RRB Group D Previous Year Paper (Held on: 23 Aug 2022 Shift 1)

The correct answer is Precipitate.

Key Points

• An insoluble substance is created by a chemical reaction or by the crystallization of a dissolved substance to form a precipitate, both of which are solids that are formed from a solution.
• A solid substance that was once dissolved in a solvent like water becomes less soluble in the first scenario.
• This may occur when:
• The solution's temperature is reduced.
• The addition of a precipitating agent.
• The substance is mixed with still another, less soluble solvent.
• The solution becomes supersaturated, and a precipitation reaction takes place when the substance's solubility falls below its concentration.
• Any chemical reaction that results in an insoluble or extremely poorly soluble product in the solvent is considered a second instance.
• The solution soon reaches saturation once this product starts to develop, and the solid starts to precipitate.

Additional Information

• The particle size and characteristics of the solid are influenced by the rate at which precipitates occur.
• Three different types of precipitates can be recognized based on the size of the particles and the type of substance that is precipitating:
• Crystalline precipitates
• Cheesy precipitates
• Gelatinous precipitate

Given:

(30 + 3-2 + 3-1) × 27 

Calculation:

= (30 + 3-2 + 3-1) × 27

= $(1+{1\over9}+{1\over 3})\times27$

= ${{(9+1+3)}\over9}\times27$

= $13\times 3$

= 39

Hence, the correct answer is option 4).

We know that:

The second-hand covers 360**°** in 1 minute.

Therefore, the angular distance covered by the second hand in 12 minutes  $= 360° * 12 =4320°$

Hence**,** the correct answer is option 2).

Given:

Persons: A, B, C, D, E, and F 

Days: Monday to Sunday.

Conditions are as follows:

1. There is no exam on Thursday. 2.  E's exam is on Saturday. 3. The exams of A and F are separated by one day which is the gap day.

4.D's exam is immediately before F but is immediately after C. 

5. B's exam is on Sunday. 

Analyzing all the conditions, we get,

So D's exam is on Tuesday.

Hence, the correct answer is option 4).

The correct answer is 9R.

Key Points

• Initially,
• Length of wire = l
• Resistance of wire = R
• Area of wire = A
• Now, the material of wire is same, 
• Length of wire = 9l
• Resistance of wire = R
• Area of wire = A
• We know that, if all the conditions are constant, then the resistance of the wire is directly proportional to the length of the wire. So,
• R = xl, where x = constant
• R' = x(9l) = 9R

The correct answer is 'Virat Kohli'.

Key Points

• Virat Kohli, born on 5 November 1988 is an Indian international cricketer and former captain of the Indian national team.
• He is widely regarded as one of the greatest batsmen of all time in international cricket.
• India will take on Sri Lanka in the upcoming two-match Test series, starting March 04 at Punjab Cricket Association IS Bindra Stadium in Mohali.
• In that match, only Virat Kohli was an Indian player to play his 100th test match against Sri Lanka in Mohali in March 2022.

Additional Information

• ​Cricket is an outdoor game played between two teams. Players try to score points, called runs, by hitting a ball with a wooden bat.
• Virat Kholi is known for his good leadership qualities and for his kind behaviour.​
• Rohit Sharma: 
• ​At Eden Gardens in Kolkata, Sharma played in his first Test match. In his first game, he scored 177.
• In an October 2019 match against South Africa, he amassed a career-high 212 runs.
• He is the third Indian cricketers to register back-to-back hundreds in the first two tests.
• On September 4, 2021, Rohit Sharma earned his first century outside of India against England, making it his eighth Test century overall.
• Ravichandran Ashwin:
• ​He amassed nine five-fours in his first 16 Tests, and after that, he became the second-fastest player (after Muthiah Muralidaran) to 300 wickets and 400.
• 30 five-fours and counting, 90-plus wickets each against Australia and England, and over 50 wickets each year four times are some of Ashwin's career highs in Test cricket.
• Ishant Sharma:
• Ishant played in lieu of the fast bowler Munaf Patel during the test series against Bangladesh in May 2007.
• ​After a strong 2008, in which he took 38 wickets in 13 Tests, his form plummeted, and over the following two years, he could only manage 43 wickets from 15 Tests.
• In 2011, he made a comeback, taking 43 wickets in 12 Test matches, including two five-wicket hauls, both during India's tour of the West Indies.

The correct answer is 'Odisha'.

Key Points

• Brackish water or briny water has more salinity than freshwater, but not as much as seawater. It may result from the mixing of seawater with fresh water, as in estuaries, or it may occur in brackish fossil aquifers.
• Bodies of water of brackish lagoons, marshes and deltas are lakes with an average salinity and a mixture of freshwater and seawater.
• The largest brackish water lake is present in **Odisha.**​

Additional Information

• ​The largest brackish water lake is named "Chilika".
• It is a shallow lagoon with estuarine character spread across the districts of Puri, Khurda and Ganjam in the state of Odisha in eastern India.
• Chilika Lake lives up to its reputation as the most picturesque spot and being Asia's largest salt-water lagoon.

The correct answer is 'Pradhan Mantri Garib Kalyan Anna Yojana'.

Key Points

• The National Food Security Act,2013 (NFSA 2013) converts into legal entitlements for the existing food security program of the Government of India.
• Food security, as defined by the United Nations Committee on World Food Security, means that all people, at all times, have physical, social, and economic access to sufficient, safe, and nutritious food that meets their food preferences and dietary needs for an active and healthy life.
• The world's largest food security program which has been extended till September 2022, is Pradhan Mantri Garib Kalyan Anna Yojana.​

Additional Information

• PMGKAY is a part of the Pradhan Mantri Garib Kalyan Package (PMGKP) to help the poor fight the battle against Covid-19.
• The scheme aimed at providing each person who is covered under the National Food Security Act 2013 with an additional 5 kg of grains (wheat or rice) for free, in addition to the 5 kg of subsidized food grain already provided through the Public Distribution System (PDS).

The correct answer is 'Gram Corporation'.

Key Points

• The Gram Sabha, Gram Panchayat, and Sarpanch are parts of the Panchayat Raj system whereas Gram Corporation is an independent organization constituted by some people.
• The Panchayati Raj system is the system that ensures the participation of individuals at the grass-root level.
• The Balwant Rai Mehta Committee recommended 3- tier structure consisting of Zilla Parishad at the District Level, Panchayat Samiti at the Block Level, and Gram Panchayat at the Village Level.

Additional Information

• The Panchayati Raj system is included in the State List of the Constitution of India under the 73rd Constitutional Amendment Act, 1992 is related to the Panchayati Raj system.
• Rajasthan is the first state to implement the Panchayati Raj system on 2nd October 1959 in its Nagaur district.
• Balwant Rai Mehta Committee recommended the Panchayati Raj system for the first time in India.
• Ashok Mehta Committee appointed in December 1977 by Janata Party Government in 1978 submitted its report stating the replacement of the 3-tier system by a 2-tier system consisting of Mandal Panchayats at the base and Zila Parishad at the top.
• 24th April every year Panchayati Raj day is celebrated.
• Part IX (Articles 243 to 243O) of the Constitution of India deals with the Panchayati Raj system.

The correct answer is 'Bengali'.

Key Points

• Bengali is not a classical language as of now.
• Currently, there are six languages that enjoy the ‘Classical’ status in India: Tamil (declared in 2004), Sanskrit (2005), Kannada (2008), Telugu (2008), Malayalam (2013), and Odia (2014).
• All the Classical Languages are listed in the Eighth Schedule of the Constitution. The Ministry of Culture provides guidelines regarding Classical languages.

Additional Information

• Guidelines for declaring a language as ‘Classical’ are: High antiquity of its early texts/recorded history over a period of 1500-2000 years, A body of ancient literature/texts, which is considered a valuable heritage by generations of speakers.
• The University Grants Commission is requested to create, to start with at least in the Central Universities, a certain number of Professional Chairs for the Classical Languages so declared.
• Two major annual international awards for scholars of eminence in classical Indian languages. A Centre of Excellence for Studies in Classical Languages is set up.

Shortcut Trick

For a rhombus, the area is half the product of its diagonals.

Area = (1/2) × 12 × 15

Area = 6 × 15 = 90 cm²

∴ The correct answer is 90 cm².

Alternate Method

Given:

First diagonal (d₁) = 12 cm

Second diagonal (d₂) = 15 cm

Formula Used:

Area of Rhombus = (1/2) × d₁ × d₂

Calculations:

⇒ Area = (1/2) × 12 × 15

⇒ Area = 6 × 15

⇒ Area = 90 cm²

∴ The correct answer is 90 cm².

Additional Information

Perimeter of Rhombus

The perimeter is 4 × side. Since all sides are equal, Perimeter = 4a.

Side and Diagonal Relationship

The side a is related to diagonals by the formula: 4a² = d₁² + d₂².

Properties of Diagonals

The diagonals of a rhombus bisect each other at right angles (90°).

The correct answer is Each gamete has two copies of the same gene.

Key Points

• The genotype refers to the plant's genetic makeup. On the other hand, phenotype refers to a plant's outward appearance.
• In pairs called alleles, the genes are passed from parents to children.
• One of the two alleles has a 50% probability of fusing with the allele of the gamete of the other parent during gametogenesis when the chromosomes are divided in half.
• Homozygous alleles are those that share the same allele, whereas heterozygous alleles are those that have distinct alleles.
• Mendel's laws, often known as the rules of inheritance, were developed as a result of the two experiments. These laws are:
• Law of Dominance
• Law of Segregation
• Law of Independent Assortment

Additional Information

• Gregor Mendel proposed the law of inheritance after seven years of research on pea plants.
• The laws of dominance, segregation, and independent assortment are among Mendel's laws of inheritance.
• According to the law of segregation, each person has two alleles, but only one of them is passed on to the next generation.
• According to the law of independent assortment, the inheritance of one set of genes is unrelated to the inheritance of another set of genes.

The series can be written as:

There are 5 such pairs where a letter is immediately preceded by a symbol and also immediately followed by a symbol.

Hence, the correct answer is option 2).

Given conditions of the seating arrangement:

• 4 people: A, B, C, and D are sitting in a straight line facing north.
• A and C are not sitting adjacent to each other.
• C and B are sitting adjacent to each other.

Option 1) DABC → Possible (Follows all the conditions)

​

Option 2) BCAD → Not possible (Does not follow all the conditions).

​

​

 

Option 3) ABCD → Possible (Follows all the conditions).

Option 4) CBAD → Possible (Follows all the conditions).

Hence, 'option 2)' is the correct answer.

The correct answer is Both the statements are true.

Key Points

• For statement I,
• Since it possesses four electrons in its valence shell, carbon is a tetravalent compound.
• These four electrons are all accessible to create covalent bonds.
• The periodic table's group 14 includes it.
• Organic substances, which include all carbon compounds, are often weak electrical conductors.
• As a result, carbon compounds lack the additional electron necessary to carry electricity.
• None of their electrons are free.
• Consequently, carbon-based molecules don't conduct electricity.
• For statement II,
• The attractive forces are very weak in these since there are no ions present.
• The interatomic interactions are relatively strong and covalent bonds are quite stable.
• Weak intermolecular forces keep covalent molecules together.
• It simply requires a small amount of energy to break because the forces are feeble.
• Since these weak intermolecular interactions can be broken at lower energies.
• The covalent compounds consequently have low melting and boiling points.

The logic followed here is:

(First number) × (Third number)² = Second number

1. Series: (7, 175, 5)

So it can be explained as 

= 7 × 5² 

= 175

2. Another series: (6, 294, 7) 

= 6 × 7² 

= 294

Let us check every option: 

option 1) (3, 192, 8)

= 3 × 8² 

= 192

In this option, logic is followed

option(2) (5, 140, 7)

= 5 × 7² 

= 245 ≠ 140

Logic isn't following

option 3) (8, 412, 9)

= 8 × 9²

= 648 ≠ 412

Logic isn't following

option 4) (6, 216, 5)

= 6 × 5² 

= 150 ≠ 216 

Logic isn't following 

Hence, the correct answer is option (1).

Shortcut Trick

Average of consecutive numbers = Middle term.

Middle number = 2457 ÷ 3 = 819.

Since they are multiples of 9, the numbers are (819 − 9), 819, and (819 + 9).

Largest number = 819 + 9 = 828.

∴ The correct answer is 828.

Alternate Method

Let the three consecutive multiples of 9 be (x − 9), x, and (x + 9).

⇒ (x − 9) + x + (x + 9) = 2457

⇒ 3x = 2457

⇒ x = 2457 ÷ 3

⇒ x = 819

⇒ Largest multiple = x + 9 = 819 + 9 = 828

∴ The correct answer is 828.

Additional Information

Arithmetic Progression (AP)

Consecutive multiples form an AP where the common difference d is the number itself (here, d = 9).

Average of Odd Number of Terms

For an AP with n terms (where n is odd), the middle term is always the Arithmetic Mean of the series.

Properties of Multiples

The difference between any two consecutive multiples of n is always n.

The correct answer is 'Tamil Nadu'.

Key Points

• Successful Qualification of High Thrust Vikas Engine. Today (July 15, 2018), a high-thrust version of the Vikas Engine was successfully qualified through a ground test for a duration of 195 seconds at ISRO Propulsion Complex (IPRC), Mahendragiri, Tamilnadu.
• The test was conducted to check the robustness of the engine by operating beyond its nominal operating conditions.
• The ISRO Is one of the most successful space agencies in the world ranking globally at 4th position according to space and science rankings

Additional InformationISRO (Indian Space Research Organisation)-

• The Indian Space Research Organisation is the national space agency of India, headquartered in Bengaluru.
• It operates under the Department of Space (DOS) which is directly overseen by the Prime Minister of India, while the Chairman of ISRO acts as the executive of DOS as well.
• It is one of six government space agencies in the world which possess full launch capabilities, deploy cryogenic engines, launch extraterrestrial missions and operate large fleets of artificial satellites.

The correct answer is 'Tsunami'.

Key Points

• The amount of UVB that reaches the Earth's surface rises as a result of ozone layer loss.
• The breakdown of ozone in the stratosphere, where it protects the earth from damaging ultraviolet radiation, is known as ozone depletion.
• Chemical processes that utilize hydrogen, nitrogen, chlorine, and bromine oxides as catalysts lead to its demise.
• Humans are exposed to dangerous UV radiation as a result of ozone layer loss, which can lead to skin conditions, cataracts, cancer, weakened immune systems, etc.​

Additional Information

• By a combination of ground-based and satellite data in the early 1980s, researchers came to the conclusion that Earth's natural sunscreen was significantly diminishing over the South Pole each spring.
• The thick layer of ozone that is present in the stratosphere, 15 to 30 kilometres above the surface of the earth, is referred to as the "ozone layer" in this context.
• By absorbing the sun's harmful ultraviolet-B (UV-B) radiation, which permeates the entire planet, it protects life on earth.

The correct answer is .

Key Points

When an object is placed beyond 2F (center of curvature) of a concave mirror, the image formed is real, inverted, and diminished. The image is formed between F and 2F on the same side of the mirror. The farther the object from the mirror, the smaller and closer the image moves towards the focus (F). If the object is placed at infinity, the image is point-sized (highly diminished) at the focal point. This is a standard behavior of concave mirrors according to ray diagram principles in optics.

Additional Information

Concave Mirror Image Characteristics:

Beyond 2F: Real, inverted, diminished (image forms between F and 2F). At 2F: Real, inverted, same size (image forms at 2F). Between F and 2F: Real, inverted, enlarged (image forms beyond 2F). At F: Image at infinity. Between Pole and F: Virtual, erect, enlarged (image forms behind the mirror).

Ray Diagram Rules:

Ray parallel to principal axis reflects through the focus. Ray through the center reflects back along the same path.

Mirror Formula:

1/f = 1/v + 1/u, where f is focal length, v is image distance, and u is object distance. Used to calculate exact image location and characteristics.

Sign Convention:

All distances measured from mirror's pole. Distances in the direction of incoming light are negative (object side), and in the direction of reflected light are positive.

Use of Concave Mirrors:

Used in telescopes, headlights, shaving mirrors, and solar concentrators due to their ability to focus light.

The pattern followed here is shown below:

ROUTINE is written as UORTENI

And,

PLAYERS is written as ALPYSRE

Similarly,

BANKING will be written as NABKGNI

Hence, the correct answer is option 4).

Given: 

12 ÷ 3 × (7 + 8 - 3)

Concept Used:

BODMAS Rule

According to the BODMAS rule, the priority of the order of operations for solving an expression is as follows:

Calculation:

12 ÷ 3 × (7 + 8 - 3)

= 12 ÷ 3 × (15 - 3)

= 12 ÷ 3 × 12

= 4 × 12

= 48

Hence, the correct answer is option 4).

Given:

125.99 - 35.92 + 3.89 × 16.11

Concept Used:

BODMAS Rule

The priority of order of operations will be based on the order of letters in the word 'BODMAS' as given below: 

Calculation:

125.99 - 35.92 + 3.89 × 16.11

= 125.99 + 62.67 - 35.92

= 188.66 - 35.92

= 152.74

From the given options, the closest approximate value of 152.74 is 154.

Hence, the correct answer is option 3).

The correct answer is Both statements are correct.

Key Points

• A modern Periodic table is a tabular arrangement of elements in groups and periods.
• It highlights the regular trend in the physical and chemical properties of the elements.
• There are total of 18 vertical columns known as groups which are divided into various families like Alkali metals, Alkali Earth Metals, D Group elements, Boron Family, Carbon Family, Nitrogen family, Oxygen family, Halogen family, and Noble Gases.
• The modern Periodic Table also contains 7 horizontal rows known as periods.

Given:

Total number power banks manufactured = 100

Manufacturing cost = ₹ 50,000

Profit = 50%

Formula used:

Selling price = $\frac{(100+ Profit\%)\times Cost \ price }{100}$

Calculation:  

Manufacturing cost of each power bank = $\frac{50000}{100}$ = ₹ 500

Total Cost of one power bank = $500\times(\frac{100\%}{30 \%})$ = ₹ $\frac{5000}{3}$

Selling price of the power banks so that the manufacturer can earn a profit of 50% 

⟹ Selling price = $\frac{(100+50)\times\frac{5000}{3}}{100 }$

⟹ Selling price = $15\times \frac{500}{3}$

⟹ Selling price = ₹ 2500

So, ₹ 2500 will be selling price of the power banks so that the manufacturer can earn a profit of 50%.

Hence, the correct answer is option 1).

Given:

 u = -30 cm ( (since the object is real and placed on the opposite side)

 v =  -10 cm (since the image is virtual and on the same side as the object).

 Image formed: Virtual and Erect

Formula Used:

$Magnification(m) = {v \over u}={height: of :image \over height: of: object}$

Calculation: 

 $m = {v \over u}={10\over 30}$

 $m ={1\over 3}$

Hence, the correct answer is "1/3".

Shortcut Trick

Exterior angle = 180° − Interior angle

Exterior angle = 180° − 120° = 60°

Number of sides (n) = 360° ÷ Exterior angle

n = 360° ÷ 60° = 6

∴ The correct answer is 6 sides.

Alternate Method

Given:

Measure of each interior angle = 120°

Formula Used:

Interior angle of a regular polygon = [(n − 2) × 180°] ÷ n

Calculations:

⇒ 120° = [(n − 2) × 180°] ÷ n

⇒ 120n = 180n − 360

⇒ 180n − 120n = 360

⇒ 60n = 360

⇒ n = 360 ÷ 60

Follow BODMAS rule to solve this question, as per the order given below,

Given Expression:

24 × 6 - 12 + 18 ÷ 3 = 46

Let's check each option:

option 1) × and +​

L.H.S

24 + 6 - 12  × 18 ÷ 3 

= 24 + 6 - 12 × 6

= 24 + 6 - 72

= 30 - 72

= - 42 ≠  R.H.S

option 2) + and -

L.H.S

24 × 6 + 12 - 18 ÷ 3

= 24 × 6 + 12 - 6

= 144 + 12 - 6

= 156 - 6

= 150 ≠ R.H.S

option 3) × and ÷ 

L.H.S

24 ÷ 6 - 12 + 18 × 3

= 4 - 12 + 18 × 3

= - 12 + 4 + 54

= - 12 + 58

= 46 = R.H.S

option 4) + and ÷ 

L.H.S

24 × 6 - 12 ÷ 18 + 3 

= 24 × 6 - 0.666 + 3

= 144 - 0.666 + 3

= 146.334 ≠ R.H.S

Thus '× and ÷' these two signs that should be interchanged to make the given equation correct.

Hence, the correct answer is option 3).

From the given information draw the following diagram,

Four houses, A, B, C, and D, are located in the same colony and are as follows,

• House A is 300 m to the north of House D.

• House A is 300 m to the south of House B.

    

• House C is 400 m to the east of House B.

Thus, from the above diagram House D is in the south direction with reference to House B**.**

Hence, the correct answer is option 3).

Shortcut Trick

Gain % of A = (576 − 384) ÷ 384 × 100 = 192 ÷ 384 × 100 = 50%.

Gain % of B = (1672 − 1254) ÷ 1254 × 100 = 418 ÷ 1254 × 100 = 33.33% or (100/3)%.

Ratio = 50 ÷ (100/3) = (50 × 3) ÷ 100 = 150 ÷ 100 = 3/2.

∴ The correct answer is 3/2.

Alternate Method

Given: Cost Price (CP_A) = Rs. 384, Selling Price (SP_A) = Rs. 576. Cost Price (CP_B) = Rs. 1,254, Selling Price (SP_B) = Rs. 1,672.

Formulas: Profit = SP − CP | Profit % = (Profit ÷ CP) × 100.

⇒ Gain of A = 576 − 384 = 192.

⇒ Gain % of A = (192 ÷ 384) × 100 = 50%.

⇒ Gain of B = 1672 − 1254 = 418.

⇒ Gain % of B = (418 ÷ 1254) × 100 = (1/3) × 100 = 100/3 %.

⇒ Ratio = 50 : (100/3) = 150 : 100 = 3 : 2.

∴ The correct answer is 3/2.

Additional Information

Profit and Loss Percentage

Profit % is always calculated on the Cost Price (CP) unless otherwise stated in the question. Formula: [(SP − CP) ÷ CP] × 100.

Ratio of Percentages

When comparing two percentages, ensure they are in the same form (either both as fractions or both as whole numbers) to find the simplest integer ratio.

Shortcut Trick

If a sum becomes n times in t years, it becomes n^k times in k × t years.

Here, the sum doubles (2 times) in 10 years.

Target is 16 times. Since 16 = 2⁴, we have k = 4.

Required time = k × t ⇒ 4 × 10 = 40 years.

∴ The correct answer is 40 years.

Alternate Method

Given: A sum of money becomes 2 times in 10 years at Compound Interest.

Formula Used: A = P(1 + r/100)ⁿ

⇒ Case 1: 2P = P(1 + r/100)¹⁰

⇒ 2 = (1 + r/100)¹⁰ → (Eq. 1)

⇒ Case 2: 16P = P(1 + r/100)^T

⇒ 16 = (1 + r/100)^T

⇒ 2⁴ = (1 + r/100)^T

⇒ [(1 + r/100)¹⁰]⁴ = (1 + r/100)^T [Substituting from Eq. 1]

⇒ (1 + r/100)⁴⁰ = (1 + r/100)^T

⇒ T = 40 years

∴ The correct answer is 40 years.

Additional Information

Compound Interest Concept

In CI, the amount grows geometrically. If it becomes n times in t years, it will become n² in 2t, n³ in 3t, and so on.

Difference between CI and SI

For 2 years, the difference D = P × (r/100)². For 3 years, D = P × (r/100)² × (3 + r/100).

Rule of 72

A thumb rule to find the time to double the money: Time ≈ 72 ÷ Rate of Interest.

The correct answer is 'Chenab'.

Key Points

• At an elevation of roughly 6387 meters above mean sea level in the district of Uttarkashi, the river Yamuna, a significant tributary of the river Ganges, rises from the Yamunotri glacier close to the Banderpoonch peaks (380 59' N 780 27' E) in the Mussoorie range of the lower Himalayas (Uttaranchal).
• The Himachal Pradesh and Jammu and Kashmir portions of two Indian States are included in the Chenab basin's watershed. In the Himachal Pradesh district of Chamba, the Upper Chenab catchment is located in the Lahoul area and Pangi Tehsil.
• Therefore, Chenab is not a tributary of the Yamuna River system.

Additional Information

• A Tributary is a little river that empties into a bigger river.
• Tons, Chambal, Hindon, Betwa, and Ken are some of the Yamuna River's significant tributaries. The Giri, Sind, Uttangan, Senger, and Rind are additional minor Yamuna River tributaries.
• Hindon:
• In India, the Upper Sivaliks of the Shakumbhari devi range are where the Hindon River, a tributary of the Yamuna River, rises in the Saharanpur district of Uttar Pradesh.
• For the rural residents of western Uttar Pradesh, India, it provides a significant supply of freshwater.
• The river receives all of its water from rain, and its catchment area is about 7,083 square kilometers (2,735 sq mi).
• Sind:
• A tributary of the Yamuna River, the Sind River traverses the Indian states of Madhya Pradesh and Uttar Pradesh.
• The Sind runs north-northeast before joining the Yamuna River where it begins on the Malwa plateau in Vidisha, M.P.
• It has a drainage area of 27,856 km² and a total stream network length of 470 kilometers.
• Chambal:
• In Central and Northern India, the Chambal River is a tributary of the Yamuna River and is thus a member of the Ganges drainage system.
• The river goes through the state of Madhya Pradesh, then turns southeast to join the Yamuna in the state of Uttar Pradesh after briefly passing through Rajasthan and creating the border between the two states.
• It is 1,024 kilometers (636 mi) long.

Shortcut Trick

Ratio of Speeds = 50 : 60 = 5 : 6

Since Distance is constant, Ratio of Time = 6 : 5

Difference in time units = 6 − 5 = 1 unit → Actual difference = 10 min − 5 min = 5 min

Time taken at 50 km/h = 6 × 5 = 30 min. Since it is 10 min late, Usual Time = 30 − 10 = 20 min

∴ The correct answer is 20 min.

Alternate Method

Given: S₁ = 50 km/h, S₂ = 60 km/h, Delay₁ = 10 min, Delay₂ = 5 min

Formula Used: Distance = [ (S₁ × S₂) / (S₂ − S₁) ] × Difference in Time

⇒ Time difference = 10 − 5 = 5 min = 5/60 hours

⇒ Distance = [ (50 × 60) / (60 − 50) ] × (5/60)

⇒ Distance = [ 3000 / 10 ] × (5/60) = 300 × (5/60) = 25 km

⇒ Time taken at 50 km/h = Distance / Speed = 25 / 50 = 0.5 hours

⇒ Time in minutes = 0.5 × 60 = 30 min

⇒ On-time journey = 30 min − 10 min = 20 min

∴ The correct answer is 20 min.

Additional Information

Speed-Time Inversity

When distance is constant, speed is inversely proportional to time: S₁ / S₂ = T₂ / T₁.

Late-Early Concept

If both cases are 'Late' or both are 'Early', subtract the times. If one is 'Late' and one 'Early', add the times to find the total difference.

Average Speed

For the same distance covered at different speeds x and y, Average Speed = 2xy / (x + y).

Shortcut Trick

Use the direct relation between Marked Price (MP) and Cost Price (CP): MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

MP ÷ CP = (100 + 10) ÷ (100 − 30) = 110 ÷ 70 = 11 ÷ 7.

Required Percentage = (Difference ÷ CP) × 100 = (11 − 7) ÷ 7 × 100 = 400 ÷ 7.

400 ÷ 7 ≈ 57.14%.

∴ The correct answer is 57.14%.

Alternate Method

Given → Discount = 30%, Profit = 10%. Formulas: SP = MP × (100 − D%) ÷ 100 | SP = CP × (100 + P%) ÷ 100 | Markup% = (MP − CP) ÷ CP × 100.

⇒ Let Marked Price (MP) = 100. ⇒ Selling Price (SP) = 100 − 30% of 100 = 70. ⇒ Since Profit = 10%, SP = CP × 1.10 ⇒ 70 = CP × 1.10. ⇒ Cost Price (CP) = 70 ÷ 1.10 = 700 ÷ 11 ≈ 63.636. ⇒ Markup Amount = MP − CP = 100 − 63.636 = 36.364. ⇒ Markup Percentage = (36.364 ÷ 63.636) × 100 = 57.14%.

∴ The correct answer is 57.14%.

Additional Information

Relation between MP and CP

The ratio of MP to CP is determined by the formula: MP/CP = (100 + G%)/(100 - D%). This is derived by equating the SP from both profit and discount perspectives.

Markup Percentage

Markup% = (Markup ÷ Cost Price) × 100. It represents how much more the price is labeled above the original cost.

The correct answer is '1950'.

Key Points

• Mother Teresa, also recognized in the Catholic Church as Saint Teresa of Calcutta, founded the Missionaries of Charity.
• On october 7,1950 mother Teresa established The Missionaries of Charity.

Additional Information

• All around the world, including the former Soviet Union and Eastern European nations, the Society of Missionaries has spread. They assist the poorest of the poor in several nations in Asia, Africa, and Latin America.
• Mother Teresa got approval from the Holy See on October 7, 1950, to create her own order, "The Missionaries of Charity," whose main goal was to love and care for those that no one else was willing to take care of.

The correct answer is the Government.

Key Points

• Fiscal policy is the term used to describe how the government uses taxation and expenditure to affect the state of the economy.
• Fiscal policy is often used by governments to encourage robust, long-term growth and to lower poverty.
• Fiscal policy typically enters the picture when conditions are deteriorating swiftly enough to call for government involvement, such as during a recession or an inflationary era.
• Purpose:
• Fiscal policy aims to encourage healthy and stable economic growth while putting in place artificial safeguards against a financial meltdown.
• There are two types of fiscal policies: expansionary and contractionary.
• ​Expansionary: The government's response to a recession by decreasing taxes and expanding government expenditure is known as expansionary policy, which is the more typical of the two.
• Contractionary: When there is inflation, contractionary policies are used. During this time, the government may cut back on funding for public projects, public sector employee numbers, or even wages.

Additional Information

• The importance of fiscal policy as a tool for policymaking has fluctuated historically.
• Before 1930, a minimal government or laissez-faire philosophy was the norm.
• A good case study in fiscal policy is the global financial crisis, which can be traced back to the collapse of the US mortgage market in 2007.
• It depends on the fiscal space a government has available for new spending program or tax cuts, that is, its access to additional money at an affordable cost or its capacity to rearrange its present expenditures.

The correct answer is "electromagnetic induction".

Key Points

• Dynamo is an electrical generator which transforms mechanical rotation into a pulsating direct current using rotating coils of wire and magnetic fields.
• This is accomplished through Faraday's laws of induction.
• The fundamental law of electromagnetism known as Faraday's law, aids in our ability to predict how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as **electromagnetic induction.**​

Additional Information

• Faraday's Law of electromagnetic induction consists of 2 laws:

1. When a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.
2. The induced emf in a coil is equal to the rate of change of flux linkage.

• Electromagnetic radiation: The waves of the electromagnetic field that are moving through space and carrying electromagnetic radiant energy are referred to as electromagnetic radiation (EMR). It comprises X-rays, gamma rays, ultraviolet, infrared, radio waves, and microwaves.
• Electromagnetism: It deals with the electromagnetic force that exists between electrically charged particles.
• Electric conduction: The passage of electrically charged particles via a transmission medium is known as electrical conduction.

The correct answer is "r₁ = r₂ = r₃ = r₄".

Key Points

• The two ends of a spherical mirror when joined form a complete circle.
• Thus, any point on the surface of the mirror joining the center of curvature will be the radius of that circle and we know that the length of all the radius in the same circle are equal.
• Therefore, r1 ^, r2 , r3 and r4  will be all of same lengths.

The correct answer is Movement of both water and food is bidirectional.

Key Points

• Bidirectional movement means the movement of two molecules in 2 opposite directions.
• A non-living tube called an xylem transports water and it runs through the stem from the roots to the leaves. It is unidirectional in nature.
• Because sucrose builds up in the phloem tissue and absorbs water, causing a high turgor pressure, phloem movement is bidirectional.
• Thus, the movement of water is unidirectional whereas the movement of food is bidirectional.

Additional Information

• Water movement is by simple physical force, which is diffusion, i.e., transport of substances from higher concentration to lower concentration.
• Whereas food transport is active transport which requires energy for transport.
• Water molecules travel from the soil into the root's living cells and eventually into the vessels and tracheids, which serve as the xylem's transport cells. These hollow, dead xylem cells enable quick water movement.
• Sieve tubes are living cells that are responsible for transporting carbohydrates throughout the plant.

The series is written as shown below:

So, by applying the logic we obtained that positions of 3 and 7 remain unchanged.

Hence, the correct answer is option 1).

The correct answer is Article 75 (3).

Key Points

• The Constitution's original text included 395 articles divided into 22 divisions and 8 schedules.
• Article 75 in the constitution states that The Council of Ministers shall be collectively responsible to the House of the People.
• Article 75(3) of the Indian Constitution, which covers the unique requirements of this principle, contains the concept of collective responsibility.
• According to Article 75(3), the council of ministers must be assembled and answerable to the Lok Sabha.
• According to the principle of collective responsibility, the Lok Sabha is accountable to the council of ministers for the general management of the government's operations.
• All decisions made by the cabinet are a collective effort of the council of ministers, which functions as a team.

​

Additional Information

• Article 75 (2):
• ​The Minister will be in office as long as the President so directs.
• Article 80 (4):
• According to Article 80(4), the elected members of the State Legislative Assembly will elect each State's delegates to the Council of States.
• This is in keeping with the proportional representation system that uses a single transferable vote.
• Article 75 (1):
• A Council of Ministers led by the Prime Minister will assist and advise the President, who will follow their recommendations when performing his duties.
• The president may request that the council of ministers reevaluate this advise, and the president must then act in accordance with the revised advice.

The correct answer is Alkene.

Key Points

• An unsaturated hydrocarbon is one which consists of a single, double, or triple bond between Carbon - Carbon atoms.
• The double-bonded hydrocarbons are known as Alkenes, which have the general formula CnH2n.
• For example: 
• Propene = C₃H2*3 = C3H6 = CH₃-HC=CH_2​

Additional Information

• The general formula for Alkyl is CnH2n+1.
• The general formula for Alkane is CnH2n+2.
• The general formula for Alkyne is CnH2n-2.

The correct answer is Regulating Act of 1773.

Key Points

• On May 1, 1707, the English and Scottish Parliaments passed the Acts of Union, which resulted in the formation of the United Kingdom of Great Britain. In October 1707, the UK Parliament convened for the first time.
• The East India Company Act of 1772, also known as the Regulating Act of 1773, was an Act of the British Parliament designed to reorganize the East India Company's administration of its rule in India. It represented the first step toward centralized administration in India and legislative oversight of the Company.
• Therefore, the answer is Regulating Act of 1773.

Additional Information

• Indian Councils Act of 1892:
• ​The British Parliament passed the Indian Councils Act of 1892, which expanded the size of India's legislative councils.
• The ability to inquire about the budget was also granted to the members.
• It marked the start of India's transition to a representative system of government.
• Pitt's India Act (1784):
• ​The dual system of authority by the British government and the East India Company was founded by Pitt's India Act (1784), named after British prime minister William Pitt the Younger.
• The Regulating Act of 1773 needed to be fixed, therefore the British Parliament passed the Pitt's India Act, 1784, also known as the East India Company Act, 1784.
• Government of India Act 1858:
• ​The East India Company's territory and authority were handed to the British Crown by the Government of India Act 1858, an act of the British parliament.
• The British East India Company, which up until this moment had been in charge of British India under the auspices of Parliament, was to be liquidated in accordance with its terms, and its duties were to be transferred to the British Crown.

The correct answer is Electric iron.

Key Points

• An electric motor is an electronic machine that converts an electric signal into mechanical signals.
• Electric motors produce force in the form of torque that is applied to the motor shaft through the interaction of the magnetic field of the motor and electric current in a wire winding.
• Electric iron works on the heating effect of electric current and not an electric motor.

Additional Information

• Electric fans, Electric mixers, and Electric washing machines use an electric motor to convert electric energy to mechanical energy such as rotation of fan blades, churning property of mixer blades, and washing of clothes respectively.

Shortcut Trick

Ratio of A : B : C : D = 4 : 7 : 9 : 3

Difference between C and D in units = 9 − 3 = 6 units

Given: 6 units = ₹720

⇒ 1 unit = 720 ÷ 6 = ₹120

D's share = 3 units = 3 × 120 = ₹360

∴ The correct answer is ₹360.

Alternate Method

Given:

Ratio A : B : C : D = 4 : 7 : 9 : 3

Let the shares be 4x, 7x, 9x, and 3x respectively.

Calculations:

⇒ Difference between C and D = 9x − 3x = 6x

⇒ 6x = 720

⇒ x = 720 ÷ 6

⇒ x = 120

⇒ D's share = 3x = 3 × 120

⇒ D's share = 360

∴ The correct answer is ₹360.

Additional Information

Ratio and Proportion Basics

If a total amount T is divided in the ratio a : b : c, then the share of the first part is (a / (a+b+c)) × T.

Difference and Ratio

If the difference between two parts in a ratio is given, find the difference in terms of ratio units and equate it to the actual value.

The correct answer is only solvent molecules but not solute molecules.

Key Points

• Selectively permeable membranes such as cell membranes allow only the passage of a few ions or solvent molecules.
• This is because selectively permeable membranes protect the cell from the outside environment. It maintains the internal environment by allowing only selective ions to go inside and by removing toxic substances from time to time.
• Selectively permeable membranes act as filters that allow only solvent molecules to pass through.
• Solute molecules can pass through it only by taking some help.
• Thus, only solvent molecules but not solute molecules can pass through the selectively permeable membranes.

The logic followed here is:

(First number × Second number) + 4 = Third number

Applying logic to the given series:

(4, 3, 16)

(4 × 3) + 4

= 16

And, 

(3,5,19)

(3 × 5) + 4

= 19

Similarly,

(8,2,20)

(8 × 2) + 4

= 20

Hence, the correct answer is option 4).

Draw the diagram according to the given information.

• Starting point is L.
• 125 m towards the south.
• Then, left turn and walk 70 m.
• Again left turn and walks 80 m.
• Again left turn and walks 115m.
• Finally, take the right turn and walk 45 m.
• Final point is M.

Thus, the person is 45 m towards the west from the starting point.

Hence, the correct answer is option 1).

Shortcut Trick

Common middle number = HCF of 357 and 609.

609 − 357 = 252. Factors of 252 are checked against 357.

Middle number = 21.

Numbers: 357/21 = 17, Middle = 21, 609/21 = 29.

Sum = 17 + 21 + 29 = 67.

∴ The correct answer is 67.

Alternate Method

Given: Three co-prime numbers x, y, and z.

Product of first two: x × y = 357

Product of last two: y × z = 609

⇒ Since x, y, z are co-prime, the common factor y must be the HCF.

⇒ HCF(357, 609): 609 = 357 × 1 + 252

⇒ 357 = 252 × 1 + 105

⇒ 252 = 105 × 2 + 42

⇒ 105 = 42 × 2 + 21

⇒ 42 = 21 × 2 + 0. ∴ y = 21.

⇒ x = 357 ÷ 21 = 17.

⇒ z = 609 ÷ 21 = 29.

⇒ Sum = 17 + 21 + 29 = 67.

∴ The correct answer is 67.

Additional Information

Co-prime Numbers

A set of numbers where the only common factor is 1; i.e., HCF(a, b) = 1.

HCF of Products

If three numbers a, b, c are co-prime, then HCF(ab, bc) = b.

Prime Factorization

357 = 3 × 7 × 17 and 609 = 3 × 7 × 29. Common factors are 3 × 7 = 21.

Given: 

${2(5х - 3) + 3(3x - 5) = 93}$

Calculation:

⇒ ${10x-6 + 9x -15 = 93}$

⇒ ${19x-21 =93}$

⇒ ${19x = 93+21 = 114 }$

⇒  $x= {114 \over 19 } = 6$

∴ The required number is '6'.

Hence, the correct answer is option 1).

Given:

Statements:

All sketches are cards.

All cards are posters.

Some sketches are folders

The possible Venn diagram is shown below:

Conclusions:

 I. Some folders are posters. → True (As sketches are the subset of posters and Some sketches are folders. So some folders are posters.)

 II. Some cards are folders. → True (As sketches are the subset of cards and Some sketches are folders. So some cards are folders.)

Thus, both conclusions I and II follow.

Hence, the correct answer is option 1).

The logic followed here is:

Next term = (Previous term × 2) + Consecutive natural number

Hence, "473" will replace the question mark (?) in the given series**.**

Shortcut Trick

The age difference between two people remains constant throughout their lives.

In 2000, Monu : Sister = 3 : 1 (Difference = 2 units).

Given age difference = 24 years, so 2 units = 24 → 1 unit = 12 years.

In 2000, Monu age = 3 × 12 = 36 years.

In 2010 (10 years later), Monu age = 36 + 10 = 46 years.

∴ The correct answer is 46 years.

Alternate Method

Given: Ratio in 2000 is 3:1. Age difference in 2010 is 24 years.

Formula Used: Age = (Ratio × Unit Value) + Years passed.

⇒ Let Sister age in 2000 = x

⇒ Monu age in 2000 = 3x

⇒ Difference (3x − x) = 24

⇒ 2x = 24 ⇒ x = 12

⇒ Monu age in 2000 = 3 × 12 = 36 years

⇒ Monu age in 2010 = 36 + 10 = 46 years

∴ The correct answer is 46 years.

Additional Information

Constant Difference Property

The difference between the ages of two persons remains the same at any point in time (past, present, or future).

Ratio Balancing

If ratios at two different times are given, multiply the ratios such that the difference between the parts remains equal to the actual year gap.

Age After 'n' Years

If the present age is A, then age after n years = A + n, and age n years ago = A − n.

The correct answer is '1000'.

Key Points

• The International Cricket Council organizes international cricket matches between teams representing different countries (ICC). Test matches, One-Day matches, and Twenty20 matches are the three main formats.
• The Indian cricket team became the first squad in history to play 1,000 One-Day Internationals on February 6.
• Two ODI World Cups and one T20 World Cup have been won by the side. India has won 519 games out of the 1000 ODIs they have played thus

Additional Information

• India played its 1000th One-Day International on Sunday, becoming the first team to do so. The team accomplished the milestone when playing the West Indies in the current first ODI at the Narendra Modi Stadium.
• Cricket is an outdoor sport in which two teams compete. By hitting a ball with a wooden bat, players attempt to score points, known as runs.

Shortcut Trick

For odd consecutive integers, the Average is always the Middle Term.

Middle term (7^th term) = 36.

Smallest term (1^st term) = 36 − 6 = 30.

Largest term (13^th term) = 36 + 6 = 42.

Required Sum = (2 × 30) + 42 = 60 + 42 = 102.

∴ The correct answer is 102.

Alternate Method

Given: Average of 13 consecutive integers = 36.

Formula: Average of n consecutive terms = (First term + Last term) ÷ 2.

⇒ Let the integers be x, x+1, x+2, ..., x+12.

⇒ Sum = [x + (x+12)] × 13 ÷ 2 = 36 × 13.

⇒ (2x + 12) ÷ 2 = 36.

⇒ x + 6 = 36 ⇒ Smallest integer (x) = 30.

⇒ Largest integer (x+12) = 30 + 12 = 42.

⇒ Required Sum = (2 × Smallest) + Largest.

⇒ Required Sum = (2 × 30) + 42 = 60 + 42 = 102.

∴ The correct answer is 102.

Additional Information

Consecutive Integers Property

For any arithmetic progression (AP), Average = (First Term + Last Term) ÷ 2 = Middle Term (if n is odd).

Number of Terms

If there are n consecutive integers, the difference between the largest and smallest is (n − 1).

Average of Even/Odd Consecutive Numbers

For consecutive even or odd numbers, the gap between each term is 2, and the average is still the middle value.

The Venn Diagram is given below: 

Thus, the shaded portion indicates that Indian industrialists make autos but are NOT steel producers.

Hence, the correct answer is option 4).

The correct answer is '1975'.

Key Points

• There are several social sector schemes and programs included in the Twenty Point Program (TPP)-2006.
• It consists of 20 points and 66 items, which are managed by different Ministries of the Indian Government and put into practice by State and UT Governments.
• It was launched by the government of India in 1975.

Additional Information

• There are 740 central sector (CS) programs in the Indian Union Budget for 2022 and 65 (+7+) government-sponsored programs (CSSs).
• The union government sought to reform, renovate, and rationalize these by the following year from 131 CSSs in February 2021.
• The Pradhan Mantri Jan-Dhan Yojana, Stand Up India Scheme, Pradhan Mantri Jeevan Jyoti Bima Yojana, and many more social welfare programs are managed by the Indian government.

Given:

Resistance of 2 resistors = 4 Ω

Voltage of battery = 5 V

Concept / Formula used:

Ohm's Law, $I= {V\over R}$

Effective resistance in parallel connection, ${1 \over R} = {1 \over R1} +{1 \over R2}$

Calculation:

Effective Resistance: 

${1 \over R} = {1 \over R1} +{1 \over R2}$

${1 \over R} = {1 \over 4} +{1 \over 4}={1 \over 2}$

$R=2: Ω$

Total current in the circuit:

$I= {V\over R}$

$I= {5\over 2}=2.5 :Amperes$

Hence, the total current in the circuit is "2.5 A".

Given: C _ P R _ D T _ R N _ T _ R N _ T P _ N

Let's check each option:

1) T N P E P F R → C T P R N D T P R N E T P R N F T P R N

2) T P N D P F R → C T P R P D T N R N D T P R N F T P R N

3) T N T E P F P  → C T P R N D T T R N E T P R N F T P P N

4) P N P E R F P → C P P R N D T P R N E T R R N F T P P N

So, by putting option 1) in the series "C/D/E/F-TPRN" is repeating itself.

Hence, the correct answer is "T N P E P F R".

The correct answer is Discharge of untreated sewage into the river

Key Points

• The main cause of contamination of the Ganges with coliform bacteria is the discharge of untreated sewage into the river.
• Coliform bacteria are a group of microorganisms commonly found in the environment, including in human and animal waste.
• The presence of coliform bacteria in the Ganges indicates that the water has been contaminated by fecal matter, which is harmful to human health.
• Untreated sewage contains a high load of pathogens, organic matter, and nutrients that contribute to the proliferation of coliform bacteria in the river.
• Efforts to clean the Ganges must focus on improving sewage treatment infrastructure and preventing the direct discharge of sewage into the river.

Additional Information

• The Ganges is one of the most important rivers in India, both culturally and economically, providing water to millions of people.
• Pollution in the Ganges also affects aquatic life and the overall ecosystem of the river.
• Various initiatives, such as the Namami Gange Programme, have been launched by the Indian government to address pollution and rejuvenate the river.
• Public awareness and participation are crucial in ensuring the success of these initiatives and in maintaining the cleanliness of the Ganges.
• Proper waste management practices and the development of adequate sanitation facilities are essential to prevent further contamination of the river.

Given:

• The vowels are changed with the following letters.
• The consonants are changed with the preceding letters.

According to the given information,

Arranging the obtained random sequence of the alphabet into alphabetic order, we get,

Alphabetic Order → CFPQRSX.

Here, P is fifth from the right side.

Hence, the correct answer is option 1).

The correct answer is Eggs are not released and no fertilization.

Key Points

• In the US, the birth control pill is the method of birth control that is most frequently prescribed.
• About 25% of women between the ages of 15 and 44 who use contraception said they prefer the pill.
• The primary mode of action is ovulation prevention, they impede follicular growth and stop ovulation.
• The oral pills stop pregnancy by preventing the release of eggs and which result in no fertilization.

Additional Information

• The pills can be either monophasic (the active tablets contain the same amount of both components) or multiphasic (varying doses weekly of both or either component in the active pills).
• The majority of OCP adverse effects are minor and go away with sustained use or switching to a different tablet formulation. Breakthrough bleeding is the most frequent side effect of combination oral contraceptives.

The correct answer is NO3 and Cl.

Key Points

• When a portion of two ionic compounds is swapped, a double displacement reaction takes place, creating two new components.
• In the given reaction the ions with Ag and Na will displace each other and as before reaction Cl is with Na so after reaction it will be with Ag.
• After reaction NO3 is with Na so before reacting, it should be with Ag.
• Final equation: AgNO3 + NaCl → AgCl + NaNO3.
• Therefore, p and q are '**NO3'**and 'Cl' respectively.

Additional Information

• The formula for the double displacement reaction is AB + CD →  AD + CB.
• A and C are positively charged cations in this process, whereas B and D are negatively charged anions.

The correct answer is Water and salts.

Key Points

• Two bean-shaped organs, the kidneys are each roughly the size of a fist. One is on either side of your spine, directly below the rib cage.
• Every minute, healthy kidneys filter about half a cup of blood, eliminating wastes and surplus water to create urine.
• Therefore, every time the regulation of water and salts carries on by kidney.

Additional Information

• Your kidneys control the amount of salt, water, and other electrolytes in your body.
• The idea is to maintain a balance between the amount of water you drink and the amount you defecate. The kidneys increase urine production to restore equilibrium if your body contains too much water.

Shortcut Trick

A Rhombus is a special type of parallelogram. A fundamental property of all parallelograms is that adjacent angles are supplementary, meaning their sum is exactly 180°. Therefore, any statement claiming the sum is not 180° is mathematically incorrect.

∴ The correct answer is Sum of any pair of adjacent angles of a rhombus is not 180°.

Alternate Method

Given: Properties of a Rhombus.

Formula Used: Angle Sum Property of parallel lines and Rhombus Definitions.

Evaluating each statement based on Geometric Properties:

⇒ Statement 1: In a rhombus, opposite sides are parallel. Adjacent angles are consecutive interior angles. ∴ ∠A + ∠B = 180°. The statement "is not 180°" is False.

⇒ Statement 2: A Square is defined as a quadrilateral with four equal sides and four right angles. Since it has four equal sides, it satisfies the definition of a Rhombus. (True)

⇒ Statement 3: A key property of a rhombus is that its diagonals bisect each other at right angles (90°). (True)

⇒ Statement 4: By definition, a Rhombus is an equilateral quadrilateral, meaning all four sides are congruent. (True)

∴ The correct answer is Sum of any pair of adjacent angles of a rhombus is not 180°.

Additional Information

Area of a Rhombus

The area can be calculated using the lengths of its diagonals: Area = ½ × d₁ × d₂.

Symmetry of a Rhombus

A rhombus has two lines of reflective symmetry, which are its diagonals, and rotational symmetry of order 2.

Relationship with Parallelograms

Every rhombus is a parallelogram, but not every parallelogram is a rhombus (only those with equal sides are).

The correct answer is 'self-employed workers.

Key Points

• Self-employed: Workers who own and operate an enterprise to earn their livelihood are known as self-employed.
• About 52 percent workforce in India belongs to this category.
• A person owning a cement shop is an example of self-employment.

Additional Information

• Regular salaried employed workers:
• When a worker is engaged by someone or an enterprise and paid his or her wages on a regular basis, they are known as a regular salaried employee.
• An example of a regular salaried worker is a civil engineer working in a construction company.
• Hired worker:
• A person casually engaged in others farm or non-farm enterprises (both household and non-household) and getting in return wage according to the terms of the daily or periodic work contract is a hired worker.
• An example of a casual worker is a construction worker.
• They account for 30 percent of India’s workforce.
• Government-employed workers: 
• Any employee of the State, a county, city, town, village, or any other political subdivision or civil division of the State, or a county, city, town, or village is a government-employed worker.
• A civil servant is a government-employed worker.

The correct answer is 'Dr. Jitendra Singh'. 

Key Points

• CSIR Jigyasa programme:-
• Science and Technology Minister, Jitendra Singh has launched India’s first Virtual Science Lab for Children under CSIR (Council of Scientific and Industrial Research) Jigyasa Programme.
• These labs will connect students with scientists across the country.
• To provide quality research exposure and innovative pedagogy for school students based on an online interactive medium.

The correct answer is 'Nichrome' .

Key Points

• Nichrome:-
• It is used for making the heating element of an electric iron.
• It has relatively high resistance and a high melting point.
• Nichrome is made of 80% nickel, 20% chromium.
• Tungsten also has a high melting point and is used as the electrodes, heating elements and as filaments in light bulbs.

The correct answer is " NaOH ".

 

Key Points

• Sodium hydroxide is the alkali used in the chlor-alkali process.
• In the process of making chlorine, sodium hydroxide is created as a byproduct.
• The crystalline solid sodium hydroxide is white and transparent.
• In the chlor-alkali process, sodium chloride in an aqueous solution is exposed to electricity, which breaks down to generate sodium hydroxide.

Additional Information

• In the chlor-alkali process, electricity is sent through the sodium chloride aqueous solution, where it breaks down to generate sodium hydroxide.
• Brine is the aqueous solution of sodium chloride.

The correct answer is '15^th'.

Key Points

• Mr. N.K. Singh is a prominent Indian economist, academician, and policymaker.
• He is currently Chairman of the 15th Finance Commission, a body established under the Indian Constitution to oversee revenue sharing and other federal fiscal policy matters.
• Prior to this position, he presided as Chairman of the Fiscal Responsibility and Budget Management Review Committee (FRBM), responsible for setting targets for the government to reduce fiscal deficits.
• He also served as a member of the Upper House of the Parliament, the Rajya Sabha, from 2008 to 2014.

Additional Information Finance Commission:

• The President shall, within two years from the commencement of this Constitution and thereafter at the expiration of every fifth year or at such earlier time as the President considers necessary, by order constitute a Finance Commission which shall consist of a Chairman and four other members to be appointed by the President. (Article 280)
• Parliament may by law determine the qualifications which shall be requisite for appointment as members of the Commission and the manner in which they shall be selected.
• It shall be the duty of the Commission to make recommendations to the President as to —
• the distribution between the Union and the States of the net proceeds of taxes which are to be, or may be, divided between them under this Chapter and the allocation between the States of the respective shares of such proceeds;
• the principles which should govern the grants in-aid of the revenues of the States out of the Consolidated Fund of India;
• the measures needed to augment the Consolidated Fund of a State to supplement the resources of the Panchayats in the State on the basis of the recommendations made by the Finance Commission of the State;
• the measures needed to augment the Consolidated Fund of a State to supplement the resources of the Municipalities in the State on the basis of the recommendations made by the Finance Commission of the State;
• any other matter referred to the Commission by the President in the interests of sound finance.
• The Commission shall determine their procedure and shall have such powers in the performance of their functions as Parliament may by law confer on them.

The series can be written as:

There are 4 such pairs where a letter is immediately preceded by a symbol and also immediately followed by a number.

Hence, the correct answer is option 2).

According to the question, the ranking diagram is shown below:

Position of  Q from top = 9th

Position of P from bottom = 9th

Students between P and Q = Total students - (position of Q from top + position of P from bottom).

= 21 - (9 + 9)

= 21 - 18

= 3

Hence**,** the correct answer is option 1).

The correct answer is 'Himalayan mountains'.

Key Points

• The Himalayan Mountains
• The Himalayas are the young fold mountains.
• They run from the west-east direction from Indus to Brahmaputra covering a distance of 2500 KM.
• Their width varies from 400 in the west and 150 KM in the East.
• The Himalayas may be divided into three parallel ranges:

1. Greater Himalayas or Himadari
2. Lesser Himalayas or Himachal
3. Outer Himalayas or Siwaliks.

Additional Information

• Northern plains 
• It is located south of the Himalayas and north of the Peninsular plateau.
• formed by the deposition of the sediments brought by three main river systems namely: the Indus, the Ganga, and the Brahmaputra.
• It mainly includes the states of Punjab, Haryana, Uttar Pradesh, Bihar, West Bengal, and Assam.
• plain is one of the largest and most fertile plains in the world.
• The peninsular plateau
• is a triangular-shaped tableland.
• It is part of an ancient land mass called the Gondwana level.
• It covers an area of nearly 5 lacks sq. km.
• It is spread over the states of Gujarat, Maharashtra, Bihar, Karnataka, and Andhra Pradesh.
• River Narmada divides the peninsular plateau into two parts: (i) The central highlands and (ii) (ii)Deccan Plateau
• Coastal plains
• The coastal plains in India run parallel to the Arabian Sea & Bay of Bengal along the Peninsular Plateau. -
• The western coastal plain is a narrow belt along the Arabian sea of about 10-20km wide. It stretches from Rann of Kachchh to Kanya Kumari. Western coastal plains comprise three sectors
• Konkan Coast (Mumbai to Goa),
• Karnataka coast from Goa to Mangalore
• Malabar Coast (Mangalore to KanyaKumari).
• The eastern coast runs along the Bay of Bengal. It is wider than the western coastal plain. Its average width is about 120 km.
• The northern part of the coast is called Northern Circar and the southern part is called Coromandel Coast.
• The eastern coastal plain is marked by Deltas made by the rivers Mahanadi, Godavari, Krishna and Kaveri.
• The Chilka largest saltwater lake in India in Odisha is located to the south of Mahanadi Delta.

The alphabet series and its position value is shown below:

The logic followed here is 

TOP ∶ VRU

 

And,

XOR ∶ ZRW

Similarly,

NOR ∶ PRW 

Thus, the pair "NOR ∶ PRW " is following the above logic.

Hence, the correct answer is option 1).

Shortcut Trick

Put a specific value for angle A, let A = 90°.

⇒ sin 90° = 1 and cos 90° = 0.

⇒ Expression = (1 ÷ (1 + 0)) + ((1 + 0) ÷ 1) = 1 + 1 = 2.

Check options for A = 90°: (1) 2 cosec 90° = 2 × 1 = 2. This matches.

∴ The correct answer is 2 cosec A.

Alternate Method

Given: The expression is sin A / (1 + cos A) + (1 + cos A) / sin A.

Formula Used: sin²A + cos²A = 1 and cosec A = 1/sin A.

⇒ Taking LCM of the denominators: sin A (1 + cos A).

⇒ [sin²A + (1 + cos A)²] ÷ [sin A (1 + cos A)]

⇒ [sin²A + 1 + cos²A + 2 cos A] ÷ [sin A (1 + cos A)]

⇒ [(sin²A + cos²A) + 1 + 2 cos A] ÷ [sin A (1 + cos A)]

⇒ [1 + 1 + 2 cos A] ÷ [sin A (1 + cos A)]

⇒ [2 + 2 cos A] ÷ [sin A (1 + cos A)]

⇒ 2(1 + cos A) ÷ [sin A (1 + cos A)]

⇒ 2 ÷ sin A

⇒ 2 cosec A

∴ The correct answer is 2 cosec A.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

Standard reciprocal relations are cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ.

Value Substitution Method

For simplifying trigonometric expressions, substituting standard angles (30°, 45°, 60°, 90°) is the fastest way to verify options.

Given:

Seven boxes: V, W, X, Y, Z, A, and B are kept one over the other.

But not necessarily in the same order as given.

Boxes are placed as follows,

• A is kept above W.

• Four boxes are kept between B and W.

• One box is between V and X.

• X is kept above A.

• B is kept at topmost position.

• Final position of the boxes is shown below.

Thus, there are three boxes kept between Z and Y.

Hence, the correct answer is option 3).

Statement: There are many cracks in the external walls of the building that need to be treated before the wall painting can begin, to prevent seepage issues that may creep in later.

<br>

Assumption 1: Painting the external walls may lead to seepage issues. The statement explicitly not given that painting leads to any seepage issue. Thus assumption 1 is False.

<br>

Assumption 2: Cracks in the external walls could cause seepage issues. The statement explicitly mentions that there are many cracks in the external wall that may lead to seepage issues. Thus assumption 2 is True.

<br>

Therefore, the correct answer is Only assumption II is implicit.

Shortcut Trick

Radius r = Diameter ÷ 2 = 12 ÷ 2 = 6 cm.

Volume = (4/3) × π × r³

Volume = (4/3) × π × 6 × 6 × 6 = 4 × π × 2 × 6 × 6 = 288π cm³.

∴ The correct answer is 288π cm³.

Alternate Method

Given:

Diameter (d) = 12 cm

Formula Used:

Radius (r) = d/2

Volume of Sphere (V) = (4/3)πr³

Calculations:

⇒ Radius (r) = 12 / 2 = 6 cm

⇒ Volume = (4/3) × π × (6)³

⇒ Volume = (4/3) × π × 216

⇒ Volume = 4 × π × 72

⇒ Volume = 288π cm³

∴ The correct answer is 288π cm³.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is given by the formula 4πr².

Volume of Hemisphere

The volume of a hemisphere is exactly half the volume of a sphere: (2/3)πr³.

Relation to Cylinder

The volume of a sphere is 2/3 the volume of a circumscribed cylinder (height = 2r, radius = r).

The place value of the alphabet series:

The logic followed here is:

All the alphabets are coded by their position value.

TOUGH is written as 20152178 

And,

PLEAD is written as 1612514

Similarly,

CLOVE will be written as 31215225

Hence, the correct answer is option 3).

The correct answer is "refraction of light".

Key Points

• Refraction of light is a phenomenon in which light when it moves from one medium to another then its direction of propagation changes, its wavelength and speed may also change but the frequency remains the same.
• Light rays travel from water to air, which is from a denser medium to a rarer media, while the lemon is preserved inside the glass.
• The lemon seems larger to the spectator as they deviate away from the normal due to the refraction effect.

Additional Information

• Scattering of Light is the phenomena of bouncing off of electromagnetic radiation by the atoms or molecules of the medium through which they are travelling.
• Dispersion of light is the splitting of white light into its constituent colors because of the refractive index of the surface and the wavelength of the light.
• Reflection of light is observed when a light ray strikes a perfectly smooth, polished surface and reflects back.

Shortcut Trick

Check the difference between the closest numbers: 117 − 78 = 39.

The HCF must be a factor of 39 (Factors: 1, 3, 13, 39).

Check the options: 45 is not divisible by 9 (no, 78 is not), 7, or 5.

All numbers 45, 78, and 117 are divisible by 3.

∴ The correct answer is 3.

Alternate Method

Given: Numbers are 45, 78, and 117.

Method: Prime Factorization Method.

⇒ 45 = 3 × 3 × 5 = 3² × 5

⇒ 78 = 2 × 3 × 13

⇒ 117 = 3 × 3 × 13 = 3² × 13

⇒ Common Factor in all three prime factorizations is 3.

⇒ HCF = 3¹ = 3.

∴ The correct answer is 3.

Additional Information

Highest Common Factor (HCF)

The greatest number which divides each of the two or more numbers exactly without leaving a remainder.

Division Method for HCF

Divide the larger number by the smaller one, then divide the previous divisor by the remainder until the remainder is zero.

Least Common Multiple (LCM)

The smallest non-zero number that is a multiple of all the given numbers in a set.

The correct answer is 12%.

Key Points 

 

• The cooperative society is an independent legal person and is subject to taxation.
• Interest on securities and income from real estate make up the income of cooperative societies.
• Cooperative societies must pay MAT at a rate of 18.5%, while  businesses must pay it at a rate of 15%.
• According to her, persons with a total annual income of more than Rs 1 crore and up to Rs 10 crore would now pay a 7% surcharge instead of the previous 12%. ​

Additional Information 

• The Union Budget contains details about projected receivables and payables of the government for a particular year.
• The Indian government releases the union budget each year, and in 2023 it will do it on February 1st.

Given :

Calculation :

Total exports of Fruits for 2018 to 2020 = 61 + 70 + 75 = 206 Crores

Total exports of IT products for 2018 to 2020 = 120 + 100 + 160 = 380 Crores

Total exports of Defence products for 2018 to 2020 = 85 + 110 + 80 = 275 Crores

Total exports of fruit, IT,  and defence products in the given period = 206 + 380 + 275 = 861 Crores

Average of fruit, IT  and defence products in given period = $\frac{861}{3}$ = 287 Crores

Therefore, the yearly average exports (combined) of fruits, IT products, and defence products for 2018 to 2020 is '287 Crores'.

Hence, the correct answer is option 1).