SSC CGL 2020 Tier-I Official Paper (Held On : 23 Aug 2021 Shift 1) (Previous Year Paper)

The logic followed here is:

Toothpaste : Teeth → Toothpaste use to clean teeth.

Similarly,

Broom : Floor → Broom use to clean Floor.

Hence, ‘Floor’ is the correct answer.

The number of triangles in the given figure is:

 

So, a total of 15 triangles in the figure.

Hence, ‘15’ is the correct answer.

Given: (63, 76, 46)

The Logic followed here is:

1^st number

2^nd number = 1^st number + 13

3^rd number = 2^nd number - 30

Now follow these steps,

1^st number → 63

2^nd number = 63 + 13 = 76

3^rd number = 76 - 30 = 46

We get, (63, 76, 46)

Now we check all the options-

Option (1): (45, 58, 28)

1^st number → 45

2^nd number = 45 + 13 = 58

3^rd number = 58 - 30 = 28

We get, (45, 58, 28)

Option (2): (83, 96, 66)

1^st number → 83

2^nd number = 83 + 13 = 96

3^rd number = 96 - 30 = 66

We get, (83, 96, 66)

Option (3): (69, 84, 52)

1^st number → 69

2^nd number = 69 + 13 = 82 ≠ 84

3^rd number = 82 - 30 = 52

We get, (69, 82, 52)

But option (3) given (69, 84, 52) this option don’t follow the pattern

Option (4): (72, 85, 55)

1^st number → 72

2^nd number = 72 + 13 = 85

3^rd number = 85 - 30 = 55

We get, (72, 85, 55)

Hence, option (3) is the correct answer.

The embedded part of this image is:

Hence, option (2) is the correct answer.

The logic followed here is:

Help : Hinder → Help is an antonym word of Hinder.

Now, check the options

Option (1) Lenient : Forgiving → Lenient is synonyms word of Forgiving.

Option (2) Impulsive : Hasty → Impulsive is synonyms word of Hasty.

Option (3) Indigent : Rich → Indigent is an antonym word of Rich.

Option (4) Insipid : Plain → Insipid is synonyms word of Plain.

Hence, ‘Indigent : Rich’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:                                

Sum of the positional values of the opposite alphabets letters × Total number of consonant in word = number.

LOWER → Total number of consonant (L, W, R) in the word is 3.           

Opposite alphabets of Given word is OLDVI

Sum of the positional values of the opposite alphabets letters →

O(15) + L(12) + D(4) + V(22) + I(9) = 15 + 12 + 4 + 22 + 9 = 62

Sum of the positional values of the opposite alphabets letters × Total number of consonant in word = number

62 × 3 = 186

And,

MULISH → Total number of consonant (M, L, S, H) in word is 4.          

Opposite alphabets of Given word is NFORHS

Sum of the positional values of the opposite alphabets letters →

N(14) + F(6) + O(15) + R(18) + H(8) + S(19) = 14 + 6 + 15 + 18 + 8 + 19 = 80

Sum of the positional values of the opposite alphabets letters × Total number of consonant in word = number

80 × 4 = 320

Similarly,

OPTIONAL → Total number of consonant (P, T, N, L) in word is 4.     

Opposite alphabets of Given word is LKGRLMZO

Sum of the positional values of the opposite alphabets letters →

L(12) + K(11) + G(7) + R(18) + L(12) + M(13) + Z(26) + O(15) = 12 + 11 + 7 + 18 + 12 + 13 + 26 + 15 = 114

Sum of the positional values of the opposite alphabets letters × Total number of consonant in word = number

114 × 4 = 456

Hence, OPTIONAL will be written as “456”.

Mistake Points 

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In the 1st diagram the line which is joining two points is present in both the sides of the diagram.

In the 2nd diagram the line which is joining two points is not present.

The image obtained when the paper is unfolded is,

Hence, option 3 is the correct answer.

 

.

We put all the option in blank area and check who create particular pattern

Option (1) P, T, T, D, D, C, G

G _ C T _ G P _ T _ G P C _ D _ P C _ D

After filling the blanks with the letters/numbers in the option given above, we get:

G P C T T / G P T T D / G P C D D / C P C G D

No particular pattern is repeating itself when the sequence is divided into equal parts.

Option (2) P, D, D, C, G, T, T

G _ C T _ G P _ T _ G P C _ D _ P C _ D

After filling the blanks with the letters/numbers in the option given above, we get:

G P C T D / G P D T C / G P C G D / T P C T D

No particular pattern is repeating itself when the sequence is divided into equal parts.

Option (3) P, C, T, D, G, T, D

G _ C T _ G P _ T _ G P C _ D _ P C _ D

After filling the blanks with the letters/numbers in the option given above, we get:

G P C T C / G P T T D / G P C G D / T P C D D

No particular pattern is repeating itself when the sequence is divided into equal parts.

Option (4) P, D, C, D, T, G, T

G _ C T _ G P _ T _ G P C _ D _ P C _ D

After filling the blanks with the letters/numbers in the option given above, we get:

G P C T D / G P C T D / G P C T D / G P C T D

A particular pattern is repeating itself when the sequence is divided into equal parts.

Hence, ‘P, D, C, D, T, G, T’ is the correct answer.

Table of alphabets place value:

The pattern follows here,

‘PAWAN’ is written as ‘SCZCQ’

And,

‘SOHAM’ is written as ‘VQKCP’

Similarly,

‘KIRAN’ is written as

Hence, ‘KIRAN’ is coded as 'NKUCQ'

The logic is here is:

(1^st number × 4) – 8 = 2^nd number.

Option (1): 17 ∶ 60

Now, follow the logic:

(17 × 4) – 8 = 68 – 8 = 60 = 2^nd number

This option follows the pattern.

Option (2): 13 ∶ 90

Now, follow the logic:

(13 × 4) – 8 = 52 – 8 = 44 ≠ 2^nd number

This option do not follow the pattern.

Option (3): 23 ∶ 84

Now, follow the logic:

(23 × 4) – 8 = 92 – 8 = 84 = 2^nd number

This option follows the pattern.

Option (4): 19 ∶ 68

Now, follow the logic:

(19 × 4) – 8 = 76 – 8 = 68 = 2^nd number

This option follows the pattern.

Hence, pair “(13 ∶ 90)” is an odd one.

Can you solve this number series puzzle? 11, 13, 19, 49, 109, 239, ? – Find the logic and the missing number with a simple and clear explanation

The pattern followed here is:

Hence, 449 is the correct answer.

The pattern followed here is:

• (4, 282, 5) → (4² + 5³) × 2 = (16 + 125) × 2 = 141 × 2 = 282

Similarly,

• (7, 152, 3) → (72 + 33) × 2 = (49 + 27) × 2 = 76 × 2 = 152

Hence, "(7, 152, 3)" is the correct answer.

 

Note:- Two opposite faces are never seen together or adjacent to each other.

In figure (A): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (B): 9 and 2 are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

In figure (C): 1 and 7 are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

In figure (D): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

Hence, ‘Only A and D’ is the correct answer.

Given:

Statements:

All teachers are doctors.

Some professors are doctors.

All professors are engineers.

 

The least possible diagram for the given statements is as follows

Conclusions:

I. All professors are doctors → False (It is possible but not definite)

II. Some doctors are engineers → True (Because some professors are doctors and all professors are engineers so, some doctors are also engineers)

III. Some teachers are engineers → False (It is possible but not definite)

IV. Some teachers are professors→ False (It is possible but not definite)

Hence,  Only conclusion II follows.

The pattern followed here is,

Step 1 → 1^st number ÷ 3 = A (A is any number)

Step 2 → A × 7 = 2^nd number

Given:

39 : 27

Now follow the pattern

Step 1 → 39 ÷ 3 = 13

Step 2 → 13 × 7 = 91

Similarly,

51 : ?

Now follow the pattern

Step 1 → 51 ÷ 3 = 17

Step 2 → 17 × 7 = 119

Hence, "119" is correct answer.

Table show alphabet serial number –

The logic is shown below –

Hence, “TBX​” is complete in the series.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘GIEY’.

Hence, “GIEY” is the odd one.

Given:

Sum of 3% of A and 6% of B is four-fifths of the sum of 4% of A and 6% of B

3% of A + 6% of B = 4/5 × (4% of A + 6% of B)

Both side take percent common;

=> 3 × A + 6 × B = 4/5 × (4 × A + 6 × B)

=> 5 × (3A + 6B) = 4 × (4A + 6B)

=> 15A + 30B = 16A + 24B

=> 16A – 15A = 30B – 24B

=> A = 6B

So, A : B = 6 : 1

Let common factor in A and B is x

A = 6x and B = x

Now,

A + B = 6x + x = 7x

A – B = 6x – x = 5x

The ratio of A + B and A – B is ‘7 : 5’.

According to the sequence in the dictionary:

The correct order of the given words is:

1. Sensational
2. Sensitize
3. Sentence
4. Sentiment
5. September

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

According to BODMAS rule:

Given equation 25 * 7 * 40 * 20 * 4 * 210

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

25 × 7 - 40 + 20 ÷ 4 = 210

By BODMAS rule

25 × 7 - 40 + 5 = 210

175 - 40 + 5 = 210

180 - 40 = 210

140 = 210 (LHS ≠ RHS)

Option 2: Using combination +, -, =, ÷, ×

25 + 7 - 40 = 20 ÷ 4 × 210

25 + 7 - 40 = 5 × 210

25 + 7 - 40 = 1050

32 - 40 = 1050

• 8 = 1050 (LHS ≠ RHS)

Option 3: Using the combination -. +, =, ÷, ×

25 - 7 + 40 = 20 ÷ 4 × 210

25 - 7 + 40 = 5 × 210

65 - 7 = 1050

58 = 1050 (LHS ≠ RHS)

Option 4: Using the combination ×, +, -, ÷, =

25 × 7 + 40 - 20 ÷ 4 = 210

25 × 7 + 40 - 5 = 210

175 + 40 - 5 = 210

215 - 5 = 210

210 = 210 (LHS = RHS)

Hence, the answer is “×, +, -, ÷, =”.

Given:

‘K $ D’ means ‘K is the father of D’.

‘K < D’ means ‘K is the wife of D’.

‘K > D’ means ‘K is the daughter of D’.

'K @ D’ means ‘K is the son of D’.

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

 

Now break the code of ‘H > R $ S @ T > N’

1) H > R

‘H > R’ means ‘H is the daughter of R’

2) R $ S

‘R $ S’ means ‘R is the father of S’.

3) S @ T

'S @ T’ means ‘S is the son of T’

4) T > N

‘T > N’ means ‘T is the daughter of N’

Hence, S is ‘Grandson’ of N.

The shaded part represents is the number of teachers who are writers, but NOT dancers.

The number of teachers who are writers, but NOT dancers = 10

Hence, ‘10’ is the correct answer.

The logic followed here is:

Except option 2, all options are the capitals of the country whereas Taka is the currency of Bangladesh.

Option (1) Manama → Manama is the capital of Bahrain.

Option (2) Taka → Taka is not a capital of any country.

Option (3) Lusaka → Lusaka is the capital of Zambia.

Option (4) Harare → Harare is the capital of Zimbabwe.

Hence, ‘Taka’ is an odd one.

The mirror image of this image is:

Hence, option 2 is the correct answer.

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

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

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

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

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

1. Broken heart

 is rotated 90° anticlockwise, and 'Slightly smiling face' 

 and Black club suit 

are the same in the 1st figure to 2nd figure.

2. 'Slightly smiling face' 

and 'broken heart'

 shape is the same in 2nd figure to 3rd figure and Black club suit 

is moving 135° anti-clockwise direction.

3. 'Black club suit' and the 'broken heart'  shape is the same in the 3rd figure to 4th figure and a 'Slightly smiling face' is moving 180° anti-clockwise direction.

4. 'Black club suit' and the 'broken heart' shape is the same in the 4th figure to 5th figure and a 'Slightly smiling face' is moving 90° anti-clockwise direction.

5. Slightly smiling face and the broken heart shape is the same in the 5th figure to 6th figure and  'black club suit' is moving 135° anti-clockwise direction.

  

Hence, ‘Option 2’ is the correct answer.

The correct answer is 2020.

Key Points

• PM SVANidhi
• The PM Street Vendor's AtmaNirbhar Nidhi (PM SvaNidhi) was launched by the Ministry of Housing and Urban Affairs on June 01, 2020.
• This is a flagship scheme of the Government of India, in line with the guidelines of Atmanirbhar Bharat.
• It is a special micro-credit facility scheme for providing affordable loans to street vendors.

Additional Information

• The scheme is aimed at enabling the street vendors to resume their livelihoods that have been adversely affected due to COVID-19 lockdown.
• The duration of the scheme is until March 2022.
• HDFC Bank has announced the launch of a micro-credit facility for PM Street Vendor's AtmaNirbhar Nidhi (PM SVANidhi) with common service centres(CSC).
• The Scheme is available for beneficiaries belonging to only those States/UTs which have notified Rules and Scheme under Street Vendors (Protection of Livelihood and Regulation of Street Vending) Act, 2014.

The correct answer is Indian Forest Act, 1878.

Key Points

• The Indian Forest Act, 1927 was enacted after repealing the Indian Forest Act, of 1878.
• Indian Forest Act, 1927
• The Indian Forest Act, of 1927- was enacted to consolidate the law related to forest, the transit of forest produce, and the duty liable on timber and other forests produced.
• The preamble to the Indian Forest Act, of 1927 states that the Act seeks to consolidate the law relating to forests, the transit of forest produce and the duty that can be levied on timber and other forest produce.
• It was largely based on previous Indian Forest Acts implemented under the British. Indian Forest Act of 1878 was the most famous one.
• The Indian Forest Act, 1927 was enacted after repealing the Indian Forest Act, 1878 for the purpose of consolidating the law relating to forests, the transit of forest produce and the duty leviable on timber and other forest produce.
• Indian Forest Act, 1878
• This act repealed the Indian forest act of 1865.
• This act was an extension of the government policy of establishing control over forests.
• It also made several provisions for the imposition of duties on timber.
• The basic aim of the act was to remove local rights in the reserved forest and keep them exclusively as Government reserves.
• The 1878 act divided forests into three categories.

1. Reserved forests.
2. Protected forests.
3. Village forests.

Additional Information

• Indian Forest Act, 1865
• The Indian Forest Act of 1865 extended British colonialism in India and claimed over forests in India.
• It empowered the British government to declare any land covered with trees as a government forest and make rules to manage it.
• It was a precursor to the Indian Forest Act of 1878.

The correct answer is Auxin.

Key Points

• Stem Elongation
• Stem elongation refers to the rapid growth in the length of the internodes of the upper stem before the reproductive phase starts for the plant.
• Stem elongation causes many problems for the plant, such as skinny stems that are too weak to support large flowers, as well as plants that grow too high vertically and appear spindly, so it should be prevented.
• Auxin
• Auxin is a group of plant hormones that regulate growth, particularly by stimulating cell elongation in stems.
• Auxins also play a role in cell division and differentiation, in fruit development, in the formation of roots from cuttings, in the inhibition of lateral branching and in leaf fall.
• The most important naturally occurring auxin is ß- indolyl acetic acid (IAA).

Additional Information

• Ethylene
• Ethylene is the first-identified plant hormone known to regulate numerous processes in plant growth, development, and response to biotic and abiotic stresses.
• Ethylene is best known for its effect on fruit ripening and thus has great commercial importance in agriculture.
• Gibberellin
• Gibberellin is a group of plant hormones that occur in seeds, young leaves, and roots.
• It stimulates the growth of main stems, especially when applied to the whole plant.
• It is commercially obtained from fungi.
• Cytokinin
• Cytokinins are plant hormones that influence not only numerous aspects of plant growth, development and physiology, including cell division.
• Cytokinins are also produced by other prokaryotic and eukaryotic organisms such as bacteria, fungi, microalgae and insects.

The correct answer is Homeostasis.

Key Points

• Homeostasis 
• Homeostasis refers to the body's need to reach and maintain a certain state of equilibrium.
• The term was first coined by a physiologist named Walter Cannon in 1926.
• Homeostasis is the body's tendency to monitor and maintain internal states, such as temperature and blood sugar, at fairly constant and stable levels.
• It is necessary because the body cells need to have suitable conditions around them for proper functioning.
• The excretory system works on the principle of homeostasis in a way that all wastes or unneeded substances are removed by the body.
• It is just like the thermostat in your house.

Additional Information

• Consciousness
• Consciousness is sentience or awareness of internal and external existence.
• It refers to your individual awareness of your unique thoughts, memories, feelings, sensations, and environments.
• Changes to consciousness can also result in changes in perception, thinking, understanding, and interpretations of the world.
• Metabolism
• Metabolism is the process by which your body converts what you eat and drink into energy.
• Its purpose is the conservation of food to building blocks for proteins, lipids, nucleic acids, and some carbohydrates, and the elimination of metabolic wastes.
• Irritability
• It is a characteristic of living organisms in being aware of and being able to respond to a stimulus that tends to disturb the steady-state or homeostasis which all organisms prefer for maintaining life.
• The most common scenario is distant dermatitis in a patient with a chronic eczematous leg ulcer.

The correct answer is Article 198.

Key Points

• Article 198 
• A Money Bill shall not be introduced in a Legislative Council, It can be presented in the Legislative Assembly only.
• No money bill can be introduced in the Legislative Assembly of a State, except on the recommendations of the Governor of the state.
• After a Money Bill has been passed by the Legislative Assembly of a State having a Legislative Council, it shall be transmitted to the Legislative Council for its recommendations, and the Legislative Council shall within a period of fourteen days from the date of its receipt of the Bill return the Bill to the Legislative.
• Assembly with its recommendations and the Legislative Assembly may thereupon either accept or reject all or any of the recommendations of the Legislative Council.
• If the Legislative Assembly accepts any of the recommendations of the Legislative Council, the Money Bill shall be deemed to have been passed by both Houses with the amendments recommended by the Legislative Council and accepted by the Legislative Assembly.
• If the Legislative Assembly does not accept any of the recommendations of the Legislative Council, the Money Bill shall be deemed to have been passed by both Houses in the form in which it was passed by the Legislative Assembly without any of the amendments recommended by the Legislative Council.

Additional Information

• Article 333
• Article 333 empowers the governor to nominate one Anglo-Indian to state assembly if he thinks it is not adequately represented.
• Article 189
• Voting in Houses, power of Houses to act notwithstanding vacancies and quorum.

The correct answer is Eight.

Key Points

• Ashoka edicts
• In Ashoka edicts, the emperor (Ashoka) refers to himself as Devnampiya Piyadasi which means beloved of Gods.
• Ashoka was the first king to make a direct connection to the people via his inscriptions.
• Ashoka edicts are the 33 inscriptions engraved on the rocks and pillars by the Mauryan Empire.
• They were the proclamation by the emperor to the public at large which carried the message about the idea and practice of dharma.
• Ashoka inscriptions were scattered throughout Afghanistan, Pakistan, India, Nepal and Bangladesh.
• There are four types of Ashoka edicts:

1. Major rock edicts
2. Minor rock edicts
3. Major pillar edicts
4. Minor pillar edicts

• Kalinga War
• The major rock edict XIII describes the victory of Ashoka in the Kalinga war.
• It explains the conquest through dhamma instead of war.
• Ashoka fought the Kalinga war, which was completed in the 8th year of Ashoka’s reign in 261 BC.

The correct answer is An Electrode.

 Key Points

• In medicine, an electrode is a device such as a small metal plate or needle that carries electricity from an instrument to the patient for treatment or surgery.
• Electrodes can also carry electrical signals from muscles, brain, heart, skin or other body parts to recording devices to help diagnose certain conditions
• Electrodes transfer the ionic current energy into electrical current in the body.

Additional Information

• An Electrolyte
• Electrolytes are minerals in your blood and other body fluids that carry an electric charge.
• Electrolytes affect how your body functions in many ways including The amount of water in your body, The acidity of your blood(pH).
• Venturimeter
• It is a device for measuring the flow through vessels.
• It converts pressure energy into kinetic energy.
• Machmeter
• It is an airspeed indicator calibrated to read Mach number directly.

The correct answer is Delhi.

Key Points

• Delhi Deputy CM Manish Sisodia, on 15th January 2021, launched the "Street Theatre and Performing Arts Fellowship" scheme.
• It will give artists an opportunity to showcase their craft.
• The flagship scheme has been started by the Sahitya Kala Parishad under the Department of Arts, Culture and Languages.
• Nearly 500 artists have been selected for this scheme.
• It offers a monthly stipend of Rs 5,000 to those who are selected for it.
• The selected artists had performed in a team of 10 every week at different public places in Delhi.
• Delhi
• Chief Minister: Arvind Kejriwal
• Deputy CM: Manish Sisodia
• Lieutenant Governor of Delhi: Vinai Kumar Saxena

The correct answer is Karnataka.

Key Points

• Panche 
• Panche is a non-stitched cloth is wrapped around the legs and knotted around the waist.
• Panche is aesthetically worn by the men of Karnataka.
• Its other name is Dhoti.
• It is a rectangular piece of cloth of 4.5 metres long.
• Karnataka men pair their panches with a shirt to various occasions.

Additional Information

• Karnataka
• Capital- Bengaluru
• Chief Minister- Siddaramaiah
• Governor- Thawar Chand Gehlot
• State bird- Indian roller
• State animal- Elephant
• State tree- Sandalwood
• State flower- Lotus
• State Parks- Anshi National Park, Bandipur National Park, Bannerghatta National Park, Kudremukh National Park, Nagarahole National Park.

The correct answer is The Little Book of Encouragement.

Key Points

• The Little Book of Encouragement
• The Book comprises 130 quotes.
• Renuka Singh has edited the book and Penguin Random House has published the book.
• It promotes human values, spills the beans on a key to happiness and comments on Sino-India ties.
• Dalai Lama praises India's rich civilisational heritage.
• The Dalai Lama rightly points to our 'emotional hygiene that helps the mind and heart to gain inner strength, peace, clarity, and happiness.
• Dalai Lama
• Dalai Lama is a title given by the Tibetan people for the foremost spiritual leader of the Gelug or "Yellow Hat" school of Tibetan  Buddhism.
• There have been only 14 Dalai Lamas in the history of Tibetan Buddhism.
• The 14th and current Dalai Lama is Tenzin Gyatso.

Additional Information

The correct answer is Convergent.

Key Points

• Convergent Boundaries
• When two tectonic plates move toward each other and collide, they form a convergent plate boundary.
• There are three types of convergent plate boundaries: oceanic-oceanic boundaries, oceanic-continental boundaries, and continental-continental boundaries. Each one is unique because of the density of the plates involved.
• Convergent plate boundaries are often the sites of earthquakes, volcanoes, and other significant geological activity.

Additional Information

• Divergent boundaries
• A divergent boundary occurs when two tectonic plates move away from each other.
• The Mid-Atlantic Ridge is an example of divergent plate boundaries.
• Transform
• Transform boundaries are places where plates slide sideways past each other.
• Transform boundaries are found on the seafloor, where they connect segments of diverging mid-ocean ridges.

The correct answer is Gujarat.

Key Points

• Mukhyamantri Bagayat Vikas Mission(Horticulture Development Mission)
• Mukhyamantri Bagayat Vikas Mission is also known as Horticulture Development Mission.
• It was launched by former Chief Minister Vijay Rupani.
• This scheme has been launched with the objective of doubling the farmer's income who are engaged in horticulture and medicinal farming.
• Under it, the wasteland of the government of Gujarat will provide a thirty-year lease for the purpose of farming the medicinal and horticulture crops.
• It has fixed the leaseholders will not be allowed to sell the instalments.
• The mission will allow growing only fruits and medicinal plants. It will not allow farmers to grow cash crops and grains.

Additional Information

• Gujarat
• Capital: Gandhinagar
• Chief Minister: Bhupendrabhai Patel (July 2021)
• Governor: Acharya Devrat
• State bird: Greater Flamingo
• State animal: Asiatic Lion
• State flower: Marigold
• National Parks: Vansda National Park, Blackbuck National Park, Gir National Park, Marine National Park.

The correct answer is INSEAD, Cornell University, WIPO.

Key Points

• Global Innovation Index 
• It provides detailed metrics about the innovation performance of 131 countries and economies around the world.
• Its 80 indicators explore a broad vision of innovation, including political environment, education, infrastructure, and business sophistication.
• It is published annually by Cornell University, INSEAD, and the WIPO.
• India is at the 46th position in the list of top 50 innovative countries.
• The theme of the 2021 report is Tracking Innovation through the COVID-19 crisis.
• INSEAD, Cornell University, WIPO
• It releases the Global Innovation Index report.
• WIPO is the global forum for intellectual property(IP) services, policy, information and cooperation.
• It is one of the 15 specialized agencies of the United Nations.
• It was founded on 14 July 1967.
• WIPO's criteria to measure innovation cover institutions, human capital and research, infrastructure, credit, investment, linkages, creation, absorption and diffusion of knowledge and creative outputs.
• HQ: Geneva, Switzerland.

Additional Information

• WTO
• WTO is an international organization set up in 1995 by replacing the General Agreement on Trade and Tariffs under the Marrakesh Agreement.
• The World Trade Organization is the only global international organization dealing with the rules of trade between nations.
• WTO has 164 members and 23 observer governments.
• HQ: Geneva, Switzerland
• Director-General of WTO: Ngozi Okonjo-Iweala
• UNDP
• It is a specialized agency of the United Nations established in 1965.
• It was formed by merging Emerging Programme for Technical Assistance & Special Fund and The Economic and Social Council.
• HQ: New York City, USA.
• Chairperson: Achim Steiner
• WEF
• The World Economic Forum is the International Organization for Public-Private Cooperation.
• It was established in 1971 as a not-for-profit foundation.
• HQ: Geneva, Switzerland
• Chairperson: Peter Brabeck-Letmathe

The correct answer is Radial.

Key Points

• Radial Pattern
• The tributaries from a summit follow slope downwards and drain down in all directions.
• The radial drainage pattern develops around a central elevated point and is common to conically shaped features such as volcanoes.
• Examples: Streams of the Saurashtra region, the rivers originating from the Amarkantak Mountain, Central French Plateau, Mt. Kilimanjaro.
• The Narmada, Son and Mahanadi originate from Amarkantak Hills and flow in different directions.

Additional Information

• Dendritic
• This is an irregular tree branch shaped pattern that develops in a terrain that has uniform lithology and where faulting and jointing are insignificant.
• Examples: Indus, Godavari, Mahanadi, Cauvery, Krishna.
• Trellis
• In this type of pattern, the short subsequent streams meet the mainstream at right angles, and differential erosion through soft rocks paves the way for tributaries.
• Examples: The old folded mountains of the Singhbhum and Seine and its tributaries in the Paris basin have drainage of trellis pattern.
• Centripetal
• In a low-lying basin, the streams converge from all sides.
• Examples: Streams of Ladakh, Tibet, and the Baghmati and its tributaries in Nepal.

The correct answer is Command area.

Key Points

• Command Area
• The area over which canal irrigation water flows by gravity is known as the command area.
• Types of Command areas in irrigation:
• Gross Command Area:
• It is the total area that can be economically irrigated from an irrigation scheme without considering the limitations of water.
• It is denoted by GCA.
• GCA= CCA + Uncultivable area
• Culturable Command Area:
• A culturable area is an area in which a crop is grown at a particular time or crop season.
• It is denoted by CCA.
• CCA= GCA - Uncultivable area
• Net Command Area
• It is the Culturable Command Area obtained after the deduction of canal networks, supply ditches, etc constructed in the field.
• It is denoted by NCA.
• NCA= CCA - the area occupied by canals, networks, and ditches.

Additional Information

• Irrigation
• Irrigation is supplying water artificially to the soil for the purpose of agricultural production.
• It is used in dry areas and during periods of inadequate rainfall.

The correct answer is Milk of magnesia.

Key Points

• pH
• The pH is a measure of free acidity.
• More precisely, pH is defined as the negative log of the hydrogen ion concentration.
• The range of pH extends from 0 to 14.
• A pH value of 7 is neutral because pure water has a pH value of exactly 7.
• Values lower than 7 are acidic values greater than 7 are basic or alkaline.
• Milk of Magnesia
• It is the magnesium compound that acts as an antacid.
• Milk of Magnesia is basic in nature.
• The pH value of the Milk of Magnesia is 10.5.

Additional Information

The correct answer is Saudi Arabia.

Key Points

• The two-day summit on 21st and 22nd November 2020 was held virtually via video conference due to the coronavirus pandemic.
• The Kingdom of Saudi Arabia was the president of the 15th G20 Summit where its king, Salman Bin Abdulaziz chaired the meeting.
• Prime Minister Narendra Modi represented India in the 15th G20 Summit Riyadh 2020.
• The theme of the summit was "Realizing Opportunities of the 21st Century for All" where all the member nations of G20 responded positively to collaborate and work together under the guidance of Saudi Arabia to focus on its three main aims:

1. Empower People by creating an intrinsic environment for all people especially women and youth to work, live together, and thrive.
2. Safeguard the Planet by encouraging unified efforts to protect our global commons.
3. Shape New Frontiers by embracing long-term, bold strategies to share the benefits of innovations and technological advancement.

Additional Information

• G20 Summit
• It is a Group of Twenty is an international forum for the Governments of 19 members countries and the European Union to discuss policies pertaining to important issues of world affairs.
• The G20 was founded in 1999 with the aim to discuss financial stability worldwide.
• The G20 Summit is held annually where a different G20 member assumes the chairmanship/presidency of the G20 Summit.
• India is set to assume the presidency of the G20 summit in 2023 a year later than planned previously.

The correct answer is Shuggie Bain.

Key Points

• Douglas Stuart
• He is a Scottish-American writer and fashion designer.
• Shuggie Bain is his debut novel, which was awarded the 2020 Booker Prize.
• Booker Prize
• It is a literary award given for novels written in English and Published in either England or Ireland.
• The Prize was constituted in the year 1969 by Booker McConnell Limited Company.
• The First winner of this prize was PH Newby who won it for his novel 'Something to Answer for'.
• The awardee is presented with a reward of 50,000 Euros.
• Shuggie Bain
• It is an autobiographical novel that tells the story of his mother and him and is set in Glasgow in the 1980s.
• The novel tells us about a boy supporting her mother suffering from alcoholism, marriage breakdown and poverty.
• The novel was rejected by 32 publishers before being published by UK based Picador Publishers.

Additional Information

• Indian winners of Booker Prize
• VS Naipaul: On a Free State
• Salman Rushdie: Midnight's Children
• Arundhati Roy: The god of small things
• Kiran Desai: The inheritance of Loss
• Aravind Adiga: The White Tiger

The correct answer is Jwala Gutta.

Key Points

• Jwala Gutta
• She is an Indian professional badminton player.
• Jwala Gutta was the first badminton player of India to qualify for two events in the Olympics women's doubles with Ponnappa and mixed doubles with V. Diju at London.
• She was awarded the Arjuna Award, India's second-highest sporting award for her achievements.
• She has a total of 316 match wins in both disciplines, the most by any Indian.
• She won a bronze medal in 2011 BWF World Championships in London and a gold and silver at the 2010 and 2014 Commonwealth Games in the women's doubles event which were the first for the country in the discipline.
• Badminton World Federation
• It is the international governing body for badminton recognized by the International Olympic Committee.
• It was founded in 1934 with nine member nations.
• Headquarters: Kuala Lumpur, Malaysia.
• President: Poul- Erik Hoyer Larsen

Additional Information

• Saina Nehwal
• She is an Indian Badminton player.
• She is the first Indian badminton player to have won an Olympic medal.
• She reached the finals in the World Badminton Championship (Women) in 2015 and played against Carolina Marin.
• She has also received the honour of - Padma Bhushan, Rajiv Gandhi Khel Ratna Award and Arjun Award.
• Ashwini Ponnappa
• She is an Indian badminton player.
• She had a successful partnership with Jwala Gutta as the pair has won many medals in international events including a gold medal at the Commonwealth Games and bronze medals at the Uber Cup and the Asian Badminton Championships.
• PV Sindhu
• ​She is an India Badminton player from Hyderabad, Telangana.
• She is the first World Badminton Champion from India.
• She fetched a Silver medal at Rio Olympics 2016, South Asian Games 2016, and Commonwealth Games held at Gold Coast Australia.
• She won the Badminton World Federation Championships and clinched a Gold.
• She has been honoured with Arjuna Award, Padma Shri, Rajiv Gandhi Khel Ratna, and Padma Bhushan.

The correct answer is Proper vectors.

Key Points

• Proper vectors
• All the non-zero vectors are called Proper vectors.

Additional Information

• Co-initial vectors

• Co-initial vectors are two or more vectors that have the same initial point.

• CoplantCoplanar vectors

• Coplanar vectors are vectors that are lying on the same in a three-dimensional plane.

• The coplanarity of three vectors is defined when their scalar product is zero.​

dg

• Equal vectors
• Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

dg

The correct answer is Prithviraj Chauhan.

Key Points

• In 1191 Muhammad Ghori attacked and captured Bhatinda, a part of Prithviraj dominion.
• This led Muhammad to come into a direct clash with Prithviraj Chauhan one of the most powerful Rajput rulers.
• It is known as the First Battle of Tarain.
• Muhammad Ghori was defeated in the battle and also wounded in the arm. The Muslim army was routed and the battle was completely won over by the Rajputs.
• Prithviraj Chauhan
• He was an Indian king from the Chahamana(Chauhan) dynasty.
• From the early years, Prithviraj Chauhan showed his sharpness and brilliance by learning all military skills.
• It was believed he mastered the skills of aiming the target based on its sound, known as the "Shabhbhedi" technique.
• His grandfather Angam, the ruler of Delhi, declared him the heir to the throne of Delhi.
• His defeat at Tarain is seen as a landmark event in the Islamic conquest of India and has been described in several semi-legendary accounts.

Additional Information

• Muhammad Ghori
• He was the founder of a Muslim ruler in India. He ruled from 1173 to 1206.
• He is known to have started the Slave Dynasty and was the first of the Five sultanates which ruled Delhi before the Mughals.
• It was the second Battle of Tarain which opened the Delhi area to Muhammad Ghori. In 1192 AD, he invaded again after the 1191 AD invasion with more soldiers and weapons. He defeated Prithvi Raj Chauhan and captured Delhi.
• He was a Sunni Muslim who was instrumental in establishing Islamic supremacy in the Indian subcontinent.
• In 1206, He was murdered and his kingdom in northern India was left in the control of his general Qutb-ud-din Aibak.

The correct answer is Facebook Inc.

Key Points

• Facebook has appointed Henry Moniz as its first chief compliance officer amid increased scrutiny from federal and worldwide regulators and competition from other social media giants.
• Facebook
• Facebook is a social networking service that was created by Mark Zuckerberg in 2004.
• CEO: Mark Zuckerberg
• Facebook's first IPO came on 17 May 2012.
• Facebook changed its name to "Meta" in October 2021 to align the company with its ambitions to build the "metaverse".

The correct answer is Malaysia.

Key Points

• Badminton World Federation
• It is the international governing body for badminton recognized by the International Olympic Committee.
• It was founded in 1934 with nine member nations.
• Headquarters: Kuala Lumpur, Malaysia.
• President: Poul- Erik Hoyer Larsen.

The correct answer is Third.

Key Points

• Ashoka:
• The third Buddhist Council was held in Pataliputra in 250 BC.
• It was held under the patronage of Emperor Ashoka.
• Mogaliputta Tissa presided over the council.
• The third part of the Tripitaka was coded in the Pali language, during the council.
• Kalinga War was a horrifying event as was mentioned in the 13th Rock Edict of Ashoka.
• Approximately hundred and fifty thousand people were wounded while hundred thousand people were killed in the course of the war.
• He preferred Dhammavijay over Dig-Vijay.
• As a result of the Kalinga War, Ashoka renounced the war and converted to Buddhism.
• In order to strengthen the Sangha, emperor Ashoka convened the third Buddhist council in 250 BCE at Pataliputra. However, this was not mentioned in any of his inscriptions.
• In his minor rock edict 1, he called himself Upasaka which means a lay follower of Buddhism.

Additional Information

The correct answer is Seventh Schedule.

Key Points

• Seventh Schedule
• The Seventh Schedule of the Constitution of India defines and specifies the allocation of powers and functions between States and the Union.
• The Schedule contains three lists - Union List, State List, and Concurrent List.
• The Union List originally had 97 subjects. Now it has 100 subjects.
• The State List has 61 subjects now, It had 66 subjects initially. State legislatures can make laws on the subjects mentioned in this list.
• The Concurrent List has 52 subjects enumerated under it. Both the State as well as the Central Government can make laws mentioned on this list.

Additional Information

Given:

8 + 2px2 – 36x – 27x3 = (2 – 3x)³

Formula used:

(a – b)³ = a³ – b³ – 3ab(a – b)

Calculation:

(2 – 3x)3 

(a – b)3 = a3 – b3 – 3ab(a – b)

(2)³ – (3x)³ – 3 × 2 × 3x (2 – 3x)

⇒ 8 – 27x³ – 18x (2 – 3x)

⇒ 8 – 27x³ – 36x + 54x²

Comparison the coefficient of both the equation, we get

8 + 2px2 – 36x – 27x³ = 8 – 27x3 – 36x + 54x²

⇒ 2px² = 54x²

⇒ 2p = 54

⇒ p = (54/2)

⇒ p = 27

∴ The required value of p is 27

Given:

The area of a square shaped field = 1764 m²

Formula used:

Area of square = (side)²

Area of rectangle = length × breadth

Calculation:

The area of a square shaped field = 1764 m²

Side of square field = √1764 = 42 m

Breadth of rectangle field = (42 × 1/6) = 7 m

Length of rectangle field = (7 × 4) = 28 m

Area of rectangular field = (28 × 7) m² = 196 m²

Cost of leveling the park = Rs. (196 × 30)

⇒ Rs. 5880

So, the required cost of leveling the park is 5880

Calculation:

Trees planted in 2016 and 2019 together in Chandigarh = (1800 + 2440) = 4240

Trees planted in 2016 and 2019 together in Ahmadabad = (2500 + 1950) = 4450

Trees planted in 2016 and 2019 together in Pune = (1800 + 1900) = 3700

Trees planted in 2016 and 2019 together in Kolkata = (2000 + 1600) = 3600

∴ Maximum trees planted in 2016 and 2019 taken together in Ahmedabad.

Given:

2x2 – 7x + 5

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

2x2 – 7x + 5 = 0

⇒ 2x² + 5 = 7x

⇒ x² + 5/2 = 7/2

⇒ x + 5/2x = 7/2

Cube of both side of equation

⇒ (x + 5/2x)³ = (7/2)³

⇒ (x)³ + (5/2x)³ + 3 × x × 5/2x(x + 5/2x) = 343/8

⇒ x³ + 125/8x³ + 15/2 (7/2) = 343/8

⇒ x³ + 125/8x³ + 105/4 = 343/8

⇒ x³ + 125/8x³ = (343/8 – 105/4)

⇒ x³ + 125/8x³ = (343 – 210)/8

⇒ x3 + 125/8x3 = 133/8

⇒ x3 + 125/8x3 = $16\frac{5}{8}$

∴ The required value is $16\frac{5}{8}$

Shortcut Trick 2x2 - 7x + 5 = 0 ⇒ $x + {5 \over2x}={7 \over 2}$

if  $x + {a \over bx}=G$ then $x^3 + ({a \over bx})^3=G^3-3\times G\times {a \over b}$

$( {7 \over 2})^3 -3 \times {7 \over 2}\times {5 \over 2}$ 

${7 \over 2}[( {7 \over 2})^2 -3 \times {5 \over 2}]$

${133 \over 8} = 16{5 \over 8}$

Calculation:

Marks of Manju in subject B = (85 × 80/100) = 68

Marks of Rekha in subject B = (75 × 80/100) = 60

Marks of Abhi in subject B = (65 × 80/100) = 52

Total number of marks of Manju, Rekha and Abhi = (68 + 60 + 52)

⇒ 180

Average marks of Manju, Rekha and Abhi = (180/3)

⇒ 60

∴ The required average mark is 60

Mistake PointsMarks present in percentage form in the table, Please read the question carefully.

Shortcut Trick

Using the Alligation Method between Expenditure and Savings to find the ratio of Income components.

Expenditure increase (20%) and Savings increase (40%) result in a total Income increase (28%).

Ratio of Expenditure : Savings = (40 − 28) : (28 − 20) = 12 : 8 = 3 : 2.

Savings percentage (x) = [Savings / (Expenditure + Savings)] × 100 = [2 / (3 + 2)] × 100 = 40%.

∴ The correct answer is 40.

Alternate Method

Given: Savings = x% of Income, Income increase = 28%, Expenditure increase = 20%, Savings increase = 40%.

Formula Used: Income = Expenditure + Savings

⇒ Let Income be 100. Then Savings = x and Expenditure = 100 − x.

⇒ New Income = 100 × 1.28 = 128.

⇒ New Expenditure = (100 − x) × 1.20 = 120 − 1.2x.

⇒ New Savings = x × 1.40 = 1.4x.

⇒ New Income = New Expenditure + New Savings

⇒ 128 = (120 − 1.2x) + 1.4x

⇒ 128 − 120 = 0.2x

⇒ 8 = 0.2x

⇒ x = 8 / 0.2 = 40.

∴ The correct answer is 40.

Additional Information

Income-Expenditure Concept

The fundamental relation is Income = Expenditure + Savings. Any percentage change in components must balance this equation.

Alligation in Income Problems

When two parts of a whole change by different percentages, the overall percentage change is the weighted average. The Alligation rule helps find the initial ratio of those parts.

Successive Percentage Change

For two successive changes of a% and b%, the effective change is [a + b + (a×b)/100]%. This is useful for problems involving multiple increases/decreases.

Concept Used:      

Follow the BODMAS rule according to the table given below:

Calculation:

7 × 4 ÷ 21 of 4 – 5 ÷ 4 × (9 –  13) + 2 – 2 ÷ 8

⇒ 7 × 4 ÷ 21 of 4 – 5 ÷ 4 × (-4) + 2 – 2 ÷ 8

⇒ 7 × 4 ÷ 84 – 5 ÷ 4 × -4 + 2 – 2 ÷ 8

⇒ 7 × 1/21 – 5/4 × -4 + 2 – 1/4

⇒ 7/21 + 20/4 + 2 - 1/4

⇒ 1/3 + 5 + 2 – 1/4

⇒ 1/3 + 7 – 1/4

⇒ (4 + 84 – 3)/12

⇒ (88 – 3)/12

⇒ 85/12

⇒ $7\frac{1}{12}$

∴ The required value is $7\frac{1}{12}$

Given:

sin2 θ - cos2 θ - 3 sin θ + 2 = 0

Formula used:

cos²θ = 1 – sin²θ 

sec30° = 2/√3

tan30° = 1/√3

(sec2θ – tan2θ) = 1

Calculation:

sin2 θ – cos2 θ – 3 sin θ + 2 = 0

⇒ sin²θ – (1 – sin²θ) – 3sinθ + 2 = 0

⇒ sin²θ – 1 + sin²θ – 3sinθ + 2 = 0

⇒ 2sin²θ – 3sinθ + 1 = 0

⇒ 2sin²θ – 2sinθ – sinθ + 1 = 0

⇒ 2sinθ(sinθ – 1) – 1(sinθ – 1) = 0

⇒ (2sinθ – 1) (sinθ – 1) = 0

⇒ sinθ = 1/2, 1

⇒ sinθ = 1/2 = 30° [sin 90° = 1, we cannot take the value of 90°]

Now,

$\frac{1}{√{\secθ-\tanθ}}$

Multiplying with the conjugate of √secθ + tanθ 

⇒ 1/√secθ – tanθ × (√secθ + tanθ/√secθ + tanθ)

⇒ √secθ + tanθ/(sec²θ – tan²θ)

⇒ √secθ + tanθ/1

Now, put the value of θ = 30° 

⇒ √sec30° + tan30° 

⇒ √(2/√3 + 1/√3)

⇒ √(3/√3)

⇒ $\sqrt[4]{3}$

So, the required value is $\sqrt[4]{3}$

Shortcut Trick Put θ = 30° 

⇒ sin230° - cos230° - 3 sin30° + 2

⇒ (1/4) - (3/4) - (3/2) + 2

⇒ (-1/2) - (3/2) + 2

⇒ - 2 + 2 = 0

Now,

$\frac{1}{√{\secθ-\tanθ}}$

Multiplying with the conjugate of √secθ + tanθ 

⇒ 1/√secθ – tanθ × (√secθ + tanθ/√secθ + tanθ)

⇒ √secθ + tanθ/(sec2θ – tan2θ)

⇒ √secθ + tanθ/1

Now, put the value of θ = 30° 

⇒ √sec30° + tan30° 

⇒ √(2/√3 + 1/√3)

⇒ √(3/√3)

⇒ $\sqrt[4]{3}$

So, the required value is $\sqrt[4]{3}$

Given:

$\rm \frac{tan^230^\circ}{sec^230^\circ}+\frac{cosec^245^\circ}{cot^245^\circ}-\frac{sec^260^\circ}{cosec^260^\circ}$

Formula used:

Calculation:

$\rm \frac{tan^230^\circ}{sec^230^\circ}+\frac{cosec^245^\circ}{cot^245^\circ}-\frac{sec^260^\circ}{cosec^260^\circ}$

⇒ (1√3)²/(2√3)² + (√2)²/(1)² – (2)²/(2/√3)²

⇒ (1/3)/(4/3) + (2)/(1) – (4)/(4/3)

⇒ (1/4 + 2/1 – 3)

⇒ (1 + 8 – 12)/4

⇒ (9 – 12)/4

⇒ - 3/4

So, the required value is -3/4

Given:

$x+\frac{1}{x}=\frac{17}{4}, x>1$

Formula used:

(a + b)² = a² + b² + 2ab

(a – b)² = a² + b² – 2ab

Calculation:

According to the question

Squaring both sides, we get

(x + 1/x)² = (17/4)²

⇒ x² + 1/x² + 2 × x × 1/x = 289/16

⇒ x² + 1/x² + 2 = 289/16

⇒ x² + 1/x² = (289/16 – 2)

⇒ x² + 1/x² = (289 – 32)/16

⇒ x² + 1/x² = 257/16

Now,

(x – 1/x)² = x² + (1/x)² – 2 × x × 1/x = 257/16

⇒ (x – 1/x)² + 2 = 257/16

⇒ (x – 1/x)² = (257/16 – 2)

⇒ (x – 1/x)² = (257 – 32)/16

⇒ (x – 1/x)² = 225/16

⇒ x – 1/x = 15/4

∴ The required value is 15/4

Alternate Method If x + 1/x = P, then

x - 1/x = $\sqrt{(P)^2 - 4}$

x - 1/x = $\sqrt{(\dfrac{17}{4})^2 - 4}$

⇒ $\sqrt{\dfrac{289}{16} - 4}$ 

⇒ $\sqrt{\dfrac{289-64}{16}}$ = $\sqrt{\dfrac{225}{16}}$ = $\dfrac{15}{4}$

Given:

Vertices A, B,C and D of a quadrilateral ABCD lie on a circle

Concept used:

We know that in cyclic quadrilateral the sum of opposite angle is 180°.

Calculation:

⇒ ∠A + ∠C = 180° 

⇒ 3θ + θ = 180° 

⇒ 4θ = 180° 

⇒ θ = 45° 

⇒ ∠C = 45° 

Again,

⇒ ∠B + ∠D = 180° 

⇒ α + 2α = 180° 

⇒ 3α = 180° 

⇒ α = 60° 

⇒ ∠B = 60° 

The value of ∠D = 2α = (2 × 60) = 120° 

The difference between the measures of ∠D and ∠C = (120° – 45°)

⇒ 75° 

∴ The required difference is 75° 

Shortcut Trick ⇒ ∠A + ∠C = 180° 

⇒ 3θ + θ = 180° 

⇒ θ = 45° 

⇒ ∠C = 45° 

⇒ ∠B + ∠D = 180° 

⇒ α + 2α = 180° 

⇒ α = 60° 

⇒ ∠B = 60° 

The difference between the measures of ∠D and ∠C = (120° – 45°)

⇒ 75°

Shortcut Trick

Increase in Total Marks = 27 + 10 + 18 = 55

Increase in Average Score = 72.6 − 67.6 = 5

Number of papers = Total Marks Increase ÷ Average Increase

Number of papers = 55 ÷ 5 = 11

∴ The correct answer is 11.

Alternate Method

Given: Initial average = 67.6, Final average = 72.6, Mathematics increase = 27, Computer Science increase = 10, History increase = 18.

Formula Used: Total Marks = Average × Number of Papers

⇒ Let the total number of papers be n.

⇒ Total initial marks = 67.6 × n

⇒ Total marks added = 27 + 10 + 18 = 55

⇒ New total marks = 67.6n + 55

⇒ New average = (67.6n + 55) ÷ n = 72.6

⇒ 67.6n + 55 = 72.6n

⇒ 72.6n − 67.6n = 55

⇒ 5n = 55

⇒ n = 11

∴ The correct answer is 11.

Additional Information

Definition of Average

Average (Mean) is the sum of all observations divided by the total number of observations. Formula: Avg = Σx ÷ n.

Effect of Constant Addition

If every observation in a set is increased by a constant value k, the new average also increases by k.

Deviation Method

The sum of deviations of all observations from their mean is always zero. This concept is useful in finding missing values or balancing averages.

Given:

Time taken to fill a tank by Pipe A = 12 hours

Time taken to fill a tank by Pipe B = 16 hours

Time taken to empty a tank by Pipe C = 24 hours

Formula used:

Work = Efficiency × Time

Calculation:

LCM of 12, 16 and 24 is 48

Efficiency of A to fill the tank = (48/12) = 4 hours/day

Efficiency of B to fill the tank = (48/16) = 3 hours/day

Efficiency of C to empty the tank = (48/24) = - 2 hours/day

All three pipes opened together for 4 hours = [(4 + 3 – 2) × 4]

⇒ (5 × 4) = 20 unit

Remaining unit = (48 – 20) = 28 unit

Time taken by A and C together = [28/(4 – 2)]

⇒ (28/2) = 14 hours

Now,

Total time is taken to fill the empty tank = (14 + 4) hours

⇒ 18 hours

∴ The required time is 18 hours

Shortcut Trick

Effective efficiency = 5

In 4 hours all three pipes will fill 5 × 4 = 20 units

Now, Remaining 48 - 20 = 28 units will be filled by A and C

So, Total efficiency of A and C = 2

So, time = 28/2 = 14 hours

Total time = 14 + 4 = 18 hours

Given:

(25 cos2 x + 9 sec2 x)

Formula used:

Minimum value of acos²x + bsec²x = 2√ab

Calculation:

According to the question:

Minimum value of acos2x + bsec2x = 2√ab

⇒ 2√(25 × 9)

⇒ (2 × 5 × 3)

⇒ 30

∴ The required value is 30.

Given:

∠A = 50° 

Concept used:

An exterior angle of the triangle is equal to the sum of the opposite interior angles.

Calculation:

In ΔBOC

∠BOC + ∠OBC + ∠OCB = 180 [OB and OC bisect ∠B and ∠C respectively]

⇒ ∠BOC + 1/2∠B + 1/2∠C = 180

⇒ ∠BOC = 180 – 1/2(∠B + ∠C)

⇒ ∠BOC = 180 – 1/2(180 – ∠A)

⇒ ∠BOC = 180 – 1/2(180 – 50)

⇒ ∠BOC = 180 – 1/2(130)

⇒ ∠BOC = 180 – 65

⇒ ∠BOC = 115

∴ The required value of ∠BOC is 115° 

Shortcut Trick ⇒ ∠BOC = 90 + A / 2

⇒ 90 + 25 = 115°

Given:

AS = 6 cm

BC = 12 cm

CR = 5 cm

Concept used:

If from one external point, two tangents are drawn to a circle then they have equal tangent segments.

Calculation:

CR = CQ = 5 cm

BQ = BC – CQ

⇒ (12 – 5) = 7 cm

BQ = BP = 7 cm ....(1)

AS = AP = 6 cm ....(2)

Adding equation (1) and (2), we get

⇒ (7 + 6)

⇒ 13 cm

So, the length of AB is 13 cm

Given:

The five-digit number = 593ab

Concept used:

Divisibility rule of 3 - A number is completely divisible by 3 if the sum of its digit is divisible by 3.

Divisibility rule of 7 - If a number is divisible by 7, then the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0

Divisibility rule of 11 - If the difference between the sum of the digits at the odd and even places equals 0 or is divisible by 11, then the number is divisible by 11.

Calculation:

LCM of 3, 7, 11 is 231

Let's assume the largest number is 59399.

Now, on dividing 59399 by 231

We get approx 257.13

So, the actual number = 231 × 257 = 59367

So, a = 6 and b = 7

Now,

The value of (a2 – b2 + ab) = (6)² – (7)² + (6 × 7)

⇒ (36 – 49 + 42)

⇒ (78 – 49)

⇒ 29

∴ The required value is 29

Alternate Method The given number is 593ab

We know that, 3, 7, and 11 divide 593ab 

Hence getting the nearest 5-digit number having first 3 digits as 593

⇒ 3 × 7 × 11 = 231

5 digit number will be

⇒ 23100 now we want 5 in 10th thousand place, 

Double of this number will be, 46200, 

We want 593_ _ 

⇒ 46200 + 4620 = 50820 now we want 9 at thousands of places, 

⇒ 50820 + 4620 + 4620 = 60060

subtracting 462 from 60060, 

⇒ 60060 - 462 = 59,598

subtracting 231 from 59,598

⇒ 59367

Hence a = 6 and b = 7

The value of (a² – b² + ab) = (6)² – (7)² + (6 × 7)

⇒ (36 – 49 + 42)

⇒ (78 – 49)

⇒ 29

∴ The required value is 29

Shortcut Trick 

Interest for one year = 5832/3 = Rs. 1944

Interest for 7% = 25600 × 7/100 = 1792

Interest for 9% = 25600 × 9/100 = 2304

The sum invested on 9%

= 152/(360 + 152) × 25600

= 152/512 × 25600 = Rs. 7600

 Alternate Method

Given:

Sum = Rs. 25600

R₁ = 7%

R₂ = 9%

The total interest at the end of 3 years = Rs. 5832

Formula used:

SI = (P × R × T)/100

Calculation:

Let the principal be x

Then,

A sum of Rs. 25600 is invested on SI at (25600 – x)

The total interest at the end of 3 years = Rs. 5832

The total interest at the end of 1 year = Rs. (5832/3)

⇒ Rs. 1944

Now,

According to the question

⇒ (x × 1 × 9)/100 + [(25600 – x) × 1 × 7]/100 = 1944

⇒ 9x/100 + (179200 – 7x)/100 = 1944

⇒ 9x + 179200 – 7x = 194400

⇒ (9x – 7x) = (194400 – 179200)

⇒ 2x = 15200

⇒ x = (15200/2)

⇒ x = 7600

∴ The money invested at 9% per annum is Rs. 7600

Shortcut Trick Let 100% bananas cost to Rs. 100.

Remaining bananas = 80%

80% bananas cost Rs. 80.

Total profit percentage on them = 2/5 × 15 + 3/5 × 10 = 12%

SP of bananas = 80 × 112/100 = 89.6

Loss = 100 - 89.6 = 10.4

Loss% = (10.4/100) × 100 = 10.4%

Alternate Method

Given:

One-fifth of them got rotten and were thrown away.

He sold two-fifth of the remaining bananas with him at a 15% profit 

The remaining bananas at 10% profit. 

Formula used:

Loss = SP – CP

Loss% = Loss/CP × 100

Calculation:

Let fruit merchant bought 100 bananas

One fifth of them got rotten and were thrown away = (1/5 of 100)

⇒ (1/5 × 100)

⇒ 20

Now,

He sold two fifth of the bananas with him at 15% profit = (2/5 of 80)

⇒ (2/5 × 80)

⇒ 32 

The remaining bananas at 10% profit = [100 – (20 + 32)]

⇒ (100 – 52) = 48

Now,

Let the CP of each banana be x

Then, CP of 100 banana be 100x

Now,

Total SP = 20x × 0 + 32x(1 + 15/100) + 48x(1 + 10/100)

⇒  0 + 32x(115/100) + 48x(110/100)

⇒ 0 + 32x(23/20) + 48x(11x/10)

⇒ 0 + 184x/5 + 264x/5

⇒ 448x/5

⇒ 89.6x

Loss = (SP – CP)

⇒ (100x – 89.6x)

⇒ 10.4x

Loss% = Loss/CP × 100

⇒ (10.4x/100x × 100)

⇒ 10.4

∴ The required Loss% is 10.4%

Given:

Discount = 10%

Profit = 20%

Formula used:

Profit = SP – CP

Profit% = Profit/CP × 100

Calculation:

Let the marked price be MP 

Let the cost price be CP

According to the question

⇒ (90% of MP) = (120% of CP)

⇒ (90/100 × MP) = (120/100 × CP)

⇒ (9/10 × MP) = (6/5 × CP)

MP/CP = 4/3

Profit = (4 – 3) = 1

Profit% = (1/3 × 100)

⇒ (100/3)%

⇒ 33.33%

∴ The required profit% is 33.33

Given:

AB = 5 cm

AC = 7.5 cm

BC = 10 cm

Concept used:

Angle bisector theorem:  The angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two-line segments is proportional to the ratio of the other two sides.

Midpoint theorem: The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

Calculation:

AD is the bisector of ∠A

⇒ AB/AC = BD/DC  [By angle bisector theorem]

⇒ 5/7.5 = BD/DC

⇒ 2/3 = BD/DC

3/2 = DC/BD

Adding 1 to both sides, we get:

$\frac{3}{2}$ + 1 = $\frac{DC}{BD}$ + 1

$\frac{5}{2}$ = $\frac{BD+DC}{BD}$ = $\frac{BC}{BD}$

Since BC = 10, we get:

The value of BD = (2/5 × 10) = 4

The value of DC = (3/5 × 10) = 6

According to the question

Midpoint of BC = (10/2) = 5

So, We take, M as a midpoint on BC = 5

Now,

The distance between D and M = (6 – 5) = 1

So, the required value is 1 cm

Given:

Fourth proportion to 12, 18, 6 is equal to the third proportion to 4, k.

Calculation:

According to the question

Let the fourth proportion be x

⇒ 12/18 = 6/x

⇒ x = (6 × 18)/12

⇒ x = 9

Now,

Third proportion is

⇒ 4/k = k/9

⇒ k² = 36

⇒ k = 6

∴ The required value of k is 6

Calculation:

Salary of Amit = 35000

Salary of Amit after 25% more is

⇒ (35000 × 25/100)

⇒ 8750

Income of Amit except salary = (6000 + 1000 + 1800) = 8800

Now,

Salary of Suresh = 38500

Salary of Suresh after 25% more is

⇒ (38500 × 25/100)

⇒ 9625

Income of Suresh = (6300 + 1100 + 1950) = 9350

Now,

Salary of Nitin = 29000

Salary of Nitin after 25% more is

⇒ (29000 × 25/100)

⇒ 7250

Income of Nitin = (5000 + 1000 + 1400) = 7400

Now,

Salary of Varun = 42000

Salary of Varun after 25% more is

⇒ (42000 × 25/100)

⇒ 10500

Income of Varun = (7500 + 1240 + 1500) = 10240

∴ Amit and Nitin income from all sources except salary is more than 25% of his salary

Given: 

A boat covers a round trip journey between two points A and B in a river in T hours

Formula used:

Downstream = (u + v) km/hr

Upstream = (u – v) km/hr

Calculation:

Let the speed of boat in still water be xkm/hr

Speed of stream = y km/hr

Let the distance between them be d 

Downstream = (x + y) km/hr

Upstream = (x – y) km/hr

According to the question

⇒ d/(x + y) + d/(x – y) = 161T

⇒ d(x - y + x + y)/ x2 - y2 = 161T

⇒d(2x)/161(x2 - y2) = T   ......... (1)

Again,

⇒ d/(2x + y) + d/(2x – y) = 80T

⇒d(2x - y + 2x + y)/(2x)2 - (y)2 = 80T

⇒d(4x) / 80(4x2 - y2) = T  ..........(2)

Now equalling both the equations,

⇒d(2x)/161(x2 - y2) = d(4x) / 80(4x2 - y2) 

⇒1/161(x2 - y2) = 2/ 80(4x2 - y2) 

⇒1/(161x2 - 161y2) = 1/(160x2 - 40y2)

⇒160x2 - 40y2 = 161x2 - 161y2

⇒x2 = 121y2

⇒x/y = 11/1

∴ The required ratio is 11 : 1

Alternate Method 

Let the speed of boat in still water be xkm/hr

Speed of stream = y km/hr

Let the distance between them be d 

Downstream = (x + y) km/hr

Upstream = (x – y) km/hr

According to the question

⇒ d/(x + y) + d/(x – y) = T

⇒ d(1/x + y) + (1/x – y) = T

⇒ d[(x – y) + (x + y)/(x² – y²)] = T

⇒ d[(2x/(x² – y²) = T

⇒ d/T = x² – y²/2x .....(1)

Again,

⇒ d/(2x + y) + d/(2x – y) = 80T/161

⇒ d(1/2x + y + 1/2x – y) = 80T/161

⇒ d(2x – y+ 2x + y)/4x² – y² = 80T/161

⇒ d(4x/4x² – y²) = 80T/161

⇒ d/T = 80(4x² – y²)/4x × 161 ......(2)

Now, substituting both the equation, we get

d/T = x2 – y2/2x =  80(4x2 – y2)/4x × 161

⇒ x² – y² = 40(4x² – y²)/161

⇒ (161x² – 161y²) = (160x² – 40y²)

⇒ (161x² – 160x²) = (161y² – 40y²)

⇒ x² = 121y²

⇒ x/y = 11/1

∴ The required ratio is 11 : 1

<br>

Hint

In this type of question, always try to make two equations equal to the same variable so that we can equalize the two equations.

Calculation:

Marks of Amit in subject E = (80 × 150/100) = 120

Marks of Abhi in subject E = (74 × 150/100) = 111

Marks of Anuj in subject E = (84 × 150/100) = 126

Total marks of Amit, Abhi an Anuj = (120 + 111 + 126)

⇒ 357

Marks of Manju in subject B = (85 × 80/100) = 68

Marks of Amit in subject B = (65 × 80/100) = 52

Marks of Rekha in subject B = (75 × 80/100) = 60

Marks of Anuj in subject B = (55 × 80/100) = 44

Marks of Abhi in subject B = (65 × 80/100) = 52

Marks of Vikram in subject B = (70 × 80/100) = 56

Total marks of all the six students in subject B = (68 + 52 + 60 + 44 + 52 + 56)

⇒ 332

Required percentage = [(357 – 332)/332 × 100]

⇒ (25/332 × 100)

⇒ (2500/332)

⇒ 7.5

∴ Required percentage is 7.5