SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4) (Previous Year Paper)

The pattern followed here is:

We have to put the mathematical signs to sequentially replace the * signs and balance the given equation.

Let's check each option one by one.

Option 1) × ÷ + -

Given: 16 * 3 * 2 * 11 * 9 = 22

⇒ 16 × 3 ÷ 2 + 11 - 9 = 22

⇒ 16 × 1.5 + 11 - 9 = 22

⇒ 24 + 11 - 9 = 22

⇒ 35 - 9 = 22

⇒ 26 ≠ 22 

⇒ LHS ≠ RHS

Option 2) × ÷ − +

Given: 16 * 3 * 2 * 11 * 9 = 22

⇒ 16 × 3 ÷ 2 - 11 + 9 = 22

⇒ 16 × 1.5 - 11 + 9 = 22

⇒ 24 - 11 + 9 = 22

⇒ 33 - 11 = 22

⇒ 22 = 22

⇒ LHS = RHS

Option 3) ÷ × + +

Given: 16 * 3 * 2 * 11 * 9 = 22

⇒ 16 ÷ 3 × 2 + 11 + 9 = 22

⇒ 5.33 × 2 + 11 + 9 = 22

⇒ 10.6 + 11 + 9 = 22

⇒ 30.6 ≠ 22

⇒ LHS ≠ RHS

Option 4) ÷ + × ÷

Given: 16 * 3 * 2 * 11 * 9 = 22

⇒ 16 ÷ 3 + 2 × 11 ÷ 9 = 22 

⇒ 5.33 + 2 × 1.22 = 22

⇒ 5.33 + 2.44 = 22

⇒ 7.77 ≠ 22

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 2".

The pattern followed here is:

Find which of the following equation will be not correct.

Let's check each option one by one:

Option 1) 8 × 3 ÷ 6 + 9 – 7 = 2

Given: 7 and 9

⇒ 8 × 3 ÷ 6 + 7 – 9 = 2

⇒ 8 × 0.5 + 7 - 9 = 2

⇒ 4 + 7 - 9 = 2

⇒ 11 - 9 = 2

⇒ 2 = 2

⇒ LHS = RHS

Option 2) 7 + 6 – 9 × 4 ÷ 2 = 2

Given: 7 and 9

⇒ 9 + 6 – 7 × 4 ÷ 2 = 2

⇒ 9 + 6 - 7 × 2 = 2

⇒ 9 + 6 - 14 = 2

⇒ 15 - 14 = 2

⇒ 1 ≠ 2

⇒ LHS ≠ RHS

Option 3) 9 + 4 × 3 – 7 ÷ 1 = 10

Given: 7 and 9

⇒ 7 + 4 × 3 – 9 ÷ 1 = 10

⇒ 7 + 4 × 3 - 9 = 10

⇒ 7 + 12 - 9 = 10

⇒ 19 - 9 = 10

⇒ 10 = 10

⇒ LHS = RHS

Option 4) 9 × 3 + 4 ÷ 2 – 7 = 14

Given: 7 and 9

⇒ 7 × 3 + 4 ÷ 2 – 9 = 14

⇒ 7 × 3 + 2 - 9 = 14

⇒ 21 + 2 - 9 = 14

⇒ 23 - 9 = 14

⇒ 14 = 14

⇒ LHS = RHS

Hence, the correct answer is "Option 2".

The logic followed here is:

Let's check each option one by one:

Option 1) EUT

Option 2) RHG

Option 3) TRQ

Option 4) TFE

Hence, the correct answer is "TRQ".

The position of the English alphabet letters is given below:

    

Hence, the correct answer is "MXJY".

The pattern followed here is:

Given:

Hence, the correct answer is "Option 3".

The pattern followed here is:

Trembling : Fear → Trembling means shaking slightly in a way that you cannot control, for example, because angry, excited, or in fear.

Similarly,

Sigh : Relief → Sigh means to take a long deep breath of Relief.

Hence, the correct answer is "Relief".

The pattern followed here is:

Interchanging the given two numbers and find which the following equation will not correct.

Let's check each option one by one.

Option 1) 4 × 3 - 8 ÷ 2 + 7 = 11

Given: 4 and 2

⇒ 2 × 3 - 8 ÷ 4 + 7 = 11

⇒ 2 × 3 - 2 + 7 = 11

⇒ 6 - 2 + 7 = 11

⇒ 13 - 2 = 11

⇒ 11 = 11

Option 2) 8 ÷ 4 × 2 - 6 + 9 = 18

Given: 4 and 2

⇒ 8 ÷ 2 × 4 - 6 + 9 = 18

⇒ 4 × 4 - 6 + 9 = 18

⇒ 16 - 6 + 9 = 18

⇒ 25 - 6 = 18

⇒ 19 ≠ 18 

Option 3) 4 - 8 × 3 + 2 ÷ 1 = –18

Given: 4 and 2

⇒ 2 - 8 × 3 + 4 ÷ 1 = –18

⇒ 2 - 8 × 3 + 4 = - 18

⇒ 2 - 24 + 4 = - 18

⇒ 6 - 24 = - 18

⇒ - 18 = - 18

Option 4) 6 × 4 - 8 ÷ 2 + 7 = 17

Given: 4 and 2

⇒ 6 × 2 - 8 ÷ 4 + 7 = 17

⇒ 6 × 2 - 2 + 7 = 17

⇒ 12 - 2 + 7 = 17

⇒ 19 - 2 = 17

⇒ 17 = 17

Hence, the correct answer is "Option 2".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given statements:

Statements:

Some benches are tables.

Some tables are chairs.

Some chairs are pencils.

Conclusions:

I. Some benches are chairs → Does not follow → As some benches are tables and some tables are chairs. So some benches are chairs is possible but not definitely followed.

II. Some tables are pencils → Does not follow ​→ As some tables are chairs and some chairs are pencils. So some tables are pencils is possible but not definitely followed.

III. Some pencils are chairs → Follow ​→ As some chairs are pencils. So some pencils are chairs is definitely followed.

IV. Some pencils are tables → Does not follow ​→ As some tables are chairs and some chairs are pencils. So some pencils are tables is possible but not definitely followed.

So, only conclusion III follows.

Hence, the correct answer is "Option 2".

The pattern followed here is:

1. We are taking figures (1) & (2) together.

Here, in the figure numbers, 2 and 3 are common in both the dice, and 4 faces opposite to 5.

2. We are taking figures (2) & (3) together.

Here, in the figure numbers, 5 and 2 are common in both the dice and 3 faces opposite to 6.

Opposite pairs are:-

⇒ 4 ⇔ 5

⇒ 3 ⇔ 6

⇒ 2 ⇔ 1

So, 3 is the number on the face opposite to 6.

Hence, the correct answer is "3".

The pattern followed here is:

Telescope : Distant Objects → A telescope is a tool that astronomers used to form magnified images of distant objects.

Similarly,

Microscope : Tiny Objects → A microscope is a tool that can be used to observe small and tiny objects.

Hence, the correct answer is "Tiny Objects".

The pattern followed here is:

The correct mirror image of the given figure when the mirror is held on the AB side.

Hence, the correct answer is "Option 1".

The logic followed here is:

‘HAIRCAP’ is written as ‘IAHRPAC’

And,

'LEADMAN' is written 'ASELDNAM'

Similarly,

‘FACTFUL’ be written '?'

Hence, the correct answer is "CAFTLUF".

The pattern followed here is:

The given words are arranged according to the English dictionary order.

3. Ambience 2. Ambiguous 6. Ambivalent 7. Ameliorate 5. Amorphous 1. Amphibian 4. Amplify

Hence, the correct answer is "3, 2, 6, 7, 5, 1, 4".

By using the symbols in the table given below, we can draw the following family tree:

Given:

‘A @ B’ means ‘A is the husband of B’.

‘A & B’ means ‘A is the father of B’.

‘A # B’ means ‘B is the son of A’.

Given: S @ T # P @ Q # R & V

Clearly, T is the Mother-in-law of Q.

Hence, the correct answer is "Mother-in-law".

The pattern followed here is:

Given: 5, 12, 26, ?, 110, 222

Hence, the correct answer is "54".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given statements.

Statements:

I. No tyre are white.

II. All grey are white.

Conclusions:

I. No white is tyre → Follow → As no tyre are white. So no white is tyre is definitely followed.

II. No tyre is grey → Follow → As no tyre are white and all grey are white. So no tyre is grey is definitely followed.

III. Some white are not grey → Does not follow → As all grey are white. So some white are not grey is not definitely followed.

So, Both conclusions I and II follow.

Hence, the correct answer is "Option 3"

The logic followed here is:

Logic: Vowel series:- A, E, I, O, U

Hence, the correct answer is "IBCD".

The pattern followed here is:

1. Arrow shifted 90º degrees anti-clockwise direction and followed the same pattern.
   

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Hence, the correct answer is "Option 1".

The logic followed here is:

Logic:- Addition of all letters + 3 = Code.

'ICE’ is coded as '20'

And,

'HOT' is coded as '46'

Similarly,

'POT' is coded as '?'

Hence, the correct answer is "54".

The pattern followed here is:

Logic: ${\sqrt{First Number} }$ : (First number)² + First number = Second number.

Let's check them one by one.

1. 16 : 20

⇒ ${ \sqrt{16} }$ = 4 : (4)² + 4 

⇒ 16 + 4 = 20

And,

2. 49 : 56

⇒ ${ \sqrt{49} }$ = 7 : (7)2 + 7

⇒ 49 + 7 = 56

Similarly,

3. 256 : ?

⇒ ${ \sqrt{256} }$ = 16 : (16)2 + 16

⇒ 256 + 16 = 272

Hence, the correct answer is "272".

The pattern followed here is:

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

1. (2, 4, 20)

⇒ (2)² + (4)²

⇒ 4 + 16 = 20

And,

2. (4, 5, 41)

⇒ (4)2 + (5)2

⇒ 16 + 25 = 41

Let's check each option one by one.

Option 1) (9, 2, 86)

⇒ (9)2 + (2)2

⇒ 81 + 4 = 85 ≠ 86. (Incorrect)

Option 2) (4, 3, 25)

⇒ (4)2 + (3)2

⇒ 16 + 9 = 25 = 25. (Correct)

Option 3) (5, 3, 32)

⇒ (5)2 + (3)2

⇒ 25 + 9 = 34 ≠ 32. (Incorrect)

Option 4) (7, 3, 59)

⇒ (7)2 + (3)2

⇒ 49 + 9 = 58 ≠ 59. (Incorrect)

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: (Third number × second number) = First number.

1. (76, 4, 19)

⇒ (19 × 4) = 76

2. (98, 2, 49)

⇒ (49 × 2) = 98

Let's check each option one by one;

Option 1) (84, 12, 4)

⇒ (12 × 4) = 48 ≠ 84. (Incorrect)

Option 2) (72, 4, 18)

⇒ (18 × 4) = 72. (Correct)

Option 3) (99, 3, 66)

⇒ (66 × 3) = 198 ≠ 99. (Incorrect)

Option 4) (88, 2, 22)

⇒ (88 × 2) = 176 ≠ 88. (Incorrect)

Hence, the correct answer is "Option 2"

By using the symbols in the table given below, we can draw the following family tree:

X × Y means that X is the mother of Y.

X - Y means that X is the father of Y.

X ÷ Y means that X is the sister of Y.

Given relation code:

Find: Which expression shows that P is the maternal grandfather of R.

Let's check each option one by one.

Option 1) Q - P × R

Q is the Father of P, and P is the Mother of R.

Here, P is the mother of R. (Incorrect)

Option 2) P - Q ÷ R

P is the Father of Q, and Q is the Sister of R.

Here, P is the father of Q. (Incorrect)

Option 3) P - Q - R

P is the Father of Q, and Q is the father of R.

Here, P is the paternal grandfather of R. (Correct)

Option 4) P × Q - R

P is the Mother of Q, and Q is the Father of R.

Here, P is the maternal grandmother of R. (Incorrect)

Hence, the correct answer is "Option 3".

The pattern followed here is:

1. The middle figure is rotated in a 45º clockwise direction.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: (First number × 4) - 4 =  Second number.

Let's check each option one by one.

Option 1) 15 - 56

⇒ (15 × 4) - 4 

⇒ 60 - 4 = 56

Option 2) 13 - 48

⇒ (13 × 4) - 4 

⇒ 52 - 4 = 48

Option 3) 11 - 39

⇒ (11 × 4) - 4 

⇒ 44 - 4 = 40 ≠ 39.

Option 4) 17 - 64

⇒ (17 × 4) - 4 

⇒ 68 - 4 = 64

Hence, the correct answer is "Option 3".

The correct answer is Tamil Nadu.

Key Points

• Neyveli is a town located in the Cuddalore district of the Indian state of Tamil Nadu.
• It is home to one of the largest lignite reserves in the country, known as the Neyveli Lignite Mines.
• Here are some key points to help explain the significance of Neyveli's lignite reserves:
• Size and scope:
• The Neyveli Lignite Mines are spread over an area of 64 square kilometers and contain reserves of around 6,000 million tonnes of lignite.
• This makes it one of the largest lignite mining operations in the world.
• Importance to the energy sector:
• Lignite is a type of coal that is relatively low in carbon content and is primarily used for generating electricity.
• Economic impact:
• The Neyveli Lignite Mines is a major employer in the region, providing direct and indirect employment opportunities to thousands of people.
• Environmental concerns:
• Lignite is considered a relatively dirty form of energy due to its high carbon emissions and other environmental impacts.
• The mining and use of lignite at Neyveli have been criticized for their contribution to air and water pollution, as well as their impact on the local ecosystem and communities.
• Overall, the lignite reserves at Neyveli are an important resource for the energy sector in India, but they also raise important questions about environmental sustainability and the trade-offs between economic development and environmental protection.

Additional Information Types of Coal

• Anthracite:
• Anthracite coal has the best coal quality.
• In India Anthracite found only in Jammu and Kashmir.
• Anthracite has more than 80% carbon content.
• Bituminous:
• Bituminous is the second-best quality of coal.
• Bituminous has 60 to 80 % Carbon Content
• Bituminous is the most popular coal in commercial use.
• Lignite:
• Lignite is a low-grade brown coal
• Lignite are used for the generation of electricity.
• The principal lignite reserves are in Neyveli in Tamil Nadu
• Peat :
• Peat is the poorest quality of coal.
• Peat has less than 40% carbon content

The correct answer is 1530.

Key Points

• Babur
• At the age of twelve, Babur faced revolt as he succeeded to the throne of Fergana in Akhsikent.
• Two years later, he took Samarkand, only to lose Fergana not long after.
• In his attempt to reconquer Fergana, he lost control of Samarkand.
• Babur was compelled to abdicate his kingdom following the Uzbeg invasion, another Mongol tribe.
• At the age of 22, he eventually conquered Kabul in 1504 after years of traveling.
• Later, in the year 1526, he took Delhi and Agra after defeating Ibrahim Lodi, in the renowned battle of Panipat.

 Additional Information Some Important Mughal Emperor

The correct answer is Land reclamation.

Key Points

• Land reclamation
• Land reclamation is the process of creating new land from the ocean, riverbeds, or lake beds.
• The process of reconverting disturbed land to its former or other productive uses.

Additional Information

• Deforestation:
• Deforestation is the process of removing trees from forests (or other places) on a big scale in order to facilitate human actions.
• It is a major environmental issue.
• Some of the major causes of deforestation are:
• Agriculture.
• Logging.
• Mining and urban expansion.
• Poaching
• Poaching is an illegal hunting process.
• Poachers are illegitimate hunters who kill wild animals for their different body parts.
• These are some examples of animals that are killed for poaching: Crocodiles, rhinos, elephants, lions, and deer.
• ​Indiscriminate use of fertilizers has led to soil pollution, water pollution, and air pollution.
• Effects of excess use of fertilizers:
• Oxygen Depletion:
• When manure or commercial fertilizers enter surface water, the nutrients they release stimulate microorganism growth.
• The growth and reproduction of microorganisms reduce the dissolved oxygen content of the water body.
• Ammonia Toxicity:
• Ammonia-contaminated runoff from fresh manure application sites is toxic to aquatic life.
• At high levels, ammonia in surface water will kill fish.
• Fish are relatively sensitive to ammonia in water.

The correct answer is Meghalaya.

Key Points

• Drums Festival
• Hundred Drum Festival also known as the 'Wangala Festival, the Wangala Festival is a traditional festival in the northeastern Indian state of Meghalaya.
• A group of 30 dancers with 10 drums would form a group and 10 such groups will be there.
• Thus, a total of 100 drummers and 300 dancers make up what is now known as the “100 Drums Wangala Festival”.
• Every year the festival is celebrated for 3 days during the month of November.
• Ordinary Garo people pay gratitude and reverence to Missi Saljong or 'Pattigipa Ra'Rongipa' (Great Giver) for blessing humans with a prosperous harvest for the season.

Important Points 

• The Wangala festival marks the end of a period of toil, that brings good results to the fields which also signifies the onset of winter.
• It is also celebrated in honour of the Sun God that marks the end of the long harvest season.
• Wangala is celebrated with different forms of dance.
• These dances are performed on the tunes of folk songs that are played on drums and primitive flute.
• Additionally, these flutes are made of buffalo horns.
• On the first day of the festival, people celebrate it with a ceremony called Ragula.
• This ceremony is performed in the house of the village’s chief.
• Then on the second day of celebration, which is called Kakkat, people begin the ceremony by dancing to the rhythms of long oval-shaped drums
• In this celebration, young and old join together while men play the drums and women perform traditional dance forms. The dance form is known as Dama Dagota.​

Additional Information

• Meghalaya:
• Lok Sabha seats - 2.
• Rajya Sabha seats - 1.
• State Animal - Clouded leopard.
• State Bird - Common hill myna.
• National Parks - Balphakram National Park, Nokrek Ridge National Park.

The correct answer is Assam.

Key Points

• The first-night navigation mobile application in rivers in the country was launched for ferries on the Brahmaputra river in Assam, in Feb 2022.
• It has been developed by the transport department in association with K Raju, the principal scientist of IIT Madras, and will survey the draft of the rivers.
• Ten Aadhar-based contactless services of the department have been also launched.

Important Points 

• These services are expected to reduce footfalls at district transport offices (DTOs) by about four lakh annually.
• An MoU was also signed between the Common Service Centres (CSCs) under the ministry of information technology and transport department for facilitating people at the panchayat level to avail the online services.
• A total of 13,568 CSCs in Assam will enable people to obtain online services of the department.
• The ten services launched by the department are six Vahan software-based services relating to vehicles and four Sarathi software-based services relating to driving license.

Additional Information

• Assam:
• Number of districts - 33.
• Lok Sabha seats - 14.
• Rajya Sabha seats - 7.
• State Animal - Indian rhinoceros.
• State Bird - White-winged duck.
• National Parks - Dibru-Saikhowa National Park, Kaziranga National Park, Manas National Park, Nameri National Park, Rajiv Gandhi Orang National Park.
• Dams - Subansiri Lower Dam(Subansiri River), Karbi Langpi Dam(Borpani River).

The correct answer is delta.

Key Points

• About River Delta-
• At the mouth of the delta river, there is a triangular form of deposition of sediments brought by it.
• First introduced by Herodotus to the Tikoune Delta of the Nile in the 5th century B.C. Hitherto, 150 large deltas have been formed.
• All major rivers have deltas.
• Rivers forming Delta-
• Ganga
• Brahmaputra
• Godavari
• Krishna
• Cauvery/Kaveri
• Mahanadi
• Note-
• The Narmada, Sabarmati and Tapti rivers of India do not form deltas.
• These rivers form estuaries instead of river deltas.

The correct answer is Right to Property.

Key Points

• The 44th Constitutional amendment act 1978 deleted the right to property from the list of Fundamental Rights.
• Right to Property is no more a fundamental right, only a legal right.
• The right to property was listed under Article 31 before its deletion.
• At present right to property is listed under Article 300A as a legal right.
• In the original constitution, there were seven categories of fundamental rights in India.
• After the deletion of the Right to property by the 44th Amendment, it was reduced to six.​

Additional Information

• Now there are six categories of fundamental rights in India.
• Right to Equality.
• Right to Freedom.
• Right against Exploitation.
• Right to Freedom of Religion.
• Cultural and Educational Rights.
• Right to Constitutional Remedies.​

Important Points

• Fundamental rights are justiciable.
• The Supreme court and the High Courts are considered as the guardians of Fundamental rights in India.

The correct answer is Pyrenoids.

Key Points

• Pyrenoids
• Pyrenoid is a protein-rich body found in the members of Chlorophyceae or green algae. It is used for the storage of reserved food material.
• It may be one to many in number in different species of algae.
• The chloroplast is a double membrane-bound cell organelle.
• Out of the two membranes, the inner membrane is relatively less permeable (the outer membrane contains porins)
• The number & shape of chloroplast also varies from one species of algae to another.

Additional Information

• Stomata ​
• Stomata are the tiny pores on the leaves which play a major role in the exchange of gases.
• The intake of carbon dioxide and the outtake of oxygen both takes place through these pores.
• The respiration in leaves takes place through these tiny pores.
• Evaporation of water from the leaf surface occurs through the stomata.
• Thus, the stomata help in the process of transpiration.
• It also closes or opens its pores based on climatic conditions to maintain the moisture balance.
• It remains open during the day and closed at night. This closure at night prevents water from escaping through open pores.
• Carotenoids
• arotenoids also called tetraterpenoids, are yellow, orange, and red organic pigments that are produced by plants and algae, as well as several bacteria and fungi.
• Carotenoids give the characteristic color to pumpkins, carrots, corn, tomatoes, canaries, flamingos, salmon, lobster, shrimp, and daffodils.
• Chlorophyll
• ​Chlorophyll or leaf green is a porphyrin derivative with magnesium (Mg) as the central atom and is hence a metal complex dye.
• It is present in the chloroplasts in all green parts of plants as a mixture of blue-green chlorophyll a and yellow-green chlorophyll b and constitutes the catalyst for photosynthesis.
• Chlorophylls are porphyrins, whose molecules contain a flat ring of four-linked heterocyclic groups, based upon magnesium.
• Chlorophyll is a green photosynthetic pigment found in plants, algae, and cyanobacteria.

The correct answer is Ilbert Bill.

Key Points

• The 'Ilbert Bill' was introduced in 1883 under the Viceroyship of Lord Ripon.
• Ilbert Bill was drafted by Sir Courtenay Ilbert on 9th February 1883 during the viceroyship of Lord Rippon.
• The main objective behind the introduction of this bill is to allow Indian judges to try cases in session courts involving Britishers.​

Additional Information

• The introduction of the bill had roused anger and resentment among people, especially English women and British tea and indigo planters in Bengal.
• English women argued that Bengali women were not respected by their male counterparts, so they shouldn't get the power to try cases involving Britishers.
• On the contrary, Bengali women who supported the bill said that they were more educated and had good academic records than English Women.

The correct answer is Murshidabad.

Key Points

• Murshid Quli Khan, also known as Mohammad Hadi and born as Surya Narayan Mishra, was the first Nawab of Bengal, serving from 1717 to 1727.
• Born a Hindu in the Deccan Plateau c. 1670, Murshid Quli Khan was bought by Mughal noble Haji Shafi.
• After Shafi's death, he worked under the Divan of Vidarbha, during which time he piqued the attention of the then-emperor Aurangzeb, who sent him to Bengal as the divan c. 1700.
• However, he entered into a bloody conflict with the province's subahdar, Azim-us-Shan.
• After Aurangzeb's death in 1707, he was transferred to the Deccan Plateau by Azim-us-Shan's father the Mughal Emperor Bahadur Shah I.
• The capital was shifted from Dhaka to Murshidabad.

The correct answer is Micronutrients.

Key Points

• Macronutrients in animal nutrition include carbohydrates, proteins, and fats, which are required in large amounts for energy, growth, and maintenance of body functions.
• Minerals such as calcium, phosphorus, and magnesium are also considered macrominerals.
• Since iron, iodine, and zinc are required in much smaller amounts than these macronutrients, they do not fall into this category.
• Micronutrient
• Micronutrients are nutrients required in much smaller amounts compared to macronutrients.​
• Iron (Fe): Iron is a critical component of hemoglobin, which is responsible for oxygen transport in the blood. It is also part of various enzymes and proteins involved in energy production and metabolism. A deficiency of iron can lead to anemia and other health issues.
• Iodine (I): Iodine is essential for the production of thyroid hormones, which regulate metabolism, growth, and development. A deficiency in iodine can lead to goiter and hypothyroidism, affecting the overall health and metabolic rate of the animal.
• Zinc (Zn): Zinc is involved in numerous aspects of cellular metabolism, acts as a cofactor for over 300 enzymes, and plays a role in immune function, protein synthesis, wound healing, DNA synthesis, and cell division. Zinc deficiency can impair growth, immune function, and reproduction.

Additional Information

• Steroid hormone inducers are substances that influence the production or action of steroid hormones (like cortisol, estrogen, testosterone). This category does not apply to iron, iodine, or zinc as these minerals do not directly induce steroid hormone production.

The correct answer is Pandit Hariprasad Chaurasia.

Key Points

• Pandit Hariprasad Chaurasia
• Hariprasad Chaurasia is an Indian film music director and classical flutist, who plays the BANSURI, in the Hindustani classical tradition.
• Chaurasia was born in Allahabad (1938) (officially called Prayagraj) in the state of Uttar Pradesh.
• Awards
• Sangeet Natak Academy - 1984
• Padma Bhushan - 1992
• Padma Vibhushan - 2000​

Additional Information

• Pandit Kumar Gandharva
• Pandit Kumar Gandharva was born in Belgaum, Karnataka on 8th April 1924.
• He was legend in the field of Hindustani classical music.
• Kumar Gandharva broke the traditional method of singing the Gharana (a form of classical music).
• Pandit Ravi Shankar (1920-2012):
• He was an Indian sitar virtuoso and a composer.
• He became the world's best-known exponent of North Indian classical music, in the second half of the 20th century and influenced many other musicians throughout the world.
• Ravi Shankar was awarded India's highest civilian honour, the Bharat Ratna in 1999 and received 4 Grammy Awards for his outstanding work.
• Pandit Shivkumar Sharma
• Pandit Shivkumar Sharma was a Santoor player from the Indian state Jammu and Kashmir.
• He co-produced a concept album, Call of the Valley (1967), in 1967 with flautist Hariprasad Chaurasia and guitarist Brij Bhushan Kabra.
• Shivkumar is the recipient of national and international awards, including honorary citizenship of Baltimore City, the USA in 1985, the 1986 Sangeet Natak Akademi Award, 1991 Padma Shri and 2001 Padma Vibhushan.

The correct answer is product method.

Key Points

• Product Method:
• Product or value added method is a way of computing the national income of a country.
• This system is also known as output or inventory method. This method calculates national income by adding value to a product at every stage of its production.

Additional Information

• expenditure method
• The expenditure method is a system for calculating gross domestic product (GDP) that combines consumption, investment, government spending, and net exports.
• It is the most common way to estimate GDP. It says everything that the private sector, including consumers and private firms, and government spend within the borders of a particular country, must add up to the total value of all finished goods and services produced over a certain period of time.
• consumption method
• These consumption inventory methods offer a radically different method of accounting for a community's contribution to greenhouse gas emissions.
• Traditional inventories evaluate the emissions associated with a diverse set of activities within a geographic area.​
• Income Method:
• In the income method, the national income is measured by adding up the pretax income generated by the individuals and companies in the economy.
• It consists of income from wages, rent of buildings and land, interest on capital, profits, etc.

The correct answer is Uttarakhand.

Key Points

• Chholiya dance ​
• Chholiya is a dance form which originated in the Kumaon division in the state of Uttarakhand and in some parts of Sudur Paschim province of Nepal.
• It has today become a symbol of Kumaoni culture.
• Kumaoni is an Indo-Aryan language spoken by over two million people of the Kumaon region of the state of Uttarakhand in northern India and parts of the Doti region in Western Nepal.
• It is basically a sword dance accompanying a marriage procession but now it is performed on many auspicious occasions.
• ​

Additional Information

• Mukhota Dance is a dance form in which the participants wear traditional dresses and masks representing their deities and evil demons and highlighting various folk tales and the culture of Uttarakhand.
• Jhora dance is a springtime celebration performed by the local people by moving around in circles and highly popular dance in the Kumaon Himalayas.
• The USP of this dance is that it aims to break caste barriers, thus allowing both higher and lower caste people to perform it together.
• Pandav Lila or Pandav Nritya is a ritual re-enactment of stories from the Hindu epic Mahabharata, through singing, dancing and recitation, that is practised in the Garhwal region of Uttarakhand.

The correct answer is Argentina.

Key Points

• The FIBA Basketball World Cup 2023 will take place in the Philippines, Japan, and Indonesia from August 25 to September 10.
• The 32 participating teams will play in 92 games played over 16 days.

Additional Information

• About FIBA:
• The International Basketball Federation is an association of public associations that governs the sport of basketball worldwide.
• Firstly known as the Fédération Internationale de Handbasket- ball amateur (hence FIBA), in 1989 it dropped the word amateur from its name but retained the acronym.
• FIBA defines the rules of basketball, specifies the outfit and installations needed, organizes transnational competitions, regulates the transfer of athletes across countries, and controls the appointment of transnational arbiters.
• An aggregate of 213 public coalitions are now members, organized since 1989 into five zones Africa, Americas, Asia, Europe, and Oceania.

The correct answer is The Damodar.

Key Points

• Damodar River:
• It was earlier known as the" River of Sorrows" as it used to flood many areas Of Bardhaman, Hooghly, Howrah, and Medinipur districts.
• Even now the floods sometimes affect the lower Damodar Valley, but the Havoc it wreaked in earlier years is now a matter of history.
• Physical Characteristics 
• Source  Location- Chulha Pani ( Chandwa/Tori), Latehar, Chota Nagpur Plateau(Jharkhand)
• Mouth location- Hooghly river, Howrah district, (West Bengal)
• Length- 592 km
• Tributaries
• Left Tributaries- Barakar, Konar, Jamuna
• Right Tributaries- Sali (West Bengal)​

Additional Information

• The Narmada
• The Narmada is a river that originates in the Amarkantak hills of Madhya Pradesh, India and flows through the states of Madhya Pradesh, Maharashtra, and Gujarat before emptying into the Arabian Sea.
• It is the fifth-largest river in India, with a length of approximately 1,312 kilometers.
• The Koshi
• The Koshi is a transboundary river that originates in Tibet.
• It is also known as the Saptakoshi River, meaning "Seven Rivers" in Sanskrit, as it is formed by the convergence of seven smaller rivers in Nepal.
• The Koshi River is known for its unpredictable and destructive nature, and it is often called the "sorrow of Bihar" due to the frequent floods that cause significant damage to the state of Bihar in India.
• The Tapi
• The Tapi river, also known as the Tapti, is a major river in central India that originates in the Satpura Range of Madhya Pradesh and flows through Maharashtra and Gujarat before emptying into the Arabian Sea.
• The river basin is home to several large dams, including the Ukai Dam in Gujarat.

The correct answer is Ahmedabad and Mumbai.

Key Points

• Ahmedabad and Mumbai bullet train project
• The Ahmedabad and Mumbai High-Speed Rail project was jointly inaugurated by the Prime Ministers of India and Japan, Narendra Modi and Shinzo Abe, in September 2017.
• The two leaders laid the foundation stone for the project at a ceremony held in Ahmedabad.
• The first bullet train project in India, officially known as the Mumbai-Ahmedabad High-Speed Rail (MAHSR).
• The project aims to run a bullet train at 320 kmph along a high-speed rail (HSR) track between the cities of Mumbai and Ahmedabad, covering a distance of approximately 508 km.
• The project is expected to reduce travel time between the two cities from the current 7-8 hours to just 2-3 hours.

The correct answer is CH3COOH.

Key Points

• Vinegar (CH3COOH)
• Vinegar is also known as acetic acid or sour wine.
• Vinegar is a sour-tasting liquid that is commonly used as a condiment in cooking and food preparation.
• There are several types of vinegar available, each with a unique flavor and usage.
• For example, balsamic vinegar is made from grapes and is commonly used in Italian cuisine.
• Apple cider vinegar is made from apples and is used in several cuisines.
• Rice vinegar is commonly used in **Asian cuisine.**​

Additional Information

• ​HCOOH
• HCOOH is the chemical formula for formic acid.
• It is an organic acid that occurs naturally in some insects and plants, such as ants and stinging nettles.
• (COOH)2
• (COOH)2 is the chemical formula for oxalic acid.
• It is a weak acid and is highly soluble in water.
• C6H5COOH
• C6H5COOH is the chemical formula for benzoic acid.
• It is a white crystalline organic compound.
• Benzoic acid is widely used in the food, cosmetic, and pharmaceutical industries.

The correct answer is Spherometer.

Key Points

• Spherometer
• A spherometer is a precision instrument used to measure the radius of curvature of a spherical surface.
• It is commonly used in fields such as optics and mechanical engineering to measure the radii of curvature of lenses, mirrors, and other curved surfaces.

Additional Information

• Viscometer
• A viscometer is an instrument used to measure the viscosity or flow properties of fluids.
• There are many different types of viscometers, including capillary viscometers, rotational viscometers, and falling ball viscometers.
• They help to determine the shear rate, shear stress, and yield stress of fluids, which are used to predict how they will behave under various conditions.
• Verniercaliper
• A Vernier caliper is a precision measuring instrument used to measure the internal and external dimensions of an object with high accuracy.
• It consists of two scales, the main scale, and the Vernier scale.
• The main scale of the Vernier caliper is typically marked in millimeters or inches.
• The Vernier scale is a secondary scale that slides along the main scale and has smaller graduations, allowing for more precise readings.
• Screw gauge
• A screw gauge, also known as a micrometer screw gauge, is a precision measuring tool used to measure the diameter of small objects with high accuracy.
• It consists of a C-shaped frame, a spindle, a thimble, and a screw.

The correct answer is batsman is out.

Key Points

• In cricket, when the umpire raises their index finger above their head, it means that the batsman is out.
• This signal is commonly known as the "out" signal or the "dismissal" signal.
• This can happen in a number of ways, including being bowled, caught, stumped, or run out.
• The umpire's decision to give an "out" signal is based on a set of rules and guidelines, which are designed to ensure fairness and consistency in the game.
• The decision is typically made after careful observation and consideration of the circumstances of the dismissal.

Additional Information

• Cricket
• Cricket is a popular sport played in many countries around the world, particularly in countries like India, England, Australia, and South Africa.
• It is a bat-and-ball game played between two teams of eleven players each, with each team taking turns to bat and bowl.
• The game is played on a circular or oval-shaped field, with a rectangular 22-yard-long pitch in the center.
• The pitch is divided into two halves, with each team taking turns to bat and bowl on each half.

The correct answer is 12000, 10000.

Key Points

• Stone Age is divided into three periods, namely-
• Paleolithic or Old Stone Age, 2) Mesolithic or Middle Stone Age, and 3) Neolithic or New Stone Age.
• The word lithic is derived from the Greek lithos, meaning stone. Paleolithic means Old Stone Age, Mesolithic means Middle Stone Age, and Neolithic means New Stone Age.
• Mesolithic Age-
• The Mesolithic Era began about 12,000 years ago and went on for about 2,000 years.
• Also called the Middle Stone Age.
• The mesolithic Age was a much shorter period than the Palaeolithic, having lasted about ten thousand years in India.
• The technological hallmark of this period is tiny stone tools or microliths.
• In addition, the Mesolithic people also used non-microlithic tools made of flakes and blades.
• Microliths
• Microliths are stone tools which are of length from 1cm to 5 cm, these are shaped like blades and are made of stones such as – chert, chalcedony, agate etc.
• These tools are really small and sharp and have been found in different kinds of shapes such as triangles, crescents, trapezes, rhombus etc.

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Additional Information

• Paleolithic Age: Paleolithic Age was developed in the Pleistocene period. 
• Robert Bruce Foote was the first person to discover a Paleolithic Stone in India in 1863.
• The tools of this period were made of hard rock 'quartzite' and hence people this age was called "Quartzite Man".
• 'Palaeo' means Old and 'Lithic' means Stone. There was basically a Hunting and food-gathering culture
• Neolithic Age: Le Mesurier discover the tools and implementation of the Neolithic Age.
• Neolithic-Chalcolithic Culture as a Self Sufficient food economy was defined by V. Gardon Childe.
• Agriculture, Domestication of Animals, and polished and grinned stone tools were practices of this age.

The correct answer is Panchayat Raj System.

Key Points

• Panchayati Raj:
• Panchayati Raj was constitutionalized through the 73rd Constitutional Amendment Act of 1992.
• The term Panchayati Raj in India signifies the system of rural local self-government.
• It has been established in all the states of India by the Acts of the state legislatures to build democracy at the grass-root level.
• It is entrusted with rural development.
• 73rd Constitutional Amendment has added a new Part-IX entitled ‘the panchayats’ and a new 11th Schedule containing 29 functional items of the panchayats.​

Important Points 

• Important Committees related to Panchayati Raj:

Additional Information

• In 1959, Jawaharlal Nehru inaugurated the 1st generation panchayat at Nagaur in Rajasthan on 2nd October.
• National Panchayati Raj Day: 24 April.

The correct answer is Iron and Steel.

Key Points

• The  Iron and Steel Factories that started during the second five-year plan were-
• Bhilai - with the help of Russia - 1959.
• Rourkela - with the help of Germany - 1959.
• Durgapur - with the help of Britain - 1962.
• BHEL - Bhopal.

Additional Information

• The first industrial policy statement of India is known as Industrial Policy Resolution.
• It was announced in the year 1948.
• It defined the role of the State in industrial development both as an entrepreneur and authority.
• Industrial Policy Resolution,1948 states that India is going to have a Mixed Economic Model.
• The Industries (Development and Regula­tion) Act was passed in 1951.
• It was passed to implement the Industrial Policy Resolution, 1948.

The correct answer is Human embryo.

Key Points

• On July 20, 2022, Union government restricted the import of human embryos in accordance with the Surrogacy (Regulation) Act, 2021 and Assisted Reproductive Technology (Regulation) Act, 2021.
• Before this, such imports were restricted or prohibited except for research purposes.

Additional Information

• Embryo
• An embryo grows into a baby by the "Mitosis division".
• Mitosis involves the division of "body cells".
• Meiosis involves the division of "sex cells".
• In mitosis cell division, a cell divides into two cells that are similar to each other and have the same number of chromosomes.
• In meiosis cell division, a cell divides into four cells, and the number of chromosomes is halved.
• The mitosis division process has the following stages such as prophase, prometaphase, metaphase, anaphase, telophase, and cytokinesis.
• ​Women’s egg
• Women's egg cells which are necessary for reproduction are also called ovum.
• Oocytes are immature egg cells.
• Sperm is the male germ cell.
• Ovaries are female sex organs.
• Stem cell
• Stem cells are undifferentiated or partially differentiated cells in multicellular animals that can specialize in many types of cells and multiply endlessly to produce additional stem cells.
• In a cell lineage, they are the earliest form of cell.
• Tissue-specific stem cells (also referred to as somatic or adult stem cells) are more specialized than embryonic stem cells.
• Kidney
• The kidneys are two bean-shaped organs in our renal system.
• Kidneys comprise a pair of kidneys, a pair of ureters, a urinary bladder, and a urethra.
• Kidneys are located on either side of the backbone on the posterior surface.
• The kidneys perform many vital functions, including maintaining overall balance fluid, regulating, verifying & filtering minerals from the blood, etc.

The correct answer is Kamalini Asthana and Nalini Asthana.

Key Points

• The President of India bestowed PADMA SHRI on duo Nalini-Kamalini Asthana (Kathak), R Muthukannammal (Sadir), Padmaja Reddy (Kuchipudi) at a special function at Rashtrapathi Bhavan, New Delhi.
• Kamalini Asthana and Nalini Asthana are a sister duo from Agra in Uttar Pradesh known for their great performances of the Benaras Gharana style of Kathak.
• They are also known for their contributions to the popularisation of the Benaras Gharana style of Kathak both in India and abroad.
• In the year 2022, Govt of India conferred the Padma shri award, the third highest award in the Padma series of awards, on Kamalini Asthana and Nalini Asthana for their distinguished service in the field of art.
• The award is in recognition of his service as an "Acclaimed Kathak Dancer Duo from Agra known for teaching and propagating it globally".​

Additional Information

• Padma Awards
• Padma Awards one of the highest civilian Awards in the country are conferred in three categories, namely, Padma Vibhushan, Padma Bhushan and Padma Shri.
• The Awards are given in various disciplines/ fields of activities,
• Art, social work, public affairs, science and engineering, trade and industry, medicine, literature and education, sports, civil service, etc.
• Padma Vibhushan is awarded for exceptional and distinguished service.
• Padma Bhushan for distinguished service of a high order.
• Padma Shri for distinguished service in any field.
• The awards are announced on the occasion of Republic Day every year.
• These awards are conferred by the President of India.

Calculation:

Number of Business Analysts who joined the organisation in 5 years = 80 + 63 + 78 + 42 + 67

⇒ 330

Number of Sales Representatives who joined the organisation in 5 years = 50 + 46 + 38 + 34 + 22

⇒ 190

Difference = 330 - 190

⇒ 140

∴ The required answer is 140.

Given:

Aarif, Arun and Abraham can do a work in 12, 20 and 24 days, respectively.

They all begin together. Arun leaves the work 3 days and Abraham 6 days before its completion.

Concept used:

Total work = Efficiency × Time

Calculation:

Let the total time taken by them be x days

Now,

LCM of 12, 20, and 24 = 120 i.e total work

So, efficiency of Aarif = 120/12

⇒ 10

Efficiency of Arun = 120/20

⇒ 6

Efficiency of Abraham = 120/24

⇒ 5

According to the question,

x × 10 + (x - 3) × 6 + (x - 6) × 5 = 120

⇒ 10x + 6x - 18 + 5x - 30 = 120

⇒ 21x = 120 + 48

⇒ 21x = 168

⇒ x = 8

∴ The required time is 8 days.

Shortcut Trick

Volume of Cone = Volume of Cylinder (since water is transferred)

(1/3) × π × r_cone² × h_cone = π × r_cyl² × h_cyl

(1/3) × 20 × 20 × 27 = 15 × 15 × H

400 × 9 = 225 × H ⇒ H = 3600 ÷ 225 = 16 cm

∴ The correct answer is 16 cm.

Alternate Method

Given:

Internal radius of conical vessel (r₁) = 20 cm

Height of conical vessel (h₁) = 27 cm

Internal radius of cylindrical vessel (r₂) = 15 cm

Formula Used:

Volume of Cone = (1/3)πr²h

Volume of Cylinder = πr²h

Calculations:

⇒ Volume of water in cone = (1/3) × π × (20)² × 27

⇒ Volume of water in cone = π × 400 × 9 = 3600π cm³

⇒ Volume of water in cylinder = π × (15)² × H

⇒ 3600π = 225π × H

⇒ H = 3600 ÷ 225

⇒ H = 16 cm

∴ The correct answer is 16 cm.

Additional Information

Volume Conservation

When a liquid is poured from one container to another, the volume remains constant regardless of the shape change.

Curved Surface Area (CSA)

CSA of a cylinder is 2πrh and CSA of a cone is πrl, where l is the slant height √(r² + h²).

Relationship between Cone and Cylinder

If a cone and a cylinder have the same radius and height, the volume of the cylinder is three times the volume of the cone.

Given:

The average age of 6 members of a family is 40 years.

If the age of a guest is included, then the average age has increased by 12.5%.

Concept used:

Average = Sum of elements/number of elements

Calculation:

Sum of the age of 6 members of a family = 40 × 6

⇒ 240 years

If the age of a guest is included, then the average age has increased by 12.5%,

The average age of 7 persons = 40 × 112.5/100

⇒ 45 years

Sum of the age of 7 persons = 45 × 7

⇒ 315 years

Age of guest = 315 – 240 

⇒ 75 years

∴ The age of the guest is 75.

Shortcut Trick

The average age of six members of a family is 40 years,

After the addition of 1 member, the average age increases by 12.5% the average age becomes = 40 × 9/8 = 45 year 

The difference of average age is (45 - 40) = 5 year

So, the guest brings (5 × 7) = 35 year age extra

So, the age of the guest is (35 + 40) = 75 year

Calculation:

Number of employees in production = 5100 × 20%

⇒ 1020

Number of male employees in production = 2050 × 48%

⇒ 984

So, female production = 1020 - 984

⇒ 36

∴ The required answer is 36.

Given:

x = 222,

y = 223

z = 224 

Formula used:

x³ + y³ + z³ - 3xyz = (1/2)(x + y + z)[(x - y)² + (y - z)² + (z - x)²]

Calculation:

x3 + y3 + z3 - 3xyz = (1/2)(222 + 223 + 224)[(222 - 223)² + (223 - 224)² + (224 - 222)²]

⇒ x3 + y3 + z3 - 3xyz = (1/2)(669)[(1) + (1) + (4)]

⇒ x3 + y3 + z3 - 3xyz = 3 × 669 

⇒ x3 + y3 + z3 - 3xyz = 2007 

∴ The value of x3 + y3 + z3 - 3xyz is 2007.

Calculation:

% of cars of type P manufactured = 40%

% of cars of type R manufactured = 15%

% of cars of type U manufactured = 5%

Total % = 40 + 15 + 5

⇒ 60%

Number of cars manufactured = 440000 × 60%

⇒ 264000

∴ The required answer is 264000.

Shortcut Trick

Given sec A = 5/4, which is a 3-4-5 Pythagorean triplet where Hypotenuse = 5 and Base = 4.

Simplify the expression: tan A / (1 + tan²A) − sin A / sec A.

Using 1 + tan²A = sec²A, the first term becomes: (sin A / cos A) / sec²A = sin A × cos A.

The second term is: sin A / sec A = sin A × cos A.

Result = sin A × cos A − sin A × cos A = 0.

∴ The correct answer is 0.

Alternate Method

Given: sec A = 5/4 ⇒ H = 5, B = 4

Formula: P² = H² − B²; sin A = P/H; tan A = P/B; 1 + tan²A = sec²A

⇒ P = √(5² − 4²) = √(25 − 16) = √9 = 3

⇒ sin A = 3/5, cos A = 4/5, tan A = 3/4

⇒ Expression = [ (3/4) / (1 + (3/4)²) ] − [ (3/5) / (5/4) ]

⇒ Expression = [ (3/4) / (1 + 9/16) ] − [ 12/25 ]

⇒ Expression = [ (3/4) / (25/16) ] − 12/25

⇒ Expression = [ (3/4) × (16/25) ] − 12/25

⇒ Expression = 12/25 − 12/25 = 0

∴ The correct answer is 0.

Additional Information

Trigonometric Identities

Fundamental identities include sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Reciprocal Relations

sec A = 1/cos A, cosec A = 1/sin A, and tan A = sin A/cos A.

Double Angle Representation

The expression tan A / (1 + tan²A) is equivalent to (sin A × cos A), which is also (1/2)sin 2A.

Calculation:

Population of villages E = 50000 × 18%

⇒ 9000

Population of villages D = 50000 × 17%

⇒ 8500

Difference = 9000 - 8500

⇒ 500

∴ The required answer is 500.

Given:

6x2 + 13x + 7 = 0

Concept used:

We know that a quadratic equation whose roots are α and β is given by x² - (α + β) x + αβ = 0

Calculation:

6x2 + 13x + 7 = 0

⇒ x2 + 13x/6 + 7/6 = 0

So, (α + β) = - (13/6)

αβ = 7/6

Now,

(α + β)² = α² + β² + 2αβ

⇒ 169/36 = α2 + β2 + 7/3

⇒ 169/36 - 7/3 = α2 + β2

⇒ (169 - 84)/36 = α2 + β2

⇒ 85/36 = α2 + β2

Now,

x² - (α2 + β2)x + α²β² = 0

⇒ x2 - 85/36x + 49/36 = 0

⇒ 36x2 - 85x + 49 = 0

∴ The required answer is 36x2 - 85x + 49 = 0.

Given:

X is directly proportional to the square of Y. When X is 12, then Y is 2

Calculation:

X : Y²

So,

12 : 2²

⇒ 12 : 4

⇒ 3 : 1

So, X : Y2 =  3 : 1

So, when Y = 3  

⇒X : Y2 = X : 9

X : Y2 = X : 9 = 3 : 1

⇒ X = 27

∴ The required answer is 27.

Given:

A policeman spotted a thief 40 meters ahead of him.

The thief was running at 10 m/sec and the policeman was chasing him at the speed of 12 m/sec.

Concept used:

Speed = Distance/Time

When two bodies move in the same direction then the Relative Speed = Difference of Speeds

Calculation:

The relative speed of police and thief = 12 - 10

⇒ 2 m/sec

Now,

Total time taken to catch the thief = 40/2

⇒ 20 sec

So, distance traveled by the police = 20 × 12

⇒ 240 m

∴ The policeman needed to cover 240 meters to catch the thief.

Shortcut Trick

From the given cos θ + cos² θ = 1, we get cos θ = 1 − cos² θ = sin² θ.

Squaring both sides, we get cos² θ = sin⁴ θ.

Substitute sin⁴ θ with cos² θ in the expression: √(cos² θ + cos² θ) = √(2 cos² θ).

Simplifying the result gives √2 cos θ.

∴ The correct answer is √2 cos θ.

Alternate Method

Given: cos θ + cos² θ = 1

Formula Used: sin² θ + cos² θ = 1

Calculations:

⇒ cos θ + cos² θ = 1

⇒ cos θ = 1 − cos² θ

⇒ cos θ = sin² θ [Since 1 − cos² θ = sin² θ]

⇒ (cos θ)² = (sin² θ)² [Squaring both sides]

⇒ cos² θ = sin⁴ θ

Now, substitute this in the required expression:

⇒ √(sin⁴ θ + cos² θ)

⇒ √(cos² θ + cos² θ)

⇒ √(2 cos² θ)

⇒ √2 × cos θ

∴ The correct answer is √2 cos θ.

Additional Information

Fundamental Trigonometric Identities

1. sin² θ + cos² θ = 1 | 2. 1 + tan² θ = sec² θ | 3. 1 + cot² θ = cosec² θ.

Reciprocal Relations

sin θ = 1/cosec θ, cos θ = 1/sec θ, and tan θ = 1/cot θ = sin θ / cos θ.

Property of Squares in Trig

If sin² θ = k, then sin⁴ θ = k². This is a common substitution technique in complex trig algebraic problems.

Given:

The numbers are 60, 148, 382.

Calculation:

60 = 2² × 3 × 5

148 = 22 × 37

382 = 2 × 191

So, HCF = 2

∴ The required answer is 2.

Given:

The prices of the three shirts are Rs. 1,250, Rs. 1,540 and Rs. 1,375

Concept used:

Marked price × (100 - Discount)% = Selling price

Calculation:

For 30% discount:

Actual cost price = (1250 + 1540 + 1375) × 70%

⇒ 4165 × 70%

⇒ 2915.5

For 80%  off on the price of the costliest shirt:

Actual cost price = 1250 + 1540 × 20% + 1375

⇒ 1250 + 308 + 1375

⇒ 2933

So, Raghav can purchase shirts at a minimum of Rs . 2915.5

∴ The required answer is Rs. 2915.5. 

Alternate MethodGiven:

Prices of 3 shirts: Rs. 1,250, Rs. 1,540 and Rs. 1,375

Two choices of discount: 30% off the total price or 80% off the costliest shirt (with the condition that he buys at least 3 shirts)

Calculation:

Total cost without discount = Sum of the prices of all shirts

⇒ Rs. 1,250 + Rs. 1,540 + Rs. 1,375 = Rs. 4,165

With first coupon: Total cost = (1 - 30%) ×  Total cost without discount = 70% of Rs. 4,165 = Rs. 2,915.5

With second coupon: Total cost = Total cost without discount - discount on costliest shirt

⇒ Rs. 4,165 - 80% of Rs.1540 = Rs. 4,165 - Rs. 1,232 = Rs. 2,933

∴  Raghav can purchase the 3 shirts at a minimum price of Rs. 2,915.5 using the first coupon.

Given:

sin A = 4/5

Calculation:

sin A = 4/5

⇒ sin² A = (4/5)²

⇒ sin2 A = 16/25

∴ The required answer is 16/25.

Given:

The radius of the sphere = 12 cm

Diameter of the base of the cone = 12 cm

Concept used:

The volume of a sphere = 4/3πr³

The volume of a cone = 1/3πr2h

Here,

r = radius

h = height

Calculation:

According to the question,

The volume of the sphere = Volume of the cone

4/3 π 123 = 1/3 π 62 ​h

⇒ 4 × 12³ = 6² × h 

⇒ 4 × 48 = h

⇒ h = 192

So, height = 192 cm

∴ The height of the cone is 192 cm.

Given:

PA and PB are tangents to the circle with center O such that ∠APB = 54°

Calculation:

We know that the radius and tangent are perpendicular at their point of contact.

So,

∠PAO = ∠PBO = 90°

So,

∠AOB = 360 - 54 - 180

⇒ 126°

Also AO = OB = Radius

So, ∠OAB = ∠OBA = 54/2

⇒ 27°

∴ The required answer is 27°

Given:

XYZ and ZT are secant and tangent respectively for the same circle

TZ = 12 cm

YZ = 8 cm and YX = x cm

Concept used:

If PAB is a secant to a circle intersecting it at A and B and PT is a tangent then PA × PB = PT²

Calculation:

By using the above concept,

ZX × ZY = ZT²

⇒ 8 × (YZ + XY) = 12²

⇒ 8 × (8 + x) = 144

⇒ 8 + x = 18

⇒ x = 10

∴ The length of XY is 10 cm

Given:

Loss% (a) = 7%

Less weight (b) = 18%

Formula used:

Profit% / Loss% = (b ± a) / (100 - b) × 100

Calculation:

As, a = 7% and b = 18%

Then,

Profit% / Loss% = (b ± a)/(100 - b) × 100

⇒ (18 - 7)/(100 - 18) × 100

⇒ (11/82) × 100

⇒ 13.4146 ≈ 13.41%

∴ The dealer’s profit% is 13.41%.

Shortcut Trick

When the sum of three variables (x + y + z) is 0, the sum of their products taken two at a time (xy + yz + zx) is always half of the negative sum of their squares.

Direct Formula: xy + yz + zx = −(x² + y² + z²) ÷ 2

Value = −40 ÷ 2 = −20

∴ The correct answer is −20.

Alternate Method

Given:

x + y + z = 0

x² + y² + z² = 40

Formula Used:

The Algebraic Identity for the square of a trinomial:

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

Calculations:

⇒ Substituting the given values into the identity:

⇒ (0)² = 40 + 2(xy + yz + zx)

⇒ 0 = 40 + 2(xy + yz + zx)

⇒ −40 = 2(xy + yz + zx)

⇒ xy + yz + zx = −40 ÷ 2

⇒ xy + yz + zx = −20

∴ The correct answer is −20.

Additional Information

Trinomial Expansion

The expansion of (a + b + c)² is always the sum of the squares of the individual terms plus twice the sum of their pairwise products: a² + b² + c² + 2(ab + bc + ca).

Special Case: Sum is Zero

If a + b + c = 0, then a² + b² + c² = −2(ab + bc + ca). This also implies that the cubes follow the property a³ + b³ + c³ = 3abc.

Sum of Squares Property

For any real numbers x, y, and z, the expression x² + y² + z² is always greater than or equal to zero. If the sum of squares is zero, then each individual variable must be zero.

Given:

The expenditure on the cost of living of a man and his family is 60% of his salary.

He gets two increment of 30% and 60% in his salary. If his saving increases by 250% of his initial saving

Calculation:

Let the salary of the man be 100a

So, expenditure = 100a × 60%

⇒ 60a

Savings = 100a - 60a

⇒ 40a

Now,

His new salary = 100a × 130% × 160%

⇒ 208a

His new savings = 40a + 40a × 250%

⇒ 140a

Expenditure = 208a - 140a

⇒ 68a

Required % = (68a/208a) × 100

⇒ 32.69 ≈ 32.70%

∴ The required answer is 32.7%.

Given:

If two isosceles triangles have their corresponding angles equal and their areas are in the ratio of x2 ∶ y2.

Calculation:

Area of 1st triangle : Area of 2nd triangle = (Height of 1st triangle)² : (Height of 2nd triangle)²

⇒ x2 ∶ y2 = (Height of 1st triangle)2 : (Height of 2nd triangle)2

⇒ x ∶ y = Height of 1st triangle : Height of 2nd triangle

∴ The required answer is x : y.

Given:

A sum of money doubles itself in 7 years at simple interest.

Concept used:

S.I = (P × T × R)/100

Calculation:

According to the question,

P = (P × 7 × R)/100

⇒ 1 = 7R/100

⇒ R = 100/7

Now,

4P = (P × T × 100)/(7 × 100)

⇒ 28P = PT

⇒ 28 = T

So, time = 28 years

∴ The required answer is 28 years.

Given:

54p3987 is divisible by 11

Concept used:

If the difference of the sum of alternative digits of a number is 0 or divisible by 11, then that number is divisible by 11 completely.

Calculation:

5 + p + 9 + 7 - 4 - 3 - 8 = 0 or multiple of 11

⇒ 21 + p - 15 = 0 or multiple of 11

⇒ 6 + p = 0 or multiple of 11

For p = 5 we get 11

So, p = 5

∴ The required answer is 5.

The correct answer is 'Transient'.

Key Points

• The most appropriate antonym of the given word 'Entrenched' is 'Transient'.
• Entrenched: means to be firmly established and difficult to change. (दृढ़ता से स्थापित और बदलना मुश्किल)
• Example: The political party's policies were so entrenched that it took years for any meaningful change to occur.
• Transient: lasting only for a short time; temporary. (अस्थायी)
• Example: The travelers only stayed in the transient town for one night before moving on to their next destination.
  

Correct Answer: Transient.

Additional Information

• Let's look at the meaning of other options:
• Averted: to prevent or avoid something from happening. For example, "She averted her gaze from the gruesome scene." (टालना/बचाना)
• Startling: causing surprise or shock. For example, "The sudden loud noise was startling." (आश्चर्यजनक)
• Entrusted: to give someone the responsibility of doing something. For example, "The CEO entrusted the company's financial management to her CFO." (सौंपा)

The correct answer is 'plea'.

Key Points

• The most appropriate synonym of the given word 'request' is 'plea'.
• Request: an act of asking politely or formally for something. (अनुरोध/विनंती)
• For example, "I would like to request a copy of the report, please."
• Plea: a request made in an urgent and emotional way. (दलील/अपील)
• For example, "The suspect entered a plea of guilty in court." 
  

Correct Sentence: Your words seemed more like a demand rather than a plea.

Additional Information

• Let's look at the meaning of other words:
• Compromise: an agreement reached between two parties in which each party gives up something they want in order to reach a mutual agreement. For example, "The two sides compromised on the terms of the contract in order to move forward." (समझौता)
• Contract: a written or spoken agreement between two or more parties that is enforceable by law. For example, "We signed a contract to rent the apartment for one year." (अनुबंध)
• Order: a command or instruction given by someone in a position of authority. For example, "The boss gave the order to start working on the project immediately." (आदेश)

The correct answer is 'stoic'.

Key Points

• The most appropriate word for the given group of words is 'stoic'.
• Stoic: a person who can endure pain or hardship without showing their feelings or complaining. (संयमी)
• For example, "He remained stoic even when he received bad news about his health." 
  

Correct Answer: stoic.

Additional Information

• Let's look at the meaning of other words:
• Strict: demanding that rules or orders are obeyed and enforced with discipline. For example, "The teacher was strict about classroom behavior." (कड़ी मेहनती/सख्त)
• Active: engaged in physical or mental activity. For example, "She is an active participant in the local theater group." (सक्रिय)
• Passive: accepting or allowing what happens or what others do, without active response or resistance. For example, "He took a passive approach to the conflict, letting others take the lead." (अनुवांशिक)

The correct answer is 'Official rules and bureaucracy that make it difficult to do something'.

Key Points

• The most appropriate meaning according to the given option for the idiom 'red tape' is 'Official rules and bureaucracy that make it difficult to do something'. (आधिकारिक नियम और नौकरशाही जो कुछ करना मुश्किल बनाते हैं)
• The idiom "red tape" refers to excessive bureaucracy or official procedures that can slow down or hinder progress. (अत्यधिक नौकरशाही या आधिकारिक प्रक्रियाएं जो प्रगति को धीमा या बाधित कर सकती हैं)
• Example: The government's red tape made it difficult for small businesses to compete with larger corporations.
  

Correct Answer: Official rules and bureaucracy that make it difficult to do something.

Additional Information

• Let's look at the origin of this idiom:
• It originated in the early 18th century in England, where legal and official documents were often tied up and sealed with red tape. The practice was intended to signify that the documents had been inspected and approved, but it also created unnecessary delays and obstacles.
• In modern usage, "red tape" refers to any kind of bureaucratic or administrative procedure that is excessively complicated, time-consuming, or burdensome. It is often associated with government agencies or large organizations, where rigid rules and regulations can impede efficiency and innovation.

The correct answer is 'madness'.

Key Points

• The most appropriate word for the given blank is 'madness'.
• The sentence implies that there are only two possible explanations for the person's behavior: either he is genuinely insane, or he is pretending to be insane. The word "feigns" means to pretend or fake, and it is used here to suggest that the person's behavior is not genuine.
• Options 1, 3, and 4 are not appropriate because they do not fit with the context of the sentence. If the person were pretending to be happy, calm, or sad, it would not necessarily indicate that he is insane or pretending to be insane.
• Therefore, option 2, "madness," is the most appropriate word to fill in the blank.
• Let's look at the meaning of each word:
• Happiness (खुशी): The state of feeling or expressing joy, contentment, or pleasure.
• Madness (पागलपन): A state of severe mental illness or insanity, or extreme and irrational behavior.
• Calmness (शांति): The state of being peaceful, quiet, and free from agitation or disturbance.
• Sadness (दुःख): The state of feeling or expressing sorrow, unhappiness, or disappointment.
  

Correct Sentence: Either he is mad, or he feigns madness.

The correct answer is 'Remorse'.

Key Points

• The most appropriate word for the given group of words is 'Remorse'.
• Remorse - (पछतावा): A feeling of deep regret or guilt for doing something wrong or hurtful.
• Example: He felt a deep sense of remorse after cheating on the test.
  

Correct Answer: Remorse.

Additional Information

• Let's look at the meaning of other words:
• Refulgence - (चमक, तेज रोशनी): Brightness or radiance shining from something; brilliance.
• Restitution - (मुआवजा): The act of restoring something that has been taken away or lost; compensation.
• Repugnance - (घृणा): A strong feeling of disgust or aversion towards something.

The correct answer is 'Subsistance'.

Key Points

• Among the given options the incorrectly spelt word is 'Subsistance'.
• Its correct spelling is 'Subsistence'.
• Subsistence - (जीवन निर्वाह; जीवित रहने के लिए पर्याप्त संसाधन होने की स्थिति; जीवित रहने के लिए न्यूनतम आवश्यक): The state of having just enough resources to stay alive; the minimum necessary to survive.
• Example: They lived a subsistence lifestyle, growing their own food and relying on hunting and fishing.
• Thus, the correct answer is Option 4.

Additional Information

• Let's look at the meaning of other words:
• Benchmark - (मानक, मापदंड): A standard or point of reference against which things may be compared or assessed.
• Knight - (सामंत): A medieval nobleman who was trained to fight on horseback and served his sovereign or lord.
• Aggravate - (ख़राब करना): To make a bad situation worse; to intensify something unpleasant or harmful.

The correct answer is 'strangely'.

Key Points

• The most appropriate word for the given blank is 'strangely'.
• The sentence states that the speaker felt a strong sense of elation at some news.
• The word "strangely" is the most appropriate choice to describe this feeling because it suggests that the speaker's reaction was unexpected or unusual in some way.
• The other options do not convey this same sense of surprise or unexpectedness, and therefore do not fit as well in the sentence.
• Let's look at the meaning of all the options:
• Commonly - (आम तौर पर): Generally, usually, or typically.
• Strangely - (अजीब तरह से): In a way that is unusual, unexpected, or surprising.
• Customarily - (रूढ़िवादी तौर पर): In a way that conforms to or is in keeping with conventional usage.
• Typically - (आमतौर पर): In most cases or under most circumstances; usually.
• Thus, the correct answer is Option 2.
  

Correct Sentence: I felt strangely elated at the news.

The correct answer is 'Iconoclast'.

Key Points

• The most appropriate word for the given group of words is 'Iconoclast'.
• Iconoclast - (एक व्यक्ति जो पोषित विश्वासों, रीति-रिवाजों या संस्थानों पर हमला करता है या उनकी आलोचना करता है): A person who attacks or criticizes cherished beliefs, customs, or institutions.
• Example: The iconoclast questioned the traditional notions of beauty in art and sought to challenge the established norms of artistic expression.
• Thus, the correct answer is Option 4.
  

Correct Answer: Iconoclast.

Additional Information

• Let's look at the meaning of other words:
• Heretic - (विधर्मी): A person who holds controversial opinions, especially ones that contradict the accepted doctrines of a religion, philosophy, or ideology.
• Absconder - (भगोड़ा): A person who has fled or escaped from a place, especially to avoid arrest or prosecution.
• Apostle - (प्रवर्तक; एक व्यक्ति जिसे एक मिशन पर भेजा जाता है या एक व्यक्ति जो किसी कारण, सिद्धांत या विचार का उत्साही समर्थक होता है): A person who is sent on a mission or a person who is an enthusiastic supporter of a cause, principle, or idea.

The correct answer is 'A lot of coffee was drunk by him before the marathon.'

Key Points

• The given sentence is in Active Voice. As per the given question, we have to change it to Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case) + was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'He'.​​
• The object of the given sentence is 'A lot of coffee'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'drank' will be changed into 'was drunk'.
• Lastly, the preposition 'by' will be added.
  

Correct Sentence: A lot of coffee was drunk by him before the marathon.

The correct answer is 'A kite was flown by them in the evening.'

Key Points

• The given sentence is in Active Voice. As per the given question, we have to change it to Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case) + was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'They'.​​
• The object of the given sentence is 'A kite'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'flew' will be changed into 'was flown'.
• Lastly, the preposition 'by' will be added.
  

Correct Sentence: A kite was flown by them in the evening.