SSC CGL 2021 Tier-I (Held On : 18 April 2022 Shift 2) (Previous Year Paper)

The logic followed here is:

Logic: The number of letter is the code of sentence

3224 means 'Taj is in Agra'

And,

4245 means 'Agra is near Delhi'.

Similarly,

'I like all fruits' is coded as,

Hence, the correct answer is "1436".

By using BODMAS Rule:

Option 1) ×, ÷, =, +, −

Interchange the mathematical signs with *,

After placed the sign we get,

⇒ 15 × 1411 ÷ 83 = 137 + 218 - 100

⇒ 15 × 17 = 355 - 100

⇒ 255 = 255

⇒ LHS = RHS

Option 2) ×, =, −, ÷, +

Interchange the mathematical signs with *,

After placed the sign we get,

⇒ 15 × 1411 = 83 - 137 ÷ 218 + 100

⇒ 21165 = 83 - 0.62844 + 100

⇒ 21165 = 183 - 0.62844

⇒ 21165 ≠ 182.37456

⇒ LHS ≠ RHS

Option 3) +, −, ×, =, ÷

Interchange the mathematical signs with *,

After placed the sign we get,

⇒ 15 + 1411 - 83 × 137 = 218 ÷ 100

⇒ 15 + 1411 - 11371 = 2.18

⇒ 1426 - 11371 = 2.18

⇒ -9945 ≠ 2.18

⇒ LHS ≠ RHS

Option 4) ×, +, ÷, −, =

Interchange the mathematical signs with *,

After placed the sign we get,

⇒ 15 × 1411 + 83 ÷ 137 - 218 = 10

⇒ 15 × 1411 + 0.60583941 - 218 = 10

⇒ 21165 + 0.60583941 - 218 = 10

⇒ 21165.60583941 - 218 = 10

⇒ 20947.60583941 ≠ 10

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 1".

Given: 

The ratio of the present ages of Charvi and Vaishnavi is 4: 5.

Calculation:

Let the present age of Charvi is 4x and the present age of Vaishnavi is 5x.

As Yuvika is 2 years older than Charvi 

So, age of Yuvika = 4x + 2.  → (i)

As Yuvika is 5 years younger than Vaishnavi

So, age of Yuvika = 5x - 5.  → (ii)

From (i) and (ii), we get

4x + 2 = 5x - 5

⇒ x = 7

Therefore, present age of Vaishnavi = 5 × 7 = 35 year 

Hence, the correct answer is "option (1)".

The pattern followed here is:

Hence, the correct answer is "107".

Given: 

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise number are the opposite numbers in the dice.

When moving in a clockwise direction from the common face (T) in dice (1) and (2):

From both dice:

Now, Q is opposite to U, thus Q will be on the face opposite to the face having the letter U.

Hence, the correct answer is "U"

According to the English alphabet series and its positional value.

The logic followed here is:

Here, WTR, MJH and SPN follow the series of '-3' and '-2'

But, WUT follows the series of '-2' and '-1'.

Hence, the correct answer is "WUT".

The logic followed here is:

Logic: (First number - 1)² = Second number.

⇒ 28 : 729

⇒ (28 - 1)² = (27)² = 729.

Similarly,

⇒ 32 : ?

⇒ (32 - 1)² = (31)² = 961

Hence, the correct answer is "961".

Given:- K _ _ N L _ N K _ N _ L N K _ M _ L M _

By checking options and substituting accordingly.

1) L, M, M, M, K, L, K, N → K L M N, L M N K, M N K L, N K L M, K L M N

2) L, M, M, K, K, L, N, N → K L M N, L M N K, K N K L, N K L M, N L M N

3) M, M, L, K, K, L, K, N → K M M N, L L N K, K N K L, N K L M, K L M N

4) L, M, M, K, K, M, K, N → K L M N, L M N K, K N K L, N K M M, K L M N

The logic here is that all the 4 letters (K,L,M,N) should be there in the group of four and in all the options except 1 they are being repeated.

• Option (1) give a pattern of K L M N - L M N K - M N K L - N K L M - K L M N

Hence, the correct answer is "L, M, M, M, K, L, K, N".

The logic followed here is:

Logic: In the column [First number × second number + first number = Third number]

First column:

⇒ 7 × 3 + 7 = 21 + 7 = 28

And,

Second column:

⇒ 9 × 8 + 9 = 72 + 9 = 81

Similarly,

Third column:

⇒ 5 × X + 5 = 50

⇒ 5X + 5 = 50

⇒ 5X = 50 - 5

⇒ 5X = 45

⇒ X = 9

Here, second number is 9

Hence, the correct answer is "9"

According to the English alphabet series and its positional value

Logic: Addition of +10 is every alphabet.

GATE is coded as QKDO

Similarly,

PLAN is coded as ?

Hence, the correct answer is "ZVKX".

Venn diagram according to the given information is:

Brother, Nephew, Uncle

Some brother are nephew as well as uncle.

Some Nephew are brother as well as uncle

And, Some uncle are brother as well as Nephew.

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

According to the English alphabet series and its positional value

The pattern followed here is:

Hence, the correct answer is "STN".

The logic followed here is 

1. The logic involves shifting the letters of the word based on their position in the alphabet. 

2. If the place value of the letter is a single digit(0 - 9) i.e. A to I; then it is shifted by +1 positions forward in the alphabet.

3. If the place value of the letter is a double-digit(10 - 26) i.e. J to Z then it is shifted by +2 positions forward in the alphabet.

DOGMATIC : EQHOBVJD

D (4^th letter) -> E (shifted by 1)

O (15^th letter) -> Q (shifted by 2)

G (7^th letter) -> H (shifted by 1)

M (13^th letter) -> O (shifted by 2)

A (1^st letter) -> B (shifted by 1)

T (20^th letter) -> V (shifted by 2)

I (9^th letter) -> J (shifted by 1)

C (3^rd letter) -> D (shifted by 1)

Similarly,

 PRODUCTS : ?

​

Hence, the correct answer is "RTQEWDVU".

The pattern followed here is:

1. Middle figure is rotate 90º anticlockwise in every next figure.

2) 

is increase by two in every next figure. 

The figure that will complete the series is shown below:

Hence, 'option 3' is the correct answer.

Confusion Points

in option no 2 are not in any corner.

Corners are being followed as per the logic so the correct answer is option 3, where there are 2

in the top right corner and 1

in the other 3 corners.

The logic followed here is:

Similarly,

Hence, '14-2-36-24-18-6' is the correct answer.

BODMAS rule:

Given equation: 15 + 90 ÷ 9 × 5 – 11 = 28

After interchanging the numbers, we get:

1. 11 and 9

15 + 90 ÷ 11 × 5 – 9 = 28

⇒ 15 + 8.18 × 5 – 9 = 28

⇒ 15 + 40.9 – 9 = 28

⇒ 55.9 - 9 = 28

⇒ 46.9 ≠ R.H.S

2. 15 and 9

9 + 90 ÷ 15 × 5 – 11 = 28

⇒ 9 + 6 × 5 – 11 = 28

⇒ 9 + 30 – 11 = 28

⇒ 39 - 11 = 28

⇒ 28 = R.H.S

3. 15 and 5

5 + 90 ÷ 9 × 15 – 11 = 28

⇒ 5 + 10 × 15 – 11 = 28

⇒ 5 + 150 – 11 = 28

⇒ 155 – 11 = 28

⇒ 144 ≠ R.H.S

4. 9 and 5

15 + 90 ÷ 5 × 9 – 11 = 28

⇒ 15 + 18 × 9 – 11 = 28

⇒ 15 + 162 – 11 = 28

⇒ 177 – 11 = 28

⇒ 166 ≠ R.H.S

Hence, '15 and 9' is the correct answer.

The image embedded in given figure is as shown below:

Hence, 'option 1' is the correct answer.

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

Clearly, Mihir is the cousin of Kaumudi.

Hence, ‘cousin’ is the correct answer.

Radha wears five different coloured clothes, red, green, yellow, purple and brown, on five different days of a week, from Monday to Friday.

1. She wears red clothes on Wednesday.

2. She does not wear green and brown clothes on Monday or Friday.

3. She wears green clothes on the next day of wearing yellow clothes.

Only Purple and Brown clothes are left, which will be put in the order as shown below:

Clearly, Radha wear brown clothes on Thursday.

Hence, 'Thursday' is the correct answer.

The logic followed here is:

Numbers at odd position: 2, 4, 10, 28, 82, ?

• 2 × 3 - 2 = 6 - 2 = 4
• 4 × 3 - 2 = 12 - 2 = 10
• 10 × 3 - 2 = 30 - 2 = 28
• 28 × 3 - 2 = 84 - 2 = 82
• 82 × 3 - 2 = 246 - 2 = 244

Numbers at even position: 31, 37, 41, 43, 47 → Prime number series

Hence, '244' is the correct answer.

The mirror image of the given combination when the mirror is place at the right side is as shown below :

Hence, 'option 1' is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 4' is the correct answer.

The logic followed here is:

Both the positions of the dice have a common face → L

Rotating clockwise direction from L in both, we get:

The faces that will be opposite to each other when the paper is folded to form a cube is shown below:

Hence, 'option 4' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. No apricot is a grape. → Do not follow (As, All lemons are apricots and All grapes are lemons → Some apricot are grape)

II. No grape is a plum. → Follow (As, No plum is an apricot, All lemons are apricots and All grapes are lemons)

III. No lemon is a plum. → Follow (As, No plum is an apricot and All lemons are apricots)

IV. Some plums are lemons. → Do not follow (No plum is an apricot and All lemons are apricots → No plum is lemon)

Hence, Only conclusions II and III follow.

The correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary is:

3. Product
4. Professor
5. Projection
6. Pronounce
7. Provide

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

The correct answer is Goa.

Key Points

• Goa became the first 'Har Ghar Jal State' in India with 100% tap water connections in October 2020.
• Goa has become the first state in India to provide 100 per cent tap water connections in the rural areas covering 2.30 lakh households.
• The Jal Jeevan Mission of the Central Government aims to provide piped water to all rural households by 2024.
• Under Jal Jeevan Mission, it is mandatory that 5 persons in every village, especially women, must be trained in using field test kits to test the water.
• Currently, Gajendra Singh Shekhawat is a Union Jal Shakti Minister.

Additional Information

• Goa is the smallest state in India.
• The state has the highest per capita income in India.
• Portugal ruled Goa for almost 450 years.
• Goa celebrates two independence days.
• India became an independent country, free from British rule, on 15^th August 1947.
• Goa celebrates this second independence day on 19^th December every year as it's get's liberated from Portuguese rule in 1961.
• Chief minister: Pramod Sawant. (June 2022)
• Governor of Goa: Shri P.S. Sreedharan Pillai. (June 2022)

The correct answer is 6.

Key Points

• The Elements of group 16 such as Oxygen, Sulfur, Selenium, Tellurium, Polonium and all have 6 electrons on the outermost cell.
• The 's' valence shells always contain 2 electrons, the 'p' valence shell contains 4 electrons.
• The elements present in group 16 consist of oxygen (0), sulfur (S), selenium (Se), tellurium (Te), and polonium (Po).
• Of all the elements, only Polonium is radioactive.
• Group 16 electron configuration indicates that its members of Group 16 have six elements in its valence shell, and therefore require two elements to complete the octet valency.
• Therefore, all the elements of group 16 are negatively charged since they can receive two electrons from other elements.

Important Points

The correct answer is All India Muslim League.

Key Points

• All India Muslim League supported the move for the partition of Bengal in 1905.
• Lord Curzon was the Viceroy of India from 1899 to 1905.
• The partition of the Bengal province came into effect during his viceroyalty on 16^th October 1905.
• The idea of using the Bengal partition as a political tool to undermine the growing nationalism in Bengal.
• As per Curzon, after the partition, the two provinces would be Bengal (including modern West Bengal, Odisha, and Bihar) and Eastern Bengal and Assam.
• Bengal would have a Hindu majority and Eastern Bengal and Assam would have a Muslim majority population. Its capital would remain Calcutta.
• Many people in Bengal regarded this partition as an insult to their motherland. Rabindranath Tagore composed the famous song ‘Amar Sonar Bangla’ which later became the national anthem of Bangladesh.
• **Muslims led by the Nawab Sallimullah of Dhaka supported the partition.**​

Additional Information

• Gadar Party
• ​The Ghadar Party was initially named the Pacific Coast Hindustan Association.
• It was formed on 15 July 1913 in the United States under the leadership of Lala Har Dayal, Sant Baba Wasakha Singh Dadehar, Baba Jawala Singh, Santokh Singh, and Sohan Singh Bhakna as its president.
• Forward Bloc​
• ​The All India Forward Bloc is a left-wing nationalist political party in India.
• It emerged in 1939, under the leadership of Subhas Chandra Bose.
• All India Muslim League​
• ​The All-India Muslim League was a political party established in 1906 in British India.
• Its strong advocacy, from 1930 onwards, for the establishment of a separate Muslim-majority nation-state, Pakistan, ultimately led to the partition of India in 1947 by the British Empire.
• Founders: Muhammad Ali Jinnah, Aga Khan III, Hakim Ajmal Khan, Khwaja Salimullah, Waqar-ul-Mulk.
• Communist Party of India
• ​The Communist Party of India is the oldest communist party in India and one of the 9 national parties in the country.
• The CPI was founded in Kanpur on 26 December 1925.

The correct answer is 500.

Key Points

• In Union Budget 2021-22, there is a proposal to provide liquid waste management in 500 AMRUT cities under Jal Jeevan Mission (Urban).
• As per Article 112 of the constitution, a union budget is basically the statement of the estimated receipts and expenditures of the government.
• It is also known as the annual financial statement of the government.
• Department of Economic Affairs, Ministry of Finance is the nodal body responsible for preparing the Budget.
• Budget 2021-22 is the first budget of the new decade 2021-30 and is also the first-ever digital union budget.
• The current Finance Minister of India is Nirmala Sitharaman.

Important Points 

• Highlights of the budget 2021-22
• ​Rs. 2,23,846 crore outlay for Health and Wellbeing in 2021-22 as against Rs. 94,452 crore in 2020-21 – an increase of 137%.
• Rs. 35,000 crores for COVID-19 vaccine in 2021-22.
• Rs. 64,180 crore outlay over 6 years for PM AatmaNirbhar Swasth Bharat Yojana.
• Rs. 2,87,000 crore over 5 years for Jal Jeevan Mission (Urban) - to be launched with an aim to provide:
• 2.86 crore household tap connections.
• Universal water supply in all 4,378 Urban Local Bodies.
• Liquid waste management in 500 AMRUT cities.
• Mega Investment Textiles Parks (MITRA) scheme, in addition to PLI.
• 7 Textile Parks to be established over 3 years.
• Under the Rs. 5.35 lakh crore Bharatmala Pariyojana, more than 13,000 km length of roads worth Rs. 3.3 lakh crore was awarded for construction.
• To increase the permissible FDI limit from 49% to 74% and allow foreign ownership and control with safeguards.
• Agricultural credit target enhanced to Rs. 16.5 lakh crore in FY22 - animal husbandry, dairy, and fisheries to be the focus areas.
• Rural Infrastructure Development Fund to be enhanced to Rs. 40,000 crore from Rs. 30,000 crore.
• To double the Micro Irrigation Fund to Rs. 10,000 crore.
• ‘Operation Green Scheme’ to be extended to 22 perishable products, to boost value addition in agriculture and allied products.

Additional Information 

• About Budget 2022-23.
• India’s economic growth is estimated at 9.2% to be the highest among all large economies.
• 60 lakh new jobs are to be created under the productivity-linked incentive scheme in 14 sectors.
• PLI Schemes have the potential to create an additional production of Rs 30 lakh crore.
• Entering Amrit Kaal, the 25-year-long lead-up to India @100, the budget provides the impetus for growth along with four priorities:
• PM GatiShakti
• Inclusive Development
• Productivity Enhancement & Investment,
• Sunrise opportunities,
• Energy Transition, and Climate Action.Financing of investments
• National Highways Network to be expanded by 25000 Km in 2022-23.
• Rs. 2.37 lakh crore direct payment to 1.63 crore farmers for procurement of wheat and paddy.
• Rs. 48,000 crores allocated for completion of 80 lakh houses in 2022-23 under PM Awas Yojana.
• Introduction of Digital Rupee by the Reserve Bank of India starting 2022-23.
• ​Total expenditure in 2022-23 is estimated at Rs. 39.45 lakh crore.
• Total receipts other than borrowings in 2022-23 are estimated at Rs. 22.84 lakh crore.
• The fiscal deficit in 2022-23 is estimated at 6.4% of GDP.

The correct answer is 11.0%.

Key Points

• India’s real GDP to record an 11.0% growth in FY2021-22 and nominal GDP to grow by 15.4% – the highest since independence.
• The Economic Survey of India is an annual document of the Ministry of Finance, Government of India.
• The Department of Economic Affairs, Ministry of Finance presents the Survey in the Parliament every year, just before the Union Budget.
• It is prepared under the guidance of the Chief Economic Adviser of India.
• Union Minister of finance: Nirmala Sitaraman
• Chief Economic Adviser of India:  V Anantha Nageswaran.

Additional Information 

• Summary of Economic Survey-2021-22
• India’s real GDP to record an 11.0% growth in FY2021-22 and nominal GDP to grow by 15.4% – the highest since independence.
• The recovery in the second half of FY2020-21 is expected to be powered by government consumption, estimated to grow at 17% YoY.
• Exports are expected to decline by 5.8% and imports by 11.3% in the second half of FY21.
• India expected to have a Current Account Surplus of 2% of GDP in FY21, a historic high after 17 years.
• On the supply side, Gross Value Added (GVA) growth was pegged at -7.2% in FY21 as against 3.9% in FY20.
• Agriculture is set to cushion the shock of the COVID-19 pandemic on the Indian economy in FY21 with a growth of 3.4%.
• Industry and services are estimated to contract by 9.6% and 8.8% respectively during FY21.
• Agriculture remained the silver lining while contact-based services, manufacturing, and construction were hit hardest, and recovering steadily.
• India remained a preferred investment destination in FY 2020-21 with FDI pouring in amidst global asset shifts towards equities and prospects of quicker recovery in emerging economies.
• Net FPI inflows recorded an all-time monthly high of US$ 9.8 billion in November 2020, as investors’ risk appetite returned.
• India was the only country among emerging markets to receive equity FII inflows in 2020$.

The correct answer is Bilateral.

Key Points

• If the body can be divided into identical left and right halves in only one plane, this type of body plan is called bilateral symmetry.
• Example - annelids, arthropods, etc.

Fig: Bilateral Symmetry

• Animals can be categorized into three types on the basis of their symmetry - Asymmetrical, Radial symmetry & Bilateral symmetry.
• Radial symmetry
• When any plane passing through the central axis of the body divides the organism into two identical halves, it is called radial symmetry.
• Radial symmetry is exhibited by Coelenterates, ctenophores, and echinoderms.

Fig: Radial Symmetry

• Asymmetrical
• If any plane that passes through the centre does not divide them into equal halves, this type of body plan is called asymmetrical. **Example - Porifera (Sponges).**​

Additional Information

• Arthropods are invertebrate animals having an exoskeleton, a segmented body, and paired jointed appendages.
• Arthropods form the phylum Arthropoda.
• They are distinguished by their jointed limbs and cuticle made of chitin, often mineralized with calcium carbonate.
• The largest phylum in the animal kingdom, includes lobsters, crabs, spiders, mites, insects, centipedes, and millipedes.
• About 84 percent of all known species of animals are members of this phylum.

The correct answer is Abul Kalam Azad.

Key Points

• ‘India Wins freedom’ is a book written by Maulana Abul Kalam Azad, who remained Congress President for almost 6 yrs (1940 - 46).
• This was a critical 2^nd world war period and very crucial from the Indian freedom movement perspective.
• During this period he was in key decision-making and negotiating role with Britishers.
• India Wins Freedom is an enlightening account of the partition from the author, Maulana Azad's perspective.
• It includes his personal experiences when India became independent and his ideas on freedom and liberty.

Additional Information

• Jawaharlal Nehru
• Nehru was a principal leader of the Indian nationalist movement in the 1930s and 1940s.
• He was the first prime minister of Independent India, and he served as the country's prime minister for 17 years.
• Famous Books:
• The Discovery of India
• Letters from a Father to his Daughter
• Glimpses of World History
• The Essential Writings, Vol 2
• The Unity of India Collected Writings 1937-1940
• Jaswant Singh​
• ​Major Jaswant Singh was an officer of the Indian Army and an Indian Cabinet Minister.
• He was one of the founding members of the Bharatiya Janata Party, and was one of India's longest-serving parliamentarians, having been a member of the Lok Sabha or the Rajya Sabha almost continuously between 1980 and 2014.
• Rajendra Prasad​
• ​Rajendra Prasad was an Indian independence activist, lawyer, and scholar.
• The first president of India was in office from 1950 to 1962.
• He joined the Indian National Congress during the Indian Independence Movement and became a major leader in the region of Bihar and Maharashtra.

The correct answer is positively charged.

Key Points

• In the flocculation method of water treatment positively charged chemical is added to the water.
• In water treatment, flocculation involves the addition of compounds that promote the clumping of fine floc into larger floc so that they can be more easily separated from the water.
• The coagulation-flocculation process can be used as a preliminary or intermediary step between other water or wastewater treatment processes like filtration and sedimentation.

Additional Information

• Water treatment through flocculation:
• Stage 1 of flocculation,
• A coagulant like aluminium sulphate is added to the wastewater.
• The positively charged coagulant molecules neutralize the negatively charged solid particles suspended in the water.
• Neutralising these particles paves the way for them to flocculate together into a larger mass.
• STAGE 2
• The wastewater must be agitated with mixers.
• High energy mixing is required initially to ensure that the coagulant spreads throughout the water.
• When flocculation is in progress the mixing energy is reduced to prevent the mass of particles from separating again.
• STAGE 3
• Once floc is beginning to form, a polymer chemical is added to the wastewater.
• Polymers bridge the flocculant from micro to macro flocculant, meaning that the mass of particles collecting together gets bigger.
• This chemical also binds the collected mass together so that it does not easily disintegrate even when the water is slightly agitated.
• STAGE 4
• After flocculation is complete, the large solid masses can be removed from the wastewater stream.
• Care must be taken when cleaning the filters to ensure that the phosphorus-rich floc is contained and treated.

The correct answer is 2009.

Key Points

• The Right of Children to Free and Compulsory Education Act or Right to Education Act (RTE) is an Act of the Parliament of India enacted on 4 August 2009.
• It describes the importance of free and compulsory education for children between the age of 6 to 14 years in India under Article 21A of the constitution.
• This act came into effect on 1 April 2010 and made India one of the 135 countries to have made education a fundamental right for every child.
• It prescribes minimum norms for elementary schools, prohibits unrecognized schools from practice, and advocates against donation fees and interviews of children at the time of admission.

The correct answer is 1915 – Mahatma Gandhi returned from South Africa.

Key Points

• After over 21 years of stay in South Africa, Gandhi returned to India on January 9, 1915, with his wife Kasturba.
• He had been in London the previous year to treat a severe bout of pleurisy, a lung inflammation.
• His doctors advised him to return to India to escape the English winter.
• A hero's welcome awaited Gandhi when he landed on January 9, 1915, at the Apollo Bunder in Bombay.
• On 4 February 1916, Gandhiji made his first public appearance after returning from South Africa to BHU. He addressed the audience in BHU.
• Pravasi Bharatiya Divas is a celebratory day observed on 9 January by the Republic of India to commemorate the return of Mahatma Gandhi from South Africa to Mumbai on 9 January 1915.

Additional Information

• 1942 – The Cripps Mission was sent by the British government to India to obtain Indian cooperation for the British war efforts in the 2^nd World War.
• 1930 – The first Round Table Conference convened from 12 November 1930 to 19 January 1931.
• 1942 – From 7 to 8 August 1942, The All India Congress Committee met in Bombay and ratified the 'Quit India' resolution.

The correct answer is New Delhi.

Key Points

• The 2020 Asian Wrestling Championships was held at the KD Jadhav Indoor Stadium, Indira Gandhi Arena, New Delhi in India.
• The event took place from February 18 to February 23.
• The event had a total of 30 weight classes in action under 3 events: Men’s freestyle, Men’s Greco-Roman, and Women’s freestyle.
• Japan topped the medal tally with 16 medals (8 Gold, 4 Silver, 4 Bronze).
• The second rank was held by Iran with a total of 17 medals including7 gold, 3 silver and 7 bronze.
• **India finished 3^rd rank with 20 medals (5 Gold, 6 Silver, and 9 Bronze).**​

Additional Information

• The 2022 Asian Wrestling Championships was the 35^th edition of the Asian Wrestling Championships of combined events and took place from April 19 to 24 in Ulaanbaatar, Mongolia.
• Indian wrestlers secured a total of 17 medals, that includes (1-Gold, 5-Silver, and 11-Bronze medals).
• Gold Medalist: Ravi Kumar Dahiya is the only Gold medalist representing India, in the men’s 57kg freestyle category, beating Kazakhstan’s Rakhat Kalzhan on technical superiority.
• Ravi Kumar became the first Indian to win 3 Gold medals in Asian Wrestling Championships which includes 2020 in New Delhi, India, 2021 in Almaty, Kazakhstan and 2022 in Ulaanbaatar, Mongolia respectively.

The correct answer is Rs.2.5 lakh.

Key Points

• The interest earned on the employee's contribution to the provident fund account will be taxed if the contribution amount in a financial year exceeds Rs 2.5 lakh.
• In the 2020 Budget, the FM had capped the tax exemption on employer's contributions to PF, NPS, and Superannuation funds exceeding an aggregate of 7.5 lakh per annum.
• Currently, the interest rate of EPF is 8.5 percent per annum.
• The government had lowered the interest rate on Employee Provident Fund to 8.50 percent for 2019-20 from 8.65 percent in 2018-19.
• The **contribution towards EPF is 12 percent of the basic salary. **​

Additional Information

• About Budget 2022-23.
• India’s economic growth is estimated at 9.2% to be the highest among all large economies.
• 60 lakh new jobs are to be created under the productivity-linked incentive scheme in 14 sectors.
• PLI Schemes have the potential to create an additional production of Rs 30 lakh crore.
• Entering Amrit Kaal, the 25-year-long lead-up to India @100, the budget provides the impetus for growth along with four priorities:
• PM GatiShakti
• Inclusive Development
• Productivity Enhancement & Investment,
• Sunrise opportunities,
• Energy Transition, and Climate Action.Financing of investments
• National Highways Network to be expanded by 25000 Km in 2022-23.
• Rs. 2.37 lakh crore direct payment to 1.63 crore farmers for procurement of wheat and paddy.
• Rs. 48,000 crores allocated for completion of 80 lakh houses in 2022-23 under PM Awas Yojana.
• Introduction of Digital Rupee by the Reserve Bank of India starting 2022-23.
• ​Total expenditure in 2022-23 is estimated at Rs. 39.45 lakh crore.
• Total receipts other than borrowings in 2022-23 are estimated at Rs. 22.84 lakh crore.
• The fiscal deficit in 2022-23 is estimated at 6.4% of GDP.

The correct answer is Bearing capacity.

Key Points

• Bearing capacity
• This is effectively the weight a soil can withstand before severe damage occurs to the structure of the soil.
• Bearing capacity varies throughout the year, for instance, a very heavy tractor that causes no damage on dry soils may cause a lot of damage to wetted soils.

Important Points 

• Bulk density
• ​The dry mass of soil per unit bulk volume of soil is called bulk density.
• Expressed as kg/m³ or g/cm³.
• Buffering capacity
• ​Buffering capacity is the ability of the soil to reduce high alkalinity or acidity levels coming perhaps from pollution (e.g. acid rain).
• Chalky or limestone soils for instance are very alkaline and can neutralize acids more effectively than acid, peat soils.
• Field capacity​
• ​Field capacity describes soil when it is completely wetted (excepting free drainage), and where there is plenty of water for plant roots.
• This occurs after ample irrigation or rainfall, when the rate of downward movement of water has substantially decreased, usually 1-3 days after rain or irrigation.
• It is expressed as a mass or volume fraction of soil water or a depth of water per metre of soil or mm m^-1.

The correct answer is B Pattabhi Sitaramayya.

Key Points

• The chairman of the House Committee of the Constituent Assembly of India was B Pattabhi Sitaramayya.
• He was a Constituent Assembly member elected from Madras Province.
• Sitaramayya was an active member of the Indian National Congress.
• In the 1939 Congress session in Tripuri, Sitaramayya was Gandhi’s nominee for President of the Congress Party.
• He stood for election against Subash Chandra Bose, however, he lost the election.

Additional Information

• IMPORTANT COMMITTEES OF THE CONSTITUENT ASSEMBLY AND THEIR CHAIRMEN

The correct answer is Kali Puja.

Key Points

• Kali Puja or Shyama Puja is conducted in temples as well as at homes, with people worshipping the Goddess Kali on the new moon day of Krishna Paksha in the Kartik month of the Hindu calendar.
• The festival, which often falls on the same day as Diwali, is considered auspicious for worshipping the goddess.
• Kali Puja (Kali worship) is celebrated in states of east India especially Bengal, Odisha, Bihar, and Assam on the new moon night (Amavasya) of the Hindu month Kartik which normally occurs in the month of October or November every year.
• **It is one of the biggest festivals in Bengal along with Durga Puja.**​

Additional Information

• Mahavir Jayanti
• ​Mahavir Janma Kalyanak is one of the most important religious festivals in Jainism.
• It celebrates the birth of Mahavir, the twenty-fourth and last Tirthankara.
• On the Gregorian calendar, the holiday occurs either in March or April.
• ​Dussehra
• ​Vijayadashami is also known as Dussehra, Dasara, or Dashain.
• It is a major Hindu festival celebrated at the end of Navaratri every year.
• It marks the end of Ramlila and remembers God Rama's victory over Ravana.
• Alternatively, it marks a reverence for one of the aspects of the goddess Devi, such as Durga or Saraswati.
• Holi​
• ​Holi is a popular ancient Hindu festival, also known as the Festival of Spring, the Festival of Colours, or the Festival of Love.
• The festival celebrates the eternal and divine love of Radha Krishna.
• Holi is celebrated on the full moon day in the month of Phalgun.

The correct answer is Bharatanatyam.

Key Points

• Bharatnatyam was performed by certain families of the Tanjore district and these inheritors were known as 'Nattuvanar'.
• The term nattuvanar connotes a man who accompanied the devadasi dance in the capacity of a dance master, music conductor, and vocal percussionist.
• Bharatnatyam is one of the most popular classical Indian dances.
• Bharatnatyam is more popular in the South Indian states of Tamil Nadu and Karnataka.
• Bharatanatyam is the oldest classical dance tradition in India.

Additional Information

The correct answer is 55.

Key Points

• 55 was the estimated national mortality rate of children under the age of five in the country as per the Census of India 2011.
• In 1990 this rate was 126.
• According to World Bank's data, the mortality rate or crude death rate in India is 7.30 per 1000 persons per year.
• In India, approximately 26789 deaths are reported per day.
• Infant mortality rate
• ​Infant mortality rate (IMR) is the number of deaths per 1,000 live births of children under one year of age.
• The rate for a given region is the number of children dying under one year of age, divided by the number of live births during the year, multiplied by 1,000.

The Formula for calculating the infant mortality rate is:

• IMR = the number of infant mortality/the number of infants in mid-year × 1000

Additional Information

• Census of India, 2011:
• Total Population of India was 1,210,193,422.
• The Sex Ratio (females per thousand males) in India was 943.
• The population density was reported at 382 persons per sq. km.
• Total districts covered- 640.
• Crude Birth Rate- 21.8.
• Crude Death Rate 7.1 per thousand population
• The national mortality rate of children under the age of five is 55.
• The literacy rate of the country is 74.04 per cent. (82.14 for males and 65.46 for females).
• The state with the highest literacy is Kerala (94.0%)
• The state with the lowest literacy is Bihar (61.8%)
• state with the highest female literacy rate- Kerala (92.1%)
• The state with the lowest female literacy is Bihar(51.5%)
• The state that has the highest decadal growth is Meghalaya (27.9%)
• State having highest Population  Uttar Pradesh (19,98,12,341)
• The state has the lowest population is Sikkim (6,10,577)
• State with Highest Population Density Bihar (1106). Hence Option 4 is incorrect.
• State with Lowest Population Density  Arunachal Pradesh (17)
• The state has the highest Sex Ratio is Kerala (1,084)
• The state has the lowest Sex Ratio  is Haryana (879)
• The highest Death Rate among states is in Odisha (98 per thousand).
• The lowest Death Rate among states is in Kerala— 16 per thousand.
• The decadal growth rate in Population is 17.7%.
• The state has the lowest population decadal growth rate in Nagaland (–0.47%).

The correct answer is diatomic.

Key Points

• Nitrogen gas is a diatomic molecule composed of two N atoms. Therefore, it exists as N₂.
• Nitrogen can form pπ−pπ multiple bonds.
• In the case of nitrogen, there is no repulsion between non-bonded electrons of the inner core, as it has only 1s electrons in the inner shell so the overlap of p orbitals to form pi bonds is easy.
• Therefore, it exists as a diatomic molecule.
• Nitrogen has atomic number 7 and electronic configuration [He] 2s2 2p3.
• Nitrogen was first discovered and isolated by Scottish physician Daniel Rutherford in 1772.
• Nitrogen is the fourth most abundant element in the body.
• It is the fifth most abundant element in the universe and makes up about 78% of the earth's atmosphere.
• The largest use of nitrogen is for the production of ammonia (NH3).

The correct answer is Irfan Khan.

Key Points

• The late actor Irrfan Khan was honoured with the Lifetime Achievement Award at the 66^th edition of the Filmfare Awards 2021 held in Mumbai.
• Irrfan Khan also won a posthumous award:
• Best Actor - for his work in Angrezi Medium.
• Irrfan Khan died on April 29 in Mumbai at the age of 53 last year after a long battle with cancer.
• Taapsee Pannu won the Best Actress Award for Thappad, which also bagged the Best Film, Best Story, and Best Editing trophies.
• Amitabh Bachchan won the Best Actor (Critics) award for his performance in Gulabo Sitabo.
• Saif Ali Khan picked the Best Actor In A Supporting Role award for his work in Tanhaji: The Unsung Warrior
• Kajol's Devi won the Best Short Film (Popular Choice) award.

The correct answer is Adil Hussain.

Key Points

• Adil Hussain became the first Indian to win Best Actor at the Norwegian National Awards in Haugesund Norway in 2018 for his film 'What Will People Say'.
• The film has already won the Kanon Award at the Kosmorama film festival, which is Norway's equivalent of the Academy Awards.
• Adil Hussain is from the Goalpara district of Assam.
• The film is directed by Norwegian-born filmmaker Iram Haq has also won the best film, best director, and best script award which is regarded as the Norwegian national film award.
• This film is about immigrants and their rigid value system.
• It also speaks volumes about the degree and intensity of democracy and the inclusiveness of the democracy that Norway practices.

The correct answer is Belgium.

Key Points

• Belgium is the reigning Olympic Men’s Field Hockey champion.
• The men's field hockey tournament at the 2020 Summer Olympics was the 24^th edition of the field hockey event for men at the Summer Olympic Games.
• It was held from 24 July to 5 August 2021.
• All games were played at the Oi Hockey Stadium in Tokyo, Japan.
• Argentina won the previous Olympic field hockey i.e., the 2016 event but was eliminated in the quarterfinals in 2020.
• Belgium captured their first gold medal after defeating Australia in the final after penalties.
• India won their first hockey medal since the 1980 Summer Olympics by defeating Germany in the bronze-medal match

The correct answer is Rs 2,000.

Key Points

• The fine for extinguishing public lamps may extend to Rs 2,000 as per Section 141 of The Electricity Act, 2003.
• Section 141 Electricity Act 2003:
• Extinguishing public lamps.
• Whoever, maliciously extinguishes any public lamp shall be punishable with a fine which may extend to two thousand rupees.
• The  Electricity Act 2003 of Parliament received the assent of the President on the 26^th of May, 2003.
• An Act to consolidate the laws relating to the generation, transmission, distribution, trading, and use of electricity and generally for taking measures conducive to the development of the electricity industry, promoting competition therein, protecting the interest of consumers, and supply of electricity to all areas.
• Rationalization of electricity tariff, ensuring transparent policies regarding subsidies, promotion of efficient and environmentally benign policies, the constitution of Central Electricity Authority, Regulatory Commissions, and establishment of Appellate Tribunal and for matters connected therewith or incidental thereto.

The correct answer is three.

Key Points

• Ozone is a molecule composed of three atoms of oxygen, also referred to as O₃.
• A layer of ozone is present in the stratosphere of Earth and prevents the UV rays from reaching the Earth's surface.
• It is an allotrope of Oxygen.
• Ozone, or tri-oxygen, is an inorganic molecule with the chemical formula O₃.
• It is a pale blue gas with a distinctively pungent smell.
• Ozone is an excellent oxidizing agent as it breaks down into oxygen gas and nascent oxygen. { O₃ → O₂ + [O] }.
• It is an allotrope of oxygen that is much less stable than the diatomic allotrope O2, breaking down in the lower atmosphere to O2 or di-oxygen.

Additional Information

• The upper stratosphere consists of a considerable amount of ozone (O3), which protects us from the harmful ultraviolet (UV) radiation coming from the sun.
• These radiations cause skin cancer (melanoma) in humans.
• Therefore, it is important to maintain the ozone shield.
• Ozone in the stratosphere is a product of UV radiations acting on dioxygen (O2) molecules.
• The UV radiations split apart molecular oxygen into free oxygen (O) atoms.
• These oxygen atoms combine with molecular oxygen to form ozone.

• The Dharmasutras and Dharmashastras also contained rules about the ideal “occupations” of the four categories or varnas.
• Brahmanas were supposed to study and teach the Vedas, perform sacrifices and get sacrifices performed, and give and receive gifts.
• Kshatriyas were to engage in warfare, protect people and administer justice, study the Vedas, get sacrifices performed, and make gifts.
• The last three “occupations” were also assigned to the Vaishyas, who were in addition expected to engage in agriculture, pastoralism and trade.
• Shudras were assigned only one occupation – that of serving the three “higher” varnas.
• The Brahmanas evolved two or three strategies for enforcing these norms. One, as we have just seen, was to assert that the varna order was of divine origin.
• Second, they advised kings to ensure that these norms were followed within their kingdoms.
• And third, they attempted to persuade people that their status was determined by birth. However, this was not always easy. So prescriptions were often reinforced by stories told in the Mahabharata and other texts.

The correct answer is Jhelum.

Key Points

• Jhelum river originates from a magnificent spring called “Chashma Verinag”.
• The Jhelum (Vyeth in Kashmiri, Vetesta in Sanskrit, and Hydaspes in Greek) is the main waterway of the Kashmir valley.
• Jhelum rises from its chief source Verinag at the foothills of Pir Panjal ranges in Jammu and Kashmir.
• Jhelum is the lifeline of the city of Srinagar that bifurcates the city into two parts.
• The Mangla Dam was built on the river.
• Dal Lake of the city is fed by the water of Jhelum.

Additional Information

• Beas
• ​The river which originates in the Beas Kund is Beas.
• At Rohtang Pass in the western (Punjab) Himalayas, in central Himachal Pradesh, the Beas rises at an elevation of 14,308 feet (4,361 meters).
• It flows south through the Kullu Valley from there, receiving tributaries from the flanking mountains, and then turns west to flow into the Kangra Valley, past Mandi.
• The Beas enters the Punjab state after entering the valley and turns south and then southwest after a course of about 290 miles to its confluence with the Sutlej River at Harike.
• Chenab​
• ​Chenab River originates from Baralacha Pass in Himachal Pradesh.
• It’s the largest tributary of the Indus river (In terms of Drain).
• It is also known as the Chandrabhaga River.
• It is a major river that flows in India and Pakistan.
• Sutlej
• ​River Sutlej originates from Rakshastal Lake.
• Rakshastal Lake is located near Lake Manasarovar and Mount Kailash.
• Sutlej River is also known as Shatadru (Ancient name).
• River Sutlej is one of the major tributaries of the Indus.
• Only tributary of Indus that originates from Tibet.
• Sutlej River enters India through Shipki La pass.
• The Bhakra-Nangal Dam is constructed across the Sutlej river.
• The Indira Gandhi canal is situated on the Sutlej river

.

Given:

(cos6 θ + sin6 θ -1) (tan2 θ + cot2 θ + 2) +1

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)³ = a³ - b³ - 3a²b + 3ab²

cos²θ = 1 - sin²θ

sin²θ + cos²θ = 1

Calculation:

(cos6 θ + sin6 θ -1) (tan2 θ + cot2 θ + 2) +1

Substituting cos⁶θ as (1- sin²θ)³

⇒ {(1 - sin2θ)3 + sin6θ - 1} ($sin^2 θ\over cos^2 θ$ + $cos^2 θ\over sin^2 θ$ + 2) + 1 

⇒ {1 - sin⁶θ - 3 sin²θ + 3 sin⁴θ + sin⁶θ - 1} ($sin^4 θ+ cos^4 θ + 2 sin^2 θ cos^2 θ\over sin^2 θ cos^2 θ$) + 1

⇒ 3 sin²θ (sin²θ - 1) ($(sin^2 θ+ cos^2 θ)^2\over sin^2 θ cos^2 θ$) + 1

⇒ - 3 sin²θ cos²θ  ($1\over sin^2 θ cos^2 θ$) + 1

⇒ -3 + 1 = -2

The answer to the equation is -2.

Alternate Method(cos6 θ + sin6 θ -1) (tan2 θ + cot2 θ + 2) +1

Put θ = 45° 

⇒ (cos⁶45° + sin645° -1) (tan245° + cot245° + 2) +1

⇒ {$({1\over\sqrt2})^6$ + $({1\over\sqrt2})^6$ - 1}{(1)² + (1)² + 2) +1} + 1

⇒ {$1\over8$ + $1\over8$ -1}{4} + 1

⇒ {${1+1-8}\over8$}{4} + 1

 ⇒ $-6\over8$ × 4 +1 = -3 + 1 = -2

∴ (cos6 θ + sin6 θ -1) (tan2 θ + cot2 θ + 2) +1 = -2

Shortcut Trick

Difference in Distance = 400 − 235 = 165 m

Difference in Time = 100 − 60 = 40 s

Speed of engine = 165 ÷ 40 = 4.125 m/s

Total distance in 60 s = 4.125 × 60 = 247.5 m

Engine length (L) = 247.5 − 235 = 12.5 m

Twice the length = 2 × 12.5 = 25 m

∴ The correct answer is 25 m.

Alternate Method

Given: Length of Bridge 1 = 400 m, Time 1 = 100 s; Length of Bridge 2 = 235 m, Time 2 = 60 s.

Formula Used: Speed = Total Distance ÷ Total Time; Total Distance = Length of Engine (L) + Length of Bridge.

⇒ Speed = (L + 400) ÷ 100 = (L + 235) ÷ 60

⇒ 60 × (L + 400) = 100 × (L + 235)

⇒ 3 × (L + 400) = 5 × (L + 235)

⇒ 3L + 1200 = 5L + 1175

⇒ 2L = 1200 − 1175

⇒ 2L = 25 m

∴ The correct answer is 25 m.

Additional Information

Train Crossing a Stationary Object with Length

When a train crosses a bridge, platform, or another stationary train, the total distance covered is the sum of the lengths of the train and the object.

Train Crossing a Point Object

When a train crosses a pole, tree, or a stationary man, the distance covered is equal to the length of the train itself.

Relative Speed

For two objects moving in the same direction, Relative Speed = S₁ − S₂. In opposite directions, Relative Speed = S₁ + S₂.

Given:

∠A = 88º

Concept used:

If P is the meeting point of bisectors of ∠CBD and ∠BCE. Then, ∠P = $1\over 2$ (180º - ∠A)

Calculation:

Substituting the value of A

⇒ ∠P = $1\over 2$ (180º - 88º)

⇒ ∠P = $1\over 2$ (92º) = 46º

Hence, the value of ∠P is 46º.

Given data:

Formula used:

Average export value of Car B (in millions) = (Total export value of car B) / 5

Calculation:

Total export value of Car B (in millions) = 225 + 250 + 200 + 275 + 325 = 1275

Average export value of Car B = $1275\over5$ = 255 million.

Expected value of car B (in millions) = 20 + 255 = 275

In the year 2016, the average export of car A is 20 million more than the average export of cars of type B.

GIVEN :

a2 + b2 + 49c2 + 18 = 2(b - 28c - a)

FORMULA USED :

1) (A + B)² = A² + B² + 2 × A × B

2) (A - B)² = A² + B² - 2 × A × B

CALCULATION :

According to question,

a2 + b2 + 49c2 + 18 = 2(b - 28c - a)

⇒ a2 + b2 + 49c2 + 18 = 2b - 56c -2a

⇒ a2 + b2  + 49c2 + 18 - 2b + 56c + 2a = 0

⇒ (a2 + 2a + 1 ) + (b² - 2b + 1) + (7c)² + 56c + 16 = 0

⇒ (a + 1)² + (b - 1)² + {(7c)2 + 56c + 4²} = 0

⇒ (a + 1)2 + (b - 1)2  + (7c + 4)² = 0      ----(1) (from formula 1 and 2)

Now In equation 1, In order it to be = 0 all the entities must be 0 

∴ (a + 1)2 = 0 

⇒ (a + 1) = 0

⇒ a = -1      ----(2)

Again,

(b - 1)2 = 0

⇒ (b - 1) = 0

⇒ b = 1      ----(3)

Again,

(7c + 4)2 = 0

⇒ (7c + 4) = 0

⇒ 7c = - 4

 ⇒ c = -4/7      ----(4)

As per question,

(a - b - 7c) = -1 -1 - 7 × (-4/7) 

⇒ (a - b - 7c) = -2 + 4

⇒ (a - b - 7c) = 2

∴ The value of (a - b - 7c) is 2.

Given data:

Total amount deposited = Rs 52,500

Time period for elder daughter = 2 years

Time period for younger daughter = 3 years

Rate = 10%

Concept used:

We would equate the amount accrued to both the daughters at the end of their time period to find the principal amount for the younger daughter. 

Formula used:

A = P × $(1+ {r \over 100})$^t 

Where A = Amount after time "t".

P = Principal, r = Rate 

Calculation:

Let us assume the amount for the younger daughter is P

⇒ Amount for the elder daughter = 52,500 - P

Amount for the younger daughter at the end of 3 years = P × (1 + $10\over 100$)³

Amount for the elder daughter at the end of 2 years = (52,500 - P) × (1 + $10\over 100$)²

Now, According to Question

⇒ P × (1 + $10\over 100$)3 = (52,500 - P) × (1 + $10\over 100$)2

⇒ $11P\over 10$ = 52,500 - P

⇒ 11P = 525,000 - 10P

⇒ 21P = 525,000

⇒ P = $525,000\over 21$ = 25,000

∴ Joseph had deposited Rs 25,000 in the name of his younger daughter.

Shortcut Trick

Base radius r = Circumference ÷ 2π = 62.8 ÷ 6.28 = 10 cm

Height h = Volume ÷ (πr²) = 8792 ÷ 314 = 28 cm

Curved Surface Area (CSA) = Circumference × h

CSA = 62.8 × 28 = 1758.4 cm²

∴ The correct answer is 1758.4 cm².

Alternate Method

Given:

Circumference of base = 62.8 cm

Volume of cylinder = 8792 cm³

Value of π = 3.14

Calculations:

⇒ Circumference = 2πr

⇒ 62.8 = 2 × 3.14 × r

⇒ 62.8 = 6.28 × r

⇒ r = 62.8 ÷ 6.28 = 10 cm

⇒ Volume = πr²h

⇒ 8792 = 3.14 × (10)² × h

⇒ 8792 = 3.14 × 100 × h

⇒ 8792 = 314 × h

⇒ h = 8792 ÷ 314 = 28 cm

⇒ Curved Surface Area (CSA) = 2πrh

⇒ CSA = (2πr) × h

⇒ CSA = 62.8 × 28

⇒ CSA = 1758.4 cm²

Comparing the calculated result with the options, we find it corresponds to Option (2).

∴ The correct answer is 1758.4 cm².

Additional Information

Total Surface Area of Cylinder

The total surface area (TSA) includes both the curved surface and the two circular bases: TSA = 2πr(r + h).

Volume and CSA Relation

The volume (V) can also be expressed in terms of Curved Surface Area (CSA) as V = (CSA × r) ÷ 2.

Base Area of Cylinder

The area of the circular base is given by πr². A cylinder has two such bases.

Given data:

Average of eight consecutive odd numbers = 28. 

Formula used:

Average of eight consecutive odd numbers = $sum\over 8$

Sum of largest and smallest odd number = Largest odd number + Smallest odd number

Calculation:

Let us assume the first odd number as (n - 7).

Other consecutive odd numbers would be (n - 5), (n - 3), (n - 1), (n + 1), (n + 3), (n + 5), and (n + 7).

Sum = (n - 5) + (n - 3) + (n -1) + (n + 1) + (n + 3) + (n + 5) + (n + 7) = 8n

Average of eight consecutive odd numbers = $8n\over 8$ 

Hence, $8n\over 8$= 28 or n = 28.

⇒ Largest odd number = n + 7 = 28 + 7 = 35

⇒ Smallest odd number = n - 7 = 28 - 7 = 21

Sum of largest and smallest odd number = 35 + 21 = 56

The sum of the largest and smallest odd numbers is 56.

Shortcut TrickGiven:

The average of 8 consecutive odd numbers is 28

Concept Used

1, 3, 5, and 7 are four consecutive odd numbers.

Average of above numbers is ,

⇒ (1 + 3 + 5 + 7)/4 = 4

Also, 4 is the middle number of the given series

Hence in such cases the average is middle number of the series.

Calculation:

Here, from the concept used we know that, 

28 is the middle term of 8 consecutive numbers series

Hence we can say that, 

There are 4 consecutive odd numbers before 28 &

There are 4 consecutive odd numbers after 28

So the series of 8 numbers is, 

⇒ 21, 23, 25, 27, 28, 29, 31, 33, 35

The sum of the smallest and largest numbers is,

⇒ 21 + 35 = 56

The sum of the largest and smallest odd numbers is 56.

Given data:

AB= 7 cm, AC= 8 cm, BC= 10 cm

AD bisects ∠BAC i.e., ∠BAD = ∠DAC

Concept used:

We would use the angular bisector theorem to proceed with the problem. According to the angular bisector theorem, the angle bisector of a triangle divides the opposite side of the angle in a proportion equal to the remaining sides of the triangle. In the Δ PQR, PS is the angular bisector of ∠QPR.

⇒ $QS\over SR$ = $PQ\over PR$ (By angular bisector theorem)

Calculation:

In ΔABC, if AD bisects ∠BAC, then

⇒ $AB\over AC$ = $BD\over DC$

Substituting the values of AB, AC, and BD as 10-DC

⇒ $7\over8$ = $10-DC\over DC$

Solving, we get-

⇒ 7 DC = 80 - 8 DC

⇒ 15 DC = 80

⇒ DC = $80\over 15$ or $16\over 3$

⇒ $DC\over 4$ = $16\over 3*4$ = $4\over 3$

Hence, $DC\over 4$ equals $4\over 3$ cm.

Given data:

Formula used:

Average car passing the road= (Total cars passing the road) ÷ 5

Calculation:

Total cars passing the road (up to 11 AM) = (70 + 105 + 130 + 115 + 95) = 515

Average car passing the road (up to 11 AM) = $515\over5$ = 103 cars.

The number of car passing from 7 AM to 8 AM = 105 > 103

The number of car passing from 8 AM to 9 AM = 130 > 103

The number of car passing from 9 AM to 10 AM = 115 > 103

Hence, in the time 7 - 8 am, 8 - 9 am, and 9 - 10 am, the number of cars passed more than the average number of cars passed from 6 am to 11 am.

Formula used:

Greatest four-digit number = 9999 – remainder – common remainder

Calculation:

Greatest four-digit number = 9999

LCM of 6, 7, and 8 = 168

Common remainder = (6 – 4) = (7 – 5) = (8 – 6) = 2

We will find the remainder for the division of 9999 by 168

⇒ Remainder = 87

Greatest four-digit number = 9999 – 87 – 2 = 9910

The greatest four-digit number is 9910 which on being divided by 6, 7, and 8 leaves 4, 5, and 6 as remainders respectively.

Data given:

Distance of man from the building = 50 m

Angle of elevation of the top of the poster = 45º

Angle of elevation of the bottom of the poster = 30º

Formula used:

tan θ = $p\over b$

Where “p” and “b” are perpendicular and base of the right-angled triangle.

Calculations:

In ∆ BCD, tan 30º = $BC \over CD$

We know that tan 30º = $1\over \sqrt3$ and CD = 50 m 

⇒ $BC \over 50$ = $1\over \sqrt3$

⇒ BC = $50\over √3$ or $50\sqrt3\over 3$

Similarly, in ∆ ACD, tan 45º = $AC\over CD$

We know that AC = AB + BC, tan 45º = 1 and CD = 50 m

⇒ AC = CD or AB + BC = CD

Substituting the values, we get -

⇒ AB + $50\sqrt3\over 3$ = 50

⇒ AB = 50 - $50\sqrt3\over 3$

⇒ AB = $50\over 3$(3 - √3)

200% of the Poster height (AB) = $100\over 3$(3 - √3)

Given data:

Ratio of profits of P and Q = 5 : 8

Investment time period of P and Q = 3 : 5

Concept used:

Profit in investment is always calculated on the product of total investment and investment time period.

Calculation:

Let the investment of “P” and “Q” be “p” and “q”.

⇒  $p\over q$ × $3\over 5$ =  $5\over 8$

Solving the equation, we get-

⇒ $p\over q$ =  $5\times 5 \over 8\times 3$ or 25 : 24

The investment ratio of P and Q is 25 : 24.

Concept used:

The divisibility test for 72 states that for a number to be divisible by 72, it should be perfectly divisible by 8 and 9.

The divisibility test for 9 states that if the sum of the digits of the number is divisible by 9, then the number is divisible by 9.

The divisibility test for 8 states that for a number to be divisible by 8, the last three digits of the number should be divisible by 8.

Calculations:

Using the divisibility test for 8, we find that 38y should be perfectly divisible by 8. 38y would be perfectly divisible if y = 4.

⇒ Hence, the number becomes 468x51384.

Sum of the digits = 39 + x

Using the divisibility test for 9, (39 + x) would be perfectly divisible by 9 if x is 6.

Thus, “x” is 6, and “y” is 4.

Using the values of "x" and "y" in the expression √( 4x + 3y)

⇒  $\sqrt {4 × 6 + 3 × 4}$ = √36 = 6

The answer to the expression is 6.

Given data:

Calculations:

Sale of computer from dealer A, B, and C in the year 2015 = 200 + 460 + 390 = 1050

Sale of computer from dealer D, E, and F in the year 2016 = 675 + 725 + 450 = 1850

Ratio = $1050\over 1850$ = $21 \over 37$

Hence, the ratio of sales from A, B, and C in the year 2015 to the sales from D, E, and F in the year 2016 is 21 : 37.

Concept used:

We will use the concept of "BODMAS"

5 + 0.9 - 3 × 1.3 – 2

⇒ 15 + 0.9 – 3.9 – 2

⇒ 15.9 – 3.9 – 2

⇒ 10

The answer is 10

Given data:

Depth of river = 6 m

Width of river = 35 m

Rate of flow = 2.5 km/h

Concept used: 

The volume of water flowing is the product of the cross-sectional area of the river and the flow rate of the river.

Formula used:

Volume of water flowing = Depth × Width ×  Rate of flow

Calculation:

Rate of flow in m/min = Rate of flow in km/hr × $1000\over 60$

Rate of flow in m/min = 2.5 × $1000\over 60$ = $125\over 3$ m/min

Volume of water flowing = 6 ×  35 × $125\over 3$ =  8750 m³/min

The amount of water running into sea per minute is 8750 m3.

Data given:

Time in which A can complete the work = 25 days

Time in which B can complete the work = 20 days

Time for which B worked = 4 days

Calculations:

Let us assume that the total work is 25 × 20 units i.e., 500 units

Portion of work done by A in 1 day = 20 units

Portion of work done by B in 1 day = 25 units

Total work done by A and B in 4 days = (20 + 25) ×  4 = 180 units

Total work remaining = 500 – 180 = 320 units

Time taken by A to complete the remaining units = 320 ÷ 20 = 16 days

Total time taken to complete the entire work = 16 + 4 = 20 days

The entire work was completed in 20 days.

Formula used:

x³ - y³ = (x - y) (x² + y² + xy)

Calculations:

The expression 2√2 x³ - 3√3 y³ could be rearranged as (√2x - √3y) (2x2 + 3y2 + √2√3xy)

⇒ (√2x - √3y) (2x2 + 3y2 + √2√3xy) = (√2x - √3y) (Ax2 - Bxy + Cy2)

Cancelling the common term (√2x - √3y) both sides-

(2x²  + √2√3xy + 3y2) = (Ax² - Bxy + Cy²)

Comparing the coefficients of x², y^2, and xy, we get-

⇒ A = 2

⇒ B = -√2√3

⇒ C = 3

Using the values of A, B, and C in the expression $\sqrt{A^2+B^2+C^2}$

⇒ $\sqrt{2^2+3^2+(-\sqrt2\sqrt3)^2 }$  = $\sqrt19$

The answer to the expression is  $\sqrt19$

Given data:

Ratio of Cost price of A and B = 4 : 5

Gain on Article A = 10%

Gain on Article B = 20%

Difference in Selling Price of A and B = Rs 480

Formula used:

SP = CP × (1+ $G \over100$)  where SP, CP, and G are Selling Price, Cost Price, and Gain % respectively.

Calculations:

Let the common ratio be "a".

⇒ Cost prices of articles A and B = 4a, 5a

SP of Article A = 4a × (1 + $10\over 100$) = 4.4a

SP of Article B = 5a × (1 + $20\over 100$) = 6a

Difference in SP = 6a - 4.4a = 1.6a

As mentioned in the question, difference in SP = Rs 480

⇒ 1.6a = 480

⇒ a = 300

Total cost price = (4+5) × 300 = Rs 2700

30% of the total cost price =  2700 × $30\over100$ = Rs 810

30% of the total cost price is Rs 810.

Formula used:

tan θ = sin θ / cos θ

cot θ = 1 / tan θ 

cos² θ = 1 - sin2 θ

Calculations:

Substituting cot θ for $1\over tan θ$-

⇒ 2 - $\sqrt{{1\over tan θ}+cos θ \over{1\over tan θ} -cos θ}$

⇒ 2 - $\sqrt{ 1+sin θ \over 1 - sin θ}$

Rationalizing  $\sqrt{ 1+sin θ \over 1 - sin θ}$, we get-

⇒ 2 - $\sqrt{ (1+sin θ)^2 \over (1-sin^2θ}$