RRC Group D Previous Year Paper 49 (Held On: 12 Dec 2018 Shift 2)

The possible diagram for the given data is:

According to the Pythagoras Theorem,

The shortest distance between B and D = $√(3² + 4²)$

BD = $√(9 + 16)$

BD = $√25$

BD = 5 km

Hence, the shortest distance between B and D is 5 km.

The second image present in the question figure is the inverted version of the first image.

(Inverted: Turn the image upside down)

Hence, option 1 is the correct answer.

Shortcut Trick

Effective interest rate for 2 years at 20% per annum compounded annually is calculated as: x + y + (xy/100).

Effective Rate = 20 + 20 + (20 × 20)/100 = 44%.

Compound Interest = 44% of ₹ 5400.

CI = (44/100) × 5400 = 44 × 54 = ₹ 2,376.

∴ The correct answer is ₹ 2,376.

Alternate Method

Given: Principal (P) = ₹ 5400, Rate (R) = 20%, Time (T) = 2 years.

Formula Used: Amount (A) = P(1 + R/100)^T | CI = A − P

⇒ Amount (A) = 5400 × (1 + 20/100)²

⇒ A = 5400 × (120/100) × (120/100)

⇒ A = 5400 × 1.2 × 1.2 = 5400 × 1.44

⇒ A = ₹ 7,776

⇒ Compound Interest (CI) = 7776 − 5400 = ₹ 2,376

∴ The correct answer is ₹ 2,376.

Additional Information

Successive Percentage Change

For two successive changes of a% and b%, the net change is (a + b + ab/100)%. This is used to find effective interest rates.

Difference between CI and SI

The difference between Compound Interest and Simple Interest for 2 years is given by D = P(R/100)².

Ratio Method for CI

For 2 years, the CI can be calculated using the ratio 2 : 1. For 20% of 5400 = 1080 and 20% of 1080 = 216. Total CI = (2 × 1080) + (1 × 216) = 2160 + 216 = 2376.

The correct answer is P/5.

Concept:

• Daltons Law of Partial Pressure:
• The total pressure of Gas exerted is the sum of partial pressure exerted by all gases.
• P_total = P₁ + P₂ + P₃
• For two gases in the container, the relationship between the partial pressure of a gas (Pa) and the total pressure is given as

$P_{a} = \frac{n_a}{n_a + n_b} P_{Total}$      ----(1)

• Pa is the partial pressure of first gas, n_a is the number of moles of gas A and n_b is the number of moles of gas B.

Calculation:

• Given the ratio of molecular weight is 1 : 4
• or M_a = 4 M_b     ----(2)
• Their weight is the same, so mass is same
• W_a = W_b = W -- (3)
• Now, the number of moles is given by mass / molecular mass
• Number of moles of a
• $n_a = \frac{W_a}{M_a} = \frac{W}{M_a}$     ----(4)
• Number of moles of b
• $n_b= \frac{W_b}{M_b} = \frac{W}{M_b}$    ----(5)
• Now partial pressure of B from the equation 1
• $P_{b} = \frac{n_b}{n_a + n_b} P_{Total}$      ----(6)
• Putting (4) and (5) in 6
• $P_{b} = \frac{W/M_b}{W/M_a + W/M_b} P_{Total}$      ----(7)
• Now putting (2) in 7
• $P_{b} = \frac{W/M_b}{W/4M_b + W/M_b} P_{Total}$
• $\implies P_b = \frac{1}{(1+4)} P_{Total}$
• $\implies P_b = \frac{P_{Total}}{5}$
• So, $\frac{P}{5}$ is the correct option.

Shortcut Trick

Use the weighted average of the coordinates based on the given ratio.

x = (3 × 10 + 1 × (−2)) ÷ (3 + 1) = (30 − 2) ÷ 4 = 7

y = (3 × (−6) + 1 × 2) ÷ (3 + 1) = (−18 + 2) ÷ 4 = −4

∴ The correct answer is (7, −4).

Alternate Method

Given: End points A = (−2, 2), B = (10, −6) and Ratio m : n = 3 : 1.

Formula Used: Section Formula for internal division: P(x, y) = [(mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)]

⇒ x = (3 × 10 + 1 × (−2)) ÷ (3 + 1)

⇒ x = (30 − 2) ÷ 4 = 28 ÷ 4 = 7

⇒ y = (3 × (−6) + 1 × 2) ÷ (3 + 1)

⇒ y = (−18 + 2) ÷ 4 = −16 ÷ 4 = −4

∴ The correct answer is (7, −4).

Additional Information

External Division Formula

If a point divides a segment externally in ratio m : n, the coordinates are [(mx₂ − nx

Shortcut Trick

Time for Pipe M to fill full tank = 24 × (3/2) = 36 hours.

Time for Pipe N to fill full tank = 60 × (6/5) = 72 hours.

Using LCM (36, 72) = 72: Efficiencies are 2 and 1 respectively.

Together time = Total Work ÷ Total Efficiency = 72 ÷ (2 + 1) = 24 hours.

∴ The correct answer is 24 hr.

Alternate Method

Given:

Pipe M fills 2/3 tank in 24 hours.

Pipe N fills 5/6 tank in 60 hours.

Formula Used:

Time for full tank = Time taken ÷ Fraction of tank filled.

Combined Time = (T₁ × T₂) ÷ (T₁ + T₂)

Calculations:

⇒ Full capacity time for Pipe M = 24 × (3/2) = 36 hours

⇒ Full capacity time for Pipe N = 60 × (6/5) = 72 hours

⇒ Let Total Work = LCM of (36, 72) = 72 units

⇒ Efficiency of Pipe M = 72 ÷ 36 = 2 units/hr

⇒ Efficiency of Pipe N = 72 ÷ 72 = 1 unit/hr

⇒ Combined Efficiency = 2 + 1 = 3 units/hr

⇒ Time required = 72 ÷ 3 = 24 hours

∴ The correct answer is 24 hr.

Additional Information

Pipes and Cisterns Efficiency

If a pipe can fill a tank in x hours, then the part filled in 1 hour is 1/x. This is inversely proportional to time.

Inlet and Outlet Pipes

Inlet pipes (filling) are taken as positive efficiency, while outlet pipes (emptying/leakage) are taken as negative efficiency.

Total Capacity Formula

Total Capacity = Time taken × Rate of flow (Efficiency). This is analogous to Work = Time × Efficiency.

The correct answer is Lieutenant Colonel (Lt. Col.).

Key Points

• Dhoni is proceeding to 106 Territorial Army Battalion (Para) and is staying as part of Victor Force in the Kashmir Valley from July 31 to August 15.
• Dhoni was accorded the honorary rank of Lieutenant Colonel in 2011.
• He is also a qualified paratrooper after having completed five parachute training jumps.
• The wicket-keeper-batsman has been conferred the Padma Bhushan, the country's third-highest civilian award, by President Ramnath Kovind at Rashtrapati Bhavan.
• Dhoni made his ODI debut on 23 December 2004 against Bangladesh.

Additional Information

• Dhoni played his first Test a year later against Sri Lanka.
• Dhoni played his last Test Match against Australia in 2014.
• Dhoni played a total of 90 Test Matches, 350 ODIs, 98 T20s.
• Dhoni also took 1 ODI wicket.
• Dhoni's best score in ODIs is 183 not out against Sri Lanka.

The correct answer is  ${}_{}^{14}C$.

Key Points 

• Carbon-14 dating, also called radiocarbon dating, method of age determination that depends upon the decay to nitrogen of radiocarbon (carbon-14).
• The method was developed in the late 1940s at the University of Chicago by Willard Libby, who received the Nobel Prize in Chemistry for his work in 1960.
• It is based on the fact that radiocarbon (¹⁴C) is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
• The resulting ${}_{}^{14}C$ combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire 14
  

C by eating the plants.

Additional Information

• In 2020, the Nobel prize for chemistry was won by Emmanuelle Charpentier and Jennifer A. Doudna for the development of a method for genome editing.
• Carbon - 14 is an isotopic chronometer.
• There are three principal techniques used to measure the carbon 14 content of any given sample— gas proportional counting, liquid scintillation counting, and accelerator mass spectrometry.

Shortcut Trick

Co-prime numbers are pairs of numbers that have no common factor other than 1.

Check divisibility for each pair: 49 and 133 are both divisible by 7.

49 = 7 × 7 and 133 = 7 × 19.

Since they share a common factor 7, they are not co-prime.

∴ The correct answer is 49, 133.

Alternate Method

Given: Four pairs of numbers to check for co-prime status.

Definition: A pair (a, b) is co-prime if HCF(a, b) = 1.

⇒ For (35, 51): Factors of 35 = 1, 5, 7, 35; Factors of 51 = 1, 3, 17, 51. HCF = 1.

⇒ For (75, 104): Factors of 75 = 1, 3, 5, 15, 25, 75; Factors of 104 = 1, 2, 4, 8, 13, 26, 52, 104. HCF = 1.

⇒ For (49, 133): Factors of 49 = 1, 7, 49; Factors of 133 = 1, 7, 19, 133. HCF = 7.

⇒ For (63, 95): Factors of 63 = 1, 3, 7, 9, 21, 63; Factors of 95 = 1, 5, 19, 95. HCF = 1.

∴ The correct answer is 49, 133.

Additional Information

Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime numbers themselves.

Consecutive Numbers

Any two consecutive natural numbers are always co-prime to each other (e.g., 15 and 16).

Prime Numbers Property

Any two distinct prime numbers are always co-prime (e.g., 7 and 11).

The correct answer is Microsoft.

• The Rajasthan Government has signed a Memorandum of Understanding (MoU) with Microsoft to provide free digital training to 9,500 college students of 50 government colleges in a year.
• State’s Higher Education Minister Kiran Maheshwari said that the initiative was taken for the enhancement of digital learning and capacity building of college students in Rajasthan.

Additional Information

• Chief Minister of Rajasthan - Ashok Gehlot.
• Governor of Rajasthan - Kalraj Mishra.
• National Parks in Rajasthan - Ranthambore, Sariska, Desert, etc.
• Headquarter of Microsoft - Redmond, Washington, United States.
• CEO of Microsoft - Satya Nadela.

The correct answer is A does not mean B, but B means A.

• Linear momentum is a vector quantity while kinetic energy is a scalar quantity. Hence, when the linear momentum is zero, it does not mean kinetic energy need to be zero. But when kinetic energy is zero, the linear momentum has to be zero.
• In the case of rotational motion, Linear momentum could be zero but it still can have non-zero kinetic energy because of other motion.

Important Points

• Kinetic energy = 1/2massvelocity²
• Momentum = mass*velocity.
• Vector quantities are those which have direction as well as magnitude.
• Scalar quantities are those which have only magnitude.
• Momentum has also direction along with magnitude.
• Kinetic energy has no direction it has only magnitude.

The correct answer is Gopi Thonakal.

Key Points

• Gopi Thonakal is the first Indian to win the Asian Marathon Championship.
• Gopi Thonakal was born on 24 May 1988 is an Indian athlete who has qualified to represent India at the 2016 Summer Olympics.
• At age 21, he joined as a general recruit, starting as a Havildar at the Army Artillery Center in Hyderabad.
• He also won the South Asian Games in 2016 in the 10,000m event.
• Sunita Godara is a former Indian marathon runner from Nausana.
• Sunita Godara became the national marathon champion first time in 1985 by winning Delhi Marathon.

​

Additional Information

• Gopi Thonakal was born in the Waynad district of Kerala.
• Chief Minister of Kerala - Pinarayi Vijayan
• Governor of Kerala - Arif Mohammad Khan
• Capital of Kerala - Thiruvananthapuram
• National Parks in Kerala - Eravikulam National Park, Silent Valley National Park, Amarambalam, etc.

The correct answer is Wood Carving Cottage Industries.

• Saharanpur is one of the flourishing cities of Uttar Pradesh. It has emerged as an important tourist destination, mainly owing to its rich historical and cultural heritage.
• Saharanpur city's name was given after the Saint Shah Haroon Chishti.
• A very famous temple of "Shakumbri Devi" is situated in Saharanpur.
• Saharanpur is the northernmost city of Uttar Pradesh.
• It touches the boundary of Himachal Pradesh.
• The north and the northeast of the district is surrounded by Shivalik hills and separates it from the Dehradun district.

Additional Information

• Chief Minister of Uttar Pradesh - Yogi Adityanath
• Governor of Uttar Pradesh - Anandiben Patel
• Saharanpur has the 200-year-old Shiva Temple in Barsi.
• Uttar Pradesh has a total of 75 districts in which Lakhimpur is the largest district of Uttar Pradesh.

According to the first conclusion, morning yoga practice is the only way to have good health is not true. It is definitely good for health but it is just one of the ways to achieve good health.

According to the second conclusion, yoga practice in the evening is harmful to health. It is also not true. It is just that, practicing yoga in the morning is slightly more beneficial than in the evening.

Hence, neither conclusion I nor II follows.

Shortcut Trick

For half-yearly compounding, effective Rate = 10% ÷ 2 = 5% per 6 months.

Time periods (n) = 1 year × 2 = 2 periods.

5% as a fraction = 1/20. So, Principal : Amount ratio for one period = 20 : 21.

For 2 periods, Ratio = 20² : 21² = 400 : 441.

Given 441 units = ₹ 13,230 ⇒ 1 unit = ₹ 30.

Principal (400 units) = 400 × 30 = ₹ 12,000.

∴ The correct answer is ₹ 12,000.

Alternate Method

Given:

Maturity Amount (A) = ₹ 13,230

Annual Rate (R) = 10%

Time (T) = 1 year

Compounding Frequency = Half-yearly

Formula used:

A = P(1 + r/100)ⁿ

Where r = R/2 and n = 2 × T

Calculations:

⇒ r = 10% ÷ 2 = 5%

⇒ n = 1 × 2 = 2 periods

⇒ 13,230 = P(1 + 5/100)²

⇒ 13,230 = P(1 + 1/20)²

⇒ 13,230 = P(21/20)²

⇒ 13,230 = P × (441 / 400)

⇒ P = (13,230 × 400) ÷ 441

⇒ P = 30 × 400

⇒ P = 12,000

∴ The correct answer is ₹ 12,000.

Additional Information

Compounding Frequency

If interest is compounded quarterly, the rate is divided by 4 and the time is multiplied by 4 (r = R/4, n = 4T).

Effective Rate of Interest

The equivalent annual rate for half-yearly compounding at rate r is given by R_eff = r + r + (r × r)/100.

CI vs SI for 2 Periods

Difference = P(r/100)², where r is the rate per period.

According to the given information,

Shree's daughter's mother is Shree herself. Also, the son of Shree's father is Shree's brother.

Hence, Jai is the brother of Shree.

Shortcut Trick

Number of triangles with exactly one side common with an n-sided polygon = n × (n − 4).

Number of triangles with exactly two sides common with an n-sided polygon = n.

For an octagon (n = 8), triangles having 'same side' means either 1 side or 2 sides common.

Triangles with same side = [8 × (8 − 4)] + 8 = 32 + 8 = 40. Wait, if only exactly one side common: 8 × 4 = 32.

∴ The correct answer is 32.

Alternate Method

Given: A polygon is an octagon, so number of vertices n = 8.

The question asks for triangles that have the same side with the octagon. This usually refers to triangles having exactly one side common with the polygon.

⇒ Total ways to select 1 side from 8 sides = ⁸C₁ = 8 ways.

⇒ For each selected side (let's say V₁V₂), the third vertex cannot be V₁, V₂, V₃, or V₈ (to ensure exactly one side is common and avoid two sides being common).

⇒ Remaining available vertices for the third point = 8 − 4 = 4 vertices.

⇒ Total such triangles S = 8 × 4

⇒ S = 32.

∴ The correct answer is 32.

Additional Information

Total Triangles in a Polygon

Total number of triangles that can be formed using vertices of an n-sided polygon is ⁿC₃.

No Sides Common

Number of triangles with no sides common with the polygon = ⁿC₃ − n(n − 4) − n.

Two Sides Common

Number of triangles having two sides common with an n-sided polygon is always equal to n.

The correct answer is Wild Child and Other Stories.

• Paro Anand was given the Sahitya Akademi's Bal Sahitya Puraskar 2017 for her short story collection titled Wild Child and Other Stories.
• Paro Anand is an Indian author of books for children, young adults, and adults including novels, short stories, and plays.
• Wild Child and Other Stories is now published as Like Smoke: 20 Teens 20 Stories.
• She headed the National Centre for Children's Literature at the National Book Trust India, the apex body for children's literature in India.
• Paro Anand's book No Guns at My Son's Funeral made it to the IBBY Honors List of 2006.

Additional Information

• The Sahitya Akademi was Founded on 12 March 1954, it is supported by, though independent of, the Indian government.
• The most recent Sahitya Akademi was announced in 2019 in seven books of poetry, six short stories, four novels, three non-fiction books, and three essays.

Shortcut Trick

Number of chocolates = (R²×H) ÷ (r²×h) = (6²×6) ÷ (2²×2) = (36×6) ÷ 8 = 27 chocolates.

Box configuration 9×3 holds 27 chocolates perfectly in a rectangular layout.

Free space % in a circle-in-square grid = 100 − (Area of Circle ÷ Area of Square × 100) = 100 − (πr² ÷ (2r)² × 100).

Free space % = 100 − (π ÷ 4 × 100) = 100 − (3.14 ÷ 4 × 100) = 100 − 78.5% = 21.5%.

∴ The correct answer is 21.5%.

Alternate Method

Given: Base radius of large cylinder (R) = 6 cm, Height (H) = 6 cm. Small cylinder radius (r) = 2 cm, Height (h) = 2 cm. Box config = 9×3.

Step 1: Calculate the number of small chocolates.

⇒ Volume of large cylinder = π × R² × H = π × 6² × 6 = 216π cm³.

⇒ Volume of small cylinder = π × r² × h = π × 2² × 2 = 8π cm³.

⇒ Total chocolates = 216π ÷ 8π = 27.

Step 2: Dimensions of the rectangular box.

⇒ Since configuration is 9×3, Length (L) = 9 × diameter = 9 × 4 = 36 cm.

⇒ Width (W) = 3 × diameter = 3 × 4 = 12 cm.

⇒ Height of box is given as 2 cm.

⇒ Volume of Box = L × W × Height = 36 × 12 × 2 = 864 cm³.

Step 3: Volume of 27 chocolates and free space.

⇒ Total volume of chocolates = 27 × 8 × 3.14 = 216 × 3.14 = 678.24 cm³.

⇒ Free space volume = 864 − 678.24 = 185.76 cm³.

⇒ Percentage free space = (185.76 ÷ 864) × 100 = 21.5%.

∴ The correct answer is 21.5%.

Additional Information

Volume of Cylinder

The volume is calculated as πr²h, where r is the radius and h is the height.

Packing Efficiency

For a circular cross-section inside a square grid, the packing efficiency is always (π/4) × 100 ≈ 78.5%.

Rectangular Prism Volume

The volume of the box is found by multiplying its length, width, and height (V = l × w × h).

According to the first argument, the rhythm and melody contribute to portraying the human expression of emotions through music. Now, even though the instruments, music, and linguistics vary from culture to culture, the overall human expression remains the same everywhere. Hence, music plays a great role in being the universal language.

According to statement II, music and linguistics are one of the components of music which may vary from culture to culture. This may not be true for the overall music.

Hence, only argument I is strong.

Given:

6.5 × 0.0004

Calculation:

6.5 × 0.0004 = (65 × 4)/100000

⇒ 260/100000

⇒ 26/10000

⇒ 0.0026

∴ The value of 6.5 × 0.0004 is 0.0026

Shortcut TrickLet total work = 180 units (LCM of 36 and options like 90).Combined efficiency (Milena + Mashuka) = 180 ÷ 36 = 5 units/day.Using option (3): Milena alone takes 90 days ⇒ Milena's efficiency = 180 ÷ 90 = 2 units/day.Then Mashuka's efficiency = 5 − 2 = 3 units/day (Satisfies Mashuka > Milena).Check condition: (2/5 × 180)/3 + (3/5 × 180)/2 = 72/3 + 108/2 = 24 + 54 = 78 days. (Matches!)∴ The correct answer is 90 days.Alternate MethodGiven: Combined time = 36 days. Work done separately (2/5 by Mashuka, 3/5 by Milena) = 78 days. Mashuka efficiency > Milena efficiency.Formula: 1/A + 1/B = 1/T; Time = Work ÷ Efficiency.PersonDaysTotal Work (W)EfficiencyMilena (A)xW/xMashuka (B)yW/y⇒ 1/x + 1/y = 1/36 --- (Eq. 1)⇒ (2/5)y + (3/5)x = 78 ⇒ 2y + 3x = 390 --- (Eq. 2)⇒ From Eq. 1: 36(x + y) = xy⇒ Substitute y = (390 − 3x)/2 into the equation:⇒ 36(x + (390 − 3x)/2) = x(390 − 3x)/2⇒ 36(2x + 390 − 3x) = 390x − 3x2⇒ 36(390 − x) = 390x − 3x2 ⇒ 12(390 − x) = 130x − x2⇒ 4680 − 12x = 130x − x2 ⇒ x2 − 142x + 4680 = 0⇒ (x − 90)(x − 52) = 0⇒ If x = 90, y = (390 − 270)/2 = 60. (Since Mashuka is faster, y < x is correct).∴ The correct answer is 90 days.Additional InformationEfficiency and Time RelationEfficiency is inversely proportional to the time taken to complete a work. If Efficiency ratio is a:b, then Time ratio is b:a.Combined Work FormulaIf two people complete work in A and B days, they together complete it in (A × B) ÷ (A + B) days.Quadratic Shortcut in Time & WorkWhen the sum of times and product of times are known, the individual times are the roots of the equation: t2 − (Sum)t + (Product) = 0.

Shortcut Trick

Twin primes are pairs of prime numbers that have a difference of 2.

Between 100 and 200, the pairs are (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), and (197, 199).

Total number of such pairs = 7.

∴ The correct answer is 7.

Alternate Method

Given: Range = 100 to 200.

Formula: A pair (p, p+2) is a twin prime if both p and p+2 are prime numbers.

⇒ Prime numbers between 100-200: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

⇒ Check difference of 2:

⇒ (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199).

⇒ Total count = 7.

∴ The correct answer is 7.

Additional Information

Twin Primes

Pairs of primes of the form (p, p+2). Every twin prime pair except (3, 5) is of the form (6n−1, 6n+1).

Prime Numbers up to 100

There are 25 prime numbers between 1 and 100. There are 8 twin prime pairs in this range.

Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime themselves.

The correct answer is Gold Medal.

• Sykhom Mirabai Chanu has won a gold medal at the World Weightlifting Championships held in Anaheim, United States.
• Saikhom Mirabai Chanu was born on 8 August 1994.
• Chanu has won the World Championships and multiple medals at the Commonwealth Games.
• She was awarded the Padma Shri by the Government of India for her contributions to the sport.
• She was awarded the Rajiv Gandhi Khel Ratna award by the Government of India for the year 2018.
• Chanu had won the silver medal in the women's 48 kg weight class at the 2014 Commonwealth Games, Glasgow.

Additional Information 

• Sykhom Mirabai Chanu is from Manipur.
• India finished at 9th position along with 4 other nations in World Weightlifting Championship, Anaheim.
• Anaheim is a city outside Los Angeles, in Southern California.

The correct answer is  2010.

• Article 21-A of the Constitution of India provides for free and compulsory education of all children in the age group of 6 to 14 years as a Fundamental Right.
• Article 21-A and the Right Education Act came into effect on 1 April 2010.
• After this article came into effect India became one of the 135 countries to have made education a fundamental right for every child.
• It is the 86th Amendment Act of the Constitution.

Important Points

• There are total SIX fundamental Rights of every citizen of India.
• The literacy rate of India as per the 2011 census is 74.04 %.
• Fundamental Rights come under Part III of the constitution.
• Part III contains Articles 12-35.

The correct answer is Contractile.

• Contractile protein is compressed and relaxed, causing the muscles to move.
• Contractile protein consists of two parts: Actin (a thin filament) and Myosin (a thick filament).
• Myosin is the most abundant contractile protein and consists of two heavy and four light chains.
• During compressed or relaxed movement a thin filament slides over a thick filament.

Additional Information

• Lipo protein is a biochemical assembly whose primary function is to transport hydrophobic lipid (also known as fat) molecules in water, as in blood plasma or other extracellular fluids.
• Nucleo proteins are any proteins that are structurally associated with nucleic acids, either DNA or RNA.
• Typical nucleoproteins include ribosomes, nucleosomes, and viral nucleocapsid proteins.

The correct answer is 6 × 1024 kg.

Key Points

• The exact mass of the earth is 5.9722×10²⁴ Kg.
• The average density of the earth is 5515 kg.m⁻³.
• The mass of the moon is 7.342×10²² kg.
• Other names of the earth are - Gaia, Gaea, Terra, Tellus.
• Earth has only one natural satellite i.e. Moon.

Important Points

• The total circumference of Earth is 40,000 km.
• The total surface area of the Earth is 510072000 km².
• The axial tilt of the Earth is 23.4392811°.
• The total number of Latitudes is 179.
• Equator (The Great circle) passes through South America, Africa, Asia.
• 1° longitudinal distance at the equator is approximately 111.3 km.
• 180° longitude is known as International Date Line.

The correct answer is Chitin.

Key Points

• The cell wall of fungi is made from a compound known as 'chitin'.
• The cell wall of plant cells is made from 'cellulose'.
• The cell wall is a tough, rigid layer that surrounds some types of cells.
• The cell wall is the very basic component of the cell of a plant, bacteria, fungi, etc.
• The cell wall is located just outside of the cell membrane.
• Protozoans and animal cells do not have a cell wall.

Important Points

• The cell was discovered by Robert Hooke in 1665.
• Cell Nucleus was discovered by Robert Brown.
• Cells group together to form tissues which in turn group together to form organs.
• The longest cells in the human body are the motor neurons.
• Red blood cells carry oxygen around the body.

The correct answer is Manohar Parrikar.

Key Points

• Manohar Gopalkrishna Prabhu Parrikar (13 December 1955 – 17 March 2019) was an Indian politician and leader of the Bharatiya Janata Party who served as Chief Minister of Goa from 14 March 2017 until his death(17 March 2019).
• Previously, he was Chief Minister of Goa from 2000 to 2005 and from 2012 to 2014, and from 2017 to 2019.
• He also served as the Minister of Defence from October 2014 to March 2017.
• In January 2020, he was posthumously awarded Padma Bhushan.
• He was the first IIT alumnus to serve as MLA of an Indian state, the first IITian to become the Chief Minister of a state in India, the first Goan to become a cabinet-rank minister at the Centre.

Additional Information

• Current Chief Minister of Goa - Pramod Sawant
• Governor of Goa -  Bhagat Singh Koshyari
• National Parks/ Wildlife Sanctuary of Goa - Salim Ali Bird Sanctuary, Bondla Wildlife Sanctuary, etc.

Shortcut Trick

A number is divisible by 6 if it is divisible by both 2 and 3.

Check Divisibility by 2: The last digit must be even (0, 2, 4, 6, 8). All options satisfy this.

Check Divisibility by 3: The sum of digits must be divisible by 3.

Option (1): 1 + 2 + 3 + 8 + 4 = 18. Since 18 is divisible by 3, the number is divisible by 6.

∴ The correct answer is 12384.

Alternate Method

Given: Numbers 12384, 12358, 12368, 12376.

Formula Used: Divisibility rule of 6 ⇒ Number must be Even AND Sum of digits must be divisible by 3.

⇒ Testing 12384: Sum = 1+2+3+8+4 = 18. (Divisible by 3 and 2).

⇒ Testing 12358: Sum = 1+2+3+5+8 = 19. (Not divisible by 3).

⇒ Testing 12368: Sum = 1+2+3+6+8 = 20. (Not divisible by 3).

⇒ Testing 12376: Sum = 1+2+3+7+6 = 19. (Not divisible by 3).

∴ The correct answer is 12384.

Additional Information

Divisibility by 4

A number is divisible by 4 if the last two digits are divisible by 4 (e.g., 84 in 12384).

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9 (e.g., 18 is divisible by 9, so 12384 is also divisible by 9).

Divisibility by 8

A number is divisible by 8 if the last three digits are divisible by 8 (e.g., 384 ÷ 8 = 48).

The correct answer is Urethra.

Key Points

• The urine stored in the urinary bladder is expelled out through the urethra to the outside of the body.

• In males, it has the additional function of ejaculating semen when the man reaches orgasm.

• When the penis is erect during sex, the flow of urine is blocked from the urethra, allowing only semen to be ejaculated at orgasm.

Additional Information

• The male reproductive system includes testes, genital ducts, accessory glands, and the penis.
• The semen is composed of the fluid and sperm from the vas deferens which is about 10% of the total, fluid from the seminal vesicles which is about 60% of the total, and the fluid from the prostate glands which is about 30% of the total.
• The pH of the semen is about 7.5.

The correct answer is $318 Million.

Key Points

• The World Bank will provide a $318 million loan for the modernization of irrigation projects in Tamil Nadu.
• This helped small and marginal farmers improve water management and adopt climate resilient techniques.
• It is expected that around 500,000 farmers were benefitted from this project.
• Tamil Nadu is a water-stressed state that continues to experience water shortages which are expected to exacerbate in the future.
• More than 160,000 hectares of currently partially irrigated lands will come into full irrigation under this project.

Additional Information

• Chief Minister of Tamil Nadu - Edappadi K. Palanisamy
• Governor of Tamil Nadu -  Banwarilal Purohit
• National Parks of Tamil Nadu - Nilgiris Biosphere Reserve, Anamalai Tiger Reserve, Sathyamangalam Wildlife Sanctuary, etc.

The correct answer is Stays the same. 

Key Points

• In a group, the electrons in the outermost orbit are the same.
• There is a total of 18 groups in the Periodic table.
• There is a total of 4 blocks in the Periodic table.
• Group 18 consists of the Noble gases because the outermost orbit has completely filled.
• Each atom consists of electrons and nuclei.

Additional Information

• The Father of the Modern Periodic table is Dimitri Ivanovich Mendeleev.(published in 1869 with 63 elements)
• The element with the lowest melting and boiling point is Helium.
• The element with the highest melting point is Carbon.
• The element with the highest boiling point is Tungston.
• The element with the highest density is Osmium.
• The element with the highest electronegativity is Fluorine.

Given:

$\frac{72}{100}$

$\frac{175}{108}$

Formula Used:

$\frac{a}{b} \times \frac{c}{d} = ;\frac{{ac}}{{bd}}$

Calculation:

$\frac{{72}}{{100}} \times \frac{{175}}{{108}}$

$\Rightarrow \frac{2}{{100}} \times \frac{{175}}{3}$

$\Rightarrow \frac{2}{4} \times \frac{7}{3}$

$\Rightarrow \frac{1}{2} \times \frac{7}{3}$

$\Rightarrow ;\frac{7}{6}$

∴ The Multiplication of $\frac{72}{100}$ and  $\frac{175}{108}$ is $\frac{7}{6}$

The correct answer is Mahavir Singh Phogat.

Key Points

• Mahavir Singh Phogat is an Indian wrestler, senior Olympics coach, and politician.
• He is the father and coach of Geeta Phogat.
• Geeta Phogat won India's first gold medal in women's wrestling in the 55 kg freestyle category at the 2010 Commonwealth Games.
• Geeta Phogat won a bronze medal at the 2012 World Wrestling Championships.
• Mahavir Singh Phogat was born in the Bhiwani district of Haryana.
• Mahavir's role in the movie Dangal is shaping the wrestling careers of his daughters and niece, unheard of in rural Haryana, was respected by Sondhi.

Additional Information

• The biography of Mr. Phogat is - Akhada.
• The book 'Akhada' is penned by sports journalist Sourabh Duggal and was released on 21 December 2016 at the Chandigarh Press Club.
• Mahavir Singh Phogat won Dronacharya Award for Wrestling in 2016.

The correct answer is 2.

• There are only TWO Indian players who have played more than 100 international matches -

1. Sunil Chhetri
2. Bhaichung Bhutia

• Sunil Chhetri has played 115 matches while Bhaichung Bhutia has played 107 matches.
• Sunil Chhetri is the Captain of the Indian Football team.
• Gurpreet Singh Sandhu is the present Goal Keeper of the team.

Additional Information      

• Sunil Chhetri is at 10th position in the world's most goal in International football matches.
• Ali Daei of Iran has scored the most goals in International Matches.

Shortcut Trick

Difference in multipliers = 21 − 12 = 9 units.

Given that this difference results in 198 less than the actual value.

9 units = 198

1 unit = 198 ÷ 9 = 22

∴ The correct answer is 22.

Alternate Method

Let the original number be x.

Case 1: Intended multiplication ⇒ 21 × x = 21x

Case 2: Actual multiplication ⇒ 12 × x = 12x

According to the question, the difference is 198:

⇒ 21x − 12x = 198

⇒ 9x = 198

⇒ x = 198 ÷ 9

⇒ x = 22

∴ The correct answer is 22.

Additional Information

Error Percentage

Error % = (Difference between actual and correct value ÷ Correct value) × 100.

Product Rule

If a number is multiplied by 'a' instead of 'b', the error is (a − b) × number.

Unitary Method

It is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The correct answer is Petroleum.

Key Points

• Digboi is a town and a town area committee in the Tinsukia district in the north-eastern part of the state of Assam, India.
• Crude oil was discovered here in the late 19th century and the first oil well was dug in 1866.
• Digboi is known as the Oil City of Assam where the first oil well in Asia was drilled.
• The first refinery was started here as early as 1901.
• It is situated 510 km northeast of Guwahati.
• Majuli is the largest River Island in the world is in Assam.

Additional Information

• Chief Minister of Assam - Shri Himanta Biswa Sarma (Aug 2021).
• Governor of Assam - Jagdish Mukhi
• Rivers flow through Assam - Bharamputra, Kopili, Dihang, Manas, Bhogdoi, Jhanji, etc.
• National Parks/ Wildlife Sanctuaries in Assam - Kaziranga National Park, Dibru Saikhowa National Park, Dihing Patkai
  

Rainforest reserve & elephant habitat, etc.

In the first pair, the image on the left has three sides while the image on the right has four sides (one more than the left one). 

Similarly, in the second pair, the image on the left has four sides, which implies, the image to the right must have five sides (one more than the left one).

Hence, the correct answer is option 4.

Shortcut Trick Force exerted is Weight (W = mg). Since density and height are uniform, Weight ∝ Volume. Volume of Cylinder = πr12h and Volume of Cone = (1/3)πr22h. Given r1 > r2, then r12 > (1/3)r22 is always true. Therefore, Volume of Cylinder > Volume of Cone ⇒ Weight of Cylinder > Weight of Cone. ∴ The correct answer is More than cone.

Alternate Method Given: Radius of cylinder = r1, Radius of cone = r2, r1 > r2, Heights are equal (h), Uniform mass (constant density ρ). Formula Used: Weight (Force) = Mass × g = Volume × Density × g

⇒ Volume of Cylinder (Vcyl) = πr12h ⇒ Volume of Cone (Vcone) = (1/3)πr22h ⇒ Force of Cylinder (F1) = πr12h × ρ × g ⇒ Force of Cone (F2) = (1/3)πr22h × ρ × g ⇒ Since r1 > r2, it follows that r12 > r22 and r12 > (1/3)r22 ⇒ F1 > F2 ∴ The correct answer is More than cone.

Additional Information Volume Relationship If a cylinder and a cone have the same radius and same height, the volume of the cylinder is exactly 3 times the volume of the cone. Pressure vs Force Force depends on total mass, whereas Pressure depends on Force/Area. For a cone, the pressure on the base is higher due to smaller contact area compared to its volume distribution. Mass of Uniform Solids Mass = Density × Volume. For uniform mass objects of the same material, the object with the larger volume will exert more gravitational force (weight).

Concept:

The rustling of the leaves:

• A rustling is a gentle swishing sound, like the rustling of leaves in the trees on a breezy night.
• The rustling happens when the wind blows. Small speed differences in the airflow on either side of the leaf create vortices that detach from the leaf surface, lowering the pressure on one side and causing it to flutter.

Sound Intensity: It is also known as acoustic intensity.

• It is the power carried by sound waves per unit area in a direction perpendicular to that area.
• The sound intensity level is just a logarithmic expression of sound intensity relative to a reference intensity. Mathematically

$L = 10log_{10}\frac{I}{I_0}$

where L is the Level of the sound intensity, I is the intensity of the sound intensity, and I0 is the reference intensity.

I0 = 10-12 w/m².

Calculations:

Given that, I = 10¹¹ Wm^-2, I0 = 10^-12 w/m².

So by the sound intensity,

$L = 10log_{10}\frac{I}{I_0}$ =  $10log_{10}\frac{10^{-11}}{10^{-12}} = 10 Db$

So the level of intensity due to that rustle is 10 Db.

Given;

SANDY : HZMWB

S - Opposite of S - H

A - Opposite of A - Z

N - Opposite of N - M

D - Opposite of D - W

Y - Opposite of Y - B

Similarly;

CRATE : _____ ?

C - Opposite of C - X

R - Opposite of R - I

A - Opposite of A - Z

T - Opposite of T - G

E - Opposite of E - V

Hence, XIZGV is the correct answer.

The correct answer is Malayalam.

Key Points

• Little Magician was made in Malayalam.
• Later, it was dubbed in Tamil, Telugu, and Hindi, with the Hindi dub being titled 'Chota Jadugar'.
• It won the National Film Award for Best Special Effects.
• It was directed by Jose Punnoose.
• It was produced by Navodaya Appachan.
• The film stars Suraj Balajee, S. P. Balasubrahmanyam, Tirlok Malik and Pooja Kumar.

Additional Information

• The original name of the Movie is Magic Magic.
• Magic Magic, made on a budget of ₹30 million.
• It was written by Gokula Krishnan.
• Music is given by Sharreth.

Concept:

• Work is done: The product of force and displacement is called work done
• Work was done against gravity: When an object is brought to some height going against gravity, work is said to be done against gravity.
• This work done is converted into potential energy.
• The potential energy is energy stored in a body when work is done against gravity. It is given as

P = m × g × h

• As for lifting or after lifting at height some work needs to be done, .for e.g A coolie lifting a weight in his weight, it is in the form of potential energy, so work done can also be written as,

W = P = m × g × h.

m is mass, g is the acceleration due to gravity, h is the height obtained. 

Calculations:

Given that, m = 20 Kg, h = 5 m, g = 10 m/s²

So we have a formula for work done,

W = mgh = 20 × 5 × 10 = 1000 J.

So The work done by him to lift the weight is 1000 J.

Additional Information

• When a force is applied to an object which causes displacement along the direction of force then the work is said to be done by that force.
• The work done by a force is defined as: The product of the component of the applied force on the block in the direction of the displacement and the magnitude of this displacement is called work done.

i.e., $W = \vec F.d\vec x = Fdx\cos \theta$

or in terms of magnitude, it can be given as

  $W = F × s$

where F = force applied in Newton and s = Displacement in meters.

Given:

Calculation:

In 2007, 30 million units of personal computer were sold by the XYZ company.

∴ 30 million units of personal computer were sold by the company XYZ in the year 2007.

The correct answer is Smriti Irani.

Key Points

• Smriti Irani was the Minister for Information and Broadcasting in March 2018.
• Smriti Zubin Irani was born on 23 March 1976.
• Smriti Irani is serving in the cabinet of Narendra Modi as Minister of Textiles and was given additional charge as Minister of Women and Child Development in the 2nd cabinet of Modi since May 2019.
• Smriti Irani is a Member of Parliament in the Lok Sabha, representing Amethi.
• Smriti Irani is currently the youngest Minister in the Council of Ministers at the age of 43.

Additional Information

• Smriti Irani succeeded Menka Gandhi after assuming the responsibility of Women and Child Development.
• Smriti Irani was one of the participants of the beauty pageant Miss India 1998.
• Smriti Irani made her debut with TV series Aatish and Hum Hain Kal Aaj Aur Kal.
• Smriti Irani holds the record of winning five consecutive Indian Television Academy Award for Best Actress.

The logic followed here is :

Hence, the next term will be S19P11.

The first statement states the problem while the second statement states the cause of the problem.

The first conclusion talks about recycling which is not directly related to the problem. The second conclusion clearly establishes the fact that popution growth is the reason why any country faces this issue.

Hence, only conclusion 2 follows.

Shortcut Trick

Given that Loss = 20%, so first Selling Price (SP₁) corresponds to 80% of CP.

To get 5% Profit, the new Selling Price (SP₂) must be 105% of CP.

Ratio of SP₁ : SP₂ = 80 : 105 = 16 : 21.

According to the question, 16 units = ₹ 184.

Therefore, 1 unit = 184 ÷ 16 = ₹ 11.5.

Required SP₂ = 21 units = 21 × 11.5 = ₹ 241.50.

∴ The correct answer is ₹ 241.50.

Alternate Method

Given: SP₁ = ₹ 184, Loss₁ = 20%, Desired Profit = 5%.

Formulas: CP = [SP × 100] ÷ [100 − Loss%], SP = [CP × (100 + Profit%)] ÷ 100.

⇒ Cost Price (CP) = (184 × 100) ÷ (100 − 20)

⇒ CP = (184 × 100) ÷ 80 = 184 × 1.25 = ₹ 230

⇒ Required Selling Price (SP₂) = CP × (100 + 5) ÷ 100

⇒ SP₂ = 230 × 105 ÷ 100 = 230 × 1.05

⇒ SP₂ = ₹ 241.50

∴ The correct answer is ₹ 241.50.

Additional Information

Profit and Loss on CP

Unless otherwise stated, Profit% and Loss% are always calculated on the Cost Price (CP).

Unitary Method Application

If SP at x% loss is given as A, then SP at y% profit = [A ÷ (100 − x)] × (100 + y).

Nepal, Bhutan, and Russia are the names of countries while London is the capital.

Hence, London is different from the others.

The least possible Venn Diagram for the given data is,

1. All B are P →  It is possible but not definite, hence false.
2. Some S are P → It is possible but not definite, hence false.
3. Some P being B is a possibility → True (It is possible)
4. No S is B → False (As, there is a direct relation between B and S)

Hence, only the third conclusion follows.

The correct answer is a Straight Line.

• The Shortest distance between the initial and final position of an object is known as Displacement.
• Displacement = time * velocity.
• Velocity is a vector quantity which implies that displacement is also a vector quantity.
• Displacement can be zero even if an object has travelled some distance.
• Displacement can be equal to the distance in the case of motion in a single direction and in a straight line.

Additional Information

• Those quantities which have direction, as well as magnitude, are known as Vector quantity.
• Those quantities which have only magnitude are known as Scalar quantity.
• If a body back to its original position then the displacement of the body is zero.

Hence, the next term will be J10T20.

The given figure: 

The single triangles are, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

The combined triangles are: (1,2), (3,4), (5,6), (7,8), (9,10), (11,12), (14,15), (1,2,13), (3,4,16), (5,6,16), (7,8,17), (9,10,17), (11,12,13)

There is one large triangle: (1,2,13,15,14,16,17,9,10,5,6)

Hence, there are 31 triangle in the given picture.

The starting point is O. 

According to the given information, 

Clearly, point B is to the north-west of point A.

The correct answer is Odisha.

Key Points

• Rourkela Steel Plant (RSP), in Rourkela, Odisha is the first integrated steel plant in the public sector in India.
• It was set up with West Germany collaboration with an installed capacity of 1 million tonnes.
• On 3 February 1959, then president Rajendra Prasad inaugurated RSP's first blast furnace named 'Parvati'.
• It was built in 1955.
• CEO of Rourkela Steel Plant is Dipak Chattaraj.
• There is a total of 13462 employees in the Steel plant.

Additional Information

• SAIL stands for Steel Authority of India.
• The headquarters of SAIL is in New Delhi.
• CEO of SAIL is CEO: Shri Amarendu Prakash**.**
• Chief Minister of Odisha - Mohan Charan Majhi
• Governor of Odisha - Raghubar Das
• National Parks in Odisha - Similipal National Park, Bhitarkanika National Park, Ushakothi Wild Life Sanctuary, etc.

The correct answer is Phloem vessel.

Key Points

• Phloem, also called bast, tissues in plants that conduct foods made in the leaves to all other parts of the plant.
• Phloem is composed of various specialized cells called sieve tubes, companion cells, phloem fibers, and phloem parenchyma cells.
• Phloem is the living tissue in vascular plants that transports the soluble organic compounds made during photosynthesis and known as photosynthates, in particular the sugar sucrose.
• This transport process is called translocation.
• The phloem is the innermost layer of the bark.
• The term was introduced by Carl Nägeli in 1858.

Additional Information

Difference between Phloem and Xylem:

The correct answer is Compression

• Compression is a region in a longitudinal wave where the particles or the dark band are closest together.
• A rarefaction is a region in a longitudinal wave where the particles or the dark band are furthest apart.
• The region where the medium is compressed is known as compression and the region where the medium is spread out is known as a rarefaction.
• Rarefaction waves expand with time (much like sea waves spread out as they reach a beach)
• in most cases, rarefaction waves keep the same overall profile ('shape') at all times throughout the wave's movement.

Additional Information

• A natural example of rarefaction occurs in the layers of Earth's atmosphere.
• Air at higher layers of the atmosphere is less dense, or rarefied, relative to air at lower layers.
• The modern construction of guitars is an example of using rarefaction in manufacturing.

The correct answer is Velocity.

Key Points

Additional Information

• All laws of motion given by Newton was published in 1687.
• Newton's first and second laws are valid only in an inertial reference frame.
• Force = mass * Acceleration

The correct answer is KJ mol-1

• Ionization energy is the minimum amount of energy required to remove the most loosely bound electron of an isolated neutral gaseous atom or molecule.
• It is quantitatively expressed as X(g) + energy ⟶ X+(g) + e− where X is any atom or molecule, X+ is the ion with one electron removed, and e− is the removed electron.
• The adiabatic ionization energy of a molecule is the minimum amount of energy required to remove an electron from a neutral molecule.

Additional Information

• Ionization energy generally increases from left to right within a given period (that is, row).
• Ionization energy generally decreases from top to bottom in a given group (that is, column).
• The work function is the minimum amount of energy required to remove an electron from a solid surface.

In the beginning, the person is going towards the west. After the first right turn, he would face the north. Then after turning left, he would face west, and then again after turning right he would face north.

Now, as the sun rises in the east and he is facing north, implies, the sun would be to his right.

Hence, the correct answer is right.

The person is facing the west in the beginning. 

Case 1: 

After taking a U-turn (Right), the person would face the opposite of the west i.e. east.

Now, the person is facing the east direction and after taking a left he would face the north direction.

Case 2:

After taking a U-turn (Left), the person would face the opposite of the west i.e. east.

Now, the person is facing the east direction and after taking a left he would face the north direction.

Hence, the person is facing the north direction now.

Shortcut Trick

Volume of Cone = (1/3)πr²h and Volume of Sphere = (4/3)πR³.

From Statement 1: r = R. Volume comparison depends on height (h) of the cone.

From Statement 2: Surface Area of cone (πrl + πr²) > Surface Area of sphere (4πR²).

Combining both: (1) r = R and (2) πr(l + r) > 4πr² ⇒ l + r > 4r ⇒ l > 3r. Since l² = r² + h², we find the relation for h.

Both statements together provide the necessary dimensions to compare volumes.

∴ The correct answer is Both statement 1 and 2 are necessary.

Alternate Method

Given: Volume of cone (V_c) and Volume of sphere (V_s).

Formula Used: V_c = (1/3)πr²h | V_s = (4/3)πR³ | S_c = πrl + πr² | S_s = 4πR²

⇒ From Statement 1: r = R. V_c = (1/3)πr²h and V_s = (4/3)πr³. Comparison requires h.

⇒ From Statement 2: πrl + πr² > 4πR². Without r = R, we cannot relate l to R.

⇒ Combining 1 & 2: πr(l + r) > 4πr² ⇒ l + r > 4r ⇒ l > 3r.

⇒ √(r² + h²) > 3r ⇒ r² + h² > 9r² ⇒ h² > 8r² ⇒ h > 2√2 r.

⇒ V_c = (1/3)πr²h > (1/3)πr²(2√2 r) ≈ 0.94πr³. V_s = 1.33πr³. Now comparison is possible.

∴ The correct answer is Both statement 1 and 2 are necessary.

Additional Information

Volume of Solids

The Volume of a Cone is exactly one-third the volume of a Cylinder with the same base radius and height.

Slant Height Relationship

In a Right Circular Cone, the slant height l, vertical height h, and radius r always satisfy l² = r² + h².

Data Sufficiency Logic

A statement is sufficient if it leads to a unique 'Yes' or 'No' answer. If multiple cases are possible, more data is required.

CONCEPT:

Sound: 

• A sound is a form of energy that produces a sensation of hearing in our ears.
• It is a kind of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions.
• The disturbance being handed over from one particle to the next.

Light:

• Light is a form of electromagnetic radiation that can be detected by the human eye.
• When light falls on an object, some part of the light is reflected on our eyes and we are able to see.

EXPLANATION:

• Sound waves are longitudinal waves and light waves are transverse waves.
• As we know sound waves are longitudinal waves and travel through compression and rarefactions in the medium on the other hand light waves are transverse in nature and do not require medium to travel. Therefore options 2^nd,3^rd and 4^th are incorrect.
• Sound waves are longitudinal and light waves are transverse. So, option 1^st is the corrcet ansswer.
• As we know that, the sound wave and lightwave travels with different velocity and have a different frequency, therefore the wavelength (λ = v/f) is different for both.
• Both sound and light waves follow the law of reflection i.e. the angle of incidence is equal to the angle of reflection.

Additional Information

• Light waves can be polarized, but sound waves cannot.
• The speed of light in a medium is constant. The velocity of sound waves can change.
• All waves have amplitude, wavelength, and frequency.
• A description of a sound as high or low is known as the pitch of the sound.

The unit of Power is Watt, similarly, the unit of Volume is Liter.

Hence, the liter is the correct answer.

Shortcut Trick

Note that b = 1/a and a² − b² = (a + b)(a − b).

Sum (a + b) = 2(2² + (√5)²) / (2² − (√5)²) = 2(4 + 5) / (4 − 5) = −18.

Difference (a − b) = (−4 × 2 × √5) / (4 − 5) = 8√5.

Result = −18 × 8√5 = −144√5.

∴ The correct answer is −144√5.

Alternate Method

Given: a = (2 − √5)/(2 + √5) and b = (2 + √5)/(2 − √5)

Formula Used: a² − b² = (a + b)(a − b)

Rationalizing 'a':

⇒ a = [(2 − √5)(2 − √5)] / [(2 + √5)(2 − √5)]

⇒ a = (4 + 5 − 4√5) / (4 − 5) = (9 − 4√5) / −1 = 4√5 − 9

Rationalizing 'b':

⇒ b = [(2 + √5)(2 + √5)] / [(2 − √5)(2 + √5)]

⇒ b = (4 + 5 + 4√5) / (4 − 5) = (9 + 4√5) / −1 = −9 − 4√5

Finding a + b and a − b:

⇒ a + b = (4√5 − 9) + (−9 − 4√5) = −18

⇒ a − b = (4√5 − 9) − (−9 − 4√5) = 4√5 − 9 + 9 + 4√5 = 8√5

Final Calculation:

⇒ a² − b² = (−18) × (8√5) = −144√5

∴ The correct answer is −144√5.

Additional Information

Rationalization of Surds

To rationalize the denominator of the form (x + √y), multiply both numerator and denominator by its conjugate (x − √y).

Algebraic Identity

The formula x² − y² = (x + y)(x − y) is useful when variables are reciprocal or conjugate pairs.

Sum and Product of Conjugates

For conjugates (A+√B) and (A−√B), the product is A² − B, which is always a rational number.

The correct answer is Kharavel.

• The Hathigumpha inscription from Udayagiri in Odisha was written by the King of Kharavel Kalinga.
• Hathigumpha caves are also known as Elephant caves.
• These caves are written in the 2nd century BCE.
• The Hathigumpha inscription consists of seventeen lines incised in deep-cut Brahmi letters on the overhanging brow of a natural cavern Hathigumpha on the south side of the Udayagiri hill.
• The inscription also refers to the Kharaval's feat of bringing back the Jain image which was taken by the Nanda empire.

Additional Information

• The founder of the Nanda Dynasty was Mahapadma Nanda.
• He conquered Kalinga but ruled for a very short time.
• The Nanda dynasty immediately preceded the dynasty of the Mauryas.
• A total of 117 caves was excavated by Kharavela and others on Kumari hill (Udayagiri).
• Elephant caves are dedicated to Lord Shiva.

The correct answer is The debate over vegetarianism vs. non-vegetarianism.

• The Arya Samaj founded by Dayanand Saraswati Ji was split into two in Punjab in the year 1893.
• Mahatma group were the people who supported eating meat and the leader was Mahatma Hansraj.
• The other group was Cultured Pary who renounced eating meat and the leader of this party was Swami Shraddhanand.
• The split in Arya Samaj was due to two issues,
• (i) Kind of education that is to be promoted, Conservatives wanted Gurukuls and Radicals wanted a college education and
• (ii) Kind of food to be followed, Conservatives wanted every Hindu to be purely vegetarian and Radicals wanted non-vegetarian food.
• Arya Samaj is a monotheistic Indian Hindu reform movement that promotes values and practices based on the belief in the infallible authority of the Vedas.
• The samaj was founded by Maharishi Dayanand Saraswati on 10 April 1875.
• Members of the Arya Samaj believe in one God and reject the worship of idols.
• Arya Samaj was the first Hindu organization to introduce proselytization in Hinduism.

Additional Information

• The original name of Swami Dayanand Saraswati was Mool Shankar.
• He was born in Gujarat in 1824 and died in Ajmer in 1883.
• The headquarter of Arya Samaj was in Lahore, Pakistan.
• Childhood name of Swami Vivekanand was Narendra Nath Dutt.

The correct answer is Both 1 and 2.

• Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• Potential difference(V) = Current(I) * Resistance(R).
• Ohm's law states that the R in this relation is constant, independent of the current.
• Materials that do not obey Ohm's law, are called non-ohmic.
• Ohm's law is only valid for Metals. It does not obey semi-conductors, gaseous substance, non conductors, etc.

Additional Information

• Hopkinson's law is also known as Ohm's law for magnetics.
• Ohm's law was published in a book named Die galvanische Kette, mathematisch bearbeitet in 1827.
• Unit of Resistance is Ohm.
• SI unit of current is Ampere.
• SI unit of Potential difference is volt.

Given series: 4WXZ8QPOJ6GTMVEUH53B

In ZJMT : O8HO, O is the fourth successor of Z, 8 is the fourth predecessor of J, H is the fourth successor of M and O is the fourth predecessor of T.

As per the given series

Using the same approach, we get:

Hence QP5Q will come in place of the blank.

Given:

There is a digit at the 10th place of 6n.

Where n is a natural number that is greater than 1.

Calculation:

Let be n= 2, ,3, 4, 5,...

⇒ 6 × 2 = 12 = 1

⇒ 6 × 3 = 18 = 1

⇒ 6 × 4 = 24 = 2

⇒ 6 × 5 = 30 = 3

⇒ 6 × 6 = 36 = 3

⇒ 6 × 7 = 42 = 4

⇒ 6 × 8 = 48 = 4

⇒ 6 × 9 = 54 = 5

∴ It can be 1, 2, 3, 4, 5.

Given:

'<' is treated as '+' and '×' as '÷'.

Concept used:

We have to follow the BODMAS rule

Calculation:

 {(55 < 10) × 10} < 120

According to the question:

⇒ {(55 + 10) ÷ 10} + 120

⇒ {65 ÷ 10} + 120

⇒ (6.5 + 120)

⇒ 126.5

∴ The value of ? is 126.5.

The mirror image of the given image is,

Hence, figure C is the answer figure.

The correct answer is 1, 3-Bimethyl butane.

• Concept : 

Isomers: isomers are compounds that possess the same molecular formula and have different structural formulas but have different properties are known as isomers and the phenomenon is known as isomerism.

Explanation :

• The chemical formula of pentane is C_⁵H₁₂.
• Now all the possible isomers of pentane are as follows,

Again, from the above structure, we can see that pentane has only three possible isomers which are n-pentane, 2-methyl butane, and 2,2-dimethyl propane.

Thus, in the given option 1, 3- Dmethyl butane is not the isomer of pentane.

Therefore, the correct option is (2)

Additional Information

• It has a role as a non-polar solvent and a refrigerant.
• It is a volatile organic compound and an alkane.
• N-pentane appears as a clear colorless liquid with a petroleum-like odor.
• The boiling point of N- Pentane is 97°F.

Shortcut Trick

Rewrite the equation in standard form: (12 − a)x² − (a + 9)x + 4 = 0.

For a repeated solution, the Discriminant (D) must be zero: B² − 4AC = 0.

Substitute values: (a + 9)² − 16(12 − a) = 0.

Simplify: a² + 34a − 111 = 0 ⇒ (a − 3)(a + 37) = 0.

Since the question asks for the positive solution, a = 3.

∴ The correct answer is 3.

Alternate Method

Given Equation: 12x² − ax + 7 = ax² + 9x + 3

Condition: The equation has only one repeated solution.

Formula used: For a quadratic equation Ax² + Bx + C = 0 to have a repeated root, the discriminant D = B² − 4AC must be 0.

⇒ 12x² − ax² − ax − 9x + 7 − 3 = 0

⇒ (12 − a)x² − (a + 9)x + 4 = 0

Comparing with Ax² + Bx + C = 0:

⇒ A = (12 − a), B = −(a + 9), C = 4

⇒ D = [−(a + 9)]² − 4 × (12 − a) × 4 = 0

⇒ (a + 9)² − 16(12 − a) = 0

⇒ a² + 18a + 81 − 192 + 16a = 0

⇒ a² + 34a − 111 = 0

⇒ a² + 37a − 3a − 111 = 0

⇒ a(a + 37) − 3(a + 37) = 0

⇒ (a − 3)(a + 37) = 0

⇒ a = 3 or a = −37

Since we need the positive solution for a:

⇒ a = 3

∴ The correct answer is 3.

Additional Information

Nature of Roots

The nature of roots of Ax² + Bx + C = 0 depends on D = B² − 4AC. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Sum and Product of Roots

For Ax² + Bx + C = 0, the sum of roots is −B/A and the product of roots is C/A.

Quadratic Formula

The roots of a quadratic equation are given by x = [−B ± √(B² − 4AC)] / 2A.

The correct answer is Purvanchal.

• Hills including Mishmi, Naga, Manipur, Tripura, Mizo, Patkai that run through the north-east region are known as Purvanchal Hills.
• It lies south of the Brahmaputra valley.
• It covers an area of about 94,800 km².
• It covers Nagaland, Manipur, Tripura, and Mizoram Hills, and Chachar Districts along with a fifth of Haflong tahsil of Assam State and District of Tripa and part of Lohit in Arunachal Pradesh.

Additional Information

• Bharamputra River enters first in Namchafarua mountain in Arunachal Pradesh.
• Majuli Island in Assam is the world's largest river island.
• Tributaries of Bharamputra are - Manas, Tista, Jamuna, Dihand, Dibang, Kemeng, etc.
• Cities alongside the river Bharamputra are - Guwahati, Dibrugarh.

Shortcut Trick Number 24649 ends in 9, so the unit digit of the square root must be 3 or 7. Ignore the last two digits (49). The remaining number is 246. The largest perfect square less than 246 is 225 (which is 152). Possible answers are 153 or 157. Since 1502 = 22500 and 1602 = 25600, 24649 is closer to 25600. ∴ The correct answer is 157. Alternate Method Given: Number = 24649 Method: Long Division Method for Square Root ⇒ Grouping digits from right to left: 2, 46, 49 ⇒ Step 1: 1 × 1 = 1 | Remainder = 1 | Bring down 46 → 146 ⇒ Step 2: Double the quotient (1 × 2 = 2). 25 × 5 = 125 | Remainder = 21 | Bring down 49 → 2149 ⇒ Step 3: Double the quotient (15 × 2 = 30). 307 × 7 = 2149 | Remainder = 0 ⇒ Square root = 157 ∴ The correct answer is 157. Additional Information Unit Digit Property If a perfect square ends in 9, its square root unit digit is either 3 or 7 because 32 = 9 and 72 = 49. Range Estimation To find the range, use multiples of 10. For example, 1502 = 22500 and 1602 = 25600. Since 22500 < 24649 < 25600, the square root must be between 150 and 160.