RRB Group D Previous Year Paper (Held on: 17 Sept 2022 Shift 1)

The correct answer is CaO + H2O → Ca(OH)2.

Key Points

• Neutralization Reaction:
• It is a chemical reaction in which an acid and base react together to form salt and water as products.
• Example of the neutralization reaction.
• Ca(OH)2 + H2CO3 → CaCO3 + 2H2O
• H3PO4 + 3KOH → K3PO4 + 3H2O
• HNO3 + KOH → KNO3 + H2O
• The reaction between calcium oxide (CaO) and water (H2O) to form calcium hydroxide (Ca(OH)2) is an example of a combination reaction and not a neutralisation reaction.

Additional Information

• Other types of Chemical Reactions:
• Decomposition reaction: The opposite of a combination reaction, a complex molecule breaks down to make simpler ones. Such reactions are represented by equations of the following form: AB → A + B.
• Precipitation reaction: Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming. Such reactions are represented by equations of the following form: A + Soluble salt B  → Precipitate + soluble salt C.
• Combination reaction: It is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY.
• Combustion reaction: Oxygen combines with a compound to form carbon dioxide and water. These reactions are exothermic, meaning they give off heat. Such reactions are represented by equations of the following form: A + O2 → H2O + CO2.
• Displacement reaction: One element takes place with another element in the compound. Such reactions are represented by equations of the following form: A + BC → AC + B.

Shortcut Trick

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

Total amount = ₹1,344.

Difference between largest (5) and smallest (3) = 5 − 3 = 2 units.

Required Difference = (1344 ÷ 12) × 2 = 112 × 2 = ₹224.

∴ The correct answer is ₹224.

Alternate Method

Given: Total amount = ₹1,344; Ratio = 3 : 4 : 5.

Let the shares be 3x, 4x, and 5x.

⇒ 3x + 4x + 5x = 1344

⇒ 12x = 1344

⇒ x = 1344 ÷ 12 = 112

⇒ Largest share = 5 × 112 = ₹560

⇒ Smallest share = 3 × 112 = ₹336

⇒ Difference = 560 − 336 = ₹224

∴ The correct answer is ₹224.

Additional Information

Ratio Division Rule

To divide a quantity A in the ratio a:b:c, the shares are [a/(a+b+c)]×A, [b/(a+b+c)]×A, and [c/(a+b+c)]×A.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd), obtained by multiplying the corresponding terms.

Mean Proportional

The mean proportional between two numbers a and b is given by √(a × b).

The correct answer is Region shown by arrow 4. 

Key Points

• The vacuole, indicated by arrow 4, is the largest organelle in most plant cells.
• It is responsible for the storage of water and a variety of chemicals including nutrients, proteins, and waste products.
• The vacuole also maintains osmotic balance, provides structural support, and is involved in the degradation of waste materials.

Additional Information

• Chloroplasts:
• Chloroplasts are specialized organelles within plant cells that conduct photosynthesis.
• Cell Wall:
• The cell wall provides mechanical strength, structural support, and protection against mechanical stress and infection.
• Plasma Membrane:
• Typically beneath the cell wall, the plasma membrane controls the movement of substances into and out of the cell.

Given: Avina has tuitions for six subjects - Maths, English, Computer Science, Physics, Biology and Chemistry.

Each on a different day of a week from Monday and ending on Saturday of the same week.

1. Biology tuition is on Monday.

2. Only three subject tuitions are scheduled between Computer Science and Physics tuitions.

3. Physics tuition is on the day immediately after the Maths tuition which is on Friday.

4. Only Chemistry tuition is scheduled between Maths and English tuitions.

So, 'English' subject's tuition is scheduled on Wednesday.

Hence, the correct answer is "Option 4".

Shortcut Trick

एक संख्या के अंकों का योग 3 से विभाज्य होता है यदि संख्या स्वयं 3 से विभाज्य हो।

यदि पहली संख्या में 2 जोड़ा जाता है, तो अंकों का कुल योग भी 2 बढ़ जाएगा।

मूल योग: 367(16), 489(21), 514(10), 632(11), 728(17)

नया योग (+2): 18, 23, 12, 13, 19

3 से विभाज्य योग: 18 और 12 (कुल 2 संख्याएँ)।

∴ The correct answer is Two.

Alternate Method

दिए गए अंक: 367, 489, 514, 632, 728

नियम: प्रत्येक संख्या के पहले अंक में 2 जोड़ें और फिर अंकों के योग की जाँच करें।

⇒ संख्या 367: 3+2=5; नई संख्या 567; योग = 5+6+7 = 18 (18 ÷ 3 = 6)

⇒ संख्या 489: 4+2=6; नई संख्या 689; योग = 6+8+9 = 23 (विभाज्य नहीं)

⇒ संख्या 514: 5+2=7; नई संख्या 714; योग = 7+1+4 = 12 (12 ÷ 3 = 4)

⇒ संख्या 632: 6+2=8; नई संख्या 832; योग = 8+3+2 = 13 (विभाज्य नहीं)

⇒ संख्या 728: 7+2=9; नई संख्या 928; योग = 9+2+8 = 19 (विभाज्य नहीं)

∴ The correct answer is Two.

Additional Information

3 की विभाज्यता का नियम (Divisibility by 3)

यदि किसी संख्या के सभी अंकों का योग 3 से पूर्णतः विभाजित होता है, तो वह संख्या 3 से विभाज्य होती है।

9 की विभाज्यता का नियम (Divisibility by 9)

यदि संख्या के अंकों का योग 9 से विभाजित हो, तो संख्या 9 से विभाज्य होती है।

अंकों में परिवर्तन का प्रभाव

यदि किसी भी अंक में n जोड़ा जाता है, तो अंकों का कुल योग भी n से बढ़ जाता है।

The correct answer is average atomic mass of the first and third elements.

Key Points

• Dobereiner’s law of triads:
• Dobereiner’s law of triads states that when elements are arranged in the order of increasing atomic masses, the atomic mass of the middle element of the triad is approximately the average of the atomic masses of the other two elements.
• Example: 
• In the triad of Lithium, Sodium, and Potassium, the atomic mass of Lithium is 7 and the atomic mass of Potassium is 39.
• The average of masses of Lithium and Potassium gives the atomic mass of Sodium 23.

Additional Information

• Newland’s law of octaves: 
• It states that when elements are arranged in order to increase atomic masses, every eighth element has properties similar to the first.
• Mendeleev’s law:
• The law states that the physical and chemical properties of the elements are the periodic function of their atomic masses.

The correct answer is HIV-AIDS.

Key Points

• Human immunodeficiency virus (HIV) is a virus that attacks a part of the immune system and damages its function.
• AIDS is a late stage of HIV infection.
• This virus targets white blood cells called CD4 (T cells).
• They are needed to fight off infections and other diseases.
• Low levels of CD4 cells make it harder for the body to stop or control infections and diseases.

Important Points 

• HIV is most commonly spread through:
• Sexual contact with an HIV-infected person, especially vaginal or anal sex.
• Transfer of HIV from a mother to child during pregnancy, childbirth, or breastfeeding.
• HIV-contaminated needle.

Additional Information

The correct answer is Black.

Concept:

• Light scattering occurs when a parallel beam of light passes through a gas and a portion of it appears in directions other than the incident direction.
• This is referred to as light scattering.
• The basic idea behind light scattering is that light is absorbed by molecules and then re-radiated in different directions.
• Red light scatters the least, while violet light scatters the most.
• Scattering of light causes the blue colour of sky and the reddening of the Sun at sunrise and sunset.

Explanation:

• The scattering of sunlight from the atmosphere causes the sky to appear blue on Earth.
• When we look at the sky, scattered light enters our eyes. It appears blue because the colour blue is present in greater proportion in sunlight, so blue colour is scattered the most. As a result, light appears blue.
• Since the moon has no atmosphere, there are no particles to scatter sunlight.
• This allows the astronaut to see the true emptiness of space, which appears black.

The correct answer is Autonomous Consumption.

Key Points

• C̅ in the consumption function represents consumption that does not depend on current income levels.
• This type of consumption is known as Autonomous Consumption.
• Autonomous Consumption is the part of consumption expenditure that would occur even if the consumer had zero income.
• It is a key component in the Keynesian consumption function, which is expressed as C = C̅ + cY, where c is the marginal propensity to consume and Y is the income.

Additional Information

The logic followed here is:

Logic: (2^nd number + 1)³ + 1 = 1^st number.

Now,

For, 28 : 2

⇒ (2 + 1)³ + 1 = 3³ + 1 = 27 + 1 = 28.

For, 126 : 4

⇒ (4 + 1)³ + 1 = 5³ + 1 = 125 + 1 = 126.

Similarly, for 65 ∶ ?

⇒ (2^nd number + 1)³ + 1 = 65.

⇒ (2^nd number + 1)³ = 65 - 1.

⇒ 2^nd number + 1 = √³64.

⇒ 2^nd number + 1 = 4.

⇒ 2^nd number = 4 - 1.

⇒ 2^nd number = 3.

Hence, the correct answer is "Option 2".

The correct answer is Salivary Amylase.

Key Points

• Starch is a complex carbohydrate that needs to be broken down into simple sugars for the body to use it as energy.
• Amylase is the enzyme responsible for breaking down starch into simple sugars like glucose and maltose.
• The majority of amylase in your body is produced by the salivary glands and pancreas.

Additional Information

• Pepsin is an enzyme produced in the stomach.
• It breaks down proteins into amino acids.
• Trypsin is an enzyme produced in the pancreas.
• It breaks down proteins into smaller peptides.
• Lipase is an enzyme that breaks down fats into fatty acids and glycerol.

The correct answer is option 4.

Key Points

• Methanoic acid is indeed secreted by Nettle plant leaves. It is one of the substances that cause the stinging sensation when a person comes into contact with the nettles. Hence, Statement 1 is correct.
• Acetic acid is the main component of vinegar, contributing to its characteristic sour taste and pungent smell. Therefore, Statement 2 is correct.
• Tooth decay is known to begin when the pH in the mouth drops below 5.5. At this acidity level, the enamel on the teeth begins to demineralize, leading to decay. Thus, Statement 3 is correct.
• Bacteria in the mouth typically produce acid from the fermentation of food particles, not base. This acid contributes to tooth decay by lowering the pH of the mouth. Consequently, Statement 4 is incorrect.

Additional Information

• The acidity produced by bacterial action on food particles in the mouth is a key factor in the development of tooth decay and dental cavities.
• Regular dental hygiene, such as brushing and flossing, can help to remove food particles and reduce the bacterial population in the mouth, thus lowering the risk of tooth decay.
• Fluoride treatments and the use of fluoridated toothpaste can help to remineralize and strengthen tooth enamel, making it more resistant to acid attack.

Shortcut Trick

Simplify the ratio (1 − tan A) / (1 − cot A) by using the property cot A = 1/tan A.

(1 − tan A) / (1 − 1/tan A) = (1 − tan A) / [(tan A − 1) / tan A] = −tan A.

Substituting this back: √(1 + (−tan A)²) = √(1 + tan² A).

Using the trigonometric identity: 1 + tan² A = sec² A.

∴ The correct answer is sec A.

Alternate Method

Given: The expression √(1 + ((1 − tan A) / (1 − cot A))²).

Formula Used: 1 + tan² A = sec² A and cot A = 1/tan A.

Calculations:

⇒ Let X = (1 − tan A) / (1 − cot A)

⇒ X = (1 − tan A) / (1 − 1/tan A)

⇒ X = (1 − tan A) / [(tan A − 1) / tan A]

⇒ X = [tan A × (1 − tan A)] / [−(1 − tan A)]

⇒ X = −tan A

⇒ Value = √(1 + X²)

⇒ Value = √(1 + (−tan A)²)

⇒ Value = √(1 + tan² A)

⇒ Value = √sec² A = sec A

∴ The correct answer is sec A.

Additional Information

Fundamental Trigonometric Identities

Standard identities: sin² A + cos² A = 1, 1 + tan² A = sec² A, and 1 + cot² A = cosec² A.

Reciprocal Relations

Key ratios: tan A = sin A/cos A, cot A = cos A/sin A, sec A = 1/cos A, and cosec A = 1/sin A.

Complementary Angles

Relations: sin(90° − A) = cos A, tan(90° − A) = cot A, and sec(90° − A) = cosec A.

The logic followed here is:​

So, '19' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Shortcut Trick

To convert a mixed recurring decimal to a fraction: Numerator = (Full number) − (Non-recurring part).

Denominator = (Write 9 for each repeating digit) followed by (Write 0 for each non-repeating digit after decimal).

Numerator = 5323 − 5 = 5318.

Denominator = 9990 (3 digits repeat, 1 digit does not).

Fraction = 5318/9990 = 2659/4995.

∴ The correct answer is 2659/4995.

Alternate Method

Given: x = 0.5323323...

Formula Used: Basic algebraic method for rationalizing recurring decimals.

⇒ Let x = 0.5323323... — (Eq. 1)

⇒ Multiply (Eq. 1) by 10: 10x = 5.323323... — (Eq. 2)

⇒ Multiply (Eq. 1) by 10000: 10000x = 5323.323323... — (Eq. 3)

⇒ Subtract (Eq. 2) from (Eq. 3): 10000x − 10x = 5323.323... − 5.323...

⇒ 9990x = 5318

⇒ x = 5318/9990

⇒ x = 2659/4995 (Dividing by 2)

∴ The correct answer is 2659/4995.

Additional Information

Pure Recurring Decimal

A decimal in which all digits after the decimal point repeat, e.g., 0.‾3 = 3/9 = 1/3.

Mixed Recurring Decimal

A decimal in which some digits do not repeat and some repeat, e.g., 0.1‾6 = (16−1)/90 = 15/90 = 1/6.

Rational Number Property

Every terminating or recurring decimal can be expressed in the form p/q and is a rational number.

Shortcut Trick

Sum of ages 10 years ago = 111 − (3 × 10) = 81 years.

Ratio of ages 10 years ago = 2 : 3 : 4 (Total units = 9).

Value of 9 units = 81 ⇒ 1 unit = 9 years.

Nikhil's age 10 years ago = 3 units × 9 = 27 years.

Nikhil's present age = 27 + 10 = 37 years.

∴ The correct answer is 37 years.

Alternate Method

Given: Present sum = 111 years. Ratio (R:N:A) 10 years ago = 2 : 3 : 4.

Formula Used: Sum of ages (T years ago) = Present Sum − (n × T)

⇒ Sum 10 years ago = 111 − (10 + 10 + 10) = 81 years.

⇒ Let ages 10 years ago be 2x, 3x, and 4x.

⇒ 2x + 3x + 4x = 81

⇒ 9x = 81 ⇒ x = 9.

⇒ Nikhil's age 10 years ago = 3x = 3 × 9 = 27 years.

⇒ Nikhil's present age = 27 + 10 = 37 years.

∴ The correct answer is 37 years.

Additional Information

Age Sum Property

If the sum of ages of 'n' persons is 'S' at present, then 'T' years ago, the sum was S − (n × T).

Ratio Application

To find a specific person's share from a total sum using a ratio a:b:c, use: Share = [Ratio Part / Total Ratio Sum] × Total Value.

The correct answer is Nowruz. 

Key Points

• ​The festival of Navroz (or Nowruz) is celebrated as the New Year by the Parsi community.
• Parsis follow Zoroastrianism, which was founded in ancient Persia (now Iran).
• Navroz, or Nowruz, means "new day" and it marks the first day of the Persian calendar.
• It usually falls on March 21, symbolizing the renewal of nature and life.
• The festival is marked by feasting, praying, and meeting family and friends.

Additional Information

• Buddhist:
• The New Year in the Buddhist tradition varies depending on the country and tradition.
• For example, in Theravada countries, the New Year is celebrated for three days from the first full moon day in April.
• Sindhi:
• The Sindhi New Year is celebrated on the second day of the lunar month Cheti, which usually falls in late March or early April, and is known as Cheti Chand.
• It is celebrated in honor of the birth of the Sindhi patron saint Jhulelal.
• Jainism:
• The Jain New Year starts right after Diwali, one of the most important festivals in India, and it generally falls in late October or early November.
• It marks the anniversary of the attainment of moksha (liberation) by Mahavira, the last of the Jain Tirthankaras.
• Jainism is an ancient Indian religion emphasizing non-violence and asceticism.

Given: Five runners are standing in a straight row facing the east.

1. Runner K is standing at the first position and M is at the end position.

2. P is standing third to the left of M.

3. L is standing to the immediate left of N, and N is standing to the immediate left of M.

So, 'K' is standing to the immediate left of P.

Hence, the correct answer is "Option 3".

The correct answer is Indira Gandhi Canal.

Key Points 

• Indira Gandhi Canal is the longest in India.
• It begins at Harike Barrage in Harike, a few kilometers below the confluence of the Sutlej and Beas rivers in the Indian state of Punjab, and ends at irrigation facilities in the Thar Desert in the northwest of the state of Rajasthan.
• Previously known as the Rajasthan Canal, it was renamed Indira Gandhi Canal on 2 November 1984 after the assassination of Prime Minister Indira Gandhi.
• The state receives much water from the rivers of Punjab, from the Western Yamuna Canal in Haryana and the Agra Canal in Uttar Pradesh, and from the Sabarmati and Narmada Sagar projects in Gujarat and Madhya Pradesh, respectively.
• Desert land in northwestern and western Rajasthan is irrigated by the Indira Gandhi Canal (formerly called the Rajasthan Canal), which carries water some 400 miles (640 km) from the Beas and Sutlej rivers in Punjab.
• Rajasthan shares the Bhakra Nangal project with Punjab and Haryana and the Chambal Valley project with Madhya Pradesh; both are used to supply water for irrigation and drinking purposes.
• Rajasthan regained its lost greenery due to it.

The correct answer is Carbon dioxide, water, sunlight, and chlorophyll.

Key Points

• Photosynthesis:
• The process by which plants make their own food in the presence of sunlight, carbon dioxide present in air, water, minerals, and chlorophyll present in leaves is termed photosynthesis.
• Components which are necessary for photosynthesis are Carbon dioxide, water, sunlight and chlorophyll.
• ​Carbon dioxide from air is taken in through the tiny pores present on the surface of the leaves.
• These pores are surrounded by ‘guard cells’. Such pores are called stomata.

Water and minerals are transported to the leaves by the vessels which run like pipes throughout the root, the stem, the branches, and the leaves.

• They form a continuous path or passage for the nutrients to reach the leaf.
• The leaves have a green pigment called chlorophyll. It helps leaves to capture the energy of the sunlight.
• This energy is used to synthesize (prepare) food from carbon dioxide and water.
• Since the synthesis of food occurs in the presence of sunlight, it is called photosynthesis (Photo: light; synthesis: to combine).

So we find that chlorophyll, sunlight, carbon dioxide, and water are necessary to carry out the process of photosynthesis.

• Thus, the sun is the ultimate source of energy for all living organisms.
• Besides leaves, photosynthesis also takes place in other green parts of the plant in green stems and green branches.
• The desert plants have the scale or spine-like leaves to reduce the loss of water by transpiration. These plants have green stems which carry out photosynthesis.
• During photosynthesis, chlorophyll-containing cells of leaves, in the presence of sunlight, use carbon dioxide and water to synthesize carbohydrates. The carbohydrates ultimately get converted into starch.
• The leaves other than green also have chlorophyll. A large amount of red, brown, and other pigments mask the green color. Photosynthesis takes place in these leaves also.

Shortcut Trick

Side of the cube (a) = ³√Volume = ³√216 = 6 cm.

Total Surface Area (TSA) = 6 × a² = 6 × 6².

TSA = 6 × 36 = 216 cm².

∴ The correct answer is 216 cm².

Alternate Method

Given: Volume of the solid cube = 216 cm³.

Formula Used:

1. Volume of a cube = a³ (where a is the side length).
2. Total Surface Area (TSA) of a cube = 6a².

Calculations:

⇒ a³ = 216

⇒ a = ³√216

⇒ a = 6 cm

⇒ Total Surface Area = 6 × (6)²

⇒ Total Surface Area = 6 × 36

⇒ Total Surface Area = 216 cm²

∴ The correct answer is 216 cm².

Additional Information

Lateral Surface Area of Cube

It is the area of the 4 vertical faces only: LSA = 4a².

Diagonal of a Cube

The longest rod that can be placed inside a cube of side a is d = a√3.

Properties of a Cube

A cube has 6 faces (all squares), 12 edges, and 8 vertices.

The correct answer is Odisha.

Key Points

• The Deomali (1672m) mountain peak is situated on the Eastern Ghat in Odisha.
• It is the highest peak of Odisha.
• Deomali is a mountain peak in the Chandragiri-Pottangi subrange of the Eastern Ghats.
• It is located near Koraput town in the Koraput district of southern Odisha, India.

Additional Information

The logic followed here is:​

So, '29' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Shortcut Trick

Sum of odd place digits = 2 + 4 + 9 = 15

Sum of even place digits = 3 + 4 + 2 = 9

Difference = 15 − 9 = 6

To make the number divisible by 11, the difference must be 0 or a multiple of 11.

Required number to add = 11 − 6 = 5 (Wait, check logic: adding to the number changes the digits). If we add 6 to 234492, we get 234498. Sum of even places becomes 3 + 4 + 8 = 15. Difference = 15 − 15 = 0.

∴ The correct answer is 6.

Alternate Method

Given: Number = 234492

Divisibility Rule of 11: The difference between the sum of digits at odd positions and the sum of digits at even positions must be 0 or divisible by 11.

⇒ Let the number to be added be x.

⇒ The new number is 234492 + x. Since x is a 1-digit number, only the units digit changes (unless there is a carry-over).

⇒ Units digit becomes 2 + x. This is an even position digit (counting from left: 1^st=2, 2^nd=3, 3^rd=4, 4^th=4, 5^th=9, 6^th=2+x).

⇒ Sum of digits at even positions = 3 + 4 + (2 + x) = 9 + x.

⇒ Sum of digits at odd positions = 2 + 4 + 9 = 15.

⇒ For divisibility by 11: |15 − (9 + x)| = 0 or multiple of 11.

⇒ 15 − 9 − x = 0

⇒ 6 − x = 0

⇒ x = 6

∴ The correct answer is 6.

Additional Information

Divisibility by 11

A number is divisible by 11 if the absolute difference between the sum of its odd-positioned digits and even-positioned digits is either 0 or a multiple of 11.

Divisibility by 9

A number is divisible by 9 if the sum of all its digits is divisible by 9.

Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Shortcut Trick

According to Thales Theorem (Basic Proportionality Theorem), if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio. Thus, PS/PQ = PT/PR is always true. Furthermore, since ST || QR, the corresponding angles are equal, making ΔPST ∼ ΔPQR by AA similarity. The statement ST = QR/2 is only true if S and T are midpoints, which is not always given.

∴ The correct answer is Only (a) and (c).

Alternate Method

Given: In ΔPQR, ∠P = 30° and ST || QR (where S is on PQ and T is on PR).

Formula Used: Basic Proportionality Theorem (BPT) and AA Similarity Criterion.

⇒ In ΔPQR, since ST || QR, by Thales Theorem: PS/SQ = PT/TR.

⇒ By adding 1 to both sides of the reciprocal ratio: (SQ/PS) + 1 = (TR/PT) + 1.

⇒ (SQ + PS)/PS = (TR + PT)/PT ⇒ PQ/PS = PR/PT.

⇒ Taking the reciprocal: PS/PQ = PT/PR. (Statement a is always true).

⇒ In ΔPST and ΔPQR, ∠P = ∠P (Common angle).

⇒ ∠PST = ∠PQR (Corresponding angles as ST || QR).

⇒ ∴ ΔPST ∼ ΔPQR by AA similarity. (Statement c is always true).

⇒ From similarity, ST/QR = PS/PQ. The condition ST = QR/2 only occurs if PS = PQ/2 (S is the midpoint).

∴ The correct answer is Only (a) and (c).

Additional Information

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

AA Similarity Criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

Midpoint Theorem

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is equal to half of the third side.

The correct answer is Space Science, Technology and Research.

Key Points

• The Vikram Sarabhai Journalism Award is awarded to recognize outstanding journalistic work in the field of space science, technology, and research.
• It is named after Dr. Vikram Sarabhai, who is widely regarded as the father of the Indian space program.
• The award aims to encourage and acknowledge comprehensive and objective reporting in space science.
• Recipients of this award are honored for their significant contribution to the dissemination of information about space activities to the public.

Additional Information

• Dr. Vikram Sarabhai was an Indian scientist and innovator widely regarded as the pioneer of the Indian space program.
• He was instrumental in establishing the Indian Space Research Organisation (ISRO) in 1969.
• Sarabhai emphasized the importance of space technology in a nation's development and was a key figure in the development of education and research in space science in India.
• His efforts in the development of the Thumba Equatorial Rocket Launching Station (TERLS), the first rocket launching station in India, were significant.

The correct answer is c---b---e---d---a.

Key Points

• The first step in dialysis involves taking blood from the patient's artery to lead it into the dialysis machine.
• In the second step, this blood is passed through a tank containing a dialysing fluid, which is carefully balanced to have the same osmotic pressure as the patient's blood except for the waste products.
• The third step ensures that the dialysing fluid has the correct osmotic pressure, facilitating the transfer of waste products from the blood into the fluid, without removing substances the body needs.
• In the fourth step, the actual exchange occurs where waste products from the blood pass into the dialysing fluid, effectively cleaning the blood.
• The final step involves returning the cleaned blood to the patient's body through a vein.

Therefore, the sequence c---b---e---d---a correctly outlines the process of dialysis from taking blood from an artery to returning it via a vein, with the cleaning process in between. Hence, Statement 2 is correct.

For Additional Information: Consider the below statements and identify the correct answer. Statement - I : Anhydrous sodium carbonate is used in soda-acid fire extinguishers. Statement - II : Anhydrous sodium carbonate is dissolved in water and recrystallized to get washing soda crystals containing 10 molecules of water of crystallisation The Correct Answer is option 4.

• Anhydrous sodium carbonate (Na₂CO₃) is the anhydrous or water-free form of sodium carbonate.
• It is a , crystalline powder with various industrial uses.
• Hydrated Form: Washing Soda: Washing soda (sodium carbonate decahydrate, Na₂CO₃·10H₂O) is the hydrated form of sodium carbonate. It contains 10 molecules of water of crystallization. Washing soda is commonly used for laundry purposes, water softening, and cleaning.

Additional Information      Applications:

• Soda-Acid Fire Extinguishers: Anhydrous sodium carbonate is not typically used in soda-acid fire extinguishers; this role is traditionally filled by substances like sodium bicarbonate (baking soda). When mixed with water, it reacts with sulfuric acid (present in the extinguisher) to produce carbon dioxide gas. The released CO₂ helps suppress fires by displacing oxygen and cooling the flames.
• Glass and Ceramics Industry: Anhydrous sodium carbonate is a crucial component in glass and ceramic production. It acts as a flux, lowering the melting point of silica (SiO₂) and aiding in the fusion of raw materials.
• Chemical Manufacturing: It serves as a precursor for various chemicals, including sodium bicarbonate (baking soda), sodium silicates, and sodium percarbonate (used in laundry detergents).
• Water Softening: Anhydrous sodium carbonate is used in water treatment to soften hard water. It reacts with calcium and magnesium ions (which cause hardness) to form insoluble carbonates, which can be removed.
• pH Regulation: In laboratories and industrial processes, it adjusts pH levels due to its alkaline nature.
• Textile Industry: It aids in dyeing and fixing colors in fabrics.

Key Points

• Giriraj Singh was the Union Minister of Rural Development & Panchayati Raj as of March 2022.
• This ministry is crucial for implementing schemes and policies aimed at enhancing rural infrastructure, livelihood, and governance.
• The Ministry plays a pivotal role in empowering Panchayati Raj Institutions (PRIs) to become instruments of socio-economic transformation in rural India.
• Giriraj Singh has been known for his advocacy for rural development and has been involved in numerous initiatives aimed at the upliftment of rural areas.

Additional Information

Shortcut Trick

Distance is covered in 5 blocks of 2 hours each.

Distances: 80, 88, 96, 104, 112 (as speed increases by 4 kmph, distance in 2h increases by 8 km).

This is an Arithmetic Progression (AP): Sum = n/2 × (a + l) = 5/2 × (80 + 112).

Sum = 2.5 × 192 = 480 km.

∴ The correct answer is 480 km.

Alternate Method

Given: Initial distance in 2 hours = 80 km; Speed increase = 4 kmph every 2 hours; Total time = 10 hours.

⇒ Initial speed = Distance ÷ Time = 80 ÷ 2 = 40 km/h.

⇒ Total 10 hours contains 5 intervals of 2 hours each.

⇒ Distance in 1^st 2 hours = 40 × 2 = 80 km.

⇒ Distance in 2^nd 2 hours = (40 + 4) × 2 = 44 × 2 = 88 km.

⇒ Distance in 3^rd 2 hours = (44 + 4) × 2 = 48 × 2 = 96 km.

⇒ Distance in 4^th 2 hours = (48 + 4) × 2 = 52 × 2 = 104 km.

⇒ Distance in 5^th 2 hours = (52 + 4) × 2 = 56 × 2 = 112 km.

⇒ Total distance = 80 + 88 + 96 + 104 + 112 = 480 km.

∴ The correct answer is 480 km.

Additional Information

Arithmetic Progression (AP) in Speed

When speed increases by a fixed amount over fixed time intervals, the distances covered in those intervals form an AP. The common difference (d) for distance is (increase in speed × interval time).

Sum of AP Formula

S_n = n/2 [2a + (n − 1)d] where n is the number of intervals, a is the first term, and d is the common difference.

Average Speed for AP

For an AP, the average speed (or distance) is simply the middle term if n is odd, or the average of the two middle terms if n is even.

According to the given Venn diagram:

The shaded area shows the "total number of students like both Samosa and Burger".

So, the total number of students like both Samosa and Burger = 8 + 5 + 18 = 31.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1^st number × 2) + 4 = 2^nd number.

Now,

For, 17 : 38

⇒ (17 × 2) + 4 = 34 + 4 = 38.

For, 23 : 50

⇒ (23 × 2) + 4 = 46 + 4 = 50.

Similarly, for 12 ∶ ?

⇒ (12 × 2) + 4 = 24 + 4 = 28.

Hence, the correct answer is "Option 1".

BODMAS Rule:

Decoding the given information:

Given Equation: 2 - 4 × 25 + 13 ÷ 2 = ?

Now replacing the signs from left to right using the BODMAS Rule, we get:

New Equation: 2 ÷ 4 + 25 - 13 × 2 = ?

Applying the BODMAS Rule:

→ 2 ÷ 4 + 25 - 13 × 2 = ?

→ 0.5 + 25 - 13 × 2 = ?

→ 0.5 + 25 - 26 = ?

→ 25.5 - 26 = -0.5.

Hence, the correct answer is "Option 1".

Shortcut Trick

Ashish CP = 5000 ÷ 0.8 = 6250.

Ashish Target SP (Bipin Selling Price) = 6250 × 1.15 = 7187.5.

Bipin Gain = 7187.5 − 5000 = 2187.5.

∴ The correct answer is Rs. 2,187.50.

Alternate Method

Given: Ashish Selling Price (SP_A) = Rs. 5,000 | Ashish Loss = 20% | Ashish Target Profit = 15%. Formulas: CP = SP × 100 ÷ (100 − Loss%) | SP = CP × (100 + Profit%) ÷ 100 | Gain = SP − CP.

⇒ Ashish Cost Price = 5000 × 100 ÷ 80 = Rs. 6,250.

⇒ Price at which Ashish would have 15% profit = 6250 × (115 ÷ 100) = Rs. 7,187.50.

⇒ Since Bipin sold the cow to Kasim at this price, Bipin Selling Price = Rs. 7,187.50.

⇒ Bipin Cost Price = Ashish Selling Price = Rs. 5,000.

⇒ Bipin Gain = 7187.50 − 5000 = Rs. 2,187.50.

∴ The correct answer is Rs. 2,187.50.

Additional Information

Chain Transactions

In a chain of sales, the Selling Price of the first person becomes the Cost Price for the second person.

Profit and Loss Percentage

Profit or Loss is always calculated on the Cost Price (CP) unless stated otherwise in the problem.

Given Series: (Left) 4 # O $ 5 T F 8 % U 2 P A & F Ø 3 @ T 4 ¥ I # H (Right)

Symbols immediately followed by a vowel and also immediately preceded by a number.

So, the pattern needed is: Number - Symbol - Vowel

Now,

So, there are 'Three' pairs i.e.: '4#O, 8%U, 4**¥**I'.

Hence, the correct answer is "Option 2"$.

Given word: 'MIRACLE'

After arranged in alphabetical order:

After arranged in alphabetical order,

Third alphabet from the left end is: E,

Third alphabet from the right end is: L,

Now,

there are 6 letters between E and L.

Hence, the correct answer is "Option 3".

Shortcut Trick

For a mean proportional relationship a : b :: b : c, the middle term is given by b = √(a × c).

Here, y is the mean proportional between 16 and 25.

⇒ y = √(16 × 25)

⇒ y = 4 × 5 = 20

∴ The correct answer is 20.

Alternate Method

Given:

The proportion is 16 : y :: y : 25.

Formula Used:

In a proportion a : b :: c : d, the product of extremes is equal to the product of means (⇒ a × d = b × c).

Calculations:

⇒ 16 / y = y / 25

⇒ y × y = 16 × 25

⇒ y² = 400

⇒ y = √400

⇒ y = 20

∴ The correct answer is 20.

Additional Information

Mean Proportional

If three quantities a, b, c are in continued proportion, then a/b = b/c, where b is the mean proportional and b² = ac.

Third Proportional

In the continued proportion a : b :: b : c, the term c is called the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

In a proportion a : b :: c : d, the term d is the fourth proportional, calculated as d = (b × c) / a.

Shortcut Trick

In a proportion a : b :: c : d, the product of extremes equals the product of means.

Product of extremes (5 × x) = Product of means (12 × 9)

5x = 108

x = 108 ÷ 5 = 21.6

∴ The correct answer is 21.6.

Alternate Method

Given: 5 : 12 :: 9 : x

Formula Used: a/b = c/d

⇒ 5 / 12 = 9 / x

⇒ 5 × x = 9 × 12

⇒ 5x = 108

⇒ x = 108 ÷ 5

⇒ x = 21.6

∴ The correct answer is 21.6.

Additional Information

Fourth Proportional

If a, b, and c are three numbers, then the fourth proportional d is calculated as d = (b × c) ÷ a.

Mean Proportional

The mean proportional between two numbers a and b is given by the formula √(a × b).

Third Proportional

For two numbers a and b, the third proportional c is such that a : b :: b : c, which means c = b² ÷ a.

Given: Six boxes A, B, C, P, U, and V are kept one over the other, but not necessarily in the same order.

1. B is the top-most box, and C is immediately below B.

2. There are only two boxes between B and V.

3. There are only three boxes between P and C.

4. There is only one box below U.

And, A will place on the remaining space.

After arranging the boxes, the box immediately below U is P.

Hence, the correct answer is "Option 4".

The correct answer is Article 50.

Key Points

• Article 50 of the Indian Constitution is part of the Directive Principles of State Policy. It aims to separate the judiciary from the executive in the public services of the State to ensure independence.
• This separation is crucial for upholding the integrity of the judiciary and avoiding any influence or bias from the executive branch of the government.
• The objective is to maintain the rule of law and ensure a fair and impartial judicial process for all citizens.
• Article 50 is not enforceable by courts, as it is a directive principle, but it guides the governance of the country to establish a system where the judiciary operates independently of the executive branch.

Additional Information

Given Statement: A > C = B, M > N > O > P > Q = A

After arranging the equation: M > N > O > P > Q = A > C = B

Now,

Conclusions:

Option 1: O < B → False (O > P > Q = A > C = B It gives O > B)

Option 2: B < M → True (M > N > O > P > Q = A > C = B It gives M > B)

Option 3: N < C → False (M > N > O > P > Q = A > C It gives N > C)

Option 4: C > N → False (M > N > O > P > Q = A > C It gives N > C)

Hence, the correct answer is "Option 2".

Given: Six girls A, C, F, H, J, and K, each has a different height. They are standing in ascending order of their heights, shortest in the front and tallest at the back.

1. C is at the beginning of the queue.

C < __ < __ < __ < __ < __

2. There is only one person taller than F.

C < __ < __ < __ < F < __

3. H is immediately taller than A.

4. There is only one other person between A and C.

C < __ < A < H < F < __

5. Both C and H are shorter than K.

C < __ < A < H < F < K

And, J will place on the remaining space.

C < J < A < H < F < K

Hence, the girl who is second from the beginning of the queue is J.

Hence, the correct answer is "Option 1".

Given:

Now, the group of numbers and symbols is: '7 % 9 # 2'

Here, Here, Second conditions followed in the given group,

So, codes of the First and Last elements will be coded as ©.

Then, the code for '7 % 9 # 2' is → '© Q A D ©'.

Hence, the correct answer is "Option 4"$.

Shortcut Trick

Ratio of Ram to Sita = 5 : 8. Sum of ratio parts = 13.

Total sum 3 years later = 58 years. Current sum = 58 − (3 × 2) = 52 years.

Value of 13 units = 52 years → 1 unit = 4 years.

Ram's present age = 5 × 4 = 20 years.

∴ The correct answer is 20 years.

Alternate Method

Given: Present ratio = 5 : 8. Sum after 3 years = 58.

⇒ Let Ram's age be 5x and Sita's age be 8x.

⇒ (5x + 3) + (8x + 3) = 58

⇒ 13x + 6 = 58

⇒ 13x = 52

⇒ x = 4

⇒ Ram's present age = 5 × 4 = 20

∴ The correct answer is 20 years.

Additional Information

Ratio and Proportion

When ages are given in a ratio a : b, they can be represented as ax and bx where x is a common multiplier.

Sum of Ages in Future/Past

If there are 'n' people, their total sum of ages after 't' years increases by (n × t) years.

Age Difference Property

The difference between the ages of two people remains constant throughout their lives, regardless of how many years pass.

Shortcut Trick

Curved Surface Area (CSA) of cylinder = π × d × h

Given: CSA = 880 cm² and Diameter (d) = 7 cm

880 = (22/7) × 7 × h

880 = 22 × h ⇒ h = 880 ÷ 22 = 40 cm

∴ The correct answer is 40 cm.

Alternate Method

Given:

Curved Surface Area (CSA) = 880 cm²

Diameter (d) = 7 cm ⇒ Radius (r) = 7/2 = 3.5 cm

Formula Used:

CSA of Cylinder = 2πrh

Calculations:

⇒ 880 = 2 × (22/7) × (7/2) × h

⇒ 880 = 22 × h

⇒ h = 880 ÷ 22

⇒ h = 40 cm

∴ The correct answer is 40 cm.

Additional Information

Total Surface Area of Cylinder

It is the sum of the curved surface area and the areas of the two circular bases: TSA = 2πr(h + r).

Volume of Cylinder

The space occupied by the cylinder is calculated as: Volume = πr²h.

Base Area and Perimeter

Base Area = πr² and Base Circumference (Perimeter) = 2πr.

Given:

Now, the group of numbers and symbols is: '%94#2'

Here, Here, Second conditions followed in the given group,

So, Third element is to be coded as the code for the second element.

Then, the code for '%94#2' is → 'MZZKP'.

Hence, the correct answer is "Option 2".

The correct answer is second largest.

Key Points

• India was ranked as the second-largest arms importer globally according to the SIPRI report titled 'Trends in International Arms Transfers, 2021'.
• This position indicates India's significant reliance on foreign sources for its military hardware.
• The country's vast imports are driven by its needs to modernize its military forces and enhance its defense capabilities.
• Major suppliers to India include countries like Russia, France, and the United States, highlighting a diversified source of imports.
• The report underscores the global arms trade dynamics and how nations prioritize defense and security through arms imports and exports.

Additional Information

Shortcut Trick

Apply the V-BODMAS rule to solve the expression step-by-step from inside to outside:

Vinculum (Bar): 16 − 10 = 6

Round Brackets: 12 − 6 = 6

Curly & Square Brackets: 14 − 6 = 8 → 12 − 8 = 4

Final Subtraction: 20 − 4 = 16

∴ The correct answer is 16.

Alternate Method

Given:

Expression = 20 − [12 − {14 − (12 − 16 − 10)}]

Concept Used:

V-BODMAS Rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)

Order of solving brackets: Bar → () → {} → []

Calculation:

⇒ 20 − [12 − {14 − (12 − 16 − 10)}]

⇒ 20 − [12 − {14 − (12 − 6)}]

⇒ 20 − [12 − {14 − 6}]

⇒ 20 − [12 − 8]

⇒ 20 − 4

⇒ 16

∴ The correct answer is 16.

Additional Information

V-BODMAS Rule

V stands for Vinculum or Bar bracket. It acts as an overarching group. Even if operations like subtraction and multiplication are present under it, they are strictly resolved first.

Order of Brackets

Evaluate nested brackets in the exact order: Vinculum (Bar) → Parentheses () → Braces {} → Square Brackets [].

Signs in Simplification

When a negative sign precedes a bracket, the sign of each term inside the bracket mathematically flips when the bracket is removed or resolved.

The logic followed here is:

For, TSRA : ZIHG

For, OLEV : EVOL

Similarly, for Option 4) ARNI : RMIZ

Hence, the correct answer is "Option 4".

Shortcut Trick For any quadratic equation ax2 + bx + c = 0, the nature of roots depends purely on the Discriminant (D). Condition: If D = 0, the roots are always real and equal. ∴ The correct answer is two equal real roots.

Alternate Method Given: The discriminant of a quadratic equation is 0. Concept Used: For a standard quadratic equation ax2 + bx + c = 0, the roots are calculated using the quadratic formula: ⇒ x = (−b ± √D) / 2a Where D = b2 − 4ac is the discriminant. Calculation: ⇒ Substitute D = 0 into the quadratic formula. ⇒ x = (−b ± √0) / 2a ⇒ x = (−b ± 0) / 2a ⇒ x = −b / 2a ⇒ Since the ± part evaluates to zero, both roots of the equation result in the exact same value. ⇒ Therefore, the quadratic equation yields two identical real roots. ∴ The correct answer is two equal real roots.

Additional Information Nature of Roots (D = b2 − 4ac) ⇒ If D > 0: The quadratic equation has two distinct real roots.⇒ If D = 0: The quadratic equation has two equal real roots.⇒ If D < 0: The quadratic equation has no real roots (roots are complex/imaginary). Sum and Product of Roots For roots α and β of ax2 + bx + c = 0:Sum of roots (α + β) = −b / aProduct of roots (α × β) = c / a Graphical Representation (Parabola) When D = 0, the graph of the quadratic polynomial touches the x-axis exactly at one point (−b/2a, 0), indicating a perfect square.

Given:

Now, the group of numbers and symbols is: '3 & % 4 6'

Here, Here, Second conditions followed in the given group,

So, codes of the First and Last elements will be coded as ©.

Then, the code for '3 & % 4 6' is → '© G C X ©'.

Hence, the correct answer is "Option 2".

Given:

9^3.5 : 3⁵

Formula used:

9 = 3², so 9^3.5 = (3²)^3.5

Then, use the property of exponents (a^m)ⁿ = a^m×n

Calculation:

⇒ 9^3.5 = 3⁷

⇒ The ratio becomes 3⁷ : 3⁵

⇒ The ratio simplifies to 3^7-5 = 3²

⇒ 3² = 9

∴ The ratio is 9:1, and the correct answer is option (2).

The correct answer is carboxylic acid.

Key Points

• Carboxylic acids contain a carboxyl group (–COOH), which includes two oxygen atoms: one in a hydroxyl group and the other in a carbonyl group.
• Carboxylic acids are more acidic than alcohols, aldehydes, and ketones due to the presence of this functional group.
• The presence of two oxygen atoms in carboxylic acids increases their ability to form hydrogen bonds, making them more soluble in water compared to other organic compounds with similar molecular weights.
• Carboxylic acids are commonly found in biological systems and are important in various chemical industries.

Additional Information

The correct answer is Arvari River.

Key Points

• Revival of Arvari River: The Arvari River, which had dried up, was successfully revived through the efforts of local villagers and the NGO Tarun Bharat Sangh.
• Community Effort: The revival process was a community-led initiative, demonstrating the power of collective action in environmental conservation.
• Water Management Techniques: Traditional water harvesting techniques were employed, including the construction of johads (small earthen check dams) to recharge groundwater.
• Impact on Livelihood: The revival of the river led to improved agricultural practices, increased water availability for irrigation, and enhanced biodiversity in the region.

Additional Information

Shortcut Trick

In an isosceles triangle, the altitude drawn from the vertex between the equal sides to the base acts as both the median and the angle bisector.

Since AB = AC, the altitude AD is drawn to the base BC.

By the properties of symmetry in an isosceles triangle, AD must bisect the vertex ∠ A.

∴ The correct answer is AD bisects ∠ A.

Alternate Method

Given: In Δ ABC, AB = AC and AD is the altitude (AD ⊥ BC).

Formula Used: RHS (Right angle-Hypotenuse-Side) Congruence Rule and CPCT (Corresponding Parts of Congruent Triangles).

In Δ ABD and Δ ACD:

⇒ AB = AC (Given)

⇒ AD = AD (Common side)

⇒ ∠ ADB = ∠ ADC = 90° (Since AD is the altitude)

⇒ Δ ABD ≅ Δ ACD (By RHS congruence rule)

⇒ ∠ BAD = ∠ CAD (By CPCT)

⇒ Since the angles are equal, AD bisects ∠ A.

∴ The correct answer is AD bisects ∠ A.

Additional Information

Isosceles Triangle Properties

In an isosceles triangle, the altitude to the base is also the median (bisects the base) and the angle bisector of the vertex angle.

RHS Congruence Rule

Two right-angled triangles are congruent if the hypotenuse and one side of one triangle are equal to the hypotenuse and the corresponding side of the other triangle.

Base Angles Theorem

The angles opposite to the equal sides of an isosceles triangle are always equal (∠ B = ∠ C when AB = AC).

Given:

5x + y = 125

5x - y = 3125

Calculation:

We have,

5x + y = 125

⇒ 5x + y = 5³

⇒ x + y = 3    ---(1)

5x - y = 3125

⇒ 5x - y = 5⁵

⇒ x - y = 5    ---(2)

Now, Add equation (1) and (2)

x + y + x - y = 3 + 5

⇒ 2x = 8

⇒ x = 4

From equation (1),

y = 3 - x = 3 - 4 = -1

∴ The correct answer is option (4).

The logic followed here is:

So, 'CID27' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The correct answer is Amount of petroleum is finite.

Key Points

• Petroleum is a non-renewable resource, meaning it cannot be replenished naturally at the rate we consume it.
• The extraction and burning of petroleum products release significant amounts of greenhouse gases, contributing to climate change.
• Dependence on petroleum makes economies vulnerable to price fluctuations and supply disruptions.
• Reducing reliance on petroleum can promote the development and adoption of cleaner, sustainable energy sources.

Additional Information

The correct answer is They laid down their lives to stop the cutting down of trees growing in their region.

Key Points

• The Bishnoi community of Rajasthan, led by Amrita Devi Bishnoi, is known for their commitment to protecting trees and wildlife.
• In 1730, the Maharaja of Jodhpur sent soldiers to cut down trees in the region for a new palace. Amrita Devi and her community opposed the cutting of trees, as they considered them sacred.
• Amrita Devi Bishnoi and 362 other members of her community sacrificed their lives to protect the trees by hugging them, a method that is now known as "Chipko Movement" in modern environmental campaigns.
• This event is one of the earliest examples of non-violent environmental protest in India and has inspired generations to protect nature.

Additional Information

• The Bishnoi sect was founded by Guru Jambheshwar in 1485 in the Marwar (Jodhpur) region of Rajasthan, with a strong emphasis on environmental preservation as a key religious tenet.
• They follow 29 principles (Bish-noi translates to Twenty-nine), many of which are directly related to flora and fauna conservation, such as prohibition against cutting trees and killing animals.
• The legacy of Amrita Devi Bishnoi and her community's sacrifice led to the creation of the Amrita Devi Bishnoi Wildlife Protection Award by the Government of India, for significant contributions in the field of wildlife protection.
• The Bishnoi villages are known for their rich biodiversity, and they often serve as oases in the desert landscape, demonstrating the environmental benefits of their practices.

The correct answer is Cheteshwar Pujara.

Key Points

• Grade A status in BCCI contracts represents a high level of remuneration and benefits for the players included.
• Cheteshwar Pujara is known for his solid technique and has been a key player in India's Test match setup.
• The central contracts list is updated annually by the BCCI, reflecting players' performances and potential contributions to the team.
• Players losing Grade A status might be due to various factors including form, fitness, and team composition needs.

Additional Information

Shortcut Trick

A quadratic equation with roots α and β is given by x² − (α + β)x + αβ = 0.

Sum of roots (α + β) = 2 − 1/2 = 3/2.

Product of roots (αβ) = 2 × (−1/2) = −1.

Equation → x² − (3/2)x + (−1) = 0 ⇒ 2x² − 3x − 2 = 0.

∴ The correct answer is 2x² − 3x − 2 = 0.

Alternate Method

Given: The roots of the required quadratic equation are 2 and −1/2.

Formula Used: For any quadratic equation ax² + bx + c = 0, the equation can be expressed as: x² − (Sum of roots)x + (Product of roots) = 0.

⇒ Sum of roots (α + β) = 2 + (−1/2)

⇒ Sum of roots = (4 − 1) / 2 = 3/2

⇒ Product of roots (α × β) = 2 × (−1/2) = −1

⇒ Equation: x² − (3/2)x + (−1) = 0

⇒ Multiply the entire equation by 2 to clear the fraction:

⇒ 2(x²) − 2(3x/2) − 2(1) = 0

⇒ 2x² − 3x − 2 = 0

∴ The correct answer is 2x² − 3x − 2 = 0.

Additional Information

Relationship between Roots and Coefficients

For a standard quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Nature of Roots

The discriminant D = b² − 4ac determines the nature: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Quadratic Formula

Roots can be found using the formula x = (−b ± √(b² − 4ac)) / 2a.

The correct answer is up to Rs. 50,000.

Key Points

• The Shishu loan under MUDRA is designed for entrepreneurs who are in the earliest stage of starting a business.
• It offers loans up to Rs. 50,000 to help small businesses get off the ground.
• This category is part of the broader MUDRA scheme, which also includes Kishore and Tarun for higher loan amounts.
• The aim is to provide financial support to micro-enterprises and individuals to promote entrepreneurship.

Additional Information

• The Micro Units Development & Refinance Agency (MUDRA) was launched by the Government of India in 2015.
• MUDRA provides refinancing support to banks and microfinance institutions to encourage them to finance micro units.
• The scheme supports a wide range of sectors, including manufacturing, trading, and services.
• It categorizes loans into three products: Shishu (up to Rs. 50,000), Kishore (from Rs. 50,001 to Rs. 5 lakh), and Tarun (from Rs. 5,00,001 to Rs. 10 lakh).
• The initiative aims to boost the small enterprise sector, which is a significant employment generator and contributes to the economic growth of the country.

BODMAS Rule:

Decoding the given information:

Given Equation: 17 ÷ 3 - 2 + 12 × 4 = ?

Now replacing the signs using the decoded meanings:

New Equation: 17 + 3 × 2 - 12 ÷ 4 = ?

Applying the BODMAS Rule, we first perform the division and multiplication:

→ 17 + 3 × 2 - 12 ÷ 4 = ?

→ 17 + 3 × 2 - 3 = ?

→ 17 + 6 - 3 = ?

→ 23 - 3 = 20.

Hence, the correct answer is "Option 2".

Formula Used:

$\rm Percentage\ Increase = \frac{Final\ Value - Initial\ Value}{Initial\ Value} \times 100$

Calculation:

For Fatima:

⇒ Percentage Increase for Fatima  = (40 - 30) / 30 × 100 = 33.33%

For Harsh:

⇒ Percentage Increase for Harsh  = (50 - 40) / 40 × 100 = 25%

∴ Fatima has the maximum percentage increase in the value of the final product as compared to the value of raw material by approximately 33%.

The correct answer is railways.

Key Points

• The British introduced the concept of railways in India in 1850 to improve the transportation system and facilitate the movement of goods and people across the vast country.
• The first passenger train journey took place on April 16, 1853, covering a distance of 34 kilometers from Bombay (now Mumbai) to Thane.
• Railways played a crucial role in the economic development of India, but they were also designed to serve the colonial interests, including the control of resources and military mobility.
• The introduction of railways significantly influenced the structure of the Indian economy by integrating markets, promoting trade, and encouraging the commercialization of agriculture.

Additional Information

• The Indian Railways is one of the world's largest railway networks, with thousands of stations and over a hundred thousand kilometers of track.
• It plays a vital role in the social and economic development of the country, connecting remote and rural areas with urban centers.
• Over the years, the Indian Railways has undergone significant modernization, including the introduction of high-speed trains and digital ticketing systems.
• The sector has also been a significant employer, providing jobs to millions of people across various capacities.

Shortcut Trick

Identify the first five 2-digit even numbers: 10, 12, 14, 16, 18.

The smallest number divisible by all is their LCM.

LCM(10, 12, 14, 16, 18) = 2⁴ × 3² × 5 × 7.

Calculation: 16 × 9 × 5 × 7 = 80 × 63 = 5040.

∴ The correct answer is 5040.

Alternate Method

Given: The numbers are the first five 2-digit positive even numbers.

Formula: Smallest number divisible by a set of numbers = Least Common Multiple (LCM).

Step-by-step prime factorization:

⇒ 10 = 2 × 5

⇒ 12 = 2² × 3

⇒ 14 = 2 × 7

⇒ 16 = 2⁴

⇒ 18 = 2 × 3²

⇒ LCM = Highest power of all prime factors present

⇒ LCM = 2⁴ × 3² × 5¹ × 7¹

⇒ LCM = 16 × 9 × 5 × 7

⇒ LCM = 144 × 35 = 5040

∴ The correct answer is 5040.

Additional Information

Definition of LCM

The Least Common Multiple of two or more numbers is the smallest number that is a multiple of each of the numbers.

Relationship between HCF and LCM

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

Even Number Sequence

The set of positive even numbers follows an Arithmetic Progression with a common difference of 2.

Shortcut Trick

Identify the most frequent observation in the given data set.

Observation 2 appears 3 times.

Observation 6 appears 2 times.

Observation 7 appears 2 times.

Since 2 has the highest frequency, it is the mode.

∴ The correct answer is 2.

Alternate Method

Given Data: 5, 18, 6, 7, 6, 2, 3, 4, 24, 2, 7, 21, 2, 81

Formula Used: Mode = The value that occurs most frequently in a data set.

⇒ Total number of observations = 14

⇒ Frequency of 2 = 3

⇒ Frequency of 6 = 2

⇒ Frequency of 7 = 2

⇒ Frequency of 3, 4, 5, 18, 21, 24, 81 = 1 each

⇒ The observation with the maximum frequency (3) is 2.

∴ The correct answer is 2.

Additional Information

Measures of Central Tendency

These include Mean (average), Median (middle value), and Mode (most frequent value). They summarize a data set with a single representative value.

Empirical Relationship

For a moderately skewed distribution: Mode = 3 × Median − 2 × Mean.

Types of Mode

A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). If no value repeats, there is no mode.

Given: Eight boxes, J, K, L, M, N, O, P and Q, are kept in a vertical pattern.

1. L is placed at the bottommost position.

2. Q is at the third place from the top.

3. Only two boxes are placed between Q and M.

4. O is just below Q.

5. K is placed somewhere between M and N.

6. N is just below J.

And, P will placed at the remaining position.

So, the box 'P' is placed at the second position from the bottom.

Hence, the correct answer is "Option 4".

The correct answer is ninth.

Key Points

• Ramadan is the ninth month of the Islamic lunar calendar.
• It is considered the holiest month, during which Muslims fast from dawn to sunset.
• The fasting during Ramadan is one of the Five Pillars of Islam, which are the foundation of Muslim life.
• The fast is meant to bring the faithful closer to God and to remind them of the suffering of those less fortunate.
• Ramadan concludes with the celebration of Eid al-Fitr, a festive day when the fast is broken.

Additional Information

• The Islamic calendar is a lunar calendar consisting of 12 months in a year of 354 or 355 days.
• Ramadan's timing changes every year because the Islamic calendar is lunar, so it moves approximately 11 days earlier each year in the Gregorian calendar.
• Fasting during Ramadan is not only abstaining from food and drink but also includes refraining from smoking, sexual relations, and sinful behavior.
• The night of Laylat al-Qadr, which falls during the last ten days of Ramadan, is considered the most sacred night, believed to be the night when the Quran was first revealed to Prophet Muhammad.

Shortcut Trick

If x − 1/x = k, then x² + 1/x² = k² + 2.

If x² + 1/x² = m, then x⁴ + 1/x⁴ = m² − 2.

Given k = 5 → x² + 1/x² = 5² + 2 = 27.

Then m = 27 → x⁴ + 1/x⁴ = 27² − 2 = 729 − 2 = 727.

∴ The correct answer is 727.

Alternate Method

Given: x − 1/x = 5

Formula Used: (a − b)² = a² + b² − 2ab and (a + b)² = a² + b² + 2ab

Squaring both sides of the given equation:

⇒ (x − 1/x)² = 5²

⇒ x² + (1/x)² − 2 × x × (1/x) = 25

⇒ x² + 1/x² − 2 = 25

⇒ x² + 1/x² = 27

Squaring both sides again to find the fourth power:

⇒ (x² + 1/x²)² = 27²

⇒ (x²)² + (1/x²)² + 2 × x² × (1/x²) = 729

⇒ x⁴ + 1/x⁴ + 2 = 729

⇒ x⁴ + 1/x⁴ = 729 − 2

⇒ x⁴ + 1/x⁴ = 727

∴ The correct answer is 727.

Additional Information

Square Algebraic Identities

If x + 1/x = k, then x² + 1/x² = k² − 2. If x − 1/x = k, then x² + 1/x² = k² + 2.

Cube Algebraic Identities

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k. If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Relationship between (x+1/x) and (x−1/x)

(x + 1/x)² − (x − 1/x)² = 4. This is useful for switching between addition and subtraction forms.

Given: Six actors are sitting in a line facing the north.

1. A is sitting at the first position, and G is sitting third to the right of A.

2. H is sitting to the immediate right of G.

3. F is sitting second to the right of A.

4. L is sitting to the immediate right of A.

5. S is sitting at the end of the line.

So, 'F' is sitting to the immediate right of L.

Hence, the correct answer is "Option 2".

The correct answer is NITI Aayog.

Key Points

• NITI Aayog is not a constitutional body; it was formed via an executive resolution and serves as the policy think tank of the Government of India, providing both directional and policy inputs.
• Comptroller and Auditor General of India (CAG), Election Commission, and Union Public Service Commission (UPSC) are established by the Constitution of India, making them constitutional bodies.
• NITI Aayog was established in 2015, replacing the Planning Commission, an institution that was part of the Government of India for over six decades.
• The main role of the NITI Aayog is to foster cooperative federalism through structured support initiatives and mechanisms with the States on a continuous basis, recognizing that strong States make a strong nation.

Additional Information

Shortcut Trick

Loss of 10% means 90% of Cost Price (CP) = Rs. 540.

Ratio of Selling Prices to percentages: 540 ⇒ 90%.

Unitary method: 1 ⇒ 90 ÷ 540 = 1/6%.

For New Selling Price Rs. 696: 696 ⇒ 696 × (1/6)% = 116%.

Profit percentage = 116% − 100% = 16%.

∴ The correct answer is 16%.

Alternate Method

Given: First SP = Rs. 540, Loss = 10%, Second SP = Rs. 696.

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

⇒ Cost Price (CP) = (540 × 100) ÷ (100 − 10) = (540 × 100) ÷ 90 = 6 × 100 = Rs. 600.

⇒ New Profit = New SP − CP = 696 − 600 = Rs. 96.

⇒ Profit Percentage = (96 ÷ 600) × 100 = 16%.

∴ The correct answer is 16%.

Additional Information

Relationship between SP, CP, and Profit/Loss

Profit occurs when Selling Price is greater than Cost Price. Loss occurs when Cost Price is greater than Selling Price.

Base for Percentage Calculation

Both Profit% and Loss% are always calculated on the Cost Price unless specified otherwise in the problem.

The correct answer is Improving the understanding of the dynamics of the Sun.

Key Points

• The HelioSwarm mission aims to provide unprecedented insights into the Sun's dynamics, specifically focusing on the turbulent nature of solar wind and its effects on space weather.
• It involves the deployment of a swarm of spacecraft to study the solar wind in three dimensions, which is crucial for understanding space weather patterns that can affect Earth and human technology.
• The mission seeks to improve predictions of space weather events, which can disrupt satellite communications, GPS systems, and power grids on Earth.
• Understanding the Sun's dynamics is also vital for the safety of astronauts in future manned missions to the Moon, Mars, and beyond, as solar radiation poses a significant risk.

Additional Information

• The HelioSwarm mission is part of NASA's initiative to enhance our understanding of the Sun and how it influences the space environment surrounding Earth.
• This mission is unique because it uses multiple spacecraft to form a "swarm" that can collect data from various points within the solar wind simultaneously.
• The knowledge gained from HelioSwarm will contribute to our overall understanding of stellar processes and could inform the study of other stars and their planetary systems.
• By studying the Sun's behavior and its impact on space weather, the mission supports efforts to protect technology and astronauts from the adverse effects of solar activity.

The correct answer is Two.

Key Points

• The chemical equation given is SO₂ + H₂S → 3S + 2H₂O.
• To balance the equation, we need equal numbers of atoms of each element on both sides.
• By adding two molecules of hydrogen sulphide (H₂S), we balance the sulphur (S) atoms: 1 from SO₂ and 2 from 2H₂S gives a total of 3 sulphur atoms on both sides.
• This also balances the hydrogen (H) atoms: 2 hydrogen atoms from each H₂S molecule make a total of 4, which matches the 4 hydrogen atoms in 2H₂O.
• Therefore, two molecules of H₂S are required to balance the given chemical equation.

Additional Information

Hydrogen sulphide (H₂S) is a colorless, poisonous, flammable gas that smells like rotten eggs. It is produced by the bacterial breakdown of organic matter in the absence of oxygen, such as in swamps and sewers; it also occurs in volcanic gases, natural gas, and some well waters. Being heavier than air, it tends to accumulate at the bottom of poorly ventilated spaces. Hydrogen sulphide is used in the manufacture of chemicals, in metallurgy, and as a nuisance odor in rotten egg bombs, but it is hazardous and can be lethal in high concentrations.

Concept:

Concave Mirror:

• A concave mirror is a spherical mirror with a reflecting surface that curves inward.
• A concave mirror's focal length (f) is the distance between the mirror's surface and the focal point.
• Mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
• Where, f = focal length, v = image distance, u = object distance.
• Magnification (M) is the ratio of the height of the image (h_i) to the height of the object (h_o).
• Magnification formula: $M = \frac{h_i}{h_o} = -\frac{v}{u}$

Calculation:

Given,

Object height, h_o = 30 μm

Image height, h_i = 60 cm

Focal length, f = 25 cm

Magnification, M = $\frac{h_i}{h_o}$

Magnification, M = $\frac{60 \times 10^4 \text{μm}}{30 \text{μm}}$

⇒ M = 20000

We know, $M = -\frac{v}{u}$

⇒ 20000 = $-\frac{v}{u}$

⇒ v = -2000u

Using mirror formula, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

⇒ $\frac{1}{25} = \frac{1}{-20000u} + \frac{1}{u}$

⇒ $\frac{1}{25} = \frac{1 - 20000}{20000u}$

⇒ $\frac{1}{25} = \frac{-19999}{20000u}$

⇒ $20000u = -19999 \times 25$

⇒ $u = -\frac{19999 \times 25}{20000}$

⇒ $u = -24.9875 \approx -25 \text{cm}$

∴ The hair should be placed in front of the mirror at 25 cm.