SSC CGL 2021 Tier-I (Held On : 20 April 2022 Shift 2) (Previous Year Paper)

The logic followed here is:

Logic: In a Row =  (First number + Second number) × 5 + second number = Third number.

1. In first row

⇒ 8 + 6 = 14 × 5 = 70

⇒ 70 + 6 = 76

And,

2. In third row

⇒ 7 + 13 = 20 × 5 = 100

⇒ 100 + 13 = 113

Similarly,

3. In second row

⇒ 12 + 10 = 22 × 5 = 110

⇒ 110 + 10 = 120

Hence, the correct answer is "120".

Family chart:

Pointing towards a boy, Shalini said, “He is my daughter’s father’s wife’s father’s wife’s only son”

Clearly, shalini is the sister of that boy.

Hence, the correct answer is "Sister".

The least possible Venn diagram is given below:

Conclusions:

I. No soldier is a girl → False → (As some girl are engineers and all engineers are soldiers. So, no soldier is a girl is definite not true)

II. No girl is an engineer → False → (As some girls are engineers. So no girl is an engineer is definite false)

III. Some soldiers are engineers → True → (As all engineers are soldiers. So some soldiers are engineers is definite true)

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

The position of letters according to the English alphabet series:

Hence, the correct answer is "DSFQ".

Given: 

1. The number of students in class 10 is 1/3 more than the number of students in class 12. 
2. Total number of students of class 10 and class 12 in the institute is 112.

Calculation:

Let,

Number of students in class 12 is  3x

So, number of student in class 10 is 4x [As  number of students in class 10 is 1/3 more than the number of students in class 12]

According to problem,

3x + 4x = 112

⇒ 7x = 112

⇒ x = 16

Therefore, Number of students in class 10 is  4x i.e.16 × 4 = 64

Hence, the correct answer is "64".

The pattern followed here is.

Hence, the correct answer is "8th".

The position of letters according to the English alphabet series:

Logic: First two letter are coded as opposite place value and addition of + 5 in the last alphabet.

FPD : UKI

Similarly,

LWP : ?

Hence, the correct answer is "ODU".

The Venn diagrams best represent the relationship between - Planet, Sun and Moon figure are shown below:

• Sun is star.
• Moon is a satellite.
• Earth, Jupiter, Venus all are Planet and different from each other.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: Addition of alphabet positional value × 2 = Code

‘MOST’ is written as ‘134’

⇒ M(13) + O(15) + S(19) + T(20) = 67 × 2 = 134

And,

‘FUR’ is written as ‘90’

⇒ F(6) + U(21) + R(18) = 45 × 2 = 90

Similarly,

‘SUCCESS’ be written as '?'

⇒ S(19) + U(21) + C(3) + C(3) + E(5) + S(19) + S(19) = 89 × 2 = 178

Hence, the correct answer is "178".

BODMAS Rule:

Given equation: 84 * 42 * 7 * 5 * 21 * 93

Option 1) +, ÷, −, ×, =

After put the mathematical sing we get:

⇒ 84 + 42 ÷ 7 - 5 × 21 = 93

⇒ 84 + 6 - 5 × 21 = 93

⇒ 84 + 6 - 105 = 93

⇒ 90 - 105 = 93

⇒ - 15 ≠ 93

⇒ LHS ≠ RHS

Option 2) ×, ÷, +, −, =

After put the mathematical sing we get:

⇒ 84 × 42 ÷ 7 + 5 - 21 = 93

⇒ 84 × 6 + 5 - 21 = 93

⇒ 504 + 5 - 21 = 93

⇒ 509 - 21 = 93

⇒ 488 ≠ 93

⇒ LHS ≠ RHS

Option 3) +, ÷, ×, −, =

After put the mathematical sing we get:

⇒ 84 + 42 ÷ 7 × 5 - 21 = 93 

⇒ 84 + 6 × 5 - 21 = 93

⇒ 84 + 30 - 21 = 93

⇒ 114 - 21 = 93

⇒ 93 = 93

⇒ LHS = RHS

Option 4) ÷, +, ×, −, =

After put the mathematical sing we get:

⇒ 84 ÷ 42 + 7 × 5 - 21 = 93 

⇒ 2 + 7 × 5 - 21 = 93

⇒ 2 + 30 - 21 = 93

⇒ 32 - 21 = 93

⇒ 11 ≠ 93

⇒ LHS ≠ RHS

Hence, the correct answer is "+, ÷, ×, −, =".

The image obtained when the paper is unfolded is,

Hence, the correct answer is "Option 2".

The pattern followed here is:

Hence, the correct answer is "262".

The position of letters according to the English alphabet series:

Logic: In Vowel - Subtraction of - 2 in vowels.

In consonant - Addition of + 2 in consonant.

‘NAILS’ is written as ‘PYGNU’

And,

‘TEXT’ is written as ‘VCZV

Similarly,

‘FOREST’ is written as '?'

Hence, the correct answer is "HMTCUV".

BODMAS Rule:

If the numbers ‘18’ and ‘30’ are interchanged,

Let check all options one by one.

Option 1) 12 – 30 × 18 ÷ 3 + 16 = 174

After interchanging the digit we get:

⇒ 12 – 18 × 30 ÷ 3 + 16 = 174

⇒ 12 - 18 × 10 + 16 = 174

⇒ 12 - 180 + 16 = 174

⇒ 28 - 180 = 174

⇒ - 152 ≠ 174

⇒ LHS ≠ RHS

Option 2) 14 × 5 – 18 ÷ 6 + 30 = 73

After interchanging the digit we get:

⇒ 14 × 5 – 30 ÷ 6 + 18 = 73

⇒ 14 × 5 - 5 + 18 = 73

⇒ 70 - 5 + 18 = 73

⇒ 88 - 5 = 73

⇒ 83 ≠ 73

⇒ LHS ≠ RHS

Option 3) 35 ÷ 5 × 5 + 30 – 18 = 23

After interchanging the digit we get:

⇒ 35 ÷ 5 × 5 + 18 – 30 = 23

⇒ 7 × 5 + 18 - 30 = 23

⇒ 35 + 18 - 30 = 23

⇒ 53 - 30 = 23

⇒ 23 = 23

⇒ LHS = RHS

Option 4) 64 + 18 × 5 ÷ 3 – 30 = 98

After interchanging the digit we get:

⇒ 64 + 30 × 5 ÷ 3 – 18 = 98

⇒ 64 + 30 × 1.666 - 18 = 98

⇒ 64 + 49.98 - 18 = 98

⇒ 113.98 - 18 = 98

⇒ 95.98 ≠ 98

⇒ LHS ≠ RHS

Hence, the correct answer is "35 ÷ 5 × 5 + 30 – 18 = 23".

The position of letters according to the English alphabet series:

Option 1) WTGD

Option 2) KHSP

Option 3) MJQN

Option 4) FCXB

Hence, the correct answer is "FCXB".

The pattern followed here is:

1) 

 shifted right bottom corner in second figure then rotate 180º clockwise. Then shifted right bottom corner in third figure then rotate 180º clockwise. At last shifted left bottom corner and rotate 180º clockwise.

2) 

 shifted right left corner in second figure and reverse their position. Then shifted left bottom corner in third figure and reverse their position. At last shifted left upper corner and reverse their position. 

3) 

 shifted left bottom corner in second figure and rotate 90° anticlockwise. Then shifted left upper corner in fourth figure and rotate 90° anticlockwise. At last shifted right upper corner in last figure and 90° anticlockwise.

4) 

 shifted left upper corner in second figure and reverse their position. Then shifted right upper corner in third figure and reverse their position. At last shifted right bottom corner and reverse their position.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Square of next number of first number + first number - 1 = Second number.

Given: 24 : 648

⇒ Next number after 24 is 25

⇒ (25)² + 24 - 1 = 625 + 24 - 1 = 648

Let's check each option one by one

Option 1) 26 : 654

⇒ Next number after 26 is 27

⇒ (27)² + 26 - 1 = 729 + 26 - 1 = 754 ≠ 654

Option 2) 25 : 652 

⇒ Next number after 25 is 26

⇒ (26)² + 25 - 1 = 676 + 25 - 1 = 700 ≠ 652

Option 3) 20 : 421

⇒ Next number after 20 is 21

⇒ (21)² + 20 - 1 = 441 + 20 - 1 = 460 ≠ 421

Option 4) 22 : 550 

⇒ Next number after 22 is 23

⇒ (23)² + 22 - 1 = 529 + 22 -1 = 550 = 550

Hence, the correct answer is "22 : 550".

Given words are arranging according to English alphabet series.

5. Disadvantage 4. Disappear 2. Disappointment 6. Disarticulate 1. Disaster 3. Discharge

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

Zainab is standing facing particular direction intially. 

1) Then she turns 90° clockwise, after that she turns 180° anticlockwise.

2) Then she turns 135° anticlockwise. She finally turns 180° clockwise.

Now, represent with direction.

Clearly, we can see at the starting Zainab is facing East.

Hence, the correct answer is "East".

Given:

Logic: If two dice have 2 faces in common then the third face of dice 1 is opposite to the third face of dice 4.

In first and third dice.

Number 4 and 1 are common here.

So 5 opposite to 6

Hence, the correct answer is "6".

Given: T _ X T U _ _ U X T _ X

1. T X X U → T T X - T U X - X U X  -T U X
2. U X T U → T U X - T U X -T U X - T U X
3. T U U X → T T X - T U U - U U X - T X X
4. X T U X → T X X - T U T - U U X - T X X

Option 2) followed the cycle of TUX/TUX/TUX/TUX

Hence, the correct answer is "U X T U".

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

Detailed Explanation:

• The PQ is the mirror.
• The word "346512" the fourth number is "5". So the mirror image should be "

" ⇒ Option 1 is eliminated.

• The word "346512" the third number is "6". So the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "346512" the second number is "4". So the mirror image should be "

" ⇒ Option 3 is eliminated.

Hence, the correct answer is "Option 4".

Given:

Mercury is used in thermometer and here the code for "mercury" is "curd".

Hence, the correct answer is "Curd".

Eight friends: P, Q, R, S, T, U, V and W.

1. Clockwise in the same order around a circular table at equal distances between them, facing the center of the table. If S is sitting in the west, then who is sitting in the south-west direction.

Clearly, R is sitting in South-west direction.

Hence, the correct answer is "R".

Given:

Hence, the correct answer is "Option 1".

The correct answer is thermosphere.

Key Points

• The thermosphere lies above the mesopause and is a region in which temperatures increase with height.
• Thermosphere:
• In the thermosphere, the temperature rises very rapidly with increasing height.
• The ionosphere is a part of this layer.
• It extends between 80-400 km. This layer helps in radio transmission.

Additional Information

• There are a total of five atmospheric layers. These are -
• Troposphere.
• Stratosphere.
• Mesosphere.
• Thermosphere.
• Ionosphere: the lowest part of the Thermosphere contains the ionosphere.
• Exosphere.
• Stratosphere:
• It lies beyond the troposphere, up to an altitude of 50 km from the earth's surface.
• The temperature in this layer remains constant for some distance but then rises to reach a level of 0°C at 50 km altitude.
• This rise is due to the presence of ozone.
• This layer is almost free from clouds and associated weather phenomena, making conditions most ideal for flying aeroplanes.
• Exosphere:
• This is the uppermost layer of the atmosphere extending beyond the ionosphere above a height of about 400 km.
• The air is extremely rarefied and the temperature gradually increases through the layer.
• Light gases like helium and hydrogen float into space from here.
• Troposphere:
• It is the lowermost layer of the atmosphere.
• The layer starts at Earth's surface and extends 8 to 14.5 km high (5 to 9 miles).
• The troposphere contains dust particles and water vapour.
• This is the most important layer of the atmosphere because all kinds of weather changes take place only in this layer.
• The zone dividing troposphere from the stratosphere is known as the tropopause.

The correct answer is Odissi.

Key Points

• Odissi is one of the 8 classical dances of India recognized by the Sangeet Natak Academy.
• Odissi is a major ancient classical dance that originated in the Indian state of Orissa.
• The famous dancers of Odissi are -
• Sujata Mohapatra, Kelucharan Mohapatra, Ratikant Mohapatra, Gangadhar Pradhan, etc.
• Kelucharan Mohapatra is the first person to receive the Padma Vibhusan from Orissa.

Additional Information

The correct answer is 72.

Key Points

• In the 2020 - 21 season, each NBA team played 72 regular-season games.
• The 2020–21 NBA season was the 75th season of the National Basketball Association (NBA), though the 75th anniversary was not celebrated until the following season.
• Due to the COVID-19 pandemic, the regular season was reduced to 72 games for each team and began on December 22, 2020.
• The season started just 72 days after the completion of the 2020 NBA Finals, the shortest off-season in league history.

Additional Information

• National Basketball Association (NBA):
• It was established on June 6, 1946, in Newyork, USA.
• NBA is composed of 30 teams and is a professional Basketball league.
• It has been recognized by the International Basketball Federation.
• Adam Silver is the current Chief Executive Officer who succeeded David Stern.
• The Los Angeles Lakers are NBA champions, defeating the Miami Heat 106-93 in Game 6 of the NBA Finals on 11 Oct 2020.
• This was the Lakers' first NBA Finals appearance since 2010 when the late Kobe Bryant won his fifth and final NBA title.
• It's the fourth championship for LeBron James, in his 10th NBA Finals.
• He became the NBA's all-time leader in playoff games played, at 260.

The correct answer is Sheet erosion.

Key Points

• Sheet erosion is the LEAST visible form of land erosion.
• Sheet erosion is the process of uniform removal of soil in thin layers by the forces of raindrops on land.
• It is caused by the force of rainfall.
• It takes place in levelled lands and plowed fields after a heavy shower and the soil, removal is not easily noticeable, but it is harmful since it removes the finer and more fertile topsoil.

Additional Information

• Rill and gully erosion:
• In rill erosion, finger-like rills appear on the cultivated land after it has undergone sheet erosion.
• These rills are usually smoothened out every year while forming.
• Each year the rills slowly increase in number and become wider and deeper.
• Gully erosion is the removal of soil along drainage lines by surface water runoff.
• When rills increase in size, they become gullies.
• Once started, gullies will continue to move by headward erosion or by slumping of the side walls.
• Gullies formed over a large area give rise to badland topography (Chambal Ravines).
• When a gully bed is eroded further due to headward erosion, the bed gradually deepens and flattens out, and a ravine is formed.
• The depth of a ravine may extend to 30 meters.
• Landslides
• Landslides and slope instability cause problems in many parts of the world.
• A landslide is primarily a combination of several geological processes that include physical factors like earth movements like extensive slope failure, rocks falling, and debris flow.
• These ground movements may take place in a coastal, offshore, or far onshore environment.
• Gravity, in addition to other factors that affect ground stability, is the main force that causes landslides.
• Normally, the ground characteristics develop particular sub-surface soil conditions that cause slope failure.
• However, the real landslide needs a trigger before it can be initiated. It is normally feasible to recognize the main landslide origin and the landslide triggers.

The correct answer is Hiuen-Tsang.

Key Points

• Hiuen-Tsang wrote the book ‘Shi-Yu-Ki’ after visiting the Harshavardhana court.
• Si-yu-ki means "Record of the Western Countries".
• Hiuen Tsang visited India during the period of emperor Harsha.
• Hiuen Tsang remained at the University of Nalanda for five years.
• Hiuen Tsang had been a guest to Bhaskara Varman, ruler of Kamarupa.
• Hiuen Tsang described Kannauj as a beautiful city.
• Pu Songling was a Qing dynasty Chinese writer.
• Pu Songling was the author of Strange Stories.

Additional Information

• Banabhatta:
• Banabhatta was the Asthana Kavi in the court of King Harsha Vardhana.
• Kadambari is the work of Banabhatta.
• The "Harshacharita" was also written by Banabhatta.

The correct answer is olericulture.

Key Points

• Olericulture is the branch of horticulture that deals with the production, processing, and marketing of vegetables.
• It is the production of plants for the use of their edible parts.
• Vegetable crops are classified into nine categories.
• It also includes organic gardening and organic farming and biotechnology.

Additional Information

• Pomology:
• It is the branch of horticulture that deals with the study of fruits and its cultivation.
• Apiculture:
• The production of honey from bees is also called beekeeping.
• Agronomy:
• It is a branch of agricultural science that deals with the study of crops and the soils in which they grow.
• Agronomists work to develop methods that will improve the use of soil and increase the production of food and fibre crops.
• Agronomy consists of two Greek words i.e. Agros =field, Nomos = to manage.
• It is mainly based on the following basic principles:
• Agrometeorology.
• Soils and Tillage.
• Soil and Water Conservation.
• Irrigation Water Management, etc.
• It has three distinct branches.
• Crop Science (mainly field crops).
• Soil science.
• Environmental Science (that deals with applied aspects).

The correct answer is Drosera.

Key Points

Explanation:

• The animals which feed on other animals are called carnivorous animals.
• In plants also there are some plants that feed on insects.
• Such plants are having modified leaves known as pitfall traps.
• Insects are attracted to these traps.
• They get digested by the pitcher plant's digestive juices.
• Other such plants are Drosera, dionaea, Utricularia, etc.
• In pitcher plants, there are leaves for photosynthesis for preparing starch like other plants.
• It fulfils its nitrogen requirements from insects.
• The area in which such plants grow lacks nitrogen in the soil.

Drosera, pitcher plant, and Utricularia is the set of plants representing insectivorous plants.

Additional Information 

• Cuscuta is parasitic plant.
• Algae has an autotropic mode of nutrition.

The correct answer is Epilepsy.

Key Points

• Epilepsy is a disorder resulting in abnormal electrical discharges from the brain cells causing seizures.
• Epilepsy is a medical condition of the brain, which results in untimely seizures or fits.
• India observes National Epilepsy Day on November 17 to create awareness about the disease.
• The World Health Organisation has described it as a "chronic non-communicable disease of the brain which is characterized by recurrent seizures".
• Symptoms include loss of consciousness, sudden twitching, etc.
• WHO has also reported that close to 50 million people in the world suffer from epilepsy.
• It is considered one of the most common neurological diseases globally.
• Nearly 80% of people with epilepsy live in low- and middle-income countries.

Additional Information

• Prostatitis:
• ​The inflammation of the prostate gland is called prostatitis. It can be a result of a bacterial infection or nerve damage.
• The prostate is a small, walnut-shaped gland that is located below the urinary bladder in all men and it is responsible for producing semen.
• Rheumatoid Arthritis (RA):
• It is a chronic autoimmune disease affecting connective tissue and the synovial membrane of joints.
• Hypoglycemia:
• It is a condition when the sugar level is very low.

The correct answer is Charaka.

Key Points

• Charaka was a contributor to the subject of medicine in ancient India.
• He was the court physician of Kaniska.
• Charaka was one of the principal contributors to Ayurveda medicine in ancient India.
• He is best known for his work Charaka Samhita.
• Charaka Samhita:
• It is also called Caraka-Samhita.
• It is a detailed text on ancient Indian medicine attributed to Charaka, a practitioner of Ayurveda, India's traditional medical system.
• Charaka-Samhita, also spelt Caraka-Samhita or Caraka- samhita, comprehensive text on ancient Indian medicine credited to Charaka.
• He was a practitioner of the traditional system of Indian medicine known as Ayurveda.
• Charaka is thought to have flourished sometime between the 2nd century BCE and the 2nd century CE.
• The Charaka-Samhita, in its current form, is believed to have originated in the first century CE.
• According to ancient Indian medicine studies, the original text was written by Agnivesha.
• One of six disciples of Ayurvedic scholar Punarvasu Atreya, many centuries ago,
• (The other five disciples were Bhela, Jatukarna, Parashara, Harita, and Ksharapani).
• Each of the disciples went on to write their own Samhitas, combining both Atreya's ideas and their own understanding of the subject.
• The Agnivesha-Samhita, written by Agnivesha, was unlike any other in terms of depth and quality.
• It came to be known as the Charaka-Samhita after Charaka refined and annotated it.
• The treatise was divided into eight parts, or ashtanga sthanas, by Charaka:
• sutra, nidana, vimana, sarira, endriya, chikitsa, Kalpa, and Siddha; each section had multiple chapters.

Additional Information

• Panini:
• He was born in Shalatula on the Indus River in present-day Pakistan.
• He was a Sanskrit grammarian and gave a comprehensive and scientific theory of phonetics, phonology, and morphology.
• He is considered the founder of the language and literature of Sanskrit.
• His major work involves a treatise called Astadhyayi (or Astaka). It consists of eight chapters, each subdivided into quarter chapters.
• Under Astadhyayi, he distinguished between the language of sacred texts and the usual language of communication.
• He gave formal production rules and definitions to describe Sanskrit grammar.
• He gave about 1700 basic elements like nouns, verbs, vowels, and consonants he put them into classes.
• Pushyamitra Shunga is a post-Mauryan king whereas the birth year of Panini is not known. Experts give dates of Panini in the 4th, 5th, 6th, and 7th centuries which are all Pre-Mauryan.
• Astadhyayi (or Astaka) is Panini's major work related to Sanskrit grammar.
• Harsha:
• Harshavardhana ruled from 606-647 CE.
• He lived from 590 to 647 CE and was the last ruler of the Vardhana Empire.
• He was the king of the Vardhana dynasty and was the son of Prabhakarvardhana.
• He took the title of sakal uttara patha natha (lord of northern India).His biography Harshacharita ("Deeds of Harsha") was written by Sanskrit poet Banabhatta.
• He authored Nagananda, Ratnavali, Priyadarshika all written in the Sanskrit language.

The correct answer is tuberculosis (TB).

Key Points

• BCG stands for Bacille Calmette-Guerin.
• It is a vaccine for tuberculosis (TB) disease.
• Tuberculosis (TB) disease is caused by Mycobacterium tuberculosis.
• Tuberculosis (TB) usually attacks the lungs.
• BCG vaccine was first considered by the WHO Expert Committee on Biological Standardization in its thirteenth report.
• BCG vaccine is one of the most widely used of all current vaccines.
• BCG vaccine has a documented protective effect against meningitis and disseminated TB in children.

Additional Information 

The correct answer is Narsimha Committee.

Key Points

• The Regional Rural Banks were established on the recommendations of the Narsimha Committee Rural Credit.
• Regional Rural Bank:
• Regional Rural Banks were established on the basis of the recommendations of the Narasimham Working Group (1975), and after the legislation of the Regional Rural Banks Act, 1976.
• They are financial institutions that ensure adequate credit for agriculture and other rural sectors.
• They were set up on the recommendations of the Narasimham Working Group (1975).
• RRBs were granted legal provisions under the Regional Rural Banks Act, 1976.
• The first Regional Rural Bank "Prathama Grameen Bank" was set up on 2nd October 1975.
• The equity of a regional rural bank is held by the Central Government, the concerned State Government, and the Sponsor Bank in the proportion of 50:15:35.
• The RRBs have combined characteristics of a cooperative and a commercial bank.
• It operates within the local limits as notified by the Government.
• The main objectives of RRBs are:
• To provide credit and other facilities to the small and marginal farmers, agricultural labourers, artisans, and small entrepreneurs in rural areas.
• To check the outflow of rural deposits to urban areas.
• To reduce regional imbalances.
• To increase rural employment generation.
• They are required to provide 75% of their total credit as priority sector lending.

Additional Information

• Rekhi Committee on Indirect Tax Reform:-
• The Rekhi Committee was constituted in 1992 under the chairmanship of K.L. Rekhi. The recommendations are a Tribunal should be set up to deal with problems between taxpayers and tax collectors.
• A High-Level India classification committee with trade and industry representatives should be set up.
• Important consignments should be cleared within 3 days.
• The monopoly of one nominated bank in each state should be supplemented by another bank.
• Coercive measures must not be used for recovery of disputed duty amount when the assessee files a stay application.
• Kelkar Committee Report on Tax Reforms:-
• A task force on Direct and Indirect Taxes was constituted under the chairmanship of DR. Vijay Kelkar in 2002. The recommendation of the Vijay Kelkar committee are:
• The income tax exemption limit must be increased to Rs. 1 Lakh from the present 50,000 tax exemption limit for senior citizens and widows should be Rs. 1.5 lakhs.
• There should be a two-tier income tax structure with a 20% tax for earnings of Rs. 1 lakh to 4 lakh and 30% tax for over Rs. 4 lakhs. The standard deduction must be abolished but suggested an exemption for conveyance
  

allowance.

• There should be the abolition of long-term capital gains tax, dividend tax, and wealth tax. There should not be any surcharge on income tax.
• There should be an interest subsidy of 2% for housing loans up to Rs. 5 lakh.
• There must be a 30% corporate tax for domestic companies and 35% for foreign companies and there should be no Minimum Alternate Tax (MAT).
• There Should be a 14% Central Value Added Tax (CENNAT) rate.
• There should be nationwide VAT and Comprehensive Service Tax.
• Exemptions for life-saving drugs, security items, and farm products.
• Exemption of tax for small-scale units with a turnover up to Rs. 50 lakh.

The correct answer is Jhumpa Lahiri.

Key Points

• The book 'Unaccustomed Earth' is a collection of short stories.
• The book deals with the lives of Bengali-American characters.

The correct answer is Medicine.

Key Points

• Presented by the President, the Bidhan Chandra Roy Award is an annual award that is given by the Medical Council of India in each of the following categories:
• Medical man-cum-Statesman
• Statesmanship of Highest Order in India
• Eminent Person in Philosophy
• Eminent Medical Person
• Eminent Person in Science
• Eminent Person in Arts
• The award is given every year in New Delhi on July 1, National Doctor's Day.

The correct answer is It should state the reasons for its adoption in the Lok Sabha.

Key Points

• With reference to the no-confidence motion, the statement that It should state the reasons for its adoption in the Lok Sabha is INCORRECT.
• No confidence motion is a motion that is introduced against the ruling government in the elected house i.e Lok Sabha or Vidhan Sabha and not in the upper house i.e Rajya Sabha or Vidhan Parishad.
• It is a special power vested in the hand opposition.
• The vote of a no-confidence motion is brought in Lok Sabha.
• In Parliament when a no-confidence motion is passed, the Government discontinues to adore the trust and confidence of the house and is thereafter removed.
• In this procedure, no-confidence voting is done against the Government by the Lok Sabha members.
• When a no-confidence motion is passed the President dissolves the Council of Ministers.
• The no-confidence motion is not mentioned in the Indian Constitution.
• Process for No Confidence Motion:
• A Requirement for the introduction of no Confidence motion is given to the speaker of the house which is to be supported by a minimum of 50 members.
• The speaker will give time within the next 10 days for discussion on the motion in the house.
• After the discussion, the voting takes place.
• If the No-Confidence Motion is passed in the house the Council of ministers must resign as they have lost the majority in the house.
• If the NO Confidence motion is passed, then the President is not bound by the aid and advice of the defeated council of ministers.

The correct answer is 65%

Key Points

• The expected returns to farmers by way of MSP (Minimum Support Price) over their cost of production for barley for marketing season 2021–22 is estimated at 65%.
• Minimum Support Price:
• Minimum Support Price (MSP) is a form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices.
• The minimum support prices are announced by the Government of India at the beginning of the sowing season for certain crops.
• The MSP is decided on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• Government announces minimum support prices (MSPs) for 22 mandated crops and fair and remunerative prices (FRP) for sugarcane.
• The list of crops is as follows:
• Cereals (7) - paddy, wheat, barley, jowar, bajra, maize, and ragi.
• Pulses (5) - gram, arhar/tur, moong, urad, and lentil.
• Oilseeds (8) - groundnut, rapeseed/mustard, toria, soybean, sunflower seed, sesamum, safflower seed, and nigerseed.
• Raw cotton.
• Raw jute.
• MSP guaranteed prices to save farmers from distress sales.
• The MSP is announced at the beginning of the sowing season for certain crops on the basis of the recommendation of the Commission for Agricultural Costs and Prices (CACP, 1985).
• The MSPs are fixed for the following purposes:
• To invest more by farmers in the farm sector.
• To motivate farmers to adopt improved farm technologies.
• To increase production and overall farmers' income.

The correct answer is Unfinished.

Key Points 

• The memoir titled ‘Unfinished’ is written by Bollywood actress Priyanka Chopra Jonas.
• With the release of her first novel, "Unfinished: A Memoir," which she described as "honest, raw and vulnerable," actor-producer Priyanka Chopra Jonas officially became an author.
• The end result is a book published by the imprint of Michael Joseph that covers her 20-year dual-continental career as an actor and producer and her role as a Goodwill Ambassador for UNICEF.
• The memoir promises to offer insights into the childhood of Priyanka Chopra Jonas in India and her formative adolescent years in the US.
• Against all odds, her return to India resulted in the newcomer to the pageant world winning Miss India and Miss World national and international beauty competitions that launched her global acting career.

The correct answer is 2019.

Key Points

• An amendment to the Right to Information Act 2005 proposing that the Chief Information Commissioner and Information Commissioners be appointed ‘for such term as may be prescribed by the Central Government’ was passed in the year 2019.
• The Lok Sabha passed the Right to Information (Amendment) Bill, 2019 on 22nd July 2019.
• In this amendment, it is proposed to amend the Right to Information Act, 2005 so as to provide that:
• The term of office
• The salaries
• Allowances
• And other  terms and conditions of service of, the Chief Information Commissioner and Information Commissioners and the State Chief Information Commissioner and the State Information Commissioners, shall be such as may be prescribed by the Central Government.
• Right to Information Act 2005:
• Right to Information Act 2005 mandates timely response to citizen requests for government information.
• It is an initiative taken by the Department of Personnel and Training, Ministry of Personnel, Public Grievances, and Pensions to provide a- RTI Portal Gateway to the citizens for quick search of information on the details of first Appellate Authorities, PIOs, etc.
• Amongst others, besides access to RTI-related information/disclosures published on the web by various Public Authorities under the government of India as well as the State Governments.

Additional Information

• The objective of the Right to Information Act:
• The basic object of the Right to Information Act is to empower the citizens, promote transparency and accountability in the working of the Government, contain corruption, and make our democracy work for the people in the real sense.
• It goes without saying that an informed citizen is better equipped to keep necessary vigil on the instruments of governance and make the government more accountable to the governed.
• The Act is a big step toward making the citizens informed about the activities of the Government.

The correct answer is Jharkhand.

Mistake Points

• You have to choose the correct answer from the given following options.
• If Bihar is in the options then it will be the correct answer.
• But as per the given options, Jharkhand will be the correct answer.
• Population Density 2011 of India State:
• Jharkhand: 414 people per square kilometer
• Goa: 394 people per square kilometer
• Maharashtra: 365 people per square kilometer
• Gujrat: 308 people per square kilometer

Key Points

• The density of the population is expressed as the number of persons per unit area.
• It helps in getting a better understanding of the spatial distribution of population concerning land.
• The density of population in India (2011) is 382 persons per sq km.
• There has been a steady increase of more than 200 persons per sq km over the last 50 years as the density of the population increased from 117 persons/ sq km in 1951 to 382 persons/sq km in 2011.
• The state of Arunachal Pradesh has a total population of roughly 1.4 million as per the census of 2011.
• On an area of 84,000 km2, approximating a population density of about 17 pop./km2.
• Delhi's population Density is 11,320 persons per sq km.
• Among the northern Indian States, Bihar (1106), West Bengal (1028), and Uttar Pradesh (829) have higher densities, while Kerala (860) and Tamil Nadu (555) have higher densities among the peninsular Indian states.
• States like Assam, Gujarat, Andhra Pradesh, Haryana, Jharkhand, and Odisha have moderate densities.

Additional Information Census 2011

• The Indian Census is the most credible source of information on Demography (Population characteristics), Economic Activity, Literacy and Education, Housing Household Amenities, Urbanisation, Fertility and Mortality, etc.
• Census 2011 was the 15th National Census of the Country.
• Census was introduced in India during the era of Lord Mayo in the year 1872. It came into force in 1881.
• This census was conducted under the guidance of Mr. C. Chandramouli.
• The slogan of census 2011 was ‘Our Census, Our future’.
• The population of the nation as per the provisional figures of Census 2011 was 1210.19 million of which 623.7 million (51.54%) were males and 586.46 million (48.46%) were females. Uttar Pradesh is the most populous state in India its population is more than the population of Brazil.

The correct answer is Sri Lanka.

Key Points

• In March 2021, cricketer Kieron Pollard hit six sixes in an over in a match against Sri Lanka.
• West Indies's all-rounder Kieron Pollard hits six sixes in an over against Sri Lanka.
• Kieron Pollard became the third player in International cricket to hits six sixes in an over.
• He plays for Mumbai Indians in the IPL.
• Pollard, who was the captain of West Indies' limited-overs teams played a total of 123 ODIs and 101 T20Is.
• The highlight of his international career is hitting six sixes in a T201.

Additional Information

• West Indies skipper Kieron Pollard on 4 March 2020 became the first player in the history of T20 cricket to feature in 500 matches when he took the field against Sri Lanka for the first T201 here.
• Dwayne Bravo is second on the list with 453 matches under his belt so far.
• Chris Gayle is at the third spot in the list as he has featured in 404 T20 matches.

The Correct Answer is Mahishasura.

Key Points

The correct answer is SDG 6.

Key Points

• Sustainable Development Goal 6 ensures availability and sustainable management of water and sanitation for all.
• Sustainable Development Goal 6 is about "clean water and sanitation for all."
• The Sustainable Development Goals are the blueprint to achieve a better and more sustainable future for all.
• They address the global challenges we face, including poverty, inequality, climate change, environmental degradation, peace, and justice.
• The United Nations Sustainable Development Goal 6 strives to ensure the availability and sustainable management of water and sanitation for all.
• The 17 Sustainable Development Goals and 169 targets are integrated and indivisible and balance the three dimensions of sustainable development: the economic, social, and environmental.

Additional Information

• There are 17 Sustainable Development Goals-
• GOAL 1: No Poverty.
• GOAL 2: Zero Hunger.
• GOAL 3: Good Health and Well-being.
• GOAL 4: Quality Education.
• GOAL 5: Gender Equality.
• GOAL 6: Clean Water and Sanitation.
• GOAL 7: Affordable and Clean Energy.
• GOAL 8: Decent Work and Economic Growth.
• GOAL 9: Industry, Innovation, and Infrastructure.
• GOAL 10: Reduced Inequality.
• GOAL 11: Sustainable Cities and Communities.
• GOAL 12: Responsible Consumption and Production.
• GOAL 13: Climate Action.
• GOAL 14: Life Below Water.
• GOAL 15: Life on Land.
• GOAL 16: Peace and Justice Strong Institutions.
• GOAL 17: Partnerships to Achieve the Goal.

The correct answer is Persian.

• The Mughal court chronicles written in Persian.

Key Points 

• ​Mughal chronicles such as the Akbar Nama were written in Persian, others, like Babur's memoirs, were translated from the Turkish into the Persian Babur Nama.
• Urdu came from the amalgamation of Persian with Hindavi.
• Chronicles commissioned by the Mughal emperors are an important source for studying the empire and its court.
• The authors of Mughal chronicles were mostly courtiers.
• The Mughals were Chaghtai Turks by origin.
• Turkish was their mother tongue hence the first ruler Babur wrote poetry and his memoirs in this language.

The correct answer is Tamil Nadu.

Key Points

• In the union budget 2022-23, a total of Rs 7,134.56 crore was earmarked for taking up various railway projects in Tamil Nadu and it is the highest budget allocated for highway projects in Union Budget 2021-22.
• Southern Railway was allocated Rs 7,134.56 crore for FY 2022-23 in addition to Rs 1,064.34 crore which was an extra-budgetary resource.
• In Kerala, Rs 9,489 crore has been allocated for 8 projects covering a length of 439 km.

Additional Information

• A new scheme, Prime Minister's Development Initiative for North-East, PM- DevINE has been announced by the Union Finance Minister Nirmala Sitharaman while presenting the Union Budget 2022-23 on 01 February 2022.
• The PM-DevINE will be implemented through the North-Eastern Council.
• The Union Budget has allocated 1,40,367.13 cr to the Railway Ministry - *20,311 cr more than the revised figures of the previous fiscal (2021-22).
• It also allocated ₹15,710.44 cr to the Dedicated Freight Corridor, whose assets will be monetized by the Railways for operations and maintenance.
• The rail sector will also develop "One Station One Product", which will leverage local produce carried on the railways.
• As a part of Atmanirbhar Bharat, a 2,000 km network will be brought under 'Kavach', the indigenous world-class technology for safety and capacity augmentation in 2022-23.
• The finance minister said 100 PM GatiShakti Cargo Terminals for multi-modal logistics facilities will be developed during the next three years.

The correct answer is Leaders of Opposition in Parliament.

Key Points

• The salary and allowances of leaders of opposition in parliament are governed by the Act passed for the first time by the parliament in the year 1977.
• Leader of the Opposition:
• In each House of Parliament, there is the 'Leader of the Opposition'.
• The leader of the largest Opposition party having not less than one-tenth of the seats of the total strength of the House is recognized as the leader of the Opposition in that House opposition cabinet.
• In a parliamentary system of government, the leader of the opposition has a significant role to play.
• His main functions are to provide constructive criticism of the policies of the government and to provide an alternative government.
• Therefore, the leader of Opposition in the Lok Sabha and the Rajya Sabha were accorded statutory recognition in 1977.
• They are also entitled to the salary, allowances, and other facilities equivalent to that of a cabinet minister.
• It was in 1969 that an official leader of the opposition was recognized for the first time.

Additional Information

• The same functionary in the USA is known as the 'minority leader'.
• The British political system has a unique institution called the 'Shadow Cabinet'.
• It is formed by the Opposition party to balance the ruling cabinet and to prepare its members for future ministerial offices.
• In this shadow cabinet, almost every member in the ruling cabinet is 'shadowed' by a corresponding member in the opposition cabinet.
• This shadow cabinet serves as the 'alternate cabinet' if there is a change of government.
• That is why Ivor Jennings described the leader of the Opposition as the 'alternative Prime Minister'.
• He enjoys the status of a minister and is paid by the government.

The correct answer is ​Power.

Key Points

• In physics, power is the rate of doing work.
• It is the amount of energy consumed per unit of time.
• The unit of power is the joule per second (J/s), known as the watt (in honor of James Watt, the eighteenth-century developer of the steam engine).

Important Points 

• Power is the rate at which work is done or the rate at which energy is transferred from one place to another or transformed from one type to another.
• A joule per second is called a watt [W] in honor of the Scottish mechanical engineer James Watt.
• Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms.
• ​There are, moreover, heat, and work i.e., energy in the process of transfer from one body to another.
• Momentum is a physics term; it refers to the quantity of motion that an object has.
• A sports team that is on the move has momentum.
• Momentum can be defined as "mass in motion".
• All objects have mass so if an object is moving, then it has momentum it has its mass in motion.

Given:

First six prime numbers i.e. 2, 3, 5, 7, 11, 13

Formula used:

Average = Sum elements/Number of elements

Calculation:

Average = (2 + 3 + 5 + 7 + 11 + 13)/6

⇒ 41/6

⇒ $6{5\over6}$

∴ Required average is $6{5\over6}$.

Given:

tan B = $5\over3$

Concept used:

tanθ = P/B

Sinθ = P/H

Cosθ = B/H

Cosecθ = 1/Sinθ

Secθ = 1/Cosθ

Here,

P = Perpendicular

B = Base

H = Hypotenuse 

Pythagoras theorem = H2 = P2 + B2

Calculation:

tanB = $5\over3$

⇒ $\rm P\over B$ = $5\over3$

Now,

H² = 5² + 3²

⇒ H2 = 25 + 9

⇒ H2 = 34

⇒ H = √34

Now,

$cosec B +sin B \over cos B - secB$ = $\frac{\sqrt{34}}{5} +\frac{5}{\sqrt{34}} \over \frac{3}{\sqrt{34}} - \frac{\sqrt{34}}{3}$

⇒ $\frac{\sqrt{34}^2 + 25}{5\sqrt{34}} \over \frac{9 - \sqrt{34}^2}{3\sqrt{34}}$

⇒ $\frac{34 + 25}{5\sqrt{34}} \over \frac{9 - 34}{3\sqrt{34}}$

⇒ $\frac{59}{5\sqrt{34}} \over \frac{- 25}{3\sqrt{34}}$

⇒ $\frac{59}{5\sqrt{34}} \times \frac{3\sqrt{34}}{- 25}$

⇒ $- {177\over125}$

∴ The required answer is $- {177\over125}$.

Given:

A reduction of 20% in the price of bananas enables a customer to buy 6 more bananas for ₹80

Calculation:

Let the C.P of each banana be x

Total number of bananas in ₹ 80 = 80/x

New price = x – x × (20/100)

⇒ (100 - 20)x/100

⇒ 80x/100 or 4x/5

New number of bananas in ₹80 = 80/(4x/5)

⇒ 80/(4x/5)

⇒ 100/x

⇒ (100/x) – (80/x) = 6 

⇒ 20/x = 6 

⇒ x = 20/6

New price of bananas = 20/6 × 4/5

⇒ 8/3

The reduced price of bananas per dozen = (8/3) × 12

⇒ 32

∴ The reduced price of bananas per dozen (in ₹) is 32.

Shortcut Trick 

Let the original price of a banana be 5x, new price will be 4x(reduced by 20%)

Now, according to the question,

⇒ $80\over 4x$ - $80\over 5x$ = 6

⇒ ${80 (5 - 4)}\over 4 \times 5 \times x$ = 6

⇒ ${80 (5 - 4)}\over 20 \times x$ = 6

⇒ $4\over x$ = 6

⇒ x = $2\over3$

The new price of bananas is,

⇒ 4x = 4 ×$2\over3$

The price per dozen is

⇒ 4 × $2\over3$ × 12 = 32

Calculation:

Total exports of cars of type A over the five years = 200 + 150 + 275 + 175 + 300

⇒ ₹1100 million

Average = 1100/5

⇒ ₹220 million

Now in 2016 export of B is ₹200 million which is ₹20 million less than the average

∴ Required answer is 2016.

Given:

The simple interest on a sum of money at 10% per annum for 4 years is ₹3200.

Concept used:

S.I = (P × T × R)/100

C.I = P(1 + R/100)^T

Here,

P = Sum

R = Rate

T = Time

Calculation:

Let the sum be P

According to the question,

3200 = (P × 4 × 10)/100

⇒ P = 3200 × (10/4)

⇒ P = 8000

So, sum is Rs. 8000

Now,

A = 8000(1 + 10/100)⁴

⇒ A = 8000(1 + 1/10)4

⇒ A = 8000(11/10)4

⇒ A = 8000(14641/10000)

⇒ A = 11712.80

∴ The amount (in ₹) of the same sum for the same period at the same rate of interest when the interest is compounded annually is 11712.80

Given:

PS ⊥ QR

∠Q = 66° and ∠R = 34°

PT is the bisector of ∠QPR

Calculation:

∠QPR = 180° - 66° - 34°

⇒ 80°

∠QPT = ∠TPR = 40°    [As PT angle bisector]

In Δ PTR

∠PTR + ∠PRT + ∠TPR = 180° 

⇒ ∠PTR = 180° - 34° - 40°

⇒ ∠PTR = 106°

Now,

∠PTS + ∠PTR = 180°

⇒ ∠PTS + 106° = 180°

⇒ ∠PTS = 180° - 106°

⇒ ∠PTS = 74°

So,

∠SPT = 180° - 90° - 74°

⇒ ∠SPT = 16°

∴ The measure of ∠SPT is 16°.

Given:

A, B and C divide an amount of ₹10,500 amount themselves in the ratio 5 : 7 : 9, respectively. 

Calculation:

Share of A = 10500 × 5/21

⇒ 2500

Share of B = 10500 × 7/21

⇒ 3500

Share of C = 10500 × 9/21

⇒ 4500

If each 500 more then the amount got by A, B and C = 3000, 4000, 5000

Ratio of new share = 3000 : 4000 : 5000 or 3 : 4 : 5

∴ The ratio of the amount with A, B and C is 3 : 4 : 5.

Given:

A fruit vendor recovers the cost of 95 oranges by selling 80 oranges

Calculation:

According to the question,

CP of 95 oranges = SP of 80 oranges

⇒ CP/SP = 80/95

⇒ CP/SP = 16/19

So, ratio of CP : SP = 16 : 19

So profit = 19 - 16

⇒ 3

Profit % = (3/16) × 100

⇒ 18.75

∴ His profit percentage is 18.75%.

Shortcut Trick For angles of elevation 30° and 60° on the same side of a tower/tree, the height (H) is related to the distance (d) between the points by the formula: H = (d × √3) ÷ 2. ⇒ Height of the tree = (50 × √3) ÷ 2 = 25√3 m. ⇒ Required value = 40% of 25√3 = 0.4 × 25√3 = 10√3 m. ∴ The correct answer is 10√3 m.

Alternate Method Given: Distance between points A and B = 50 m. Angles of elevation are 60° and 30°. Formula: tan θ = Perpendicular ÷ Base

Let the height of the tree be H and the distance from the base of the tree to point A be x. ⇒ In Δ PAC (smaller triangle): tan 60° = H ÷ x ⇒ √3 = H ÷ x → x = H ÷ √3 --- (i) ⇒ In Δ PBC (larger triangle): tan 30° = H ÷ (x + 50) ⇒ 1 ÷ √3 = H ÷ (x + 50) → x + 50 = H√3 --- (ii) ⇒ Substitute (i) in (ii): (H ÷ √3) + 50 = H√3 ⇒ 50 = H√3 − (H ÷ √3) ⇒ 50 = (3H − H) ÷ √3 ⇒ 50 = 2H ÷ √3 → H = 25√3 m. ⇒ 40% of height = (40 ÷ 100) × 25√3 ⇒ Required value = 0.4 × 25√3 = 10√3 m. ∴ The correct answer is 10√3 m.

Additional Information Distance formula for same side When points are on the same side of a tower of height H, the distance d = H(cot θ2 − cot θ1), where θ1 > θ2. Distance formula for opposite sides When points are on opposite sides of a tower, the distance d = H(cot θ1 + cot θ2). Standard Trigonometric Ratios For 30°: tan 30° = 1/√3, cot 30° = √3 | For 60°: tan 60° = √3, cot 60° = 1/√3.

Given:-

Athletic club of 232 members and their height's frequency.

Concept used:-

Frequency Polygon:-  A frequency polygon is a graph constructed by using lines to join the midpoints of each interval or bin. The heights of the points represent the frequencies. A frequency polygon can be created from the histogram or by calculating the midpoints of the bins from the frequency distribution table.

Formula Used:

Class size = Upper limit - Lower limit

Calculation:

From histogram -

Class size = Upper limit - Lower limit

Class size = 125 - 120 = 5

∴ Mid point of a class = 5/2 = 2.5

So, Starting point of Line graph -

X - co-ordinate = 120 - 2.5 = 117.5

Y - co-ordinate = frequency of point = 0

∴ Starting point = (117.5,0)

End point of Line graph -

X - co-ordinate = 170 + 2.5 = 172.5

Y - co-ordinate = frequency of point =  0

∴ End point = (172.5,0)

∴ Required points are (117.5,0) and (172.5,0).

Given:

Total surface area of a right pyramid, with base as a square of side 8 cm, is 208 cm2

Formula used:

Total surface area = Lateral surface area + Area of the base

Lateral surface area = 1/2 × Perimeter of base × slant height

Calculation:

According to the question,

208 = Lateral surface area + 8²

⇒ 208 - 64 = Lateral surface area

⇒ 144 = Lateral surface area

Again,

144 = 1/2 × 4 × 8 × slant height

⇒ 144/16 = slant height

⇒ 9 = slant height

∴ The slant height (in cm) of the pyramid is 9.

Given:

tan2A - 6tanA + 9 = 0

Concept used:

tanθ = P/B

cotθ = 1/tanθ

cosθ = B/H

Here,

P = Perpendicular

B = Base

H = Hypotenuse 

Pythagoras theorem = H2 = P2 + B2

Calculation:

tan2A - 6tanA + 9 = 0

⇒ tan2A - 2 × 3 × tanA + 9 = 0

⇒ (tanA - 3)² = 0

⇒ (tanA - 3) = 0

⇒ tanA  = 3

So, P/B = 3/1

Now,

H² = 3² + 1²

⇒ H2 = 9 + 1

⇒ H2 = 10

⇒ H = √10

So, cosA = 1/√10

Now,

6 cot A + 8$√{10}$ cos A = 6 × (1/3) + 8$√{10}$ × (1/√10)

⇒ 2 + 8

⇒ 10

∴ Required answer is 10.

Shortcut Trick

tan2A - 6tanA + 9 = 0

⇒ (tanA - 3)2 = 0

⇒ (tanA - 3) = 0

⇒ tanA  = 3

⇒ cotA = 1/3

cosA = 1 ÷  $\sqrt{sec^2A}$

⇒ 1 ÷$\sqrt{1 + tan^2A}$

⇒ 1 ÷$\sqrt{1 + 9}$ = $\frac {1}{\sqrt{10}}$

Now,

6 cot A + $8\sqrt{10}$ cos A

⇒ 6 × (1/3) + $8\sqrt{10}$ × $\frac {1}{\sqrt{10}}$

⇒ 2 + 8 = 10

∴ The value of 6 cot A + 8$\sqrt{10}$ cos A is 10.

Given:

48k2048p6 is divisible by 99

Concept used:

If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

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

Calculation:

99 = 9 × 11

So, the number should be divisible by both 9 and 11

Now,

4 + 8 + k + 2 + 0 + 4 + 8 + p + 6 = 32 + k + p

Now,

Possible values of k + p = 4, 13

Again,

(4 + k + 0 + 8 + 6) - (8 + 2 + 4 + p) = 0 or multiple of 11

⇒ 18 + k - 14 - p = 0 or multiple of 11

⇒ 4 + k - p = 0 or multiple of 11

Now, 

k - p can be - 4 or 7

Now,

For k + p = 4 and k - p = - 4

We can say by adding both 2k = 0

⇒ k = 0

So, p = 4   [Both are possible]

Again,

For k + p = 4 and k - p = 7

We can say by adding both 2k = 11

⇒ k = 5.5  [Not possible]

Again,

For k + p = 13 and k - p = - 4

We can say by adding both 2k = 9

⇒ k = 4.5  [Not possible]

Again,

For k + p = 13 and k - p = 7

We can say by adding both 2k = 20

⇒ k = 10  [Not possible]

So, only possible values of k and p is 0 and 4

Now,

k × p = 0 × 4

⇒ 0

∴ Required answer is 0.

Calculation:

Number of employees in office C = 3600 × (54/360)

⇒ 540

Number of female employees in office C = 540 × (100 - 20)%

⇒ 540 × 80%

⇒ 432

Number of employees in office D = 3600 × (90/360)

⇒ 900

Number of female employees in office C = 900 × 40%

⇒ 900 × 0%

⇒ 360

Required ratio = 360 : 432

⇒ 5 : 6

∴ Required answer is 5 : 6.

Given:

$\sqrt{x}{}-{1\over\sqrt{x}}=\sqrt5$

Concept used:

If (a + 1/a) = b

Then,

a³ + 1/a³ = b³ - 3b

(a - 1/a)² = a² + 1/a² - 2

Calculation:

$\sqrt{x}{}-{1\over\sqrt{x}}=\sqrt5$

By squaring both sides we get

x + 1/x - 2 = 5

⇒ x + 1/x = 7

Now,

$(x^4+{1\over{x^2}})\over(x^2+1)$

⇒ $(x^3+{1\over{x^3}})\over(x+\frac{1}{x})$   [By dividing x from both ]

⇒ ${7^3 - 3\times(7)}\over7$ 

⇒ ${343 - 21}\over7$

⇒ ${322}\over7$

⇒ 46

∴ The required answer is 46.

Given:

A shopkeeper offers a discount of 18% on a machine and sells it for ₹48,380.

Concept used:

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

Selling price = Cost price × (100 + profit)%

Calculation:

Without the discount selling price would be 48380 × (100/82)

⇒ Rs. 59000

According to the question,

Cost price × (118/100) = 59000

⇒ Cost price = 59000 × (100/118)

⇒ Cost price = 50000

∴ The cost price (in ₹) of the machine is 50000.

Given:

P and Q completed a work together and were paid ₹1,080 and ₹1,440

P can complete the work in 20 days

Concept used:

Total work = Efficiency of the worker × time taken by them

Efficiency is directly proportional to the amount gets

Calculation:

Ratio of amount paid to P and Q = 1080 : 1440

⇒ 3 : 4

Now,

Total work = 20 × 3

⇒ 60 units

So, time taken by both of them to complete the work = 60/7

⇒ $8{4\over7}$ days

∴ They take $8{4\over7}$ days to complete the work together.

Given:

$6{\sqrt6}$ p3 + $2\sqrt2$ q3 = ($\sqrt6$ p + $\sqrt2$ q)(Sp2 + Mq2 - Npq)

Concept used:

a³ + b³ = (a + b)(a² + b² - ab)

Calculation:

$6{\sqrt6}$ p3 + $2\sqrt2$ q3 = ($\sqrt6$ p + $\sqrt2$ q)[($\sqrt6$p)2 + ($\sqrt2$q)2 - $\sqrt6$ × $\sqrt2$pq)

⇒ ($\sqrt6$ p + $\sqrt2$ q)(6p2 + 2q2 - $\sqrt{12}$pq)

So,

S = 6

M = 2

N = $\sqrt{12}$

Now,

$\sqrt{S^2+M^2+2N^2}$ = $\sqrt{6^2+2^2+2 \times\sqrt{12}^2}$

⇒ $\sqrt{36+4+2 \times12}$

⇒ $\sqrt{36+4+24}$

⇒ $\sqrt{40+24}$

⇒ $\sqrt{64}$

⇒ 8

∴ Required answer is 8.

Calculation:

Expenditure in 2018 = 75 lakhs

Expenditure in 2019 = 80 lakhs

Increase in expenditure = 80 - 75 = 5 lakhs

Required % = (5/75) × 100

⇒ $6{2\over3}$%

∴ Required answer is $6{2\over3}$%.

Given:

In a ΔABC, X and Y on AB and AC respectively

XY ∥ BC

XY : BC = 2.5 : 7 

Formula used:

In two similar triangles, the ratio of the area is equal to the ratio of the square of their corresponding sides.

Calculation:

Here,

XY : BC = 2.5 : 7 

As, It is given that XY || BC

So, ΔAXY ~ ΔABC

(Area of ΔAXY)/(Area of ΔABC) = (XY/BC)²

⇒ (Area of ΔAXY)/(Area of ΔABC) = (2.5/7)2

⇒ (Area of ΔAXY)/(Area of ΔABC) = 6.25/49

Now,

Area of ΔAXY = 6.25

So, area of trapezium BCYX = 49 - 6.25

⇒ 42.75

Ratio = 42.75/6.25

⇒ 171/25

∴ The ratio of the area of the trapezium BCYX to that of the ΔAXY is $171\over25$.

Given:

If Raman drives his bike at a speed of 24 km/h, he reaches his office 5 minutes late

If Raman drives his bike at a speed of 30 km/h, he reaches his office 4 minutes early

Concept used:

Time = Distance/speed

Calculation:

Let total distance be x km

Now,

According to the question,

(x/24) - (x/30) = 9 minutes or 3/20 hours   [As 1 hour = 60 min]

⇒ [(5x - 4x)/120] = 3/20

⇒ [x/120] = 3/20

⇒ x = 18

So, total distance = 18 km

Now,

If he travelles at a speed of 27 km/h then time taken = 18/27

⇒ 2/3 hours or 40 minutes

∴ He will take 40 minutes to reach his office at a speed of 27 km/h.

Given:

The number are 4, 5, 6 and 8

Concept used:

The least number which is exactly divisible by a, b and c is the L.C.M of a, b and c

Calculation:

LCM of 4, 5, 6 and 8 is 120

Now,

By dividing 120 from 3627 we get 27 as the remainder

So,

Required number which should be added to the next multiple of 120 = 120 - 27

⇒ 93

∴ The required number is 93.

Given:

∠CBE = 75°

Concept used:

The diameter of a circle subtends an angle of 90° at any point on the circle.

Angles formed by the endpoints of the chord in either major or minor segments are always equal.

Calculation:

∠CBE = ∠CAE = 75°    [Angles formed by the endpoints of the chord in either major or minor segments are always equal.]

∠AEC = 90°   [The angle subtended from a diameter is 90]

So,

∠ECA = 180° - 90° - 75°

⇒ 15°

Now,

ED ∥ AC

So, ∠ECA = ∠CED = 15°

∴ The measure (in degrees) of ∠CED is 15°.

Given:

$\rm 25 \div10-({7\over4}\times{1\over3}) ,of, {6\over5}+{14\over3}\times{9\over10}+({1\over5}\div{1\over25})$

Concept used:

Calculation:

$\rm 25 \div10-({7\over4}\times{1\over3}) ,of, {6\over5}+{14\over3}\times{9\over10}+({1\over5}\div{1\over25})$

⇒ $\rm 25 \div10-({7\over12}) ,of, {6\over5}+{14\over3}\times{9\over10}+({1\over5}\times{25\over1})$

⇒ $\rm 25 \div10-{7\over12} ,of, {6\over5}+{14\over3}\times{9\over10}+5$

⇒ $\rm 25 \div10-{7\over10}+{14\over3}\times{9\over10}+5$

⇒ $\rm {5\over2}-{7\over10}+{14\over3}\times{9\over10}+5$

⇒ $\rm {5\over2}-{7\over10}+{14\over3}\times{9\over10}+5$

⇒ $\rm {25 - 7+42+50\over10}$

⇒ $\rm {110\over10}$

⇒ 11

∴ Required value is 11.