SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4) (Previous Year Paper)

The pattern followed is:

$First : number \over10$ = Second number 

$Second : number \over10$ = Third number

Let us check each option:

1. (400 – 40 – 4) 

The pattern followed here is:

⇒$400\over10$ $= 40$ 

⇒ $40\over 10$ $= 4$ 

Then, it will be (400 – 40 – 4).

2. (300 – 30 – 7) 

The pattern followed here is: 

⇒$300\over10$ $= 30$ 

⇒$30 - 23$ $= 7$

Then, it will be (300 – 30 – 7). 

3. (1000 – 100 – 10) 

The pattern followed here is:

⇒ $1000\over10$ $= 100$

⇒$100\over10$ $= 10$ 

Then, it will be (1000 – 100 – 10) 

4. (500 – 50 – 5) 

The pattern followed here is:  

⇒$500\over 10$ $= 50$

⇒$50 \over 10$ $= 5$

Then, it will be (500 – 50 – 5).

The pattern followed is:

$First : number \over10$ = Second number 

$Second : number \over10$ = Third number

Option 1, Option 3 and Option 4 have the same pattern only Option 2 has a different one then, and the odd one out is Option 2.

Hence, the correct answer is 'Option 2'.

Given:

108 ÷ 2 * 10 + 70 – 10 = 480

Calculation:

Checking each options calculation.

(1) Option 1: + and –

⇒108 ÷ 2 * 10 + 70 – 10 = 480

 + and – is interchanged:

⇒108 ÷ 2 * 10 - 70 + 10 

⇒108 ÷ 2 * 10 - 70 + 10

⇒54*10 - 70 + 10 

⇒540 - 70 + 10 

⇒540 - 60 

⇒480

(2) Option 2: ÷ and *

⇒108 * 2 ÷ 10 + 70 – 10 = 480

 ÷ and * is interchanged:

⇒108 * 2 ÷10 + 70 – 10 

⇒*108 5 + 70 – 10 

⇒540 + 70 – 10

⇒610 - 10

⇒600

(3) Option 3: + and *

⇒108 + 2 ÷ 10 * 70 – 10 = 480

 + and * is interchanged:

⇒108 + 2 ÷10 * 70 – 10 

⇒108 +5 70* – 10 

⇒108 +14 – 10 

⇒122 - 10

⇒112 

(4) Option 4: ÷ and –

⇒108 + 2 - 10 * 70 ÷ 10 = 480

 ÷ and – is interchanged:

⇒108 + 2 - 10 * 70 ÷ 10 

⇒108 + 2 - *10 7

⇒108 + 2 - 70

⇒110 - 70

⇒40

Hence, two signs that should be interchanged to make the given equation correct is '+ and –'.

Statements:

I. All N are K.

II. All K are P.

The least possible diagram for the given statements is as follows:

  

Conclusions:

I. Some P are not K →False (All K are P so some P are K is definite but some P are not K is not definite so it is possible but not definite).

II. No P is N→ False (All N are P in the statement so it is not possible.)

Hence, "Neither conclusion follows".

Family Chart:

Given:

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

 

Given:  'H @ V @ U # W & E ^ X # Z & R ^ S' 

**1)**H @ V means ‘H is the sister of V’.

2) V @ U means ‘V is the sister of U’.

**3)**U # W means ‘U is the wife of W’.

4) W & E means ‘W is the brother of E’.

**5)**E ^ X means ‘E is the mother of X’.

**6)**X # Z means ‘X is the wife of Z’.

7)Z & R means ‘Z is the brother of R’.

**8)**R ^ S means ‘R is the mother of S’.

 

Now, check all the options:

1) Z is the maternal grandfather of S → False (Z is the maternal uncle of S).

2) W is the husband of U → True

3. E is the mother-in-law of Z → True

4. U is the sister of H → True

Hence, “Z is the maternal grandfather of S” is the correct answer.

Family Chart:

Given:

'A – B' means that 'A is the brother of B'.

'A + B' means that 'A is the sister of B'.

'A ÷ B' means that 'A is the father of B'.

Let us first decode the given symbols and Family chart:

Now, let us check all the options.

1. P + Q ÷ R → False (P is the sister of Q and Q is the father of R).

2) P ÷ Q – R → False (P is the father of Q and Q is the brother of R).

3. P – Q ÷ R → True (P is the brother of Q and Q is the father of R that means P is the paternal uncle of R).

4. P – Q + R → False (P is the brother of Q and Q is the sister of R).

Hence, 'P – Q ÷ R' is the correct answer.

Given:

189 ÷ 2 × 30 + 18 – 5 = 159

Calculation:

Let us check each option:

Option 1: 189, 30 and +, ÷

Given: 189 ÷ 2 × 30 + 18 – 5 = 159

After interchanging: 30 + 2 × 189 ÷ 18 – 5 = 159

⇒ 30 + 2 × 189 ÷ 18 – 5 = 159

⇒ 30 + 2 × 10.5 – 5 = 159

⇒ 30 + 21 – 5 = 159

⇒ 46 ≠ 159

This is not correct the equation.

Option 2: 18, 30 and ÷, −

​Given: 189 ÷ 2 × 30 + 18 – 5 = 159

After interchanging: 189 - 2 × 18 + 30 ÷ 5 = 159

⇒ 189 - 2 × 18 + 30 ÷ 5 = 159

⇒ 189 - 2 × 18 + 6 = 159

⇒ 189 - 36 + 6 = 159

⇒ 159  = 159

This is correct the equation.

Option 3 : 2, 30 and ÷, ×

​Given: 189 ÷ 2 × 30 + 18 – 5 = 159

After interchanging: 189 × 30 ÷ 2 + 18 – 5 = 159

⇒ 189 × 30 ÷ 2 + 18 - 5 = 159

⇒ 189 - 15 + 13 = 159

⇒ 187 ≠ 159

This is not correct the equation.

Option 4 : 30, 18 and −, ×

​Given: 189 ÷ 2 × 30 + 18 – 5 = 159

After interchanging: 189 ÷ 2 - 18 + 30 × 5 = 159

⇒ 94.5 - 18 +  30 × 5 = 159

⇒ 94.5 - 18 + 150 = 159

⇒ 226.5 ≠  159

This is not correct the equation.

Hence, 'Option 2' is the correct answer.

The option in which the given figure is embedded is,

Hence, the correct answer is 'Option 2'.

The logic followed here is :

The figure is vertically flipped and each flip reduced one ring in the embedded spring.

1. Pattern of Star: In each consecutive circle, the star is moving vertically upwards and downwards. Thus, in the following circle the star will be placed at downward. 

2. Pattern of Spring: In each consecutive circle, the rings in spring reduce by one. Thus, in the following circle, the number of rings will be 6 in the spring. 

so the next figure will be,

 

Hence, 'Option 3' is the correct answer.

The logic followed here is:

hence, 'NEHO' is the correct answer.

The correct mirror image of the given figure when the mirror is placed at the right side of the figure is :

Hence, 'Option 3' is the correct answer.

Additional Information 

In the Mirror image left side and right side changed vice-versa where the top and bottom remain the same.

The reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

The water image is just a reflection where the top and bottom parts of the images changed and the left and right sides of the image remain the same.

The pattern followed here is:

‘Nest’ is the living and breeding place of ‘Birds'.

Let us check each option:

1. 'Garden' is the living and breeding place of 'many fauna and flora'.
2. ‘Burrow’ is the living and breeding place of ‘Rabbits'.
3. 'Den' is the living and breeding place of 'Lions'.
4. 'Cage' is the living and breeding place of ' many animals'.

Hence, 'Burrow' is the correct answer.

The logic followed here is: 

Numbers in a set are squares of three consecutive numbers. 

Similarly, apply the logic on each option,

Option 1 : (49, 64, 81)

The set is a square of three consecutive numbers.

Option 2 : (1, 16, 49)

The set is not a square of three consecutive numbers.

Option 3 : (36, 81, 49)

The set is not a square of three consecutive numbers.

Option 4 : (49, 36, 81)

The set is not a square of three consecutive numbers.

Hence, 'Option 1' is the correct answer.

Taking dice positions 2 and 4 with 5 as common,

Moving clockwise from the Common number 5,

Pair of opposite numbers:

5 - 6

4 - 1

2 - 3

So, the opposite number to 2 is 3.

Hence, the correct answer is "3".

Statements:

All gorillas are bears.

All pigs are bears.

All bears are tigers.

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Conclusions:

I. All pigs are tigers → Follow → Since 'All pigs are bears.' and  'All bears are tigers.' we can say that All pigs are tigers and the same can be seen in the Venn diagram so the conclusion follows.

II. All tigers are gorillas → Does not follow → From the given statements  'All gorillas are bears.' and 'All bears are tigers.' Therefore 'All tigers are gorillas' is a possibility and the same can be seen in the Venn diagram so the conclusion does not follows.

III. Some tigers are pigs → Follow → Since 'All pigs are bears.' and 'All bears are tigers.' we can say that Some pigs are tigers and the same can be seen in the Venn diagram so the conclusion follows.

Hence, Only conclusions I and III follow.

Let us find the pattern in each option,

Option 1: OIGE

Option 2: QKJH

Option 3: SMLJ

Option 4: WQPN

Here, the odd letter-cluster. is 'OIGE'.

Hence, 'OIGE' the correct answer.

The logic followed here is : 

First number + Third number = New Number x 3 = Second number.

1. (12, 51, 5)

2. (8, 30, 2)

Applying the logic on each options,

Option 1: (14, 120, 16)

The logic does not apply.

Option 2: (13, 10, 7)

The logic does not apply.

Option 3: (19, 44, 3)

The logic does not apply.

Option 4: (11, 51, 6)

 

The logic apply here.

Hence, 'Option 4' is the correct answer.

The logic followed here is:

'LUNGS' is written as ‘OXQJV’,

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‘POWER’ is written as ‘SRZHU’,

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 Similarly, for 'ELOQUENT'

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‘ELOQUENT’ is written as ‘HORTXHQW’.

Hence, the correct answer is "Option 1".

Given:

Interchange 7 and 3.

Calculation:

Let us check each option:

Option 1: 3 ÷ 1 – 7 × 2 + 4 = 8

After interchanging: 7 ÷ 1 – 3 × 2 + 4 = 8

⇒ 7 ÷ 1 – 3 × 2 + 4 = 8

⇒ 7 - 6 + 4 = 8

⇒ 5 ≠ 8

This is not correct the equation.

Option 2: 3 × 2 + 7 – 6 ÷ 3 = 18

After interchanging: 7 × 2 + 3 – 6 ÷ 7 = 18

⇒ 7 × 2 + 3 – 6 ÷ 7 = 18

⇒ 14 + 3 - 0. 85  = 18

⇒ 16.15  ≠ 18

This is not correct the equation.

Option 3: 3 + 7 × 4 – 6 ÷ 2 = 20 

After interchanging: 7 + 3 × 4 – 6 ÷ 2 = 20

⇒ 7 + 3 × 4 – 6 ÷ 2 = 20

⇒ 7 +12 - 3 = 20

⇒ 16 ≠ 20

This is not correct the equation.

Option 4: 7 + 3 × 2 – 4 ÷ 1 = 13

After interchanging: 3 + 7 × 2 – 4 ÷ 1 = 13

⇒ 3 + 7 × 2 – 4 ÷ 1 = 13

⇒ 3 + 14 - 4 = 13

⇒ 13 = 13

This is correct the equation.

Hence, 'Option 4' is the correct answer.

The logic followed here is:

1. BASE: EASB 

2.  MINE: EINM

Similarly, in CALM: ?

Hence, 'MALC' is the correct answer.

The logic followed here is :

Hence, 'CVXU' is the correct answer.

The order of words according to dictionary,

4. Telecast
5. Telegram
6. Telepath
7. Telephone
8. Telescope

Here Telepath will come at ‘Third’ position.

Hence, 'Option 1' is the correct answer.

The logic followed here is:

​​(First Number )/ 2 + (Second number) × 1.5 = Third Number.

(52, 10, 41)

(46, 18, 50)

Apply the logic on each options,

Option 1 : (68, 26, 73)

The logic apply here.

Option 2 : (19, 33, 69)

The logic does not apply here.

Option 3 : (41, 17, 36)

The logic does not apply here.

Option 4 :(23, 18, 40)

The logic does not apply here.

Hence, 'Option 1' is the correct answer.

The logic followed here is :

Hence, '-14' is the correct answer.

Here is the logic followed:

• Pattern of Shapes (Triangle, Round and Square): In each successive box, the shapes are moving in circular motion from left to right. Thus, the pattern of shapes in the following box will be square, triangle and circle from left to right.

• Color pattern: In consecutive boxes, the rightmost shape is filled with black. Thus, the round shape in the following box will be filled with black.

• Letter pattern: In each successive box, the characters are increasing with 3 place values. Thus, the following box will contain the letter M.

Hence, the correct answer is 'option 4'.

The logic followed here is:

Shift reverse of second half of word in front of First half of word.

1. ‘TRIGONOMETRY’ :  ‘YRTEMOTRIGON’

2. ‘ACCELERATION’ :  ‘NOITARACCELE’

Similarly,

‘APPRECIATION’ :  ‘NOITAIAPPREC’

Hence, 'NOITAIAPPREC' is the correct answer.

The correct answer is Karnataka.

Key Points

• Bronze Age civilization included the Harappan culture.
• Objects connected to copper, bronze, gold, silver, and lead are visible.
• With the exception of iron, practically all metals were known to the Harappans.
• They produced items made of gold and silver.
• It's possible that South India's riverbeds (Karnataka) and the Himalayas provided gold, while Mesopotamia provided silver.
• Beads, armlets, needles, and other accessories are among the gold items.
• Silver, however, was used more frequently than gold.
• There have been many silver plates, decorations, and other items found.
• Moreover, a variety of copper tools and weapons have been found.

Additional Information

• Karnataka
• Current Chief Minister is Siddaramaiah. (June 2023)
• Current Governor is Thawar Chand Gehlot.  (April 2023)
• The state of Karnataka was formed in 1956 and renamed as Karnataka in 1973.
• The capital of Karnataka is Bengaluru.
• The official language of Karnataka is Kannada.

The correct answer is Interest payments.

Key Points

• Capital expenditure
• The money that the government spends on developing buildings, machinery, equipment, schools and other infrastructure is known as capital expenditure.
• Additionally, it covers the costs made by the government for investments that will generate profits or dividends in the future, such as land acquisition costs.
• According to the budget, the government would spend $1,084,748 on capital projects in 2020–21.
• The 2019-20 Budget's revised capital expenditure estimates came in at Rs. 1,059,472 crores, while the 2018-19 Budget's actual capital expenditures came in at Rs. 915,670 crores.
• Spending on investments or development is referred to as capital spending, and these types of expenditures have long-term advantages.
• The following expenses are included in capital expenditures:
• Purchasing fixed and immovable assets
• Enhancing a current asset
• Restoring a current asset
• Repayment of a loan

The correct answer is Rajasthan.

Key Points

• Rajasthan has been the first State in the nation to receive the L-root server, allowing the State government to enforce e-governance and offer its signature digital services with seamless internet connectivity.
• The new facility will help increase the security and resilience of internet-based businesses while strengthening internet infrastructure.
• In collaboration with the Internet Corporation for Assigned Names and Numbers, the new server has been set up in the Bhamashah State Data Centre here (ICANN).
• Following the completion of the new facility, the **State would no longer rely on any root servers for the domain name system, according to Chief Minister Ashok Gehlot.**​

Additional Information

• L - root is one of the 13 Domain Name System 'root servers' which together make up the infrastructure known as the Root Server System.
• A root server is part of the supporting infrastructure of the Internet and facilitates Internet use by acting as the backbone of online access.

The correct answer is Linguistic and religious.

Key Points

• Minorities are granted the freedom to create and run their educational institutions. Also known as the "Charter of Education Rights," Article 30.
• Article 30(1)
• All minorities must have the freedom to create and run the educational institutions of their choice, regardless of whether they are classified as religious or linguistic minorities.
• 1 (A):
• The State shall ensure that the amount fixed by or determined under such law for the acquisition of any property of an educational institution established and administered by a minority, as referenced in clause (1), is such as would not restrict or abrogate the right guaranteed under that clause.
• Article 30(2)
• The state is prohibited from discriminating against any educational institution on the grounds that it is run by a minority, regardless of their religion or language, while providing financial support to educational institutions.​​

Additional Information

• The Indian Constitution went into effect on January 26, 1950. The Constitution was the longest national constitution ever approved at the time of its ratification.
• It had 395 Articles, 8 Schedules, and was about 145,000 words long.
• During the course of 11 sessions and 167 days, spanning two years and eleven months, the members of the Constituent Assembly deliberated on every article of the Constitution.
• The Articles are divided into 22 different portions, which corresponds to how the Constitution of India, 1950's text has them arranged.
• The Schedules to the Constitution, which now number 12, give into more detail about government policy or regulations in respect to particular Constitutional Articles.

The correct answer is Tundra.

Key Points

• Among all the biomes, the tundra is the coldest.
• In addition, the tundra experiences little precipitation, which resembles a desert.
• Arctic tundra can be found in the areas immediately below the ice caps, and it can be found in Siberia in Asia, North America, and Europe.
• The tundra biome encompasses most of Alaska and roughly half of Canada.
• Several places throughout the world also have tundra on the summits of very tall mountains.
• With mean annual temperatures below 0°C during six to ten months of the year, tundra winters are protracted, dark, and cold.
• Permafrost, or permanently frozen ground, results from the area's extremely low temperatures.
• The tundra biome is distinguished by this permafrost.
• Only a few inches of the top layer of soil thaws during the tundra summers, giving vegetation roots a growth surface.

Additional Information

• Humid subtropical:
• ​A climate zone characterised mid summers and cold to mild winters is known as a humid subtropical climate.
• Highland:
• Highland climate features include high insolation, low temperatures, low air pressure, wide diurnal temperature fluctuations, and relatively heavy precipitation at higher altitudes.
• Humid continental:
• It is characterized by four distinct seasons, significant seasonal temperature changes, and frigid (often extremely cold) winters.

The correct answer is 1791.

Key Points

• The Hindu college was established in 1791 to encourage the study of ancient Sanskrit texts.
• Sri Jonathan Duncan and Governor General Lord Cornwallis established the Sanskrit college.
• Jonathan Duncan suggested establishing a Sanskrit college to develop and preserve Sanskrit Vangmaya to demonstrate British support for Indian education.
• The Governor of Uttar Pradesh is the chancellor of the College.
• Chancellor - Anandiben Patel
• Vice Chairman - Hare Ram Tripathi

Confusion Points 

• Hindu college, now called Presidency University, is a public state university in Calcutta.
• It was established in the year 1817.​

Additional Information

• In 1958 The Sanskrit college became a university and in 1974 the name was changed to Sampumanand Sanskrit University.
• On 22 March 1958 the then Chief Minister Dr Sampurnanand and Education Minister Pt. Kamlapati Tripathi at Varanasi.
• A.N. Jha was the First Vice-Chancellor. It Was Renamed Sampurnanand Sanskrit University under the U.P. State University Act, of 1973.
• Introduction of Civil service by Lord Cornwallis.
• Permanent Settlement 1793 by Lord Cornwallis.
• Kumar Gupta I of the Gupta dynasty founded Nalanda University in the 5th century CE.
• Dharmapala founded Vikramshila University.

The correct answer is 39.

Key Points

• We know that mass no. is given as,
• Mass no.= No. of protons + No. of neutrons.
• Potassium has an atomic number of 19, and an element's atomic number is determined by how many protons it contains.
• Hence, potassium contains 19 protons.
• Twenty neutrons make up potassium.
• The mass number of potassium is calculated using the formula above as,
• Mass no. = 20+19=39.

Additional Information

• Potassium is a member of the alkali group of the periodic table.
• Symbol: K.
• Atomic number: 19.
• Belongs to group 1 in the periodic table.
• First isolated in 1807 by Humphry Davy.
• Sodium and Potassium are the elements known as soft metals(can cut with a knife with little force).
• Potassium metal is kept in kerosene due to its high reactivity with water.
• Potassium bicarbonate is the chemical used in fire extinguishers.
• Potassium is the most common radioisotope in the human body.
• Potassium is the second least dense metal after lithium.

The correct answer is Zakir Hussain.

Key Points

• Hussain is a well-known innovator, yet he believes that innovation and continuity need to coexist.
• Hussain has worked with artists as diverse as Van Morrison and the London String Quartet in addition to some of the best Indian musicians over the years.
• He received the Sangeer Natak Akademi award from India's premier cultural organisation in 1991, and in 1996, he contributed to the music for the opening ceremonies of the Summer Olympics in Atlanta.
• Ustad Zakir Hussain is an Indian tabla player.

Additional Information

• Ravi Shankar:
• At the Fillmore East in New York City, Hussain performed for the first time in the United States alongside Ravi Shankar.
• His connection with guitarist John McLaughlin, whom he met in New York, and violinist L. Shankar, an Indian, led to the creation of the musical group Shakti.
• Ravi Shankar was a well-known composer, performer, and expert in Indian classical music.
• He was a key character in 20th-century culture, and his contributions made him the figurehead of a significant musical heritage.
• ​In 1999, Ravi Shankar received the Bharat Ratna, India's highest civilian honor.
• Pt. Ravi Shankar was a famous Sitar player.
• Bismillah Khan:
• ​The Indian musician Bismillah Khan, often known as "Ustad," was instrumental in introducing the shehnai, a reed instrument, to the classical realm of Indian music.
• He was the third classical musician to win the Bharat Ratna, the nation's highest civilian honour, and one of the greatest exponents of Indian classical music.
• India's highest civilian honour, the Bharat Ratna, was given to Khan in 2001, and after his passing in 2006, the nation held a national day of mourning.
• Lata Mangeshkar:
• The "Swar Kokila" or "Nightingale of Bollywood," Lata Mangeshkar, was born in Indore in 1929.
• Her grandfather, father, and mother were all somehow connected to the music business, therefore music was in her blood.
• India's highest civilian honour, the Bharat Ratna, was given to Lata Mangeshkar in 2001.​

The correct answer is Secondary productivity.

Key Points

• Primary productivity is the pace at which producers - plants and other photosynthetic organisms - create new organic matter.
• The rate at which consumers are creating new organic matter is known as secondary productivity. Protists, fungi, bacteria, Deer, cows, goats, horses, etc. are a few examples.
• The entire dry biomass of all living things at a certain trophic level is referred to as a standing crop.
• It stands for biomass that is above ground. It could vary during the course of the year.
• There are two forms of primary productivity:
• Gross primary productivity, which measures the total rate of photosynthesis and the amount of organic matter consumed during respiration and is influenced by chlorophyll content.
• The difference between gross primary production and ecosystem organisms' respiration is known as net primary production.

Additional Information

• Tertiary productivity:​
• ​The quantity of fresh biomass (weight) that carnivores (animals that eat meat) create over a certain amount of time.
• Primary Productivity:
• ​The process by which organisms produce their own sustenance from inorganic sources is known as primary productivity. Terrestrial plants and microbiological life, such as algae, make up the majority of primary producers.
• Net Productivity:
• ​The total amount of food or biomass produced by primary producers minus energy losses, which is also the total amount of food stored by producers, is referred to as net primary productivity.

The correct answer is Twelfth.

Key Points

• Quwwat-ul-Islam Mosque is situated in the Qutb complex in Delhi.

• It was built by Qutub-ud-din-Aibak in 1193 AD.

• The Quwwat-ul-Islam is best known for its tower of victory, celebrating the Muslim conquest of India.

• It is an intricately designed structure built on the principles of construction and ornamentation which was another feature of Islamic architecture.

• Qutub-ud-din Aibak:

• ​He was the founder of the Slave dynasty.

• He made Lahore the capital and later Delhi.

• He was also known as 'Lakh Baksh' or giver of lakhs for his magnanimity, as he gave a lot of liberal donations.

• He started the construction of the Qutub Minar in the memory of Khawaja Qutubuddin Bhaktiyar Kaki but could complete only the first storey.

• Aibak is known for having commissioned the Qutb Minar in Delhi, and the Adhai Din Ka Jhopra in Ajmer.

• Iltutmish got recognition as the Muslim Sultan of India by the Khalifa of Baghdad,

The correct option is Three-tier.

Key Points

• The Indian judiciary is organized into a three-tier system:
• Supreme Court:
• At the top is the Supreme Court of India, which is the highest judicial authority in the country.
• It has original, appellate, and advisory jurisdiction.
• The Supreme Court has the power to hear appeals from lower courts, issue writs, and interpret the Constitution.
• High Courts:
• Each state in India has a High Court.
• High Courts are the second-highest courts in the country and have jurisdiction over their respective states or union territories.
• They have the power of superintendence over the subordinate courts within their jurisdiction.
• Subordinate Courts:
• The third tier consists of the subordinate courts, which include District Courts, Sessions Courts, and other lower courts.
• These courts are established by the state governments and are responsible for hearing civil and criminal cases within their territorial jurisdiction.
• District Courts are at the lowest level and are presided over by District Judges.

The correct answer is Debasish Panda.

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Key Points

• Debasish Panda assumed leadership of the office on March 14, 2022, in the Insurance Regulatory and Development Authority (IRDAI) office in Hyderabad, three days after being named as the organization's chairwoman.
• Panda is an IAS officer from the Uttar Pradesh cadre and is from Odisha. He worked as the department of financial services (DFS) secretary in the Union finance ministry from February 2020 until January 2022, when he retired, before joining IRDAI.
• At the Center, Panda has also held the positions of joint secretary (health), additional secretary, and special secretary. He held the positions of principal secretary and district magistrate at Uttar Pradesh's Deoria, Tehri, Uttarkashi, and Ghaziabad (vigilance).
• Since its founding, IRDAI has had five chairpersons: N Rangachary (1996–2003), CS Rao (2003–08), Hari Narayan (2008–13), TS Vijayan (2013–18), and SC Khuntia (2018–21). Only TS Vijayan comes from an industry background; the others are bureaucrats. Panda has served on the boards of New India Assurance and Life Insurance Corporation, two of the biggest players in the public insurance market.

Additional Information

• **Ajay Bhushan Pandey:**​
• Director General of the Indian Unique Identification Authority. The Appointments Committee of the Cabinet (ACC) presided over by the prime minister named Pandey as the chief executive officer (CEO) of the Unique Identification Authority of India in May 2016. He began serving in this capacity on May 31, 2016.
• Sanjeev Sanyal:
• Indian economist and author Sanjeev Sanyal is the government of India's principal economic advisor at the moment. He is both an urban thinker and an environmentalist.
• Ashwin Yardi:
• ​Ashwin is the CEO of Capgemini Technology Services India and a member of the executive committee for the Capgemini Group.

The correct answer is Allahabad.

Key Points

• The Allahabad area known as Prayag is where the Ganga and Yamuna rivers converge or merge.
• Prayagraj is the present name for Allahabad, which was formerly known as Kausambi.
• It is situated at the meeting point of the Ganga, Yamuna, and Saraswati rivers in the Indian state of Uttar Pradesh.

Additional Information

• One of the oldest towns in the world, Allahabad is revered for its history and religious significance in India.
• Akbar, the Mughal emperor, had it built in 1583 and gave it the name Allahabad, which translates to "City of God."
• The primary crops in this area are wheat, barley, and rice.
• The historic Hindu and Buddhist monuments of Pratisthanpur and Kausambi are close to Allahabad City.
• The city is also known as Pilgrimage Land, Sangam City, and the City of Prime Ministers, and it annually hosts the Kumbh Mela.

The correct answer is Leipzig, Germany.

Key Points

• The second of tournament previews looks at the 12 women's teams that will compete in the Arena Leipzig for the championship.
• Females: Pool A
• World Champions in Excess Together with Germany, Austria, Ukraine, Australia, Canada, and Belgium, they compete in Pool A.
• It's not a big surprise that Germany (FIH Indoor World Ranking: 1) starts the competition as the favourite because of the supportive home audience. But, the club must get over the shock of losing star attacker Lisa Altenburg, who suffered a knee injury at the weekend's German indoor championships.
• Luisa Steindor has taken Altenburg's slot, and she will be confident going into the competition after helping Düsseldorf HC win the German indoor championship. Jamilon Mülders, the team's head coach, is enthusiastic about his squad's chances of winning.

The correct answer is Lipase.

Key Points

• Lipase, 
• Triglycerides are broken down by a class of enzymes called lipases into free fatty acids and glycerol.
• They are present and functional in a variety of tissues; for instance, hepatic lipases are found in the liver, hormone-sensitive lipases in adipocytes, lipoprotein lipase is found on the surface of vascular endothelial cells, and pancreatic lipase is found in the small intestine.
• This enzyme functions in conjunction with the bile your liver produces.
• Your body will have problems absorbing fat and the crucial fat-soluble vitamins if you don't have enough lipase (A, D, E, K).
• Poor fat absorption is characterized by diarrhea and greasdiarrheay bowel motions.

Additional Information

• Protease,
• Proteases have more specialised uses in the extraction of mucopolysaccharides and carbohydrate gums, which are nonprotein compounds made from animal or plant extracts.
• Proteases can be employed to dissolve keratin-containing materials, such as feather debris, to provide protein concentrates for animal diets. Streptomyces species' alkaline proteases have potent keratinolytic activity as well.
• Your diet's protein is broken down by this enzyme.
• Also, it aids in defending you against microorganisms like certain bacteria and yeast that could reside in your intestines.
• Amylase,
• Any member of the class of enzymes known as amylases is responsible for catalysing the breakdown of starch into smaller carbohydrate molecules like maltose (a molecule composed of two glucose molecules).
• Alpha-amylase is present in many biological things.
• Ptyalin, an alpha-amylase produced by salivary glands in the digestive tracts of humans and many other mammals, is secreted into the small intestine by pancreatic amylase.
• The undigested carbs may cause diarrhea if you don't have enough amylase.
• Pepsin,
• Pepsin, a potent digestive enzyme found in gastric juice, breaks down proteins found in foods including meat, eggs, seeds, and dairy products.
• The mature active version of the inactive protein pepsinogen is called pepsin.
• Pepsinogen is produced and stored by glands in the mucous membrane lining of the stomach. Pepsinogen is released into the stomach under the influence of vagus nerve impulses and the hormonal secretions gastrin and secretin, where it is combined with hydrochloric acid and quickly transformed into the active enzyme pepsin.

The correct answer is Prerana Deshpande.

Key Points

• Prerana Deshpande is a well-known Kathak dancer worldwide.
• Prerana Deshpande, one of the top complete solo Kathak dancers of her time, is regarded by aficionados as a solo dancer of acclaim and a creative choreographer of uncommon talent.
• Prerana is regarded for her exquisite command over the fundamentals of Kathak - Rhythm, Grace, & Expression - as well as for her creativity that is rooted in the tradition of this dance form.
• She is an internationally acclaimed creative dancer whose work reveals the perpetually expanding horizons of the traditional form.
• She is frequently invited to perform as a solo artist at all important venues and festivals in India and abroad because of how well-liked she is by audiences of all demographics for her proficiency in Kathak.

The correct answer is West Bengal and Kerala.

Key Points

• At the time of independence, the land tenure system was under the control of zamindars who were only responsible for the collection of revenue and they did not contribute to renovating or modernizing farmlands.
• Land reforms were fruitful in Kerala and West Bengal because these states had governments who were committed to the policy of land to the tiller and they brought necessary legislations for the same.
• Bhoodan and Gramodan movements led by Vinoba Bhave played role in land reforms in Zamindari areas.

Additional Information

• In West Bengal due to “Operation Barga” maximum sharecroppers were given ownership of land.
• Cooperative farming is advocated to solve the problem of sub-divisions of landholdings.
• Main objectives of Land Reforms-
• To legitimize tenancy with the ceiling limit.
• To register all the tenancy with the village Panchayats.
• To establish a relation between tenancy and ceiling.
• To remove rural poverty.
• Proliferating socialist development to lessen social inequality
• Empowerment of women in the traditionally male-driven society.

The correct answer is Boxing.

Key Points

• A "ring" that is 18 to 22 feet (5.5 to 6.7 meters) square and enclosed by four strands of rope is often where fights take place.
• Professional fights can be scheduled to go up to 12 rounds of three minutes each, but women's fights and other fights hosted in Great Britain frequently employ two-minute rounds.
• Professional championship fights had typically gone 15 rounds since the late 1920s, but by the late 1980s, the WBC, WBA, and IBF titles were all being scheduled for 12 rounds.
• The fight is governed by a referee who is stationed inside the ring alongside the participants.
• In some places, the referee and two judges outside the ring score the match.
• However, the referee is typically not involved in the scoring, which is done by three ringside officials.

The correct answer is Bihar.

Key Points

• According to the 2011 Census, Bihar has the lowest rate of literacy (61.8%) among all the states.
• Bihar has the lowest male and female literacy rates (71.2% and 51.5%, respectively), while Kerala has the highest rates (96.1% and 92.1%, respectively).
• Reason for low literacy rate in Bihar is:
• ​Due to Bihar's poor educational infrastructure, there is a wide gap between supply and demand.

Additional Information 

The correct answer is Bharatnatyam.

Key Points

• Bharatnatyam (Tamil Nadu)
• One of the primary texts used to study the technique and grammar of body movement in Bharatnatyam dance is the Abhinaya Darpana by Nandikesvara.
• In Bharatnatyam dance, one dancer plays various characters in a single performance, a technique known as ekaharya.
• Leg, hip, and arm transitional movements are used in the dance.
• The dance has seven primary sections that are typically split down into Alarippu, Jatiswaran, Shabda, Varna, Pada, Thillana, and Sloka.
• The Chidambaram temple's gopurams feature Bharatnatyam positions (Tamil Nadu).
• E. Krishna Iyer and Rukmini Devi Arundale were instrumental in restoring the dance's standing and popularity.
• ​

Additional Information

• Kathak
• ​The idea of storytelling is central to Kathak, one of India's most exquisite dance styles. Kathak, the sole dance from northern India among the eight Indian classical dance styles, is an art form with an enigmatic beauty, captivating footwork, and beautiful motions.
• Kuchipudi
• ​Kuchipudi is renowned for its dynamic storytelling, dramatic characterization, outstanding, rapid dancing, and expressive eye movements. Tandava (the regal, masculine) and Lasya are combined in this dance (lyrical graceful and feminine energy).
• Mohiniyattam
• ​The traditional solo dancing style of Kerala is called Mohiniyattam, which is simply translated as "the dance of Mohini," the celestial enchantress from Hindu mythology.

The correct answer is T Raja Kumar.

Key Points

• The global agency responsible for monitoring money laundering and terrorism financing is the Financial Action Task Force (FATF).
• It establishes worldwide norms with the intention of stopping these criminal activities and the damage they do to society.
• T Raja Kumar, a Singaporean of Indian descent, was named the new president of the Financial Action Task Force (FATF) on 1st July 2022.
• The FATF stated that the new president would prioritize increasing asset recovery, as well as the efficiency of international anti-money laundering and counter-terrorism funding measures.
• Earlier, he served as the Ministry's Deputy Secretary (International) from January 2015 to July 2021 and the Home Team Academy's Chief Executive from 2014 to 2018.

Additional Information

• Sanjiv Kapoor: CEO-designate, Jet Airways. Former President, Oberoi Hotels & Resorts; Former Chief Strategy and Commercial Officer, Vistara and Former COO, SpiceJet.
• Ashwani Bhatia: Whole Time Member, SEBI (Securities and Exchange Board of India).
• Mahesh Verma: Chairperson of NABH (National Accreditation Board for Hospitals and Healthcare Providers).

The correct answer is 'Amphibians'.

Key Points

• Amphibians-
• The characteristics of the organisms present in class amphibia are as follows:
• These can live both on land and in water.
• They are ectothermic animals, found in a warm environment.
• Their body is divided into head and trunk. The tail may or may not be present.
• The skin is smooth and rough without any scales, but with glands that make it moist.
• They have no paired fins. Unpaired fins might be present.
• They have two pairs of limbs for locomotion.
• They respire through the lungs and skin. Gills might be present externally in some adults.
• The heart is three-chambered.
• They possess ten pairs of cranial nerves.
• The lateral line is present during their development.
• The sexes are separate and fertilization is usually external. However, in salamanders, the fertilization is internal.
• Development is indirect with metamorphosis.
• Breeding occurs in water. The copulatory organs are absent in males.
• Example- Frogs, Salamanders

Additional Information

• Pisces
• Pisces belong to the phylum Chordata.
• Pisces includes three classes: 
• Placodermi (Aphstohyoids)
• Chondrichthyes
• Osteichthyes​
• Reptiles-
• These are creeping and burrowing terrestrial animals with scales on their body.
• They are cold-blooded animals found in most of the warmer regions of the world.
• Their skin is dry, and rough, without any glands.
• The body is divided into head, neck, trunk, and tail.
• Few of these shed the scales on their skin as skin cast.
• The respiration takes place with the help of the lungs.
• They have two pairs of pentadactyl limbs, each bearing claws. Snakes are an exception.
• The heart is 3 chambered. However, crocodiles have a 4-chambered heart.
• The nervous system comprises of 12 pairs of cranial nerves.
• The lateral line system is absent in reptiles.
• Except for snakes, all the reptiles have well-developed ears.
• They possess a typical cloaca.
• Fertilization is internal.

Aves​​

• Birds are warm-blooded animals.
• Their forelimbs are modified into wings.
• They have well-developed flight muscles that help during the flight.
• Their hind limbs are adapted for walking, hopping, perching, grasping, wading and swimming.
• There are epidermal scales on their legs.
• The endoskeleton is bony with long hollow bones filled with air cavities. known as pneumatic bones.
• Their spindle-shaped body minimizes the resistance of the wind.
• The feathers help in preventing heat loss and reduce air friction by providing passage to the air.
• There is no skin gland except the oil gland.
• The lower and upper and jaws are modified into a beak.
• They have no teeth.
• They have sharp eyesight.

The correct answer is Eid-ul-Fitr.

Key Points

• Eid ul-Fitr is a significant Islamic holiday that starts the minute the new moon is sighted, marks the conclusion of the month-long fasting of Ramadan.
• The only day in the month of Shawwal when Muslims are not allowed to fast is this religious Eid.
• Fasting during the month of Ramadan is one of the most significant Islamic practices, and it is one of the most important festivals observed by Muslims worldwide.
• One of the five pillars of Islam is the Ramadan fast.

Additional Information

• Milad-un-Nabi:
• ​The yearly festival of Eid Milad-un-Nabi honours the birthday of Prophet Muhammad, takes place in Rabi-ul-Awwal, the third month of the Islamic lunar calendar, which begins with the sighting of the moon.
• The date also commemorates the Prophet's passing anniversary.
• Shab-e-Barat:  ​
• ​The Muslim festival of Shab-e-Barat commemorates the halfway point of the month before Ramadan, has arrived.
• Eid-ul-zuha:
• ​​The Feast of Sacrifice, also known as Eid al-Zuha, is one of the most important Islamic holidays.
• The enthralling chants of 'Allah hu Akbar' are spread throughout the world during the exuberant Eid ul-zuha celebrations.
• While it is known as Bakr-id in India, it is also known as Eid al-Adha, Id-ul-zuha, Id-ul-Azha, and Hari Raya Haji in other nations.
• On the tenth day of the lunar-based Islamic calendar's 12th month, this auspicious day is observed.

The correct answer is Copper and Silver.

Key Points

• The town of Bidar is situated in the modern Indian state of Karnataka.
• Bidar became known as Bidri because the artisans there were so well known for their inlay work in **copper and silver.**​

The correct answer is Andaman and Nicobar Islands.

Key Points

• The Andaman and Nicobar Islands are located in the Bay of Bengal, southeast of the Indian mainland.
• There are numerous beaches on the island, which draw vacationers.
• The capital of Andaman and Nicobar Islands is Port Blair.
• The Indira Point on the island of Andaman & Nicobar is where India's southernmost point is situated.

Additional Information

• Lakshadweep islands: An archipelago of 36 islands called Lakshadweep islands is made up of the Arabian Sea, 200 to 440 kilometres off the Malabar Coast.
• Mannar island: Mannar Island, which is a part of Sri Lanka's Mannar District, is located off the country's northwestern coast.
• Maldives islands: A sovereign island nation called The Maldives is located in the north-central Indian Ocean.

Given: 

$\frac{{{{\sin }^2}{{63}^°} + {{\sin }^2}{{27}^°}}}{{{{\cos }^2}{{17}^°} + {{\cos }^2}{{73}^°}}}$

Concept used:

sinθ = cos (90 - θ)

cosθ = sin (90 - θ)

cos²θ + sin²θ = 1

Calculations:

⇒ $\frac{{{{\sin }^2}{{63}^°} + {{\sin }^2}{{27}^°}}}{{{{\cos }^2}{{17}^°} + {{\cos }^2}{{73}^°}}}$ 

⇒ $\frac{{{{\sin }^2}{({90}^°- {27}^°)} + {{\sin }^2}{{27}^°}}}{{{{\cos }^2}{{17}^°} + {{\cos }^2}{({90}^°-{17}^°})}}$

⇒ $\frac{{{{\cos }^2}{{27}^°} + {{\sin }^2}{{27}^°}}}{{{{\cos }^2}{{17}^°} + {{\sin }^2}{{17}^°}}}$

⇒ ${1 \over 1}$

⇒ 1

Hence, the value of the given expression is 1.

Given:

a : b = 4 : 5

b : c = 3 : 10

a : c = ?

Concept used:

To find a : c, b is made same in both the ratios.

Calculation:

a : b = ${4 \over 5}$ = ${ 4 \times 3 \over 5 \times 3} = {12 \over 15}$

b : c = $3 \over 10$= ${3 \times 5 \over 10 \times 5}= {15 \over 50}$

Equating both these equations with each other, we get:

 a : c = ${12 \over 50} = {6 \over 25}$

Therefore, the value of a : c is 6 : 25.

Given:

Vikas's wrongly entered marks = 98

Vikas's actual marks = 89

Average marks = Actual Average + 0.25

Concept used:

Let the number of students in the class be x 

If marks entered are 98 in place of 89, the increase in marks will be: 98 - 89 = 9.

Thus, the average marks are increased by $9 \over x$.

Calculation:

Increase in average marks: 

$9 \over x$ = 0.25

x = $9 \over 0.25$

x = 36

∴ The total number of students in the class is 36.

Given:

A certain sum of money is given at a certain rate for 3 years. 

At 5% higher rate, increase of SI for 3 years = Rs. 600

Concept used:

Let the sum be x.

Calculation:

At 5 % higher rate, SI for 1 year will be = $600 \over 3$ = Rs. 200

which means that Rs. 200 is 5% of the invested sum.

$5 \over 100$ × x = 200 

x = $20000 \over 5$

x = 4000

∴ The invested sum is Rs. 4000.

Given:

Company's profit in 2001-02 = Rs. 650 lakhs

Company's profit in 2002-03 = Rs. 730 lakhs

Company's profit in 2003-04 = Rs. 520 lakhs

Company's profit in 2004-05 = Rs. 680 lakhs

Company's profit in 2005-06 = Rs. 740 lakhs

Company's profit in 2006-07 =Rs.  490 lakhs

Company's profit in 2007-08 = Rs. 660 lakhs

Company's profit in 2008-09 = Rs. 810 lakhs

Concept used:

Average profit = $Sum : of : profits \over No. :of : years$

Calculation:

Average profit = $650+730+520 +680 +740+490+660+810 \over 8$ 

⇒ $5280 \over 8$

⇒ 660

Thus, number of years in which the company's profit is above the average profit = 4

and number of years in which the company's profit is below the average profit = 3

Ratio = 4 : 3 

∴ The ratio of the number of years in which the company's profit is above the average profit, to those in which the profit is below the average is 4 : 3.

Given:

Time when the thief stole the jewellery = 8:15 p.m.

Speed of thief's bike = 60 km/h

Time when police were informed = 8:30 p.m.

Formula used:

Minimum speed of police officer = $\text {Distance between the thief and the police} \over \text{Time taken by police to reach the thief}$

Calculation:

If the thief left at 8:15 p.m. and the police wants to catch him at 9:00 p.m., the time for which the thief was on the bike = 45 minutes = $3 \over 4$ hours = 0.75 hours

Distance travelled by the thief = 60 km/h × 0.75 h = 45 km 

Time taken by the police to reach the thief = 30 minutes = 0.5 hours

Thus, minimum speed of the police jeep should be = $45: \text{km} \over 0.5 :\text{h}$ = (45 × 2) km/h = 90 km/h 

∴ The minimum speed of the police jeep should be 90 km/h.

Given:

Companies and the number of officers working in it:

Calculation:

Number of officers working in Q = 250

Number of officers working in R = 350 

Ratio = $\text { Number of officers wroking in Q} \over \text{Number of officers working in R}$ = $250 \over 350$ = $5 \over 7$

∴ The ratio of number of officers working in Q to the number of officers working in R is 5:7.

Given:

$K + \frac{1}{K} = 3$

Formula used:

(a + b)² = a² + 2ab + b²

Calculation:

Let us square both sides:

$(K + \frac{1}{K} )^2$ = 3²

k² + (2 × k × $1 \over k$) + $1 \over k^2$ = 9

k2 + 2+ $1 \over k^2$ = 9

k2 + $1 \over k^2$ = 9 - 2

k2 + $1 \over k^2$ = 7

∴ The value of k2 + $\bf 1 \over k^2$  is 7.

Given:

a + b + c = 9

ab + bc + ca = 23

Formula used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculation:

For equation a + b + c = 9, squaring both sides:

(a + b + c)2 = 9²

a2 + b2 + c2 + 2(ab + bc + ca) = 81

a2 + b2 + c2 + 2(23) = 81

a2 + b2 + c2 + 46 = 81

a2 + b2 + c2 = 81 - 46

a2 + b2 + c2 = 35

∴ The value of a2 + b2 + c² is equal to 35.

Given:

tan⁡ (4α − 50°) = cot ⁡(50° − α)

Formula used:

cotθ = tan (90° - θ) 

If tan(a) = tan (b), then a = b.

Calculation:

tan⁡ (4α − 50°) = cot ⁡(50° − α)

tan⁡ (4α − 50°) = tan (90° - ⁡(50° − α))

By the above equation, we have:

⇒ 4α - 50° = 90° - ⁡(50° - α)

⇒ 4α - 50° = 90° - ⁡50° + α

⇒ 4α - α = 90°  

⇒ 3α = 90°  

⇒ α = $90° \over 3$ 

⇒ α = 30° 

∴ The value of α (in degrees) is 30°.

Given: 

l || m 

Concept used:

For two parallel lines,

Corresponding angles are equal.

Vertically opposite angles are equal.

Calculation:

∠110° = ∠p (Vertically opposite angles) 

∠p + ∠r₁ + ∠r₂ + ∠110° = 360°

⇒ ∠110° + ∠r1 + ∠r2 + ∠110° = 360°  (∠r1 = ∠r_2, vertically opposite angles)

⇒ 2∠r1 = 140°

⇒ ∠r1 = 70°

Now, ∠r1 = ∠a (Corresponding angles)

∠a = 70°

Also, ∠a + ∠b = 180° (supplementary angles)

⇒ ∠b = 180° - 70° = 110°

∴ The measure of angles marked by a and b is 70° and 110° respectively.

Given:

Radius of the circle = 6 cm

Central angle of a sector = 40°

Formula used:

Area of sector = $\theta \over 360°$ × πr²

Calculation:

Area of the given sector =  $40° \over 360°$ × π × (6 cm)2 

⇒ ($1 \over 9$× π × 36) cm²

⇒ (π × 4) cm2

⇒ 4π cm2 

∴ The area of the sector is 4πcm2 .

Given:

Time in which A can complete a piece of work = 13 days

Time in which B can complete a piece of work = 17 days

Concept used:

L.C.M. of 13 and 17 = 221

Thus, total work done = 221 units.

Unit of work done by A in 1 day = 17 units

Unit of work done by B in 1 day = 13 units

Calculation:

If A and B work alternatively, work done by them in 2 days = 30 units

Work done in 14 days = 30 × 7 = 210 units

Work left = 11 units

Work done remaining by A on 15th day = $11 \over 17$ 

Thus, the time taken to complete the work = 14$11 \over 17$ days.

∴ The whole work will be completed in 14$\bf 11 \over 17$ days.

Given: 

Nihit's investment = Rs. 700

After 5 months,

Amit's investment = Rs. 300

Patel's investment = Rs. 400

Total profit = Rs. 627

Concept used:

Capital earned = Time of investment (in months) × Amount invested

Calculation:

Capital earned by Nihit = 12 × 700 = Rs. 8,400

Capital earned by Amit = 7 × 300 = Rs. 2,100

Capital earned by Patel = 7 × 400 = Rs. 2,800

Ratio of their capitals = 84 : 21 : 28 = 12 : 3 : 4

Total = 12 + 3 + 4 = 19

Patel's profit = $4 \over 19$ × 627 = Rs. 132

∴ The share of Patel in the profit is Rs. 132.

Given:

Radius of first circle = 17 cm

Radius of second circle = 7 cm

Circles touch each other externally.

BC is a direct common tangent of these two circles.

Concept used:

External tangents are lines that do not cross the segment joining the centers of the circles.

Calculation:

Join A to O and B. Join O to C. Draw AQ perpendicular to OC.

Now, AQ = BC, as they are opposite sides of rectangle AQCB.

⇒AO = AP + PQ

⇒AO = 7 + 17

⇒AO = 24 cm

⇒OQ = CO - CQ

⇒OQ = 17 - 7

⇒OQ = 10 cm

Now, applying pythagoras theorem in triangle AOQ:

⇒$AO^2$ = $AQ^2+OQ^2$

⇒AQ = $\sqrt{AO^2-OQ^2}$

⇒AQ = $\sqrt{24^2-10^2}$

⇒AQ = $2\sqrt{119}$

 ∴ The length of BC is $2\sqrt{119}$.

Given:

PA = PQ - AQ = 6 - 3 = 3cm

Concept used:

In △PAB and △PQR 

∠PAB = ∠PQR (corresponding angles)

and  ∠P is common.

∴ △PAB ∼ △PQR ( AA similarity criterion)

Since corresponding sides are proportional,

${AB\over QR}= {PA\over PQ}:$

$AB={QR× PA\over PQ}$

Calculation:

AB = (8 × 3) / 6 = 4 cm

Hence, 'Option A' is the correct answer.

Given:

Sector C = 12%

Sector D = 2%

Sector F = 6%

Sector A = 19%

Sector G = 14%

Sector H = 10%

Formula used:

Angle= ${percent: of :sector\over 100}$ × 360

Calculation:

Angle of following sectors: 

C = ${12\over100}$ × 360 = 43.2

D = ${2\over100}$ × 360 = 7.2

F = ${6\over100}$ × 360 = 21.6

Total= 72

A = ${19\over100}$ × 360 = 68.4

G = ${14\over100}$ × 360 = 50.4

H = ${10\over100}$ × 360 = 36

Total= 154.8

Ratio= 72:154.8 = 20:43

∴ The ratio of total central angle formed by sector C, D and F to the total central angle formed by sector A, G and H is 20:43.

Given :

 x + $\frac{1}{x}$ = $2√ 5 :$ where x > 1,

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

(a - b)³ = a³ - b³ - 3ab (a - b)

Calculation:

 (x + $\frac{1}{x}$ )² = x² +  ($\frac{1}{x}$ )² + 2 

20 =  x2 +  ($\frac{1}{x}$ )2 + 2 

x2 +  ($\frac{1}{x}$ )2 = 20 - 2 =18 .....(1)

(x - $\frac{1}{x}$ )2 = x2 +  ($\frac{1}{x}$ )2 - 2  , Put the value of equation (1),

 (x - $\frac{1}{x}$ )2 = 18 - 2 = 16

 (x - $\frac{1}{x}$ ) = 4 ....(2)

apply cube power to equation 2 both side,

 => (x - $\frac{1}{x}$ )³ = 4³

=> (x - $\frac{1}{x}$ )3 =  x3 - $\frac{1}{{{x^3}}}$  - 3( x - $\frac{1}{x}$ ) = 64, put the value of equation (2)

=>  x3 - $\frac{1}{{{x^3}}}$  - 3( 4 ) = 64

=> x3 - $\frac{1}{{{x^3}}}$  = 64 + 12 

=> x3 - $\frac{1}{{{x^3}}}$  = 76

Hence, '76' is the correct answer.

Shortcut Trick

If x + $\frac{1}{x}$ = a then x - 1/x = √(a² - 4)

If  x - 1/x = k then x³ - 1/x³ = k³ + 3k

Here, x + $\frac{1}{x}$ = $2\sqrt 5 :$ then  x - 1/x = √(20 - 4) = 4, then x3 - 1/x3 = (4³ + 12) = 76

Given:

7-digit number 678p37q is divisible by 75 and p is not a composite.

Concept:

Divisibility law of 5: A number divisible by 5 if its last digit must be either 0 or 5.

Divisibility law of 3: A number is divisible by 3 if sum of its digit is divisible by 3.

Calculation:

⇒ 7 digit number 678p37q is divisible by 75 means number divisible by 3 and 5 both.

Divisibility rule of 3 apply on 7 digit number 678p37q , then,

⇒ 678p37q should be divisible by 3, then sum of its digit

⇒ 6 + 7 + 8 + p + 3 + 7 + q 

⇒ 31 + p + q

Next values which divisible by 3 i.e 33, 36 ,39. .....(1)

Means p + q can be 2, 5, 8

Now,

Divisibility rule of 5 apply on 7 digit number 678p37q. Then,

q = 0 or 5

If we take q = 0, then p = 2 or 5 or 8. These values of p not given in any option. so,

The value of q must be 5.

Now,

31 + p + 5 

⇒ p + 36 

According to equation (1), next value can be 39. so,

⇒ p + 36 = 39

 =>  p = 3

∴ The value of p and q are 3 and 5 respectively.

Alternate Method

A number is divisible by 75, which means the number is divisible by 25 and 3

If last 2-digit of a number is divisible by 25, then the number is divisible by 25, so q = 5 [ as 75 divisible by 25]

If sum of all the digits divisible by 3, then the number also divisible by 3, so (6 + 7 + 8 + p + 3 + 7 + 5) = 36 + p, here p = 3 [as 6,  9 are composite numbers]

∴ The value of p = 3 and q = 5

Given :

Tan A Tan B + $\frac{{\cos x}}{{\cos A\cos B}}$ = 1

Formula used:

$Tan:\theta={Sin:\theta\over Cos:\theta}$

Cos (a + b)= cos a cos b - sin a sin b

Calculation:

Tan A Tan B + $\frac{{\cos x}}{{\cos A\cos B}}$ = 1

⇒ Tan A Tan B  Cos A Cos B + Cos x  = Cos A Cos B

⇒ Sin A Sin B + Cos x = Cos A Cos B

⇒ Cos x = Cos A Cos B - Sin A Sin B

⇒ Cos x = Cos (A + B)

⇒ x = A + B

Hence, 'Option 3' is the correct answer.

Shortcut Trick

If we put A = 45° and B = 45°, we get

Tan A Tan B + $\frac{{\cos x}}{{\cos A\cos B}}$ = 1

⇒ 1 +  $\frac{cos x}{(\frac{1}{\sqrt2})^2}$ = 1

⇒ 1 + 2cos x  = 1

⇒ cos x = 0

so, x = 90° = A + B

Given:

The cost price of 20 books = Selling price of 18 books

Concept:

Gain: The amount gained by selling a product with more than its cost price.

Formula Used:

Profit = Selling price – Cost Price

Profit percentage = (Profit/Cost Price) × 100

Calculation:

Let the Selling price of one book be 10x So,

the selling price of 18 books = 180x

Cost price of 20 books = 180x

⇒ Cost price of 1 book = $\frac{18x}{20}$ = 9x

Profit = 10x - 9x = x

Profit % = ${x\over 9x}\times 100 = {100\over 9}:$

Profit % = $11\frac{1}{9}\%$

∴ The gain percent is $11\frac{1}{9}\%$

Shortcut Trick 

For article-based questions, if Cost article > Selling article then there is a gain.

Gain% = \(\frac{costarticle - sellingarticle}{selling~article} \times 100\) = $\frac{(20 -18)}{18} \times 100$ = $11\frac{1}{9}\%$