SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 2) (Previous Year Paper)

The pattern  followed here is:

Find which two number from the among the given options should be interchanged to make the given equation correct.

Let's check each option one by one:

Option 1) 78 and 216

Given: 168 ÷ 4 + 216 ÷ ( 78 × 1 - 8) = 14

After interchanging the numbers we get the;

⇒ 168 ÷ 4 + 78 ÷ ( 216 × 1 - 8) = 14

⇒ 168 ÷ 4 + 78 ÷ 208 = 14

⇒ 42 + 0.375 = 14

⇒ 42.375 ≠ 14 

⇒ LHS ≠ RHS

Option 2) 14 and 8

Given: 168 ÷ 4 + 216 ÷ ( 78 × 1 - 8) = 14

After interchanging the numbers we get the;

⇒ 168 ÷ 4 + 216 ÷ ( 78 × 1 - 14) = 8

⇒ 168 ÷ 4 + 216 ÷ 64 = 8

⇒ 42 + 3.375 = 8

⇒ 45.375 ≠ 8 

⇒ LHS ≠ RHS

Option 3) 78 and 14

Given: 168 ÷ 4 + 216 ÷ ( 78 × 1 - 8) = 14

After interchanging the numbers we get the;

⇒ 168 ÷ 4 + 216 ÷ (14 × 1 - 8) = 78

⇒ 168 ÷ 4 + 216 ÷ 6 = 78

⇒ 42 + 36 = 78

⇒ 78 = 78

⇒ LHS = RHS

Option 4) 216 and 168

Given: 168 ÷ 4 + 216 ÷ ( 78 × 1 - 8) = 14

After interchanging the numbers we get the;

⇒ 216 ÷ 4 + 168 ÷ ( 78 × 1 - 8) = 14

⇒ 216 ÷ 4 + 168 ÷ 70 = 14

⇒ 54 + 2.4 = 14

⇒ 56.4 ≠ 14

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The pattern followed here is:

1. Bees : Swarm ⇒ A large number of groups of bees moving and staying together is called a Swarm.

Similarly.

2. Monkeys : Troop ⇒ A large number of groups of Monkeys is called Troop.

Hence, the correct answer is "Troop".

Additional Information

The pattern followed here is:

1. Calf : Cattle ⇒ Calf is the young of some animals, for example, Elephants, Cow, etc.,

Similarly,

2. Foal : Horse ⇒ The young of an animal of the horse family called a foal.

Hence, the correct answer is "Horse".

Additional Information

The logic followed here is:

Step 1) Letter 'D' and 'Z' are shifting it's position Diagonally.

​

Step 2) Letter 'V', 'T', and 'S' are also shifting it's position Diagonally and getting exchanged with Letter 'A', 'X' and 'F' respectively.

So, the complete series will be:

Hence, the correct answer is "Option 3".

The pattern followed here is:

1. Given triangle shifted downward in the second figure, then upward in the third figure, then again shifted downward in the fourth figure, and finally again shifted upward in the last figure.

2. Given circle is blank in the first figure, then the circle is dark in the second figure, then blank in the third figure, then again the circle is dark in the fourth figure, and again blank in the last figure.

3. Given left upper side arrow is rotated 90º clockwise direction in every next figure.

4) Given right upper side arrow is rotated in a 90º anti-clockwise direction in every next figure.

Hence, the correct answer is "Option 3".

The pattern followed here is:

Logic: (First number - Third number)³ = Second number.

1. (9, 343, 2)

⇒ (9 - 2)³

⇒ (7)³ = 343

And,

2. (12, 729, 3)

⇒ (12 - 3)3

⇒ (9)3 = 729

Let's check each option one by one:

Option 1) (98, 49, 92)

⇒ (98 - 92)3

⇒ (1)3 = 1 ≠ 49. (Incorrect)

Option 2) (13, 4, 89)

⇒ (13 - 89)3

⇒ (-76)3 = 438976 ≠ 4. (Incorrect)

Option 3) (12, 66, 20)

⇒ (12 - 20)3

⇒ (-8)3 = -512 ≠ 66. (Incorrect)

Option 4) (12, 125, 7)

⇒ (12 - 7)3

⇒ (5)3 = 125 = 125. (Correct)

Hence, the correct answer is "Option 4".

The position of the English alphabet series is given below:

1. 'ORGANIZATION' is written as 'ORGANINOITAZ'

And,

2. 'MANAGEMENT' is written as 'MANAGTNEME'

Similarly,

3. 'RESOURCE' is written as '?'

Hence, the correct answer is "RESOECRU".

The pattern followed here is:

Hence, the correct answer is "207".

The pattern followed here is:

The least possible Venn diagram is given below according to the given statements:

Statements:

I. Some Z are X.

II. Some W are Z.

Conclusions:

I. Some X are not W → Does not follow → As some Z are X and Some W are Z. So some X are not W is not definitely followed.

II. Some X are not Z → Does not follow → As some Z are X. So some X are not Z is not definitely followed.

So, Neither conclusion follows.

Hence, the correct answer is "Option 4".

The position of the English alphabet series is given below:

1) 'ANNUAL' is written as 'CPRYGR'

And,

2) ‘AMOUNT’ is written as ‘COSYTZ’

Similarly,

3) 'AGENDA' be written as '?'

Hence, the correct answer is "CIIRJG".

The pattern followed here is:

Given:

Hence, the correct answer is "Option 4".

The position of the English alphabet series is given below:

Option 1) FHG

Option 2) WZY

Option 3) LON

Option 4) ADC

Hence, the correct answer is "Option 1".

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

P × Q means that P is the mother of Q.

P + Q means that P is the father of Q.

P ÷ Q means that P is the sister of Q.

Given relation code:

Find: Which expression shows that A is the Maternal aunt of C?

Let's check each option one by one.

Option 1) A ÷ B + C

A is the sister of B, and B is the father of C.

Here, A is the paternal aunt of C. (Incorrect)

Option 2) C × B ÷ A

C is the mother of B, and B is the sister of A.

Here, the gender of A is not identified. (Incorrect)

Option 3) A ÷ B × C

A is the sister of B, and B is the mother of C.

Here, A is the maternal aunt of C. (Correct)

Option 4) B ÷ C × A

B is the sister of C, and C is the mother of A.

Here, the gender of A is not identified. (Incorrect)

Hence, the correct answer is "Option 3"

The position of the English alphabet letters is given below:

    

Hence, the correct answer is "RVJ".

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

Given: 

A - B means ‘A is the mother of B’

A * B means ‘A is the husband of B’

A % B means ‘A is the brother of B’

A $ B means ‘A is the sister of B’

Find how is I related to N.

Given:- I * J - K % L $ M * N

Clearly, I is the father-in-law of N.

Hence, the correct answer is "Father-in-law".$

The pattern followed here is:

Given:

Hence, the correct answer is "Option 1".

The pattern followed here is:

The given word is arranged according to the English dictionary order.

2. Threadbare
3. Threat
4. Thresh
5. Threw
6. Thrice

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

The pattern followed here is:

We have to interchange the mathematical signs with & and find the correct option.

Let's check each option one by one.

Option 1) ×, ÷, ×, ×, -, +, =

Given: - [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10

After putting the mathematical we get the;

⇒ [{(42 × 26) ÷ (12 × 2)} × (4 - 5)] + 5 = 10

⇒ [{(1092 ÷ 24)} × (4 - 5)] + 5 = 10

⇒ [(45.5 × (4 - 5)] + 5 = 10

⇒ [(45.5 × (-1)] + 5 = 10

⇒ - 45.5 + 5 = 10

⇒ - 40.5 ≠ 10

⇒ LHS ≠ RHS.

Option 2) ×, -, +, ×, ÷, ×, =

Given: - [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10

After putting the mathematical we get the;

⇒ [{(42 × 26) - (12 + 2)} × (4 ÷ 5)] × 5 = 10

⇒ [{1092 - 14} × (4 ÷ 5)] × 5 = 10

⇒ [(1078) × (0.8)] × 5 = 10

⇒ 862.4 × 5 = 10

⇒ 3449.6 ≠ 10

⇒ LHS ≠ RHS

Option 3) -, +, ×, ×, ÷, ×, =

Given: - [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10

After putting the mathematical we get the;

⇒ [{(42 - 26) + (12 × 2)} × (4 ÷ 5)] × 5 = 10

⇒ [{16 + 24} × (4 ÷ 5)] × 5 = 10

⇒ [(40) × (0.8)] × 5 = 10

⇒ 32 × 5 = 10

⇒ 160 ≠ 10

⇒ LHS ≠ RHS

Option 4) -, +, ×, ÷, ×, ×, =

Given: - [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10

After putting the mathematical we get the;

⇒ [{(42 - 26) + (12 × 2)} ÷ (4 × 5)] × 5 = 10

⇒ [{16 + 24} ÷ (4 × 5)] × 5 = 10

⇒ [40 ÷ (4 × 5)] × 5 = 10

⇒ [40 ÷ 20] × 5 = 10

⇒ 2 × 5 = 10

⇒ 10 = 10

⇒ LHS = RHS

Hence, the correct answer is "Option 4".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given statements:

Statements:

Some mobiles are flat.

All flats are TVs.

Some TVs are plastic.

Conclusions:

I. Some mobiles are TVs → Follow → As some mobiles are flat and all flats are TVs. So some mobiles are TVs is definitely followed.

II. Some flats are plastic → Does not follow → As all flats are TVs and some TVs are plastic. So some flats are plastic is possible but not definitely followed.

III. All plastic are TVs → Does not follow ​→ As all flats are TVs and some TVs are plastic. So all plastic are TVs is possible but not definitely followed.

So. the only conclusion I follow.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Here, interchange the given two numbers and find which of the following equation will be not correct.

Let's check each option one by one.

Option 1) 8 ÷ 6 × 9 + 7 - 4 = 12

Given: 7 and 4

After interchanging the numbers we get the;

⇒ 8 ÷ 6 × 9 + 4 - 7 = 12

⇒ 1.33 × 9 + 4 - 7 = 12

⇒ 11.97 + 4 - 7 = 12

⇒ 15.94 - 7 = 12

⇒8.94 ≠ 12. 

⇒ LHS ≠ RHS. (Incorrect)

Option 2) 7 × 8 + 4 - 6 ÷ 3 = 37

Given: 7 and4

After interchanging the numbers we get the;

⇒ 4 × 8 + 7 - 6 ÷ 3 = 37

⇒ 4 × 8 + 7 - 2 = 37

⇒ 32 + 7 - 2 = 37

⇒ 39 - 2 = 37

⇒ 37 = 37

⇒ LHS = RHS (Correct)

Option 3) 9 - 4 × 3 + 6 × 7 ÷ 1 = 12

Given: 7 and 4

After interchanging the numbers we get the;

⇒ 9 - 7 × 3 + 6 × 4 ÷ 1 = 12

⇒ 9 - 7 × 3 + 6 × 4 = 12

⇒ 9 - 21 + 24 = 12

⇒ 33 - 21 = 12

⇒ 12 = 12

⇒ LHS = RHS. (Correct)

Option 4) 4 × 8 - 9 ÷ 3 + 7 = 57

Given: 7 and 4

After interchanging the numbers we get the;

⇒ 7 × 8 - 9 ÷ 3 + 4 = 57

⇒ 7 × 8 - 3 + 4 = 57

⇒ 56 - 3 + 4 = 57

⇒ 60 - 3 = 57

⇒57 = 57

⇒ LHS = RHS. (Correct)

So, the option 1 equation in not correct.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Logic: (First number × Third number) - 2 = Second numbers.

1. (3, 16, 6)

⇒ (3 × 6) - 2 

⇒ 18 - 2 = 16

And,

2. (4, 22, 6)

⇒ (4 × 6) - 2 

⇒ 24 - 2 = 22

Let's check each option one by one:

Option 1) (12, 50, 5)

⇒ (12 × 5) - 2 

⇒ 60 - 2 = 58 ≠ 50. (Incorrect)

Option 2) (9, 70, 8)

⇒ (9 × 8) - 2 

⇒ 72 - 2 = 70 = 70. (Correct)

Option 3) (7, 43, 6)

⇒ (7 × 6) - 2 

⇒ 42 - 2 = 40 ≠ 43. (Incorrect)

Option 4) (9, 10, 11)

⇒ (4 × 11) - 2 

⇒ 44 - 2 = 42 ≠ 10. (Incorrect)

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, the correct answer is "BRJG".

The pattern followed here is:

Logic: Two opposite faces of the dice are never adjacent to each other.

⇒ In the given T is common in both the dice.

⇒ Figure is rotated in a clockwise direction from the common letter T.

Clearly, U is on the face opposite to K.

Hence, the correct answer is "U".

The pattern followed here is:

Logic: (First number + Second number) × 15 = Third number

⇒ (4, 7, 165)

⇒ (4 + 7) × 15 ⇒ 11 × 15 = 165

And,

⇒ (14, 26, 600)

⇒ (14 + 26) × 15 ⇒ 40 × 15 = 600

Let's check each option one by one:

Option 1) (23, 29, 567)

⇒ (23 + 29) × 15

⇒ 52 × 15 = 780 ≠ 567. (Incorrect)

Option 2) (5, 19, 225)

⇒ (5 + 19) × 15

⇒ 24 × 15 = 360 ≠ 225. (Incorrect)

Option 3) (3, 6, 135)

⇒ (3 + 6) × 15

⇒ 9 × 15 = 135 = 135. (Correct)

Option 4) (17, 6, 325)

⇒ (17 + 6) × 15

⇒ 23 × 15 = 345 ≠ 325. (Incorrect)

Hence, the correct answer is "Option 3".

The pattern followed here is:

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

Let's check each option one by one.

Option 1) 22 - 40

⇒ (22 ×  2) - 1 

⇒ 44 - 1 = 43 ≠ 40. (Incorrect)

Option 2) 24 - 47

⇒ (24 ×  2) - 1 

⇒ 48 - 1 = 47 = 47. (Correct)

Option 3) 18 - 35

⇒ (18 ×  2) - 1 

⇒ 36 - 1 = 35 = 35. (Correct)

Option 4) 16 - 31

⇒ (16 ×  2) - 1 

⇒ 32 - 1 = 31 = 31. (Correct)

Hence, the correct answer is "Option 1".

The correct answer is Glenn T Seaborg.

• The Nobel Prize in Chemistry in 1951 was awarded jointly to Edwin McMillan and Glenn T. Seaborg "for their discoveries in the chemistry of the transuranium elements."

Key Points

• Edwin McMillan and Glenn T. Seaborg were American chemists who collaborated extensively in the field of nuclear chemistry.
• Their discovery of transuranium elements, which are elements with atomic numbers greater than uranium, was a groundbreaking achievement.
• McMillan and Seaborg developed a new method for synthesizing these elements, which involved bombarding heavier elements with neutrons.
• The first transuranium element they synthesized was neptunium in 1940, followed by plutonium in 1941.
• They also discovered other important transuranium elements, including americium, curium, berkelium, and californium.
• Their work paved the way for the development of nuclear energy and the atomic bomb.
• McMillan and Seaborg's discoveries also had important applications in medicine, including the development of new cancer treatments.

Additional Information Nobel Awards

• The Nobel Prizes are annual awards given to individuals or organizations for outstanding achievements in various fields.
• The awards were established by the will of Swedish chemist and inventor Alfred Nobel and were first awarded in 1901.
• The Nobel Prizes are awarded in the fields of Physics, Chemistry, Medicine or Physiology, Literature, and Peace.
• Each Nobel Prize consists of a medal, a diploma, and a cash prize.
• The amount of the cash prize varies from year to year and is funded by the interest earned on Nobel's fortune.
• The Nobel Peace Prize is awarded by the Norwegian Nobel Committee, while the other prizes are awarded by the respective Swedish academies.
• The Nobel Prize winners are announced in October every year, and the awards ceremony is held in Stockholm, Sweden, on December 10^th, the anniversary of Alfred Nobel's death.
• In addition to the five main categories, the Nobel Memorial Prize in Economic Sciences was established in 1968 by the Sveriges Riksbank (Sweden's central bank).
• The Nobel Prize has become one of the world's most prestigious awards, and many laureates have gone on to become household names and leaders in their respective fields.
• As of 2021, a total of 603 Nobel Prizes have been awarded to 962 laureates.

The correct answer is North-East.

Key Points

• The Tripuri people of the Bru Reang tribe perform the folk dance known as hojagiri.
• It is performed in the state of Tripura, India.
• A team of four to six ladies and young girls do it while singing, balancing on an earthen pitcher, and controlling various props like a bottle on top of the head and an earthen lamp in one hand.
• while the body is only moved in the lower half.
• Other folk dances of North-East:
• Garia, Jhum, Maimita, Masak Sumani and Lebang boomani dances of Tripuri community,
• Bijhu dance of Chakma community,
• Cheraw and Welcome dances of the Lusai community
• Hai-Hak dance of the Malsum community,
• Wangala dance of Garo Community.

Additional Information

The correct answer is Mizoram.

Key Points

• About Mizoram
• It is a state in northeastern India, with Aizawl as its seat of government and capital city.
• It attained statehood on February 20, 1987, following the 53^rd Amendment of the Indian Constitution in 1986
• It is located in the southern tip of the northeastern region is bounded by Myanmar to the east and south, Bangladesh to the west, Tripura to the northwest, Assam to the north, and Manipur to the northeast.
• The ‘Land of Mizos’ was earlier known as the Lushai Hills district of Assam before it was renamed the Mizo Hills District in 1954.
• Mizoram became a union territory in 1972 and in achieved statehood on February 20, 1987.
• The name is derived from “Mizo”, the name of the native inhabitants, and “Ram”, which in the Mizo language means “land.”
• Mizo-ram - “land of the Mizos".
• It is the 2^nd least populous state in the country.
• As per the 2011 census, the literacy rate of Mizoram in 2011 was 91.33%, higher than the national average of 74.04 percent.​

Additional Information

• Observation from the Census of India, 2011:
• Overall literacy in India is approximately 74.04 percent (2011).
• While female literacy is 65.46 percent. Total literacy as well as female literacy is higher than the national average in most of the states from south India.
• There are wide regional disparities in literacy rates across the states of India.
• In India, the states/UTs which have literacy rates of more than 90% are Kerala (93%), Mizoram (91%), Lakshadweep Islands (92%).
• The developed states/UTs like NCT Delhi, Daman & Diu, Tripura, Chandigarh have literacy rates in the range of 85-90%.

The correct answer is Goal scored.

Key Points

• If the umpire signals by pointing both arms horizontally toward the centre of the field it means goal scored.
• If the umpire raises both arms horizontally in the direction of the goal, it is a penalty corner of the signal.
• A defensive violation within the penalty circle or a willful violation within the defensive 23-meter zone results in a penalty corner being issued.
• A penalty corner, sometimes referred to as a short corner in field hockey, is a sanction imposed on the opposing side.
• Attacking players seek them out eagerly because they offer a great chance to score. Players learn specialised abilities for this phase of the game, such as the drag flick, and there are specific rules that only apply in penalty corners.​

​

Additional Information

• Hockey 
• ​The term "hockey" refers to a group of different summer and winter team games that were first played on an outdoor field, a sheet of ice, or a dry floor, like in a gymnasium. While the specific regulations, player counts, attire, and most notably the playing field differ amongst these games, they all include two opposing teams utilising sticks to direct a ball or disc towards a goal.
• Hockey comes in a variety of forms.
• Skates, whether wheeled or bladed, are used in some games yet not in others.
• The word "hockey" is frequently followed by another word, such as "field hockey," "ice hockey," "roller hockey," "rink hockey," or "floor hockey," to assist distinguish between these different games.

The correct answer is Ashwini Kumar Dutta.

Key Points

• Ashwini Kumar Dutta founded the Swadesh Bandhab Samiti on 6^th August 1905 after the partition of Bengal.
• The organisation was formed to promote the consumption of swadeshi goods.
• It was established in the Barisal district(Present day Bangladesh).
• It published its weekly paper called, 'Barisal Hitaishi.'
• The organisation had its own shops.
• Ashwini Kumar Dutta was responsible for the creation of the Co-operative Hindusthan Bank in 1908 to help Indians start their own business.

Additional Information Bhagat Singh

• He was born on 27 September 1907 in Banga, Lyallpur District, Punjab Province, British India (present-day Faisalabad District, Punjab, Pakistan).
• In December 1928, Bhagat Singh and an associate, Shivaram Rajguru, were both members of a small revolutionary group, the Hindustan Socialist Republican Association.
• He was an Indian revolutionary.
• He participated in a massive symbolic bombing of the Central Legislative Assembly in Delhi and a hunger strike in prison.

 Chandrasekhar Azad

• Chandra Shekhar Tiwari who was popularly known as Chandrashekhar Azad was an Indian Revolutionary leader and a Freedom fighter.
• Azad along with Bhagat Singh and other revolutionaries secretly restructured the Hindustan Republican Association (HRA) in 1928 and renamed it the Hindustan Socialist Republican Association (HSRA) on 8-9 September in order to achieve their primary goal of an independent India based on the idea of socialism.
• He was involved in the Kakori Train Action Case that happened in 1925. Now UP government renames Kakori kand to Kakori train action on 9 August 2021.

The correct answer is 1835.

Key Points

• In 1834 Thomas Babington Macaulay came to India as a Legal Member of the Council of India.
• He formulated his policy proposal in his Minute on Indian Education, delivered in Kolkata on 2^nd February 1835.
• As per Lord Macaulay’s “Minutes on Indian Education” ‘Literature’ meant English literature and not Sanskrit or Arabic or Persian literature.
• He emphasized that the medium of instruction should be English.
• His thinking was to change Indian culture.
• The Governor-General of India, William Bentinck, approved the proposal of Lord Macaulay on 7^th March 1835.
• It became the cornerstone of British-Indian educational policy until Independence (and remained largely in force after that as well)

Additional InformationHunter Commisssion

• The Hunter Commission has an important place in the field of education in India.
• At the primary level, the commission emphasized on teaching useful subjects in the local language.
• Lord Ripon set up a commission under the chairmanship of Sir William Hunter in 1882 AD, whose task was to consider the irrelevance of the Woods Dispatch of 1854.

Woods Dispatch

• The education system of present India is the gift of Charles Wood.
• The East India company policy to change renews the charter after every 20 years, so that time in 1853.
• The parliament board surveyed Indian Education System and determined that there was a huge need for education.
• Wood was the President and he sent the report to East India Company the report was forwarded as a dispatch to the Indian Government on 19^th July 1854 and this is known as Wood’s Dispatch 1854.
• The Wood’s Dispatch is considered the Magna Carta of English education in India.
• Despatch expressed that education in English, as well as Indian local languages, should be enhanced and encouraged throughout the Nation.
• They wanted to establish a Department of Public Instruction in every province.

• The correct answer is the Ministry of Development of the North Eastern Region.

Key Points

• "Nari Shakti of North East" is a celebration of the power and strength of women in the northeastern region of India.
• The event is usually held on International Women's Day, which is on March 8^th every year and is organized by the Ministry of Development of the North Eastern Region (DoNER).
• The event is aimed at recognizing the contributions and achievements of women in the northeastern region of India.
• It provides a platform for women to showcase their talents, skills, and achievements in various fields, including arts, culture, sports, and entrepreneurship.
• The event includes various activities such as panel discussions, cultural performances, exhibitions, and award ceremonies.
• The award ceremony recognizes women who have made significant contributions in various fields and includes categories such as entrepreneurship, education, social work, and sports.
• The event also provides an opportunity for women to interact and network with each other and share their experiences and challenges.
• The "Nari Shakti of North East" celebration is an important initiative that highlights the role of women in the development of the northeastern region of India.
• It is also a way to promote gender equality and empowerment and to inspire and motivate more women to pursue their dreams and aspirations.

The correct answer is Padma Bhushan.

Key Points

• Mrinalini Sarabhai is famous for Bharatanatyam.
• Mrinalini's older sister Lakshmi Sehgal was the commander-in-chief of the Rani of the Jhansi regiment which was an all-women combat regiment of the Indian National Army.
• Mrinalini was born to a Tamil Brahmin father and Malayali Nair mother in present-day Kerala on 11 May 1918. Bharatanatyam is a dance of Tamil Nadu in southern India.
• She trained over 18,000 students in Bharatnatyam and Kathakali.

Additional Information

• Uday Shankar is known as the Father of Modern Dance in India.
• The Marshal of the Indian Air Force Arjan Singh is the first and the only five-star rank officer in the Indian Air Force. Singh was conferred Padma Vibhushan in 1965.
• It's a known fact that Sachin Tendulkar is the only sportsperson who was conferred with the Bharat Ratna in 2014.
• Yoga Guru Swami Sivananda, Ghulam Nabi Azad Among Winners.
• Sonu Nigam receives Padma Shri Award, Victor Banerjee conferred with Padma Bhushan.

The correct answer is Marginal standing facility, Reverse repo rate.

Key Points

• MSF(Marginal Standing Facility) Rate is the rate at which commercial banks borrow funds overnight from the central bank.
• The reverse repo rate is the rate at which banks earn interest when they park surplus funds with the RBI. The repo rate helps control inflation, and the reverse repo rate increases liquidity.
• The weighted average of the marginal standing facility (MSF) and the reverse repo rate (RRR) determine the corridor for daily movement in the call money rate.

Additional Information

• Repo Rate: The rate at which the Central bank (RBI) grants loans to the commercial banks against government securities for Short Term Financial Needs.
• It controls the inflation in the economy.
• MSF>REPO RATE >REVERSE REPO RATE

The correct answer is Bangladesh.

Key Points

• Bangladesh and India share a 4,096-kilometre-long (2,545 mi) International border, the fifth-longest land border in the world.
• Includes 262 km (163 mi) in Assam, 856 km (532 mi) in Tripura, 318 km (198 mi) in Mizoram, 443 km (275 mi) in Meghalaya, and 2,217 km (1,378 mi) in West Bengal.
• After the Partition of India in 1947, the Radcliffe line became the border between India and East Pakistan and following the liberation of Bangladesh in 1971, the same line became the border between India and Bangladesh.
• Bangladesh lies east of India.

Additional Information

• India has 15,106.7 Km of land border and a coastline of 7,516.6 Km including island territories.
• The length of our land borders with neighbouring countries is as under:

The correct answer is Freedom of speech and expression.

Key Points

• The right to Freedom of speech and expression is guaranteed under the Constitution in Article 19(1)(a)
• It is also considered as the ‘Hallmark of Democracy.
• Right to Freedom of Religion
• To all religions, there is equal respect given.
• It indicates the secular nature.
• There is freedom of profession, practice, conscience, and propagation of religion.
• Every person has the right to establish and maintain religious and charitable institutions, freely practice his or her faith.
• The State has no religion (official).

Additional Information

• There are 6 fundamental rights of the Constitution are following
• Right to Equality - Article 14-18
• Right to Freedom - Article 19-22
• Right against Exploitation - Article 23-24
• Right to Freedom of Religion - Article 25-28
• Cultural and Educational Rights - Article 29-30
• Right to Constitutional Remedies - Article 32

The correct answer is Chhattisgarh.

Key Points

Kaushalya Matritva Yojana

• Chief Minister Bhupesh Baghel launched the ‘Kaushalya Matritva Yojana’ by providing checks of Rs 5000 each to five beneficiaries for safe motherhood in a state-level women’s conference held at BTI Ground in the capital Raipur.
• Under this scheme, there is a provision to give a lump sum assistance of Rs. 5 thousand to women beneficiaries on the birth of a second daughter. The scheme will help in the upbringing and education of the girl child.
• The Chief Minister felicitated Anganwadi workers, who have done excellent work in Anganwadi services, self-help groups, who have made women financially independent by taking benefit of Chhattisgarh Mahila Kosh, at the state level women’s conference.
• Similarly, he also honored the officers doing excellent work in the direction of women protection under ‘Sakhi One Stop Center’ and ‘Nava Bihaan Yojna’.
• He also released Kanya Vivah Yojana Coffee Table Book, Sakhi One Stop Center Telephone Directory and brochures of schemes related to women empowerment on the occasion.
• The Chief Minister also visited the stalls of exhibition of products prepared by women self-help groups from across the state in the four-day state level Mahila Madai organized at BTI Ground. From the stalls of women’s groups of Bastar, the Chief Minister bought artwork made of bell metal and encouraged the women by playing trumpet.

Additional Information 

The correct answer is Louise Lightfoot.

Key Points

• Louise Lightfoot was an Australian dancer, choreographer, and dance historian, born in Sydney in 1902.
• She is best known for her work as a pioneer of modern dance in Australia, and for her contributions to the development of dance as an academic discipline.
• Lightfoot studied dance in Europe and the United States, where she trained with some of the leading figures of modern dance, including Martha Graham and Doris Humphrey.
• In 1936, she founded the New South Wales Ballet Company, which was the first professional ballet company in Australia.
• Lightfoot was also a respected dance critic and historian, and wrote several books and articles on the history and theory of dance.
• She was popularly called the ‘Australian Mother of Kathakali’

Additional Information

• Kathakali is a classical Indian dance form which is a story play genre of art is the folk dance form of Kerala.
• It is a combination of 5 forms of fine art which are –
• Natyam (expressions)
• Nritham (dance)
• Nrithyam (enactment)
• Sangeetam (music)
• Vadya (instruments)
• Various costumes of characters of Kathakali –
• Sathwika (Hero)
• Katti (Villain)
• Minukku (females)
• Thathi (other characters)
• Types of Drums used in Kathakali – Maddalam, Chenda, and Idakka
• Kathakali is the most difficult style of the traditional dance form in which actors speak ‘sign language’ where hand gestures are used to dictate word part of the character and facial and eye movements express emotions and mood.
• Kathakali is based on the epics of Ramayana and Mahabharata. ​

​

The correct answer is Bihar.

Key Points

• The university at Nalanda was established in the fifth century and shut down in the thirteenth.
• In the ancient Indian kingdom of Magadha, which is now called Bihar, Nalanda University served as the epicenter of learning.
• King of the Gupta Dynasty, Kumargupta I, founded the University of Nalanda.
• When it was at its busiest, it drew a lot of academics and students, even from abroad.
• Even from Central Asia, China, Korea, and Tibet, several academics and students visited.
• The focus of Nalanda University extended beyond Buddhist studies.
• Additionally, it gave pupils training in politics, the art of battle, medicine, algebra, and astronomy.
• Each structure was nine floors tall and housed a sizable library.
• Books covered a variety of topics, including religion, literature, astrology, astronomy, medicine, and much more

Additional Information

• The knowledge of this place was in the state of its climax. Due to international reputation, a large number of students had come to study from China, Mongolia, Tibet, Korea and other Asian countries.
• The level of teaching was extremely high here, to get an education in Mahavihar one was tested by A teacher. The leading centre of teaching of Mahayana Buddhism was Nalanda but other topics of education were also featured here.
• Finally, at the end of the 12^th century, invader Bakhityar Khilji demolished the monastery, killed the monks and burned the valuable library.

The correct answer is He/She should be qualified for election as a member of the Lok Sabha. 

Key Points

• The Vice-President of India is elected by members of an electoral college consisting of both Houses of Parliament in accordance with the system of proportional representation by means of a single transferable vote.
• State Legislatures do not take part in the election of Vice-President.
• Qualification [Article 66 (3)]:
• Should be a citizen of India.
• Should have completed 35 years of age.
• Should be qualified for election as Member of Rajya Sabha.
• Should not hold any office of profit.

Additional Information

• Article 63 provides that there shall be a Vice-President of India.
• Article 64  says that the Vice-President shall be the ex-officio Chairman of the Council of States and shall not hold any other office of profit.
• The current Vice President of India is Shri C. P. Radhakrishnan.
• He is the 15^th Vice President of India.

The correct answer is sodium hydrogen carbonate.

Key Points

• Chemically known as sodium hydrogencarbonate, the formula of baking soda is NaHCO3.
• Baking soda is a white and crystalline salt that is made up of bicarbonate anion and sodium cation.​

Additional Information 

The correct answer is Victoria.

Key Points

• Lake Victoria is located at the border of Uganda, Kenya, and Tanzania in the African continent.
• River Nile originates from Lake Victoria and drains into the Mediterranean sea.
• Victoria Lake is the largest tropical lake in the world and one of the largest freshwater lakes in the world by area.
• Its area is 26,828 square miles (69,484 square km).
• Among the freshwater lakes of the world, it is only behind the Lake Superior of North America.
• Its waters fill a shallow depression in the center of the great plateau that stretches between the Western and Eastern Rift Valleys.

Additional Information

• The Great Lakes are a group of five large lakes in North America on or near the Canada-United States border
• These are from west to east as Superior Lake, Michigan Lake, Huron Lake, Erie Lake, and Ontario Lake.
• They are the largest group of freshwater lakes on Earth.
• They are sometimes referred to as inland seas.
• The Great Lakes are:
• Lake Superior - the largest by volume and deepest, larger than Scotland or South Carolina
• Lake Michigan - the second-largest by volume and third-largest by area; the only one entirely in the U.S.
• Lake Huron - the third-largest by volume; the second-largest in the area
• Lake Erie - the smallest by volume and shallowest
• Lake Ontario - is the second-smallest in volume and smallest in area, with a much lower elevation than the rest
• These Great Lakes are being extensively used for transport, though cargo is used as a major mode of transport for bulk goods.
• The Great Lakes were formed at the end of the last ice age
• They are a dominant part of the physical and cultural heritage of North America.

The correct answer is Both I and II.

Key Points

• A tissue is a group of cells having a common origin and usually performing a common function.
• A plant is made up of different kinds of tissues.
• Tissues are classified into two main groups-  
• Meristematic Tissue- Cells have a capacity for division.
• Permanent Tissue- Cells have no capacity for division.

Additional Information

• Types of permanent tissue:
• Permanent tissues are of three types, namely –
• (a) Simple tissue, (b) Complex tissue and (c) Secretory tissue.
• ​Simple permanent tissue
• Simple permanent tissue is composed of a single type of cells that have comparable origin, structure, and function.
• This tissue is called epithelium in animals and epidermis in plants.
• They are homogenous of structurally and functionally comparable cells.
• Types of simple permanent tissue
• Parenchyma – Parenchyma mostly serves as a storage tissue. They are accountable for photosynthesis, storage of food, secretion, etc.
• Collenchyma – It helps in photosynthesis. They often have some chloroplast to hold on to photosynthesis.
• Sclerenchyma – It mainly helps in mechanical support to plant body in the form of plasticity.
• Complex permanent tissue
• Complex permanent tissue is composed of two or more two types of cells and contributes to a general function.
• They organize together to carry out similar particular functions in the plant body.
• It is also known as vascular tissue.
• Types of complex tissue:
• Xylem – The xylem tissue is accountable for the transmission of water and minerals from the roots to the leaves and stems.
• Phloem – This complex permanent tissue helps in the translocation of food that is prepared by photosynthesis in the leaves to diverse parts of the plant.
• Secretory tissues
• Secretory tissues are specialized tissue having secretory functions. They secrete diverse types of chemicals.
• Types of secretory tissue –
• Lactiferous tissues: It is thin-walled tubes like tissue that produce latex (milky juice).
• Glandular tissue: This tissue forms glandular structures which secrete or excrete chemical substances
• There are three types of meristematic tissues-

1. Apical meristem- these are located at the shoot tips and root tips.
2. Intercalary meristem- located between pemanent tissues, at the leaf base and nodes.
3. Lateral meristem- located at the sides(edges).

The correct answer is trail is valid.

Key Points

Triple jump:

• Landing Area: 9 meters in length and 2.75 meters in width.
• Take-off Board: 13 meters behind the pit (Men) and 11 Meters behind for (Women) and is white in color, 1.22 Meter length, and 20 cm in width.
• Plasticine Indicator Board: Indicate foul in the long jump. The length is 1.22 Meters and the Width is 10 cm
• Runway of Triple Jump: 40-45 meter
• Triple jump Phases are Approach run, Take off, Hop, Step, Jump, and Landing.
• In Triple Jump, white flag indicates: trail is valid.​

Additional Information

Jumping event: 

• These are basically events in which the main focus is a jump.
• These come under field events.
• Names of jumping events are:

1. Long Jump,
2. High jump,
3. Triple Jump,
4. Pole vault.

The correct answer is Sodium hydroxide.

Key Points 

• Sodium hydroxide (NaOH) dissociates completely in water to give Na+ and OH−
• Sodium hydroxide is considered a strong base as all the available [OH] in NaOH is present in the solution as [OH−] and available to accept protons.
• Sodium hydroxide is the strongest base because it totally dissociates to form sodium ions and hydroxide ions.
• These hydroxide ions are treated with hydrogen ions further from the acid and totally ionize the hydrogen ions.
• Producers may utilize sodium hydroxide to manufacture soaps, rayon, paper, products that explode, dyes, and petroleum products.
• Other works that may utilize sodium hydroxide comprise preparing cotton fabric, metal cleaning and preparing, oxide coating, electroplating, and electrolytic extraction.
• It has the pH value of about 14.​

Additional Information

• ​The blood has a normal pH range of 7.35 to 7.45.
• Milk of Magnesia is basic in nature. The pH value of the Milk of Magnesia is 10.5.
• Lemon juice has a pH between 2 and 3.

The correct answer is Munari.

Key Points

• Cheraw Dance: Also known as the Bamboo Dance, it is one of the most popular dances of Mizoram. It involves dancers moving between a pair of horizontal bamboo poles, which are rhythmically struck against each other. The dancers step in and out of the poles, creating intricate patterns and rhythms with their movements.
• Khuallam Dance: This is a community dance that is performed during festivals and other cultural events. It is typically performed by women, who wear colorful traditional dresses and move in a circle, clapping and singing.
• Chheihlam Dance: This is a traditional dance of the Lusei tribe, which is known for its graceful movements and delicate hand gestures. It is typically performed by women, who wear traditional dresses and move in a slow, swaying rhythm.

Additional Information

• The Indian States and Folk Dances
• Andhra Pradesh- Kuchipudi, Bhamakalpam, Lambadi, Dhimsa, Kolattam, Butta Bommalu.
• Assam- Bihu, Bichhua, Natpuja, Maharas, Kaligopal, Bagurumba, Naga dance, Khel Gopal, Tabal Chongli, Canoe, Jhumura Hobjanai
• Bihar- Jata-Jatin, Bakho-Bakhain, Panwariya, Sama Chakwa, Bidesia.
• Gujarat- Garba, Dandiya Ras, Tippani Juriun, Bhavai.
• Haryana- Jhumar, Phag, Daph, Dhamal, Loor, Gugga, Khor, Gagor.
• Himachal Pradesh- Jhora, Jhali, Chharhi, Dhaman, Chhapeli, Mahasu, Nati, Dangi.
• Jammu and Kashmir- Rauf, Hikat, Mandjas, Kud Dandi Nach, Damali.
• Karnataka- Yakshagan, Huttari, Suggi, Kunitha, Karga, Lambi.
• Kerala- Kathakali (Classical), Ottamthullal, Mohiniattam, Kaikottikali.
• Maharashtra- Lavani, Nakata, Koli, Lezim, Gafa, Dahikala Dasavtar or Bohada.
• Odisha- Odissi (Classical), Savari, Ghumara, Painka, Munari, Chhau.
• West Bengal- Kathi, Gambhira, Dhali, Jatra, Baul, Marasia, Mahal, Keertan.
• Punjab- Bhangra, Giddha, Daff, Dhaman, Bhand, Naqual.
• Rajasthan- Ghumar, Chakri, Ganagor, Jhulan Leela, Jhuma, Suisini, Ghapal, Kalbeliya.
• Tamil Nadu- Bharatanatyam, Kumi, Kolattam, Kavadi.
• Uttar Pradesh- Nautanki, Raslila, Kajri, Jhora, Chappeli, Jaita.
• Uttarakhand- Garhwali, Kumayuni, Kajari, Jhora, Raslila, Chappeli.
• Goa- Tarangamel, Koli, Dekhni, Fugdi, Shigmo, Ghode, Modni, Samayi nrutya, Jagar, Ranmale, Gonph, Tonnya mell.
• Madhya Pradesh Jawara, Matki, Aada, Khada Nach, Phulpati, Grida Dance, Selalarki, Selabhadoni, Maanch.
• Chhattisgarh Gaur Maria, Panthi, Raut Nacha, Pandwani, Vedamati, Kapalik, Bharthari Charit, Chandaini.
• Jharkhand Alkap, Karma Munda, Agni, Jhumar, Janani Jhumar, Mardana Jhumar, Paika, Phagua,Hunta Dance, Mundari Dance, Sarhul, Barao, Jhitka, Danga, Domkach, Ghora Naach.
• Arunachal Pradesh Buiya, Chalo, Wancho, Pasi Kongki, Ponung, Popir, Bardo Chham.
• Manipur Dol Cholam, Thang Ta, Lai Haraoba, Pung Cholom, Khamba Thaibi, Nupa Dance, Raslila, Khubak Ishei, Lhou  Sha.
• Meghalaya Ka Shad Suk Mynsiem, Nongkrem, Laho.
• Mizoram Cheraw Dance, Khuallam, Chailam, Sawlakin, Chawnglaizawn, Zangtalam, Par Lam, Sarlamkai/Solakia, Tlanglam.
• Nagaland Rangma, Bamboo Dance, Zeliang, Nsuirolians, Gethinglim, Temangnetin, Hetaleulee.
• Tripura Hojagiri.
• Sikkim Chu Faat Dance, Sikmari, Singhi Chaam or the Snow Lion Dance, Yak Chaam, Denzong Gnenha, Tashi Yangku Dance, Khukuri Naach, Chutkey Naach, Maruni Dance.

The correct answer is Cotton.

Key Points 

• Black soil is also called as ‘Regur Soil’ or the ‘Black Cotton Soil’.
• It is well suited for the cultivation of cotton so it is also called cotton soil.
• They are generally clayey, deep, and impermeable.
• They are formed by the disintegration of basalt.
• It has the ability to retain moisture for a very long time.
• They are rich in soil nutrients, such as calcium carbonate, magnesium, and potash.

Additional Information

• Alluvial soil is suitable for the growth of sugarcane, paddy, wheat, and other cereal and pulse crops.
• Laterite soil is very useful for growing tea, coffee, and cashew nut.

The correct answer is Rajesh Verma.

Key Points 

• Odisha cadre IAS officer Rajesh Verma has been appointed as the Secretary to President Droupadi Murmu.
• He replaces the incumbent Kapil Dev Tripathi, a 1980-batch IAS officer.
• Verma is currently serving as Secretary, Ministry of Corporate Affairs & has also served as principal secretary to Odisha CM Naveen Patnaik.
• Droupadi Murmu took oath as the 15^th President of India on 25 July 2022.

Additional Information

• Important Appointments:
• Sanjay Arora, director general of the ITBP and a 1988-batch IPS officer, has been appointed as the new Delhi Police Commissioner.
• IFS officer of the 1994 batch Pranay Kumar Verma has been appointed as India’s next High Commissioner to Bangladesh.
• Govt of Bangladesh has appointed Mustafizur Rahman as the next High Commissioner of Bangladesh to India.
• The Public Enterprises Selection Board (PESB) panel has appointed Brajesh Kumar Upadhyay as Chairman and managing Director (CMD) of Goa Shipyard Limited (GSL).
• Shri B.V.R. Subrahmanyam joined as Chief Executive Officer of NITI Aayog on 25.02.2023. An Indian Administrative Service Officer of the 1987 batch (Chhattisgarh).
• New Development Bank (NDB) of the BRICS countries has appointed Dr D J Pandian as the Director-General of its India Regional Office in Gujarat International Finance Tec-City (GIFT City).
• Senior Diplomat Ruchira Kamboj has been appointed as the Ambassador and Permanent Representative of India to the United Nations.

The correct answer is Rabindranath Tagore.

Key Points

• Rabindranath Tagore was a Bengali poet, writer, and painter.
• He was honored with the Nobel Prize in Literature in 1913.
• He is the first non-European to receive the Nobel Prize for Literature.
• Rabindranath Tagore got the Nobel Prize for his work Gitanjali.
• India's national anthem" Jana Gana Mana" was written by Rabindranath Tagore.
• He also created Bangladesh's national anthem, "Amar Shonar Bangla".
• Shanti Niketan is a school established by Rabindranath Tagore.
• Rabindranath Tagore first sang Vande Mataram in 1896 at the Calcutta Congress Session.
• Notable works:
• Gitanjali.
• Ghare-Baire.
• Gora,
• Gitimalya.
• Balaka.
• Sonar Tari.

Additional Information

• M.K. Gandhi
• He was born on October 2, 1869, in Porbandar in what is today India’s western state of Gujarat.
• Upon return to British-controlled India in January 1915, Gandhi had acquired the skills both of an accomplished lawyer and a community organizer dedicated to peaceful protest.
• In South Africa (1893-1915), he had successfully fought the racist regime with a novel method of mass agitation, which he called satyagraha.
• The idea of satyagraha emphasized the power of truth and the need to search for truth.
• The International Day of Non-Violence is observed on 2^nd October, the birthday of Mahatma Gandhi.
• Gandhi's Peace Prize is given for social, economic, and political transformation through non-violence and other Gandhian methods.
• He returned to India from South Africa on 9^th January 1915.
• Pravasi Bharatiya Divas (PBD) is celebrated on 9^th January every year to mark the contribution of the Overseas Indian community to the development of India.​
• Jawaharlal Nehru 
• He was the first Prime Minister of India.
• He is the Prime Minister who has had the longest term in office.
• He served as the prime minister of India from 15^th August 1947 to 1964.
• He is the architect of the Preamble of the Indian constitution.
• He was the Prime Minister of India during the Indo-China war in 1962.
• He served as the first chairman of the planning commission of India.
• He was honored with the Bharat Ratna in 1955.
• The name Panchayati raj was given by Jawaharlal Nehru.
• National herald is the newspaper started by Jawaharlal Nehru.
• Jyotiba Phule
• He was born on April 11, 1827, in Pune, Maharashtra.
• He was a merchant, author as well as a municipal council member.
• He was inspired by Thomas Paine’s book titled The Rights of Man.
• He believed that the only solution to remove the social evils was the enlightenment of women and members of the lower castes.
• He opened schools for girls to support their education and educated his wife.
• His well-known books include Gulamgiri (Slavery) and Shetkarayacha Aasud (Cultivator’s Whipcord).
• He wrote Gulamgiri — one of the first critiques of the caste system. It is written in Marathi, with an English preface, the text has been translated into English as Slavery.
• In 1873, Jyotiba Phule formed the Satya Shodhak Samaj to promote equality in society.
• He is believed to be the first Hindu to start an orphanage for the unfortunate children.​

The correct answer is Fifth Five-Year Plan - Indira Gandhi.

Key Points

Fifth Five-Year Plan: 

• The period of the fifth five-year pan was from 1974 to 1979.
• The  Draft of the fifth plan was prepared and launched by D.P. Dhar in the backdrop of an economic crisis arising out of run-away inflation fuelled by a hike in oil prices and the failure of the Government takeover of the wholesale trade in wheat.
• The targeted growth rate was 4.4% but the actual growth achieved was 4.8%
• The main Objectives of the fifth five-year plan are:
• The removal of poverty
• Economic Independence
• It was also launched under the leadership of Indira Gandhi.

Additional Information

List of the Five-Year Plans of India:

Given:

a = 45° and b = 15

Concept used:

a² - b² = (a + b)(a - b)

(a - b)² = a² - 2ab + b²

Calculation:

(a - b) = 45° - 15° = 30°

(a + b) = 45° + 15° = 60°

Now, ${\cos (a - b ) - \cos (a + b)} \over {\cos(a - b) + \cos(a + b)}$

⇒ ${\cos 30^\circ - \cos 60^\circ} \over {\cos30^\circ + \cos 60^\circ}$

⇒ ${\frac {\sqrt3}{2} - \frac {1}{2} } \over {\frac {\sqrt3}{2} + \frac {1}{2} }$

⇒ ${\sqrt3 - 1} \over {\sqrt3 + 1}$

⇒ ${(\sqrt3 - 1)(\sqrt3 - 1)} \over {(\sqrt3 + 1)(\sqrt3 - 1)}$

⇒ $(3 + 1 - 2\sqrt3) \over {3 - 1}$

⇒ 2 - √3

∴ The simplified value is 2 - √3.

Calculation:

Now, the required percentage

⇒ $\frac {120}{200} \times 100\%$ = 60%

∴ The sales turnover of company A is 60% of the sales turnover of company C.

Given:

A triangle and a parallelogram have the same base 28 cm and the same area.

The height of the parallelogram is 12 cm.

Concept used:

1. Area of a parallelogram = Base × Height
2. Area of a triangle = 1/2 × Height × Base

Calculation:

Area of the parallelogram = 28 × 12 = 336 cm²

Let the length of the altitude of the triangle be H cm.

​According to the question,

1/2 × H × 28 = 336

⇒ H = 12 × 2

⇒ H = 24

∴ The length of the altitude of the triangle is 24 cm.

Calculation:

$1 \over11$, $2 \over9$, $2 \over3$, $4 \over5$

LCM of 11, 9, 3 and 5 is 495

Multiplying the above fraction by 495

⇒ ${1 \over11} \times 495$, ${2 \over9} \times 495$, ${2 \over3} \times 495$, ${4 \over5} \times 495$

⇒ 45, 110, 330, 396

∴ Fractions only in option 2 are in the correct ascending order.

Given:

The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. 

Concept used:

Chord Length Using Perpendicular Distance from the Center = $2 × \sqrt{(r^2 − d^2)}$ (Where r = radius of the circle, d = distance between the centre and the chord)

Calculation:

Let the radius of the circle be R.

Here,

AB = 24 cm long chord

OD = Perpendicular distance between the centre and chord

OB = Radius

​According to the concept,

24 = $2 × \sqrt{(R^2 − 5^2)}$

⇒ 12 = $\sqrt{(R^2 − 5^2)}$

⇒ 144 = R² - 5²

⇒ R² = 169

⇒ R = 13

∴ The radius of the circle is 13 cm.

Given:

A student walked 6 km from his house to reach the metro station, then boarded a metro that has an average speed of 60 km/h, and reached the destination.

It took 3 hours for the entire journey.

The average speed of the entire journey is 32 km/h.

Concept used:

1. Average speed = Total distance covered ÷ Total time taken 2. Distance = Speed × Time

Calculation:

Total distance travelled by him = 32 × 3 = 96 km

Distance covered on metro = 96 - 6 = 90 km

Time taken by the metro to cover 90 km = 90/60 = 1.5 hours

Remaining time = 3 - 1.5 = 1.5 hours

Speed of walking = 6 ÷ 1.5 = 4 km/h

∴ The speed of walking is 4 km/h.

Given:

A, B and C can all together do a piece of work in 10 days, in which B takes 3 times as long as A and C together to do the work. 

Concept used:

If A and B alone can complete a task in X and Y days respectively, then they together will take = XY/(X + Y) days to complete the work.

Calculation:

Let's suppose, A and C together can complete the work in N days.

So, B takes = 3N days

According to the concept,

$\frac {3N \times N}{3N + N}$ = 10 (Here, A and C are being considered a single entity)

⇒ $\frac {3N}{4}$ = 10

⇒ 3N = 40

∴ B alone will take 40 days to complete the work.

Given:

A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 1 each, the interest being simple. 

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount

R = Rate of interest per year

T = Time in years

Calculation:

Let the rate of interest be R% p.a.

Total interest paid = 11 - 10  = Rs. 1

Since the installments are being paid monthly, the first, second, ...., and second-last EMI will incur interest for the next 10, 9, ...., and 1 month respectively. Since the last EMI completes the repayment, it will not incur any interest.

According to the concept,

(1 × R/100 × 10/12) + (1 × R/100 × 9/12) + (1 × R/100 × 8/12) + .... + (1 × R/100 × 1/12) = 1

⇒ $\frac {R}{1200}$ (10 + 9 + ... + 1) = 1

⇒ $\frac {R}{1200} \times \frac {11 \times 10}{2}$ = 1

⇒ R = 1200/55

⇒ R = $21{ 9 \over 11}$%

∴ The rate of interest is $21{ 9 \over 11}$%.

Given:

The sum of two numbers is 680.

The bigger number is decreased by 15% and the smaller number is increased by 15%.

Calculation:

Let the bigger number be Q.

Smaller number = (680 - Q)

​According to the question,

Q(1 - 15%) = (680 - Q)(1 + 15%)

⇒ Q/(680 - Q) = 23/17

⇒ 17Q = 23 × 680  - 23Q

⇒ 40Q = 23 × 680

⇒ Q = 23 × 17

⇒ Q = 391

So, the smaller number = 680 - 391 = 289

∴ The smaller number is 289.

Given:

a - b = 8 and ab = 9

Concept used:

(a - b)2 = (a + b)2 - 4ab

Calculation:

(a - b) = 8

⇒ (a - b)² = 8²

⇒ (a + b)² - 4ab = 64

⇒ (a + b)2 = 64 + 4 × 9

⇒ (a + b)2 = 100

⇒ (a + b) = ±10

∴ The value of (a + b) is ±10.

Calculation:

The first three statements are correct.

But the last statement is incorrect. Because the perpendicular distance from the centre of the circle decreases when the length of the chord increases.

∴ Option 4 is the incorrect statement with respect to the properties of a circle.

Given:

Sita gets a discount of 20% on Rs. 3,000 juicer mixer machine.

Since she pays cash, she gets an additional 5% discount too.

Concept used:

1. Selling Price = Marked Price × (1 - Discount%) 2. Final discount percentage after two successive discounts of A% and B% = $(A + B - {AB \over 100})\%$

Calculation:

Final discount% = 20 + 5 - (20 × 5)/100 = 24%

Now, she pays = 3000(1 - 24%) = Rs. 2280

∴ She pays Rs. 2280.

Given:

cosec 15° sec 15°

Concept used:

1. 2 × sin α × cos α = sin 2α
2. sin 30° = 1/2
3. cosec α = 1/sin α
4. sec α = 1/cos α

Calculation:

cosec 15° sec 15°

⇒ $\frac {1}{\sin 15^\circ × \cos 15^\circ}$

⇒ $\frac {2}{2\sin 15^\circ × \cos 15^\circ}$

⇒ $\frac {2}{\sin (15 × 2)^\circ}$

⇒ $\frac {2}{\sin 30^\circ}$

⇒ $\frac {2}{\frac {1}{2}}$

⇒ 4

∴ The value of cosec 15° sec 15° is 4.

Calculation:

So,

J1 = ((6 + 5)/2)% × 15000 = 825

J2 = (28 - 20)% × 15000 = 1200

Now, (J2 - J1)

⇒ 1200 - 825 = 375

∴ The value of (J2 - J1) is 375.

Shortcut Trick

Numbers are obtained by multiplying their HCF with the co-prime factors of their LCM.

Given HCF = 17 and the other two factors of LCM are 11 and 19.

Smaller Number = HCF × Smaller factor

Smaller Number = 17 × 11 = 187

∴ The correct answer is 187.

Alternate Method

Given:

HCF of two numbers = 17

Other two factors of their LCM = 11 and 19

Formula Used:

If HCF of two numbers is H, then the numbers can be expressed as Hx and Hy, where x and y are co-prime factors.

LCM of these numbers = Hxy

HCF = 17

× 11

Smaller Number 17 × 11 = 187

× 19

Larger Number 17 × 19 = 323 Result: Smaller Number = 187

Calculation:

⇒ Let the two numbers be 17x and 17y.

⇒ LCM = 17xy

⇒ It is given that the factors of the LCM (other than the HCF) are 11 and 19.

⇒ So, the values are x = 11 and y = 19.

⇒ First number = 17 × 11 = 187

⇒ Second number = 17 × 19 = 323

⇒ Therefore, the smaller number is 187.

∴ The correct answer is 187.

Additional Information

Relation between HCF and LCM

The product of two given numbers is always exactly equal to the product of their HCF and LCM. Formula: Product of two numbers = HCF × LCM

Co-prime Factors

When we divide the LCM of two numbers by their HCF, the resulting quotient gives the product of two co-prime factors. These specific factors multiply individually with the HCF to yield the original two numbers.

Given:

$\rm {\cos A \over {1 - \tan A}} + {\sin A \over {1 - \cot A}}$

Concept used:

1. a² - b² = (a - b)(a + b)
2. tan θ = 1/ cot θ = sin θ/cos θ

Calculation:

$\rm {\cos A \over {1 - \tan A}} + {\sin A \over {1 - \cot A}}$

⇒ ${\cos A \over {1 - \frac {\sin A}{\cos A}}} + {\sin A \over{1 - \frac {\cos A}{\sin A}}}$

⇒ $\frac {\cos^2 A}{\cos A - \sin A} + \frac {\sin^2 A}{\sin A - \cos A}$

⇒ $\frac {\cos^2 A}{\cos A - \sin A} - \frac {\sin^2 A}{\cos A - \sin A}$

⇒ $\frac {\cos^2 A -\sin^2 A}{\cos A - \sin A}$

⇒ $\frac {(\cos A - \sin A)(\cos A + \sin A)}{\cos A - \sin A}$

⇒ sin A + cos A

∴ $\rm {\cos A \over {1 - \tan A}} + {\sin A \over {1 - \cot A}}$ equals to sin A + cos A.

Given:

2p + q = 19 and 8p3 + q3 = 361

Concept used:

a3 + b3 = (a + b)3 - 3ab(a + b)

Calculation:

8p3 + q3 = 361

⇒ (2p + q)³ - 3 × 2p × q (2p + q) = 361

⇒ (2p + q)3 - 6pq(2p + q) = 361

⇒ 193 - 6pq × 19 = 361

⇒ 19² - 6pq = 19

⇒ 6pq = 19² - 19

⇒ 6pq = 342

⇒ pq = 57

∴ The value of pq is 57.

Given:

I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 720

II. If x + y = 48 and 4xy = 128, then s the value of 4x2 + 4y2 is 8960

Concept used:

a² + b² + 2ab = (a + b)²

Calculation:

I.  x3 + y3 + z3 

⇒ (12)³ + (-2)3 + (-10)3 

⇒ 1728 - 8 - 1000

⇒ 720

II. Here, 4xy = 128

⇒ 2xy = 64      ....(1)

x + y = 48

⇒ (x + y)² = 48²

⇒ x² + y² + 2xy = 2304

⇒ x2 + y2 = 2304 - 64 (From 1)

⇒ x2 + y2 = 2240

⇒ 4x2 + 4y2 = 4 × 2240

⇒ 4x2 + 4y2 = 8960

Hence, both I and II follow.

∴ Both I and II are correct statements.

Given:

A girl purchases 9 mangoes for Rs. 90 and sells 10 mangoes for Rs. 95.

Concept used:

Loss% = ${(Cost\ Price\ -\ Selling\ Price) \over Cost\ Price} \times 100\%$

Calculation:

Cost price of each mango = 90/9 = Rs. 10

Selling price of each mango = 95/10 = Rs. 9.5

Now, her percentage loss = $\frac {10 - 9.5}{10} \times 100\%$ = 5%

∴ She incurred a 5% loss.

Calculation:

​According to the question,

x% × 2500 = 600

⇒ x% = 24

∴ The value of x is 24.

Given:

A four-digit pin, say abcd, of a lock, has different non-zero digits.

The digits satisfy b = 2a, c = 2b, d = 2c.

Calculation:

c = 2b

⇒ c = 2 × 2a = 4a      ...(1)

d = 2c

⇒ d = 2 × 4a = 8a      ....(2)

Now, the pin

⇒ abcd = 1000 × a + 100 × b + 10 × c + 1 × d

⇒ abcd = 1000 × a + 100 × 2a + 10 × 4a + 1 × 8a

⇒ abcd = 1000a + 200a + 40a + 8a

⇒ abcd = 1248a

⇒ abcd = (78 × 16)a

⇒ abcd = ((2 × 3 × 13) × 16)a

Hence, the pin is divisible by 2, 3, 13.

∴ The pin is divisible by 2, 3, 13.

Given:

A horse is grazing in a field. It is tied to a pole with a rope of a length of 6 m.

The horse moves from point A to point B making an arch with an angle of 70°. 

Concept used:

Area of a sector of a circle = πR² × θ/360 (R = Radius and θ = Angle obtain by the sector)

Calculation:

The area of the sector grazed by the horse

⇒ π × 6² × 70/360

⇒ 22/7 × 62 × 70/360

⇒ 22 m²

∴ The area of the sector grazed by the horse is 22 m².

Given:

ΔABC and ΔDEF are similar triangles and their areas are 49 cm2 and 144 cm2 respectively.

EF = 16.80 cm

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Calculation:

Since ΔABC and ΔDEF are similar triangles,

$\frac {AB}{DE} = \frac {BC}{EF} = \frac {AC}{DF} = \sqrt { \frac {area (\Delta ABC)}{area (\Delta DEF)}}$

⇒ $\frac {BC}{EF} = \sqrt { \frac {area (\Delta ABC)}{area (\Delta DEF)}}$

⇒ $\frac {BC}{16.80} = \sqrt { \frac {49}{144} }$

⇒ BC = 7/12 × 16.80

⇒ BC = 9.8

∴ The length of BC is 9.8 cm.

Given:

A can of water and milk mixture contains 60% milk. A part of this mixture is replaced by another mixture containing 50% milk and the percentage of milk was found to be 52%. 

Calculation:

Using mixture and alligation,

So, the ratio of the original solution that has 60% milk concentration to the solution that has 50% milk concentration = 2 : 8 = 1 : 4

Now, the quantity of mixture replaced is

⇒ $1 - \frac {1}{1 + 4}$

⇒ $4 \over 5$

∴ The quantity of mixture replaced is $4 \over 5$.