SSC CGL 2021 Tier-I (Held On : 19 April 2022 Shift 2) (Previous Year Paper)

According to given conditions,

• Shweta starts walking from her office and walks 150 m towards the south.

• Then she turns right and walks 80 m.

• Then she turns left and walks 60 m.

• She finally turns left and walks 280 m to reach a bank.

Now, the shortest distance between Shweta's office and bank can be calculated by the pythagoras theorem :-

⇒ Here, x stands for shortest distance.

So, (x)² = (60 + 150)² + (280 - 80)²

⇒ (x)2 = (210)2 + (200)2

⇒ (x)2 = 44100 + 40000

⇒ (x)2 = 84100

⇒ x = 290 M

Hence, "290 m" is the correct answer.

According to the sequence in the dictionary.

3. Southern 6. Sovereignty 5. Spacious 1. Speaking
4. Stampede 2. Standardize 

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

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

Detailed Explanation:

• The line PQ is the mirror
• The word "Ewbaz4" the fourth letter is "a". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "Ewbaz4" the first letter is "E". So, the mirror image should be "

" ⇒ Option 3 is eliminated..

• The word "Ewbaz4" the second letter is "w". So, the mirror image should be "W" ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option 1".

Preparing the family tree using the following symbols,

• Father of Swati is the maternal grandfather of Divya. So, there have two possibilities.

​Case(1): Swati can the mother of Divya.

Case(2):  Swati's sister can the mother of Divya.

• Father of Swati is the maternal grandfather of Divya, who is the daughter of Manya. That means Divya is daughter of Manya. Manya is either father or mother of Divya.

Case(1):

Manya is the father of Divya i.e Manya is married to Swati.

Case(2a):  Manya is father of Divya i.e Manya is married to Swati's sister.

Case(2b):  Manya is mother of Divya i.e Manya is the sister of swati.

​

As it is asked in the question that how is Manya's husband's father related to Divya 

⇒ Here "Manya's husband" clarify that Manya is a female. So, both case(1) and case (2a) is eliminated.

So, according to the question asked the family tree is :-

Cleary, Manya's husband's father is the paternal grandfather of Divya.

Hence, the correct answer is "Paternal grandfather".

According to the question,

Given that: 126 $ 7 % 3 @ 19 # 21

After replacing the symbols with their meanings, we get :-

126 ÷ 7 × 3 + 19 - 21

= 18 × 3 + 19 - 21 

= 54 + 19 - 21

= 73 - 21

= 52

Hence, the correct answer is "52".

Logic: Multiplied each letter's position value by two. Like position value of 'G' is 7 , then 7 is multiplied by 2 and the code for 'G' is 14.

So,

• 'GALLERY' is coded as :-

​

Similarly,

• 'NOSTALGIA' is coded as :-

Hence, the correct answer is "2830384022414182".

The pattern followed here is :-

Hence, the correct is "209".

Given: P Q _ Q P P Q R _ P P Q R Q _ P Q R Q _

By checking options:-

1. Q R P P → P Q Q Q P P Q R R P P Q R Q P P Q R Q P → (It doesn't Follows the pattern)
2. R Q P P → P Q R Q P P Q R Q P P Q R Q P P Q R Q P → **(**It follows the pattern of : PQRQP - PQRQP - PQRQP - PQRQP)
3. P Q R P → P Q P Q P P Q R Q P P Q R Q R P Q R Q P → (It doesn't Follows the pattern)
4. P P R Q → P Q P Q P P Q R P P P Q R Q R P Q R Q Q → (It doesn't Follows the pattern)

Option (2) gives a pattern of P Q R Q P - P Q R Q P - P Q R Q P - P Q R Q P

Hence, the correct answer is "R Q P P".

Given: Six persons Raghav, Manpreet, Sunaina, Prakrit, Vedika and Arwa are sitting around a circular table facing the center.

1. Raghav is second to the left of Prakrit.

2. Manpreet is to the immediate left of Sunaina. So, there are two possibilities for the position of Sunaina and Manpreet.

• Case(1):

• Case(2):

3. There are an equal number of persons between Raghav and Manpreet from both the ends.

• Case(1): There are an equal number of persons i.e two between Raghav and Manpreet from both the ends.
• Case(2): There are an unequal number of persons between Raghav and Manpreet i.e one and three between Raghav and Manpreet from both the ends respectively.

⇒ Thus Case(2) will be eliminated.

4. Arwa is second to the right of Vedika.

• Case(1):

Thus, from the final arrangement we can see that 'Arwa' is sitting third to the left of Sunaina.

Hence, the correct answer is "Arwa".

Here, we use the table given below-

The logic followed here is-

• All the letters are rearranged according to their position values in descending order.

So,

• 'FIXED' is coded as :-

• 'MOUSE' is coded as :-

Similarly, 

• 'GAMBIT' is coded as:-

Here, 'GAMBIT' is written as  TMIGBA.

Hence, the correct answer is "TMIGBA".

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

Every symbol follows same rotation pattern.

1.  For

 →

2. For 

 →

3. For 

 →

4. For 

 →

5. For 

 →

So, the final series is :-

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

Refer to the diagram as shown below:

Here, D represents Coffee-lovers who are car-owners and social workers also.

Hence, 'option(2)' is the correct answer.

According to BODMAS rule : 

Given equation:  22 * 66 * 33 * 11 * 44 * 0 

• Option (1) : Using the combination +, ÷, ×, -, =

22 + 66 ÷ 33 × 11 - 44 = 0

⇒ 22 + 2 × 11 - 44 = 0

⇒ 22 + 22 - 44 = 0

⇒ 44 - 44 = 0

⇒ 0 = 0 (LHS = RHS)

• Option (2) : Using the combination ×, ÷, +, -, =

22 × 66 ÷ 33 + 11 - 44 = 0  

⇒ 22 × 2 + 11 - 44 = 0

⇒ 44 + 11 - 44 = 0

⇒ 55 - 44 = 0

⇒ 11 ≠ 0 (LHS ≠ RHS)

• Option (3) : Using the combination +, ÷, -, ×, =

22 + 66 ÷ 33 - 11 × 44 = 0  

⇒ 22 + 2 - 11 × 44 = 0

⇒ 22 + 2 - 484 = 0

⇒ 24 - 484 = 0

⇒ - 460 ≠ 0 (LHS ≠ RHS)

• Option (3) : Using the combination ÷, +, ×, -, =

22 ÷ 66 +33 × 11 - 44 = 0

⇒ 1/3 + 33 × 11 - 44 = 0

⇒ 1/3 + 363 - 44 = 0

⇒ 1090/3 - 44 = 0

⇒ 958/3  ≠ 0 (LHS ≠ RHS)

Hence, the correct answer is **"**Option (1): +, ÷, ×, -, =".

The pattern followed here is :-

(sum of the digits of first number)3 = 2^nd number

25 : 343

(2 + 5)3 = (7)3

(7 × 7 × 7) = 343 

343 = 343 (LHS = RHS)

Similarly,

• Option(1) → 24 : 216 ​

(2 + 4)3 = (6)3

(6 × 6 × 6) = 216 

216 = 216 (LHS = RHS) 

• Option(2) → 29 : 121 ​

(2 + 9)3 = (11)3

(11 × 11 × 11) = 1331

1331 ≠ 121 (LHS ≠  RHS)

• Option(3) → 34 : 510

(3 + 4)3 = (7)3

(7 × 7 × 7) = 343

343 ≠ 510 (LHS ≠  RHS)

• Option(4) → 30 : 729 ​

(3 + 0)3 = (3)3

(3 × 3 × 3) = 27

27 ≠ 729 (LHS ≠  RHS)

Therefore, Option(1) follows the logic. 

Hence, "24 : 216" is correct answer.

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As K is common on both the dice, it is clear that U, W, A and N are adjacent to it and remaining number i.e., P will be opposite to it.

Opposite pairs:

N → U

A → W

K → P

So, the opposite side of "N" will be side "U".

Hence, the correct answer is "U".

Given:

• The image must not to be rotated

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

Logic : 

1. First letter → Immediate succeeding letter or (+1)
2. Second letter → 3^rd succeeding letter or (+3)
3. Third letter → 5^th succeeding letter or (+5)

​

Hence, "TSZ" is the correct answer.

Let,

Total amount Mayank get be = Rs. 2x

Total amount Vineet get be = Rs (2x/2) = Rs. x

Total amount Prateek get be = Rs. (x - 25,000)

Given :

Total amount distributed = Rs. 2,95,000

So,

As per the question, sum of amount to be distributed among Mayank, Vineet and Prateek should be equal to the total amount to be distributed.

Therefore;

⇒ 2x + x + (x - 25,000) = 2,95,000

⇒ 4x - 25,000 = 2,95,000

⇒ 4x = 3,20,000

⇒ x = 80,000

As 'x' is the total amount Vineet gets,

Hence, Vineet gets "Rs. 80,000".

The logic followed here is :

Hence, the correct answer is "1052".

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

Conclusions:

I. All universities are schools → Does not follow (As some schools are colleges and all colleges are universities, all universities are schools is false.)

II. Some universities are colleges → Follow (As all colleges are universities so, some Universities are colleges is true.)

∴ Here, Conclusion II is true.

Hence, the correct answer is "Only conclusion II follow".

Logic : 

1. First letter → (+5) ⇒ Second letter
2. Second letter → opposite ⇒ Third letter

So,

• LQJ

​

• HLP

​

• SXC

​

• FKP

​

∴ Here, 'HLP' is different from other three alternatives.

Hence, the correct answer is "HLP".

According to the given information,

As, the code for 'I' and 'India' are either 'Fig' or 'Vic', thus the code for 'love' is 'jig'.

Hence, "jig" is the correct answer.

The logic followed here is:

At first, we should arrange the diagram in a suitable form. Then we can solve it.

​

Here, middle number = 7 × 4 = 28

And

Here, middle number = 4 × 5 = 20

Similarly,

Here, middle number(?) = 3 × 8 = 24

Hence, "24" is the correct answer.

Logic: Next alternate or (+2) of each letter is written and then reversed.

So, 

• QUICKER: TGMEKWS

​

⇒ Therefore, 'REPORTS' is written as :

​

Hence, "UVTQRGT" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, the correct answer is "option (3)".

The correct answer is Kanchenjunga.

Key Points

• Kanchenjunga
• It is the world's third-highest mountain that connects the borders of India and Nepal.
• It rises with an elevation of 8,586 m in a section of the Himalayas called Kanchenjunga Himal delimited in the west by the Tamur River.
• It lies between Nepal and Sikkim, India, with three of the five peaks directly on the border, and the remaining two in Nepal's Taplejung District of Province No 1.
• Until 1852, Kanchenjunga was assumed to be the highest mountain in the world.
• Kanchenjunga was first climbed on 25 May 1955 by Joe Brown and George Band.

Additional Information 

• World's highest mountain- Great Himalayas.
• Mount Everest is the world's highest peak at 8848.86 m, it is also known as Sagarmatha.
• Kanchenjunga is India's highest peak that is in Sikkim.
• Nanda Devi is India's second-highest peak in Uttarakhand.
• The average height of the Great Himalayas is 6100m.
• Important passes of Himalayas- Zojila, Burzil, Khar-dung-la, Bara-la-cha, Rohtang, etc.

The correct answer is Zakir Hussain.

Important Points

• On 8 February 2009 for the 51^st Grammy Awards, Zakir Hussain won the Grammy in the Contemporary World Music Album category for his collaborative album "Global Drum Project" along with Mickey Hart, Sikiru Adepoju & Giovanni Hidalgo.
• "Global Drum Project" is Hart and Hussain's second collaboration, following their compilation "Planet Drum," which won the first-ever Grammy Award in the World Music category in 1991.
• The Grammy Award for Best Global Music Album is given to recording artists for globally influential music at the Grammy Awards, which were first held in 1958 and were originally known as the Gramophone Awards.
• Ustad Zakir Hussain is a tabla master, composer, percussionist, music producer, and film actor from India.
• President Ramaswamy Venkataraman honoured him with the Padma Shri in 1988 and the President  Abdul Kalam honoured him Padma Bhushan in 2002 from the Government of India.

Additional Information

• Pt. Bhimsen Gururaj Joshi was a legendary Indian vocalist from Karnataka in the Hindustani classical tradition.
• He is known for the khayal form of singing, as well as for his popular renditions of devotional music (bhajans and abhangs).
• Pandit Ravi Shankar was an Indian sitar virtuoso and a composer. 
• He became the world's best-known exponent of North Indian classical music, in the second half of the 20^th century.
• Shankar was awarded India's highest civilian honour, the Bharat Ratna, in 1999.
• Pandit Hariprasad Chaurasia was a famous flute player in India.
• Pandit Hariprasad was born on 1 July 1938 in Allahabad
• In 2000, Pandit Hariprasad Chaurasia was awarded the Padma Vibhushan by the Government of India.

The correct answer is 6.7.

Key Points

• According to the Union Budget 2020-2021, the bank credit growth as of January 1, 2021, stood at 6.7%
• At present (June 2022), Bank credit grew 13.1 per cent year-on-year (YoY) in the fortnight ended June 3.
• The highest in the past three years, the latest data released by the Reserve Bank of India (RBI) shows.
• Growth in bank credit in the previous year was 5.7 per cent.

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.

Explanation:-

Amorphous Solid:-

• There is a lack of long-term planning.
• The constituent particles of an amorphous solid do not have a long-range order of arrangement.
• There is no distinct melting point. Amorphous solids do not have a distinct melting point and melt at a variety of temperatures.
• Conversion from a liquid to a crystalline state.
• Amorphous solids have two distinct characteristics.
• When cleaved or split, they form pieces with irregular, typically curved surfaces, and when exposed to x-rays, their components are not ordered in a regular array, resulting in poorly defined patterns.
• Glass is an amorphous, translucent substance.
• Amorphous solids are solids that lack a distinct geometry, have identical characteristics along all axes, melt across a wide range, and shatter into curved or irregular shapes.
• It's vital to remember that these phrases represent two opposite ends of a spectrum.
• Short-range order exists in most amorphous substances.

The correct answer is Both 1 and 2.

Key Points

• Ion-exchange method is also called the zeolite/permutit process.
• In this method, the permanent hardness of water is removed by using resins.
• Distillation is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation.
• Carding is a form of credit card fraud in which a stolen credit card is used to charge prepaid cards.
• Both Ion exchange and distillation are used for reducing the TDS in water. 
• Hence Both 1 and 2 is the correct answer.

Additional Information

• Total Dissolved Solids (TDS):
• Total solids mean all solids i.e suspended or dissolved solids.
• It is measured by evaporating (at a temperature of 104°C ) the sample and measuring the residue.
• It can also be measured by the electrical conductivity of water.
• TDS = Suspended solids + Dissolved solids
• The drinking water standard for TDS is less than 500 mg/litre

The correct answer is 8(1).

Key Points

• The Constituent Assembly was recognised by Section 8(1) of the Indian Independence Act, 1947.
• Under the Plan, the members of the 1946 Provincial Legislative Assemblies, who were elected by the limited franchise, would select the members of the Constituent Assembly through a single transferrable vote.

Additional Information

• The Indian Independence Act, 1947:
• It was based upon the Mountbatten Plan of 3^rd June 1947 and was passed by the British parliament on July 5, 1947.
• It received royal assent on July 18, 1947.
• It declared India as an independent and sovereign state
• It provided for the partition of India and the creation of two new dominions- India and Pakistan
• It abolished the position of secretary of state for India
• It abolished the office of the viceroy and provided for each dominion, a governor-general, who was to be appointed by the British King on the advice of the dominion cabinet
• It empowered the constituent assemblies of the two dominions to frame and adopt any constitution for their respective nations and to repeal any act of the British parliament, including the independence act itself.
• The constituent assemblies were empowered to legislate for their respective dominions till the new constitutions were drafted and enforced.
• It granted the princely states the freedom to join either of the dominions or to remain independent.
• Governance of each dominion was to be conducted based on the provisions of the GoI act, 1935
• British monarchs could no longer ask for bills or veto them. However, this was reserved for Governor-General.
• The Constitutional Assemblies of the two nations would enjoy their respective legislative authorities.
• The British emperor would no longer be called the Emperor of India.
• The Indian Independence Act, of 1947 was repealed by the Constitution of India.

The correct answer is 2012.

Key Points

• To deal with child sexual abuse cases, the Government has brought in a special law, namely, The Protection of Children from Sexual Offences (POCSO) Act, 2012.
• The Act has come into force with effect from 14^th November 2012 along with the Rules framed thereunder.

Additional Information 

• The POCSO Act, 2012 is a comprehensive law to provide for the protection of children from the offences of:
• sexual assault
• sexual harassment
• pornography
• While safeguarding the interests of the child at every stage of the judicial process by incorporating child-friendly mechanisms for reporting, recording of evidence, investigation and speedy trial of offences through designated Special Courts.

The correct answer is Maharashtra.

Important Point

• Lalita is a form of folk music from Maharashtra.
• Other forms of folk music in Maharashtra.
• Gondhal,
• Lavani,
• Povadas and
• Tamasha

Additional Information

• Folksongs found in Maharashtra
• Bhajan,
• Bharud,
• Gondhal,
• Kirtan,
• Abhangas and
• Tumbadi

The correct answer is IX-A.

• The 74^th Amendment Act of 1992 added a new Part IX-A to the Constitution of India.
• The 74^th Amendment Act of 1992 provides a basic framework of decentralisation of powers and authorities to the Municipal bodies at different levels.  However, responsibility for giving it a practical shape rests with the States.
• The term ‘Urban Local Government’ in India signifies the governance of an urban area by the people through their elected representatives. The jurisdiction of an urban local government is limited to a specific urban area, which is demarcated for this purpose by the state government.

Key Points

• 74^th Amendment act has introduced a new Part IXA in the Constitution.
• It deals with Municipalities in an article 243 P to 243 ZG.
• This amendment, also known as Nagarpalika Act, came into force on 1^st June 1993.

The correct answer is Ghadar Party.

• One of the co-founders of the Ghadar Party is Har Dayal.​

Key Points

• The Ghadar Party was formed by a group of Indian revolutionaries that included migrant workers from Punjab and Bengali and Punjabi intellectuals and students.
• Its main objective is to reflect the values ​​of independent India by overthrowing the British rule and adopting secularism and unity despite regional, religious and linguistic differences.
• It was established in the year 1913.
• The party was dissolved in 1948 after India gained independence.
• Its founders were Hardayal, Sohan Singh Bhakna, Santokh Singh, Baba Jwala Singh, Vashakha Singh Dandekar.
• The party launched its first newspaper 'Gadar' (Weekly) in November 1913.
• The title of the newspaper is 'Angrezi Raj Ka Dushman' (Enemy of British Raj).

Additional Information 

The correct answer is Goa.

Important Points

• Fatorpa Zatra is one of the most famous zatras of Goa and is celebrated at the temple of Shantadurga Kuncolienkarin at Fatorpa in Quepem taluka.
• 'Kuncolienkarin' means 'from Cuncolim'.
• During the festival, people from all over Goa, belonging to different religions, communities and castes come to worship the deity.
• The zatra is held for five days during December or January, during paushya shuddha panchami upto dashmi of the Hindu calendar.
• The highlight of this event is the chariot procession over four days.
• The first day is called Hathi Ambari, which includes an elephant chariot.
• The second day is the procession of the flower chariot, popularly known as Fulancho Rath.
• The procession of the Vijayrath, a chariot of horses, is held on the third day.
• The Maharath procession, which has the main chariot is held on the last day and is thronged by crowds of devotees, marking the finale of the zatra rituals.

Additional Information

• Goa is a state in western India with coastlines stretching along the Arabian Sea. 
• Its long history as a Portuguese colony prior to 1961 is evident in its preserved 17^th-century churches and the area’s tropical spice plantations.
• Goa is also known for its beaches, ranging from popular stretches at Baga and Palolem to those in laid-back fishing villages such as Agonda.
• Land area: 3,702 km²
• Capital: Panaji
• Chief minister: Pramod Sawant
• Population: 18.2 lakhs

The correct answer is West Bengal.

Important Points

• The proportion of households that had health insurance increased in Bihar, Assam and Sikkim from 2015-16 to 2019-20 by 89% while it decreased by 12% over the same period in West Bengal.
• From 2015-16 to 2019-20, infant mortality rates declined by 20% for West Bengal and by 28% for the three neighbouring states.
• Modern methods of contraception, female sterilization and pill usage went up by 36%, 22% and 28% respectively in the three neighbouring states while the respective changes for West Bengal were negligible.
• While West Bengal did not witness any significant decline in the unmet need for spacing between consecutive kids, the neighbouring three states recorded a 37% fall.

Additional Information

• The economic survey is an annual report card of the economy.
• It represents a day before the budget examines the performance of each and every sector and then suggests future moves.
• The economic survey was de-linked from the Budget in 1964.
• And unveiled in advance in order to provide a context of the latter.
• Last year the theme was Saving Lives and Livelihoods.
• The central theme of Economic Survey 2021-22 is the "Agile Approach".
• Another theme highlighted in this Economic Survey relates to the art and science of policy-making under conditions of extreme uncertainty.

The correct answer is Chilli.

Important Points

• Capsaicinoids, carotenoids, phenolics, and vitamins are dominant chemicals in Chilli.
• Capsaicinoids are a major spice-producing group of alkaloids present in chilli peppers.
• Carotenoids are also called tetraterpenoids.
• They are yellow, orange, and red organic pigments that are produced by plants and algae, as well as several bacteria and fungi.
• Carotenoids give the characteristic colour to pumpkins, carrots, corn, tomatoes, canaries, fla mingos, salmon, lobster, shrimp, and daffodils.

The correct answer is 7.

Key Points

CONCEPT:

• ATOMIC NUMBER: 
• ​It is defined as the number of protons present in the nucleus.
• It is denoted by the letter Z.
• MASS NUMBER: 
• ​The total number of protons and neutrons present in a nucleus is called the mass number of the element.
• It is denoted by the letter A.
• For neutral atom,
• Number of protons in an atom = Z
• Number of electrons in an atom = Z
• Number of nucleons in an atom = A
• Number of neutrons in an atom = N = A – Z

CALCULATION:

• Given – A = 14 and Number of electrons in an atom (e)  = 7
• As we know that the number of protons is equal to the number of electrons in an atom. Therefore, the number of protons is 7.
• As we know that, Mass number (A) = Number of protons (p) + Number of neutrons (n)

∴ n = A – p

⇒ n = 14 – 7 = 7

The correct answer is Subarnarekha River.

Key Points

• Subarnarekha is a rain-fed river flowing in the eastern part of India.
• It flows in the state of Jharkhand, West Bengal, and Orissa.
• It originates near Nagri village in the Ranchi district.
• It runs through some major industrial towns and cities:
• Jamshedpur, Chaibasa, Ranchi, and Bhadrak before joining to the Bay of Bengal at Kirtania port in Orissa.
• Hundru Falls Ranchi is created on the course of the Subarnarekha River, where it falls from a height of 320 feet.
• It is the 34^th highest waterfall in India
• it falls from a height of 98 meters (322 ft) creating one of the highest waterfalls in the state.

Additional Information 

• Some important mineral deposits of the Subarnarekha River basin are ores of copper, iron, uranium, chromium, gold, vanadium, kyanite, asbestos, barytes, apatite, and china clay, talc, limestone, dolomite, and building stones.
• The Kanchi and Karkari rivers are their chief tributaries.
• Getalsud reservoir is located across the Subernarekha

Important Points 

• CM of Jharkhand: Hemant Soren.
• Governor of Jharkhand: Santosh Gangwar.
• Capital of Jharkhand: Ranchi

The correct answer is Sharankumar Limbale.

Key Points

• Dr Sharan Kumar Limbale has bagged the Saraswati Samman, the country's highest literary award, for year 2020 for his Marathi novel 'Sanaatan' published in 2018.
• He is the former head of Nashik's Yashwantrao Chavan Open University and the author of 40 books.
• He is the first Dalit writer to get the award.
• The award carries a cash prize of Rs 15 lakh and a citation.

Additional Information

• Noted poet and litterateur Prof Ramdarash Mishra was awarded the prestigious Saraswati Samman, 2021, for his collection of poems ‘Mein to Yahan Hun’.

The correct answer is Mughals.

Key Points

• After the death of Shri Guru Gobind Singh, the Sikhs revolted against the Mughals under the leadership of Banda Bahadur.
• After Guru Gobind Singh's death, the institution of Guruship came to an end and the leadership of the Sikhs passed to his trusted disciple Banda Singh Bahadur.
• Banda Singh Bahadur was a Sikh warrior & a commander of the Khalsa army.
• Since creating his Khalsa rule in Punjab, Banda Singh Bahadur had abolished the zamindari regime & had given "property rights" to the land tiller.
• Banda Singh had rallied together with the lower castes & peasants of Punjab from "Delhi to Lahore" and had undertaken a vigorous "unequal struggle" against the army of Mughals for almost 8  years.
• However, in the year 1715, he was captured and put to death.
• There are many reasons for his failure. One, the Mughal army was very strong, and second, the upper castes & classes of Punjab had joined forces against Banda Singh Bahadur because of his campaign for the rural poor & the lower castes.

Additional Information

• Gurus of Sikh-

1. Guru Nanak - founder of Sikhism
2. Guru Angad
3. Guru Amar Das
4. Guru Ram Das
5. Guru Arjan
6. Guru Hargobind
7. Guru Har Rai
8. Guru Har Krishan
9. Guru Tegh Bahadur
10. Guru Gobind Singh - introduced Khalsa, 'five Ks', proclaimed Guru Granth Sahib as the future and final Guru

The correct answer is Pranab Mukharjee.

Key Points

• Pranab Mukharjee :
• Pranab Mukherjee is an Indian politician who served as the thirteenth president of India from 2012 to 2017.
• He was awarded India's highest civilian honour, the Bharat Ratna, in 2019, by the President of India, Ram Nath Kovind.​

Additional Information 

• Satya Nadella:
• ​Satya Narayana Nadella is an Indian-American corporate executive.
• He is the CEO of Microsoft.

The correct answer is Viktor Axelsen.

Key Points

• Viktor Axelsen won the All England Open Badminton Championship Men’s Singles 2020 title.
• The championship was held in Birmingham, England.
• It was a part of the All England Open championships, which had been held since 1899.
• In the women's category,  Tai Tzu-Ying won the championship.
• Viktor Axelsen is a Danish badminton player.
• He is the 2017 World champion and the 2020 Olympic champion.
• He won the 2010 World Junior Championships, beating South Korea's Kang Ji-Wook in the final to become the first-ever European player to hold the title.

Additional Information 

• Lee Zii Jia won the All England Open Badminton Championship 2021 in the men's category.
• Nozomi Okuhara won the All England Open Badminton Championship 2021 in the women's category.
• Lin Dan is a Chinese former professional badminton player.
• He is a two-time Olympic champion, five-time World champion, as well as a six-time All-England champion.
• Lee Chong Wei is a Malaysian former badminton player.
• As a singles player, Lee was ranked first worldwide for 349 weeks, including a 199-week streak from 21 August 2008 to 14 June 2012.
• Chou Tien-Chen is a badminton player from Taiwan.
• He became the first local shuttler in 17 years to win the men's singles title of the Chinese Taipei Open in 2016 since Indonesian-born Fung Permadi won it in 1999.

The correct answer is 1918.

Key Points

• The reforms were outlined in the Montagu-Chelmsford Report, prepared in 1918, and formed the basis of the Government of India Act 1919.
• These are related to constitutional reforms.
• This act made the central legislature bicameral.
• Establishment of Public Service Commission.
• The act made a provision for the classification of the central and provincial subjects.
• The provincial subjects were divided into two groups - reserved and transferred.

Additional Information

• Government of India Act, 1919
• Government of India Act, 1919 is popularly known as Montagu-Chelmsford Report.
• The Act embodied the reforms recommended in the report of the Secretary of State for India, Edwin Montagu, and the Viceroy, Lord Chelmsford.
• The Government of India Act 1919 was an Act of the Parliament of the United Kingdom.
• It was passed to expand the participation of Indians in the government of India.
• The Act received royal assent on 23 December 1919.
• The act came into force in 1921.
• The Act covered ten years, from 1919 to 1929.
• It was set to be reviewed by the Simon Commission in 10 years.
• This Act represented the end of benevolent despotism (the act of authorities enhancing themselves) and began the genesis of responsible government in India.

The correct answer is Continental shelf.

Important Points

• The continental shelf is the extended margin of each continent occupied by relatively shallow seas and gulfs.
• It is the shallowest part of the ocean showing an average gradient of 1° or even less.
• The shelf typically ends at a very steep slope, called the shelf break.
• The width and depth of the continental shelves vary from one ocean to another.
• The continental shelves are covered with variable thicknesses of sediments brought down by rivers, glaciers, and wind, from the land and distributed by waves and currents.
• Massive sedimentary deposits received over a long time by the continental shelves become the source of fossil fuels.​

Additional Information

• The ocean floors can be divided into four major divisions:
• the Continental Shelf
• the Continental Slope
• the Deep Sea Plain
• the Oceanic Deeps
• Besides, these divisions there are also major and minor relief features on the ocean floors like ridges, hills, seamounts, guyots, trenches, canyons, etc.

The correct answer is Neeraj Chopra.

Key Points

• Neeraj Chopra created a national record in the javelin throw event at the third Indian Grand Prix meet in March 2021.
• He is a javelin thrower, and became only the second Indian to win an Olympic gold medal.
• At the 2020 Tokyo Olympics, he earned a gold medal in the Javelin Throw event.
• He became India's seventh medalist and first gold medalist in the Olympics, joining shooter Abhinav Bindra (2008 Beijing Games) as an individual gold medalist.
• India won 1 Gold, 2 Silver, and 4 Bronze medals.

Additional Information

• Vipin Kasana is an Indian athlete who competes in the Javelin throw.
• Shivpal Singh is an Indian athlete who competes in the Javelin throw.
• He is from Uttar Pradesh.
• Devendra Jhajharia is associated with the Indian Paralympic javelin throw. 
• He won his first gold in the javelin throw at the 2004 Summer Paralympics in Athens, becoming only the second gold medalist at the Paralympics for his country.

The correct answer is BNP Paribas.

Important Points

• BNP Paribas is a foreign bank operating in India as of 31^st May 2021.
• BNP Paribas is a French multinational bank and financial services company with global headquarters in Paris.
• It is one of the largest banks in the world.
• It appointed Sanjay Singh as CEO of India.
• This is the first time an Indian has been appointed as BNP’s country chief since it set up its office here in 1860.
• Based on 2012 information, BNP Paribas was ranked as the third-largest bank in the world, as measured by total assets, by Bloomberg and Forbes.
• It was established on 27 January 1872.

The correct answer is 5^th May.

Key Points

• World Hand Hygiene Day is observed on May 5 every year, the theme for this year was SAVE LIVES: Clean your hands
• The day is organized by the World Health Organization. The primary objective is to make everyone aware of how important it is to keep our hands clean which not only protects us but others too.
• This theme is perfectly in sync with the current pandemic of COVID-19.
• Everyone needs to keep their hands clean in order to save themselves from coronavirus.
• WHO has suggested washing our hands for 20 seconds to thoroughly clean them.

Additional Information

• Important Days Celebrated in India:-

The correct answer is Cholera.

Key Points

Explanation:

• Water-Borne diseases: 
• These are conditions caused by pathogenic micro-organisms that are transmitted in water.
• The disease can spread while bathing, washing or drinking water, or by eating food exposed to infected water and can cause severe, life-threatening diseases.
• Examples are typhoid fever, cholera and Hepatitis A or E.
• Other microorganisms induce less dangerous diseases such as diarrhoea.

Additional Information

• Cholera: Cholera is a waterborne disease and is diarrhoeal in nature.
• Typhoid: It is another disease that gets transmitted by drinking contaminated water that carries ‘Salmonellae Typhi bacteria’.
• Diarrhoea: Diarrhoea is one of the most common waterborne diseases that mostly affects children under the age of 5.
• Hepatitis A: Another type of waterborne disease is Hepatitis A and it is caused by the Hepatitis A virus, which affects the liver.
• Some common communicable diseases are:

Mistake Points

• Polio is spread when the stool of an infected person is introduced into the mouth of another person through contaminated water or food (faecal-oral transmission).

Shortcut Trick

In an equilateral triangle, the circumcentre coincides with the centroid.

The centroid divides the altitude (median) in the ratio 2 : 1.

Distance from base to circumcentre = 1 unit = 3.2 cm.

Total altitude = 2 + 1 = 3 units.

⇒ Altitude = 3 × 3.2 = 9.6 cm.

∴ The correct answer is 9.6 cm.

Alternate Method

Given: Distance of circumcentre from the base = 3.2 cm.

Formula Used: In an equilateral triangle, the inradius (r) is the distance from the incentre/circumcentre to the base. Altitude (h) = 3 × r.

⇒ In an equilateral triangle, the circumcentre, orthocentre, incentre, and centroid are the same point.

⇒ The distance from the centroid to the base is 1/3 of the altitude.

⇒ Let the altitude be h.

⇒ 1/3 × h = 3.2 cm

⇒ h = 3.2 × 3

⇒ h = 9.6 cm

∴ The correct answer is 9.6 cm.

Additional Information

Inradius and Circumradius

For an equilateral triangle of side 'a', Inradius (r) = a / (2√3) and Circumradius (R) = a / √3. Note that R = 2r.

Altitude Formula

The altitude (h) of an equilateral triangle is given by (√3/2) × a. Also, h = R + r = 3r.

Centroid Property

The centroid divides each median (which is also the altitude in this case) in the ratio 2 : 1 from the vertex to the base.

Given data:

∠A = 66º

Concept:

The angle formed by the internal bisectors of the angles of the triangle is equal to 90 degrees plus half the third angle. 

In Δ ABC,

∠BQC = 90º + $∠BPC\over 2$

Calculations:

In the quadrilateral AEPD

∠EAD + ∠PEA + ∠EPD + ∠PDA = 360º

⇒ ∠EPD = 360º - (66º + 90º + 90º)

⇒ ∠EPD = 114º

From figure-

∠EPD = 114º = ∠BPC

∠BQC = 90º + $∠BPC\over 2$

∠BQC = 90º + $114º\over 2$ = 90º + 57º = 147º (since ∠EPD and  ∠BPC are vertically opposite angles).

∴ , The value of ∠BQC is 147º.

Given data:

AB - BC = 4 cm

AB - AC = 2 cm

Perimeter = 32 cm

Calculation:

According to the question-

BC = AB - 4 cm

AC = AB - 2 cm

AB + BC + AC = 32 cm

Substituting the value of BC and AC-

⇒ AB + (AB - 4) + (AB - 2) = 32 cm

⇒ 3AB - 6 = 32

⇒ AB = $38\over 3$ cm.

Substituting the value of AB in equation of BC-

BC = $38\over 3$ - 4 = $38-12\over 3$ = $26\over 3$ cm

∴ $BC\over 2$ = $13\over 3$ cm.

The answer is $13\over 3$ cm.

Calculation:

Let c be "a".

B = 0.65a

A = 1.2 × 0.65a = 0.78a

According to the question-

⇒ 0.78a + 0.65a + a = 121.5

⇒ 2.43a = 121.5

⇒ a = 50       (∴ C = 50)

⇒ B = 0.65 × 50 = 32.5

⇒ A = 0.78 × 50 = 39.0

Substituting the value of A, B, and C in the expression-

⇒ (50 - 2 × 32.5 + 39) 

⇒ 24

The answer is 24.

Alternate MethodA = 120% of B, & B = 65% of C

⇒ A = 120/100 B & B = 65/100 C

⇒ A = 6/5 B & B = 13/20

⇒ A : B = 6 : 5 & B : C = 13 : 20 

⇒ A + B + C = 78 + 65 + 100 = 243

According to the question, 

⇒ 243 = 121.5

⇒ 1 = 121.5/243 = 1/2

C - 2B + A = 100 - 2(65) + 78 = 48

⇒ 48 × 1/2 = 24

The answer is 24.

Calculations:

Let the cost price be Rs 100.

SP for 13$1\over 4$% profit = Rs 100 + 13.25 = Rs 113.25

SP for 16$1\over 5$% profit = Rs 100 + 16.20 = Rs 116.20

Difference in profit = Rs 116.20 - Rs 113.25 = Rs 2.95

Difference                     Cost Price

Rs 2.95                             100

Rs 76.70                              x

⇒ x = $76.7\times 100 \over 2.95$ = Rs 2600

∴ 50% of the cost price is Rs 1300.

Alternate Method

Difference of profit% of ($16\frac{1}{5}$ - $13\frac{1}{4}$) = (16.2 - 13.25) = 2.95% makes the difference of price of Rs. 76.70

So, 2.95% → 76.70, then 100% → (76.70/2.95 × 100) = Rs. 2600 (which is the CP)

Now, 50% of the cost price is = 2600/2 = Rs 1300.

Given data:

a2 + b2 + 49c2 + 18 = 2(b + 28c - a)

Formula Used:

1) (a + b)2 = a2 + b2 + 2ab

2) (a - b)2 = a2 + b2 - 2ab

Calculations:

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 = $4\over7$     ----(4)

As per question,

(2a - b + 7c) = (2 × -1) - 1 + 7 × $4\over7$

⇒  -2 - 1 + 4

⇒ 1

∴ The value of (2a - b + 7c) is 1.

Calculations:

Dividing equation (x2 - 5x - 1), both sides by x

⇒ x - 5 - $1\over x$= 0

⇒ x - $1\over x$ = 5

$x^3$ - $1\over x^3$ = (x - $1\over x$)³ + 3 × x × $1\over x$ × (x - $1\over x$)

⇒ 5³ + 3 × 5 = 140

Seperating the fractions-

⇒ $x^6\over x^3$ - $x^4\over x^3$ + $x^2\over x^3$ - $1\over x^3$

⇒ $x^3$ - x + $1\over x$ - $1\over x^3$

Rearranging the equation, we get-

⇒ ($x^3$ - $1\over x^3$) - (x - $1\over x$)

Substituting the values, we get-

⇒ 140 - 5 = 135

∴ The answer of the expression is 135.

Given data:

AB = 7 cm

CD = 1 cm

PD = 5 cm

Calculation:

From the basic proportionality theorem,

PB × PA = PD × PC

Substituting the values-

⇒ PB × (7 + PB) = 5 × (5 + 1)

⇒ PB × (7 + PB) = 5 × 6 = 30

⇒ PB² + 7PB -30 = 0

⇒ PB2 + 10PB - 3PB -30 = 0

⇒ PB × (PB + 10) - 3 × (PB + 10) = 0

⇒ (PB - 3) × (PB + 10) = 0

Either PB = 3 or -10 (PB cannot be negative. Hence, PB = 3)

∴ PA = AB + BP = 7 + 3 = 10

Now,

⇒ 50% of PA = 50 × 10/100 = 5

∴ The value of 50% PA is 5 cm.

Shortcut Trick The equation PB × (7 + PB) = 30 could be solved by breaking 30 into appropriate factors to match the equation PB × (7 + PB).

⇒ 30 = 10 × 3 and 10 = 7 + 3

∴ 30 = 3 × (7 + 3)

⇒ PB × (7 + PB) = 3 × (7 + 3)

∴ PB = 3 cm and PA = 10 cm

⇒ 50% of PA = 50 × 10/100 = 5

∴ The value of 50% PA is 5 cm.

Given data:

Discount (d₁) = 10%

Discount (d2) = 20%

Discount (d3) = 25%

Formula Used:

Effective discount = d₁ + d₂ - $d_1 × d_2 \over 100$

Where “d₁” and “d₂” are successive discounts offered.

Calculation:

Effective discount = 10 + 20 - $10 × 20 \over 100$ = 30 - 2 = 28

Final discount = 28 + 25 - $25 × 28\over 100$ = 53 - 7 = 46

∴ The final effective discount is 46%.

Alternate Method Let the initial price be 100.

Price after 1^st discount = 100 - 10 = Rs 90

Price after 2^nd discount = 90 - $20 \over 100$ × 90 = 90 - 18 = 72

Price after 3^rd discount = 72 - $25 \over 100$ × 72 = 72 - 18 = 54

Effective discount = 100 - 54 = 46%

∴ The effective discount is 46%.

Shortcut Trick

Make the number of decimal places equal for all numbers: 3.600, 1.800, and 0.144.

Remove decimals and find LCM of 3600, 1800, and 144.

Since 3600 is a multiple of 1800 (1800 × 2) and 144 (144 × 25), the LCM is 3600.

Place the decimal back after 3 places: 3.600.

∴ The correct answer is 3.6.

Alternate Method

Given: Numbers are 3.6, 1.8, and 0.144.

Formula Used: LCM of fractions = LCM of Numerators ÷ HCF of Denominators

⇒ Convert decimals to fractions with common denominators:

⇒ 3.6 = 3600/1000

⇒ 1.8 = 1800/1000

⇒ 0.144 = 144/1000

⇒ LCM = LCM(3600, 1800, 144) ÷ 1000

⇒ 3600 = 144 × 25 and 3600 = 1800 × 2

⇒ LCM = 3600 ÷ 1000 = 3.6

∴ The correct answer is 3.6.

Additional Information

LCM of Decimals

Always equate the number of decimal places by adding zeros before finding the LCM of the resulting integers.

HCF of Fractions

HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

Product Rule

For two numbers a and b, LCM(a, b) × HCF(a, b) = a × b.

Used data:

Distance = 90 km

Time = 50 min

Calculation:

Time = $50\over 60$ hrs =  $5\over 6$ hr.

Speed in km/hr = $90\over {5\over 6}$ = 108 km/hr

Speed in m/s = 108 × $5\over 18$ = 30 m/s

∴ The speed in m/s is 30 m/s.

Used data:

Rate = 21% p.a

Time = 2 years

CI = Rs 11,138.40

Formula used:

Effective rate for two years = r1 + r2 + $r_1 × r_2 \over 100$

Where “r1” and “r2” are successive rates offered in the two-year period.

A = P + CI

Where A is the Amount and P is the Principal.

Calculation:

Effective rate for two years = 21 + 21 + $21 × 21 \over 100$ = 42 + 4.41 = 46.41%

∴ Principal = $11,138.40 × 100 \over 46.41$ = Rs 24,000

⇒ Amount = 24,000 + 11,138.40 = Rs 35,138.40

∴ The total amount for the two-year period was Rs 35,138.40.

Shortcut Trick

In a 30°−60°−90° right-angled triangle, the side opposite the 30° angle is always half of the hypotenuse.

The ladder acts as the hypotenuse (20 m) and the distance from the wall is the side opposite to the 30° angle.

Required Distance = 20 m ÷ 2 = 10 m.

∴ The correct answer is 10 m.

Alternate Method

Given:

Length of the ladder (Hypotenuse) = 20 m

Angle between ladder and wall = 30°

Formula Used:

In a right-angled triangle, sin θ = Opposite Side ÷ Hypotenuse

Calculations:

Let the distance of the base of the ladder from the wall be x.

⇒ In right-angled triangle ABC, sin(30°) = BC ÷ AC

⇒ 1 ÷ 2 = x ÷ 20

⇒ x = 20 × (1 ÷ 2)

⇒ x = 10 m

∴ The correct answer is 10 m.

Additional Information

30°−60°−90° Triangle Rule

The sides of a 30°−60°−90° triangle follow the ratio 1 : √3 : 2. The side opposite 30° is x, the side opposite 60° is x√3, and the hypotenuse is 2x.

Trigonometric Ratios

Key values to remember: sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3. Use SOH CAH TOA as a mnemonic for ratios.

Complementary Angles

If the angle with the wall is 30°, the angle with the ground is 90° − 30° = 60°. Therefore, base distance = Ladder × cos(60°) = 10 m.

Calculation:

Total capital invested by A = 60,000 × 12 + 90,000 × 12 = 720,000 + 1,080,000 = Rs 1,800,000

Total capital invested by B = 80,000 × 9 + 75,000 × 12 = 720,000 + 900,000 = Rs 1,620,000

Ratio = 1,800,000 : 1,620,000 = 10 : 9

Let the total profit earned is 4p

Now, out of 4p profit, 2p is equally divided between A and B.

A's profit-

⇒ p + $10 \over 19$ × 2p = 35,880

⇒ 39p = 35,880 × 19

⇒ p = 35,880 × $19\over 39$ = Rs 17,480

Now,Profit earned by B = p + $9 \over 19$ × 2p  = $37p\over 19$ = $37\over 19$ × 17,480

⇒ Profit of B = Rs 34,040.

∴ The profit of B is Rs 34,040.

Given data:

Calculation:

Total export of Car A from 2015 to 2018 = 150 + 275 + 175 + 300 = 900

Total export of Car B from 2015 to 2018 = 250 + 200 + 275 + 325 = 1050

Difference in export of Car B = 1050 - 900 = 150

Difference % = $150\over900$ × 100 = 16.7% 

∴ 16.7% more cars of type B was exported.

Given data:

Height of smaller jug = 8 cm

Height of bigger jug = 12 cm

Volume of smaller jug = 80 cm3 

Concept:

Volume of similar surfaces is equal to the cube of similar sides. 

⇒ ${Height_A}^3 \over {Height_B}^3$ = $Volume_A \over Volume_B$

Calculation:

From the proportionality concept-

⇒ $8^3\over12^3$ = $80\over Volume_B$

⇒ Volume_B = $12\times 12\times 12\times 80\over 8\times 8\times 8$ = 270 cm3 .

The capacity of the bigger jug is 270 cm3.

Additional InformationCapacity of any vessel is equal to the Volume of that vessel

The volume of any body is directly proportional to the cube of its side. 

The volume of first jug / Volume of second jug = Side of figure(1)3/Side of figure(2)3

Shortcut Trick

Average of all 3 numbers = 15

Deviation of the 2^nd and 3^rd numbers from the total average = 12.5 − 15 = −2.5

Total deviation for these 2 numbers = −2.5 × 2 = −5

To balance the average, the 1^st number must be +5 more than the total average.

First number = 15 + 5 = 20

∴ The correct answer is 20.

Alternate Method

Given:

Average of three numbers = 15

Average of the second and third number = 12.5

Formula Used:

Sum of given numbers = Average × Number of terms

Calculations:

⇒ Let the three numbers be a, b, and c.

⇒ Average of a, b, and c = (a + b + c) ÷ 3 = 15

⇒ Sum of all three numbers (a + b + c) = 15 × 3 = 45

⇒ Average of b and c = (b + c) ÷ 2 = 12.5

⇒ Sum of the second and third number (b + c) = 12.5 × 2 = 25

⇒ Substitute the value of (b + c) in the first equation:

⇒ a + 25 = 45

⇒ a = 45 − 25

⇒ a = 20

∴ The correct answer is 20.

Additional Information

Combined Average

If the average of n₁ items is A₁ and n₂ items is A₂, then the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Weighted Average

Used when different items have varying levels of importance or frequencies. Formula: Weighted Average = (w₁x₁ + w₂x₂ + ...) ÷ (w₁ + w₂ + ...).

Average of Arithmetic Progression

For a set of numbers that form an Arithmetic Progression (equal difference between consecutive terms), the average is simply the middle term, calculated as (First Term + Last Term) ÷ 2.

Given data:

cos B = $5 \over 7$

Concept:

In a right-angled triangle ABC, 

cos θ = $b\over h$

b² + p² = h² (From Pythagora's theorem)

Calculation:

we know that cos B = $5 \over 7$

AC² = AB² + BC²

⇒ 7² = AB² + 5²

⇒ AB = √(49 - 25)

⇒ AB = 2√6 cm  

cosec B +  cot B

⇒ (AC/AB) + (BC/AB)

⇒ $7\over 2√6$ + $5\over 2√6$ = $12\over 2√6$ = √6

∴ The value of cosec B + cot B is √6.

Shortcut Trick The side opposite to the angle is the perpendicular. Hence, from ∠ACB, AB is the perpendicular and BC is the base. Similarly, for ∠CAB, BC is the perpendicular, and AB is the base.

Given data:

Total students in the year 2019 = 2000

Total students in the year 2020 = 2400

Calculations:

Students studying science in 2019 = $18\over 100$ × 2000 = 360

Students studying science in 2020 =  $19\over 100$ × 2400 = 456

Ratio = 360 : 456 = 15 : 19

∴ The ratio is 15 : 19.

Concept:

In a right-angled triangle ABC

 

cos θ = $b\over h$

sec θ = $1\over cosθ$ = $h\over b$

tan θ = $sin θ \over cosθ$ = $p\over b$

Calculation:

cos 53° = $x\over y$

sec 53° = $y\over x$

cot 37° = $1\over tan 37°$  = ${\sqrt {(y^2-x^2)}}\over{x}$

Using the value of sec 53° and cot 37°-

⇒ sec 53° + cot 37° = $y\over x$ + ${\sqrt (y^2-x^2)}\over x$ = $\frac{{y + \sqrt {{y^2} - {x^2}} }}{x}$

∴ The value of the expression is $\frac{{y + \sqrt {{y^2} - {x^2}} }}{x}$.

Calculation:

Students who obtained less than 50% marks approximately = 10

Students who obtained more than 90% marks and above = 25

Difference = 25 - 10 = 15

Difference % = $15\over 25$ × 100 = 60%

∴ The answer is 60%.

Given data:

Total startups in Education = 1280

Successful startup in Education = 520

Total startups in Health and sports = 1050

Successful startup in Health and sports = 300

Calculation:

Successful startup % in education = $520\over 1280$ × 100 = 40.625%

Requisite successful startups in Health and sports = $40.625\over 100$ × 1050 = 427 (approximately)

Total increase in the successful startups required for health and sports = 427 - 300 = 127

∴ The answer is 127.

Concept:

The divisibility rule of 8 states that for a number to be divisible by 8, its last three-digit should be perfectly divisible by 8.

The divisibility rule of 11 states that for a number to be divisible by 11, the difference between the sum of odd and even digits should be completely divisible by 11. 

Calculations:

Using Divisibility rule of 8, we get-

∴ 46B is completely divisible by 8 if B is 4. (∴ B = 4)

Similarly using divisibility rule of 11, we get-

⇒ (8 + 5 + 4 + 4) - (A + 1 + 6) = 21 - 7 - A = 14 - A 

⇒ The number is perfectly divisible if A = 3 (∴ A = 3)

∴ value of A^B = 3⁴ = 81

The value of AB is 81.

Given data:

Days in which X can complete the work = 46 days

Days in which Y can complete the work = 92 days

Days in which Z can complete the work = 23 days

Days after which Y joined = 7 days

Days after which Z joined = 8 days

Formula used:

Efficiency = Total work / Time taken to complete work individually

Calculation:

LCM of 23, 46, 92 = 92

Assuming that the total work is 92 units.

Efficiency of x-

⇒ $92\over 46$ = 2 units of work/day

Efficiency of y-

⇒ $92\over 92$ = 1 unit of work/day

Efficiency of z-

⇒ $92\over 23$ = 4 units of work/day

Work done in 7 days by X working alone = 2 units × 7 = 14 units

Work done by X and Y on 8^th day =  (2 + 1) × 1 = 3 units

Total work done until 8^th day = 14 + 3 = 17 units

Remaining work = 92 - 17 = 75 units

Work done by X , Y and Z in one day = 2 + 1 + 4 = 7 units

Total time taken = $75\over 7$ days

Total days worked by Y = $75\over 7$ + 1 = $82\over 7$ = 11$5\over 7$ days.

∴ Y worked for 11**$5\over 7$ days.**

Shortcut TrickLet the total work be 92 units.

x = 46 days = 2 units/day

y = 92 days = 1 unit/day

z = 23 days = 4 units/day

Let the work be completed in Q days.

According to the question,

2Q + 1 × (Q - 7) + 4 × (Q - 8) = 92

⇒ 7Q - 39 = 92

⇒ Q = 131/7

⇒ Q - 7 = 131/7 - 7 (Subtracting 7 from both sides)

⇒ Q - 7 = $11\frac{5}{7}$

∴ Y worked for $11\frac{5}{7}$ days.