RRC Group D Previous Year Paper 36 (Held On: 20 Sept 2018 Shift 3)

The Correct Answer is Option 4 i.e combination.

• Displacement reaction:
• In these reactions, an atom/ion present in a compound gets replaced by an atom/ion of another element.
• Example: FeSO₄ + Zn → ZnSO₄ + Fe
• Decomposition reaction:
• In these reactions, compound either of its own or upon heating decomposes to given two or more components out of which at least one is in the elemental state.
• Example: 2NaH → Na + H₂​
• Combination reaction:
• In these reactions, compounds are formed as a result of the chemical combination of two or more elements.
• Examples:
• C + O₂  → CO₂
• 2Cu + O2 → 2CuO
• Double displacement reaction:
• In these reactions, two compounds exchange ions to form two new compounds.
• Example: Na₂S + 2HCL → 2NaCl + H₂S

Shortcut Trick From Statement 1: z2 − 1 = 0 ⇒ z = 1 or z = −1 (Two values, insufficient). From Statement 2: z = √n where n ∈ N ⇒ z ≥ 1 (Infinitely many values, insufficient). Combining 1 & 2: Since z must be positive from (2), the only valid root from (1) is z = 1. Both statements together are required to find the unique value of z. ∴ The correct answer is Both Statements 1 and 2 together are sufficient. Alternate Method Given: Statement 1: z2 + (−1) = 0 Statement 2: z = √n, where n is a natural number {1, 2, 3, ...} Analysis of Statement 1: ⇒ z2 − 1 = 0 ⇒ z2 = 1 ⇒ z = √1 or z = −√1 ⇒ z = 1 or z = −1 ⇒ Since we have two possible values, Statement 1 alone is not sufficient. Analysis of Statement 2: ⇒ z = √n ⇒ If n = 1, z = 1; if n = 4, z = 2; if n = 2, z = 1.414... ⇒ Since z can take multiple values depending on n, Statement 2 alone is not sufficient. Combining Statement 1 and Statement 2: ⇒ From (1), z ∈ {1, −1} ⇒ From (2), z must be the principal square root of a natural number (z > 0). ⇒ The only value from Statement 1 that satisfies the condition in Statement 2 is z = 1. ⇒ Together, they provide a unique value for z. ∴ The correct answer is Both Statements 1 and 2 together are sufficient. Additional Information Principal Square Root The symbol √x specifically denotes the non-negative root of a number. Therefore, z = √n always implies z ≥ 0. Quadratic Equations An equation of the form ax2 + bx + c = 0 generally has two roots. If a constant is found via x2 = k, then x = ±√k. Data Sufficiency Logic A statement is sufficient only if it leads to exactly one unique value. If it leads to multiple possible values, it is insufficient.

The pattern followed is,

The circle symbol on and the triangle symbol in the figure are facing different directions.

In the first figure, they are facing north, in the second figure they are facing south, in the third figure they are facing west and in the fourth figure they will be facing east.

The figure that will come next in the pattern is,

Hence, option 2 is the correct answer.

Shortcut Trick

If 5% are absent, then 95% are present.

95% of total strength = 38

Total strength = (38 ÷ 95) × 100

Total strength = 0.4 × 100 = 40

∴ The correct answer is 40.

Alternate Method

Given:

Absent students percentage = 5%

Present students count = 38

Calculations:

⇒ Let the total strength of the class be 'x'.

⇒ Percentage of present students = 100% − 5% = 95%

⇒ 95% of x = 38

⇒ (95 ÷ 100) × x = 38

⇒ x = (38 × 100) ÷ 95

⇒ x = 3800 ÷ 95

⇒ x = 40

∴ The correct answer is 40.

Additional Information

Percentage Base Change

To find the original value when a percentage decrease is known: Original = Result ÷ (1 − decrease%).

Complementary Percentages

The sum of all parts in a whole always equals 100%. If part A is p%, then part B is (100 − p)%.

Unitary Method in %

If p% = Value, then 1% = Value/p, and 100% = (Value/p) × 100.

The Correct Answer is Option 3 i.e Hip - hop.

• Bharatnatyam, Kathakali, and Odissi are among the eight recognized classical dance forms of India.
• Whereas Hip-hop does not belong to the category of eight Indian classical dance forms of India.
• Indian Classical Dances:
• Bharatnatyam Dance
• Kathakali Dance
• Kathak Dance
• Manipuri Dance
• Odissi Dance
• Kuchipudi Dance
• Sattriya Dance
• Mohiniyattam Dance
• Bharatnatyam: 
• Bharatnatyam dance is known to be ekaharya, where one dancer takes on many roles in a single performance.
• It is originated in the state of Tamil Nadu.
• Kathakali:
• Kathakali is a blend of dance, music, and acting and dramatizes stories.
• It is one of the best dance forms from the state of Kerala.
• Odissi Dance:
• It is a classical dance form of Odisha.
• It incorporates two major postures - Tribhanga and Chowk.
• Hip-Hop Dance:
• It is one of the popular western dances.
• This is done to hip-hop music.
• It refers to street dance styles.

Shortcut Trick

For two people A and B, time taken together = (Product of days) ÷ (Sum of days).

Time taken = (8 × 12) ÷ (8 + 12)

Time taken = 96 ÷ 20 = 24/5 hours.

∴ The correct answer is 24/5 hr.

Alternate Method

Given:

Time taken by A = 8 hours

Time taken by B = 12 hours

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time

Calculations:

⇒ Total Efficiency of A + B = 3 + 2 = 5 units/hr

⇒ Total Work = 24 units

⇒ Time taken by A and B together = Total Work ÷ Combined Efficiency

⇒ Time = 24/5 hours

∴ The correct answer is 24/5 hr.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete the work. Efficiency = 1 ÷ Time.

Pipes and Cisterns

This logic also applies to filling tanks. If two pipes fill a tank, the net rate is the sum of individual filling rates.

Work & Wages

Wages are distributed in the ratio of work done or the ratio of efficiencies when workers work for the same duration.

The Correct Answer is Option 1 i.e cutin.

• Cutin:
• In desert plants, the epidermis has a thick waxy coating layer called cutin.
• Cutin helps in the prevention of water loss through transpiration.
• lignin:
• It is a complex polymer that is responsible for the plant's shape and stability.
• cellulose:
• Cellulose is a polysaccharide compound that gives rigidity to the cells.
• Fats:
• It is a type of nutrient just like protein and carbohydrates.

The Correct Answer is Option 4 i.e Bibhuti Lahkar. 

• Bibhuti Lahkar:
• He is an Assam based conservation activist and ecologist.
• He has become the first Asian and also the first individual from Assam to be nominated for IUCN’s prestigious ‘Heritage Heroes Award’ 2016.
• This award recognizes the outstanding efforts of conservationists around the world in making a difference to the conservation of World Heritage sites in challenging situations.
• Henry Blogg:
• He is a lifeboatman from England.
• He received three Gold and four Silver Medals from the RNLI.
• Mohan Lal:
• He is an Indian actor.
• He received Padma Bhushan in the year 2019.
• He also received Padma Shri in the year 2001.
• Trisha Krishnan:
• She is an Indian actress.
• She won the 2019 Filmfare Award for Best Actress – Tamil.

Considering the given equation,

$\frac{{0.12 \div 0.15}}{2}$

We can write the above equation as

$\Rightarrow \frac{{12}}{{100}} \times \frac{{100}}{{15}} \times \frac{1}{2}$

⇒ 12/30

⇒ 0.4

Shortcut Trick

For a scalene triangle, the area can be calculated directly using Heron's formula.

Semi-perimeter (s) = (25 + 39 + 56) ÷ 2 = 120 ÷ 2 = 60 m.

Area = √[s × (s − a) × (s − b) × (s − c)]

Area = √[60 × (60 − 25) × (60 − 39) × (60 − 56)]

Area = √[60 × 35 × 21 × 4] = √[176400] = 420 m².

∴ The correct answer is 420 m².

Alternate Method

Given:

Sides of the triangular field:

a = 25 m

b = 39 m

c = 56 m

Formula Used:

Heron's Formula for the area of a triangle:

Area = √[s(s − a)(s − b)(s − c)]

Where, semi-perimeter s = (a + b + c) ÷ 2

Calculations:

⇒ s = (25 + 39 + 56) ÷ 2

⇒ s = 120 ÷ 2 = 60 m

⇒ Area = √[60 × (60 − 25) × (60 − 39) × (60 − 56)]

⇒ Area = √[60 × 35 × 21 × 4]

⇒ Area = √[(15 × 4) × (7 × 5) × (7 × 3) × 4]

Grouping the similar terms to find square roots:

⇒ Area = √[(4 × 4) × (7 × 7) × (15 × 5 × 3)]

⇒ Area = √[16 × 49 × 225]

⇒ Area = 4 × 7 × 15

⇒ Area = 420 m²

∴ The correct answer is 420 m².

Additional Information

Area of Equilateral Triangle

For a triangle with all three equal sides (a), Area = (√3 ÷ 4) × a².

Area of Isosceles Triangle

For a triangle with two equal sides (a) and a base (b), Area = (b ÷ 4) × √(4a² − b²).

General Area of a Triangle

When the base length and the perpendicular vertical height are known, Area = (1 ÷ 2) × Base × Height.

Mango and Cherry both are fruits. 

Hence, option 3) is the correct answer.

The Correct Answer is Option 4 i.e Canada.

Shortcut Trick

To find the exact count of Yellow balls, we must know the Total balls and the counts of Blue and Red balls.

Total = 6 (from Statement 1).

Blue = 1/3 × 6 = 2 (requires Statement 2).

Red = 1/2 × 6 = 3 (requires Statement 3).

Yellow = 6 − (2 + 3) = 1. Thus, all three statements are mandatory to solve the logic.

∴ The correct answer is Statement 1, 2 and 3 together are necessary.

Alternate Method

Given:

From Statement 1: Total balls = 6

From Statement 2: Blue balls = 1/3 of Total

From Statement 3: Red balls = 1/2 of Total

Formula Used:

Yellow Balls = Total Balls − (Blue Balls + Red Balls)

Calculations:

⇒ Number of Blue balls = 1/3 × 6 = 2

⇒ Number of Red balls = 1/2 × 6 = 3

⇒ Number of Yellow balls = 6 − (2 + 3)

⇒ Number of Yellow balls = 6 − 5 = 1

Since the question asks if we can say "how many", we need a definite numerical value. To reach this value, we utilized information from all three statements.

∴ The correct answer is Statement 1, 2 and 3 together are necessary.

Additional Information

Data Sufficiency Logic

In problems involving multiple categories, the sum of individual parts must equal the Total. If N categories exist, you generally need N−1 values and the Total to find the last part.

Fractional Parts

If parts are given as fractions (a, b, c), then a + b + c = 1. Here, 1/3 + 1/2 + Yellow_fraction = 1. This gives Yellow_fraction = 1/6, but to find the number of balls, the total (6) is mandatory.

Redundancy Check

If any statement is removed, the system of equations becomes underdetermined, meaning multiple answers for Yellow balls would be possible.

In all the figures, except in figure C there are lines present at both the sides.

Whereas,

In figure C lines are only on one side.

Hence, figure C is the odd one out.

The Correct Answer is Option 2 i.e stamens.

• Stamens:
• The male reproductive parts of the flower are called stamens.
• It consists of Anther and Filament.
• Anther: produces pollen grains
• Filament: a stalk-like structure and gives support to the anther.
• Carpels:
• The female reproductive part in a plant is called carpel.
• It consists of stigma, style, and ovary.
• Ovary: contains ovules that develop into seeds.
• Style: a tube on top of the ovary connecting ovary to stigma.
• Stigma: receives the pollen during fertilization.
• Sepals: 
• These are outermost parts of the flower and are located under the flower.
• All sepals are called the calyx.
• Petals:
• These are modified leaves.
• All the petals of a flower are called a corolla.

The Correct Answer is Option 4 i.e 2 × 108 m/s.

• The Refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.
• Refractive index (n)= c/v, where c is the velocity of light in a vacuum ( 3 × 10⁸ m/s) and v is the velocity of light in a substance.
• The speed of light in a medium of refractive index 1.5 is 2 × 108 m/s.

The Correct Answer is Option 2 i.e Kochi.

• Swasth Bachche, Swasth Bharat:
• It was launched by Union HRD Minister Prakash Javdekar in Kochi, Kerala in the month of August 2017.
• It is an initiative of Kendriya Vidyalaya Sangathan to prepare a physical Health and Fitness Profile Card for more than 12 lakhs of Kendriya Vidyalaya students.
• Kochi:
• It is a major port city in the southwest Indian state of Kerala.
• It is often called the "Queen of the Arabian Sea".
• It was occupied by the Portuguese in 1503 and remained under the control of Portuguese till 1530.
• Mysore:
• It is a city in the state of Karnataka.
• It is the second most populated city in Karnataka.
• It was the capital of the Mysore Kingdom from 1399 to 1947
• Thiruvananthapuram:
• It is the capital of Kerala.
• Sree Padmanabha Swamy Temple is located in Thiruvananthapuram.
• Hyderabad:
• Hyderabad is known as the City of Pearls.
• It is the de jure capital of Andhra Pradesh.

The Correct Answer is Option 4 i.e Andhra Pradesh.

• Andhra Pradesh:
• Toray Industries (India), a subsidiary of Toray Industries, Inc, a Japanese company producing industrial products, plans to invest ₹1,000 crores in setting up its new facility in Sri City, Andhra Pradesh.
• Toray Industries, Inc., established in 1926 is a multinational corporation headquartered in Japan.
• Toray industries were initially established as Toyo Rayon in 1926.
• Andhra Pradesh is also known as “Rice Bowl of India”.
• Jaganmohan Reddy is the current CM of Andhra Pradesh.
• Biswabhusan Harichandan is the current governor of Andhra Pradesh.

Extra facts:

• Tamil Nadu:

• Chennai is the capital and largest city of Tamil Nadu.

• K Palaniswami is the current CM of Tamil Nadu.

• Shri Banwarilal Purohit is the current governor of Tamil Nadu.

• Karnataka:

• Bengaluru is the capital of Karnataka.

• It is commonly referred to as the “Silicon Valley of India”.

• Chief Minister of Karnataka - Basavaraj Bommai.

• Governor of Karnataka  - Thawar Chand Gehlot

• Maharashtra:

• Mumbai is the capital city of Maharashtra.

• Eknath Shinde is the current CM of Maharashtra.

• Bhagat Singh Koshyari is the governor of Maharashtra.

The Correct Answer is Option 1 i.e 17.2 m.

• The sound that is heard after getting reflected from the surface is called as Echo.
• As the sensation of sound persists in our brain for about 0.1 s, to hear a distinct echo the time interval between the reflected sound and the original sound must be at least 0.1s.
• If we take the speed of sound to be 344 m/s at a given temperature in air
• Hence, the total distance covered by the sound from the point of source to the reflecting surface and back should be at least (344 m/s) × 0.1 s = 34.4 m.
• Thus, to hear distinct echoes**, the minimum distance of the obstacle from the source of sound** must be half of this distance i.e 34.4/2  i.e 17.2 m.
• This distance will change with the temperature of the air.

The Correct Answer is Option 4 i.e Madhya Pradesh.

Shortcut Trick

Total distance = 40 km. Case 1: 16 km (Walk) + 24 km (Tonga). Case 2: 16 km (Tonga) + 24 km (Walk).

In Case 2, 8 km extra is walked (24 − 16 = 8 km) and 8 km less is traveled by Tonga.

Time difference = (Time for 8 km walk) − (Time for 8 km Tonga) = 1 hour.

⇒ 8/4 − 8/V = 1 ⇒ 2 − 1 = 8/V ⇒ 1 = 8/V.

∴ The correct answer is 8 km/h.

Alternate Method

Given: Total Distance = 40 km, Walking speed = 4 km/hr, Tonga speed = T km/hr.

Formula Used: Time = Distance ÷ Speed

⇒ Case 1 Time (T₁) = 16/4 + 24/T = 4 + 24/T

⇒ Case 2 Time (T₂) = 16/T + (40 − 16)/4 = 16/T + 24/4 = 16/T + 6

⇒ T₂ − T₁ = 1 hour

⇒ (16/T + 6) − (4 + 24/T) = 1

⇒ 2 − 8/T = 1

⇒ 8/T = 1

⇒ T = 8 km/h

∴ The correct answer is 8 km/h.

Additional Information

Average Speed

Total distance divided by total time. For two equal distances with speeds x and y, Average Speed = 2xy/(x+y).

Relative Speed

Speeds add up if objects move in opposite directions (S₁ + S₂) and subtract if in the same direction (S₁ − S₂).

Conversion Factor

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

‘ø’, ‘Θ’ and ‘β’ are mathematical symbols.

Whereas,

‘D’ is an alphabet.

Hence, “D” is the odd one out.

The least possible Venn diagram is as follows,

Conclusion 1: All crossroads are circles → False (This is definitely false)

Conclusion 2: All crossroads are parks → False (This is definitely false)

Hence, “neither conclusion 1 nor conclusion 2” follows.

The mirror image for the following figure when the mirror is kept at the MN line is,

Hence, option 3 is the correct answer.

The Correct Answer is Option 3 i.e Shahrukh Khan.

• Shah Rukh Khan:
• Shah Rukh Khan has been honored with the 24th Crystal Award at the World Economic Forum 2018 in Davos, Switzerland.
• He was awarded this humanitarian award along with Sir Elton John and Cate Blanchett.
• He received the award for his leadership in championing children’s and women’s rights in India.
• He also received Padma Shri in the year 2005.
• Salman Khan:
• He received the IIFA Habitat Humanity Ambassadorship Award in the year 2010.
• He also won the Airtel Superstar Hero Award 2011 for the film Bodyguard.
• Aamir Khan:
• He received the Deenanath Mangeshkar Award 2017 for Dangal movie.
• He received Padma Shri in the year 2003.
• He also received Padma Bhushan in the year 2010.
• Akshay Kumar:
• He received Padma Shri in the year 2009.
• He received the ITA Popular Icon Award in the year 2008.

• The greenhouse effect occurs when Earth's atmosphere traps solar radiation because of the presence of certain gases called green house gases.
• This results in an overall increase in the average temperature of the earth’s atmosphere.
• Some major greenhouse gases are- Carbon dioxide, Methane, Nitrous oxide, Chlorofluorocarbons, etc.

Shortcut Trick

Substitute standard values of x from options into the equation 3 sec²x − 2 tan²x = 6.

For x = 60°: sec 60° = 2 and tan 60° = √3.

LHS = 3(2)² − 2(√3)² = 3(4) − 2(3) = 12 − 6 = 6.

LHS = RHS, so x = 60° is the correct value.

∴ The correct answer is 60°.

Alternate Method

Given: 3 sec²x − 2 tan²x = 6 where 0° ≤ x ≤ 90°

Formula Used: Fundamental identity sec²x = 1 + tan²x

⇒ 3(1 + tan²x) − 2 tan²x = 6

⇒ 3 + 3 tan²x − 2 tan²x = 6

⇒ 3 + tan²x = 6

⇒ tan²x = 6 − 3

⇒ tan²x = 3

⇒ tan x = √3

⇒ x = tan⁻¹(√3) = 60°

∴ The correct answer is 60°.

Additional Information

Trigonometric Identities

Standard identities: sin²x + cos²x = 1, 1 + tan²x = sec²x, and 1 + cot²x = cosec²x.

Standard Values (60°)

At 60°: sin = √3/2, cos = 1/2, tan = √3, cot = 1/√3, sec = 2, cosec = 2/√3.

Range of x

For the first quadrant (0° to 90°), all trigonometric ratios are positive.

The number of triangles in the given figure is,

Triangles: ALM, AMB, MBN, BNC, NCO, OCP, CPD, PDQ, DQE, EQF, FGQ, GQH, QHP, HPI, PIO, OIN, INJ, NJM, JMK, MKL, AMK, CNI, CPI, EQG, CNP, PIN

Hence, 26 is the correct answer.

Shortcut Trick

Since AOB is a straight line, the sum of angles on it is 180°.

∠BOC = 180° − ∠AOC = 180° − 67° = 113°

Since OD is the angle bisector of ∠BOC, it divides the angle into two equal halves:

∠BOD = ∠BOC ÷ 2 = 113° ÷ 2 = 56.5°

∴ The correct answer is 56.5°.

Alternate Method

Given:

• AOB is a straight line.

• ∠AOC = 67°

• OD is the angle bisector of ∠BOC.

Formula Used:

• Sum of angles on a straight line = 180° (Linear Pair Axiom)

• An angle bisector divides an angle into two equal parts.

Calculations:

⇒ Since AOB is a straight line, the adjacent angles ∠AOC and ∠BOC form a linear pair.

⇒ ∠AOC + ∠BOC = 180°

⇒ 67° + ∠BOC = 180°

⇒ ∠BOC = 180° − 67°

⇒ ∠BOC = 113°

⇒ Since OD is the angle bisector of ∠BOC, it divides ∠BOC into two equal angles, ∠BOD and ∠COD.

⇒ ∠BOD = ∠BOC ÷ 2

⇒ ∠BOD = 113° ÷ 2

⇒ ∠BOD = 56.5°

Thus, the value of ∠BOD is 56.5°.

Explanation of incorrect options:

• Option (2) 55°: If ∠BOD = 55°, then ∠BOC = 2 × 55° = 110°. This would mean ∠AOC = 180° − 110° = 70°, which contradicts the given value of 67°.

• Option (3) 55.5°: If ∠BOD = 55.5°, then ∠BOC = 2 × 55.5° = 111°. This would mean ∠AOC = 180° − 111° = 69°, which contradicts the given value of 67°.

• Option (4) 56°: If ∠BOD = 56°, then ∠BOC = 2 × 56° = 112°. This would mean ∠AOC = 180° − 112° = 68°, which contradicts the given value of 67°.

∴ The correct answer is 56.5°.

Additional Information

Linear Pair Axiom

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°. These angles are supplementary.

Angle Bisector Property

An angle bisector is a ray that divides an angle into two equal adjacent angles. If OD bisects ∠BOC, then ∠BOD = ∠COD = ∠BOC ÷ 2.

Angles on a Straight Line

The sum of all angles formed on one side of a straight line at a given point is always equal to 180°.

Shortcut Trick

The metric prefix pico represents the factor 10⁻¹².

Similarly, nano = 10⁻⁹ and femto = 10⁻¹⁵.

Therefore, 1 picometre (pm) = 10⁻¹² metres.

∴ The correct answer is 10⁻¹² m.

Alternate Method

Given: Unit name is picometre.

Formula Used: SI prefix conversion table.

⇒ 1 millimetre (mm) = 10⁻³ m

⇒ 1 micrometre (μm) = 10⁻⁶ m

⇒ 1 nanometre (nm) = 10⁻⁹ m

⇒ 1 picometre (pm) = 10⁻¹² m

∴ The correct answer is 10⁻¹² m.

Additional Information

SI Prefixes (Small Values)

Commonly used prefixes for small measurements include milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²), and femto (10⁻¹⁵).

SI Prefixes (Large Values)

Commonly used prefixes for large measurements include kilo (10³), mega (10⁶), giga (10⁹), and tera (10¹²).

Atomic Scale

The unit Angstrom (Å) is also used at the atomic scale, where 1 Å = 10⁻¹⁰ m or 100 pm.

The Correct Answer is Option 3 i.e Partnerships for a Resilient Planet. 

• World Sustainable Development Summit (WSDS) 2018:
• The 2018 edition of the World Sustainable Development Summit held at Vigyan Bhawan in New Delhi from February 15 to 17.
• It was inaugurated by the PM Narendra Modi.
• WSDS is the flagship forum of The Energy and Resources Institute (TERI).
• The theme of WSDS 2018 is 'Partnerships for a Resilient Planet'.
• The theme of the WSDS 2020 edition is 'Towards 2030 Goals: Making the Decade Count'.

The least possible Venn diagram is as follows,

Conclusion 1: All gifts are toys → True (This is definitely true)

Conclusion 2: Some toys are gifts → True (This is definitely true)

Hence, “both conclusion 1 and conclusion 2” follow.

The Correct Answer is Option 1 i.e Meristematic tissue.

• Meristematic tissue:
• Growing regions of the plants are called Meristem.
• Meristematic tissue has the capability of cell division.
• It is round, oval, and multisided.
• It grows and constitutes the different parts of the plant.
• Permanent tissue:
• Permanent tissues are made of those mature tissues that have lost their capacity of division and attain a definite form of various works.
• Permanent tissues are of simple tissue and complex tissue.
• If permanent tissue is made up of similar types of cells, it is called simple tissue.
• If permanent tissue is made up of one or more types of cells, it is called complex tissue.
• Xylem and Phloem are the Complex Permanent tissues.
• Parenchyma, Sclerenchyma, and Collenchyma are the Simple Permanent Plant tissues.
• Sclerenchyma: supporting tissue in higher plants.
• Parenchyma: makes up most of the cells within leaves, flowers, and fruits.
• Collenchyma: provides support, structure, tensile strength, and flexibility which helps the plant to bend.

Important Points

 There are three types of meristematic tissues-

• Apical meristem- these are located at the shoot tips and root tips.
• Intercalary meristem- located between permanent tissues, at the leaf base and nodes.
• Lateral meristem- located at the sides(edges).​

Let weight of brick be x kg

According to the question,

7x/16 = 21/8

⇒ x = 21/8 × 16/7

⇒ x = 6

∴ 5/12 of the weight of the brick = 6 × 5/12 = 5/2 kg

Considering the given equation

$\frac{{{5^{0.25}} \times {{\left( {125} \right)}^{0.25}}}}{{{{\left( {256} \right)}^{0.1}} \times {{\left( {256} \right)}^{0.15}}}}$

We can write the above equation as

$\Rightarrow \frac{{{5^{0.25}} \times {{\left( {{5^3}} \right)}^{0.25}}}}{{{{\left( {{4^4}} \right)}^{0.1}} \times {{\left( {{4^4}} \right)}^{0.15}}}}$

$\Rightarrow \frac{{{5^{0.25}} \times {5^{0.75}}}}{{{4^{0.4}} \times {4^{0.6}}}}$

Applying the surds rule

If a^m × aⁿ = a^{(m + n)}

$\Rightarrow \frac{{{5^{\left( {0.25 + 0.75} \right)}}}}{{{4^{\left( {0.4 + 0.6} \right)}}}}$

⇒ 5/4

Shortcut Trick

Find the difference between the closest numbers: 64 − 28 = 36, and 96 − 64 = 32.

The HCF must be a factor of the difference 32.

Factors of 32 are 1, 2, 4, 8, 16, 32.

Checking the options, the largest number that divides 64, 28, and 96 is 4.

∴ The correct answer is 4.

Alternate Method

Given: Numbers are 64, 28, and 96.

Formula Used: Prime Factorisation Method for HCF.

Prime factors of each number:

⇒ 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

⇒ 28 = 2 × 2 × 7 = 2² × 7¹

⇒ 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3¹

⇒ Common prime factors with lowest power = 2²

⇒ HCF = 2² = 4

∴ The correct answer is 4.

Additional Information

Highest Common Factor (HCF)

The largest positive integer that divides each of the given integers without leaving a remainder is called the HCF or Greatest Common Divisor (GCD).

Relation between LCM and HCF

For any two positive numbers a and b, Product of numbers = LCM × HCF ⇒ a × b = LCM(a, b) × HCF(a, b).

HCF of Fractions

HCF of Fractions = HCF of Numerators ÷ LCM of Denominators.

The Correct Answer is Option 1 i.e Salil Parekh.

• Salil Parekh:
• He is the CEO of Infosys as of July 2018.
• He is also the CEO of Infosys as of May 2020.
• Infosys Limited is a global multinational corporation with its headquarters in Bangalore, Karnataka.
• C.P Gurnani:
• He is the current CEO & Managing Director of Tech Mahindra.
• He won the Business Standard 'CEO of the Year' in 2014.
• Rajesh Gopinathan:
• He is the CEO and managing director of Tata Consultancy Services.
• He was ranked ‘Best CEO’ in Institutional Investor's 2018 All Asia Executive Team rankings.

The pattern followed here is,

B + 3 → E; E + 3 → H; H + 3 → K, K + 3 → N;

2 + 3 → 5; 5 + 3 → 8; 8 + 3 → 11; 11 + 3 → 14

Hence, “N - 14” is the correct answer.

The Correct Answer is Option 1 i.e Table Tennis.

The pattern followed here is,

D + 1 = E; E + 1 = F; F + 1 = G;

W - 1 = V; V - 1 = U; U - 1 = T

Hence, “GT” is the correct answer.

The Correct Answer is Option 3 i.e transpiration.

• Respiration:
• The exchange of gases in organisms between their body cells and the environment is called respiration.
• Transpiration:
• Evaporation of water from plant leaves is called transpiration.
• Plants can get rid of excess water by this transpiration.
• Excretion:
• The process of removal of metabolic wastes from the body is called excretion.

CONCEPT

• Newton’s First Law: It states that a body continues in its state of rest or uniform motion in a straight line until and unless an unbalanced force acts on it.
• It is valid only in an inertial frame of reference.
• Newton’s First Law is also known as the law of inertia.
• Inertia is the property of the inability of a body to change its position of rest or uniform motion in a straight line.
• Mass is the measure of the inertia of a body.
• Inertial Frame: A frame of rest or uniform motion. Ex- A bus moving with constant acceleration.
• Non-inertial frame: A-frame which is accelerating either in a linear fashion or rotating around its axis. Ex- A car turning with constant speed at corners.

EXPLANATION:

• Newton’s First law of motion says about the state of rest or uniform motion and is valid on only Inertial Frame.
• Thus newton’s laws are not valid in a non-inertial frame.

​

Additional Information

• Newton’s first law always seen wrong in an accelerating frame because An object is a rest at an inertial frame can see accelerating in a non-inertial frame even though no force acting on it.
• For Example: Suppose a man standing in a truck, and the truck is moving with acceleration ‘a’ and another person is standing still on the ground.
• Case 1: Still person on the ground sees a man standing still but the truck moves forward and person in it.
• Case 2: Man in bus sees the still person on the ground move with an acceleration ‘a’ backward where no force is visible.

The Correct Answer is Option 4 i.e 55%.

• According to the World Bank, 55 percent of new bank accounts, opened globally during the period 2014-2017, are from India.
• World Bank Global Findex 2017 stated that Pradhan Mantri Jan Dhan Yojana (PMJDY) has resulted in the opening from India of 55% of all new bank accounts in the world during the period 2014-2017.
• As per the World Bank Global Findex Report, the percentage of adult bank account holders in India increased to 80% in 2017 as compared to 53% in 2014.

Shortcut Trick

Use the direct formula for two pipes: Time = (X × Y) ÷ (X + Y)

Given: X = 45 hours, Y = 36 hours

Time = (45 × 36) ÷ (45 + 36) = 1620 ÷ 81 = 20 hours

∴ The correct answer is 20 hr.

Alternate Method

Given:

Time taken by Pipe A = 45 hours

Time taken by Pipe B = 36 hours

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time taken

Calculations:

⇒ Total Efficiency of (A + B) = 4 + 5 = 9 units/hr

⇒ Total Time taken = Total Work ÷ Total Efficiency

⇒ Total Time = 180 ÷ 9

⇒ Total Time = 20 hours

∴ The correct answer is 20 hr.

Additional Information

Inlet and Outlet Pipes

Inlet pipes fill the tank (positive efficiency) while outlet/leakage pipes empty it (negative efficiency).

Pipes & Cisterns Logic

If a pipe fills a tank in 'n' hours, part filled in 1 hour = 1/n. This is the same principle as Time and Work.

Combined Work Formula

For three pipes A, B, and C, the combined time is 1/T = 1/A + 1/B + 1/C.

The Correct Answer is Option 3 i.e Four.

• Asian Games:
• The Asian Games, also known as Asiad.
• The Asian Games is a multi-disciplinary sports event held once every four years.
• It is the second-largest multi-sport event after the Olympics.
• It is held every four years among athletes from all over Asia.
• The first-ever Asian Games were held at New Delhi in 1951.

The figure that will come next in the pattern is

Hence, option 2 is the correct answer.

Shortcut Trick

Daughter current age = 10 years.

Mother current age = 3 × 10 = 30 years.

Father current age = 30 + 7 = 37 years.

Father age at daughter birth = Current Father age − Daughter age = 37 − 10 = 27 years.

∴ The correct answer is 27 years.

Alternate Method

Given:

Current age of Daughter = 10 years

Mother age = 3 × Daughter age

Father age = Mother age + 7

Calculations:

⇒ Mother current age = 3 × 10 = 30 years

⇒ Father current age = 30 + 7 = 37 years

⇒ Years since daughter was born = 10 years

⇒ Father age at daughter birth = 37 − 10 = 27 years

∴ The correct answer is 27 years.

Additional Information

Age Difference Constant

The difference between the ages of two persons remains constant regardless of the number of years passed.

Ratio of Ages

Unlike the age difference, the ratio of ages changes every year as both individuals grow older by the same amount.

Past Age Calculation

To find the age 'n' years ago, subtract 'n' from the present age. To find age 'n' years later, add 'n'.

The Correct Answer is Option 4 i.e Maharashtra. 

• Maharashtra:
• Maharashtra government has approved a 1% reservation in government jobs and education for orphans in the state in the year 2018.
• Mumbai is the capital city of Maharashtra.
• Eknath Shinde is the current CM of Maharashtra.
• Bhagat Singh Koshyari is the governor of Maharashtra.
• New Delhi:
• New Delhi is situated on the banks of River Yamuna.
• Delhi is surrounded on all sides by Haryana except the east, where it borders Uttar Pradesh.
• The current Lt. Governor of Delhi is Anil Baijal.
• Arvind Kejriwal is the current CM of Delhi.
• Uttar Pradesh:
• It shares a boundary with a maximum number of Indian states.
• Yogi Adityanath is the CM of Uttar Pradesh.
• Anandiben Patel is the governor of Uttar Pradesh.
• Rajasthan:
• Jaipur is a famous city and capital of Rajasthan.
• Ashok Gehlot is the current CM of Rajasthan.
• Kalraj Mishra is the current governor of Rajasthan.

GIVEN:

RBC count initial = 54000

Rate = 5% per day

Time = 2 days

FORMULAE USED:

RBC count final = RBC count initial(1 + (r/100))^t

CALCULATION:

RBC count final = 54000 (1 + (5/100))² 

∴ RBC count final = 59535

The Correct Answer is Option 1 i.e Ketone.

• Acetone also is known as Propanone is an organic compound with the formula (CH₃)₂CO.
• In propanone((CH₃)₂CO), the functional group present is a ketone (- C=O) group.
• In propanol (C₃H8OH), the functional group present is an alcohol (- OH) group.
• In propanoic acid (CH₃CH₂CO₂H), the functional group present is a carboxylic acid (- COOH) group.
• In ethanal (CH₃CHO), the functional group present is an aldehyde(- CHO) group.
• In propanal (C₂H₅CHO), the functional group present is an aldehyde(- CHO) group.

According to the given information,

He is in the north – east direction with respect to his initial position.

Hence, “north – east” is the correct answer.

According to the given information,

Sravan is facing in the east direction now.

Hence, “east” is the correct answer.

The pattern followed here is,

Hence, “M13N” is the correct answer.

The Correct Answer is Option 2 i.e 6 × 1024kg.

• Earth:
• The Earth is 23 ½^o tilted on its axis and thus makes 66 ½^o angles.
• It is known as a watery planet or blue planet due to the presence of huge amounts of water in it.
• Earth is the only known planet that provides sustenance or life on it.
• The mass of the Earth is 6×10²⁴ kg.

The Correct Answer is Option 4 i.e Aluminium sulphate. 

Key Points

• Aluminium sulphate:
• Its molecular formula is Al₂(SO₄)₃.
• It is soluble in water.
• It is a widely used aluminium coagulant.
• It is also used as a chemical agent in the purification of drinking water and wastewater treatment plants.
• Aluminium sulphite:
• Its Molecular formula is Al₂(SO₃)₃.
• Aluminium sulphide:
• Its molecular formula is Al₂S₃.
• It is used to produce hydrogen sulfide.

The Correct Answer is Option 4 i.e Srishti Kaur. 

• Srishti Kaur:
• She is a resident of Noida, UP, India.
• She has been crowned Miss Teen Universe 2017 at the annual beauty pageant.
• The event was held in Managua, the capital of Nicaragua.
• She also won an award for the best national costume, which featured the Indian national bird peacock.
• Neeru Chadha:
• She has been elected as the Judge of the International Tribunal for the Law of the Sea (ITLOS).
• She became the first Indian woman to be appointed as a judge at the tribunal.

CONCEPT:

• Electric current: The rate of flow of electric charge is called electric current. It is denoted by I.
• The SI unit of electric current is Ampere (A).

Electric current (I) = Charge (Q)/ Time (t)

So electric charge flown (Q) = I × t

CALCULATION:

Given that:

Time taken (t) =1 min = 60 sec

Electric current (I) = 1.0 A

Q is the charge that flows through resistor

Q = I x t

Q = 1 A x 60 sec

Q = 60 C

• The amount of charge that flows through this resistor in on minute will be 60 C. So option 3 is correct.

Shortcut Trick

Convert Speed to m/s: 66 × (5/18) = 55/3 m/s.

Total Distance (Train + Platform) = Speed × Time = (55/3) × 30 = 550 m.

Train Length = Total Distance − Platform Length = 550 − 410 = 140 m.

∴ The correct answer is 140 m.

Alternate Method

Given:

Speed of the Train = 66 km/h

Length of the Platform = 410 m

Time taken to cross = 30 seconds

Formula Used:

Distance = Speed × Time

Total Distance = Length of Train (L) + Length of Platform (P)

⇒ Speed in m/s = 66 × (5/18) = 11 × (5/3) = 55/3 m/s

⇒ Total Distance = (55/3) × 30

⇒ L + 410 = 55 × 10

⇒ L + 410 = 550

⇒ L = 550 − 410

⇒ L = 140 m

∴ The correct answer is 140 m.

Additional Information

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Train Crossing Objects

When a train crosses a stationary point object (pole, man), distance = length of train. When it crosses a platform or bridge, distance = train length + platform length.

Relative Speed

If two objects move in opposite directions, relative speed = S₁ + S₂. If they move in the same direction, relative speed = |S₁ − S₂|.

The Correct Answer is Option 4 i.e Environment – related Issues.

• 2018 New Delhi World Book Fair (NDWBF):
• The 26th edition of the New Delhi World Book Fair was organized from January 6 to January 14.
• European Union was the ‘guest of honor’ for the 2018 new Delhi world book fair.
• The theme of 2018 NDWBF was environmental issues such as climate change, global warming, and water pollution i.e Environment-related Issues.
• The theme for NDWBF 2020 is Gandhi: The Writers’ Writer.
• NDWBF was organized by the National Book Trust (NBT) in association with India Trade Promotion Organisation.

The least possible Venn diagram is as follows,

Conclusion 1: Some flowers are pink → True (This is definitely true)

Conclusion 2: Some fragrant are flowers → True (This is definitely true)

Hence, “all conclusions” follow.

CONCEPT:

• Fleming Left-hand rule gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
• It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other. If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

Force is given by:

F = q v B

Where F is force, q is a charge, v is velocity and B is the magnetic field.

EXPLANATION:

• Here the alpha particle projected towards the north i.e current is towards the north (middle finger).
• Particle deflects towards east i.e direction of force is towards the east (thumb).
• So the direction of a magnetic field will be in the upward direction (forefinger). So option 2 is correct.

Concept:

When we have to find the ascending or descending order of a fraction or relation between two fractions we can take the LCM of the denominator and multiply all the terms to get a whole number.

Calculation:

Given:

\(\frac{3}{{ - 4}};______;\frac{{ - 5}}{6}\)

The denominator here is 4 and 6. The LCM of 4 and 6 will be 12.

$\frac{3}{{ - 4}}\times 12 =-9$

$\frac{-5}{{6}}\times 12 =-10$

\(\frac{3}{{ - 4}};______;\frac{{ - 5}}{6}\) can be written as \(-9;______;-10\)

In number line, left side number is always less than right side number. Here -10 is on the left of -9, therefore -10 is lower than -9.

∴ -10 < -9

$\frac{-5}{{6}}<\frac{{ - 3}}{4}$ or

$\frac{{ - 3}}{4}> \frac{-5}{{6}}$

The Correct Answer is Option 4 i.e Rashtrapati Bhavan.

• Rashtrapati Bhavan:
• India's first underground museum was opened at the Rashtrapati Bhavan in New Delhi on October 2, 2016.
• The museum showcases a collection of relics associated with each of the past presidents of India along with a range of vestiges reflecting upon the history of India's freedom struggle.
• Edwin Lutyens of British was the chief architect of Rashtrapati Bhavan.
• Purana Qila:
• It is one of the oldest Forts located in Delhi.
• It is built on the banks of river Yamuna.
• It is also formerly called Shergarh and Sher Fort.
• Sansad Bhavan:
• The Sansad Bhavan is the house of the Parliament of India.
• It contains the Lok Sabha and the Rajya Sabha.
• It is located in New Delhi.
• Qutub Minar:
• Qutub-Minar in red and buff sandstone is the highest tower in India.
• It has been declared as UNESCO world heritage site.
• The construction of the Qutub Minar was started by Qutub-ud-Din Aibak and was completed by Iltutmish.

The Correct Answer is Option 2 i.e Mumbai Indians.

• Mumbai Indians:
• The 2017 Indian Premier League trophy was won by Mumbai Indians for the third time.
• 2017 IPL final was held between the Mumbai Indians and the Rising Pune Supergiant, on 21 May 2017, at Rajiv Gandhi International Cricket Stadium, Hyderabad.
• 2019 IPL trophy was also won by Mumbai Indians making it the fourth time.
• 2019 final was held between Chennai Super Kings and Mumbai Indians at Rajiv Gandhi International Cricket Stadium, Hyderabad.
• Mumbai Indians have the maximum number of titles, won four titles.
• Chennai Super Kings:
• 2010, 2011, 2018 IPL titles have been won by the CSK.
• Sunrisers Hyderabad: 
• Sunrisers Hyderabad has won the IPL trophy so far only once i.e in the 2016 IPL season.
• 2016 IPL final was held between Sunrisers Hyderabad and Royal Challengers Bangalore at M. Chinnaswamy Stadium.
• Delhi Daredevils:
• Delhi Daredevils have never won the IPL trophy.

Sale of store A on year 1 = 12 units

Sale of store B on year 1 = 14 units

Sale of store C on year 1 = 14 units

Sale of store A on year 2 = 10 units

Sale of store B on year 2 = 12 units

Sale of store C on year 2 = 13 units

Sale of store A on year 3 = 9 units

Sale of store B on year 3 = 8 units

Sale of store C on year 3 = 5 units

In year 3 sales of store C is less compared to other two years

Shortcut Trick

Difference in percentage = 45% − 40% = 5%

Difference in marks = 30 − (−20) = 50 marks

Equating: 5% = 50 marks ⇒ 1% = 10 marks

Pass marks = 40% + 20 marks = 40% + (20 ÷ 10)% = 42%

∴ The correct answer is 42%.

Alternate Method

Let the Maximum Marks be M.

⇒ Passing Marks Equation: 40% of M + 20 = 45% of M − 30

⇒ 45% of M − 40% of M = 20 + 30

⇒ 5% of M = 50

⇒ M = (50 × 100) ÷ 5 = 1000

⇒ Passing Marks = 40% of 1000 + 20 = 400 + 20 = 420

⇒ Pass Percentage = (420 ÷ 1000) × 100

⇒ Pass Percentage = 42%

∴ The correct answer is 42%.

Additional Information

Percentage Change

Percentage change represents the relative difference between two values: % Change = (Difference ÷ Base Value) × 100.

Base Change Property

When a value increases by x%, to return to the original value, it must decrease by [x ÷ (100 + x)] × 100%.

Successive Percentage

If a value changes by a% and then by b%, the net change is given by the formula: a + b + (a × b)/100.

The pattern followed here is,

For T20H8,

The place value of T is 20 and H is 8

For R18J10,

The place value of R is 18 and J is 10

For P15L11

The place value of P is 16, not 15 and L is 12, not 11

For N14N14,

The place value of N is 14

All follow the same pattern, except ‘P1511’.

Hence, “P1511” is the odd one.

The Correct Answer is Option 1 i.e 1773.

• Boston Tea Party: 
• It was a political protest that occurred on December 16, 1773, at Griffin's Wharf in Boston, Massachusetts.
• The sons of liberty organized the Boston tea party.
• It was a protest by American Colonists against the British government.
• The introduction of the Tea Act 1773 was one of the causes that leads to the Boston tea party.

The Correct Answer is Option 3 i.e Mass.

• Velocity:
• It is defined as the displacement of the object in a unit time interval.
• SI unit is meter/second.
• Momentum:
• It is the property of a moving body and is defined as the product of mass and velocity of the body.
• SI unit is kg.m/s.
• Mass:
• Mass is defined as the amount of matter present in an object.
• The mass of the object remains the same and does not change with the place.
• SI unit of mass is kg.
• Weight:
• Weight of an object changes from places to place since acceleration due to gravity g is different for different places.

Assumption 1: This is not implicit, because there is nothing about holding objects in the statement.

Assumption 2: This is implicit, because they are young to write anything.

Hence, “only 2” is implicit.

15 November 2018 is Thursday

Number of odd days between 15 November 2018 to 15 November 2021 = (odd days in 2019 + odd days in 2020 + odd days in 2021) = 1 + 2 + 1 = 4 days

4 days after Thursday is Monday.

Hence, "Monday" is the correct answer.

The Correct Answer is Option 2 i.e 63.

• Mendeleev’s periodic law: The physical and chemical properties of the elements are the periodic function of their atomic masses.
• Mendeleev’s arranged all the elements known at the time in increasing order of atomic mass and this arrangement became a periodic table.
• In Mendeleev’s periodic table: The total number of periods in the periodic table was seven and the total number of groups was nine.
• That is 63 elements were known when Mendeleev started his work.

Total number of mobile phone units manufactured = 1240000

Company PQR manufactured 25% of the mobile phones of the total mobile phones manufactured

∴ Number of mobile phone units manufactured by company PQR = (25/100) × 1240000 = 310000

The correct answer is Buddha, dhamma(dharma), sangha.

Key Points

Triratna in Sanskrit means 'Three Jewels'

• The Buddha
• Dhamma(dharma): his teaching
• Sangha: the community of all those who follow his teachings.

​Buddhism

• It is faith that was founded by Siddhartha Gautama("the Buddha").
• Siddhartha Gautam, the Lord Buddha was born in 563 B.C at Lumbini in Nepal.
• Attained Nirvana under a Pipal tree at Bodh Gaya & henceforth known as Buddha(The enlightened one).
• Delivered his first sermon at Sarnath (Banaras) know called the Dhammacakkappavattana.
• Died at the age of 80 at Kushinagar (U.P).

Noble truth by Buddha

• The world is full of sorrow.
• People suffer on account of desires
• If desires are conqueredNirvana can be achieved i.e., free from the cycle of birth and death can be achieved by following 8 fold path(ashtangika marga)
• Right View
• Right Resolve
• Right Speech
• Right Action
• Right Livelihood
• Right Effort
• Right Mindfulness
• Right Concentration

Teaching by Buddha

• Buddha was a practical reformer and did not believe in the soul or God or the metaphysical world and concerned himself with worldly problems.
• Suggested that a person should avoid an excess of both luxury & austerity and prescribed a middle path.
• Laid great emphasis on Karma(Varna based on action not on birth) & Ahimsa.
• Opposed the varna system and laid down the principle of social equality.
• Buddhist Text
• Tripitaka's: All written in Pali Language
• Sutta-Pitaka
• Vinaya-Pitaka
• Abhidhamma-Pitaka
• Buddhist Councils

Conclusion 1: This follows, because they are selecting the students for their participation in the event.

Conclusion 2: This does not follow, because there is nothing mentioned about the teacher favouring the students.

Hence, “only conclusion 1” follows.

Shortcut Trick

For a period of 3 years, the difference between CI and SI is given by the formula: D = P(R/100)² × (3 + R/100).

Substituting the values: Principal (P) = ₹4500, Rate (R) = 8%.

Difference = 4500 × (8/100)² × (3 + 8/100) ⇒ 4500 × 0.0064 × 3.08.

Difference = 28.8 × 3.08 = 88.704.

∴ The correct answer is ₹88.70.

Alternate Method

Given: Principal (P) = ₹4500, Time (T) = 3 years, Rate (R) = 8% per annum.

Formula Used: SI = (P × R × T) / 100 | CI = P[(1 + R/100)ⁿ − 1]

⇒ Simple Interest (SI) = (4500 × 8 × 3) ÷ 100

⇒ SI = 45 × 24 = ₹1080

⇒ Compound Interest (CI) = 4500 × [(1 + 8/100)³ − 1]

⇒ CI = 4500 × [(1.08)³ − 1]

⇒ CI = 4500 × [1.259712 − 1] = 4500 × 0.259712

⇒ CI = ₹1168.704

⇒ Difference = CI − SI = 1168.704 − 1080 = ₹88.704

∴ The correct answer is ₹88.70.

Additional Information

Difference for 2 years

The difference between CI and SI for 2 years is calculated as: D = P(R/100)².

Effective Rate of Interest

For 3 years at 8%, the effective CI rate is (1.08³ − 1) × 100 = 25.9712%, while the SI rate is 8 × 3 = 24%.

Successive Percentage Change

CI can be viewed as successive percentage increases: R_net = x + y + (xy/100).

The pattern followed here is,

E + 2 = G;

G + 2 = I;

I + 3 = L;

L + 3 = O;

O + 4 = S;

S + 4 = W

Hence, “W” is the correct answer.

The pattern followed here is,

The geometric figure which is inside is represented normally and the outside figure is represented by a dotted line.

The figure which will come next in the pattern is,

Hence, option 4 is the correct answer.

Drawing the diagram,

Ganesh is the brother of Seeta.

Hence, “brother” is the correct answer.

CONCEPT:

• Force: The interaction which after applying on body changes or try to change the state of rest or state of motion is called force. It is denoted by F.

Force (F) = Mass (m) × Acceleration (a)

The equation of motion is given by:

V = u + a t

Where V is final velocity, u is initial velocity, a is acceleration and t is time.

CALCULATION:

Given that:

Initial velocity (u) = 90 km/h = 90× 5/18 = 25 m/s  

Time taken to stop the car (t) = 5s

Final velocity (after stoping) = V = 0 m/s

Mass of car (m) = 800 kg

To find: Force =?

Use V = u + a t

0 = 25 + a × 5

So Acceleration (a) = - 25/5 = - 5 m/s²

Force (F) = Mass (m) × Acceleration (a) = 800 × (-5) = - 4000 N

• Negative sign show that the force acting is in opposite direction of the motion of the car.

Shortcut Trick

Identify the nature of the given numbers: a quantitative number represents a specific, exact numerical value or ratio that can be fully computed, whereas certain mathematical constants are transcendental/irrational numbers representing proportions.

Check the options:

√1728 = 12√12 ≈ 41.569 (computable algebraic real number)

2.48762787 and 8.36712846781 are terminating decimals (rational numbers).

π is a famous transcendental, non-algebraic irrational number representing the ratio of a circle's circumference to its diameter, hence classified as a mathematical constant rather than a standard quantitative numerical value in algebraic terms.

∴ The correct answer is π.

Alternate Method

Given:

Numbers: π, √1728, 2.48762787, 8.36712846781Analysis:

⇒ Option 1: π is an irrational and transcendental number. It cannot be expressed as the root of any non-zero polynomial equation with rational coefficients.

⇒ Option 2: √1728 is an algebraic number because it is a root of the polynomial equation x² − 1728 = 0.

⇒ Option 3: 2.48762787 is a rational number (finite decimal fraction).

⇒ Option 4: 8.36712846781 is a rational number (finite decimal fraction).

⇒ Among the choices, π is a mathematical constant of a non-algebraic (transcendental) nature, making it the non-quantitative option in this classification.

∴ The correct answer is π.

Additional Information

Transcendental Numbers

A real number that is not algebraic (i.e., not a root of any non-zero polynomial equation with rational coefficients). Examples include π and e.

Algebraic Numbers

Numbers that can be expressed as roots of polynomial equations with integer coefficients, such as all rational numbers and roots like √2 or √1728.

Shortcut Trick

Apply BODMAS rule: Brackets → Of → Division → Multiplication → Addition → Subtraction.

78 − [5 + 3 of (25 − 20)]

⇒ 78 − [5 + 3 × 5]

⇒ 78 − 20 = 58.

∴ The correct answer is 58.

Alternate Method

Given Expression: 78 − [5 + 3 of (25 − 2 × 10)]

Step 1: Solve the innermost small bracket ( ).

⇒ 25 − 2 × 10 = 25 − 20 = 5

Step 2: Solve the 'of' operation inside the square bracket [ ].

⇒ 3 of 5 = 3 × 5 = 15

Step 3: Solve the addition inside the square bracket [ ].

⇒ 5 + 15 = 20

Step 4: Final subtraction from the outer value.

⇒ 78 − 20 = 58

∴ The correct answer is 58.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), {}, [], Of, Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

'Of' Operator

In mathematical expressions, 'of' acts as a multiplication but holds higher priority than standard division and multiplication.

Brackets Priority

Always solve in the order: Parentheses ( ) → Curly Braces { } → Square Brackets [ ].

Month codes:

Code for Days:

Code for Centuries:

For,

2 October 2010,

Date = 2

Code for October = 0

Code for Century = 6

2010 = 2000 + 10

For, 2000 it is 6

For,

10 it is 10

Adding all these = 2 + 0 + 6 + 10 + 2 = 20

20 / 7 = 6 (here we consider the remainder)

6 is the code for Saturday.

2 October, 2010 is Saturday.

Hence, “Saturday” is the correct answer.

Drawing the diagram,

Lata is pointing to her ‘sister – in – law’.

Hence, “her sister – in – law” is the correct answer.

The Correct Answer is Option 3 i.e Manoj Kumar.

• Manoj Kumar was appointed as the State Election Commissioner for Uttar Pradesh on 18th January 2018.
• Article 243K(1): It states that the superintendence, direction and control of the preparation of electoral rolls for, and the conduct of, all elections to the Panchayats (Municipalities under Article 243ZA) shall be vested in a State Election Commission.
• State Election Commission consists of a State Election Commissioner, to be appointed by the Governor.
• Ved Prakash Verma:
• He is a doctor by profession and a urologist in Jharkhand, India.
• T Venkatesh:
• T. Venkatesh was appointed as Chief Election Officer of Uttar Pradesh in 2016.

Shortcut Trick

Identify the modal class with the maximum frequency (9), which is 3 − 5.

Apply the formula: Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

Substitute values: l = 3, f₁ = 9, f₀ = 7, f₂ = 2, h = 2.

Mode = 3 + [(9 − 7) / (18 − 9)] × 2 = 3 + (2 / 9) × 2 = 3 + 4/9 = 3.444.

∴ The correct answer is 3.444.

Alternate Method

Given:

Modal Class = 3 − 5 (Highest frequency f₁ = 9)

Lower limit of modal class (l) = 3

Frequency of preceding class (f₀) = 7

Frequency of succeeding class (f₂) = 2

Class size (h) = 2

Formula Used:

Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

1-3 3-5 5-7 7-9 9-11 7

Considering the given equation

(72)² = 51X4

Square of 72 = 5184

While comparing we get,

⇒ 5184 = 51X4

∴ X = 8

Shortcut Trick

Convert all dimensions to centimeters: Hall = 1600 cm × 1000 cm.

Number of bricks = (Area of Hall) ÷ (Area of one Brick)

Number of bricks = (1600 × 1000) ÷ (20 × 10)

Number of bricks = 1600000 ÷ 200 = 8000

∴ The correct answer is 8000 bricks.

Alternate Method

Given:

Length of the hall (L) = 16 m = 1600 cm

Width of the hall (W) = 10 m = 1000 cm

Length of a brick (l) = 20 cm

Width of a brick (w) = 10 cm

Formula Used:

Area of rectangle = Length × Width

Number of bricks = Total Floor Area ÷ Area of one Brick

Calculations:

⇒ Area of the hall = 1600 × 1000 = 16,00,000 cm²

⇒ Area of one brick = 20 × 10 = 200 cm²

⇒ Required bricks = 16,00,000 ÷ 200

⇒ Required bricks = 8000

∴ The correct answer is 8000 bricks.

Additional Information

Unit Conversion

Always ensure all units are the same before calculation. 1 meter = 100 centimeters and 1 m² = 10,000 cm².

Area of a Rectangle

The space occupied by a flat shape is its area. For a rectangle, Area = Length × Breadth.

Number of Items in a Space

To find the quantity of small items (like tiles or bricks) needed for a larger area, divide the Total Area by the Area of one item.

CONCEPT:

• Work done: Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of a force.

$W = \vec F \cdot \vec s = Fs;cos\theta$

Where F = force, s = distance, and cos θ = angle between F and s.

CALCULATION:

Given that:

Force = 10 N

Displacement = 2 m

• Here the angle between the force and displacement is zero because the displacement is in the direction of the force.

Work done = force x displacement 

W = F x s

W= 10 x 2 

W = 20 J (N.m)

The work done by the force will be 20 J.