RRB Group D Previous Year Paper (Held on: 29 Aug 2022 Shift 3)

The correct answer is 'blue'.

Key Points

• The color of the scattered light depends on the size of the scattering particles.
• Very fine particles scatter mainly blue light while particles of larger size scatter light of longer wavelengths.
• If the size of the scattering particles is large enough then the scattered light may even appear white.

Shortcut Trick

In any triangle, the sum of all three interior angles is always 180°.

If one angle is equal to the sum of the other two, it means that angle represents exactly half of the total sum of the angles.

Calculation: 180° ÷ 2 = 90°.

Since one angle of the triangle is 90°, it must be a right-angle triangle.

∴ The correct answer is a right-angle triangle.

Alternate Method

Given:

Let the three angles of the triangle be ∠A, ∠B, and ∠C.

According to the problem: ∠A = ∠B + ∠C

Formula Used:

Angle Sum Property of a triangle: ∠A + ∠B + ∠C = 180°

Calculations:

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + (∠B + ∠C) = 180°

⇒ Substitute ∠B + ∠C = ∠A into the equation:

⇒ ∠A + ∠A = 180°

⇒ 2 × ∠A = 180°

⇒ ∠A = 180° ÷ 2

⇒ ∠A = 90°

Since one of the angles is 90°, the triangle is a right-angle triangle.

∴ The correct answer is a right-angle triangle.

Additional Information

Angle Sum Property

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

Classification by Angles

A triangle is acute if all angles < 90°, right-angled if one angle = 90°, and obtuse if one angle > 90°.

Right-Angle Triangle Properties

In a right triangle, the square of the hypotenuse (side opposite 90°) is equal to the sum of the squares of the other two sides (Pythagoras Theorem).

The correct answer is 'Both statements are correct. Statement II is correct explanation of Statement I'. 

Key Points

• Metals are electropositive in nature because all metals lose electrons from their outermost shell in order to become stable and hence become positively charged.
• Non-metals are electronegative in nature because all non-metals gain electrons in order to become stable and hence become negatively charged.

The correct answer is 'Chauri-Chaura incident'.

Key Points

• The Non-Cooperation Movement was called off by Gandhiji after the incident of Chauri Chaura in Uttar Pradesh.
• On 5th Feb of 1922, the protest became violent when protesting people set fire a police station, burning 22 policemen alive

Additional Information Rowlatt Act endorsement : 

• The Rowlatt Act was passed by the British government to increase their grip on power over the common folk.
• This law was passed in March 1919 by the Imperial Legislative Council which gave them the power to arrest any person without any trial.
• To abolish this act, Gandhi and the other naram-dal leaders called for a Strick (suspension of work) to show Indians’ objection to this rule, called the Rowlatt Satyagraha.

Jallianwala Bagh massacre :

• The Lieutenant-Governor of Punjab at that time was Michael O’Dwyer. Lord Chelmsford was India’s Viceroy.
• On the day of the festival of Baisakhi on 13th April 1919 in Jallianwala Bagh, a public garden in Amritsar, a crowd of non-violent protestors had gathered. Also, among the crowd were pilgrims who had come to celebrate Baisakhi.
• General Dyer came there with his troops and blocked the only narrow entrance to the garden. Then, without warning, he ordered his troops to fire at the unarmed crowd, which included children as well.

Khilafat Movement :

• The Khilafat Movement was launched by  Ali Brothers.
• The movement was aimed to unite the Muslim community under the umbrella of a unified national movement.
• At the Calcutta Session of the Congress in September 1920, Gandhiji convinced other leaders to start a Non-Cooperation Movement in support of Khilafat Movement.
• The Khilafat Movement (1919-1924), was a pan-Islamic, political protest campaign launched by Muslims in British India to influence the British Government and to protect the Ottoman empire during the consequence of First World War.

Shortcut Trick

Ratio of numbers = 3 : 2

Let the common factor be the HCF.

Numbers = 3 × 4 and 2 × 4

Greater number = 3 × 4 = 12

∴ The correct answer is 12.

Alternate Method

Given:

Ratio of two numbers = 3 : 2

LCM = 24

HCF = 4

Formula Used:

Product of two numbers = LCM × HCF

Calculations:

⇒ Let the numbers be 3x and 2x.

⇒ 3x × 2x = 24 × 4

⇒ 6x² = 96

⇒ x² = 96 ÷ 6

⇒ x² = 16

⇒ x = √16 = 4

⇒ Greater number = 3x = 3 × 4 = 12

∴ The correct answer is 12.

Additional Information

Fundamental Property

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

Ratio and HCF

If two numbers are in ratio a : b, then the numbers are (a × HCF) and (b × HCF). Their LCM is (a × b × HCF).

HCF property

The HCF of two numbers is always a factor of their LCM.

Shortcut Trick

Identify the cube root of the given volume directly.

Since 9³ = 9 × 9 × 9 = 729,

The edge of the cube is √³(729) = 9 cm.

∴ The correct answer is 9 cm.

Alternate Method

Given:

Volume of the cube (V) = 729 cm³

Formula Used:

Volume of a cube = (edge)³

Calculations:

⇒ Let the edge of the cube be 'a' cm.

⇒ a³ = 729

⇒ a = ³√729

⇒ a = ³√(9 × 9 × 9)

⇒ a = 9 cm

∴ The correct answer is 9 cm.

Additional Information

Total Surface Area of Cube

The Total Surface Area (TSA) of a cube with edge 'a' is 6a².

Diagonal of a Cube

The length of the longest diagonal of a cube is given by a√3.

Lateral Surface Area

The Lateral Surface Area (area of 4 walls) is calculated as 4a².

Given:

 Focal length of the concave mirror $f=15 cm$ 

Object distance $v=45 cm$

Formula used:

Len's maker formula for a concave mirror 

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Calculation:

After putting the values we get,

$\frac{1}{15}=\frac{1}{45}+\frac{1}{v}\\Rightarrow \frac{1}{15}-\frac{1}{45}=\frac{1}{v}\\Rightarrow \frac{3-1}{45}=\frac{1}{v}\\Rightarrow \frac{2}{45}=\frac{1}{v}\\Rightarrow v=22.5$

Hence the object distance is' 22.5 cm'.

The correct answer is' NaHCO3, CO2'

Key Points

• Since the gas produced in the reaction is used in a type of fire extinguisher, the gas ‘Y’ must be carbon dioxide.
• Since carbon dioxide is produced when ‘X’ reacts with hydrochloric acid, we can say that 'X' must be either sodium carbonate or sodium bicarbonate.
• But sodium carbonate is a caustic base, which means it is able to burn, damage or destroy organic tissue slowly by chemical action. Thus, it is not edible and cannot be used as an antacid.
• ‘X’ is sodium bicarbonate (baking soda) and ‘Y’ is carbon dioxide gas.
• The balanced chemical equation for the reaction is given as: 
• $\mathrm{NaHCO}_3+\mathrm{HCl} \rightarrow \mathrm{NaCl}+\mathrm{CO}_2+\mathrm{H}_2 \mathrm{O}$​

The correct answer is 'baking soda and mild edible acid'.

Key Points

• Baking powder is a dry chemical leavening agent, a mixture of a carbonate or bicarbonate and a weak acid.
• The base and acid are prevented from reacting prematurely by the inclusion of a buffer such as cornstarch.

Given:

 

 

Given code - '2 @ 7 # = 5'

Here, Rule number 3 is applied in the given code.

If both the first and third elements are numbers, the third element is to be coded as the code for the first element.

So, the code for  '2 @ 7 # = 5' is “A T A Y D X”.

Hence, the correct answer is "Option 1".

Given:

7.44... + 3.77... - 2.55... 

Concept used:

The numbers of the form (p/q), where q ≠ 0 and p and q is integer is known as rational number.

Calculation:

By applying BODMAS rule on given number,

7.44... + 3.77... - 2.55... 

=> 7.44 + 1.22

=> 8.66.....

Let x = 8.66....      ----(1)

Multiply equation (1) by 10, we have

10x = 86.66....      ----(2)

Subtract equation (1) from equation (2), we have

10x - x = (86.66...) - (8.66....)

⇒ 9x = 78

⇒ x = $\large{78\over9}$

The 7.44... + 3.77... - 2.55....... can be written as  $\large{78\over9}$ in the form of p/q.

Hence, 'option 1' is the correct answer.

The logic follows here is: [(Sum of First number and second number × 3) - First number = Third number]

Now

For, (3, 5, 21)

[(3 + 5) × 3] - 3

(8× 3) - 3

24 - 3 = 21 = Third number.

Similarly, 

For, (4, 2, 14)

[(4 + 2) × 3] - 4

(6 × 3) - 4

18 - 4 = 14 = Third number.

Let's check each option one by one:

option 1. (6, 3, 12)

[(6 + 3) × 3] - 6

(9 × 3) - 6

27 - 6 = 21

21 ≠ 12

option 2. (8, 4, 28)

[(8 + 4) × 3] - 8

(12 × 3) - 8

36 - 8 = 28

28 = 28

option 3. (5, 2, 19)

[(5 + 2) × 3] - 5

(7 × 3) - 5

21 - 5 = 16

16 ≠ 19

option 4. (7, 1, 23)

[(7 + 1) × 3] - 7

(8 × 3) - 7

24 - 7 =17

17 ≠ 23

Hence, 'option 2' is the correct answer.

The logic followed here is :

The difference between each consecutive number is increasing by the square of odd numbers.

Hence, the correct answer is "183".

Shortcut Trick

Speed = 54 × (5/18) = 15 m/s.

Total distance (Train + Platform) = Speed × Time = 15 × 60 = 900 m.

Train length = 900 − 90 = 810 m.

Time to cross pole = Train length ÷ Speed = 810 ÷ 15 = 54 seconds.

∴ The correct answer is 54 sec.

Alternate Method

Given:

Platform length = 90 m

Time taken = 60 sec

Speed = 54 km/h

Formula Used:

Distance = Speed × Time

1 km/h = 5/18 m/s

Calculations:

⇒ Speed in m/s = 54 × (5/18) = 15 m/s

⇒ Total distance to cross platform = (Train length + Platform length)

⇒ (L + 90) = 15 × 60

⇒ L + 90 = 900

⇒ L = 810 m (Length of the train)

⇒ Time to cross an electric pole = Train length ÷ Speed

⇒ Time = 810 ÷ 15

⇒ Time = 54 seconds

∴ The correct answer is 54 sec.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed is the difference of their speeds. In the opposite direction, it is the sum.

Conversion Units

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

Train Crossing Stationary Objects

When crossing a point object (pole/man), distance = Length of train. When crossing a platform/bridge, distance = Length of train + Length of object.

The correct answer is '2022'.

Key Points

• To achieve the objective of providing “Housing to All” by the year 2022, the Government of India rolled out the revamped rural housing scheme,
• Pradhan Mantri Awaas Yojana-Gramin (PMAY-G) was launched on 20th November, 2016 with effect from 1 April 2016.
• Ministry of Rural Development along with States and UTs have undertaken various activities like Bhoomi Pujan, Gruh Pravesh, visit of beneficiaries to demonstration houses, and sensitization of beneficiaries about PMAY-G to celebrate Awaas Diwas.

Additional Information

• Pradhan Mantri Awas Yojana (PMAY):
• The Pradhan Mantri Awas Yojana (PMAY) scheme is a government initiative that aims to provide affordable houses to the urban poor keeping a target of building 2 crore (20 million) houses by 31 March 2022.
• The two basic components of the scheme are Pradhan Mantri Awas Yojana (Urban) (PMAY-U) for the urban poor and Pradhan Mantri Awaas Yojana (Gramin) (PMAY-G or PMAY-R ) for the rural poor.PMAY has been collated with other schemes to ensure that houses have a toilet or sanitation rooms.
• It also encompasses the Saubhagya Yojana electricity connection scheme, Ujjwala Yojana LPG connection scheme, acquiring clean drinking water, and Jan Dhan Yojana, a renowned banking facility scheme for the poor.

The correct answer is 'To give the elements positions according to their colour'.

Key Points

• The method of grouping the elements into different classes is known as the periodic classification of elements.
• The classification is done based on similarities in properties and the classification gives a systematic study of elements that helps to understand the properties of elements.
• Classification helps us to understand the properties of the elements and their compounds.
• Based on their position in the periodic table one can predict the properties of the elements and their compounds.
• It is easier to study, compare, and differentiate the properties of the elements and compounds from different groups

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Given:

$(\sqrt{142}+52 \div 26 \times5- \sqrt{80}) \times2$

 using the BODMAS rule,

= ( 11.9 + 52 ÷ 26 × 5 - 8.9) x 2

= ( 11.9 + 2 × 5 - 8.9) x 2

= ( 11.9 + 10 - 8.9) x 2

= (21.9 - 8.9) x2

= 13 x 2

= 26

Hence, “option 4” is the correct answer.

The correct answer is 'Rajasthan'. 

Key Points

• The canal traverses seven districts of Rajasthan: Barmer, Bikaner, Churu, Hanumangarh, Jaisalmer, Jodhpur, and Sriganganagar.
• Indra Gandhi Canal Project is Previously known as the Rajasthan Canal.
• It was renamed the Indira Gandhi Canal on 2 November 1984 following the assassination of Prime Minister Indira Gandhi.
• The Indira Gandhi Canal is the longest canal of India.
• It starts from the Harike Barrage at Harike, a few kilometres below the confluence of the Satluj and Beas rivers in the Indian state of Punjab and terminates in irrigation facilities in the Thar Desert in the north-west of Rajasthan state.

Given:

Formula used:

$\large Average = {Total:Sale\over Total:Shops}$

Calculation: 

Total sale from all the shops  for the year 2020 = 75 + 105 + 65 + 80 + 70 = 395

Total number of shops (A, B, C, D, E) = 5

=> Average sale from all the shops  for the year 2020 = $\large{395\over 5} = 79$

Hence, 'option 3' is the correct answer.

The correct answer is 'Amylase'.

Key Points

• Amylase is the enzyme present in saliva.
• It helps break down starch into simpler sugars like dextrin and maltose.
• These simpler sugars are then further broken down in the small intestine.

Additional Information

• ​ Lipase
• It is produced in the pancreas, mouth, and stomach.
• Most people produce enough pancreatic lipase, but people with cystic fibrosis, Crohn disease, and celiac disease may not have enough lipase to get the nutrition they need from food
• Peptidase
• Peptidases are produced in the stomach, small intestine, and pancreas helps in digestion process.
• Enterokinase
• Enterokinase (also known as enteropeptidase) is an enzyme secreted from the brush border of the small intestine, also in response to secretin and CCK.

The correct answer is 'Siachen'. 

Key Points

• Siachen Glacier is the second-longest glacier in the World’s Non-Polar areas.
• It is 78km long and the source of the Nubra River that waters the Nubra Valley near Leh in the Trans Himalayas.
• The Siachen Glacier is part of Ladakh, which has now been converted into a Union Territory.
• It is located in the eastern Karakoram range in the Himalayan mountains.
• It lies to the south of the great drainage divide that separates the Eurasian Plate from the Indian subcontinent in the glaciated portion of the Karakoram. Hence, it is also called the “Third Pole”.

Additional Information

• Hispar:
• ​Hispar Glacier is a 49 km (30 mi) long glacier in the Karakoram Mountains of Gilgit–Baltistan, Pakistan
• which meets the 67 km (42 mi) long Biafo Glacier at the Hispar La (Pass) at an altitude of 5,128 m (16,824 ft)
• It create the world's longest glacial system outside of the polar regions.
• Baltaro:
• ​The Baltoro Glacier at 63 km (39 mi) in length.
• It is located in the Shigar District of Gilgit-Baltistan in Pakistan, home to some of the world’s highest mountains.
• The glacier runs through the Karakoram mountain range, close to Chogori or K2, the highest mountain in the region at 8,611 meters (28,251 feet).
• Batura:
• Batura Glacier is 57 km (35 mi) long.
• It lies in the upper Hunza (Gojal) region of Hunza District, Gilgit-Baltistan in Pakistan.
• It is just north of the massifs of Batura, at 7,795 metres, and Passu, at 7,500 metres.

<br>

Given:

444.033 ÷ 15.998 ÷ 37.02 × 11.992

 using the BODMAS rule,

= 444.033 ÷ 15.998 ÷ 37.02 × 11.992

= 27.755 ÷ 37.02 × 11.992

= 0.749 × 11.992

= 8.99

The approximate value of 8.99 is 9.

Hence, “9” is the correct answer.

Given:

143 - 144 ÷ 16 × 3 - 1 

using the BODMAS rule,

= 143 - 144 ÷ 16 × 3 - 1

= 143 - 9 × 3 - 1

= 143 - 27 - 1

= 116 - 1

= 115

Hence, “115” is the correct answer.

Given: S,T, U, V, W, X, Y and Z were eight ministers, sitting around a circular table, facing the centre.

(1)  Only V was sitting between S and X. 

(2) S was sitting fourth to the left of T.

(3) Only T was sitting between Z and W. 

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(4) Y was sitting fourth to the left of W.

• It is possible Only in Case 1(b) and Case 2(a).

(5)  Z was sitting second to the left of Y.

• It is possible only in Case 2(a).

(6) U will sit on unoccupied seat. 

Here, U was sitting fourth to the left of X.

Hence, 'option 1' is the correct answer.

Statement:

Following Country G’s decision, which was taken a decade ago to control pollution, Country N has also decided to keep a cap on the number of cars in the country. So, now if someone in Country N wants to buy a car, they will have to wait until someone in the country sells their car or a car is registered as completely non-functional and is scrapped.

Assumptions:

I. The other transport options in Country N are enough to cater to the ‘non-car owning’ population of the country.  $\rightarrow$ True (This is more likely true because If a country adopted a major decision to keep a cap on car. So they must have other transport options in Country N are enough to cater to the ‘non-car owning’ population . Hence  Assumption I can be assumed.) 

II. The decision was most likely successful in Country G in controlling pollution. $\rightarrow$ True (This is more likely true because the decision is successful in Country G , thereafter Country N has decided to adopt it. Hence  Assumption Ii can be assumed.) 

Hence, Both I and II can be assumed.

The correct answer is 'All India Trinamool Congress (AITC)'.

 Key Points

• All India Trinamool Congress (AITCC).
• Founded on: 1 January 1998 but on 2 September 2016 the Election Commission recognised AITC as a national political party.
• Election symbol:  Jora Ghas Phool (grass with two flowers)

Additional Information

• Communist Party of India (CPI):
• The CPI was formed on 25 December 1925 at the party congress held in Kanpur.
• But the Communist Party of India (Marxist), which was formed after the party split in 1964.
• Election symbol: Bali-Sickle
• Nationalist Congress Party (NCP):
• It was founded on 25 May 1999 by Sharad Pawar, P A Sangma and Tariq Anwar after they were expelled from the Congress over the issue of Sonia Gandhi's nationality and leadership.
• Election symbol: Analogue alarm clock. The clock is drawn in blue and has two legs and an alarm button. It is situated on the tricolour Indian flag.
• Bahujan Samaj Party (BSP):
• The ideology of the party is inspired by the humanistic philosophy of Bhimrao Ambedkar as well as Buddhist philosophy. The party was formed on 14 April 1984 by Kanshi Ram, who was once a charismatic leader of Dalits.
• Election symbol: Elephant

Shortcut Trick

Ratio of Mother to Son age is 5 : 2 (since 2/5).

After 5 years, the ratio becomes 2 : 1 (since 1/2).

Equalize ratio difference: 5 : 2 (diff 3) and 6 : 3 (diff 3 by multiplying 2:1 by 3).

Change in ratio parts = 6 − 5 = 1 unit. Given 1 unit = 5 years.

Present age of Mother = 5 units = 5 × 5 = 25 years.

∴ The correct answer is 25 years.

Alternate Method

Given:

Present age of Son = 2/5 × Mother's age.

After 5 years, Son's age = 1/2 × Mother's age.

Let Mother's present age be 5x and Son's present age be 2x.

After 5 years:

⇒ (2x + 5) = 1/2 × (5x + 5)

⇒ 2 × (2x + 5) = 5x + 5

⇒ 4x + 10 = 5x + 5

⇒ 5x − 4x = 10 − 5

⇒ x = 5

⇒ Mother's present age = 5x = 5 × 5 = 25 years.

∴ The correct answer is 25 years.

Additional Information

Ratio Balancing Method

To solve age problems quickly, make the numerical difference between the ratio terms equal by multiplying with the difference of the other ratio.

Age Gap Consistency

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

Algebraic Verification

Always verify by substituting the answer: if mother is 25, son is 10. In 5 years, mother is 30 and son is 15 (which is 1/2 of 30).

The correct answer is 'sterilisation by surgery'.

Key Points

• Concept:
• Vasectomy is a permanent method of birth control.
• There are two processes of sterilization:
• In women: tubectomy
• In men: vasectomy
• Explanation:
• Sterilization is a surgical procedure for permanent contraception.
• During the procedure, the vasa deferentia are cut and tied or sealed to prevent sperm from entering the urethra, thereby preventing fertilization of the female through intercourse.

Shortcut Trick

Total Surface Area (TSA) of a cube = 6 × (side)²

⇒ 6 × a² = 1014

⇒ a² = 1014 ÷ 6 = 169

⇒ a = √169 = 13 cm

∴ The correct answer is 13 cm.

Alternate Method

Given:

Total Surface Area (TSA) of the closed cube = 1014 cm²

Formula Used:

⇒ Total Surface Area of a cube = 6a², where a is the length of each edge.

Calculations:

⇒ 6a² = 1014

⇒ a² = 1014 ÷ 6

⇒ a² = 169

⇒ a = √169

⇒ a = 13 cm

∴ The correct answer is 13 cm.

Additional Information

Volume of a Cube

The volume (V) of a cube with edge length a is given by V = a³.

Lateral Surface Area (LSA)

The area of the four vertical faces of a cube is LSA = 4a².

Diagonal of a Cube

The length of the longest diagonal in a cube is given by d = a√3.

The correct answer is 'Toyota Mirai'.

Key Points

• Union Minister for Road Transport and Highways Shri Nitin Gadkari launched the world's most advanced technology-developed Green Hydrogen Fuel Cell Electric Vehicle (FCEV) Toyota Mirai along with Union Minister Shri Hardeep Puri, Union Minister Shri RK Singh, Union Minister Shri Mahendra Nath Pandey, MD Toyota Kirloskar Motor Ltd. Shri Masakazu Yoshimura, VC TKM Ltd. Shri Vikram Kirloskar and officials at New Delhi today.
• Toyota Kirloskar Motor Pvt Ltd and International Center for Automotive Technology (ICAT) are conducting a Pilot Project to study and evaluate the world’s most advanced Fuel Cell Electric Vehicle (FCEV) Toyota Mirai which runs on hydrogen, on Indian roads and in climatic conditions.
• This is a first-of-its-kind project in India which aims to create a Green Hydrogen-based ecosystem in the country by creating awareness about the unique utility of Green Hydrogen and FCEV technology.

Additional Information

• Budget 2023-24:
• ​The Budget has reinforced the outlay of Rs. 19,744 crore for the National Green Hydrogen Mission that targets 5 million metric tonnes of production by 2030.
• This would require an additional renewable energy capacity of at least 125 GW, which is almost the entire current capacity of renewables in India.

Shortcut Trick

The debt of ₹8,000 is due in 12 months, but it is being settled after 2 months.

The remaining time for which interest is saved is 10 months (12 − 2).

Payment = (Due Amount × 100) ÷ (100 + (Rate × Remaining Time))

Payment = (8000 × 100) ÷ (100 + (9 × 10/12)) = 800000 ÷ 107.5

Payment ≈ ₹7,441.86

∴ The correct answer is ₹7,442.

Alternate Method

Given:

Due Amount (A) = ₹8,000

Total tenure = 12 months

Time elapsed = 2 months

Rate of Interest (R) = 9% per annum

Formula Used:

Present Worth (PW) = (Amount × 100) ÷ [100 + (Rate × Time)]

Calculations:

⇒ Remaining time (T) = 12 months − 2 months = 10 months

⇒ T in years = 10 ÷ 12 = 5/6 years

⇒ PW = (8000 × 100) ÷ [100 + (9 × 5/6)]

⇒ PW = 800000 ÷ [100 + (3 × 5/2)]

⇒ PW = 800000 ÷ [100 + 7.5]

⇒ PW = 800000 ÷ 107.5

⇒ PW = 8000000 ÷ 1075

⇒ PW = 320000 ÷ 43

⇒ PW ≈ 7441.86

Rounding off to the nearest rupee:

⇒ PW = ₹7,442

∴ The correct answer is ₹7,442.

Additional Information

Present Worth (PW)

The actual money that, when invested at a given rate for a given time, grows to the specified due amount. PW = (100 × Amount) ÷ (100 + RT).

True Discount (TD)

The difference between the amount due and the present worth. It is the simple interest on the present worth. TD = Amount − PW = (PW × R × T) ÷ 100.

Bankers Discount (BD)

Simple interest calculated on the face value (due amount) rather than the present worth for the unexpired time. BD = (Amount × R × T) ÷ 100.

Bankers Gain (BG)

The difference between the Banker's Discount and the True Discount. BG = BD − TD = (TD²) ÷ PW.

Given

 

Concept used:

Difference between the number of boys and girls from all the departments(2018) = Total Boys of all departments - Total Girls of all departments.

Calculation:

Total Boys in departments A, B, C, D in 2018 = 100 + 100 + 150 + 100 = 450

Total Girls in departments A, B, C, D in 2018 = 80 + 100 + 140 + 120 = 440

Difference between the number of boys and girls from all the departments(2018)  = 450 - 440 = 10.

Hence, 'option 4' is the correct answer.

Given: Six friends P,Q,R,S,T and U.

1. R was born in may .

 

2. Only one person was born between the months of P and R’s birth months

 

3. U was born in the immediate next month of Q’s birth month.

 

4. S was not born in April.

 

From the above arrangement, T was born in April.

Hence, the correct answer is **"**APRIL".

Shortcut Trick

Ratio of Boys : Girls = 7 : 9

Given: 9 units = 189

1 unit = 189 ÷ 9 = 21

Boys (7 units) = 7 × 21 = 147

∴ The correct answer is 147.

Alternate Method

Given:

Ratio of Boys to Girls = 7 : 9

Number of Girls = 189

Formula Used:

Value of a part = Total quantity ÷ Total ratio units

Calculations:

⇒ Let the number of boys be 7x and girls be 9x.

⇒ 9x = 189

⇒ x = 189 ÷ 9

⇒ x = 21

⇒ Number of boys = 7x

⇒ Number of boys = 7 × 21

⇒ Number of boys = 147

∴ The correct answer is 147.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a:b = c:d, then a × d = b × c (Product of extremes = Product of means).

Unitary Method

Find the value of a single unit first, then multiply by the required number of units to find the final total.

Compound Ratio

For ratios a:b and c:d, the compound ratio is (a × c) : (b × d).

Given:

Focal length of convex mirror $f=+10 cm$ .

Object distance $u=-15 \mathrm{~cm}$ 

Formula used:

The len's maker formula 

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$  [Where v is the image distance]

Calculation:

After putting all the values in the equation

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\Rightarrow \frac{1}{10}=\frac{1}{-15}+\frac{1}{v}\\Rightarrow \frac {1}{v}=\frac{1}{15}+\frac{1}{10}\\Rightarrow \frac{1}{v}=\frac{5}{30}\\Rightarrow v=6$   

'An object is placed in front of a convex mirror of focal length 10 cm, at a distance of 15 cm. Its image is formed at a distance of 6 cm and is virtual '.

Shortcut Trick

The value of (a + b) is directly given as 25.

The required value is (a + b)².

Substitute the value: (25)² = 25 × 25 = 625.

∴ The correct answer is 625.

Alternate Method

Given:

Sum of numbers (a + b) = 25

Difference of numbers (a − b) = 13

Method Used:

Basic Algebraic Squaring of the sum.

⇒ Given equation: a + b = 25

⇒ To find (a + b)², we square both sides of the equation.

⇒ (a + b)² = (25)²

⇒ (a + b)² = 25 × 25

⇒ (a + b)² = 625

∴ The correct answer is 625.

Additional Information

Square of a Sum

The identity for the square of a sum is (a + b)² = a² + 2ab + b².

Square of a Difference

The identity for the square of a difference is (a − b)² = a² − 2ab + b².

Relation between Sum and Difference

The relationship between the square of the sum and the square of the difference is (a + b)² − (a − b)² = 4ab.

Difference of Squares

The product of the sum and difference of two numbers is a² − b² = (a + b)(a − b).

Shortcut Trick Since sin θ > cos θ, we can choose a specific value like θ = 90° to verify the expression. At θ = 90°: sin 90° = 1, cos 90° = 0, and tan 90° is undefined (approaching ∞). Expression = (√(1−0) + √(1+0)) / (2 × ∞) = 2 / ∞ = 0. Checking options at θ = 90°: (1) cot 90° = 0, (2) sin 90° = 1, (3) cos 90° = 0, (4) tan 90° = ∞. Since θ must be acute for standard simplification, use θ = 60°: expression → cos 60° × (2 sin θ / 2 sin θ) → cos θ. ∴ The correct answer is cos θ. Alternate Method

Given: sin θ > cos θ Formula Used: sin2θ + cos2θ = 1 and (a ± b)2 = a2 + b2 ± 2ab ⇒ √(1 − 2 sin θ cos θ) = √(sin2θ + cos2θ − 2 sin θ cos θ) = √(sin θ − cos θ)2 ⇒ Since sin θ > cos θ, the value is (sin θ − cos θ) ⇒ √(1 + 2 sin θ cos θ) = √(sin θ + cos θ)2 = (sin θ + cos θ) ⇒ Numerator = (sin θ − cos θ) + (sin θ + cos θ) = 2 sin θ ⇒ Expression = (2 sin θ) / (2 tan θ) ⇒ Expression = (2 sin θ) / (2 sin θ / cos θ) ⇒ Expression = cos θ ∴ The correct answer is cos θ. Additional Information Trigonometric Identity The identity 1 ± sin 2θ = (sin θ ± cos θ)2 is a core transformation in calculus and trigonometry. Modulus Property The square root √x2 = |x|. Therefore, √(sin θ − cos θ)2 depends on which term is larger based on the quadrant. Tangent Ratio tan θ = sin θ / cos θ. Reciprocal of tan θ is cot θ = cos θ / sin θ.

The correct answer is 'the same ,opposite'.

Key Points

• A potential difference can be induced (created) in a conductor when there is movement between the conductor and a magnetic field.
• This can occur in two different ways: a coil of wire is moved in a magnetic field. a magnet is moved into a coil of wire.
• The induced emf depends upon the magnetic field and number of turns and it is independent of the resistance of the coil.

The correct answer is 'ABG Shipyard'. 

Key Points

• The Central Bureau of Investigation (CBI) on Saturday filed a case against ABG Shipyard Limited.
• ABG Shipyard directors/promoters Rishi Kamlesh Agarwal, Santhanam Muthaswamy, Ashwani Kumar, Sushil Kumar Agarwal and Ravi Vimal Nevetia for allegedly duping 28 banks of Rs 22,842 crore.
• It was alleged that the accused had cheated the consortium of 28 banks including the branches of the erstwhile State Bank of Patiala, Commercial Finance Branch, New Delhi, the erstwhile State Bank of Travancore, Commercial Branch, New Delhi, State Bank of India, Overseas Branch, Mumbai etc.
• The consortium was led by ICICI Bank

Shortcut Trick

Mode is the observation that occurs most frequently in a data set.

Count the frequency of each observation:

⇒ 27 appears 2 times.

⇒ All other numbers (23, 38, 42, 45, 58, 69, 71) appear only 1 time.

Since 27 has the highest frequency, the mode is 27.

∴ The correct answer is 27.

Alternate Method

Given:

Observations: 23, 27, 38, 42, 27, 58, 69, 71, 45

Formula Used:

Mode = Observation with the maximum frequency

Calculations:

Let us arrange the given data in ascending order to easily count the frequencies:

⇒ Arranged Data: 23, 27, 27, 38, 42, 45, 58, 69, 71

Now, let us construct a frequency table for the observations:

⇒ Frequency of 23 = 1

⇒ Frequency of 27 = 2

⇒ Frequency of 38 = 1

⇒ Frequency of 42 = 1

⇒ Frequency of 45 = 1

⇒ Frequency of 58 = 1

⇒ Frequency of 69 = 1

⇒ Frequency of 71 = 1

Since the observation 27 occurs the maximum number of times (frequency = 2), it is the mode of the given data set.

Let us analyze why the other options are incorrect:

⇒ Option (1) 71 is incorrect because its frequency is only 1.

⇒ Option (3) 45 is incorrect because its frequency is only 1.

⇒ Option (4) 42 is incorrect because its frequency is only 1.

∴ The correct answer is 27.

Additional Information

Definition of Mode

The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), two modes (bimodal), multiple modes (multimodal), or no mode at all if all values occur with equal frequency.

Empirical Relationship between Mean, Median, and Mode

For a moderately skewed distribution, the relationship is given by: Mode = 3 × Median − 2 × Mean.

Mean and Median

Mean is the average of all observations (Sum ÷ Total count). Median is the middlemost value when the data is arranged in ascending or descending order.

Shortcut Trick

Distance = Efficiency (km/l) × Quantity (l)

Total distance = 25 × 5.5

Total distance = 137.5 km

∴ The correct answer is 137.5 km.

Alternate Method

Given:

Mileage of car = 25 km/l

Petrol filled = 5½ litres

Calculation:

⇒ Quantity of petrol = 5½ = 11/2 litres = 5.5 litres

⇒ Distance = Petrol × Mileage

⇒ Distance = 5.5 × 25

⇒ Distance = (5 × 25) + (0.5 × 25)

⇒ Distance = 125 + 12.5

⇒ Distance = 137.5 km

∴ The correct answer is 137.5 km.

Additional Information

Mileage Calculation

Mileage is calculated as total distance covered divided by the quantity of fuel consumed: Mileage = Distance ÷ Fuel.

Unit Conversion

Ensure the fuel unit (Litres) and the mileage unit (km/Litre) are consistent to obtain the result in km.

Mixed Fraction to Decimal

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

The logic followed here is:

Thus, the number which will replace the question mark in the series is '108'.

Hence, the correct answer is Option (4).

Given: (Left) 32578641 (Right).

If 2 is added to each odd digit,

and 2 is subtracted from each even digit.

Then, the new number formed:

Now, Third number from the left = 7

Third number from the right = 4

Difference = 7 - 4 = 3.

Hence, the correct answer is Option (3).

Given: (Left) £ & 6 @ 4 f 2 4 % 1 3 ^ 3 ¥ @ 8 8 % 7 (Right)

Symbols immediately followed by a number and immediately preceded by a symbol:

Needed pattern: Symbol - Symbol - Number.

Thus, there are two such pairs:

• £ & 6
• ¥ @ 8

​Hence, the correct answer is Option (4).

The logic followed here is: 

Logic: (First number + Third number) × 5 = Second number.

Now,

For (7, 150, 23)

→ 7 + 23 = 30 

→ 30 × 5 = 150.

For, (14, 100, 6)

→ 14 + 6 = 20

→ 20 × 5 = 100.

Now, checking the options:

Option 1: (9, 80, 11) 

→ 9 + 11 = 20

→ 20 × 5 = 100 ≠ 80.

Option 2: (15, 140, 13) 

→ 15 + 13 = 28

→ 28 × 5 = 140.

Option 3: (8, 90, 11)

→ 8 + 11 = 19

→ 19 × 5 = 95 ≠ 90.

Option 4: (4, 108, 16)

→ 4 + 16 = 20

→ 20 × 5 = 100 ≠ 108.

Hence, the correct answer is Option (2).

Shortcut Trick

Simplify the expression by directly summing coefficients of like terms.

Coefficient of x²: 2 × (3/2) − 3 = 3 − 3 = 0

Coefficient of x: 2 × (−24) − 3 × 4 = −48 − 12 = −60

Constant term: 2 × 12 − 3 × (−13) = 24 + 39 = 63

Combining the results gives −60x + 63.

∴ The correct answer is −60x + 63.

Alternate Method

Given: 2(3/2 x² − 24x + 12) − 3(x² + 4x − 13)

We use the Distributive Property to open the brackets:

⇒ 2 × (3/2)x² − 2 × 24x + 2 × 12 − 3 × x² − 3 × 4x − 3 × (−13)

⇒ 3x² − 48x + 24 − 3x² − 12x + 39

Now, group and combine the Like Terms (x² terms, x terms, and constants):

⇒ (3x² − 3x²) + (−48x − 12x) + (24 + 39)

⇒ 0x² − 60x + 63

⇒ −60x + 63

∴ The correct answer is −60x + 63.

Additional Information

Distributive Property

This property states that multiplying a sum by a number is the same as multiplying each addend individually: a(b + c) = ab + ac.

Signs of Multiplication

When multiplying, a negative number times a negative number results in a positive number (− × − = +), while a negative times a positive is negative (− × + = −).

BODMAS Rule

Always follow the order: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction for accurate simplification.

The correct answer is 'Level of output'.

Key Points

• An isoquant curve is a concave-shaped line on a graph, used in the study of microeconomics, that charts all the factors, or inputs, that produce a specified level of output.
• This graph is used as a metric for the influence that the inputs—most commonly, capital and labor—have on the obtainable level of output or production.

The correct answer is 'Indus River System'.

Key Points

• Indus River System is a Himalayan river system and is one of the largest river basins in the world.
• The Indus Rivier is also known as Sindhu.
• Therefore, the Sindhu River System is a part of one of the most fertile regions of the Indian sub-continent and the world.
• Some of the Indian subcontinent's river systems existed long before civilizations existed.
• One such river system is the Indus River System. The main Tributaries of the Indus River form the Indus River System, which includes Indus, Jhelum, Chenab, Ravi, Beas, and Satluj.
• As the Indus River flows through both India and Pakistan, the Indus water treaty was signed in 1960 for water sharing. Indus River System

​

 

 

 

 

 

 

Additional Information

• Narmada River System:
• ​The Narmada, the largest west flowing river of the Peninsula, rises near Amarkantak range of mountains in Madhya Pradesh.
• It is the fifth largest river in the country and the largest one in Gujarat. It traverses Madhya Pradesh, Maharashtra and Gujarat and meets the Gulf of Cambay.
• Godavari River System: 
• ​The Godavari is the largest Peninsular river system. It is also called the Dakshin Ganga.
• Godavari river rises from Trimbakeshwar near Nasik in Maharashtra and flows for a length of about 1450 km before falling into the Bay of Bengal.
• Tributaries: Pravara, Purna, Manjra, Penganga, Wardha, Wainganga, Pranhita, Indravati, Maner and the Sabri.
• Brahmaputra River System:
• The river originates from the Kailash ranges of Himalayas at an elevation of 5300 M.
• After flowing through Tibet it enters India through Arunachal Pradesh and flows through Assam and Bangladesh before it joins Bay of Bengal.
• ​The Brahmaputra River System (3848 km) is one of the longest rivers of the world. It is known as the Yarlung Tsangpo River in Tibet, the Brahmaputra, Lohit, Siang, and Dihang in India, and the Jamuna in Bangladesh.
• Tributaries: 
• Left bank tributaries are the Burhi Dihing, Dhansari (South) and Kalang.
• Right bank tributaries are the Subansiri, Kameng, Manas and Sankosh.

Shortcut Trick

For a mean proportion a : b :: b : c, the middle term is b = √(a × c).

x = √(12 × 27) = √324 = 18

y = √(25 × 36) = 5 × 6 = 30

x : y = 18 : 30 = 3 : 5

∴ The correct answer is 3 : 5.

Alternate Method

Given: 12 : x :: x : 27 and 25 : y :: y : 36

Formula Used: Product of extremes = Product of means

⇒ x × x = 12 × 27

⇒ x² = 324

⇒ x = 18 (since x is positive)

⇒ y × y = 25 × 36

⇒ y² = 900

⇒ y = 30 (since y is positive)

⇒ x : y = 18 : 30

⇒ x : y = 3 : 5

∴ The correct answer is 3 : 5.

Additional Information

Mean Proportional

If three numbers a, b, and c are in continued proportion, then b is the mean proportional such that b = √(ac).

Third Proportional

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

Fourth Proportional

If four numbers a, b, c, and d are in proportion (a : b :: c : d), then d = (b × c)/a.

Shortcut Trick

Identify factors of (coefficient of x² × constant) = 2 × (−3) = −6 that sum to −1.

The factors are −3 and +2.

Divide these factors by the coefficient of x² (2): −3/2 and +2/2 = +1.

Change the signs to get the roots: +3/2 and −1.

∴ The correct answer is -1, 3/2.

Alternate Method

Given Quadratic Equation: 2x² − x − 3 = 0

Formula used: Middle Term Splitting

⇒ 2x² − 3x + 2x − 3 = 0

⇒ x(2x − 3) + 1(2x − 3) = 0

⇒ (2x − 3)(x + 1) = 0

⇒ Case 1: 2x − 3 = 0 ⇒ x = 3/2

⇒ Case 2: x + 1 = 0 ⇒ x = −1

∴ The correct answer is -1, 3/2.

Additional Information

Quadratic Formula

The roots of any quadratic equation ax² + bx + c = 0 can be found using x = [−b ± √(b² − 4ac)] / 2a.

Nature of Roots

The Discriminant (D = b² − 4ac) determines the nature: D > 0 (real and distinct), D = 0 (real and equal), and D < 0 (imaginary).

Relationship between Roots and Coefficients

For roots α and β, the Sum of roots (α + β) = −b/a and the Product of roots (αβ) = c/a.

The correct answer is 'Lack of oxygen and pyruvate converted to lactic acid'.

Key Points

• During heavy exercise, enough oxygen is not delivered to the muscle cells.
• The condition is referred to as an oxygen-deficient. This deficiency leads to anaerobic respiration.
• Glucose breaks down into lactic acid (accumulated in muscle cells).
• It causes cramps and pain in the legs.
• Anaerobic respiration is a type of respiration which occurs in absence of oxygen.

The correct answer is 'one reactant breaks down to give simpler products'.

Key PointsDecomposition reaction:

• A decomposition reaction can be defined as a chemical reaction in which one reactant breaks down into two or more simpler products.
• The reaction occurs as follows: Nacl → Na + cl

Additional Information

Combination reaction:

• Formation of water from hydrogen and oxygen is a combination reaction because hydrogen and oxygen are combining to form single product.
• Those reactions in which two or more substances combine to form a single substance are called combination reactions.
• The reaction occurs as follows:
• 2H2 (g) + O2 (g) → 2H2O(l).

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Displacement reaction:

• Displacement reaction is a chemical reaction in which a more reactive element displaces a less reactive element from its compound
• The reaction occurs as follows: 2K +Mgcl2 → 2Kcl + Mg

 

Oxidation: 

• According to Classical or earlier concept oxidation is a process which involves the addition of oxygen or any electronegative element or the removal of hydrogen or any electropositive element.
• According to electronic concept oxidation is defined as the process in which an atom or ion loses one or more electrons.
• The reaction occurs as follows: C + O2 → CO2

Reduction: 

• According to Classical or earlier concept reduction is a process which involves the addition of hydrogen or any electropositive element or the removal of oxygen or any electronegative element.
• According to electronic concept reduction is defined as the process in which an atom or ion gains one or more electrons.
• The reaction occurs as follows: N2 + 3H2 → 2NH3

The correct answer is 'Delhi'.

Key Points

• The Delhi government has formulated a policy for the welfare of street children in view of the pandemic situation, which emphasizes the role of various stakeholders in promoting COVID-appropriate behavior and creating awareness about the infection.
• The policy, prepared by the Women and Child Development Department (WCD), Government of Delhi, encourages direct involvement of civil society organizations and highlights their role in identifying hotspot areas and distributing masks among them.
• It also suggested that the district administration may consider training children rescued from the streets (on attaining the age of 18) as civil defense volunteers, as this would give them respectable employment and enable them to look after themselves. Due to experience can also help many other people. Children who come from similar backgrounds.
• The policy also proposes the structure of District Child Protection Convergence Committee (DCPCC) over and above the District Task Force (DTF) to protect children.
• The DCPCC will have the District Magistrate as its chairman along with other members, including representatives from two NGOs and the Delhi Commission for Protection of Child Rights (DCPCR).
• The mandate of the NGOs would include bringing all the cases of children identified by them to their respective Child Welfare Committee and working with the concerned departments for their rehabilitation.

The correct answer is 'Brahma'.

Key Points

• Brahma is the first deity in the Hindu Trimurti or Trimurti.
• The trinity consists of three deities who are responsible for the creation, maintenance and destruction of the world.
• The other two deities are Vishnu and Shiva.
• Vishnu is the preserver of the universe, while Shiva's role is to destroy in order to recreate it.
• Brahma's job was to create the world and all beings.
• His name should not be confused with Brahman, the supreme divine power present within all things.
• Brahma is the least worshiped deity in Hinduism today.
• There are only two temples dedicated to him in the whole of India.

Given: Seven people with the initials of their names G, H, I, J. K, L and M were sipping their tea, sitting around a circular table, facing the centre. They were equidistant to one another.

K was sitting to the immediate right of I.

G was sitting third to the right and fourth to the left of J.

 

 

Only H was sitting between M and J.

L was an immediate neighbour of M.

Therefore, the immediate neighbours of G are K and L.

Hence, the correct answer is Option (4).

The correct answer is '36 W'.

Key Points

• Electric Power: The rate at which electrical energy is dissipated into other forms of energy is called electrical power i.e.,

P = VI = I² R

• Where V = Potential difference, R = Resistance and I = current.
• Given - Potential difference (V) = 12 V and current (I) = 3 A
• Electric power can be written as,

P = VI                   

P = 12 × 3 = 36 W

The correct answer is 'Only i and ii'.

Key Points

• Monopoly:
• Characteristics associated with a monopoly market make the single seller the market controller as well as the price maker.
• There are restrictions to prevent any other firm from entering the market and to start selling the same commodity.
• A monopoly refers to a market situation in which there is only one seller with many buyers of a commodity.
• He enjoys the power of setting the price for his goods.
• No other commodity works as a substitute for this commodity.

The correct answer is 'Workers' salary'.

Key Points

• A fixed cost is a cost that does not change with an increase or decrease in the number of goods or services produced or sold.
• Fixed costs are expenses that have to be paid by a company, independent of any specific business activities.
• In general, companies can have two types of costs, fixed costs or variable costs, which together result in their total costs. Shutdown points tend to be applied to reduce fixed costs.
• Workers' salary is an example of Fixed cost.
• Variable costs are directly related to the level of production.
• Waste disposal, Electricity, and Water are examples of variable costs.

The correct answer is 'Part-IX'.

Key Points

• Article 40 of the constitution directs to state to organize Village Panchayats as a unit of self-government.
• Most states began implementing this Directive Principle along the lines of the recommendations of the government's Balwantrai Mehta Commission report.
• 73rd Constitution Amendment Act, 1992 and 74th Constitution Amendment Act, 1992 inserted part IX (Panchayats) and part IXA (Municipalities) in the constitution respectively as well as XIth and XIIth schedules respectively.
• Rajasthan was the first state to set up Panchayati Raj System in 1959 by Jawaharlal Nehru followed by Andhra Pradesh.

Additional Information

• Parts of the Indian Constitution:

The correct answer is 'Jharkhand'.

Key Points

• The Sports Authority of India has approved a total amount of Rs 75 Lakh to host the Khelo India National Ranking Women Archery Tournament over six phases.
• TATA Archery Academy, Jamshedpur (Jharkhand) is successfully hosted the first phase of the tournament on April 12 and 13.
• The tournament had been held across the Recurve and Compound events in the senior, Junior and Cadet Categories, and  conducted as per the World Archery Rules.
• The Archery Association of India (AAI), in collaboration with the Jharkhand Archery Association and TATA Steel, are organising the tournament.

The pattern followed here is:

For, POT : UPQ

For, EST : UTF 

 

Similarly: for CAT : UBD

 

Hence, the correct answer is Option (1).

Statements:

Few mice are rats

Most rats are vultures

All vultures are hawks

The least possible Venn diagram for the given statements is:

Conclusions:

(I) Few mice are vultures → False (There is no direct relationship between mice and vultures, so it can be possible not definite).

(II) Some hawks are mice → False (There is no direct relationship between mice and hawks, so it can be possible not definite).

(III) Some rats are hawks → True (As most rats are vultures and all vultures are hawks, some rats are also hawks).

So, 'Only conclusion III follows '.

Hence, the correct answer is "Option 3".

Important Points

1) “ALL” can be written as: Each, Every, Only, 100%.

2) “Some” and “Some not” can be written as: Almost, Little, Few, At most, At least, Many, Mostly, 1-99%.

3) “No” can be written as: None, 0%.

The pattern followed here is:

'ASSURED' is written as 'TTBUEFS'.

‘BENEFIT’ is written as ‘OFCEUJG’.

Similarly, 'CABINET' will be written as:

So, 'CABINET' will be written as 'CBDIUFO'.

Hence, the correct answer is Option (2).

Diagram of arrangement is drawn as per the given information:

1. Only one box is kept between Q and R. W is kept immediately above Q.

2. Only one box is kept between R and U. T is kept immediately below R.

There are total 3 boxes between T and W.

Hence, the correct answer is Option (3).

The correct answer is 'Cross-fertilisation of plants was performed initially, followed by self-fertilisation'. 

Key Points

• Monohybrid Cross: A cross between two types of plants of the same species considering only the transmission of one character is called a monohybrid cross.
• Explanation:
• Gregor Johann Mendel used the monohybrid cross to determine the dominant and recessive traits in the case of peas.
• He first crossed true-breeding tall pea plants with true-breeding dwarf pea plants.
• The homozygous allele for the tall pea plant is represented by TT, and the homozygous allele for the short/dwarf pea plant is represented by tt.
• A monohybrid cross between the two plants results in the production of a heterozygous genotype (Tt).
• In terms of phenotype, the F1 generation has all tall pea plants, thus indicating that the tall trait is the dominant trait and the short trait is a recessive trait.
• The F1 generation is then self-fertilized to get F2 generation.
• In F2 generation tall and dwarf plants can be seen in a ratio 3:1.

                                                                         

• Phenotype: It refers to the external appearance.
• Genotype: It refers to the genetic constitution i.e., the types of genes present in the organism.

The correct answer is 'Bodo'.

Key Points

• The Sino-Tibetan is also known as the Mongoloid Family and Bodo is the type of SinoTibetan language.
• It stretches all over the sub-Himalayan tracts up to the north-western frontier and covers the Indian states of North Bihar, North Bengal, and Assam.
• These languages are considered to be older than the Indo-Aryan languages and are referred to as Kiratas in the oldest Sanskrit literature.

Additional Information

• Maithili:
• ​Maithili language, with Magadhi (Magahi) and Bhojpuri, one of the three main languages of Bihar state.
• It is an Indo-Aryan language of the Indo-European language family.
• Maithili is one of India's 22 scheduled languages.
• Santhali:
• ​Santali language, Santali also spelled Santhali, a Munda language spoken primarily in the east-central Indian states of West Bengal, Jharkhand, and Orissa.
• Santali is one of India's 22 scheduled languages.
• Dogri:
• ​Dogri language is spoken in the UT of Jammu & Kashmi, also spoken in some regions of Himachal Pradesh and Punjab.
• Dogri is the language of the Dogras, living mainly in the Jammu region of Jammu and Kashmir.
• Dogri language is a member of the Indo-Aryan i.e. language of Vedas and Laukik Sanskrit group within the Indo-European languages of India.
• Dogri is one of India's 22 scheduled languages

The correct answer is 'Ravi k Dahiya'.

Key Points

• Indian wrestler Ravi Kumar Dahiya won the gold medal
• while Bajrang Punia and Gourav Baliyan settled for silvers
• at the Asian Wrestling Championships 2022 in Ulaanbaatar, Mongolia on Saturday.

Additional Information

• Ravi Kumar Dahiya: 
• Ravi Kumar Dahiya is an Indian freestyle wrestler who won a silver medal at the 2020 Summer Olympics in the 57 kg category.
• He is also a bronze medalist from 2019 World Wrestling Championships and a two-time Asian champion.
• He hails from Haryana. Ravi Kumar is the fifth Indian wrestler after KD Jadhav, Sushil Kumar, Yogeshwar Dutt, and Sakshi Malik to finish on the Olympic podium.
• Dahiya became the second Indian wrestler ever to win an Olympic silver after Sushil Kumar.

Shortcut Trick

Total Cost Price (CP) = 5,50,000 + 25,000 = 5,75,000.

Selling Price (SP) = 5,37,625.

Loss = 5,75,000 − 5,37,625 = 37,375.

Loss % = (37,375 ÷ 5,75,000) × 100 = 6.5%.

∴ The correct answer is 6.5%.

Alternate Method

Given: Purchase Price = Rs. 5,50,000, Overhead Expenses = Rs. 25,000, Selling Price (SP) = Rs. 5,37,625.

Formulas: Total CP = Purchase Price + Overhead Expenses | Loss = CP − SP | Loss% = (Loss ÷ CP) × 100

⇒ Total Cost Price = 5,50,000 + 25,000 = Rs. 5,75,000

⇒ Loss Amount = 5,75,000 − 5,37,625 = Rs. 37,375

⇒ Loss Percentage = (37,375 ÷ 5,75,000) × 100

⇒ Loss Percentage = 37,375 ÷ 5,750 = 6.5%

∴ The correct answer is 6.5%.

Additional Information

Total Cost Price

The actual cost price includes the purchase price plus any additional overhead expenses like repair, transport, or labor costs.

Loss Condition

A loss occurs when the Selling Price (SP) is less than the Cost Price (CP). Formula: Loss = CP − SP.

Shortcut Trick

Total distance to be covered = Sum of lengths = 300 + 340 = 640 m.

Relative speed (opposite direction) = Sum of speeds = 35 + 45 = 80 m/s.

Time taken = Total Distance ÷ Relative Speed = 640 ÷ 80 = 8 sec.

∴ The correct answer is 8 sec.

Alternate Method

Given:

Length of Train P (L₁) = 300 m

Length of Train Q (L₂) = 340 m

Speed of Train P (S₁) = 35 m/s

Speed of Train Q (S₂) = 45 m/s

Formula Used:

Time = (Total Length) ÷ (Relative Speed)

Relative Speed (Opposite Direction) = S₁ + S₂

Calculations:

⇒ Total Distance = L₁ + L₂ = 300 + 340 = 640 m

⇒ Relative Speed = 35 + 45 = 80 m/s

⇒ Time taken = 640 ÷ 80

⇒ Time taken = 8 sec

∴ The correct answer is 8 sec.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference between their speeds: S_rel = |S₁ − S₂|.

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Crossing Stationary Objects

To cross a stationary pole or point, distance = length of train. To cross a platform or bridge, distance = length of train + length of platform.

The correct answer is 'becomes $({I \over4})$'.

Key Points

• Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

V = IR          

• Where V is the voltage difference, I is current passes through conductor and R is the resistance.
• If the resistance of the conductor is made four times, R₂ = 4R, then I₂ is,

 V = IR = R2 I₂

4R I₂ = IR    

I₂ = $({I \over4})$

The correct is the '(i) - zinc displaces copper from copper sulphate'.

Key Points

• Zinc sulphate Solution and copper are obtained when a strip of zinc metal is placed in copper Sulphate Solution.

CuSO4(aq.) +Zn(s)→ ZnSO4(aq.) +Cu(s)

• When a strip of zinc metal is placed in copper sulphate solution:
• zinc displaces copper from copper sulphate
• the blue colour of copper sulphate solution fades up.
• a blue deposit of copper metal is formed on the copper strip
• it is an example of Displacement reaction.

The correct answer is 'Dr. Mansukh Mandaviya'.

Key Points

• Dr. Mansukh Mandaviya, Union Minister of Health and Family Welfare launched the “ICMR/ DHR Policy on Biomedical Innovation & Entrepreneurship for Medical Professionals, Scientists and Technologists at Medical, Dental, Para-Medical Institutes/Colleges..

Important Points

• As per the Policy, the medical professionals/ doctors will be encouraged to pursue entrepreneurial ventures by forming start-up companies, taking adjunct position in Company- Non-Executive Director or Scientific Advisor.
• The doctors will also be permitted to undertake inter-institutional and industry projects alone or through companies, license technologies to business entities leading to commercialisation, revenue generation for selfsustenance and societal benefit.
• The medical professionals will also be permitted to take-up sabbatical for translational and commercialisation of their innovation through their start-up company set-up following institute’s permission.

Given word: 'COMPARE'

Each consonant is changed to the letter following it in the English alphabetical order,

and each vowel is changed to the letter preceding it in the English alphabetical order.

Then,

Here, two letters 'D and N' are repeated twice in the letter cluster.

Hence, the correct answer is Option (2).

The correct answer is '$\large{1\over 2}$'.

Key Points

• Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

V = IR          

• Where V is the voltage difference, I is current passes through conductor and R is the resistance.
• A conductor is connected to a battery of 2V. Let V1 be the potential difference across the conductor, then

 V₁ = IR = 2 ...(1)

• When a battery of 4V is connected, the potential difference becomes V2.

V₂ = I2 R = 4....(2)

• Divede equation (1) by equation (2) .

$\large{V1\over V2} = {IR\over I2R} ={2\over 4} = {1\over 2}$

Shortcut Trick Let x = 20a and y = 20b, where a and b are co-prime numbers. Given x + y = 320 → 20(a + b) = 320 → a + b = 16. Pairs (a, b) such that HCF(a, b) = 1 and a < b: (1, 15), (3, 13), (5, 11), (7, 9). ∴ The correct answer is 4. Alternate Method

Given: Sum of x and y = 320, HCF = 20, and x < y. Formula: If HCF of two numbers is H, then the numbers are Ha and Hb, where a and b are co-prime. ⇒ 20a + 20b = 320 ⇒ 20(a + b) = 320 ⇒ a + b = 320 ÷ 20 = 16 ⇒ Possible pairs (a, b) where a < b and HCF(a, b) = 1: ⇒ Case 1: a = 1, b = 15 (Co-prime) ⇒ Case 2: a = 3, b = 13 (Co-prime) ⇒ Case 3: a = 5, b = 11 (Co-prime) ⇒ Case 4: a = 7, b = 9 (Co-prime) ∴ The correct answer is 4. Additional Information Co-prime Numbers Two numbers are said to be co-prime if their Highest Common Factor (HCF) is exactly 1. Product Property For any two numbers x and y, the product of numbers = HCF × LCM. Number Representation Any two numbers can always be expressed as Hx and Hy, where H is the HCF and x, y are co-prime integers.

Shortcut Trick

For any quadratic equation ax² + bx + c = 0, if the signs of a and c are opposite (i.e., a × c < 0), the discriminant D will always be greater than zero.

In √3x² + 6x − √3 = 0, we have a = √3 and c = −√3.

Since a × c = −3 (negative), the roots are guaranteed to be real and distinct.

∴ The correct answer is The roots are real and distinct.

Alternate Method

Given:

Quadratic Equation: √3x² + 6x − √3 = 0

Comparing with the standard form ax² + bx + c = 0:

a = √3, b = 6, c = −√3

Formula Used:

The nature of roots is determined by the Discriminant (D) = b² − 4ac.

Calculations:

⇒ D = (6)² − 4 × (√3) × (−√3)

⇒ D = 36 − 4 × (−3)

⇒ D = 36 + 12

⇒ D = 48

⇒ Since D > 0 (48 > 0), the roots of the given quadratic equation are real and distinct.

∴ The correct answer is The roots are real and distinct.

Additional Information

Nature of Roots Summary

For a quadratic equation ax² + bx + c = 0, the nature of roots depends on D = b² − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are non-real (imaginary).

Quadratic Formula

The roots can be calculated using the formula: x = (−b ± √D) ÷ 2a.

Sum and Product of Roots

Sum of roots = −b/a and Product of roots = c/a.