000 for (12 − 4) = 8 months. Total profit = 51,840. Formulas: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) : (I₃ × T₃).

⇒ A's profit share = (4 ÷ 10) × 51,840 = 20,736. ⇒ B's profit share = (5 ÷ 10) × 51,840 = 25,920. ⇒ C's profit share = (1 ÷ 10) × 51,840 = 5,184.

∴ The correct answer is 20736, 25920, 5184.

Additional Information

Partnership Concept

In a partnership, the profit is distributed in the ratio of the product of capital invested and the time period for which it was invested.

Effective Capital

If A invests Rs. X for T₁ months and B invests Rs. Y for T₂ months, the ratio of their profits is (X × T₁) : (Y × T₂).

Option 4 is correct, i.e. Thallophyta

Algae:

• Algae are chlorophyll-bearing, simple, thalloid, autotrophic and largely aquatic (both freshwater and marine) organisms.
• They occur in a variety of other habitats: moist stones, soils, and wood.
• Some of them also occur in association with fungi (lichen) and animals (e.g., on sloth bear).
• The algae are divided into three main classes: Chlorophyceae, Phaeophyceae, and Rhodophyceae.

Bryophyta:

• Bryophytes are also called amphibians of the plant kingdom because these plants can live in soil but are dependent on water for sexual reproduction. Bryophytes include the various mosses and liverworts.
• They usually occur in damp, humid and shaded localities. They play an important role in plant succession on bare rocks/soil.

Pteridophyta:

• They are the first terrestrial plants to acquire vascular tissues – xylem and phloem.
• Pteridophytes are used for medicinal purposes and as soil-binders.
• The pteridophytes are found in cool, damp, shady places though some may flourish well in sandy-soil conditions.

Gymnosperm:

• The gymnosperms (gymnos : naked, Sperma: seeds) are plants in which the ovules are not enclosed by any ovary wall and remain exposed, both before and after fertilization.
• Gymnosperms include medium-sized trees or tall trees and shrubs.
• One of the gymnosperms, the giant redwood tree Sequoia is one of the tallest tree species.

Option 3 is correct, i.e. Testes

The Testes is a male reproductive organ. The formation of sperms takes place in the testes. A pair of testes are situated outside the abdominal cavity within a pouch known as the scrotum.

Option 3 is correct, i.e. Reacts with metals and bicarbonates to produce H,0, CO, and salt.

• Acids react with metals and bicarbonates to produce H,0, CO, and salt.
• Acids are sour in taste. Generally, bases are bitter in taste and soapy to touch.
• Acid turns blue litmus red. Bases turn red litmus blue.
• Substances that are neither acidic nor basic are called neutral. The Litmus remains purple for neutral substances.
• Solutions of substances that show different colour in acidic, basic and neutral solutions are called indicators.
• An acid and a base neutralize each other and form a salt. Salt may be acidic, basic or neutral in nature.

In problem figure if we observe first and third figure the line with dot changed place to opposite end but inside the inner square and arrow remained on the same side but changes direction.

Therefore, in the fourth problem figure the line with a dot will be on the lower side outside the inner square and arrow will be on the same side but will be inside the inner square and facing upward.

Hence, the above figure will be the correct answer.

The assumption I is not implicit because the statement does not say that Manisha is the best aerobic trainer. Manisha is a good trainer but whether she is best or not is not clear from the statement.

The assumption II is also not implicit because the statement does not mention any other aerobic trainer.

Hence, neither I nor II is implicit.

Given:

The speed of a wave in a medium = 600 m/s

Number of waves passing in 1 min = 600 waves

Concept used:

The wavelength of a wave = Total distance/Number of waves

Calculation:

⇒ Distance covered by a wave in 1 second = 600 m.

⇒ So, Total distance covered by the wave in 60 seconds = 60 × 600 =  36000 m.

= 36000/600 = 60 m.

The pattern when the given sheet is folded is as follows:

Hence, answer figure b will be the correct answer.

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of sides opposite to these angles is 1 : √3 : 2.

The horizontal distance (base) is opposite to 60° ⇒ √3 units = 36 m.

The height of the tower is opposite to 30° ⇒ 1 unit = 36/√3 m.

Rationalizing: (36 × √3) / 3 = 12√3 m.

∴ The correct answer is 12√3 m.

Alternate Method

Given:

Angle of depression = 30° ⇒ Angle of elevation (θ) = 30°.

Distance between tower and building (Base) = 36 m.

Formula Used:

tan θ = Perpendicular / Base

30° h (Height) 36 m (Distance) Tower Top Building Foot

30°

Calculations:

⇒ tan 30° = Height / 36

⇒ 1/√3 = Height / 36

⇒ Height = 36 / √3

⇒ Height = (36 × √3) / (√3 × √3)

⇒ Height = 36√3 / 3

⇒ Height = 12√3 m

∴ The correct answer is 12√3 m.

Additional Information

Angle of Depression and Elevation

The angle of depression from the top is always equal to the angle of elevation from the bottom due to alternate interior angles of parallel lines.

Trigonometric Ratios

Standard values: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3. These are essential for solving Height and Distance problems.

Rationalization

To remove a square root from the denominator, multiply the numerator and denominator by that same root: a/√b = (a√b)/b.

Option 1 is correct, i.e. Electrons

• Proton is a stable subatomic particle that has a positive charge(1.60217662 × 10^-19 coulombs) which is equal in magnitude to an electron's charge(1.6 × 10^-19 coulombs) and a rest mass of 1.67262 × 10^-27 kg, which is 1,836 times the mass of an electron. It is discovered by Eugen Goldstein.
• Neutron: A neutral subatomic particle that is constituent in every atomic nucleus except ordinary hydrogen's isotope Protium. The neutron was discovered in 1932 by the English physicist James Chadwick.
• Electron is the lightest stable subatomic particle. The electron was discovered in 1897 by the English physicist J.J Thomson.
• Positrons: Positron, also called positive electron, positively charged subatomic particle having the same mass and magnitude of charge as the electron and constituting the antiparticle of a negative electron. The first of the antiparticles to be detected, positrons were discovered by Carl David Anderson.

Shortcut Trick

Convert fractional ratio 1/2 : 1/3 : 1/4 to integer ratio by multiplying with LCM(2, 3, 4) = 12.

New Ratio → 6 : 4 : 3 | Total units = 6 + 4 + 3 = 13 units.

13 units = 286 pencils ⇒ 1 unit = 22 pencils.

First child (6 units) = 6 × 22 = 132 pencils.

∴ The correct answer is 132 pencils.

Alternate Method

Given: Total pencils = 286 | Ratio = 1/2 : 1/3 : 1/4

Step 1: Simplify the ratio

⇒ Ratio = (1/2 × 12) : (1/3 × 12) : (1/4 × 12)

⇒ Ratio = 6 : 4 : 3

Step 2: Find the value of one share

⇒ Sum of ratio parts = 6 + 4 + 3 = 13

⇒ Value of 1 unit = 286 ÷ 13 = 22

Step 3: Calculate the share of the first child

⇒ First child share = 6 × 22

⇒ First child share = 132

∴ The correct answer is 132 pencils.

Additional Information

Ratio Simplification

To convert a fractional ratio a/b : c/d to integers, multiply both terms by the Least Common Multiple (LCM) of the denominators b and d.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (a × c : b × d). It is used when two different sets of related proportions need to be combined.

Proportional Division

To divide a quantity Q in ratio a : b : c, the share of first part is calculated as [a ÷ (a + b + c)] × Q.

• The valve present on the right auriculo-ventricular septum between the right atrium and right ventricle is called the Tricuspid valve.
• The bicuspid valve, also known as the left atrioventricular valve or the mitral valve is a valve having 2 flaps in the heart. It lies between the left auricle and left ventricle.

Option 3 is correct, i.e. Sexual reproduction

• Sexual reproduction: Involves the formation of the male and female gametes, either by the same individual or by different individuals of the opposite sex. These gametes fuse to form the zygote which develops to form the new organism. It is an elaborate, complex and slow process as compared to asexual reproduction. (E.g. Mammals)
• Asexual reproduction: The reproduction in which an offspring is produced by a single parent without the fusion of gametes is called asexual reproduction. (E.g. Amoeba, Hydra)
• Vegetative propagation: It is the mode of asexual reproduction in plants. Plant parts are detached from the parent & form a new plant.(E.g. Roses)
• Tissue culture: Whole plants could be regenerated from any part of a plant taken out (explants) and grown in a test tube, under sterile conditions in special nutrient media.

⇒ Mass of the object (m) = 10 kg.

⇒ Height raised against gravity = 4m.

⇒ Gravity acting upon the object (g) = 10 m/s².

⇒ Now we know that work is done by gravity hence we take ‘g’ as ‘+ g’.

⇒ Total work is done against gravity G = mgh

⇒ J is energy expressed as Joule.

⇒ Now we are substituting values in above equation we get

⇒ G = (10)(4)(10)

⇒ G = 400 Joule

⇒ Work done by force acting on the object is 400 J.

• Mohan Bhatt is best known for his Grammy award-winning album “A Meeting by the River with Ry Cooder”.
• The 2017 Padma Bhushan Award in the field of Art-Music was awarded to Vishwa Mohan Bhatt. Bhatt is a Grammy-winning Hindustani classical music instrumentalist who plays the Mohan Veena.

As movies have a huge influence on masses, film makers are obliged to show such warnings in public interest, and it does not matter whether they change the mood of audience or create disturbance on the screen.

Hence, both I and II are not strong arguments.

The correct answer is April 21^st.

Key Points

• The Government of India celebrates April 21 every year as 'Civil Services day' as an occasion for the civil servants to rededicate themselves to the cause of citizens and renew their commitments to public service and excellence in work.
• The first such function was held in Vigyan Bhawan, New Delhi 21 April 2006.
• The first Home Minister was Sardar Vallabhbhai Patel who addressed the first Batch of officers in 1947.

Here, each alphabet is replaced by the alphabet which appears at same positional value in reverse alphabetical order.

Therefore, BRING will be coded as YIRMT.

Hence, YIRMT is the correct answer.

Option 3 is correct, i.e. New Delhi

• FSSAI stands for the Food Safety and Standard Authority of India. It had been established under Food Safety and Standards, 2006 and is headquartered in New Delhi.
• It functions under the Ministry of Health and Family welfare.
• The motto of FSSAI is Inspiring Trust, Assuring Safe and Nutritious Food.

The pattern followed here is:

The triangles in the given figure are as follows:

Hence, the correct answer is "12".

Alternate Method

The triangles in the given figure are as follows:

ABD, ABC, ACD, FBD, FBC, FCD, ABE, ABF, AFE, AFD, EBD and FED

Hence, there are 12 triangles in the given figure.

Statement 1: Y arrives after K and U.

The person who came first can be either K or U.

Hence, statement I alone is insufficient.

Statement 2: K arrives before U.

K arrives before U but no information is given about Y

Hence, statement II alone is insufficient.

Both statement I and statement II:

Combining both the statements, it can be determined that K is first to arrive followed by U and then Y.

Hence, both statement I and statement II together are sufficient.

Shortcut Trick

According to the Tangent-Secant Theorem, when a tangent and a secant meet at an external point D, the property states: DE² = BD × AD.

Given: DE = 12 cm and AB = 10 cm. Let BD = x. Then AD = x + 10.

⇒ 12² = x × (x + 10)

⇒ 144 = x² + 10x

By testing options, if x = 8, then 8 × (8 + 10) = 8 × 18 = 144.

∴ The correct answer is 8 cm.

Alternate Method

Given:

Length of chord AB = 10 cm

Length of tangent DE = 12 cm

Formula Used:

For a circle, if a tangent DE and a secant DAB are drawn from an external point D, then DE² = DB × DA.

Calculations:

⇒ Let the length of BD be x cm.

⇒ Total length DA = AB + BD = (10 + x) cm.

⇒ Applying the theorem: DE² = BD × DA

⇒ 12² = x × (x + 10)

⇒ 144 = x² + 10x

⇒ x² + 10x − 144 = 0

⇒ x² + 18x − 8x − 144 = 0

⇒ x(x + 18) − 8(x + 18) = 0

⇒ (x − 8)(x + 18) = 0

⇒ x = 8 or x = −18

⇒ Since length cannot be negative, x = 8.

∴ The correct answer is 8 cm.

Additional Information

Tangent-Radius Property

A tangent at any point on a circle is always perpendicular to the radius at the point of contact (OE ⊥ DE).

Intersecting Chords Theorem

If two chords AB and CD intersect at an internal point P, then AP × PB = CP × PD.

Two Secants Theorem

If two secants PAB and PCD are drawn from an external point P, then PA × PB = PC × PD.

The above directions can be depicted in diagram as follows:

Hence, Surya is facing East direction after the final movement.

Shortcut Trick

Use the MDH / W formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

M₁ = m, D₁ = p, W₁ = 1/n

M₂ = x (required), D₂ = q, W₂ = 1 (whole work)

⇒ (m × p) / (1/n) = (x × q) / 1 ⇒ mnp = xq ⇒ x = mnp/q

∴ The correct answer is mnp/q.

Alternate Method

Given:

Number of men (M₁) = m

Number of days (D₁) = p

Work done (W₁) = 1/n

Target work (W₂) = 1 (Whole work)

Target days (D₂) = q

Formula Used:

M₁ × D₁ × W₂ = M₂ × D₂ × W₁

Calculations:

⇒ m × p × 1 = M₂ × q × (1/n)

⇒ mp = M₂ × q / n

⇒ mp × n = M₂ × q

⇒ M₂ = mnp / q

∴ The correct answer is mnp/q.

Additional Information

General Work Formula

For different numbers of men, days, hours, and work: (M₁D₁H₁)/W₁ = (M₂D₂H₂)/W₂.

Efficiency and Time

Total Work = Efficiency × Time. If efficiency is constant, the number of persons is inversely proportional to time.

Work and Wages

Wages are generally distributed in the ratio of the work done by each individual (Efficiency × Time).

Option 2 is correct, i.e. 0.6 g

• Mole: One mole is the amount of a substance that contains as many particles or entities as there are atoms in exactly 12 g (or 0.012 kg) of the 12C isotope.

⇒ mole = given mass / molar mass

⇒ 1 mole of Hydrogen atom contains 1 gram of Hydrogen. which implies 0.6 moles of Hydrogen atom will contain 0.6 g.

The logic followed here is:

9 × 2 = 18;

18 × 2 = 36;

36 × 2 = 72;

72 × 2 = 144;

144 × 2 = 288;

Hence, ? will be replaced by 288.

⇒ 4² × {(2 + 3) - 11}

⇒ 4² × {5 - 11}

⇒16 × {-6}

⇒ Required answer = -96

Concept used:

40 – (7 × 3 + 24 ÷ 8 × 3 – 4 × 2) + 12

⇒ 40 – (7 × 3 + 3 × 3 – 4 × 2) + 12

⇒ 40 – (21 + 9 – 8) + 12

⇒ 40 – 22 + 12

⇒ 52 – 22

⇒ 30

Statement I is implicit as the core issue is increased number of four wheelers and the argument I insists on a cap on the number of four wheeler in the market. Statement II insists on well-disciplined traffic rules. But well – disciplined traffic can also result in jam and create menace for bicycle riders. So, argument II is not implicit.

Hence, only statement I is implicit.

Option 4 is correct, i.e. 1904

• It All Started With The Summer Games Medals.
• The 1904 Olympic Games in St Louis, were the first at which gold, silver and bronze medals were awarded for first, second, and third place.
• Headquarters of the International Olympic Committee is in Lausanne, Switzerland.

Statement I do not follows as putting a ban on new registration of vehicles is not feasible as it will not allow people to buy new vehicles which may have new technology and solution for harmful emissions.

Statement II follows as 15-year-old vehicles are outdated and have old technologies and due to wear and tear their harmful emission are higher than new vehicles. So, old vehicles should be stopped from moving in the city X.

Hence, only conclusion II follows.

Shortcut Trick

Total ratio units = 3 + 4 + 5 = 12 units.

Sum of angles in a triangle = 180°.

Value of 1 unit = 180° ÷ 12 = 15°.

Angles: 3 × 15° = 45°, 4 × 15° = 60°, 5 × 15° = 75°.

∴ The correct answer is 45°, 60°, 75°.

Alternate Method

Given: Ratio of angles = 3 : 4 : 5.

Formula Used: Sum of internal angles of a triangle = 180°.

⇒ Let the angles be 3x, 4x, and 5x.

⇒ 3x + 4x + 5x = 180°

⇒ 12x = 180°

⇒ x = 180° ÷ 12

⇒ x = 15°

⇒ First angle = 3 × 15° = 45°

⇒ Second angle = 4 × 15° = 60°

⇒ Third angle = 5 × 15° = 75°

∴ The correct answer is 45°, 60°, 75°.

Additional Information

Angle Sum Property

The sum of all interior angles of any triangle is always 180°.

Types of Triangles by Angles

Acute-angled (all < 90°), Right-angled (one = 90°), and Obtuse-angled (one > 90°).

Ratio Distribution

To find a part: (Individual Ratio ÷ Total Ratio Sum) × Total Value.

Option 4 is correct, i.e. Odisha

Know about Odisha:

• Capital- Bhubaneshwar
• State animal- Sambar deer
• It is bounded by the states of Jharkhand and West Bengal to the north and northeast, by the Bay of Bengal to the east, and by the states of Andhra Pradesh and Telangana to the south and Chattisgarh to the west.
• Loksabha seats- 21
• Rajya Sabha seats- 10

Let the age of A be x, B be y and C be z.

x = y; x + y + z = 5z

→ x + y = 4z.

→ 2x = 4z; x = 2z

three years ago

x – 3 = 3 (z – 3)

→ 2z – 3 = 3z – 9 (as x = y = 2z)

→ 9 – 3 = z

→ 6 = z

Present age of C is 6 years and after 4 years from now C will be 10 years old.

Hence, 10 is the correct answer.

Shortcut Trick

Initial petrol = 128/7 l

Final petrol = 48/7 l

Consumed petrol = (128 − 48) / 7 = 80/7 l

Fraction consumed = (80/7) ÷ (128/7) = 80/128 = 5/8

∴ The correct answer is 5/8.

Alternate Method

Given:

Initial quantity = 18 2/7 l

Leftover quantity = 6 6/7 l

⇒ Initial petrol = (18 × 7 + 2) / 7 = 128/7 l

⇒ Leftover petrol = (6 × 7 + 6) / 7 = 48/7 l

⇒ Consumed petrol = 128/7 − 48/7 = 80/7 l

⇒ Fraction consumed = (80/7) / (128/7)

⇒ Fraction consumed = 80 / 128 = 5 / 8

∴ The correct answer is 5/8.

Additional Information

Mixed Fraction Conversion

To convert a mixed fraction a b/c to an improper fraction, use the formula: (a × c + b) / c.

Fraction Subtraction

When denominators are the same, subtract the numerators directly: a/c − b/c = (a − b) / c.

Calculation of Fraction Part

The fraction of a quantity consumed is given by the ratio: (Consumed Amount) / (Original Total Amount).

Shortcut Trick Use the multiplier method where SP = CP × (100 + P%) ÷ 100. SP = 1525 × (112 ÷ 100) = 1525 × 1.12. Calculation: 1525 × 1.12 = 1708. ∴ The correct answer is Rs. 1,708.

Alternate Method Given: Cost Price (CP) = Rs. 1,525, Profit Percentage = 12%. Formulas: Profit = (Profit% ÷ 100) × CP | SP = CP + Profit.

⇒ Profit = (12 ÷ 100) × 1525 ⇒ Profit = 0.12 × 1525 = 183 ⇒ SP = CP + Profit = 1525 + 183 ⇒ SP = 1708 ∴ The correct answer is Rs. 1,708.

Additional Information Cost Price & Selling Price The Cost Price (CP) is the price at which an item is purchased, and the Selling Price (SP) is the price at which it is sold. Profit occurs when SP > CP. Profit Percentage Profit % is always calculated on the Cost Price unless stated otherwise. Formula: Profit% = (Profit ÷ CP) × 100.

Option 1 is correct, i.e. Planning Commission

• Narendra Modi is the Chairperson of the NITI Aayog as of January 2019.
• NITI Aayog:
• Abbreviation of National Institution for Transforming India.
• Is a policy think tank of the Government of India.
• Established with the aim – “To achieve sustainable development goals with cooperative federalism by fostering the involvement of State Governments of India in the economic policy-making process using a bottom-up approach.”
• It was established in 2015, by the NDA government, to replace the Planning Commission which followed a top-down model.​
• The NITI Aayog comprises of the following:

• In addition, it also comprises a Governing Council composed of -
• All the state Chief Ministers
• The Chief Ministers of Delhi and Puducherry
• The Lieutenant Governor of Andaman and Nicobar

As Run (faster form) is related to Walk (slower form).

Similarly,

Rush(fast) is related to Slow.

Hence, Slow is the correct answer.

i) +, ÷, × → 8 + 10 ÷ 20 × 6 = 8 + (0.5 × 6) = 8 + 3 = 11

ii) ÷, ×, + → 8 ÷ 10 × 20 + 6 = (8 ÷ 10) × 20) + 6 = 16 + 6 = 22

iii) ÷, -, × → 8 ÷ 10 – 20 × 6 = 0.8 – 120 = 119.2

iv) ÷, +, × → 8 ÷ 10 + 20 × 6 = (8 ÷ 10) + (20 × 6) = 0.8 + 120 = 120.8

Hence, +, ÷, × is the correct answer.

The conservation of energy principle is applied in both positions.

⇒ The energy possessed at launch is given by Ke = 1/2m v²  where m is the mass of the object and V is the velocity.

⇒ V  = √0.8 x V_e where V_e is the escape velocity given by √(2GM) / R, where G is the universal Gravity constant.

⇒ Ke = 1/2 x m x 0.8 X 2GM/R

⇒ Potential energy is possessed by the object when it is on the surface of the earth as g, gravity acts downwards until the core of the earth, hence will be negative.

⇒ P_earth = -GMm / R and the Potential energy at a height H, when thrown vertically up, is P_{height H} = -GMm/ (R + H) Where M is the mass of Earth, m is the mass of the object, R is the radius of Earth and H is the Maximum height which the object attains.

⇒ Applying the conservation of energy we have 

⇒ (- GMm / R ) +  (0.8GMm/R) =  ( -GMm/ (R + H))

⇒ Cancelling out G, M, m we have

⇒ (-1/R) + (0.8/R) = -1/(R+H) , Solving for H , we have

⇒ H= 4R

Shortcut Trick

Identify the LCM of 21, 35, and 175: 21 = 3 × 7, 35 = 5 × 7, 175 = 5² × 7.

LCM = 3¹ × 5² × 7¹ = 525.

To make it a perfect square, every prime factor must have an even power.

Multiply by 3 and 7 to complete the pairs: 525 × 3 × 7 = 525 × 21 = 11025.

∴ The correct answer is 11025.

Alternate Method

Given: Divisors are 21, 35, and 175.

Step 1: Find the prime factorization of each number.

⇒ 21 = 3 × 7

⇒ 35 = 5 × 7

⇒ 175 = 5 × 5 × 7 = 5² × 7

Step 2: Find the LCM by taking the highest power of all prime factors.

⇒ LCM = 3¹ × 5² × 7¹ = 11025 ÷ 21 = 525

Step 3: To find the least perfect square, multiply the LCM by prime factors that do not have pairs.

⇒ Factors of 525 = 3 × 5² × 7

⇒ Missing factors for pairing = 3 × 7

⇒ Least perfect square = (3 × 5² × 7) × (3 × 7) = 3² × 5² × 7²

⇒ Calculation: 9 × 25 × 49 = 11025

∴ The correct answer is 11025.

Additional Information

Perfect Square Property

A number is a perfect square if and only if all the exponents in its prime factorization are even numbers.

Least Common Multiple (LCM)

The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.

Prime Factorization Method

To find the least perfect square divisible by certain numbers, first find the LCM and then multiply it by the minimum factors required to make all prime exponents even.

The logic followed here is:

B (2) O (15) X (24) → 17 + 24 → 41

M (13) A (1) P (16) → 13 + 1 + 16 → 30

R (18) A (1) T (20) → 18 + 1 + 20 → 39

Hence, RAT will be coded as 39.

Shortcut Trick

Convert the percentage to a fraction: 25/3% = 25/(3 × 100) = 1/12.

If 1/12 of a number is 150, then 1 unit = 150 × 12.

Total value = 1800.

∴ The correct answer is 1800.

Alternate Method

Given: 25/3% of a number is 150.

Formula Used: Percentage value = (Percentage/100) × Original Number

⇒ Let the number be x.

⇒ (25/3) × (1/100) × x = 150

⇒ (25/300) × x = 150

⇒ (1/12) × x = 150

⇒ x = 150 × 12

⇒ x = 1800

∴ The correct answer is 1800.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide the value by 100. For example, x% = x/100.

Base Change in Percentage

If a% of X is Y, then the original number X can be calculated as (Y × 100) / a.

Common Percentages

8.33% is equivalent to 1/12, and 16.66% is equivalent to 1/6.

Left Side: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z : Right Side

18^th letter from the left is: R

6^th letter to the right of R: X

Hence, X is the correct answer.

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

​

1987 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 1900 + 86 year + year 1987

• In 1900 year the odd days = 1 odd day
• In 86 years, odd days = 21 leap year + 65 ordinary years
• 21 Leap year = 42 Year = 0 odd day
• 65 Normal Year = 65 Year = 2 odd day
• Odd days in 1 January to 1 August:
• In 1987, the number of days up to 1 August = 31 (Jan) + 28 (Feb - normal year) + 31(Mar) + 30(Apr) + 31(May) + 30 (June) + 31(July) + 1 (Aug) = 213 / 7 = 3 odd days.
• Total = 1 + 0 + 2 + 3 = 6 days
• 6 is the code for Saturday.

Hence, 1st August, 1987 is Saturday.

Option 4 is correct, i.e. Good Conductor

• Resistance: It is the opposition that a substance offers to the flow of electric current.
• The resistance of the conductor depends on:
• its length
• on its area of cross-section
• on the nature of its material.
• R = ρl /A wherein R is Resistance, ρ is resistivity, l is the length of the conductor, A is the area of cross-section.
• The symbol of resistance is Ω and its unit is the ohm.​
• Conductivity: electrical conductivity is the ability of electric current to flow through a material. Its unit is mho.
• Silver is a natural element which has high conductivity and low resistivity.

Shortcut Trick

When two people start simultaneously and meet at a point, the ratio of their speeds is the inverse square root of the ratio of time taken to reach their destinations after meeting.

Ratio of Speeds (S_P ÷ S_G) = √(T_G ÷ T_P)

40 ÷ S_G = √(4 ÷ 16) = √(1 ÷ 4) = 1 ÷ 2

S_G = 40 × 2 = 80 km/h

∴ The correct answer is 80 km/h.

Alternate Method

Given: Speed of Parvez (S₁) = 40 km/h, Time taken by Parvez after meeting (t₁) = 16 hours, Time taken by Gautam after meeting (t₂) = 4 hours.

Formula Used: S₁ ÷ S₂ = √(t₂ ÷ t₁)

⇒ S₁ ÷ S₂ = √(4 ÷ 16)

⇒ 40 ÷ S₂ = √(1 ÷ 4)

⇒ 40 ÷ S₂ = 1 ÷ 2

⇒ S₂ = 40 × 2

⇒ S₂ = 80 km/h

∴ The correct answer is 80 km/h.

Additional Information

Meeting Point Logic

If two objects start at the same time, the time taken to meet is T = √(t₁ × t₂), where t₁ and t₂ are times taken after meeting.

Relative Speed

For objects moving towards each other, Relative Speed = S₁ + S₂. For objects moving in the same direction, Relative Speed = |S₁ − S₂|.

Distance Formula

Total Distance = (S₁ × Time to meet) + (S₂ × Time to meet) or S₁(T + t₁).

• The first subsidiary treaty was signed by the Nizam of Hydrabad in 1798.
• The Subsidiary Alliance System was “Non-Intervention Policy” used by Lord Wellesley who was the Governor-General (1798-1805) to establish British Empire in India.
• The Nizam of Hyderabad’ was the first to sign this policy in 1798 AD.
• The Second state to sign this policy was Mysore in1799 AD.

Shortcut Trick

Total Quarterly sales (3 months) = ₹1,50,000

Average Monthly sales = 1,50,000 ÷ 3 = ₹50,000

Sales from other healthy drinks = 100% − 85% = 15%

Required monthly sales = 15% of 50,000 = ₹7,500

∴ The correct answer is Rs. 7,500.

Alternate Method

Given:

Average Quarterly sales = ₹1,50,000

Sales from Shakes = 85%

Formula Used:

Monthly Sales = Quarterly Sales ÷ 3

Value of non-shake sales = (100% − Shakes%) × Monthly Sales

Calculations:

⇒ Average monthly sales = 1,50,000 ÷ 3

⇒ Average monthly sales = ₹50,000

⇒ Sales percentage of other healthy drinks = 100% − 85% = 15%

⇒ Monthly sale from other health drinks = 15% of 50,000

⇒ Sales = (15 ÷ 100) × 50,000

⇒ Sales = 15 × 500

⇒ Sales = ₹7,500

∴ The correct answer is Rs. 7,500.

Additional Information

Time Conversions in Sales

A Quarter consists of 3 months. To convert quarterly figures to monthly, divide by 3. To convert annual figures to monthly, divide by 12.

Percentage Breakdown

In any business scenario, the sum of all category percentages must equal 100%. If one category is x%, the remaining categories represent (100 − x)%.

Average Calculation

Average = Total Sum ÷ Number of units. In this case, Average Monthly Sale = Total Quarterly Sale ÷ Number of months in a quarter.

The logic followed here is :

The symbols in four parts of square are moving in clockwise direction and the plus is one and two in alternate figures.

Hence, the figure given above will replace the question mark.

5.032 + 150.03 + 40.00 - 30.50

⇒ 195.062 - 30.50

⇒ Required answer 164.562

Option 1 is correct, i.e. Transition element

• The d-block elements are known as transition elements.
• There total of 4 blocks in the modern periodic table. They are as follows: s block, p block, d block, f block.
• There are 18 groups and 7 periods in the modern periodic table.
• Total elements are 118 out of which 91 are metals, 7 are metalloids, and 20 are non-metals.

Option 4 is correct, i.e. Architecture

• Balkrishna Vithaldas Doshi is an Indian Architecture.
• He is the first Indian who won the Pritzker Prize in 2018.
• The prestigious Pritzker Prize, considered architecture field’s Nobel, has been awarded to renowned Indian architect Balakrishna Doshi for 2018.
• Doshi has designed many educational institutions like IIM Bangalore, IIM Lucknow, etc. and is noted for his contributions to many low - cost housing projects.

The above figure will be the mirror image of the question figure.

The correct answer is Inder Kumar Gujral.

Key Points

• I.K Gujral was the 12^th Prime Minister of India. First Prime Minister of India was Pt. Jawaharlal Nehru.
• Gujral Doctrine is viewed as an achievement in India's international strategy.
• It was verbalized that the Gujral Doctrine as India's foreign policy as to accomplish better relations with immediate neighbours and to establish harmony in South Asia.
• It was executed by Inder Kumar Gujral, the then Minister of External Affairs in H. D. Deve Gowda Government in 1996.
• This doctrine says that India as a bigger nation among the South Asian nations should give one-sided preferences to her immediate small neighbours and build cordial relations with them.
• Similar Policies: Panchsheel of Jawaharlal Nehru.

Shortcut Trick

Total CP = SP × 100 ÷ (100 + P%)

Total CP = 58000 × 100 ÷ 116 = 50000

Purchase Price = Total CP − Repair Cost

Purchase Price = 50000 − 3000 = 47000

∴ The correct answer is Rs 47,000.

Alternate Method

Given: Selling Price (SP) = Rs. 58,000, Repair Cost = Rs. 3,000, Profit% = 16%. Formulas: Total CP = SP ÷ (1 + Profit%/100) | Purchase Price = Total CP − Overhead Expenses.

⇒ Let the Total Cost Price be x.

⇒ SP = x + 16% of x = 1.16x.

⇒ 58000 = 1.16x ⇒ x = 58000 ÷ 1.16 = 50,000.

⇒ Purchase Price = Total CP − Repairing Cost = 50,000 − 3,000 = 47,000.

∴ The correct answer is Rs 47,000.

Additional Information

Total Cost Price

Total CP includes the purchase price plus any overhead expenses like repairs, transportation, or installation.

Profit and Loss Calculation

Profit or Loss is always calculated on the Total Cost Price, not just the initial purchase price.

Option 4 is correct, i.e. Jharkhand and Bihar

Gautam Buddha Wildlife Sanctuary is situated in Jharkhand and Bihar.

The correct answer is By absorbing radiating heat energy.

Key Points

• A substance can change from one state of matter (solid, liquid, or gas) to another by absorbing or releasing heat energy.
• When a substance absorbs heat energy, the kinetic energy of its particles increases, causing changes such as melting (solid to liquid) and vaporization (liquid to gas).
• Similarly, when heat is removed, processes such as condensation (gas to liquid) and freezing (liquid to solid) occur.
• Heat energy affects the intermolecular forces between particles, enabling the change of state without altering the chemical composition of the substance.
• Hence, the change of one state of matter into another is primarily achieved by absorbing (or releasing) heat energy.

Additional Information

• Melting:
• Conversion of a solid into a liquid by absorbing heat.
• Example: Ice melting into water at 0°C.
• Vaporization:
• Conversion of a liquid into a gas by absorbing heat.
• Example: Water changing into steam at 100°C under normal atmospheric pressure.
• Condensation:
• Conversion of a gas into a liquid by releasing heat.
• Example: Formation of water droplets on a cold surface.
• Sublimation:
• Direct conversion of a solid into a gas without passing through the liquid state.
• Examples: Camphor, naphthalene, and dry ice.
• Effect of Pressure:
• Increasing pressure can also change the state of matter in some cases, especially gases.
• However, the most fundamental and commonly accepted factor responsible for change of state is heat energy.

Important Points

• Latent Heat is the heat absorbed or released during a change of state without any change in temperature.
• Latent Heat of Fusion: Heat required to convert a solid into a liquid at its melting point.
• Latent Heat of Vaporization: Heat required to convert a liquid into a gas at its boiling point.
• The three common states of matter are solid, liquid, and gas, while plasma and Bose-Einstein Condensate are additional states under special conditions.

Option 3 is correct, i.e. 30^th April

• International Jazz Day is an International Day declared by the United Nations Educational, Scientific and Cultural Organization in 2011.
• It is celebrated on 30th April and observed by UNESCO.
• UNESCO was founded on 16 November 1945 and is headquartered in Paris, France.

• IOC stands for the International Olympic Committee and is headquartered is in Lausanne, Switzerland. It was founded on 23 June 1894 in Paris France.
• XXIII Olympic Winter was organized in Pyeongchang, South Korea from 9 February to 25 February 2018 in which 92 countries participated.
• The first winter Olympics was organized in Chamonix, France in 1924.
• Upcoming Winter Olympic games-
• 2022- Beijing, China
• 2026-Milan-Cortina, Italy

Option 3 is correct, i.e. Cricket

The shaded area represents the people who are government employees as well as self-employee.

Hence “n” will be the correct answer.

The correct answer is  ns²np⁵

• Fluorine is the most electronegative element. It has an atomic configuration of 1s² 2s² 2p⁵.
• The s subshell has 1 orbital that can hold up to 2 electrons, the p subshell has 3 orbitals that can hold up to 6 electrons, the d subshell has 5 orbitals that hold up to 10 electrons, and the f subshell has 7 orbitals with 14 electrons.
• As in the above option, the last option has 5 electron in p subshell which means it needs only one 1 electron to complete the orbit so it will try to accept an electron which will make it the most electronegative element in the given options.

Concept Used:

Calculation:

40 - 2(12 + 13 ÷ 5 × 3 - 5 × 2) + 19

⇒ 40 - 2(12 + 39/5 - 5 × 2) + 19

⇒ 40 - 2(12 + 7.8 - 10) + 19

⇒ 40 - 2(19.8 - 10) + 19

⇒ 40 - 2 × 9.8 + 19

⇒ 40 - 19.6 + 19

⇒ 59 - 19.6

⇒ 39.4

Shortcut Trick

Total Work (LCM of 6, 3, 5) = 30 units

Efficiencies: A = +5, B = +10, C = −6

Cycle (A+B+C) in 3 hours = 5 + 10 − 6 = 9 units

In 2 cycles (6 hours), work done = 18 units. Remaining = 12 units.

Next hour (A) fills 5 units (Total 23). Next hour (B) fills remaining 7 units in 7/10 hours.

Total time = 6 + 1 + 7/10 = 77/10 hours.

∴ The correct answer is 77/10 hr.

Alternate Method

⇒ In the 1^st hour, Tap A fills 5 units.

⇒ In the 2^nd hour, Tap B fills 10 units.

⇒ In the 3^rd hour, Tap C empties 6 units.

⇒ Net work in 1 cycle (3 hours) = 5 + 10 − 6 = 9 units.

⇒ In 2 full cycles (6 hours), work done = 9 × 2 = 18 units.

⇒ Remaining work = 30 − 18 = 12 units.

⇒ 7^th hour: Tap A fills 5 units. Remaining = 12 − 5 = 7 units.

⇒ 8^th hour: Tap B can fill 10 units/hr, so it takes 7/10 hours to fill the rest.

⇒ Total time = 6 hours + 1 hour + 7/10 hour = 7 + 7/10 = 77/10 hours.

∴ The correct answer is 77/10 hr.

Additional Information

Alternate Work Concept

When taps work alternately, calculate the net work done in one complete cycle (sum of individual hours) before proceeding to the final steps.

Inlet and Outlet Taps

Efficiency of an inlet tap is taken as positive (+), while the efficiency of an outlet (emptying) tap is taken as negative (−).

Total Work via LCM

Total capacity of the tank is assumed to be the Least Common Multiple (LCM) of the individual times taken by each tap.

Shortcut Trick

Total like (J₁ + J₂ + J₃) = 45 + 60 + 40 = 145

Exactly one = Sum of individuals − [Exactly two + 3 × All three]

Exactly two = At least two − All three = 30 − 20 = 10

Exactly one = 145 − [10 + 3 × 20] = 145 − [10 + 60] = 145 − 80 = 65

∴ The correct answer is 65.

Alternate Method

Given:

n(J₁) = 45, n(J₂) = 60, n(J₃) = 40

n(J₁ ∩ J₂ ∩ J₃) = 20

People liking at least two = 30

Calculations:

⇒ Sum of individuals = n(J₁) + n(J₂) + n(J₃) = 45 + 60 + 40 = 145

⇒ People liking exactly two juices = (At least two) − (All three) = 30 − 20 = 10

⇒ Sum of individual sets = (Exactly one) + 2(Exactly two) + 3(All three)

⇒ 145 = (Exactly one) + 2(10) + 3(20)

⇒ 145 = (Exactly one) + 20 + 60

⇒ Exactly one = 145 − 80 = 65

∴ The correct answer is 65.

Additional Information

Venn Diagram Formula for Three Sets

n(A∪B∪C) = n(A) + n(B) + n(C) − [n(A∩B) + n(B∩C) + n(C∩A)] + n(A∩B∩C).

Exactly One and Exactly Two

Exactly one = Σn(A) − 2Σn(A∩B) + 3n(A∩B∩C) is incorrect; use Σn(A) = (Exactly 1) + 2(Exactly 2) + 3(Exactly 3).

At Least Two Concept

At least two = (Exactly two) + (Exactly three). This is a common point of confusion in set theory exams.

The above figure will replace the question mark.

• Work is defined as a force acting upon an object to cause a displacement.
• It is a scalar quantity because it is the cross product of two vectors.
• Its S.I unit of work is Joule and c.g.s unit erg. (1Joule= 10⁷erg)
• It is expressed as a product of force and displacement W=F×D.

Similarly,

Hence, PIANO will be coded as UNFST.

Let the angle of projection be ∅, u is the initial velocity.

We know,

⇒ Maximum Height = u²sin²θ/2g

⇒ Horizontal range = u²sin 2θ/g

According to the question,

⇒ u²sin²θ/2g = u²sin2θ/g      [Using, sin2x = 2sinx.cosx]

⇒ sin²θ/2 = 2sinθ.cosθ

⇒ tanθ = 4

⇒ θ = tan^-1( 4)

⇒ Angle of projection = tan^-1 (4)

Option 2 is correct, i.e. Rajputs

Key Points

• Abu'l-Fath Jalal-ud-din Muhammad Akbar, popularly known as Akbar. He reigned from 1556 to 1605.
• He was the son of Humayun, who was one of the Mughal King. Akbar’s age was 13 when he became emperor.
• Akbar was the third Mughal emperor of India and established a sprawling kingdom through military conquests, but he is known for his policy of religious tolerance.

Additional Information

• Akbar made marriage alliances with the Rajputs. These marriages were a result of the Rajpur policy of Akbar which was a deliberate policy and was based on the principles of enlightened self-interest, recognition of merit, justice and fair play.