SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1) (Previous Year Paper)

According to the question, after interchanging the given two signs and two numbers i.e :

• × and +
• Two numbers 3 and 9

So,

I. 7 + 3 – 8 ÷ 2 × 9

⇒ 7 + 3 - 4 × 9

⇒ 7 + 3 - 36

⇒ 10 - 36

⇒ -26

II. 4 + 3 – 9 × 8 ÷ 2

⇒ 4 + 3 - 9 × 4

⇒ 4 + 3 - 36

⇒ 7 - 36

⇒ -29

Here, values of equation (I) and (II)  are (-26) and (-29) respectively.

Hence, "Option - (2)" is the correct answer.

Logic : Letters of the word are arranged in ascending order according to English alphabetic series.

So,

• 'BEHOLD’ is written as 'BDEHLO'

• 'INDEED' is written as 'DDEEIN'

Similarly,

• 'COURSE' is written as :​

Hence, "CEORSU" is the correct answer.

The logic followed here is :

⇒ Library is a place where books are kept.

Similarly,

⇒ Museum is a place where artefacts are kept.

Hence, "Artefacts" is the correct answer.

Additional Information

• Building can be used for multipurpose reasons.
• People are the living beings, thus is not any particular place or item.
• Gallery is a room or a building for the display or sale of work of art.

The logic followed here is : Decreasing consecutive multiples of 10.

Hence, "182" is the correct answer.

Given:

• The image must not to be rotated

Hence, the correct answer is "Option - (2)".

Given : 21 * 4 * 156 * 13 * 11 = 83

According to the question, after replacing the * signs:

So,

• Option - (1) : −, ÷, ×, +

21 - 4 ÷ 156 × 13 + 11 = 83

21 - 0.02 × 13 + 11 = 83

21 + 11 - 0.26 = 83

32 - 0.26 = 83

31.74 ≠ 83 (LHS ≠ RHS)

• Option - (2) : ×, +, ÷, −

​21 × 4 + 156 ÷ 13 - 11 = 83

21 × 4 + 12 - 11 = 83

84 + 12 - 11 = 83

96 - 11 = 83

85 ≠ 83 (LHS ≠ RHS)

• Option - (3) : ×, −, ÷, +

​21 × 4 - 156 ÷ 13 + 11 = 83

21 × 4 - 12 + 11 = 83

84 + 11 - 12 = 83

95 - 12 = 83

83 = 83 ( LHS = RHS)

• Option - (4) : +, ÷, −, ×

​21 + 4 ÷ 156 - 13 × 11 = 83

21 + 0.02 - 13 × 11 = 83

21 + 0.02 - 143 = 83

21.02 - 143 = 83

- 121.98 ≠ 83 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

The logic followed here is :

Hence, "FU" is the correct answer.

Logic : (Cube of 1^st number + Cube of 3^rd number) / 2 = 2^nd number

Given :

• (3, 14, 1)

⇒${(3)^3 + (1)^3 \over 2}$ = 14

⇒${27 + 1 \over 2}$ = 14

⇒${28 \over 2}$ = 14

⇒14 = 14 (LHS = RHS)

• (4, 36, 2)​

⇒${(4)^3 + (2)^3 \over 2}$ = 36

⇒${64 + 8 \over 2}$ = 36

⇒${72 \over 2}$ = 36

⇒36 = 36 (LHS = RHS)

So,

• Option - (1) : (8, 12, 2)​

⇒${(8)^3 + (2)^3 \over 2}$ = 12

⇒${512 + 8 \over 2}$ = 12

⇒${520 \over 2}$ = 12

⇒260 ≠ 12 (LHS ≠ RHS)

• Option - (2) : (5, 81, 4)

⇒${(5)^3 + (4)^3 \over 2}$ = 81

⇒${125 + 64 \over 2}$ = 81

⇒${189 \over 2}$ = 81

⇒94.5 ≠ 81 (LHS ≠ RHS)

• Option - (3) : (7, 40, 3)

⇒${(7)^3 + (3)^3 \over 2}$ = 40

⇒${343 + 27 \over 2}$ = 40

⇒${370 \over 2}$ = 40

⇒185 ≠ 40 (LHS ≠ RHS)

• Option - (4) : (8, 260, 2)

⇒${(8)^3 + (2)^3 \over 2}$ = 260

⇒${512 + 8 \over 2}$ = 260

⇒${520 \over 2}$ = 260

⇒260 = 260 (LHS = RHS)

Hence, "Option - (4)" is the correct answer.

Given : 12 * 24 * 4 * 2 * 60

According to the question, after replacing the * signs:

So,

• Option - (1) : +, ×, ÷, =

​12 + 24 × 4 ÷ 2 = 60

12 + 24 × 2 = 60

12 + 48 = 60

60 = 60 (LHS = RHS)

• Option - (2) : −, ×, +, =

​12 - 24 × 4 + 2 = 60

12 + 2 - 96 = 60

14 - 96 = 60

82 ≠ 60 (LHS ≠ RHS)

• Option - (3) : +, ×, −, =

12 + 24 × 4 - 2 = 60

12 + 96 - 2 = 60

108 - 2 = 60

106 ≠ 60 (LHS ≠ RHS)

• Option - (4) : +, ÷, ×, =

12 + 24 ÷ 4 × 2 = 60

12 + 6 × 2 = 60

12 + 12 = 60

24 ≠ 60 (LHS ≠ RHS)

Hence, "Option - (1)" is the correct answer.

Logic : All the letters are arranged in descending order or immediate preceding letter order according to English alphabetic series.

So,

• HGF

​

​

• RQP

​

• UVW

​

• LKJ

Here, Only 'UVW' is not arranged in descending order or immediate preceding letter order.

Hence, "UVW" is the correct answer.

The logic followed here is :

⇒ Phone is a device by which one can talk.

Similarly,

⇒ Television is a device by which can view.

Hence, "View" is the correct answer

Additional Information

• Remote is device used to control any equipment like television, fan etc.
• Read is to look at words or symbols and understand what they mean.
• Channel is one of the feature of a television.

The faces opposite to each other are shown below:

⇒ As the alternate positions becomes opposite to each other and the remaining two faces becomes opposite to each other.

So, opposite pairs are:

• 1 → 5
• 2 → 6
• 3 → 4

Therefore, according to the question :

• Given figure A → 

• ⇒ Can be formed as a cube from the given sheet (As 2,5 and 3 are one of the numbers of each opposite pairs)

• Given figure B → 

• ​⇒ Cannot be formed as a cube from the given sheet (As 5 is opposite to 1)

• Given figure C → 

​

• ⇒ Cannot be formed as a cube from the given sheet (As 2 is opposite to 6)

• Given figure D → 

• ​⇒ Cannot be formed as a cube from the given sheet (As 5 is opposite to 1)

​Here, Only figure A can be formed as a cube from the given sheet.

Hence, "Only A" is the correct answer.

The correct mirror image of the given combination when mirror is placed at PQ is as shown below:

Detailed Explanation:

• The line PQ is the mirror

• The word "BLZK541M" the second letter is "L". So, the mirror image should be "

• " ⇒ Option 2 is eliminated.

• The word "BLZK541M" the seventh digit is "1". So, the mirror image should be "

• " ⇒ Option 3 is eliminated..

• The word "BLZK541M" the seventh digit is "1". So, the mirror image should be "

• " ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - (1)".

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For '

' element - Shifting in the clockwise direction. 

2. For '

' element - Shifting in the clockwise direction.

3) For '

' element - Only the middle triangle '

' is flipping vertically and both the corner triangles remain constant.

Final series is :

Hence, ‘option - (1)’ is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. All shoes are torches → Does not follow (As all torches are shoes. So, it is possible but not definitely true)

II. All torches are boxes → Does not follow (As all boxes are torches. So, it is possible but not definitely true)

III. All boxes are cards → Does not follow (As all cards are boxes. So, it is possible but not definitely true)

IV. All cards are shoes → Follow (As all cards are boxes, all boxes are torches and all torches are shoes. So, it is definitely true)

∴ Here, Only conclusion IV follows.

Hence, the correct answer is "Only conclusion IV follows".

Logic : Sum of all the position values according to English alphabetic series.

So,

• 'FRUCTUS' is coded as :

• 'SPRINTER' is coded as :

Similarly,

• 'MASCULINE' is coded as :

​

Hence, "97" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some S are W → Follow (As all W are S. So, it is definitely true)

II. All S are D → Does not follow (As all W are S and no D is W. So, it is definitely false)

III. No W is D → Follow (As no D is W. So, it is definitely true)

∴ Here, Both conclusions I and III follow.

Hence, the correct answer is "Both conclusions I and III follow".

The logic followed here is :

1. First letter - Remains same.
2. Second letter - First subtraction of (9) and then addition of (17) in the position value in the alternate order.
3. Third letter - (8) is added to the position value.
4. Fourth letter - First subtraction of (10) and then addition of (16) in the position value in the alternate order.

So,​

Hence, "NCXC" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. The elements which are placed at the corner, moving anticlock wise direction, and the elements placed in the middle of the side interchanged their position. The center element disappeared and a new element came in the next step. This movement happens in every alternative step.

2. All elements are moving according to a fixed pattern. This movement happens in every alternative step.

3) The elements which are placed at the corner, moving anticlock wise direction, and the elements placed in the middle of the side interchanged their position. The center element disappeared and a new element came in the next step. 

4) All elements are moving according to a fixed pattern. 

The final series is :

Hence, ‘option - (1)’ is the correct answer.

Logic : First number = (Square root of second number + 1)

So,

• 19 : 324

​19 = $\sqrt{324}$ + 1

19 = 18 + 1

19 = 19 (LHS = RHS)

And,

• 25 : 576

25 = $\sqrt{576}$ + 1

25 = 24 + 1

25 = 25 (LHS = RHS)

Similarly,

• 9 : ?

9 = $\sqrt{x}$ + 1

9 - 1 = $\sqrt{x}$

8 = $\sqrt{x}$

$x$ = ${8^2}$

$x$ = 64

Hence, "64" is the correct answer.

According to the sequence in the dictionary:

4. Pope
5. Poppy
6. Populace
7. Popular
8. Population

Here, the fifth word is 'Population'.

Hence, the correct option is "Population".

Logic : First number = Square of second number - Square of third number

Given :

• (20, 6, 4)

20 = $(6)^2 - (4)^2$

20 = 36 - 16

20 = 20 (LHS = RHS)

And, 

• (24, 7, 5)

​24 = $(7)^2 - (5)^2$

24 = 49 - 25

24 = 24 (LHS = RHS)

So,

• Option - (1) : (65, 9, 4)​

65 = $(9)^2 - (4)^2$

65 = 81 - 16

65 = 65 (LHS = RHS)

• Option - (2) : (22, 5, 2)

​22 = $(5)^2 - (2)^2$

22 = 25 - 4

22 ≠ 21 (LHS ≠ RHS)

• Option - (3) : (40, 8, 5)

​40 = $(8)^2 - (5)^2$

40 = 64 - 25

20 ≠ 39 (LHS ≠ RHS)

• Option - (4) : (42, 7, 3)

​42 = $(7)^2 - (3)^2$

42 = 49 - 9

42 ≠ 40 (LHS ≠ RHS)

Hence, "Option - (1)" is the correct answer.

Given :

Statement given : A % B & C # D @ E

Explanation :

• A % B → A is the father of B.

​

• B & C → B is the husband of C.

​

• C # D → C is the sister of D.

​

• D @ E → D is the daughter of E.

​

Thus, from the final family tree B is the son-in-law of E.

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

Given :

So,

• Option - (1) : P – Q × R → P is the sister of Q who is the brother of R.

​

Here, P is the sister of R.

• Option - (2) : P – Q + R → P is the sister of Q who is the father of R.

​

Here, P is paternal aunt of R.

• Option - (3) : P × Q + R → P is the brother of Q who is the father of R.

​

Here, P is the paternal uncle of R.

• Option - (4) : P + Q – R → P is the father of Q who is the sister of R.

​

Here, P is the father of R.

Thus, only option - (2), 'P – Q + R' shows that P is the paternal aunt of R.

Hence, "Option - (2)" is the correct answer.

Logic :

• First number = Cube root of second number
• Second number - Third number = 10

So,

• Option - (1) : (7 – 343 – 331)

​7 = 3√343

7 = 7 (LHS = RHS)

And, 

343 - 331 = 12

• Option - (2) : (6 – 216 – 206)

6 = 3√216

6 = 6 (LHS = RHS)

And,

216 - 206 = 10

• Option - (3) : (5 – 125 – 115)

5 = 3√125

5 = 5 (LHS = RHS)

And,

125 - 115 = 10

• Option - (4) : (3 – 27 – 17)​

3 = 3√27

3 = 3 (LHS = RHS)

And,

27 - 17 = 10

Here, only in option - (1) the difference of the second number and third number is 12 instead of 10. Thus, it is the odd one out.

Hence, "Option - (1)" is the correct answer.

The correct answer is Hockey.

Key Points

• A number of different types of foul may be punished in a game of hockey. 
• Backsticks- This is awarded against a player who strikes the ball with the rounded back of the hockey stick.
• Obstruction- This is awarded against a hockey player who uses their body or stick to prevent an opponent from reaching the ball.
• Third-party obstruction- This is awarded when a hockey player positions themselves between the ball and an opponent, allowing a team-mate an unobstructed play on the ball.
• Advancing- This is awarded against a player who shoves, pushes, or advances the ball in any way, using any part of their body.
• Hockey stick interference- This is awarded against a player who uses their stick to hit an opponent’s stick, either intentionally or unintentionally.
• Undercutting- This is awarded against a player who lifts the ball in a dangerous manner.
• Sticks- This is awarded against a player who raises their stick dangerously near another player.

Additional Information

• Hockey players can only hit the ball with the flat side of their stick.
• Hence Against the player who hits the ball using the flat side of the stick is NOT considered as a type of foul in the game of hockey.

The correct answer is Baisakhi.

Key Points

• The festival of Baisakhi is celebrated with enthusiasm in Punjab, Haryana and Chandigarh.
• It is a spring harvest festival for the Sikhs.
• Baisakhi also commemorates the formation of Khalsa Panth by Guru Gobind Singh in 1699.

Additional InformationLohri

• Lohri, the bonfire harvest festival of Punjab celebrated in the month of Magh, is symbolic of new beginnings.
• The festival is celebrated every year on January 13 with much enthusiasm and zeal.
• It is primarily the harvest festival of the Punjabis.
• This festival denotes the harvesting of the Rabi crops and hence all the farmers get together in order to thank god for giving them such a wonderful harvest.
• The rituals related to Lohri symbolize the attachment of the people with Mother Nature.

Hola Mohalla

• Hola Mohalla likewise called Hola, is a three-day long Sikh celebration which ordinarily falls in Spring.
• It happens on the second day of the lunar month of Chett, a day after the Hindu spring celebration Holi[ however some of the time corresponds with Holi
• Hola Mohalla is a major bubbly occasion for Sikhs all over the planet.
• The fair held during Holi and Hola at Anandpur Sahib is customarily a three-day occasion however members go to Anandpur Sahib for seven days.

Teej

• Kajari Teej is the grand festival of Rajasthan.
• It celebrates the spirit of womanhood.
• Married women undertake a day-long fast in prayer for their husbands' health and wealth.
• Hariyali Teej, Hartalika Teej, and Kajari Teej are the three teej festivals observed in Rajasthan.
• The Bhadra pad of the Hindu calendar's Shravan or monsoon season is when this festival is fervently observed.
• According to the Gregorian calendar, the celebration takes place in July or August.

The correct answer is Yoga for the achievement of Sustainable Development Goals.

Key Points

• Themes of International Yoga Day :
• 2015: Yoga for Harmony and Peace
• 2016: Yoga for the achievement of the Sustainable Development Goals
• 2017: Yoga for Health
• 2018: Yoga for Peace
• 2019: Yoga for Heart
• 2020: Yoga at Home and Yoga with Family
• 2021: Yoga For Wellness
• 2022: Yoga for Humanity
• 2023: Yoga for Vasudhaiva Kutumbakam
• 2024: Yoga for Self and Society

Additional Information

• On 11^th December 2014, the United Nations proclaimed 21 June as the International Day of Yoga by resolution 69/131.
• The idea of the International Day of Yoga was proclaimed by the current Prime Minister of India, Narendra Modi, during his speech at the United Nations General Assembly in 2014.
• International Yoga Day is celebrated every year on 21 June to raise awareness worldwide about the benefits of Yoga in Daily Life.
• June 21, also called the summer solstice, is the longest day of the year.

The correct answer is CaO.

Key Points

• The chemical formula for calcium oxide is CaO.
• It is also known as quicklime, burnt lime, or quicklime.
• It reacts with water to form calcium hydroxide.
• The chemical formula for calcium hydroxide is Ca(OH)2. It is also known as hydrated lime or slaked lime.
• It reacts with carbon dioxide to form calcium carbonate.

Important Points

• Uses of  calcium oxide (CaO)
• Quicklime is used in the Basic Oxygen Steelmaking (BOS) process.
• Small amounts of quicklime are used in other processes such as the production of glass, calcium aluminate cement, and organic chemicals.
• Calcium oxide (quick lime) is used in the production of cement.

The correct answer is Joule.

Key Points

• Work is said to be done by a force when it moves its point of application through a distance.
• Work done = Force × Distance moved
• SI unit of work is joule.
• 1 J = 1 N.m

Additional Information

• Watt (W) is the S.I. unit of power.
• Ampere (A) is the S.I. unit of current.
• Decibel is a unit of intensity of sound.

The correct answer is Vijaywada.

Key Points

• Vijayawada has a thermal power station named after Dr Narla Tata Rao
• Nuclear power is the fifth-largest source of electricity in India after coal, gas, hydroelectricity and wind power.
• Under Homi J. Bhabha’s direction, India’s nuclear energy programme was started around the time of independence.
• Tarapur Atomic Power Plant-1 is the first and the oldest Nuclear Power Station In India.

Additional Information

• Presently, India has 22 nuclear power reactors operating in 7 states, with an installed capacity of 6780 MegaWatt electric
• Nuclear Power Corporation of India Limited -NPCIL is a government-owned corporation of India that is responsible for the generation of electricity through nuclear power.
• NPCIL is administered by the Department of Atomic Energy, Government of India.

The correct answer is salvation.

Key Points

• Ramakrishna Mission (RKM) is a Hindu religious and spiritual organization that forms the core of a worldwide spiritual movement known as the Ramakrishna Movement or the Vedant
• The mission is named after and inspired by the Indian saint Ramakrishna Paramahamsa and founded by Ramakrishna's chief disciple Swami Vivekananda on 1^st May 1897.
• The mission bases its work on the principles of karma yoga, the principle of selfless work done with a dedication to God.
• The Ramakrishna Mission has centered around the world and publishes many important Hindu texts.
• It is affiliated with the monastic organization. Vivekananda was greatly influenced by his guru (teacher) Ramakrishna.
• The motto of the mission is - Atmano mokshartham Jagat hitaya cha (For one’s own salvation and for the welfare of the world).

Additional Information

• Swami Vivekananda
• His original name was Narendranath Dutt.
• He attended the Parliament of Religions held at Chicago in 1893 AD and published two papers, Prabhudhha Bharat in English and Udbodhana in Bengali.
• He urged people to inculcate the spirit of liberty, equality and free-thinking.
• He worked for the emancipation of women.
• He emerged as a preacher of Neo-Hinduism.
• He advocated the Doctrine of Service–the service of all human beings.
• He was considered the spiritual father of the modern nationalist movement.

The correct answer is 2 October.

Key Points

• The International Day of Non-Violence is observed on 2 October in honor of the birthday of Mahatma Gandhi.
• The International Day of Non-Violence is a global observance that promotes non-violence through education and public awareness.
• On 15 June 2007 the United Nations General Assembly establish 2 October as the International Day of Non-Violence.

The correct answer is Sangama Dynasty.

Key Points

• Vijayanagara was founded in 1336 by Harihara and Bukka of the Sangama dynasty. On the south bank of the Tungabhadra river, they founded a new city named Vijayanagara.

Additional Information Vijayanagar Dynasties:

The correct answer is 1981.

Key Points

• Vayudoot
• It was a regional airline in India established in 1981.
• It is a joint venture between Indian Airlines and Air India.
• It was headquartered at New Delhi's Safdarjung Airport.
• The airline was primarily used to serve the Northeastern part of India.

Additional Information

• Air India
• It is the flag carrier airline of India.
• It is headquartered in New Delhi.
• It is owned by a Special-Purpose Vehicle of Tata Sons known as 'Talace Private Limited'.
• It operates Airbus and Boeing aircraft to serve 102 domestic and international destinations.
• The airline was founded by J.R.D. Tata as Tata Airlines in 1932.
• Indian Airlines
• The airline became a division of Air India Limited.
• It is after the merger of eight pre-Independence domestic airlines.
• The airline is based in Delhi.

The correct answer is Erosion.

Key Points

• Geologic Erosion or "natural" erosion, is the action of the wind, water, ice and gravity in wearing away rock to form soil and shape the ground surface. Except for some stream and shore erosion, it is a relatively slow, continuous process that often goes unnoticed.

Additional Information

• Accelerated Erosion is the speeding up of erosion due to human activity. Whenever we destroy the natural vegetation or alter the contour of the ground without providing some sort of surface protection, we greatly increase the rate of erosion.
• Soil erosion is the process of detachment transportation and deposition of soil particles by wind, water or other phenomenon.
• Water erosion is the process of detachment transportation and deposition of soil particles by water.

Weathering

• Weathering describes the breaking down or dissolving of rocks and minerals on the surface of the earth.
• Weathering occurs when physical processes affect the rock, such as changes in temperature or when the rock is exposed to the effects of wind, rain, and waves.
• Water, ice, acids, salts, plants, animals, and changes in temperature are all agents of weathering.
• Thus, this weathering which leads to both the mechanical breakup of rocks and the chemical weathering of minerals contributes to soil formation.
• Therefore, weathering leads to soil formation.

Metamorphosis

• Metamorphosis is the process by which animals undergo rapid physical changes sometime after birth. Examples of metamorphosis include the process undergone by most insects and the transformation of tadpoles into frogs.

Sedimentation

• Sedimentation is the process of allowing solid particles in suspension in water to settle out of the suspension under the effect of gravity.
• The particles which settle down during sedimentation are called sediments.
• This method is used for the separation of insoluble substances which are heavier than liquid or water.
• In this process, heavier components of the mixture settle on the bottom on their own due to gravity.

The correct answer is Nitin Gupta.

Key Points

• IRS officer Nitin Gupta has been appointed as the new Central Board of Direct Taxes (CBDT) chairman.
• Mr Gupta is an Indian Revenue Service (IRS) officer of the 1986 batch of the Income Tax cadre and is currently serving as the Member (investigation) in CBDT.
• The post of the CBDT chief was being held in an additional capacity by Board member and 1986-batch IRS officer Sangeeta Singh.

Additional Information

• ​Important Appointments:
• Former IAS officer BVR Subrahmanyam was appointed the Chief Executive Officer (CEO) of NITI Aayog.
• New Development Bank (NDB) of the BRICS countries has appointed Dr D J Pandian as the Director-General of its India Regional Office in Gujarat International Finance Tec-City (GIFT City).
• Senior Diplomat Ruchira Kamboj has been appointed as the next Ambassador and Permanent Representative of India to the United Nations.
• Somali president Hassan Sheikh Mohamud on 15 June 2022 appointed Hamza Abdi Barre as the country's Prime Minister.
• Justice Bhimanagouda Sanganagouda Patil has been appointed as the new Lokayukta of Karnataka.
• President Ram Nath Kovind has given Justice Pradip Kumar Mohanty the additional charge of the Lokpal chairperson.​
• Dinkar Gupta, a 1987-batch IPS officer and former chief of Punjab Police, has been appointed Director-General of the National Investigation Agency (NIA).

The correct answer is Amjad Ali Khan.

Key Points

• Ustad Amjad Ali Khan-
• A distinguished maestro in the field of playing the sarod, Ustad Amjad Ali Khan is popularly known as the “Sarod Samrat“.
• He is the sixth generation sarod player in his family.
• He learned from his father Haafiz Ali Khan, who was a court musician in Gwalior up until Independence in 1947.
• He was awarded India's second-highest civilian honor Padma Vibhushan in 2001.
• The name sarod comes from the Persian ‘sarod’ meaning ‘melody’, alluding to its more melodic tone.

Additional Information

The correct answer is Banking method.

Key Points

• National income is the total value of a country’s final output of all new goods and services produced in one year.
• Methods of measuring national income are:

1. Expenditure Method - Under this method, we estimate the disposal of income on the purchase of final goods and services.
2. Income Method - The Income Method measures national income from the side of payments made to the primary factors of production in the form of rent, wages, interest, and profit for their productive services in an accounting year.
3. Production method - In this method, national income is measured as a flow of goods and services. This method is also called an output method.

Additional Information

• Measurement of National Income
• There are three methods to measure national income:

1. Income Method
2. Production (Value-Added) Method
3. Expenditure Method

• Measurement of National Income – Income Method
• Estimated by adding all the factors of production (rent, wages, interest, profit) and the mixed-income of self-employed.
• In India, one-third of people are self-employed
• This is the ‘domestic’ income, related to the production within the borders of the country
• Measurement of National Income – Production Method
• Estimated by adding the value added by all the firms.
• Value-added = Value of Output – Value of (non-factor) inputs

1. This gives GDP at Market Price (MP) – because it includes depreciation (therefore ‘gross’) and taxes (thus ‘market price’)
2. To reach National Income (that is, NNP at FC)

• Add Net Factor Income from Abroad: GNP at MP = GDP at MP + NFIA
• Subtract Depreciation: NNP at MP = GNP at MP – Dep
• Subtract Net Indirect Taxes: NNP at FC = NNP at MP – NIT
• Measurement of National Income – Expenditure Method
• The expenditure method to measure national income can be understood by the equation given below: 
• Y = C + I + G + (X-M),
• where Y = GDP at MP, C = Private Sector’s Expenditure on final consumer goods, G = Govt’s expenditure on final consumer goods, I = Investment or Capital Formation, X = Exports, X- M = Net Exports (difference between exports (X) and imports (M))

Important Points

• GDP: Gross Domestic Product is the sum of the money of all the final goods and services produced solely within the boundaries of a country, at a specific time.
• GDP includes the income of foreigners staying in the country.
• It excludes the income of nationals of the country staying abroad and also excludes the remittances sent from abroad.
• GNP: Gross National Product is the sum of the money of all the final goods and services produced both within and outside of a country by nationals during a specific period of time.
• GNP includes remittances.
• It excludes income generated locally by non-nationals.

The correct answer is National legislature.

Key Points

 The Constitution's Part V (Articles 79–122) deals with the Parliament's organisation, composition, duration, officers, processes, privileges, and powers.

• The Indian Constitution's framer chose the British model for Parliament above the American model.
• The Parliament is the legislative organ of a Union government and the Parliament of India is the top legislative body of the country.
• The Parliament is the National legislature, whereas the state legislature is known as the State Legislature.
• it holds a preeminent and prominent place in the Indian democratic political system because of the adoption of the parliamentary form of government.
• Parliamentary Organs: 
• President of India
• Rajya Sabha (Upper House)
• Lok Sabha (Lower House)
• The Indian Parliament is bicameral, the Rajya Sabha and the Lok Sabha.

Additional Information

• It is the Upper House that represents the Indian Union's states and union territories.
• It is the Lower House that represents all of India's citizens.
• The President of India is not a member of either House and does not attend any of the Parliament's proceedings.

The correct answer is Kerala.

Key Points 

• Kerala Chief Minister Pinarayi Vijayan inaugurated a project of the Women and Child Development department to provide milk and eggs to children at all anganwadis in the state.
• Kerala government has set aside over Rs 61.5 crore to include milk and eggs in the anganwadi menu.
• Each child will be given 125 ml of milk two days a week for 44 weeks (10 months) and an egg twice a week.

Additional Information 

• Kerala:
• Chief Minister - Pinarayi Vijayan.
• Governor - Arif Mohammad Khan.
• Number of Districts - 14.
• Lok Sabha seats - 20.
• Rajya Sabha seats - 9.
• State Animal - Indian elephant.
• State Bird - Great hornbill.

The correct answer is Rajasthan.

Key Points 

• Faced with a declining number of camels in Rajasthan, the state govt has announced a 'Camel Protection and Development Policy' in its budget 2022-23.
• CM Ashok Gehlot has proposed a budget of Rs 10 cr in the next financial year under the new policy for rearing, protection, and overall development of the state animal.
• The Rajasthan govt had declared camel as the state animal in the year 2014.

Additional Information 

• Important Current affairs related to Rajasthan in 2021-22:
• To provide local access to government services in the remotest villages of the state, Rajasthan Government has launched a mega campaign named ‘Prashasan Gaon Ke Sang’ in October 2021.
• Rajasthan CM Ashok Gehlot has approved a 3-year action plan to strengthen farmer producer organizations (FPOs) in the state.
• India’s 1^st Emergency Landing Facility on a National Highway in Rajasthan was inaugurated in September 2021.
• Chief Minister of Rajasthan: Ashok Gehlot
• Governor: Kalraj Mishra
• The Rajasthan government has launched the ‘Mission Niryatak Bano’ campaign to promote aspiring exporters in the state in August 2021.​
• Drinking water supply schemes of Rs. 6,872.28 crore have been approved for Rajasthan under Jal Jeevan Mission.
• They were approved in the State-level Scheme Sanctioning Committee (SLSSC) meeting held on 5^th January 2022.

The correct answer is Pranab Mukherjee.

Key Points 

• Pranab Mukherjee
• He was an Indian politician and has served as the 13^th President of India, from 2012 to 2017.
• A veteran in Indian politics, he has the rare distinction of having served as Foreign, Defence, Commerce, and Finance Minister at different times over his long and illustrious political career spanning several decades. In 1997, Pranab Mukherjee was voted an Outstanding Parliamentarian.
• Active in West Bengal politics, he was the president of the state's unit of Congress since 1985 but resigned in July 2010.
• Well-respected by politicians of all parties, Pranab Mukherjee is the Congress party's main troubleshooter and has often been called upon to guide the party through difficult situations.
• He is married to Suvra Mukherjee and has two sons and one daughter.
• In 2008, he was honoured with the Padma Vibhushan, the second-highest civilian award in India.
• He became Deputy Chairman of the Planning Commission from 1991 to 1996. Hence, Option 4 is correct.
• He was awarded India's highest civilian honour, the Bharat Ratna, in 2019, by his successor as president, Ram Nath Kovind.

The correct answer is concave.

Key Points 

• Concave or trans face of Golgi is maturing face which produce Golgian vacuoles.
• The Golgi apparatus in animal cells is positioned near the centrosome-based microtubule organizing center.
• Golgi pericentrosomal position is a striking feature of mammalian cells.
• It is mostly the result of secretory and Golgi membrane movement toward the minus end of microtubules by the dynein motor complex.
• Regulation of Golgi positioning is also important, it can occur at  different stages of the cell cycle such as:
• Membrane association is regulated during mitosis.
• During cycles of membrane capture and release for inward secretory and Golgi movements.
• Golgi positioning is maintained after inward movement by Golgi-nucleated microtubules.
• Golgi positioning may be a consequence of a rearranged centrosome-meditated microtubule array.
• Centrosome-meditated microtubule array orient their Golgi to perform directed secretion toward sites of rapid or specialized growth.

Important Points 

STEP-1:

• Newly synthesized proteins and lipids of the secretory pathway are packaged into membrane carriers that bud from the endoplasmic reticulum (ER).
• These membranes fuse with each other and/or preexisting ER-Golgi intermediate compartment membranes (ERGIC).
• ERGIC is transported along microtubules toward the centrosome by the dynein motor protein complex.

STEP-2:

​Two models are suggested in this step:

1. By the cisternal progression model, the membranes generate new cis-Golgi cisternae as they near the centrosome. This is due to fusion with recycling vesicles bearing cis-Golgi components including processing enzymes.
2. ​​By the Stable compartments model, the membranes fuse with preexisting cis-Golgi cisternae thereby delivering their content for processing.

• By either model, the continuous inward movement of membrane carriers will contribute to the steady state localization of Golgi membranes near the centrosome.
• This is principal because the membranes bear active dynein at the time of their delivery.
• Dynein is likely recruited directly from the cytoplasm onto Golgi membranes.
• Dynein further contributes to Golgi pericentrosomal positioning.

The correct answer is Brahmo Samaj

Key Points  

• The Brahmo Samaj was established in 1828 by Raja Ram Mohan Roy.
• The movement began between meetings of Bengalis in Calcutta in 1828.
• The conflict between Keshab Chandra Sen and Debendranath Tagore was broadened in 1865 when Tagore allowed the Brahmos conducting services to wear their sacred threads.
• Keshab objected to this decision and withdrew from the Brahmo Samaj along with his followers.
• He established the Brahmo Samaj of India on 15^th November 1866.
• While on the other hand, Tagore grouped themselves in Adi Brahmo Samaj.

​ 

Additional Information 

• The main agenda of the Brahmo Samaj is to purify Hinduism and teach monotheism.
• The ideals of Brahmo samaj relied on the twin pillars of reason and Vedas and Upanishads.

The Correct Answer is  Xylem parenchyma.

 Key PointsXylem:

• It is plant tissue that transports food water and other dissolved minerals from roots to other parts of the plant.
• It also provides mechanical strength to the plant body.
• Xylem consists of Tracheids, Vessels, Xylem Fibres, Xylem Parenchyma.
• Tracheids and vessels are the conducting elements of Xylem.
• Xylem fibres provide strength to the tracheids and vessels.
• The xylem parenchyma cells are mainly involved in the storage of carbohydrate, fats and water conduction.

The correct answer is Rickey Kej.

Key Points 

• City-based musician Ricky Kej walked away with a Grammy for his collaborative album Winds Of Samsara with South African flautist Wouter Kellerman for the Best New Age Album category at the 57^th Annual Grammy Awards in Los Angeles.
• Kej also serves as a UNESCO - MGIEP "Global Ambassador for Kindness", UNICEF Celebrity Supporter, and is an ambassador for the Earth Day Network.
• In 2020, Kej was named a GQ Hero 2020 by GQ magazine.
• Kej is credited with over 3,500 placements for radio and television jingles.

The Harappan cities  not been found in Uttarakhand

Key Points 

• The Indus Valley Civilization was established around 3300 BC.
• It flourished between 2600 BC and 1900 BC (Mature Indus Valley Civilization).
• It started declining around 1900 BC and disappeared around 1400 BC.
• This is also called Harappan Civilization after the first city to be excavated, Harappa (Punjab, Pakistan).
• The cities of Indus Valley Civilization were found in the Punjab and Sind in Pakistan, and in Gujarat, Rajasthan, Haryana and the Punjab in India.
• Archaeologists have found a set of unique objects in almost all these cities: red pottery painted with designs in black, stone weights, seals, special beads, copper tools, and paralleled sided long stone blades.
• Many of these cities were divided into two or more parts - Citadel and lower town.

Hence, we can conclude that the Harappan cities have not been found in Uttarakhand

The correct answer is a Combination Reaction.

Key Points 

• The combustion of coal is an example of Combination Reaction.
• A combination reaction is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY.
• The combination of two or more elements to form one compound is called a combination reaction.

​

Additional Information 

Other types of Chemical Reactions:

• Decomposition reaction:
• The opposite of a combination reaction, a complex molecule breaks down to make simpler ones. Such reactions are represented by equations of the following form: AB → A + B.
• Precipitation reaction: 
• Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming. Such reactions are represented by equations of the following form: A + Soluble salt B  → Precipitate + soluble salt C.
• Neutralization reaction: 
• An acid and a base react with each other. Generally, the product of this reaction is salt and water. Such reactions are represented by equations of the following form: Acid + Base → Salt + Water.
• Combustion reaction: 
• Oxygen combines with a compound to form carbon dioxide and water. These reactions are exothermic, meaning they give off heat. Such reactions are represented by equations of the following form: A + O2 → H2O + CO2.
• Displacement reaction: 
• One element takes place with another element in the compound. Such reactions are represented by equations of the following form: A + BC → AC + B.
• Double displacement reaction:
• Double displacement reactions occur when a part of two ionic compounds is exchanged and makes two new components.
• Double displacement reactions take place mostly in aqueous solutions wherein the ions precipitate and the exchange of ions takes place.

The correct answer is 'Right to life and personal liberty'

Key Points 

• The foremost right among rights to freedom is the right to life and personal liberty. No citizen can be denied his or her life except by procedure as laid down under the law.
• Right to life and personal liberty is one of the Fundamental Rights guaranteed by the Constitution of India.
• Inspired by America's Bill of Rights Articles 12 to 35 in part -III of the Indian constitution is fundamental rights
• Fundamental rights are not absolute, in other words, these rights can be suspended under special circumstances (except Articles 20 and 21).

Right to freedom:-

Given:

A dishonest merchant sells goods at a 12.5% loss on the cost price but uses 28 g weight instead of 36 g. 

Concept used:

Final percentage change after two successive increments of A% and B% = (A + B + $AB \over 100$) %

Calculation:

Percentage gain by using 28 g weight instead of 36 g = $\frac {36 - 28}{28} × 100$ = $\frac {200}{7}\%$

Percentage loss = 12.5%

Considering 12.5% loss as -12.5% profit,

Now, the final percentage profit/loss = ${\frac {200}{7} - 12.5 - {\frac {200}{7} × 12.5 \over 100}}$ = +12.5%

Here, the positive sign indicates a percentage profit.

∴ His percentage profit is 12.5%

Shortcut TrickCalculation:

Merchant sells goods at a 12.5% loss:

C.P : S.P = 8 : 7

Merchant uses 28 g weight instead of 36 g

C.P : S.P = 28 : 36 = 7 : 9

We can use successive methods:

So, C.P : S.P = 56 : 63 = 8 : 9

Profit% = {(9 - 8)/8} × 100 

⇒ 12.5%

∴ The correct answer is 12.5%.

Given:

The HCF of two numbers is 12. 

Concept used:

1. If P is the HCF of A and B then, A = P × m and B = P × n. 2. LCM is the smallest common multiple of two or more numbers.

Calculation:

Let the ratio of two numbers be A : B and their HCF be H and LCM be L.

Then, the numbers are AH and BH respectively.

LCM (AH, BH) i.e. L = H × A × B

Hence, L is a multiple of H.

Accordingly, if the HCF of two numbers is 12, then their LCM has to be multiple of 12.

Hence, 90 can't be their LCM.

∴ 90 can never be their LCM.

Given:

Two circles touch each other externally at P.

AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40°.

Concept used:

If two circles touch each other externally at some point and a direct common tangent is drawn to both circles, the angle subtended by the direct common tangent at the point where two circles touch each other is 90°.

Calculation:

According to the concept, ∠APB = 90°

Considering ΔAPB,

∠ABP

⇒ 90° - ∠PAB

⇒ 90° - 40° = 50°

∴ The measure of ∠ABP is 50°.

Given:

The mean proportion of 169 and 144

Concept used:

If A : B :: C : D then (B × C) = (A × D)

Calculation:

Let the mean proportion be Q.

The proportion becomes = 169 : Q :: Q : 144

​According to the concept,

(144 × 169) = (Q × Q)

⇒ Q² = (144 × 169)

⇒ Q = 12 × 13

⇒ Q = 156

∴ The mean proportion of 169 and 144 is 156.

Given:

The length and breadth of a rectangle are increased by 8% and 5%, respectively. 

Concept used:

Final percentage change after two successive increments of A% and B% = $(A + B + {AB \over 100})\%$

Calculation:

Final percentage increment in area = $8 + 5 + \frac {8 \times 5}{100}$ = 13.4%

∴ The area will increase by 13.4%.

Given:

$\frac{\cos 45^{\circ }}{\sec 30^{\circ}+ cosec30^{\circ}}$

Concept used:

Calculation:

$\frac{\cos 45^{\circ }}{\sec 30^{\circ}+ cosec30^{\circ}}$

⇒ $\frac {\frac {1}{\sqrt2}} {\frac {2}{\sqrt3}+ \frac {2}{1}}$

⇒ $\frac {\frac {1}{\sqrt2}} {2(\frac {\sqrt3 + 1}{\sqrt3})}$

⇒ $\frac {\sqrt3} {2{\sqrt2}({\sqrt3 + 1})}$

⇒ $\frac {\sqrt3({\sqrt3 - 1})} {2{\sqrt2}({\sqrt3 + 1})({\sqrt3 - 1})}$

⇒ $\frac {\sqrt3({\sqrt3 - 1})} {2{\sqrt2}({3 - 1)}}$

⇒ $\frac {({3 - \sqrt3})} {4{\sqrt2}}$

⇒ $\frac {({3\sqrt2 - \sqrt6})} {8}$

∴ The required answer is $\frac {({3\sqrt2 - \sqrt6})} {8}$.

Given:

$(49^{15} - 1)$

Concept used:

aⁿ​​​​​​ - bⁿ is divisible by (a + b) when n is an even positive integer.

Here, a & b should be prime number.

Calculation:

$(49^{15} - 1)$

⇒ $({(7^2)}^{15} - 1)$

⇒ $(7^{30} - 1)$

Here, 30 is a positive integer.

​According to the concept,

$(7^{30} - 1)$ is divisible by (7 + 1) i.e., 8.

∴ 8 is a divisor of $(49^{15} - 1)$.

Given:

In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m.

Concept used:

Time × Speed = Distance

Calculation:

According to the question,

Anil goes 1500m while Bakul goes (1500 - 150) i.e. 1350m.

Ratio of speed of Anil and Bakul = 1500 : 1350 = 10 : 9 = 200 : 180

According to the question,

Bakul goes 1500m while Charlie goes (1500 - 75) i.e. 1425m.

Ratio of speed of Bakul and Charlie = 1500 : 1425 = 20 : 19 = 180 : 171

So, the ratio of the speeds of Anil, Bakul and Charlie = 200 : 180 : 171

Let the speeds of Anil, Bakul and Charlie be 200k, 180k and 171k m/s respectively.

Time taken by Anil to finish the race = 1500/200k = 7.5/k seconds

Now, Anil beats Charlie by = (200 - 171)k ×7.5/k = 217.5m

∴ Anil beat Charlie by 217.5m.

Shortcut Trick

In a 1500 m race, Anil beats Bakul by 150 m

When Anil completes the race, Bakul covered (1500 - 150) = 1350 m

In a 1500 m race Charles is 75 m behind Bakul

So, in 1350 m race Charles is 75/1500 × 1350 = 67.5 m behind Bakul

So, Charles is (67.5 + 150) = 217.5 m behind from Anil in 1500 m race

∴ Anil beat Charlie by 217.5m.

Shortcut Trick

Simple Interest for 8 years = 3725 − 2500 = 1225

Interest for 1 year = 1225 ÷ 8 = 153.125

Rate % = (153.125 ÷ 2500) × 100 = 6.125%

∴ The correct answer is 6.125%.

Alternate Method

Given:

Principal (P) = ₹2500

Amount (A) = ₹3725

Time (T) = 8 years

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

T = 0 Years P = ₹2500 T = 8 Years A = ₹3725 SI = ₹1225 Rate = R%

Calculations:

⇒ SI = 3725 − 2500 = 1225

⇒ 1225 = (2500 × R × 8) ÷ 100

⇒ 1225 = 200 × R

⇒ R = 1225 ÷ 200

⇒ R = 6.125%

∴ The correct answer is 6.125%.

Additional Information

Sum Becoming 'n' Times at SI

When a certain sum of money becomes 'n' times of itself in 'T' years at Simple Interest, the rate of interest is given by R = 100 × (n − 1) ÷ T.

Compound Interest Formula

Amount under Compound Interest is calculated as A = P × (1 + R ÷ 100)^T, where interest is compounded annually.

Difference Between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest is calculated directly using the formula D = P × (R ÷ 100)².

Total pages printed by Z in 3 days = 210 + 160 + 218 ⇒ 588

Average = 588/3 ⇒ 196

Given:

The batting average for 27 innings of a cricket player is 47 runs.

His highest score exceeds his lowest score by 157 runs.

If these two innings are excluded, the average of the remaining 25 innings is 42 runs.

Formula used:

Average run = Total run in total innings/Total number of innings

Calculation:

Sum of runs for 27 innings of a cricket player = 47 × 27 = 1269

Sum of runs for 25 innings of a cricket player = 42 × 25 = 1050

Sum of remaining 2 innings = 1269 - 1050 = 219

Let the minimum score be x and the maximum score be x + 157

According to the question,

x + x + 157 = 219

⇒ 2x = 219 - 157

⇒ 2x = 62

⇒ x = 31

So, highest score = 157 + 31

⇒ 188

∴ His highest score in an innings is 188.

Shortcut Trick

The batting average for 27 innings of a cricket player is 47 runs.

The batting average for 25 innings is 42 runs (High and Low score excluded)

Here, Average decreases by (47 - 42) = 5

So, Total runs in that two innings (H + L) = 47 + 47 + (25 × 5) = 219 runs

Difference of runs in that two innings (H - L) = 157 runs

So, 2H = 219 + 157

⇒ H = 376/2 = 188 runs

(P + Q)'s 1 day's work = 1/15 + 1/10

⇒ (2 + 3)/30

⇒ 5/30

⇒ 1/6 

Work done by P and Q in 2 days = 1/6 × 2

⇒ 1/3

Remaining work = 1 - 1/3

⇒ 2/3

Now,

1/15 work is done by P in 1 day.

So, 2/3 work will be done by P in 15 × 2/3 = 10 days

So, the total time is taken = 10 + 2

⇒ 12 days

∴ The whole work was completed in 12 days.

Alternate MethodCalculation: 

LCM of 15, 10 is 30

Efficiency of P = 30/15 = 2

Efficiency of Q = 30/10 = 3

Two days of work will be (2 + 3) × 2 = 10

Remaining work = 30 - 10 = 20

As Q left remaining work will be done by P = 20/2 = 10 days

Total work done in 10 + 2 = 12 days

Calculation:

Total percentage of trucks sold in B, C, F and H = 27 + 18 + 7 + 14

⇒ 66%

Difference = 100% - 66%

⇒ 34%

∴ The required answer is 34 percent.

Given:

$x^{2} - 5x + 1 = 0$

Concept used:

If a + 1/a = b, then

a³ + 1/a³ = b³ - 3b

Calculation:

x² - 5x + 1 = 0

⇒ x2 + 1 = 5x

⇒ x + 1/x = 5

Now,

$\frac{x^{6}+x^{4}+x^{2}+1}{5x^{3}}$

⇒ $\frac{x^{3}+x+\frac{1}{x}+\frac{1}{x^3}}{5}$   [By dividing $\frac{1}{x^3}$]

⇒ $\frac{5^3 -3\times5+5}{5}$

⇒ $\frac{125 - 15 +5}{5}$

⇒ $\frac{115}{5}$

⇒ 23

∴ The required answer is 23.

Given:

PR = 17

QR = 8

PQ = 15

Concept used:

Sinθ = P/H

Cosθ = B/H

Here,

P = Perpendicular

B = Base

H = Hypotenuse

Calculation:

sin α + cos α

⇒ 8/17 + 15/17

⇒ (8 + 15)/17

⇒ 23/17

∴ The required answer is $\frac{23}{17}$.

Given:

$\frac{\left(17\right) ^{3}+\left( 7\right) ^{3}}{(17^{2}+7^{2}-k)} =24$

Concept used:

a³ + b³ = (a + b)(a² + b² - ab)

Calculation:

$\frac{\left(17\right) ^{3}+\left( 7\right) ^{3}}{(17^{2}+7^{2}-k)} =24$

⇒ $\frac{(17+7)(17^{2}+7^{2}-7\times17)}{(17^{2}+7^{2}-k)} =24$

⇒ $\frac{(17^{2}+7^{2}-119)}{(17^{2}+7^{2}-k)} =1$

⇒ 17² + 7² - 119 = 17² + 7² - k

⇒ k = 119

∴ The value of k is 119.

Given:

The circumference of the two circles is 198 cm and 352 cm respectively.

Concept used:

Circumference of the two circles = 2πr

Where, r = radius

Calculation:

Let the radius of two circle is r₁ & r₂ 

According to the question,

2πr2 - 2πr1 = 352 - 198

⇒ 2π(r2 - r1) = 154

⇒ π(r2 - r1) = 77

⇒ r2 - r1 = 77 × 7/22

⇒ r2 - r1 = 49/2

⇒ r2 - r1 = 24.5

∴ The required answer is 24.5 cm

Shortcut Trick

In any circle, if the central angle subtended by a chord is 60°, the triangle formed by the center and the chord's endpoints is an equilateral triangle (since two sides are equal radii, and the base angles must be (180° − 60°) ÷ 2 = 60° each).

For an equilateral triangle, all sides are equal.

∴ Chord AB = Radius = 10 cm.

∴ The correct answer is 10 cm.

Alternate Method

Given:

The radius of a circle is 10 cm. The angle subtended by chord AB at the centre of the circle is 60°.

Concept Used:

1. In an isosceles triangle, the angles opposite to the equal sides are equal.
2. In an equilateral triangle, all three sides are equal and each angle measures 60°.

Calculation:

OA = OB = 10 cm

ΔOAB is an isosceles triangle.

Therefore, ∠OAB = ∠OBA = (180° − 60°) ÷ 2 = 60°

Since ∠OAB = ∠OBA = ∠AOB = 60°, ΔOAB is an equilateral triangle.

Therefore, OA = OB = AB = 10 cm

∴ The length of the chord is 10 cm.

Additional Information

Equilateral Triangle in Circle

When a chord subtends a 60° angle at the center, it forms an equilateral triangle with the radii, meaning chord length = radius.

General Chord Length Formula

For any central angle θ, the chord length is 2r sin(θ/2). If θ = 90°, length = r√2. If θ = 120°, length = r√3.

Angle at Circumference

The angle subtended by a chord at the circumference is half the angle subtended at the center (30° in this case).

Given:

Diameter of each lead shot = 8.4 cm

Dimension of the rectangular solid = 88 × 63 × 42 (cm)

Concept used:

1. Volume of a sphere = $\frac {4\pi × (Radius)^3}{3}$
2. Volume of a cuboid = Length × Breadth × Height
3. The collective volume of all lead shots obtained should be equal to the volume of the rectangular solid.
4. Diameter = Radius × 2

Calculation:

Let N number of shots can be obtained.

Radius of each lead shot = 8.4/2 = 4.2 cm

​According to the concept,

N × $\frac {4\pi × (4.2)^3}{3}$ = 88 × 63 × 42

⇒ N × $\frac {4 × 22 × (42)^2}{3 × 7 × 1000}$ = 88 × 63

⇒ N = 750

∴ 750 lead shots can be obtained.

Calculation:

Now, the ratio of number of spoon manufactured by P to the number of spoon manufactured by R

⇒ 100 : 150

⇒ 2 : 3

∴ The ratio of number of spoon manufactured by P to the number of spoon manufactured by R is 2 : 3.

Given:

In the triangle, ABC, AB = 12 cm and AC = 10 cm, and ∠BAC = 60°.

Concept used:

According to the law of cosine, if a, b, and c are three sides of a triangle ΔABC and ∠A is the angle between AC and AB then, a² = b² + c² - 2bc × cos∠A

 

Calculation:

​According to the concept,

BC² = AB² + AC² - 2 × AB × AC × cos60°

⇒ BC² = 12² + 10² - 2 × 12 × 10 × 1/2

⇒ BC² = 124

⇒ BC ≈ 11.13

∴ The measure of BC is 11.13 cm.

Shortcut Trick

Use the Value Substitution Method by assuming θ = 45°.

Substitute the standard values: tan 45° = 1, cot 45° = 1, sec 45° = √2, and cosec 45° = √2.

Expression = (1)² + (1)² − (√2)² × (√2)²

⇒ 1 + 1 − (2 × 2) = 2 − 4 = −2

∴ The correct answer is -2.

Alternate Method

Given: tan²θ + cot²θ − sec²θ cosec²θ

Formula Used: In a right-angled triangle with sides a (perpendicular), b (base), and c (hypotenuse): tanθ = a/b, cotθ = b/a, secθ = c/b, cosecθ = c/a, and a² + b² = c².

⇒ Expression = (a/b)² + (b/a)² − (c/b)² × (c/a)²

⇒ Expression = (a²/b²) + (b²/a²) − (c⁴)/(a²b²)

⇒ Expression = (a⁴ + b⁴ − c⁴) / (a²b²)

⇒ From Pythagoras theorem: (a² + b²)² = (c²)² ⇒ a⁴ + b⁴ + 2a²b² = c⁴

⇒ a⁴ + b⁴ − c⁴ = −2a²b²

⇒ Value = (−2a²b²) / (a²b²) = −2

⇒ Thus, the result is −2, which corresponds to Option (2).

∴ The correct answer is -2.

Additional Information

Pythagorean Identities

1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ are essential for converting between squared trigonometric functions.

The Product-Sum Identity

A useful property is sec²θ + cosec²θ = sec²θ × cosec²θ, which simplifies expressions involving the product of reciprocals.

Angle Substitution Trick

For trigonometric identities, substituting θ = 45° is the fastest way to solve because tan(45°) and cot(45°) both equal 1.

Calculation:

The total sales of the first branch for both years = 80 + 105 = 185 thousand

The total sales of the fourth branch for both years = 85 + 95 = 180 thousand

Now, the ratio = 185 : 180 = 37 : 36

∴ The ratio of the total sales of the first branch for both years to the total sales of the fourth branch for both years is 37 : 36.