SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 2) (Previous Year Paper)

Statements:

I. All M are A.

II. No A is R.

The least possible Venn diagram from the given statement is:

Conclusion:

I. No M is R → Follow (Because All M are A and No A is R).

II. Some A are M → Follow (Because All M are A, so some A are definitely M).

III. Some R are A  → Does not follow (Because No A is R)

So, Both conclusions I and II follows.

Hence, the correct answer is "Option 1".

We apply the options to the given equation & solve it by using BODMAS rule:

Given Equation: 98 − 9 × 21 ÷ 7 + 56 = 69

Option 1) 56 and 9, + and ×

After Interchanging:

⇒ 98 − 56 + 21 ÷ 7 × 9 = 69

⇒ 98 − 56 + 3 × 9 = 69

⇒ 98 − 56 + 27 = 69

⇒ 125 - 56 = 69

⇒ 69 = 69

Given Equation: 98 − 9 × 21 ÷ 7 + 56 = 69

Option 2) 56 and 21, + and ×

After Interchanging:

⇒ 98 − 9 + 56 ÷ 7 × 21 = 69

⇒ 98 − 9 + 8 × 21 = 69

⇒ 98 − 9 + 168 = 69

⇒ 266 - 9 = 69

⇒ 257 ≠ 69

Given Equation: 98 − 9 × 21 ÷ 7 + 56 = 69

Option 3) 98 and 9, + and ×

After Interchanging:

⇒ 9 − 98 + 21 ÷ 7 × 56 = 69

⇒ 9 − 98 + 3 × 56 = 69

⇒ 9 − 98 + 168 = 69

⇒ 177 - 98 = 69

⇒ 79 ≠ 69

Given Equation: 98 − 9 × 21 ÷ 7 + 56 = 69

Option 4) 21 and 7, + and −

After Interchanging:

⇒ 98 − 9 + 7 ÷ 21 × 56 = 69

⇒ 98 − 9 + 0.33 × 56 = 69

⇒ 98 − 9 + 18.66 = 69

⇒ 116.66 - 9 = 69

⇒ 107.66 ≠ 69

Hence, the correct answer is "Option 1".

BODMAS rule:

We interchange the signs '+ and –' in the given options:

Option 1) 55 ÷ 11 – 15 + 3 × 2 = 15

55 ÷ 11 + 15 - 3 × 2 = 15

5 + 15 - 3 × 2 = 15

5 + 15 - 6 = 15

20 - 6 = 15

14 ≠ 15

Option 2) 4 × 3 – 6 ÷ 2 + 7 = 7

4 × 3 + 6 ÷ 2 - 7 = 7

4 × 3 + 3 - 7 = 7

12 + 3 - 7 = 7

15 - 7 = 7

8 ≠ 7

Option 3) 15 – 7 × 8 + 18 ÷ 3 = 65

15 + 7 × 8 - 18 ÷ 3 = 65

15 + 7 × 8 - 6 = 65

15 + 56 - 6 = 65

71 - 6 = 65

65 = 65

Option 4) 529 ÷ 23 + 10 – 5 × 4 = 30

529 ÷ 23 - 10 + 5 × 4 = 30

23 - 10 + 5 × 4 = 30

23 - 10 + 20 = 30

43 - 10 = 30 

33 ≠ 30

Hence, the correct answer is "Option 3".

The correct order according to the English dictionary is:

2. Remain
3. Remanent
4. Remark
5. Remember
6. Remnant

From the arrangement, we can see that word 'Remember' comes at the Fourth position.

Hence, the correct answer is "Option 4".

Alphabets & their positional values:

The pattern followed in the given series is:

The first alphabet is increased by + 5, 

The second alphabet is decreased by - 6,

The third alphabet is increased by + 7,

The fourth alphabet is decreased by - 8.

So, 'HOVM' will complete the series.

Hence, the correct answer is "Option 3".

Family Chart:

From the given information:

Now we consider the given options:

Option 1) Q – P + R means,

Q is the mother of P, P is the brother of R  

Here, P is the brother of R.

Option 2) P – Q + R means, 

P is the mother of Q, Q is the brother of R

Here, P is the mother R.

Option 3) P – Q ÷ R means,

P is the mother of Q, Q is the father of R

Here, P is the grandmother of R.

Option 4) R + P – Q means,

R is the brother of P, P is the mother of Q

Here, P is the Brother of R.

Hence, the correct answer is "Option 2".

The pattern followed in the given series is:

Each pattern repeats itself in an alternative step.

Next step:

The pattern in the second step will repeat itself in the fourth step.

Now we consider the given options:

Option 1) 

There is one extra circle.

Option 2) 

The pattern is correct.

Option 3) 

There is one extra circle & the rectangle is upside down.

Option 4) 

The rectangle is shaded upside.

Hence, the correct answer is "Option 2".

According to the English alphabets & their positional values:

The pattern followed in the given options is:

Option 1) 

Option 2) 

Option 3) 

Option 4) 

So, 'HBL' does not belong to the group.

Hence, the correct answer is "Option 1".

The mirror image of the given combination is:

We consider the given options:

Option 1) 

The positions of 'U' & 'I' is interchanged.

Option 2) 

The positions of 'U' & 'I' and 'F' & 'U' is interchanged.

Option 3) 

The positions of 'F' & 'U' is interchanged.

Option 4) 

The combination is correct.

Hence, the correct answer is "Option 4".

BODMAS rule:

Given Equation: [{(32 % 28) % (6 % 4)} % (1 % 7)] % 5 % 20

Option 1) −, +, ×, ÷, ×, ×, =

[{(32 - 28) + (6 × 4)} ÷ (1 × 7)] × 5 = 20

[{(4) + (24)} ÷ 7] × 5 = 20

[{28} ÷ 7] × 5 = 20

4 × 5 = 20

20 = 20.

Option 2) ×, ÷, ×, ×, −, +, =

[{(32 × 28) ÷ (6 × 4)} × (1 - 7)] + 5 = 20

[{(896) ÷ (24)} × (- 6)] + 5 = 20

[{37.3} × (-6)] + 5 = 20

-223.8 + 5 = 20

-218.3 ≠ 20

Option 3) ×, −, +, ×, ÷, ×, =

[{(32 × 28) - (6 + 4)} × (1 ÷ 7)] × 5 = 20

[{(896) - (10)} × 0.14] × 5 = 20

[{886} × 0.14] × 5 = 20

124.04 × 5 = 20

620.2 ≠ 20

Option 4) −, +, ×, ×, ×, ×, =

[{(32 - 28) + (6 × 4)} × (1 × 7)] × 5 = 20

[{(4) + (24)} × 7] × 5 = 20

[{28} × 7] × 5 = 20

196 × 5 = 20

980 ≠ 20

Hence, the correct answer is "Option 1".

When comparing figures 1 and 2, we get:

When '1' and '6' are visible in both dices, we get '5' and '2' are opposite to each other.

Now we compare figures 2 and 3, we get:

When '1' and '2' are visible in both dices, we get '4' and '6' are opposite to each other.

Since there are six sides on a dice the remaining two sides will be opposite to each other i.e., '3' and '1'.

So, the opposite of '3' will be '1'.

Hence, the correct answer is "Option 1".

The pattern followed in the given series is:

The figure in the series moves in the anticlockwise direction facing inside & outside every alternate step & it skips space in every step.

Next step: The figure will skip 4 spaces from the previous step and will face outside.

Now we consider the given options:

Option 1) 

The figure skips 5 spaces.

Option 2) 

The pattern is correct.

Option 3) 

The figure slips 5 spaces & faces inside.

Option 4) 

The figure faces inside.

Hence, the correct answer is "Option 2".

Alphabets & their positional values:

The pattern followed here is:

First, second, fourth & fifth alphabets are decreased by - 2.

The third alphabet is increased by + 2.

Now,

'ABOUT’ is written as 'YZQSR'

'PARTS' is written as 'NYTRQ'

Similarly, for 'PLANT'

So, 'PLANT' will be written as 'NJCLR'.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: First term² × (First term + 1) = Second term

Now we apply the pattern to the given series:

For, 5 ∶ 150

52 × (5 + 1) = 150

25 × 6 = 150

150 = 150

For, 8 ∶ 576

82 × (8 + 1) = 576

64 × 9 = 576

576 = 576

Similarly, For 6 ∶ ?

62 × (6 + 1) = ?

36 × 7 = ?

252.

Hence, the correct answer is "Option 1".

Alphabets & their positional values:

The pattern followed in the given series is:

Alphabets are decreased by - 2.

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

Hence, the correct answer is "Option 1".

We consider each option:

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: (First term + Second term) × 6 = Third term

Now apply the pattern on the given rows:

First row - 6, 9, 90

(6 + 9) × 6 = 90

15 × 6 = 90

90 = 90

Second row - 12, 8, 120

(12 + 8) × 6 = 120

20 × 6 = 120

120 = 120

Third row - 13, 6, ?

(13 + 6) × 6 = ?

19 × 6 = ?

114.

Hence, the correct answer is "Option 1".

Mistake PointsOperations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.

E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed.

Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed.

The pattern followed in the given series is:

The difference between odd terms is - 23

The difference between even terms is - 16.

So, '194' will complete the series**.**

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: First term × Third term + 4 = Second term.

Now apply the pattern:

For, (12, 112, 9)

12 × 9 + 4 = 112

108 + 4 = 112

112 = 112.

For, (10, 84, 8)

10 × 8 + 4 = 84

80 + 4 = 84

84 = 84.

Now checking the options:

Option 1) (12, 149, 12)

12 × 12 + 4 = 149

144 + 4 = 149

148 ≠ 149

Option 2) (13, 55, 4)

13 × 4 + 4 = 55

52 + 4 = 55

56 ≠ 55

Option 3) (11, 99, 9)

11 × 9 + 4 = 99

99 + 4 = 99

103 ≠ 99

Option 4) (18, 94, 5)

18 × 5 + 4 = 94

90 + 4 = 94

94 = 94

Hence, the correct answer is "Option 4".

Statements:

All c are f.

No f is t.

All p are c.

Venn diagram:

Conclusions:

I. Some t are c → Does not follow → (Because All C is F and No F are T, so No C will be T)

II. No p is t → Follow → (Because All P are C and All C is F, so No P will be T is definitely true)

So, only conclusion II follows.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Logic: First term × 3 + 3 = Second term

Now we consider the given options:

Option 1) 7 – 24

7 × 3 + 3 = 24

21 + 3 = 24

24 = 24

Option 2) 13 – 42

13 × 3 + 3 = 42

39 + 3 = 42

42 = 42

Option 3) 11 – 37

11 × 3 + 3 = 37

33 + 3 = 37

36 ≠ 37

Option 4) 5 – 18

5 × 3 + 3 = 18

15 + 3 = 18

18 = 18

So, 11 – 37 is an odd one.

Hence, the correct answer is "Option 3".

Family Chart:

Let us first decode the given symbols and then draw a family tree.

Given:  V ∞ U @ W # Y * Z

Therfore, V is sister of Z.

Hence, the correct answer is "Sister".

The pattern followed here is:

Thermometer ∶ Temperature → Thermometer is a device used to measure temperature.

Similarly,

Oximeter is a device used to measure the oxygen level of blood.

Hence, the correct answer is "Option 3".

Additional InformationGlucometer → It is a Device used to measure blood glucose levels

Odometer → It is a Device in vehicles to measure distance traveled.

Pedometer → It is a Device to count a person's steps, not related to bone fractures.

The pattern followed in the given series is:

‘PRESIDENT’ is written as ‘RPESDINTE’

‘KNOWLEDGE’ is written as ‘NKOWELGED’

Similarly, for ‘EDUCATION’

So, ‘EDUCATION’ will be written as 'DEUCTAONI'.

Hence, the correct answer is "Option 1".

According to the English alphabets & their positional values:

The pattern followed in the given codes is:

The alphabets are decreased by -1 & are arranged backwards to form the code.

 BEAR becomes QZDA

DUST becomes SRTC

Similarly,

GOLD becomes CKNF

Hence, the correct answer is "Option 1".

The correct answer is Maharashtra.

Key Points

• Lezim
• ​The Indian state is the Lezim folk dance associated with Maharashtra.
• Lezim dancers use a small musical instrument with jingling cymbals called the Lezim or lezium, after which the dance style is named, which is often also spelt as "Lezium."
• In a lezim, there are at least 20 dancers. The wooden idiophone to which tiny metal discs have been affixed and which the dancers utilise while performing the classical dance is the source of the name of this dance.
• The primary percussion music is played on the drum instrument dholki.
• It is performed while wearing vibrant outfits. With the dance's numerous callisthenic motions and potential for physical exertion, Maharashtra schools, militias, and other organisations regularly use it as a fitness exercise.

Additional Information

The correct answer is 2002.

Key Points

• Fundamental Duties

• Respect the Indian Constitution, its goals, and its institutions, as well as the National Anthem and Flag

• Respect and uphold the great principles that motivated the nation's fight for freedom.

• Uphold and defend India's independence, unity, and integrity.

• When required, defend the nation and perform national service.

• Promote harmony and a sense of common brotherhood among all Indians, notwithstanding their differences in religion, language, area, or social class, and condemn practises that are offensive to women's dignity.

• Value and safeguard the rich history of the nation's diverse culture.

• To preserve and enhance the natural world, including its woods, lakes, rivers, and wildlife, as well as to show compassion for all living things.

• Develop a humanistic outlook, a scientific mindset, and a spirit of reformation.

• Protecting public property and avoiding violence

• Strive for excellence in all areas of personal and societal endeavour so that the country is always striving for greater levels of ambition and success.

• To his ward or child between the ages of six and fourteen, provide educational possibilities. The 86th Constitutional Amendment Act of 2002 added this duty.

Additional Information

• Indian Constitution
• The Indian Constitution is the country's highest law. The document outlines the framework that delineates the core political code, as well as the fundamental rights, guiding principles, and responsibilities of citizens.
• It also spells out the organisation, methods, powers, and duties of governmental institutions. It is the world's longest-written national constitution.
• It confers constitutional supremacy (as opposed to parliamentary supremacy, given that a constituent assembly rather than Parliament produced it), and its preamble contains a proclamation that it was ratified by the people.
• The constitution cannot be overruled by parliament. B. R. Ambedkar and the Indian Constitution are featured on an Indian postage stamp from 2015.
• On 26 November 1949, the Indian Constituent Assembly approved it, and on 26 January 1950, it went into effect.
• The Dominion of India became the Republic of India when the constitution took the place of the Government of India Act 1935 as the primary law governing the nation.

The correct answer is 436.

Key Points

• Indian National Congress
• The second session of the Indian National Congress featured 436 delegates.
• The Congress Party, usually referred to as the INC or just the Congress is a reputable political organisation in India.
• In the British Empire's Asia and Africa, it was the first modern nationalist movement to emerge after its founding in 1885.
• Beginning in the late 19th century and particularly after 1920, Congress assumed command of the Indian independence movement under Mahatma Gandhi's guidance.
• Both the independence of India from the United Kingdom and the different anti-colonial nationalist movements within the British Empire was made possible by the Congress.

Additional Information

• Important Sessions of Indian National Congress

The correct answer is Mental health.

Key Points

• Tele MANAS
• The Union Ministry of Health and Family Welfare started the "Tele-MANAS" project in October 2022. M stands for mental health in MANAS.
• In October 2022, the Tele-MANAS (Telemental Health Assistance and Networking Across States) initiative was launched by the Ministry of Health & Family Welfare.
• In order to provide free, round-the-clock tele-mental health services to everyone in the country, Tele-MANAS is concentrating on underprivileged or isolated communities.
• The plan includes a network of 23 centres for tele-mental health excellence, with NIMHANS acting as the scheme's nodal body and the International Institute of Information Technology-Bangalore (IIITB) offering technical support.
• The National Health Systems Resource Center (NHRSC) and the Indian Institute of Technology (IIT) Bangalore would provide technical support.

Additional Information

• Mental health
• Our mental health includes all aspects of our emotional, psychological, and social well-being. It has an impact on our attitudes, feelings, and actions. It also affects how we deal with stress, communicate with others, and make wise decisions.
• From childhood and youth to adulthood, every stage of life is important for maintaining mental health.
• Despite the fact that the terms are commonly used interchangeably, poor mental health and mental illness are not the same. A person can have poor mental health even if they do not have a mental condition.
• A person who suffers from a mental illness may also experience periods of excellent physical, mental, and social health.

The correct answer is Manipur

Key Points

• Nupa Dance
• ​The Manipuri form of dance and music has spawned Nupa Pala (also known as Kartal Cholom or Cymbal Dance).
• It is mostly performed by men who sing and dance to the beat of Pung while using cymbals, white Pheijom (Dhoti), and round turbans (Mridanga).
• The Khamba Thoibi dance, which is a male-female duet performance, is another significant aspect of Manipuri dance.
• Together with the Maibi Dance (Priestess Dance), Leima Jagoi, etc. from the "Laiharaoba" dance, there is the Khamba Thoibi dance.

Additional Information

The correct answer is Tamil Nadu.

Key Points

• The largest wind energy cluster is found in Tamil Nadu's Kanyakumari district.
• Muppandal Wind Farm is the name given to it.
• With a 1500 MW capacity, it is the third-largest operating onshore wind farm in the world.
• Wind parks, wind power plants, and wind power stations are other names for wind farms.
• The wind is a low-cost, dependable, and clean energy source that can be used to create power.
  

Additional Information

• Important wind farms are also located in Andhra Pradesh, Karnataka, Gujarat, Kerala, Maharashtra, and Lakshadweep.
• Wind energy is used by windmills.
• In steep areas, open meadows, or coastal areas, wind farms are erected. India is the fifth-largest country in the world after Germany, Denmark, the USA, Spain, and the UK.
• The largest cluster of wind farms in India is located in Tamil Nadu, between Nagercoil and Madurai. Additionally, Gujarat, Karnataka, and Kerala. Maharashtra and Lakshadweep both have significant wind farms.

The correct answer is Son.

Key Points

• Son River
• ​Son is a right bank tributary of the Ganga.
• Central India is home to the perennial Son River. It starts near Amarkantak Hill in the Chhattisgarh district of Gaurela-Pendra-Marwahi, and eventually, it joins the Ganges River close to Patna, Bihar.
• After the Yamuna River, the Sone River is the Ganges' second-largest tributary in the south.
• Arrah and Patna are connected by India's oldest river bridge, the Koilwar Bridge over the Sone River.
• Sand from the Sone River is well-known throughout the nation. Throughout its path towards the Ganges, numerous hydroelectric projects and dams are present.

Additional Information

• Gomati
• ​The Ganges River receives water from the Gomti, Gumti, or Gomati Rivers is believed that bathing in the Gomti on Ekadashi, the eleventh day of the two lunar phases of the Hindu calendar month, will wash away sins because the river is thought to be the son of Rishi Vashishtha.
• Gomti is one of the five transcendental rivers of India, according to the Bhagavata Purana, one of the most important theological texts in Hinduism. There is a rare Gomti Chakra to be found.
• Gandak
• ​One of the main rivers in Nepal and a left-bank tributary of the Ganges in India is the Gandaki River, sometimes referred to as the Narayani and the Gandak. 46,300 km2 (17,900 sq mi) make up its whole catchment area, the majority of which is in Nepal.
• is renowned for having a deep canyon in the Nepalese Himalayas. The Dhaulagiri, Manaslu, and Annapurna I mountains, which are all over 8,000 metres (26,000 feet), are all found in the basin. The Gandaki basin's highest point is Dhaulagiri.
• Koshi
• ​A transboundary river called the Kosi or Koshi passes through China, Nepal, and India. It drains the southern slopes of Nepal and the northern slopes of the Himalayas in Tibet.
• The Kosi River and its seven upper tributaries are collectively known as Saptakoshi from a significant confluence of rivers north of the Chatra Gorge onwards.

The correct answer is March 25, 2022

Key Points

• Delhi Municipal Corporation
• On March 30, 2022, the Lok Sabha approved a bill that would merge the three municipal corporations of Delhi into a single organisation.
• The House adopted the Delhi Municipal Corporation (Amendment) Bill, 2022 following a response from Home Minister Amit Shah.
• The bill aims to provide a solid system for coordinated planning, efficient resource use, and enhanced governance.

Additional Information

• An Act of Parliament established MCD on April 7, 1958. Previous to that, Delhi's main civic organisation was the DMC (Delhi Municipal Committee).
• The MCD councillor that served the longest consecutively was Guru Radha Kishan (initially Delhi Municipal Committee).
• The 1993 revision to the Act changed the corporation's makeup, operations, governance, and management in significant ways.
• ​The majority of Delhi, India is governed by the Municipal Corporation of Delhi (MCD).
• The MCD is one of the biggest municipal organisations in the world, offering civic services to the estimated more than 11 million residents of the nation's capital.
• The New Delhi Municipal Council, Delhi Cantonment Board, and MCD are the other two municipalities in the National Capital Region of Delhi.
• The municipal corporation is located within a 539.5-mile (1,397.3-km2) region. It is the only municipality in Delhi that residents can vote on.

The correct answer is Lohri.

Key Points

• Lohri
• ​Lohri is a festival that is not associated with Sikkim.
• Popular Lohri celebrations take place mostly in Northern India during the winter.
• The Lohri celebration has various meanings and tales, many of which relate it to the Punjab region. Many people think that the festival signifies the end of the winter solstice.
• People in the northern part of the Indian subcontinent celebrate Lohri to welcome the end of winter and the arrival of longer days and the sun in the northern hemisphere.
• According to the lunisolar Punjabi calendar, it is marked the night before Maghi and usually invariably falls on January 13.

Additional Information

• Losar
• Tibetan Buddhism celebrates Losar, also referred to as the Tibetan New Year.
• Depending on local tradition, the event is observed on a variety of dates throughout Tibet, Bhutan, Nepal, India, and Pakistan.
• Sakewa
• For the Kirat Khambu Rai group in Sikkim, Sakewa is one of the most important cultural and religious celebrations.
• Community dances and other ceremonies are performed after the Bhumi Puja, which is observed as a tribute to Mother Earth.
• Yenya
• The largest event for the Sikkim-based Nepalese "NEWAR" population is Indra Jatra, also known as "Yenya," and it is widely observed.

The correct answer is Digesting Proteins.

Key Points

• Trypsin
• ​The function of the enzyme trypsin is to digest proteins.
• By breaking up lengthy chains of amino acids into smaller pieces, the enzyme trypsin in the early part of the small intestine initiates the breakdown of protein molecules.
• It is a serine protease from the PA clan superfamily that hydrolyzes proteins in the digestive tracts of numerous animals.
• When the pancreatic enzyme trypsinogen, in the proenzyme form, is activated, trypsin is generated in the small intestine.
• The carboxyl side of the amino acids lysine or arginine is where trypsin primarily breaks peptide chains. It is employed in a variety of biotechnological procedures.

Additional Information

• One significant protease, trypsin, has the unique ability to catalyze the hydrolysis of peptide and ester bonds with lysine and arginine amino acids at the carboxyl-terminus.
• Additionally, an autocatalytic, trypsin produces additional trypsin by converting trypsinogen.
• In addition to its basic function of breaking down dietary protein, trypsin also transforms the other two zymogens into chymotrypsin and carboxypeptidase.

The correct answer is Union Legislature.

Key Points

• Union Legislature
• The Indian Union Legislature serves as both the country's legislative body and the hub of all democratic political activity.
• The central legislature is the Parliament, and the state legislature is referred to as the "State Legislature."
• The Rajya Sabha (the Council of States) and the Lok Sabha, make up India's bicameral parliament, (the House of the People).

Additional Information

• Supreme Court- 
• The Supreme Court of India is the supreme judicial body of India and the highest court of the Republic of India under the constitution.
• The Chief Justice of India is the head and chief judge of the Supreme Court, which consists of a maximum of 33 judges under him.
• Article 124 has provisions for the establishment and organizational structure of the Supreme court.
• SC of India was established on 1st October 1937 as the Federal Court of India.
• H J Kania was the first Chief Justice of India.
• Sir Maurice Gwyer was the first chief justice of the Federal Court of India prior to the formation of the Supreme Court of India.
• State Legislature
• In India's states and union territories, the legislature is known as the State Legislative Assembly, commonly known as Vidhan Sabha or Saasana Sabha.
• It is the only legislative body in the 28 states and 3 union territories that have a unicameral state legislature, and in 6 states that have bicameral state legislatures, it is the lower house, with the State Legislative Council serving as the upper chamber.
• Ministry
• ​The administration of the Companies Act 2013, the Companies Act 1956, the Limited Liability Partnership Act of 2008, and the Insolvency and Bankruptcy Code of 2016 are the primary concerns of the Ministry of Corporate Affairs, a department of the Indian government.

The correct answer is Marginal standing facility rate.

Key Points

• Marginal standing facility rate
• The penal rate at which banks can borrow, on an overnight basis, from the Reserve Bank by dipping into their Statutory Liquidity Ratio (SLR) portfolio up to a predefined limit (2 per cent).
• This provides a safety valve against unanticipated liquidity shocks to the banking system. The MSF rate is placed at 25 basis points above the policy repo rate.

Additional Information

• Reverse repo rate
• ​The rate at which a nation's central bank borrows money from its own domestic commercial banks is known as the Reverse Repo Rate. It is a tool for the RBI's monetary policy that can be used to manage a nation's money supply. Assuming all other factors stay constant, the money supply decreases when the reverse repo rate increases and vice versa.
• The amount of money accessible in the market will decrease if the Reverse Repo rate rises because commercial banks will be more enticed to deposit their funds with the RBI.
• Repo rate
• The interest rate at which the Reserve Bank provides liquidity under the liquidity adjustment facility (LAF) to all LAF participants against the collateral of government and other approved securities.
• Leverage rate
• ​A leverage ratio is any of a number of financial metrics that examine the amount of capital that comes from debt (loans) or evaluates a company's capacity to satisfy its financial obligations. Companies employ a combination of stock and debt to finance their operations, therefore the leverage ratio category is crucial.
• By understanding how much debt a firm has, you can assess its ability to pay off its loans when they become due.

The correct answer is India.

Key Points

• Jute
• India is the world's top exporter of finished jute products and raw jute, coming in second place to Bangladesh.
• ​Long, silky, and lustrous, jute is a bast fibre that may be spun into strong, coarse threads.
• It is made from Corchorus flowering plants, which are from the Malvaceae family of mallows.
• Although Corchorus olitorius is the main source of fibre, Corchorus capsularis is thought to produce superior fibre.
• The plant or fibre known as "jute" is what is used to create burlap, hessian, or gunny cloth.

Additional Information

The correct answer is Chola.

Key Points

• Thanjavur (Tanjore) served as the Cholas' capital. The Chola Empire was founded by Vijayalaya.
• Within the eighth century, he overthrew the Pallavas, seized control of the Tanjore kingdom, and paved the way for the foundation of the powerful Chola kingdom.
• Tanjore was thus designated as the principal capital of the illustrious Chola Empire.
• Tanjore is situated in Tamil Nadu's Cauvery Delta. Later, it took the name Thanjavur.
• It is a well-known location for South Indian architecture, art, and religion.

Additional Information

The correct answer is Tissue

Key Points

• Tissue
• ​Tissue is a group of cells similar in structure and function.
• A biological organisational level between cells and an entire organ, tissue is historically derived.
• Hence, a tissue is frequently considered to be an amalgamation of comparable cells and their extracellular matrix from the same origin that work together to perform a certain function.
• Afterwards, various tissues are functionally grouped together to form organs.

Additional Information

• Organ system
• ​A group of organs that cooperate to carry out one or more functions is known as an organ system in biology.
• Each organ in a plant or animal body is composed of certain tissues and serves a specific purpose.
• Organ
• ​Organs are groups of tissues that serve the same purpose. The brain, heart, kidneys, liver, and lungs are the five main organs that humans need to survive. Organs with similar functions frequently work together to create whole organ systems.
• Parenchyma and stroma make up an organ. The primary tissue that is peculiar to an organ, such as the myocardium, the primary tissue of the heart, is known as the parenchyma. Nerves, blood vessels, and connective tissues can all be found in the stroma, which is sporadic tissue.
• Molecule
• ​According to the context, the term may or may not include ions that meet this requirement. A molecule is a collection of two or more atoms held together by attractive forces known as chemical bonds.
• When speaking of polyatomic ions, the distinction between them and ions is frequently ignored in the fields of quantum physics, organic chemistry, and biochemistry.

The correct answer is the Law of octaves.

Key Points

• ​Law of octaves was based on notes of the music.
• The 56 elements that were known at the time were attempted by British scientist John Newlands in 1864.
• Based on their atomic masses, he sorted them in ascending order and saw that every eighth element shared comparable characteristics. This observation led to the formulation of Newland's law of octaves.
• According to the law of octaves, every eighth element possesses characteristics that are identical when the elements are ordered in ascending order of atomic mass.

Additional Information

• Newton law
• ​According to Newton's first law of motion, an external force must be applied in order for an object to begin moving, stop moving, or change direction.
• Inertia is the ability of large entities to resist changes in their state of motion. The law of inertia is another name for the first law of motion.
• Mendeleev law
• ​Mendeleev organised the elements in horizontal rows, increasing the order of their atomic masses until he discovered an element whose characteristics matched those of the first element.
• Modern periodic law
• ​According to the Modern Periodic Law, an element's chemical and physical characteristics are periodic functions of its atomic number.
• The elements with identical properties reoccur after predetermined regular intervals if elements are put in increasing atomic number sequence.

The correct answer is 10.

Key Points

• The 103rd Constitution Amendment 2019, which provides for 10% EWS reservation among the advanced castes, was maintained by the Supreme Court on Monday, November 7, 2022, by a 3-2 majority.
• The decision was made by a five-judge panel that included Chief Justice of India (CJI) UU Lalit, Justices Dinesh Maheshwari, S Ravindra Bhat, Bela M Trivedi, and JB Pardiwala.
• There were three concurring rulings and one dissenting ruling by Justice Ravindra Bhat. CJI Lalit declared that he wholeheartedly concurred with Bhat's viewpoint.

Additional Information

• Supreme Court
• ​According to the constitution, the Supreme Court of India is both the highest court in the Republic of India and the country's top judicial authority.
• It has the final say in all legal matters and is the highest constitutional court. Also, it is capable of judicial scrutiny.
• The Supreme Court of India, which has a maximum of 34 judges and the Chief Justice of India as its head, has a wide range of authority in the form of original, appellate, and advisory jurisdictions.

The correct answer is Sixth.

Key Points

• Sixth Five-Year Plans
• In October 1980, then-prime minister Indira Gandhi reorganised and rebranded the Food For Work Program as the National Rural Employment Program.
• As of April 1981, it became a regular programme.
• The Sixth Five Year Plan saw the beginning of the Program. It tries to implement more employment for those who are underemployed.
• The Rural Landless Employment Guarantee was a central government-funded programme that provided landless people with work guarantees for at least 100 days.
• 10% of the money was also set aside for the sole benefit of SC/ST communities, with the remaining 25% going to social forestry and the remaining 20% to housing.
• On April 1, 1989, Rajiv Gandhi, the prime minister, merged the Rural Landless Employment Guarantee Program and the National Rural Employment Program to create the Jawahar Rozgar Yojana (JRY).

Additional Information

• Seventh Five-Year Plans
• ​In 1985, when Rajiv Gandhi led the Congress party to power, the seventh five-year plan was unveiled. The seventh planet's time period spanned from 1 April 1985 to 31 March 1990.
• From 1985 to 1987, Mr Manmohan Singh served as the Deputy Chairman of the Planning Commission. Food, work, and production were the first three plans included in the seventh strategy.
• Fifth Five-Year Plans
• ​The government of Indira Gandhi created India's Fifth Five-Year Plan (1974–1979).
• It put an emphasis on agriculture, reducing poverty, and creating jobs.
• Additionally, the plan attempted to lessen social and economic disparities within society.
• Fourth Five-Year Plans
• ​The Fourth Five-Year Plan embraced the goal of reversing the prior trend of greater economic and wealth power concentration.
• It was based on the Gadgil formula, which put an emphasis on growth while maintaining stability and moving towards independence.
• Indira Gandhi was in office as prime minister at the time.

The correct answer is Aryabhatiyam.

Key Points

• Aryabhatiyam
• ​Aryabhatiyam was written by Aryabhata.
• The only known surviving work of the Indian mathematician Aryabhata, who lived in the fifth century, is the Sanskrit astronomical treatise known as Aryabhatiya or Aryabhatiyam.
• Roger Billard, an astronomy philosopher, hypothesises that the book was written around 510 CE based on historical references it makes.
• There are four Adhyys, or portions, in the Aryabhatiya. Gtkpa, the opening portion, is made up of 13 slokas.
• The "Dasageethika" or "Ten Stanzas," the introduction to Aryabhatiya, is the book's first section.

Additional Information

• Books and Writers​

The correct answer is Rohtak.

Key Points

• Rohtak
• Not a Main Centre: Rohtak was not classified as a main centre because it lacked large-scale military resources, strategic political importance, and major British administrative establishments compared to key centers like Delhi, Kanpur, and Lucknow.
• Local Leadership: Led by Bisarat Ali (Risaldar in British Army) and Sabar Khan (local worker leader), who mobilized Ranghars and other communities.
• Resistance Actions: Attacks on British properties, government buildings, release of prisoners, and killing of British officials; Deputy Commissioner fled due to uprising.
• Military Engagements: Rebellion suppressed by British forces under Lt. W.S.R. Hodson on August 15, 1857.
• Broader Context: Rohtak’s uprising highlighted the widespread discontent and resistance in Haryana.
• Revolt of 1857
• ​The 1857 uprising marked the consciously initiated start of the fight for independence from British colonial tyranny.
• The 1857 uprising went by many names, including the Sepoy Mutiny and India's First War of Independence.
• As a sepoy mutiny, the uprising got its start in Meerut on May 10, 1857. Sepoys in the Bengal Presidency started it against the British authorities.
• The British East India Company's era of power came to an end with this Independence War.

Additional Information

• Centres of The Revolt
• From the Patna neighbourhood to Rajasthan's borders, the uprising swept throughout the entire region. The primary rebel strongholds in these areas are in Bihar's Arrah, Lucknow, Bareilly, Jhansi, and Gwalior.
• Lucknow
• ​The Awadhi kingdom's capital was Lucknow. One of the begums of the former monarch of Awadh, Begum Hazrat Mahal, assumed control of the uprising.
• Kanpur
• ​Nana Saheb, Peshwa Baji Rao II's adoptive son, was in charge of the uprising.
• Finally, Tantia Tope was vanquished, taken into custody, and executed.
• Although Nana Saheb managed to flee, his leader Tantia Tope persisted in the conflict.
• Brutal retribution was used to put down the uprising.
• The triumph was fleeting. After receiving further reinforcements, the British were able to retake Kanpur.
• He joined the uprising primarily as a result of the British depriving him of his pension.

The correct answer is Mahanadi.

Key Points

• Mahanadi
• The river basin present in Odisha is Mahanadi.
• In East-Central India, the Mahanadi River is an important river.
• It has a length of 900 kilometres overall and drains an area of around 132,100 square kilometres.
• Mahanadi is also home to the Hirakud Dam.
• Before joining the Bay of Bengal, the Mahanadi River travels through the states of Odisha and Chhattisgarh.
• Like many other seasonal Indian rivers, the Mahanadi originates from the confluence of many Himalayan streams, making it difficult to pinpoint its exact source.

Additional Information

• Narmada
• ​The Narmada River, also known as the Reva and formerly as Narbada or Nerbudda in English, is the fifth-longest river in India and the longest west-flowing river altogether.
• It is also the state of Madhya Pradesh's greatest flowing river. This river traverses the Indian states of Gujarat and Madhya Pradesh.
• Krishna
• ​After the Ganges and the Godavari, the Krishna River is a river in the Deccan plateau and is the third-longest river in India.
• In terms of water inputs and river basin area, it ranks fourth in India, behind the Ganges, Indus, and Godavari.
• Kaveri
• ​One of the largest rivers in India, the Kaveri flows through the states of Karnataka and Tamil Nadu.
• The Kaveri River originates at Talakaveri in the Brahmagiri range in the Western Ghats, Kodagu district of the state of Karnataka, at an elevation of 1,341 metres above mean sea level. It then flows for about 800 kilometres until emptying into the Bay of Bengal.

​

The correct answer is 26th November.

Key Points

• Every year on November 26th, India commemorates the adoption of its Constitution by observing Samvidhan Divas, or Constitution Day.
• The inaugural Constitution Day was observed in 2015 as a memorial to Bhim Rao Ambedkar, India's first law minister, who was instrumental in the Constitution's writing.
• On October 11, 2015, Prime Minister Narendra Modi made the announcement as he laid the cornerstone for the Statue of Equality in Mumbai.

Additional Information

• Important Days of November

The correct answer is Edinburgh.

Key Points

• Edinburgh
• ​The first edition of the Commonwealth Youth Games was held at Edinburgh.
• Scotland's capital and one of its 32 council areas is Edinburgh.
• The city was traditionally a part of Midlothian County (officially known as the "county of Edinburgh" or Edinburghshire until 1947), but from 1482 onward, it was governed separately from the neighbouring country.
• It is situated in Lothian on the Firth of Forth's southern side. After Glasgow, Edinburgh has the second-highest population in Scotland, and it ranks seventh in the UK.

Additional Information

• Commonwealth Youth Games
• ​The Commonwealth Games Federation hosts the annual multisport Commonwealth Youth Games (CYG).
• Up until 2008, the events took place in the years between the Commonwealth Games and those years.
• From 2011 to 2015, they were still held every four years, but they did so the year after the Commonwealth Games.
• They have been held the year prior to the Commonwealth Games since 2017.

The correct answer is Backstroke.

Key Points

• Backstroke
• The stroke in swimming that does NOT start with a dive into the pool from outside is Backstroke.
• One of the four swimming strokes used in competitive events governed by FINA is the backstroke or back crawl, which is the only one swum on the back.
• The benefit of easy breathing comes at the expense of swimmers being unable to see where they are going when swimming in this manner.
• In contrast to the other three competition swimming styles, it also has a different start.
• Backstroke is the second style swum in the individual medley, although it is the first style swum in the medley relay.

Additional Information

• Butterfly Stroke
• The butterfly is a swimming stroke performed on the chest with the hips and both arms moving symmetrically. The butterfly kick, also referred to as the "dolphin kick," is also used.
• While novices can swim competently in other strokes like the backstroke, front crawl, or breaststroke, the butterfly is a more challenging type that calls for both solid technique and strong muscles.
• Breaststroke
• ​The swimming stroke known as "breaststroke" is one in which the torso does not rotate, and the swimmer is on their chest.
• Because it can safely swim at slow rates and the swimmer's head is out of the water for a significant percentage of the swim, it is the most popular leisure technique.
• Freestyle 
• The International Swimming Federation (FINA) has established the category of swimming competition known as "freestyle," where participants are restricted to a few modest restrictions on their swimming stroke.
• The majority of swimming contests are freestyle races, which range in length from 50 metres (55 yards) to 1,500 metres (1,600 yards), or the mile. Since front crawl is the fastest surface swimming stroke, the word "freestyle stroke" is occasionally used as a synonym for "front crawl." Today, it is the stroke that is most frequently utilised in freestyle contests.

The correct answer is CaSO4.2H2O.

Key Points

• The chemical formula of gypsum is CaSO4.2H2O.
• A soft sulphate mineral called gypsum is made up of calcium sulphate dihydrate.
• It is widely mined, used as fertiliser, and the primary component of numerous plaster, sidewalk or blackboard chalk, and plasterboard products.
• Several cultures, including Ancient Egypt, Mesopotamia, Rome, the Byzantine Empire, and the Nottingham alabasters of Medieval England, have employed alabaster, a fine-grained, white or subtly coloured type of gypsum, for sculpture.
• Gypsum can also form selenite crystals, which are .

Additional Information

• Gypsum
• The Greek word "o" (gypsos), which means "plaster," is where the name "gypsum" comes from.
• Gypsum which has been dehydrated and used for various purposes for a long time has acquired the name plaster of Paris thanks to the quarries in the Parisian neighbourhood of Montmartre.
• Plaster of Paris hardens or "sets" in ways that are beneficial for casting and construction after adding water and after a few dozen minutes returns to being ordinary gypsum (dihydrate).

Given:

The perimeter of the square = 124 meters

Formula used :

The perimeter of the square = 4a

Area of the square = a²

Calculation 

⇒ Perimeter of the square = 4a

⇒ 124 = 4a

a = 31 m

⇒ Area of the square = a²

⇒ Area = 31² = 961 m²

⇒ Hence, The area of the square is 961 m²

Given:

P is the incentre of the triangle

Angle XYZ = 50°

Formula used :

If P is incentre, then

Angle XPZ = 90 + angle Y/2

Calculation:

According to the formula,

⇒ Angle XPZ = 90 + 50/2

⇒ Angle XPZ = 90 + 25 = 115°

⇒ Hence, The angle XPZ is 115°

Given:

Shopkeeper sells an article at a loss of 13.5%

If he sells it for Rs. 1274 more, there will be profit of 11%

Formula used:

CP = $\frac{Amount } {Loss + Profit} \times 100$

Calculation:

According to the formula, 

⇒ CP = $\frac{1274 } {13.5 +11}\times 100$

⇒ CP = 52 × 100 = Rs. 5200

⇒ Hence, The cost price of an article is Rs. 5200

Concept used:

The concept of the ratio is used

Calculation:

According to the question,

J1 = 200 + 150 + 300 + 100 + 400 = 1150

J2 = 500 + 350 + 250 + 150 + 100 = 1350

J1 : J2 = 1150 : 1350

J1 : J2 = 23 : 27

⇒Hence, The ratio of J1 : J2 is 23 : 27

Given:

The average weight of 12 persons increased by 3.5 when a new person replaced a 58 kg person

Formula used:

Weight of new person = previous person weight + Increased × number of persons

Calculation:

According to the formula, 

⇒ Weight of new person = 58 + 3.5 × 12

⇒ Weight = 58 + 42 =100

⇒ Hence, The weight of the new person is 100 kg

Alternate Method

 Let average weight of 12 persons be x.

Total weight of 12 persons = 12x

If a person with 58 kg weight is replaced by a new person of y kg weight,

Average weight increases by 3.5 kg.

Then, 12x – 58 + y = 12(x + 3.5)

⇒ 12x – 58 + y = 12x + 42

∴ y = 58 + 42 = 100 kg

Therefore, the weight of new person is 100 kg.

Given:

Total cars sold by all company's = 10000

Formula Used:

Average = $\frac{\text{Sum of observation}}{\text{Total observations}}$

Calculations:

⇒ Total percentage of cars sold by all company's = 7 + 8 + 13 + 16 + 12 + 14 + 10 + 20 = 100%

⇒ Total car sold by all company's = 10000

⇒ 100% = 10000

⇒ 1% = 100 cars

Now statement I,

⇒ Cars sold by company B = 8% = 8 × 1% = 8 × 100 = 800 cars

⇒ Cars sold by company F = 12% = 12 × 1% = 12 × 100 = 1200 cars

⇒ Cars sold by company H = 10% = 10 × 1% = 10 × 100 = 1000 cars

⇒ Total cars = 800 + 1200 + 1000 = 3000 cars

⇒ Average = $\frac{3000}{3}$ = 1000 cars

So, Statement I is incorrect

Now, For statement II

⇒ Car sold by company A = 20% = 20 × 1% = 20 × 100 = 2000

⇒ Car sold by company E = 16% = 16 × 1% = 16 × 100 = 1600

Ratio of company A and company E is

⇒ Company A : company E = 2000 : 1600 = 5 : 4

So, This statement is also incorrect

⇒ Hence, Both statement is incorrect

Shortcut Trick Whenever K + 1/K = −2, the unique value satisfying this for K < 0 is K = −1. Substituting K = −1 into the expression K10 + 1/K11: ⇒ (−1)10 + 1/(−1)11 = 1 + (−1) = 0. ∴ The correct answer is 0. Alternate Method Given: K + 1/K + 2 = 0 and K < 0 Formula Used: (a + b)2 = a2 + 2ab + b2 ⇒ K + 1/K + 2 = 0 ⇒ (K2 + 1 + 2K) ÷ K = 0 ⇒ K2 + 2K + 1 = 0 ⇒ (K + 1)2 = 0 ⇒ K + 1 = 0 ⇒ K = −1 Now, substitute the value of K in the required expression K10 + 1/K11: ⇒ (−1)10 + 1 ÷ (−1)11 ⇒ 1 + 1 ÷ (−1) (Since −1 to an even power is 1 and to an odd power is −1) ⇒ 1 − 1 = 0 ∴ The correct answer is 0. Additional Information Standard Algebraic Conditions If x + 1/x = 2, then x = 1. If x + 1/x = −2, then x = −1. Powers of Negative Unity (−1)n = 1 if n is an even number, and (−1)n = −1 if n is an odd number. Quadratic Roots For a quadratic equation ax2 + bx + c = 0, if b2 − 4ac = 0, the equation has two equal real roots.

Calculations:

⇒ cos 45° sin 15°

⇒ $\frac{1}{\sqrt2}\times\frac{\sqrt3-1}{2\sqrt2}$

⇒ $\frac{\sqrt3-1}{2\times2}$

⇒ $\frac{\sqrt3-1}{4}$

⇒ Hence, Option 2 is correct

Given:

x + ${{1} \over x}$ = 2

Formula Used:

x3 +  ${{1} \over x^{3}}$= a³ - 3a

Calculations:

⇒ x + ${{1} \over x}$ = 2

⇒ here, a = 2

Now put the value of a in the formula

⇒ x3 +  ${{1} \over x^{3}}$= a3 - 3a = (2)³ - 3(2) = 8 - 6 = 2

⇒ Hence, Value of the above equation is 2

Given:

The table is given above

Concept Used:

Simple assumption is used

Calculations:

As we see the table from bottom to top,

The height is increasing and weight is also increasing

⇒ Hence, Option 1 is correct

Given:

Bigger circle radius(R) = 20 cm

Smaller circle radius(r) = 16 cm

Formula Used:

(Hypotenuse)² = (Base)² + (Perpendicular)²

Calculations:

As BOC is an right-angled triangle at C

by Pythagoras theorem,

⇒ (BO)2 = (CO)2 + (BC)²

⇒ (20)² = (16)² + (BC)²

⇒ 400 = 256 + BC²

⇒ BC = $\sqrt{400 - 256}$

⇒ BC = $\sqrt{144}$

⇒ BC = 12 cm

When a line from centre fall on chord, It divide it into 2 equal parts

⇒ AB = 2BC = 2(12) = 24 cm

⇒ Hence, The length of the chord is 24 cm

Given:

circumference of the two circles is 308 cm and 440 cm

Formula Used:

Circumference of the circle = $2\pi r$

Calculations:

⇒ Circumference of the circle = $2\pi r$

⇒ 308 = $2\times \frac{22}{7}\times r_1$

⇒ r₁ = 49 cm

⇒ Circumference of the circle =​​ $2\pi r$

⇒ 440 = $2\times \frac{22}{7}\times r_2$

⇒ r₂ = 70 cm

⇒ Difference between the radius and the circle = r₂ - r₁ = 70 - 49 = 21 cm

⇒ Hence, The difference is 21 cm

Formula used:

a³ - ${{1} \over a}$³ = (a - b)[ a² + ${{1} \over a^2}$ + 1]

Calculations:

⇒ 3[a - ${1{} \over a}$] + [a - ${{1} \over a}$]³

⇒ (a - ${1{} \over a}$) [ 3 + (a - ${{1} \over a}$)2 ]

⇒ (a - ${1{} \over a}$) [ 3 + a2 + ${{1} \over a^2}$ - 2 ]

⇒ (a - ${1{} \over a}$) [ a2 + ${{1} \over a^2}$ + 1]

⇒ a3 - ${{1} \over a^{3}}$

⇒ Hence, The value of the above equation is  a3 - ${{1} \over a^3}$

Given:

Number divisible by 7 and 11

Concept used:

The concept of LCM is used

Calculations:

⇒ LCM of 7 and 11 = 77

The number divisible by 7 and 11 both should by divisible by 77

Numbers are

⇒ 77, 154, 231, 308, and 385

and next number will be greater than 430

⇒ Hence, Total number divisible by 7 and 11 is 5

Given:

Vijay complete the work in 12 weeks

Praveen complete the work in 8 weeks

They work on alternate weeks starting with Praveen 

Formula used:

Total work = Efficiency $\times$Time taken

Calculations:

⇒ Total work = LCM of 12 and 8 = 24

⇒ Efficiency of Vijay = Work / Time = 24 / 12 = 2

⇒ Efficiency of Praveen = 24 / 8 = 3

As they work on the alternative basis

⇒ 1 week = 3 work done

⇒ 2 week = 3 + 2 = 5 

similarly,

⇒ In 8 week = 20 work

⇒ 9 week = 20 + 3 = 23 work

Remaining work is done by Vijay

⇒ Time taken to complete = 1 / 2 = 0.5 week

⇒ Total time taken to complete the work = 9 + 0.5 = 9.5 week

⇒ Hence, The work done on alternative basis will take 9.5 weeks

Given:

14 ∶ 30 ∶∶ 7 ∶ x

Concept used:

The concept of Proportional values is used

Calculations:

⇒ 14 ∶ 30 ∶∶ 7 ∶ x

This can be written as

⇒ $\frac{14}{30}=\frac{7}{x}$

⇒ $\frac{7}{15}=\frac{7}{x}$

⇒ x = 15

⇒ Hence, The value of x is 15

Given:

A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm and AC = 24 cm

Side AB, BC and AC touch circle at D, E and F

Concept used:

When two tangent is drawn from same point on the circle then the length of the both of the chord will be same

Calculation:

As from point A two tangent is drawn on the circle

⇒ AD = AF = a

Similarly, From point B two tangent is drawn on the circle

⇒ BD = BE = b

Similarly, From point C two tangent is drawn on the circle

⇒ CE = CF = c

According to the question

⇒ AB = a + b

⇒ 16 = a + b  .......(1)

BC = b + c

⇒ 20 = b + c  .......(2)

⇒ AC = a + c

⇒ 24 = a + c  .......(3)

Now, On adding eq (1), (2), and (3), we get

⇒ 16 + 20 + 24 = a + b + b + c + a + c

⇒ 60 = 2(a + b + c)

⇒ a + b + c = 30

Now put the value of b + c in above equation, we get

⇒ a + 20 = 30 

⇒ a = 10 cm

⇒ Hence, The value of AD is 10 cm

Given:

 ∆ ABC ~ ∆DEF

2AB = DE

BC = 8 cm

Concept used:

The ratio of the corresponding side of the similar triangle is equal

Calculations:

As, ∆ ABC ~ ∆DEF

⇒ $\frac{AB}{DE}=\frac{BC}{EF}$

As we know, 2AB = DE

⇒ $\frac{AB}{2AB}=\frac{8}{EF}$

⇒ EF = 8 $\times$ 2 = 16 cm

⇒ Hence, The value of EF is 16 cm.

Given:

Number divisible by 9, 24 and 36

Concept used:

The concept of LCM is used

Calculations:

⇒ LCM of 9, 24 and 36 = 72

⇒ Hence, The least number divisible by 9, 24 and 36 is 72

Given:

1 + sin θ = m cos θ

Formula Used:

(a + b)² = a² + b² + 2ab

sec² θ = 1 + tan² θ

Calculations:

As from given part

⇒ 1 + sin θ = m cos θ

⇒ m = 1 / cos θ + sin θ / cos θ

⇒ m = sec θ + tan θ

squaring both side

⇒ m² = sec² θ + tan² θ + 2(sec θ)(tan θ)

⇒ m2 = 1 + tan2 θ + tan2 θ + 2(sin) / (cos² θ)

⇒ m2 = 1 + 2tan2 θ + 2(sin) / (cos2 θ)

⇒ m2 = $1 + \frac{2sin^2 θ}{cos^2 θ} + \frac{2sin θ}{cos^2 θ}$

⇒ m2 = $\frac{cos^2 θ+2sin^2 θ+2sin θ}{cos^2 θ}$

Applying componendo and dividendo rule

⇒  $\frac{m^2-1}{m^2+1} = \frac{cos^2 θ+2sin^2 θ+2sin θ-cos^2 θ}{cos^2 θ+2sin^2 θ+2sin θ+cos^2 θ}$

⇒  $\frac{m^2-1}{m^2+1} = \frac{2sin^2 θ+2sin θ}{2cos^2 θ+2sin^2 θ+2sin θ}$

⇒  $\frac{m^2-1}{m^2+1} = \frac{2sin θ(1+sin θ)}{2+2sin θ}$

⇒  $\frac{m^2-1}{m^2+1} = \frac{2sin θ(1+sin θ)}{2)1+sin θ)}$

⇒  $\frac{m^2-1}{m^2+1} = sin θ$

⇒ Hence proved

Given:

Sohan buys a book of cost Rs. 513

On buying 2 book he get 20% discount

On buying more than 2 book he get 25% discount

On buying 1 book he get 10% discount

For students they get 5% additional discount

Formula Used:

SP = MP $\times$ (100 - Disocunt%)

Calculations:

According to the question,

Sohan is a student and he buys a book

So, he will get a discount of 5% and 10%

So the Marked Price of the book will be

⇒ MP $\times$ 5% $\times$ 10% = 513

⇒ MP $\times$ (100 - 5%) $\times$ (100 - 10%) = 513

⇒ MP $\times$ 95% $\times$ 90% = 513

⇒ MP = $\frac{513\times100\times100}{95\times90}$

⇒ MP = 600

⇒ Hence, The Marked Price of the book is Rs 600

Given:

A man row to a place 48 km and comes back in 14 h

Formula used:

Speed = Distance / Time

Calculation:

Let he move 4 km in x hours in downstream

⇒ Speed = 4 / x

And He moves in upstream

⇒ Speed = 3 / x

According to the question, 

⇒ $\frac{48} {\frac{4} {x} } + \frac{48} {\frac{3} {x} } = 14$

⇒ $12x + 16x = 14$

⇒ x = 1 / 2

⇒ Speed in downstream = $\frac{4} {\frac{1 } {2} }$ = 8 km/h

⇒ Speed in upstream = $\frac{3} {\frac{1 } {2} }$ = 6 km/h

⇒ Speed of stream = $\frac{1(x-y)} {2 } =\frac{1(8-6)} {2 } = \frac{2} {2}$ = 1 km/h

⇒ Hence, Speed of stream is 1 km/h