SSC CGL 2020 Tier-I Official Paper (Held On : 16 Aug 2021 Shift 1) (Previous Year Paper)

The paper when unfolded will appear as shown below:

Hence, ‘option 3’ is the correct answer.

The description is as follows:

Except option 3, all options are synonyms to each other.

 

Hence, ‘Empathy’ is the odd one out.

Find the missing number using: [2^nd − (1^st ÷ 2)] + (product of 1^st’s digits) = 3^rd. A fun logic puzzle to test your brain. Can you solve it?

The logic followed here is:

In a row:

[2^nd number - (1^st number ÷ 2)] + (multiply of digits of 1^st number) = 3^rd number

Row 1: 14, 16, 13

= [16 - (14 ÷ 2)] + (1 × 4)

= [16 - 7] + 4

= 9 + 4 = 13

Row 3: 12, 21, 17

= [21 - (12 ÷ 2)] + (1 × 2)

= [21 - 6] + 2

= 15 + 2 = 17

Similarly, 

Row 2: 18, 6, ?

= [6 - (18 ÷ 2)] + (1 × 8)

= [6 - 9] + 8

= -3 + 8 = 5

Hence, the correct answer is "5".

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

2. Solitary
3. Solution
4. Solvent
5. Sophisticate
6. Sorting

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

The pattern followed here is:

According to the alphabetical positions of the letters,

1. 

2. 

3. 

4. 

Hence, ‘FHDB’ is the odd one out.

The logic is:

16 : 144 → 16 × (16 ÷ 2) + 16 = 16 × 8 + 16 = 128 + 16 = 144

Similarly,

28 : ? → 28 × (28 ÷ 2) + 28 = 28 × 14 + 28 = 392 + 28 = 420

Hence, ‘420’ is the correct answer.

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

The Opposite of 2 is 4.

The Opposite of 6 is 1.

The Opposite of 3 is 5.

 → Can be formed.

 → Cannot be formed as 4 and 2 are faces opposite to each other and no two opposite faces can appear together in a dice.

 → Can be formed.

 → Cannot be formed as 5 and 3 are faces opposite to each other and no two opposite faces can appear together in a dice.

The dice A and C can be formed when the given sheet is folded because the opposite faces is not appear together in these dice.

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

Additional Information

• Dices are of two types :

1. Standard Dice
2. Non-Standard Dice.

• Dice has:-

1. faces = 6
2. sides = 12
3. corners = 8

• Two opposite faces are never seen together.
• Adjacent faces are never the opposite of each other.

Given: 

The logic follows here is:

(1) All the signs are rotating in the anticlockwise direction within the square.

(2) In every step, alternate signs are changing.

Therefore, by checking options only option (3) follows above conditions. In all the other options one sign that should be changed is the repeated sign from the previous steps, it should not be repeated.

The complete series is:

Hence, option (3) is the correct answer.

The number of triangles in the figure is shown below:

 

Hence, '17' is the correct answer.

The logic follows here is:

At first, letters of the word are coded according to the equivalent opposite letter of a particular letter of the word.

Then, the letters obtained are coded according to their positional values in English alphabetical series.

Code = Sum of positional values of opposite letter + Number of letters in each word

  

Similarly,

Hence, ‘87’ is the correct answer.

The Venn diagram that best illustrates the relationship between Coriander seeds, Spices, and Cinnamon is shown below:

Coriander and Cinnamon are spices.

Hence, ‘option 4’ is the correct answer.

The logic is:

Anger : Emotion → Anger is an emotion.

Similarly,

Pomegranate : Fruit → Pomegranate is a fruit.

Hence, ‘Pomegranate : Fruit’ is the correct answer.

Additional Information

• Anger is an emotion characterized by antagonism toward someone or something you feel has deliberately done you wrong. Anger can be a good thing. It can give you a way to express negative feelings, for example, or motivate you to find solutions to problems. But excessive anger can cause problems.
• Moods and emotions are linked. When you are in a bad mood, you are inclined to have negative emotions such as being sad, angry, or afraid about something. But when you are in a good mood, you are inclined to have positive emotions such as being happy or hopeful about something.

Important Points

• Do not get tensed by the complexity of the figures.
• Carefully understand the structure of the given question figure.
• The embedded figure may not be of exact size. It may be small or big.
• Sometimes the rotation or reflection of the figures may be confusing.
• So think wisely before selecting the answer.

The option that is embedded in the given figure when rotation is NOT allowed is shown below:

Hence, ‘option 3’ is the correct answer.

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

Hence, ‘option 2’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1) 1^st, 3^rd and 5^th letters are reversed their position with addition of 5.

2) 2^nd and 4^th letters are coded as their equivalent opposite letter.

First, Third and Fifth letters are moved 5 steps forward and Second and Fourth letters are coded according to the equivalent opposite letter of a particular letter of the word.

Similarly,

Hence, ‘HRLZR’ is the correct answer.

1. 14 and 22

Given equation: 36 × 81 ÷ 9 – (88 ÷ 4) + 14 + (22 + 7) = 169

After replacing the numbers, we get:

L.H.S = 36 × 81 ÷ 9 – (88 ÷ 4) + 22 + (14 + 7)

= 36 × 9 – 22 + 22 + 21

= 324 + 21

= 345 ≠ R.H.S

2. 9 and 36

Given equation: 36 × 81 ÷ 9 – (88 ÷ 4) + 14 + (22 + 7) = 169

After replacing the numbers, we get:

L.H.S = 9 × 81 ÷ 36 – (88 ÷ 4) + 14 + (22 + 7)

= 9 × 2.25 – 22 + 14 + 29

= 20.25 – 22 + 43

= 63.25 – 22

= 41.25 ≠ R.H.S

3. 36 and 14

Given equation: 36 × 81 ÷ 9 – (88 ÷ 4) + 14 + (22 + 7) = 169

After replacing the numbers, we get:

L.H.S = 14 × 81 ÷ 9 – (88 ÷ 4) + 36 + (22 + 7)

= 14 × 9 – 22 + 36 + 29

= 126 – 22 + 65

= 191 – 22

= 169 = R.H.S

4. 81 and 36

Given equation: 36 × 81 ÷ 9 – (88 ÷ 4) + 14 + (22 + 7) = 169

After replacing the numbers, we get:

L.H.S = 81 × 36 ÷ 9 – (88 ÷ 4) + 14 + (22 + 7)

= 81 × 4 – 22 + 14 + 29

= 324 – 22 + 43

= 367 – 22

= 345 ≠ R.H.S

Hence, ‘36 and 14’ is the correct answer.

The logic is:

Leaves : Rustle → Soft, muffled crackling sound caused by the movement of dry leaves or paper is called rustle.

Similarly,

Owl : ? → Hoot is a low, wavering musical sound which is the typical call of many kinds of owl.

Hence, ‘Hoot’ is the correct answer.

 

Code for Days:

 

Code for Centuries:

1600 → 6

1700 → 4

1800 → 2

1900 → 0

2000 → 6

2100 → 4

2200 → 2

2300 → 0

For, 17 April 2014

Date = 17

Code for month = 6

Code for Century = 6

2014 = 2000 + 14

For, 2000 it is 6

For, 14 it is 14

And, 14 ÷ 4 = 3

Adding all these = 17 + 6 + 6 + 14 + 3 = 46

46 ÷ 7 = 4 (here we consider the remainder)

4 is the code for Thursday.

17 April 2014 is Thursday.

Hence, ‘Thursday’ is the correct answer.

Additional Information

Year - One year has 365 days or 366 days on this basis the year is divided into two parts:

• Normal year - It has 365 days.
• Leap year - It has 366 days and completely divisible by 4.

Century leap year - The year which is exactly divisible by 400. Example - 1200, 1600, 2000 etc.

Counting of Odd days

Ordinary Year: 365 days (52 weeks + 1 days)

= 1 Odd days

Leap Year: 366 days (52 weeks + 2 days)

= 2 Odd days

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘FTAS’ is the correct answer.

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

 

M @ R % K # G # N & T → M is mother of R, R is sister of K, K is son of G, G is son of N, N is wife of T.

1. T is the paternal grandfather of M. → False (T is father-in-law of M)

2. N is the paternal grandmother of K. → True 3. M is the mother of K. → True 4. R is the daughter of G. → True

Hence, ‘T is the paternal grandfather of M’ is the correct answer.

The pattern followed here is:

1. C, D, A, T, U, D, C, D

Given sequence: U A _ B _ T U _ C B D _ _ A C B _ T U A C _ _ T

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

U A C B D T U A C B D T U A C B D T U A C C D T

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

2. C, D, A, U, U, D, B, D

Given sequence: U A _ B _ T U _ C B D _ _ A C B _ T U A C _ _ T

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

U A C B D T U A C B D U U A C B D T U A C B D T

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

3.  C, D, A, T, U, D, B, D

Given sequence: U A _ B _ T U _ C B D _ _ A C B _ T U A C _ _ T

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

U A C B D T / U A C B D T / U A C B D T / U A C B D T

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

4.  D, C, A, T, U, D, D, B

Given sequence: U A _ B _ T U _ C B D _ _ A C B _ T U A C _ _ T

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

U A D B C T U A C B D T U A C B D T U A C D B T

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

Hence, ‘C, D, A, T, U, D, B, D’ is the correct answer.

The logic follows here is:

Hence, the correct answer is "133".

The least possible Venn diagram is:          

Conclusions:

I. No bank is a stall. → False (As, No bank is an office and All offices are stalls → Some bank are not stalls)

II. No stall is a bank. → False (As, No bank is an office and All offices are stalls → Some stalls are not bank)

III. Some stalls are offices. → True (As, All offices are stalls → Some stalls are offices)

IV. All the stalls are offices → False (As, All offices are stalls → Some stalls are offices)

Hence, Only conclusion III follows.

The logic is:

(1^st number + second number) × (2^nd number - 1^st number) = third number

(6, 9, 45) → (6 + 9) × (9 - 6) = 15 × 3 = 45

Similarly,

(8, 10, 36) → (8 + 10) × (10 - 8) = 18 × 2 = 36

Hence, ‘(8, 10, 36) ’ is the correct answer.

The logic is:

1^st number × 7 - 8 = second number

1. 21 ∶ 139 → 21 × 7 - 8 = 147 - 8 = 139
2. 25 : 167 → 25 × 7 - 8 = 175 - 8 = 167

3. 15 : 197 → 15 × 7 - 8 = 105 - 8 = 97 ≠ 197

4. 27 : 181 → 27 × 7 - 8 = 189 - 8 = 181

Except option 3, all options are follow the given logic. thus option 3 is an odd one.

Hence, ‘15 : 197’ is the odd one out.

The correct answer is Johannes Kepler.

Key Points

• Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun.
• The laws modified Nicolaus Copernicus' heliocentric theory, replacing its circular orbits and epicenters with elliptical trajectories, and explained how the velocities of the planets varied.
• The three laws state that:
• The orbit of a planet is an ellipse in which the Sun is at one of the two centers.
• A line segment joining a planet and the Sun crosses equal areas during equal time intervals.
• The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.

Additional Information

• Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his own laws of motion and law of universal gravitation.
• The elliptical orbits of planets were indicated by calculations of the orbit of Mars.
• The second law helps to establish that when a planet is closer to the Sun, it travels faster.
• The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa.

The correct answer is Bhikaji Cama.

Key Points

• Bhikaji Cama was one of the pioneers of India's struggle for independence.
• On August 21, 1907, an International Socialist Conference was being held in Stuttgart, a city in Germany.
• On this occasion, Bhikaji Rustam Cama unfurled the first version of the Indian National Flag.
• She was one of a small group that helped design the flag, which represented various elements of the Indian nation and identity.
• She is credited with designing India's first tricolor flag with green, saffron, and red stripes bearing the immortal words – Vande Mataram.
• Bhikaiji Rustam Cama or Madam Cama was born on 24 September 1861 in Bombay.
• She was an outstanding woman of great courage, fearlessness, integrity, perseverance and passion for freedom and is considered the mother of Indian revolution because of her contribution to the Indian freedom struggle.
• After fighting tirelessly for India's freedom struggle on foreign lands for many years, she returned to India and died on August 13, 1936.

Additional Information

• ​Annie Besant :
• Annie Besant was a British socialist, theosophist, women's rights activist, writer, orator, educationist, and philanthropist.
• Regarded as a champion of human freedom, she was an ardent supporter of both Irish and Indian self-rule.
• She was a prolific author with over three hundred books and pamphlets to her credit.
• She worked tirelessly to revive the Hindu faith, its foundational philosophy, and its modes of worship.
• Begum Hazrat Maha :
• Begum Hazrat Mahal, or 'Begum of Awadh', was one of India's first female freedom fighters, leading the battle in the First Indian War of Independence in 1857.
• She is known for the leading role she had in the rebellion against the British East India Company during the Indian Rebellion of 1857.
• Lakshmi Sehgal :
• Lakshmi Sahgal was a revolutionary of the Indian independence movement, an officer of the Indian National Army, and the Minister of Women's Affairs in the Azad Hind government.
• Lakshmi is commonly referred to in India as Captain Lakshmi, a reference to her rank when taken prisoner in Burma during the Second World War.
• She was one of the founding members of the All India Democratic Women's Association in 1981 and led many of its activities and campaigns.

The correct answer is Arunachal Pradesh.

Key Points

• Former Arunachal Pradesh Governor Mata Prasad has passed away at the age of 95.
• He served as a minister in the Congress government in Uttar Pradesh in 1988–89 and was appointed as the governor of Arunachal Pradesh in 1993.
• He is a retired Indian Administrative Service officer.
• The Government of India honored him with the third highest civilian honor of Padma Bhushan in 2012 for his contribution to the civil service.
• Mata Prasad was a resident of the Jaunpur district of Uttar Pradesh.
• Mata Prasad promoted Hindi and wrote several books on Arunachal Pradesh including the book 'Manorambhoomi-Arunachal'.

Additional Information

• As of November 2021:
• Chief Minister of Goa -​ Pramod Sawant
• Chief Minister of Arunachal Pradesh - Pema Khandu
• Chief Minister of Uttar Pradesh - Yogi Adityanath
• Chief Minister of Uttarakhand - Pushkar Singh Dhami

The correct answer is Mountain building.

Key Points 

• Mountain building is formed by the collision of convergent plate boundaries.
• Orogeny, or mountain building, is the result of a collision between two landmasses.
• This can happen through the collision of continental crust (continent-continent collision) or when oceanic and continental crust collide (continent-continent collision).

Additional Information 

• Soil Erosion
• Soil erosion is the loosening and displacement of topsoil particles from the land.
• Soil erosion in nature may be
• a slow process (or geological erosion) or
• a fast process promoted by deforestation, floods, tornadoes, or other human activities.
• Oceanic trenches:
• Trenches are formed through subduction, which occurs when tectonic plates collide and push one plate beneath the other. Trenches can be found all over the surface floor of the ocean at subduction zones.
• The Mariana trench is the deepest known point in the ocean at over 35,000 feet deep.
• Mid-Oceanic Ridges or Submarine Ridges
• A mid-oceanic ridge is composed of two chains of mountains separated by a large depression. [Divergent Boundary]
• The mountain ranges can have peaked as high as 2,500 m and some even reach above the ocean’s surface.
• Running for a total length of 75,000 km, these ridges form the largest mountain systems on earth.
• These ridges are either broad, like a plateau, gently sloping, or in the form of steep-sided narrow mountains.
• These oceanic ridge systems are of tectonic origin and provide evidence in support of the theory of Plate Tectonics.
• Iceland, a part of the mid-Atlantic Ridge, is an example.
• Major Ocean Relief Features
• Four major divisions in ocean relief are:
• the continental shelf,
• the continental slope,
• the continental rise,
• the Deep Sea Plain, or the abyssal plain.

The correct answer is a boar.

Key Points 

• According to the Puranas, Lord Vishnu took the shape of a boar to save the earth, which had drowned in water.
• Vishnu in the form of Varaha - an image from Eran, Madhya Pradesh.
• This magnificent statue is of a special form of Vishnu, Varaha or Boar.
• The idea of ​​Bhakti is present in the Bhagavad Gita, a sacred text of the Hindus, which is included in the Mahabharata.
• Krishna, the Lord asks Arjuna, His devotee and friend, to renounce all religions and take refuge in Him, because only He can free Arjuna from all evil.
• This form of worship gradually spread to different parts of the country.

Additional Information 

• The development of the Bhakti movement took place in Tamil Nadu between the seventh and twelfth centuries.
• It was reflected in the emotional poems of the Nayanars (devotees of Shiva) and Alvars (devotees of Vishnu).
• These saints looked upon religion not as cold formal worship but as a loving bond based upon love between the worshipped and worshipper.
• Originally began in South India in the 9^th century with Shankaracharya spread over all parts of India and by the 16^th century was a great spiritual force to reckon with, especially after the great wave made by Kabir, Nanak, and Shri Chaitanya.

The correct answer is Vitamin C.

Key Points 

• The vitamins are natural and essential nutrients, required in small quantities, and play a major role in growth and development, repair, and healing wounds.
• Types of Vitamins -
• Fat-Soluble Vitamins:
• Fat-soluble vitamins are stored in the fat cells and as the name suggests, these vitamins require fat in order to be absorbed.
• Vitamin A, D, E, and K are fat-soluble vitamins.
• Water-Soluble Vitamins:
• Water-soluble vitamins are not stored in our body as their excess gets excreted through the urine.
• Therefore, these vitamins need to be replenished constantly.
• Vitamin B and C are water-soluble vitamins.​

Additional Information 

• Vitamin B12:
• Vitamin B12, also known as cobalamin, is a water-soluble vitamin involved in the metabolism of every cell of the human body.
• It is a cofactor in DNA synthesis and in both fatty acid and amino acid metabolism.
• Found in fish, poultry, meat, and dairy products.
• Vitamin C:
• Vitamin C is an essential nutrient involved in the repair of tissue and the enzymatic production of certain neurotransmitters.
• Found in citrus fruits and juices, such as oranges and grapefruits.
• Vitamin K :
• Vitamin K refers to structurally similar, fat-soluble vitamers found in foods and marketed as dietary supplements.
• The human body requires vitamin K for post-synthesis modification of certain proteins that are required for blood coagulation or for controlling binding of calcium in bones and other tissues.
• Found in dark green leafy vegetables and in turnip or beet green.

The correct answer is Osman Ali.

Key Points

• Seven Nizams, who were also known as Asaf Jahis, ruled Hyderabad – the seventh, Asaf Jah Nawab Mir Osman Ali Khan Bahadur reigned till 1948.
• From 1724 to 1948, Hyderabad underwent immense growth, both culturally and economically.
• The Nizam chose not to join the Indian Union after India gained independence in August 1947.
• However, his rule ended in September 1948, when the Indian Army launched Operation Polo under the leadership of Sardar Vallabhbhai Patel, the then Home Minister and Deputy Prime Minister of India.
• The State of Hyderabad was invaded and the Nizam was forced to step down.
• The Asaf Jahis were allowed to keep their titles even after their reign ended.
• Asaf Jah VII chose his grandson Nawab Mir Barakat Ali Khan Bahadur Mukarram Jah as his successor, but he was Nizam only in name.

Additional Information

• Nasir Jung
• Mir Ahmed Ali Khan Siddiqi Bayafandi, Nasir Jung, was the son of Nizam-ul-Mulk by his wife Saeed-un-Nisa Begum.
• He was born on 26 February 1712. He succeeded his father as the Nizam of Hyderabad State in 1748.
• He had taken up a title of Humayun Jah, Nizam ud-Daula, Nawab Mir Ahmad Ali Khan Siddiqi Bahadur, Nasir Jung, Nawab Subadar of the Deccan. However, he is most famously known as Nasir Jung.
• The Mughal Emperor Muhammad Shah bestowed him with the title Nasir Jung and later the next Mughal Emperor Ahmad Shah Bahadur appointed him as the Subedar of the Deccan and bestowed him with the title Nasir-ud-Daula.
• His official name was Humayun, Nizam ud-Daula, Nawab Mir Ahmad Ali Khan Siddiqi Bayafandi Bahadur, Nasir Jang, Nawab Subadar of the Deccan.
• He ruled Hyderabad State in India from 1 June 1748 to 1750.
• He was appointed as his father's Deputy during his absence in Delhi from 1737 to 1741.
• In 1741 he attempted to seize power but was defeated by his father at the Eid Gah Maidan in Aurangabad, on 23 July 1741.
• After his father's death, he ascended the throne on 2 June 1748 at Burhanpur.

The correct answer is Malaria.

Key Points 

• Malaria is caused by a parasite that usually infects a certain type of mosquito that feeds on humans.
• The parasites, spread by the female Anopheles mosquito, deposit sporozoites in the skin of the human host.
• World Malaria Day 2020 is being celebrated by the World Health Organization (WHO) on 25 April with the theme 'Zero Malaria Start with Me'.
• Chloroquine is a drug used to prevent and treat malaria, primarily in areas where malaria is sensitive to its effects.​​​​​

Additional Information 

• Goiter is a swelling of the thyroid gland that causes a lump in the front of the neck.
• The lump will move up and down when you swallow.
• The thyroid gland is a small butterfly-shaped gland in the neck, just in front of the windpipe (trachea).
• Pneumonia is an infection that inflames the air sacs in one or both lungs.
• The air sacs may fill with fluid or pus (purulent material), causing cough with phlegm or pus, fever, chills, and difficulty breathing.
• A variety of organisms, including bacteria, viruses, and fungi, can cause pneumonia.
• Plague is a disease that affects humans and other mammals.
• It is caused by the bacterium, Yersinia pestis.
• Humans usually get plague after being bitten by a rodent flea that is carrying the plague bacterium or by handling an animal infected with plague.

The correct answer is Cricket.

Key Points 

• Chinaman
• A Chinaman bowler is basically a left-arm spin bowler who brings the ball into a right-handed batsman using his wrist as the source of spin.
• Usually, a left-arm spin bowler spins the ball away from a right-handed batsman, called orthodox left-arm spin.

Additional Information

• Sports Terminology – Important Sports Terms
• Sports Term of Polo: Polo-Bunker, Mallet, Chukker,  etc.
• Sports Term of Table Tennis: Volley, Late service, Drive spin, Half volley, Backhand, Chop, etc.
• Sports Term of Swimming: Freestyle, Backstroke, Breaststroke, Butterfly stroke, Lane, Pool, Crawl, etc.

The correct answer is Article 279A.

Key Points

• GST Council
• It is a constitutional body under Article 279A.
• It makes recommendations to the Union and State Government on issues related to Goods and Service Tax and was introduced by the Constitution (One Hundred and First Amendment) Act, 2016.
• The GST Council is chaired by the Union Finance Minister and other members are the Union State Minister of Revenue or Finance and Ministers in charge of Finance or Taxation of all the States.
• It is considered as a federal body where both the center and the states get due representation.
• Every decision of the Goods and Services Tax Council shall be taken at a meeting by a majority of not less than three-fourths of the weighted votes of the members present and voting

Additional Information

• In India, GST Bill was first introduced in 2014 as The Constitution (122^nd Amendment) Bill).
• This got approval in 2016 and was renumbered in the statute by Rajya Sabha as The Constitution (101^st Amendment) Act, 2016.
• Its provisions:
• Central GST to cover Excise duty, Service tax, etc, State GST to cover VAT, luxury tax, etc.
• Integrated GST to cover inter-state trade. IGST per se is not a tax but a system to coordinate state and union taxes.
• Article 246A – states have the power to tax goods and services.​
• Excise Duty :
• Excise duty is a form of tax imposed on goods for their production, licensing, and sale.
• Today, excise duty applies only to petroleum and liquor.
• Excise duty was levied on manufactured goods and levied at the time of removal of goods, while GST is levied on the supply of goods and services.
• Value Added Tax :
• Value-added tax (VAT) is a type of indirect tax levied on goods and services for value-added at every point of production or distribution cycle, starting from raw materials and going all the way to the final retail purchase.
• Because the consumer bears the entire tax, VAT is also a consumption tax.
• Service Tax :
• Service tax is a tax levied by the government on service providers on certain service transactions but is actually borne by the customers.
• It is categorized under Indirect Tax and came into existence under the Finance Act, 1994.
• This tax is not applicable in the state of Jammu & Kashmir.

The correct answer is Tall gateway.

Key Points 

• The formal gateway to the iwan is called pishtaq, a Persian term for a portal projecting from the facade of a building, usually decorated with calligraphy bands, glazed tilework, and geometric designs.
• Iwans are most commonly associated with Islamic architecture; however, the form is Iranian in origin and was invented much earlier and fully developed in Mesopotamia around the 3^rd century CE, during the Parthian period of Persia.

Additional Information 

• Mughal Architecture:
• About:
• This is a building style that flourished in northern and central India under the patronage of the Mughal emperors from the mid-16^th to the late 17^th century.
• The Mughal period marked a striking revival of Islamic architecture in northern India. Under the patronage of the Mughal emperors, Persian, Indian, and various provincial styles were fused to produce works of unusual quality and refinement.
• It became so widespread especially in north India that these can be seen further in the colonial architecture of Indo-Saracenic style.
• Important Features:
• Mixed Architecture: It was a blend of Indian, Persian, and Turkish architectural styles.
• Diversity: Different types of buildings, such as majestic gates (entrances), forts, mausoleums, palaces, mosques, sarais, etc.
• Building material: Mostly, red sandstone and white marble were used.
• Speciality: Specific features such as the Charbagh style of the mausoleums, pronounced bulbous domes, slender turrets at the corners, broad gateways, beautiful calligraphy, arabesque, and geometric patterns on pillars and walls, and palace halls supported on pillars.
• The arches, chhatri, and various styles of domes became hugely popular in Indo-Islamic architecture and were further developed under the Mughals.
• Some Examples:
• Taj Mahal:
• Built by Shah Jahan between 1632 and 1653, in memory of his wife Mumtaz Mahal.
• UNESCO recognized the Taj Mahal as a World Heritage Site in 1983. It is located in Agra.
• Red Fort:
• Built by Shah Jahan in 1618 when he decided to move the capital from Agra to Delhi. It was the residence of Mughal rulers.
• UNESCO designated it as the World Heritage Site in 2007.
• Jama Masjid:
• Built by Shah Jahan in Delhi. The construction was completed in 1656.
• Badshahi Mosque:
• Built during the reign of Aurangazeb. At the time of completion in 1673, it was the largest mosque in the world.
• It is located in Lahore, the capital of the Pakistani province of Punjab.​

The correct answer is It envisions a world in which people and planet can thrive in balance.

Key Points 

• 'Doughnut Model' of development
• The Doughnut, or Doughnut economics, is a visual framework for sustainable development – shaped like a doughnut or lifebelt – combining the concept of planetary boundaries with the complementary concept of social boundaries.
• It envisions a world in which people and the planet can thrive in balance.
• The name derives from the shape of the diagram, i.e. a disc with a hole in the middle.
• The center hole of the model depicts the proportion of people that lack access to life's essentials (healthcare, education, equity and so on) while the crust represents the ecological ceilings (planetary boundaries) that life depends on and must not be overshot.

Additional Information 

• Austrian economic thought
• Austrian economic thought talks about methodological individualism or the idea that people will act in meaningful ways which can be analyzed.
• The Austrian school uses the logic of a priori thinking—something a person can think on their own without relying on the outside world—to discover economic laws of universal application, whereas other mainstream schools of economics, like the neoclassical school, the new Keynesians, and others, make use of data and mathematical models to prove their point objectively.
• In this respect, the Austrian school can be more specifically contrasted with the German historical school that rejects the universal application of any economic theorem.
• Keynesian Economics
• Keynesian economics is a macroeconomic economic theory of total spending in the economy and its effects on output, employment, and inflation.
• Keynesian economics was developed by the British economist John Maynard Keynes during the 1930s in an attempt to understand the Great Depression.
• Keynesian economics is considered a "demand-side" theory that focuses on changes in the economy over the short run.
• Laissez-Faire
• Laissez-faire is an economic theory from the 18^th century that opposed any government intervention in business affairs.
• Laissez-faire economics is a key part of free-market capitalism.

The correct answer is Acceptability.

Key Points

• Food security, as defined by the United Nations’ Committee on World Food Security, means that all people, at all times, have physical, social, and economic access to sufficient, safe, and nutritious food that meets their food preferences and dietary needs for an active and healthy life.
• Food security is the combination of the following three elements:
• Food availability i.e. food must be available in sufficient quantities and on a consistent basis. It considers stock and production in a given area and the capacity to bring in food from elsewhere, through trade or aid.
• Food access i.e. people must be able to regularly acquire adequate quantities of food, through purchase, home production, barter, gifts, borrowing, or food aid.
• Food utilization: Consumed food must have a positive nutritional impact on people. It entails cooking, storage and hygiene practices, individuals health, water and sanitation, feeding and sharing practices within the household.

Additional Information

• The National Development Council (NDC) in its 53^rd meeting held on 29^th May 2007 adopted a resolution to launch a Food Security Mission comprising rice, wheat, and pulses to increase the annual production of rice by 10 million tonnes, wheat by 8 million tonnes, and pulses by 2 million tonnes by the end of the Eleventh Plan (2011-12).
• Accordingly, a Centrally Sponsored Scheme, 'National Food Security Mission (NFSM)', was launched in October 2007.
• The approximate percentage of funds allocated for pulses under the National Food Security Mission for 2017-18 is 60%.

The correct answer is Gulzarilal Nanda.

Key Points

• Gulzarilal Nanda never became the Vice President of India.
• He served as the secretary of the Indian Labor Welfare Organization and as the chairman of the Bombay Housing Board.
• He was also a member of the National Planning Committee.
• He was largely instrumental in organizing the Indian National Trade Union Congress and later became its President.
• He was the former Prime Minister of India for two short periods after the death of Jawaharlal Nehru in 1964 and Lal Bahadur Shastri in 1966.
• The Government of India honored Nanda with the Bharat Ratna Award in 1997.

Additional Information

• ​Varahagiri Venkata Giri:
• He was the fourth president of India from 24 August 1969 to 24 August 1974.
• VV Giri was Vice-President and ex officio Chairman of the Rajya Sabha from 13 May 1967 to 3 May 1969 and Acting President from 3 May 1969 to 19 July 1969.
• He was the only president to be elected as an independent candidate.
• He was succeeded by Fakhruddin Ali Ahmed as president in 1974.
• He was honoured by the Government of India with the Bharat Ratna in 1975.
• In 1922, he was arrested for the first time for demonstrating against the sale of liquor shops.
• Zakir Husain Khan:
• He was an Indian economist and politician who served as the third president of India, from 13 May 1967 until his death on 3 May 1969.
• He was the first Muslim president of India and the first Indian president to die in office.
• He previously served as the governor of Bihar from 1957 to 1962 and as the second vice president of India from 1962 to 1967.
• He was awarded the Bharat Ratna, India's highest civilian honour, in 1963.
• Basappa Danappa Jatti:
• He was the fifth vice president of India, serving from 1974 to 1979.
• He was acting president of India from 11 February to 25 July 1977.
• The soft-spoken Jatti rose from a humble beginning as a Municipality member to India's second-highest office during a five-decade-long chequered political career.
• He was appointed Minister of Health and Labour of the then Bombay Government and held that post till the reorganization of states.'
• His autobiography, 'I'm my own model', is very popular.

The correct answer is Seven.

 Key Points

• The halogens are a group in the periodic table that consists of five or six chemically related elements: fluorine, chlorine, bromine, iodine (I), and astatine.
• Halogens have 7 electrons in their outermost shell.
• The boiling points of halogens tend to move down the group due to the increasing strength of van der Waals forces as the size and relative atomic mass of the atoms increase.
• Halogens are the only periodic table group containing elements in all three familiar states of matter (solid, liquid, and gas) at standard temperature and pressure.
• Halogens are highly reactive, and they can be harmful or even fatal to biological organisms in sufficient quantities.
• This reactivity is due to the high electronegativity and high effective nuclear charge.
• Halogens can react with atoms of other elements to gain an electron.

Additional Information

• The elements of Group 2 include beryllium, magnesium, calcium, strontium, barium, and radium.
• These elements with the exception of beryllium are commonly known as alkaline earth metals.
• These elements are called Alkaline Earth metals because of two reasons:
• Their oxides exist in the earth’s crust and are very stable to heat.
• Their oxides and hydroxides show basic (alkaline) natures.
• Beryllium fulfills the first criterion but not the second one since its oxides and hydroxides show amphoteric behavior, rather than alkaline.

The correct answer is Ramchandra Guha.

Key Points

• The book "Democrats and Dissenters" is written by Ramachandra Guha.
• The book consists of 16 essays on a wide range of issues such as India's relations with its neighbours, freedom of expression, discrimination against tribals.

Additional Information

• Ramachandra is an Indian historian, writer, and public intellectual whose research interests include social, political, contemporary, environmental, and cricket history, and the field of economics.
• He is also a columnist for The Telegraph, Hindustan Times, and Hindi daily newspaper Amar Ujala.
• He has also written for The Caravan and Outlook magazines.
• The American Historical Association (AHA) has conferred its Honorary Foreign Member prize for the year 2019 on Ramchandra Guha.
• Nalini Singh: 
• Nalini Singh is a New Zealand author of Indo-Fijian descent.
• She has authored numerous paranormal romance novels.
• Alpha Night won the Favourite Paranormal Romance at the 2020 Australian Romance Readers Awards.

The correct answer is Uttarakhand.

Key Points

• Ranikhet is at an altitude of 1,869 meters above sea level and is within sight of the western peaks of the Himalayas.
• Ranikhet is a hill station and cantonment town in Almora district in the Indian state of Uttarakhand.
• Mankameshwar, Haidakhan Temple, Jhula Devi and Ram Mandir are the revered temples near Ranikhet.​

Additional Information

• The Aravalli Range is a mountain range in Northwestern India, running approximately 670 km in a southwest direction, starting near Delhi, passing through southern Haryana and Rajasthan, and ending in Gujarat.
• The highest peak is Guru Shikhar at 1,722 meters.
• Malwa Plateau, plateau region in north-central India.
• It is bounded by the Madhya Bharat Plateau and Bundelkhand Upland to the north, the Vindhya Range to the east and south, and the Gujarat Plains to the west of volcanic origin, the plateau comprises central Madhya Pradesh state and southeastern Rajasthan state.
• Dodda Betta is the highest mountain in the Nilgiri Mountains at 2,637 meters (8,652 feet).
• There is a reserved forest area around the peak.
• It is 9 km from Ooty, on the Ooty-Kotagiri Road in the Nilgiris District of Tamil Nadu, India.
• Mahendragiri is a mountain in the Rayagada subdivision of the district of Gajapati, Odisha, India.
• It is situated amongst the Eastern Ghats at an elevation of 1,501 meters.
• The Western Ghats
• The Western Ghat is a region where there is a high number of species and biodiversity.

The correct answer is dance form.

Key Points

• Bolak-aat is a folk dance form of Karnataka.
• It is believed that Lord Vishnu, on his mission to kill the evil spirit 'Bhasmasura', performed 30 different dance forms, and ‘Bolkat’ is one among them.
• The dancers dress up in traditional Kodava dress and are Performed by Kodava men in the back of an oil lamp in an open field.
• The performers hold 'chavari', Yak-animal's fur on one hand and 'Kodava', (Sickle) on another hand.
• If only the sickle is used in the dance, then it is called 'kattiyaata'.
• The musical instrument used for this dance is called ‘Dudi’.
• The theme of the dance is based on the heroic activities of the Kodava gods and goddesses.

Additional Information

• The origin of the Bagurumba may be found in the original naturalistic beliefs of the Bodo tribes, as its few songs are just simple images of nature.
• This dance is an amalgamation of rhythm and vivacity.
• More folk dances of Assam Bihu dance, Bhortal Dance, Jhumur Dance.
• Kalbelia dance
• Kalbelia dance is a folk dance of the Rajasthan state of India. Also, known as It is well known as the 'Sapera Dance' or 'Snake Charmer Dance'.
• It is mainly performed by a Rajasthani tribe called 'Kalbelia'.
• It is listed under UNESCO's representative list of the Intangible Cultural Heritage of Humanity from the year 2010.
• The Mudiyettu, the ritual dance-drama annually performed after the harvest of summer crops in Kerala.
• This art form involves elaborate drawings on floors, masks made of areca nut fronds, and the playing of drums.
• The Chhau dance, known for its crafted masks and mock combat movements, is prevalent in the tribal parts of Orissa, Jharkhand, and West Bengal.

The correct answer is Amuktamalyada.

Key Points

• Krishnadevaraya, the most famous ruler of Vijayanagara, composed a work on statecraft in Telugu known as the Amuktamalyada. 
• About traders he wrote :
• A king should improve the harbors of his country and so encourage its commerce that horses, elephants, precious gems, sandalwood, pearls, and other articles are freely imported.
• He should sailors who land in his country on account of storms, illness and exhaustion are looked after in a suitable manner.
• Amuktamalyada describes the story of the wedding of the Hindu Lord Ranganayaka an avatar of Vishnu and Goda Devi aka Andal the Tamil Alvar poet and daughter of Periyalvar, at Srirangam.
• Krishnadevaraya was the king of the Vijayanagara Empire reigning between 1509–1530.
• He was the third ruler of the Tuluva Dynasty and presided over the Vijayanagara empire at its zenith.
• Krishnadevaraya built huge irrigation tanks and reservoirs for harvesting rainwater.
• He distributed the wealth he gained in wars to all major temples of South India for the purpose of constructing temple gateways (gopura), called 'Rayagopuram,' in his honour.

Additional Information

• Vijayanagara Empire:
• Vijayanagara or “city of victory” was the name of both a city and an empire.
• The empire was founded in the fourteenth century (1336 AD) by Harihara and Bukka of the Sangama dynasty.
• They made Hampi the capital city.
• In 1986, Hampi was declared a World Heritage site by UNESCO.

The correct answer is 24 January.

Key Points

• National Girl Child Day in India is celebrated on January 24 every year.
• National Girl Child Day was first initiated in 2008 by the Ministry of Women and Child Development to : 
• Spread awareness among people about all the inequalities faced by girls in the country.
• Promote awareness about the rights of a girl child.
• Increase awareness on the importance of girls' education, health, and nutrition.
• The objective behind celebrating the National Girl Child Day is to provide support and opportunities to the girls of India.

Additional Information

• Several campaigns and programs such as Save the Girl Child, Beti Bachao Beti Padhao, free or subsidized education for the girl children, reservations for women in colleges and universities have been initiated to reduce this discrimination.
• The purpose of this day is to spread awareness about the gender-based discrimination that girls face in our society and to bring change in the attitude towards girls.
• According to a government press release, National Girl Child day 2021 is being celebrated across the country to raise awareness on the issue of the declining Child Sex Ratio (CSR).
• While Punjab has announced January 2021 to be the “month of the girl child", the scheme Dheeiyan Di Lohri has also been launched.
• Odisha government has decided to honour individuals and organizations who have worked towards mitigating child marriage on National Girl Child Day.

The correct answer is Uttarakhand.

Key Points

• Tapovan Vishnugarh Power Plant is a 520MW run-of-river project being built on the Dhauliganga River in the Chamoli district of Uttarakhand, India.
• It was constructed by National Thermal Power Corporation Limited (NTPC) on the Dhauliganga river in the Chamoli district of Uttarakhand.
• The Tapovan Vishnugarh Hydroelectric Project will consist of four 130MW Pelton turbines and a barrage built on the Dhauliganga River.
• The barrage will be 200 meters long and 22 meters high and will have four gates 12 meters high and 14 meters wide.
• The construction of the Tapovan-Vishnugarh HEP started in November 2006 and was scheduled to be commissioned in 2012-2013, with the first unit scheduled to go online in September 2012, although it did not go as planned.

Additional Information

• ​Seven projects, all in Uttarakhand**, have been allowed to complete construction primarily on the ground that they were over 50% complete.**
• The seven projects are the:
• Tehri Stage 2: 1000 MW on Bhagirathi river
• Tapovan Vishnugadh: 520 MW on Dhauliganga river
• Vishnugadh Pipalkoti: 444 MW on Alaknanda river
• Singoli Bhatwari: 99 MW on Mandakini river
• Phata Bhuyang: 76 MW on Mandakini river
• Madhyamaheshwar: 15 MW on Madhyamaheshwar Ganga
• Kaliganga 2: 6 MW on Kaliganga river

The correct answer is Eight.

Key Points

• Prime Minister Narendra Modi has flagged off eight trains connecting the Statue of Unity in Kevadiya, Gujarat with different regions of the country through video conferencing.
• PM Modi informed that it was the first time in history that so many trains from different locations were flagged off for a common destination.
• The trains flagged off by Prime Minister today will connect Kevadiya from Varanasi in Uttar Pradesh, Dadar in Maharashtra, Ahmedabad in Gujarat, Nizamuddin in Delhi, Rewa in Madhya Pradesh and Chennai in Tamil Nadu. A MEMU train to and fro Pratapnagar from Kevadiya was also inaugurated.

Additional Information

• PM also inaugurated other railway projects in Kevadiya, including Dabhoi-Chandid gauge, converted broad gauge rail line, Chandod-Kevadiya new broad gauge rail line, Pratapnagar-Kevadiya newly electrified section, and new station buildings of Dabhoi Junction, Chandod, and Kevadiya.
• These trains will facilitate seamless connectivity to the Statue of Unity.
• Gujarat Chief Minister Vijay Rupani and Union Railway Minister Piyush Goyal were also present on the occasion.
• The Prime Minister stressed the need for skilled and specialist manpower and professionals to meet the requirement of the Railways' transformation.

The correct answer is Bones.

Key Points

• Rickets is a preventable bone disease that affects infants and young children and causes soft and weakened bones.
• Rickets is caused by a lack of vitamin D, calcium, or phosphorus.
• Vitamin D deficiency can occur as a result of having dark skin, lack of exposure of the skin to sunlight, nutritional deficiencies, and disorders of the liver, kidney, or small intestine.
• Treatment options include improved sunlight exposure, diet, vitamin D, and mineral supplements.
• Rickets is most common in children who are between 6 and 36 months old.
• During this time period, children usually experience rapid growth.

Additional Information

• ​Signs and symptoms of rickets :
• Painful bones, muscle weakness, cramps, and spasms.
• Slowed growth and development.
• Increased risk of broken bones, including spontaneous breaks that occur by themselves without pressure or trauma.
• Dental problems such as teeth failing to form or being slow to emerge, deformed teeth, or soft tooth enamel.
• Prominent forehead and a large front fontanelle in infants.
• Vitamin D is a steroid hormone that is produced in the skin by the action of sunlight’s ultraviolet rays on its precursor, 7-dehydrocholesterol (provitamin D3).

The correct answer is Russia.

Key Points

• India and Russia have become the joint winners of the FIDE online Chess Olympiad.
• World chess governing body FIDE declared both the finalists as joint winners after at least two games in the second match were affected by internet connectivity issues.
• India and Russia were declared joint winners of the 2020 Online FIDE Chess Olympiad after the final was marred by internet disconnection.
• Russia was initially declared winners after 2 Indian players, Nihal Sarin and Divya Deshmukh, lost out on time in the final after suffering a disconnection with the server.
• India had appealed against the controversial decision.
• The international chess federation Fide's president Arkady Dvorkovich decided to award the gold medal to both teams.

Additional Information

• The FIDE Online Chess Olympiad was held for the first time due to the coronavirus pandemic.
• The first round of the final ended in a 3-3 draw with all six games finishing in a stalemate.
• Russia won the second round 4.5-1.5 with wins for Andrey Esipenko over Sarin and Polina Shuvalova over Deshmukh, leading to controversy as the Indians claimed the losses were due to connection issues.
• In the second round, Anand, coming in for P Harikrishna, had drawn with Ian Nepomniachtchi while captain Vidit Gujrathi drew with Daniil Dubov.
• This is the biggest team championship in chess as around 163 countries took part in the online tournament.​
• The Indian team comprised of the following players:
• Vidit Gujrathi (captain), Viswanathan Anand, Pendyala Harikrishna, Koneru Humpy, Dronavalli Harika, R. Vaishali, Bhakti Kulkarni, Nihal Sarin, R. Praggnanandhaa, Aravindh Chithambaram, R. Vaishali, Bhakti Kulkarni, Divya Deshmukh and Vantika Agrawal.

The correct answer is Sanjeev Kumar.

Key Points

• Shri Sanjeev Kumar, Director (Technical), MTNL has been appointed as the Chairman-cum-Managing Director of Telecommunications Consultants India Limited.
• The Appointments Committee of the Cabinet (ACC) has approved the appointment of Sanjeev Kumar.
• According to an order of the Department of Personnel and Training (DoPT), he has been appointed to the post for a period of five years from the date of joining the post or till the age of superannuation or until further orders. , whichever is earlier.
• He is presently working as Director (Technical) in Mahanagar Telephone Nigam Limited (MTNL).

Additional Information

• ​Telecommunications Consultants India Limited (TCIL):
• It is a Miniratna PSU under the administrative control of the Department of Telecommunications, Ministry of Communications. TCIL, a premier telecommunication consultancy, and engineering company is making available its vast and varied telecom expertise to friendly developing countries.
• Founded in 1978
• Headquarters - New Delhi.

Given:

The ratio of present age of mother to that of the daughter = 7 : 1

After 5 years the ratio will become = 4 : 1

Calculation:

Let the present age be x

Then,

According to the given question

⇒ (7x + 5)/(x + 5) = 4/1

⇒ 7x + 5 = 4x + 20

⇒ 3x = 15

⇒ x = 5

Present age of mother = 7x = 7 × 5 = 35

Present age of daughter = x = 5

Required difference = (35 – 5) = 30 years

∴ The difference in their present ages is 30

Given:

 3cos2θ - 4sinθ + 1 = 0

Formula used:

cos²θ = 1 – sin²θ 

Calculation:

 3 cos2θ - 4sinθ + 1 = 0

⇒ 3(1 – sin²θ) – 4 sinθ + 1 = 0

⇒ 3 – 3sin²θ – 4 sinθ + 1 = 0

⇒ -(3sin²θ) – 4 sinθ + 4 = 0

⇒ 3sin²θ + 4 sinθ – 4 = 0

⇒ 3sin²θ + 6sinθ – 2sinθ – 4 = 0

⇒ 3sinθ(sinθ + 2) – 2(sinθ + 2) = 0 

⇒ (3sinθ – 2) = 0 and (sinθ + 2) = 0

⇒ sinθ = 2/3, sinθ = -2 (not possible as range of sin is -1 to +1).

In Δ ABC

⇒ AC² = AB² + BC²

⇒ BC² = AC² –  AB²

⇒ BC = √(AC² – AB²)

⇒ √(3² – 2²)

⇒ √(9 – 4)

⇒ √5

tanθ = P/B = 2/√5

secθ = H/B = 3/√5

⇒ tanθ + secθ = 2/√5 + 3/√5

⇒ 5/√5

⇒ √5

∴ The required value is √5

Given:

Area of square = 784 cm²

Formula used:

Area of square = side²

Area of circle = πr² 

Calculation:

Area of square = 784 cm²

⇒ a² = 784 cm²

⇒ a = 28 cm

Side = Diameter of circle = 28 cm

Radius of circle = 28/2 cm = 14 cm

Area of the circle = πr²

⇒ 22/7 × 14 × 14 cm²

⇒ 616 cm²

∴ Area of circle inscribed in a square is 616

Given:

∠A = 90° 

 AD ⊥ BC at D

AB = 12 cm

AC = 16 cm

Concept used:

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Calculation:

AB² + AC² = BC²

⇒ 12² + 16² = BC²

⇒ 144 + 256 = BC²

⇒ 400 = BC²

⇒ 20 = BC

Now, using similarity of triangle ABC and DBA.

$BC\over AB$ = $AB\over BD$ = $AC\over AD$

Length of BD = (AB × AB) / BC

⇒ (12 × 12)/20 = 7.2

So, the Length of BD is 7.2 cm.

Given:

Distance covered by train at a certain uniform speed = 75 km

Distance covered by train at 10 km/h more than the normal speed = 90 km

Total time taken to complet

⇒ e the journey = 3 hours

Formula used:

Time = Total distance ÷ Speed

Calculation:

Let the speed at which it cover first 75 km be x km/hr

Now, according to the question

(75/x) + [90/(x + 10)] = 3 hours

⇒ (75x + 750 + 90x)/(x² + 10x) = 3

⇒ 3x² + 30x = 165x + 750

⇒ 3x² - 135x - 750 = 0

⇒ 3x² - 150x + 15x - 750 = 0

⇒ 3x(x - 50) + 15(x - 50) = 0

⇒ (3x + 15) (x - 50) = 0

⇒ x = 50, -5

As speed can't be in negative, so, speed will be 50 km/hr

Time to cover 300 km = 300/50 hours

⇒ 6 hours

∴ Time to cover 300 km is 6 hours

Given:

Work done by A = 15 days

B is 25% more efficient than A

A and B worked together = 4 days

C alone completed the remaining work = 8 days

Formula used:

Work done = Time × Efficiency

Calculation:

B is 25% more efficient than A

⇒ (15 × 100/125) 

⇒ 12 days

B can do the work on 12 days

Now,

 LCM of 15 and 12 is 60

A's 1 day work = 4 units

B's 1 day work = 5 units

Work done by A and B work together for 4 days = (4 + 5) × 4 = 36 work

 Work left  = 60 – 36 = 24 units

C can do the remaining work = 24/8 units = 3 units

Now, A, B and C completed the whole work = 60/(4 + 5 + 3)

⇒ 60/12 days

⇒ 5 days

∴ A, B, and C completed the same work together in 5 days

Given:

a³ + b³ = 405

a + b = 9

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

Substituting the values in the formula

⇒ (9)³ = 405 + 3ab (9)

⇒ 729 = 405 + 27ab

⇒ 27ab = 324

⇒ ab = 12

∴ The value of ab is 12

Given:

The length of one chord (AB) = 6 cm

The radius of the circle (OA or OC)  = 5 cm

MN = 7 cm, CD = ?

Formula used:

Using Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

h = Hypotenuse, p = Perpendicular, and b = Base

Calculation:

Using Pythagoras Theorem,

OM = $\sqrt{(OA)^2-(MA)^2}$

⇒ $\sqrt{(5)^2-(3)^2}$ = $\sqrt{16}$ = 4 cm

⇒ OM = 4 cm

ON = MN - OM

⇒ ON = 7 - 4 = 3 cm

Again, Using Pythagoras Theorem,

NC = $\sqrt{(OC)^2-(ON)^2}$

⇒ $\sqrt{(5)^2-(3)^2}$ = $\sqrt{16}$ = 4cm

⇒ NC = DN = 4 cm

DC = NC + DN 

⇒ DC = 4 + 4 = 8cm

∴ The required answer is 8 cm.

Calculation:

The total number of students enrolled for VC in institutes A, C and E in 2016 = (135 + 138 + 147)

⇒ 420

The total number of students enrolled in institutes B and D in 2018 = (142 + 138)

⇒ 280

Required ratio = (420 : 280)

⇒ 3 : 2

∴ The required ratio is 3 : 2

Given:

$\left(2x-\frac{3}{x}\right)=2$

Formula used:

If x – 1/x = a

then x⁴ + 1/x⁴ = (a² + 2)² – 2

Calculation:

$\left(2x-\frac{3}{x}\right)=2$

Squaring both sides, we get

⇒ (2x – 3/x)² = (2)²

⇒ 4x² + 9/x² = 4 + 2 × 2 × 3

⇒ 4x² + 9/x² = 16

Now,

$\left(16x^4+\frac{81}{x^4}\right)$ = (16)² – 2 × 4 × 9

⇒ 256 – 72

⇒ 184

∴ The value of  $\left(16x^4+\frac{81}{x^4}\right)$ is 184

Given:

∠ABC = 34° 

CD = BD

Calculation:

∠ACB = 90° 

In Δ BCD

∠ B = ∠ C = ?, due to BD = CD

In cyclic quadrilateral ABDC

∠ ACD + ∠ DBA = 180^o

⇒ 90^o + ? + 34^o + ? = 180^o

⇒ 2 ? = 180 - 124

⇒ ? = 56/2

⇒ ? = 28° 

⇒ ∠DBC = 28° 

So, the measure of ∠DBC is 28°

Calculation:

Trees were planted in Ahmedabad from 2016 to 2020 = (2500 + 2300 + 2400 + 1950 + 2100)

⇒ 11250

Trees were planted in Pune from 2016 to 2020 = (1800 + 1850 + 1840 + 1900 + 2000)

⇒ 9390

Required difference = 11250 – 9390

⇒ 1860

∴ Required difference is 1860

Given:

Average of 22 numbers = 37.5

Average of first 12 numbers = 40.6

Average of last 12 numbers = 35.4

Formula used:

Sum of observations = Average × Number of Observations

Calculation:

Sum of all 22 numbers = 37.5 × 22

⇒ 825

Sum of first 12 numbers and last 12 numbers = (40.6 × 12) + (12 × 35.4)

⇒ 912

Sum of 11^th and 12^th number = (912 - 825)

⇒ 87

Now, Sum of remaining 20 numbers = (825 - 87)

⇒ 738

Average of 20 numbers = 738/20

⇒ 36.9

∴ Average of remaining numbers is 36.9

Given:-

$\frac{cosec θ+\cot θ}{cosec θ-\cot θ}=7$

Concept used :-

Pythagoras's theorem and Trigonometric ratio.

Calculation:

According to question -

⇒ cosecθ + cotθ = 7cosecθ – 7cotθ 

⇒ 6cosecθ – 8cotθ = 0

⇒ 3cosecθ = 4cotθ 

⇒ 3 × 1/sinθ = 4 × cosθ/sinθ  

⇒ 3/sinθ = 4cosθ/sinθ 

⇒ cosθ = 3/4

By pythagoras theorem

P² = h² – b²

p² = 4² – 3²

p² = 16 – 9

p² = 7

⇒ p = √7

Now,

The value of $\frac{4\sin^2\theta-1}{4\sin^2\theta+5}$ = (4 × 7/16 – 1)/(4 × 7/16 + 5)

⇒ (7/4 – 1)/(7/4 + 5)

⇒ (3/4)/(27/4)

⇒ 3/27

⇒ 1/9

∴ The value is 1/9

Given:

x + y + z = 2 and xy + yz + zx = -11

Formula used:

(x + y + z) (x² + y² + z² – xy – yz – zx) = x3 + y3 + z3 - 3xyz

Calculation:

x + y + z = 2

⇒ (x + y + z)² = 4

x² + y² + z² + 2xy + 2yz + 2zx = 4

⇒ x2 + y2 + z² = 4 – 2 × (-11) = 26

Putting the values in the given formula we get,

⇒ 2 × [26 – (-11)]

⇒ 2 × 37

⇒ 74

∴ The required value is 74

Given:

1 + 2tan2θ + 2sinθ sec2θ = ?, 0° < θ < 90°

Formula used:

1.1 – sin2θ = cos²θ

2. tanθ = sin θ/cosθ 
3. (a + b)² = a² + 2ab + b²
4. (a + b)(a - b) = a² - b² 

Calculation:

1 + 2tan2θ + 2 sinθ sec2θ

⇒ 1 + 2sin²θ/cos²θ + 2sinθ/cos²θ 

⇒ [cos²θ + 2sin²θ + 2sinθ]/cos²θ

Using the formula (1),

⇒ [1 – sin²θ + 2sin²θ + 2sinθ]/[1 - sin2θ]

⇒ [1 + sin²θ + 2sinθ]/[1 - sin²θ] 

Using the identity (3) & (4), we get

⇒ (1 + sinθ)²/(1 – sinθ) (1 + sinθ)

⇒ 1 + sinθ/(1 – sinθ)

So, the value of 1 + 2 tan2 θ + 2 sin θ sec2 θ is $\frac{1+\sin\theta}{1-\sin\theta}$

Given:

The income of A = 30% less than the income of B

The income of B = 137.5% more than that of C

Income of A = Rs. 28500 less than that of B

Calculation:

Let the income of A be Rs. A, B be Rs. B and C be Rs. C respectively

Income of B is 137.5% more than that of C 

⇒ B = C × (100 + 137.5)/100

⇒ B = C × (2375/1000)

⇒ B = Rs. 19C/8 ......(1)

Income of A is 30% less than the income of B

⇒ A = B × (100 – 30)/100

⇒ A = B × 70/100

Substituting the value of B in equation (1)

⇒ A = (19C/8) × 7/10

⇒ A = 133C/80 .......(2)

Difference between B's income and A's income = Rs. 28500

⇒ B – A = 28500

Substituting the values of A and B from equation (1) and (2)

⇒ 19C/8 – 133C/80 = 28500

⇒ (190C – 133C)/80 = 28500

⇒ 57C/80 = 28500

⇒ C = (28500 × 80)/57

⇒ C = 500 × 80

⇒ C = Rs. 40000

∴ The income of C is Rs. 40000

Alternate Method137.5% = 100% + 37.5% = 1 + 3/8 = 11/8

Let income of C be 8

Then, income of B = 19

Income of A is 30% less than the income of B,

⇒30/100 × 19 = 5.7

Thus, Income of A = 19 - 5.7 = 13.3

Difference of incomes of A and B = 5.7

Actual Difference = 28500

5.7-----------28500

1-----------5000

∴ Income of C = 5000 × 8 = Rs. 40,000

Given:

Marked Price = Rs. 10,000

Three discounts = 20%, 10% and k%

Selling Price = Rs. 6120

Formula used:

SP = MP × [(100 - Discount%)/100]

Calculation:

SP after 1^st discount = Rs. 10,000 × [80/100]

⇒ Rs. 8,000

SP after 2^nd discount = Rs. 8,000 × [90/100]

⇒ Rs. 7,200

Final discount = Rs. (7,200 – 6,120)

⇒ Rs. 1,080

Discount% = Rs. (1,080/7,200) × 100

⇒ 15%

Single discount of (K + 20) = (15 + 20)%

⇒ 35%

Now, SP after 35% discount = Rs. (10,000 × 35%)

⇒ (10,000 × 35/100)

⇒ Rs. 3,500

Selling price = Rs. (10,000 – 3,500)

⇒ Rs. 6,500

∴ Required selling price is Rs. 6,500

Calculation:

The total number of students enrolled for VC in institute C in 2013, 2014 and 2017 = (125 + 120 + 140)

⇒ 385

The total number of students enrolled in all the five institutes in 2018 = (140 + 142 + 135 + 138 + 145)

⇒ 700

Required percentage = 385/700 × 100

⇒ 385/7

⇒ 55

∴ Required percentage is 55

Calculation:

To check the divisibility by 88, it should be divisible by 11

Difference of sum of alternative terms should be 0

⇒ 5 + 4 + 3 = x + 2 + y

⇒ x + y = 10

To check the divisibility by 88, it should be divisible by 8

Last three digit should be divisible by 8

23y should be divisible by 8

For least value of y = 2, 23y is divisible by 8

For y = 2 and x = 8

the value of (5x – 8y) = (5 × 8 – 8 × 2)

⇒ 40 – 16 = 24

∴ The value of (5x – 8y) is 24

Given:-

Angle between bisectors of ∠B and ∠C = 132°   

Concept:

If bisector of angles ∠B and ∠C of a triangle ABC meets at I then ∠BIC = 90° + 1/2 ∠A

Calculation:

∠BIC = 132° 

∠BIC = 90° + 1/2 ∠A

∠A/2 = (132° – 90°)

⇒∠A/2 = 42° 

⇒ ∠A = 42 × 2 

⇒ ∠A = 84° 

∴ The value of ∠A is 84°

Calculation:

Arrears of Amit and Suresh = (6000 + 6300)

⇒ 12300

Arrears of Nitin and Varun = (5000 + 7500)

⇒ 12500

Required difference = (12500 – 12300)

⇒ 200

Required percentage = 200/12500 × 100

⇒ 200/125

⇒ 8/5

⇒ 1.6

∴ The Arrears of Amit and Suresh taken together less than the Arrears of Nitin and Varun taken together is 1.6

Given:

A = 9075

P = 7500

R = 10%

Formula used:

A = P(1 + r/100)ⁿ

SI = (P × R × T)/100

where,

A = Amount

P = Principal

r = Rate of Interest

n = number of years

SI = Simple Interest

Calculation:

A = P (1 + r/100)ⁿ

⇒ 9075 = 7500( 1 + 10/100)^T

⇒ 9075/7500 = (1 + 1/10)^T

⇒ 121/100 = (11/10)^T

⇒ (11/10)² = (11/10)^T

⇒T = 2 years

Now, 

P = 7500

R = 10%

T = 2 years

SI = P × R × T/100

⇒ (7500 × 10 × 2)/100

⇒ 1500

∴ The simple interest is 1500

Calculation:

$\frac{52-1170÷26+13×2}{2+1\frac{1}{8}\ \rm of\ 2-1\frac{1}{4}}$

⇒ (52 – 1170 ÷ 26 + 13 × 2)/(2 + 9/8 of 2 – 5/4)

⇒ (52 – 45 + 13 × 2)/(2 + 9/8 of 2 – 5/4)

⇒ (52 – 45 + 26)/(2 + 9/8 of 2 – 5/4)

⇒ (52 – 45 + 26)/(2 + 9/4 – 5/4)

⇒ (33)/(8 + 9 – 5)/4

⇒ (33)/(12/4)

⇒ 33/3

⇒ 11

∴ The value is 11

Given:

When article sold at Rs. 246.80 it gains

When article sold at Rs. 216 it losses

Gain is 20% more than the loss

Gain or loss when article sold at Rs. 220.75

Formula used:

Loss = cost price –  selling price

Profit = selling price –  cost price

Loss% = (Loss/cost price) × 100

Calculation:

Let the cost price be x

It losses when selling price = Rs. 216

⇒ Loss = (x – 216)     ----(1)

It gains when selling price = Rs. 246.80

⇒ Gain = (246.80 –  x)

According to the question

(246.80 – x) = (x – 216) × (120/100)

⇒ 2468 –  10x = 12x –  2592

⇒ 22x = 5060

⇒ x = 230

So, cost price = Rs. 230

Now,

Selling price = 220.75

⇒ Loss = 230 – 220.75

⇒ Loss = 9.25

⇒ Loss% = (9.25/230) × 100

⇒ Loss% = 4.02% ~ 4%

∴The loss percent is 4%

The correct answer is 'voluminous'.

Key Points

• 'Souvenir' is a thing that is kept as a reminder of a person, place, or event. (यादगार)
• Example: The recording provides a souvenir of a great production.
• 'Voluminous' means having or marked by great volume or bulk; large. (विशाल-काय)
• Example: A voluminous purple cloak.
• In the given sentence, it is clearly mentioned that a large souvenir will be released on the occasion of the World Meet.
• Some synonyms of the word 'voluminous' are large, bulky, ample, abundant, massive.
• Some antonyms of the word 'voluminous' are little, small, slight, tiny.
• Therefore, the most appropriate option to be filled in the given blank is 'voluminous'.
• Hence, option 2 is the correct answer.

The complete sentence is: A voluminous souvenir will be released on the occasion of the World Meet.

Additional InformationLet's learn about other given options:

• 'Considerable' means notably large in size, amount, or extent. (पर्याप्त)
• Example: A position of considerable influence.
• 'Generous' means showing a readiness to give more of something, as money or time, than is strictly necessary or expected. (उदार)
• Example: She was generous with her money.
• 'Bountiful' means large in quantity. (भरपूर)
• Example: The ocean provided a bountiful supply of fresh food.

The correct answer is 'Hangar'.

Key Points

• 'Hangar' is a covered and usually enclosed area for housing and repairing aircraft. (विमान घर)
• Example: On take-off, he almost crashed into a hangar.
• Therefore, the most appropriate word for the given sentence is 'hangar'.
• Hence, option 3 is the correct answer.

Additional InformationLet's learn about other given options:

• 'Shed' means a simple roofed structure, typically made of wood or metal, used as a storage space, a shelter for animals, or a workshop. (छप्पर)
• Example: A bicycle shed.
• 'Airport' means a complex of runways and buildings for the takeoff, landing, and maintenance of civil aircraft, with facilities for passengers. (हवाई अड्डा)
• Example: They arrived late at the airport.
• 'Bam' is used to show that something happened very suddenly or quickly. 
• Example: I wrote the order and bam, I sent it off.

The correct answer is "the teacher's".

Key Points

• In the given sentence the error lies in the part "the teacher's".
• We use an apostrophe +"s" to show that one person/thing owns or is a member of something.
• Example: The shop's customers.
• We use an apostrophe after the "s" (s') at the end of a plural noun to show possession.
• If a plural noun doesn't end in "s," add an apostrophe + "s" to create the possessive form.
• We use 's' to pluralize the regular nouns.
• Example: I have one cat; you have two cats.
• In the given sentence there are many teachers who have to take care of the children.
• Therefore, "the teacher's" should be replaced with "the teachers".
• Hence, option 1 is the correct answer.

The correct sentence is: The Principal requested the teachers to monitor and take care of the small children.

Additional Information

• Let's learn about some more rules of possessives:
• When something belongs to more than one person and we give a list of names, we put 's on the last name.
• Examples:
• Sam's and Emma's house. (Incorrect)
• Sam and Emma's house. (Correct)
• Possessives have no long form.
• Examples: 
• Here is Jack is room. (Incorrect)
• Here is Jack's room. (Correct)

The correct answer is 'BADC'.

Key Points

• While carefully reading all the statements, it is clear that sentence B is the introductory statement.
• Sentence B will come in the first place because it is introducing us to the topic of 'penicillin'.
• Sentence A will come in the second place because it is telling us how the invention of penicillin has helped us.
• It is telling us that it has helped us to heal wounds caused by bacteria.
• Sentence D will come in the third place because it is telling us that by healing wounds it has saved the lives of hundreds of thousands of soldiers.
• Sentence C will come in the last place because it is telling us that its discovery and use were known to very few people in the beginning.
• Therefore, the correct sequence is 'BADC'.
• Hence, option 4 is the correct answer.

 

The correct sequence is: Penicillin is one of the most useful drugs man has invented. This invention has helped us to heal wounds caused by bacteria. Its use has saved the lives of hundreds of thousands of soldiers. In the beginning, however, very few people knew of this discovery and its use.

Additional Information

• 'Heal' means (of a person or treatment) cause (a wound, injury, or person) to become sound or healthy again. (ठीक होना)
• Example: His concern is to heal sick people.
• 'Wound' means an injury to living tissue caused by a cut, blow, or other impact, typically one in which the skin is cut or broken. (घाव)
• Example: A knife wound.