SSC CGL 2020 Tier-I Official Paper (Held On : 18 Aug 2021 Shift 3) (Previous Year Paper)

Given: 

The logic followed here is:

Let us say, that the symbols form a series inside the square starting from 

 , and ending with 

in the first figure.

Then, in each step, the symbol at the end of the series moves in the front of the series.

So, by following this condition, the answer figure should have 

in the front of the series, the complete series is as follows,

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Hence, option (3) is the correct answer.

From the given information,

(1) Rani is the sister of Piyush and the daughter of Kamal.

(2) Kamal is the son of Gaurav and the brother of Aryan.

(3) Aryan is the father of Rajneesh. Therefore, the final family tree is as follows:

Hence, Aryan is the paternal uncle of Piyush.

Given: 

The logic followed here is: line AB is the mirror,

Hence, option (3) is the correct answer.

Let the present age of Ramesh be 'R', Sangeeta be 'S', and that of Mayank be 'M'.

(1) The present age of Ramesh is 7 years more than the present age of his wife Sangeeta.

.

(2) 6 years hence, the age of Ramesh will be three times that of his son Mayank. If the present age of Mayank is 10 years, implies M = 10,

⇒ (R + 6) = 3 × (M + 6)

⇒ (R + 6) = 3 × (10 + 6)

⇒ R + 6 = 3 × 16

⇒ R + 6 = 48 

⇒ R = 48 - 6

⇒ R = 42

Then, we know R = 7 + S,

⇒ S + 7 = 42

⇒ S = 42 - 7

⇒ S = 35 years

Hence, 35 years is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Step 1: Arrange letters according to the alphabets series.

Step 2: If alphabet place value in unit digit then its place value multiply by 2.

Step 3: If the alphabet place value is two digits then both digits plus each other.

'REFUSAL' is coded as '2101239103'.

Step 1: REFUSAL → Alphabetical order → AEFLRSU.

Step 2: Here A, E, F place value is unit digit i.e. 1, 5 and 6 respectively. then its place value multiply by 2.

Step 3: Here L, R, S, U place value is two digits i.e 12, 18, 19 and 21 respectively. then both digits plus each other.

'POETRY' is coded as '1067927'.

Step 1 : POETRY → Alphabetical order → EOPRTY.

Step 2: Here E place value in unit digit i.e. 5 then its place value multiply by 2.

Step 3: Here O, P, R, T, Y place value is two digits i.e. 15, 16, 18, 20 and 25then both digits plus each other.

Similarly, 

PROFIT = ?

Step 1: PROFIT → Alphabetical order → FIOPRT.

Step 2: Here F, I place value in unit digit i.e. 6, 9 then its place value multiply by 2.

Step 3: Here, O, P, R and T place value is two digits i.e. 15, 16, 18 and 20 then both digits plus each other.

Hence, the correct answer is "12186792 ".

Given: 483 * 23 * 93 * 16 * 4 * 50

Given: 483 * 23 * 93 * 16 * 4 * 50

By checking options and substituting the signs accordingly:

(1) +, ÷, -, ×, =

We get,

LHS = 483 + 23 ÷ 93 - 16 × 4  

= 483 + 0.25 - 16 × 4  

= 483 + 0.25 - 64

= 483.25 - 64

= 419.25

≠ 50 

LHS ≠ RHS

(2) ÷, -, +, ×, =

We get,

LHS = 483 ÷ 23 - 93 + 16 × 4 

= 21 - 93 + 16 × 4 

= 21 - 93 + 64

= 85 - 93

= - 8

≠ 50 

LHS ≠ RHS

(3) ÷, +, -, ×, =

We get,

LHS = 483 ÷ 23 + 93 - 16 × 4 

= 21 + 93 - 16 × 4

= 21 + 93 - 64

= 114 - 64

= 50

LHS = RHS

(4) ÷, +, -, =, ×

We get,

LHS = 483 ÷ 23 + 93 - 16

= 21 + 93 - 16

= 114 - 16

= 98

RHS = 4 × 50

= 200

≠ 98

LHS ≠ RHS

Hence, ÷, +, -, ×, = is the correct answer.

Given: Jharkhand ∶ Ranchi

The logic followed here is:

Ranchi is the capital of Jharkhand.

Similarly,

Shillong is the capital of Meghalaya

Hence, Meghalaya ∶ Shillong is the correct answer.

Additional Information 

Given: Circle ∶ Arc ∶∶ Plant ∶ ?

The logic followed here is:

An arc is a part of a Circle.

Similarly,

A stem is a part of a Plant.

Hence, stem is the correct answer.

Important PointsChlorophyll → It is a substance present in leaves that gives the leave its green color.

Plasma → the colourless fluid part of blood, lymph, or milk, in which corpuscles or fat globules are suspended.

By counting the triangles:

Hence, 18 is the correct answer.

Given: CUH, HQK, MMN, RIQ, ?

The logic followed here is:

Hence, WET is the correct answer.

By checking options:

(1) BDYF 

(2) XZTB  

(3) NPKR 

(4) TVQX 

hence, XZTB is the odd one.

Given: (4, 10, 53)

The logic followed here is:

The first number × 3 - 2 = second number

The second number × 5 + 3 = third number

(4, 10, 53) → 4 × 3 - 2 = 12 - 2 = 10, 10 × 5 + 3 = 50 + 3 = 53

By checking options:

(1) (8, 20, 104) → 8 × 3 - 2 = 24 - 2 = 22 ≠ 20, 20 × 5 + 3 = 100 + 3 ≠  104 

(2) (5, 13, 62) → 5 × 3 - 2 = 15 - 2 = 13, 13 × 5 + 3 = 65 + 3 = 68 ≠ 62 

(3) (7, 19, 98) → 7 × 3 - 2 = 21 - 2 = 19, 19 × 5 + 3 = 95 + 3 = 98

(4) (11, 31, 152) → 11 × 3 - 2 = 33 - 2 = 31, 31 × 5 + 3 = 155 + 3 = 158 ≠ 152

Hence, (7, 19, 98) is the correct answer.

Given: 6, 6, 8, 24, 28, 140, ?

The logic followed here is

Hence, 146 is the correct answer.

The image obtained when the paper is unfolded is,

Hence, option 4 is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. No quilt is a carpet → False (it is possible but not definite because some quilts can be carpet as there is no direct relation between them) 

II. No blanket is a mat → False (it is possible but not definite because some blankets can be mat as there is no direct relation between them) 

III. Some carpets are mats → True (as some mats are carpets)

Hence, only conclusion III follows.

Additional Information

Given: Neptune, Planet, Moon

The logic followed here is: Neptune is a Planet, but Moon is not. Moon is a natural satellite.

Hence, option (4)  is the correct answer.

Given: 

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise rotation of the face is formed the opposite pair in dice.

While moving in a clockwise direction from the common face (B) of dice (1) and dice (3):

From both dices:

 

Now, only pair B and D left implies 'B' will be on the face opposite to the face having the letter 'D'.

Hence, B is the correct answer.

By checking options:

All devotion, zeal, and fury are strong emotions.

Whereas, 

Vision is not an emotion.

Hence, vision is the odd one.

Important PointsDevotion → love, loyalty, or enthusiasm for a person or activity.

Zeal → great energy or enthusiasm in pursuit of a cause or an objective.

Vision → the ability to think about or plan the future with imagination or wisdom.

Fury → extreme strength or violence in an action or a natural phenomenon.

Arranging all the words as per their order in the dictionary:

3. Gestation
4. Gesture
5. Glycerine
6. Glycogen
7. Gravity

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

Given:  'VIRTUE' is written as 'DBZBNX'.

The logic followed here is: 

(1) Vowels: - 7 in the positional value.

(2) Consonants: + 8 in the positional value.

Similarly,

Hence, HUBVHNA is the correct answer.

The logic followed here is:

Hence, option (1) is the correct answer.

The logic followed here is:

The second number × 3 + 5 = first number.

By checking options:

(1) 308 : 101 → 3 × 101 + 5 = 303 + 5 = 308

(2) 239 : 78 → 3 × 78 + 5 = 234 + 5 = 239

(3) 326 : 107 → 3 × 107 + 5 = 321 + 5 = 326

(4) 197 : 66 → 3 × 66 + 5 = 198 + 5 = 203 ≠ 197

Hence, 197 : 66 is the odd one.

Given:

 

Here the pattern followed in each Row is:

(1^st number)² + 3^rd number = 2^nd number

Row 1: (1^st number)² + 3^rd number = 2^nd number

3² + 4 = 9 + 4 = 13

Row 2: (1^st number)² + 3^rd number = 2^nd number

6² + 31 = 36 + 31 = 67

Similarly

Row 3: (1^st number)² + 3^rd number = 2^nd number

5² + 20 = 25 + 20 = 45

Hence, “45” is correct answer.

The logic followed here is:

(1st number + 4) ÷ 5] × 2 = 2nd number

• 16 ∶ 8 ⇒ 16 + 4 = 20; 20 ÷ 5 = 4 and 4 × 2 = 8
• 21 : 10 ⇒ 21 + 4 = 25; 25 ÷ 5 = 5 and 5 × 2 = 10
• 11 ∶ 6 ⇒ 11 + 4 = 15; 15 ÷ 5 = 3 and 3 × 2 = 6

Hence, 10 is the correct answer.

Given: H, Q, I, T, K, ?, N

The logic followed here is:

Hence, Y is the correct answer.

The correct answer is Sulphuric acid.

Key Points

• When an onion is cut or cut, the cells of the onion release these compounds into the air. When this happens, the "enzyme" works to convert the amino acids into lachrymator compounds. This form of sulfuric acid irritates the nerves around the eyes causing them to shed tears.
• Lachrymatory factor synthase is released into the air when we cut an onion.
• The synthase enzyme converts the amino acids sulfoxides of the onion into sulfenic acid.

Additional Information

The correct answer is 93.

• The total membership of the Constituent Assembly was 389, of which 93 were representatives of princely states.

Key Points

• The total membership of the Constituent Assembly was 389, out of which 292 were representatives of the provinces.
• 93 represented the princely states and four were from Delhi, Ajmer-Merwara, Coorg and Chief Commissioner provinces of British Balochistan.
• The Constituent Assembly of India was elected to frame the Constitution of India.
• It was elected by the provincial assembly. After India's independence from the British government in 1947, its members served as the country's first parliament.
• Constituent Assembly resolution in 1934 by M.N. Roy, a pioneer of the communist movement in India and an advocate of radical democracy.
• This became an official demand of the Indian National Congress in 1935, the Indian National Congress held its session in Lucknow in April 1936 under the chairmanship of Pt. Jawahar Lal Nehru.

Additional Information

Committees of the Constituent assembly:

The correct answer is The Prime Minister of India.

• The Prime Minister of India became the co-chair of the 17th ASEAN-India Summit in November 2020.

Key Points

• Prime Minister Shri Narendra Modi along with Prime Minister of Vietnam H.E. Nguyen Xuan Phuc has co-chaired the 17th ASEAN-India Summit on 12 November 2020.
• The Leaders of all ten ASEAN Member States will participate in the Summit. The Summit has been held online.
• The Summit will review the status of the ASEAN-India Strategic Partnership and take stock of progress made in key areas such as connectivity, maritime cooperation, trade and commerce, education and capacity building, etc.
• The Leaders will discuss ways to further strengthen ASEAN-India engagement and in this context will note the adoption of the ASEAN-India Plan of Action (2021-2025).
• ASEAN-India Strategic Partnership stands on a strong foundation of shared geographical, historical, and civilizational ties.
• India’s Act East Policy, underlining ASEAN centrality, reflects the importance, India attaches to engagement with ASEAN.

Additional Information 

• Narendra Modi:
• He is an Indian politician serving as the 14th and current prime minister of India since 2014.
• Narendra Modi was the chief minister of Gujarat from 2001 to 2014 and is a Member of Parliament from Varanasi.
• Modi led the BJP in the 2014 general election which gave the party a majority in the Indian lower house of parliament, the Lok Sabha, the first time for any single party since 1984.

The correct answer is Article 98.

• Article 98 of the Constitution of India defines a separate secretarial staff for each House of Parliament.

Key Points

• **Article 98 (**Secretariat of Parliament):
• Each House of Parliament shall have a separate secretarial staff: Provided that nothing in this clause shall be construed as preventing the creation of posts common to both Houses of Parliament.
• Parliament may by law regulate the recruitment, and the conditions of service of persons appointed, to the secretarial staff of either House of Parliament.
• Until provision is made by Parliament under clause (2), the President may, after consultation with the Speaker of the House of the People or the chairman of the Council of States, as the case may be, make rules regulating the recruitment, and the conditions of service of persons appointed, to the secretarial staff of the House of the People or the council of States, and any rules so made shall have effect subject to the provisions of any law made under the said clause Conduct of Business.

Additional Information

The correct answer is Aryabhatta.

• Aryabhatta is the first artificial satellite launched by India in 1975.

Key Points

• The Aryabhata spacecraft, named after the famous Indian astronomer, was India's first satellite, it was completely designed and fabricated in India and launched by a Soviet Kosmos-3M rocket from Kapustin Yar on April 19, 1975. 
• The satellite launch came from an agreement between India and the Soviet Union directed by UR Rao and signed in 1972.
• Aryabhata was created with the aim of experimenting with X-ray astronomy, agronomics, and solar physics.
• The Aryabhata satellite's image appeared on the reverse of the Indian two rupee banknotes between 1976 and 1997.
• The Indian satellite program began in the 1970s after the success of the Indian Space Research Organisation's (ISRO) success of the Rohini rocket program in the 1980s.

Additional Information

• ISRO:
• The Indian Space Research Organisation is the national space agency of India, headquartered in Bengaluru.
• It operates under the Department of Space (DOS) which is directly overseen by the Prime Minister of India, while the Chairman of ISRO acts as the executive of DOS as well.
• ISRO was established on 15 August 1969 and ISRO founder is Vikram Sarabhai.
• As of now January 2022 ISRO chairman in S Somanath.

The correct answer is Singer.

• SP Balasubramaniam was a Singer who was conferred with the Padma Vibhushan posthumously in January 2021.

Key Points

• SP Balasubrahmanyam was an Indian playback singer, television presenter, music director, actor, and film producer who worked predominantly in Telugu, Tamil, Kannada, Hindi, and Malayalam films.
• SP Balasubrahmanyam was born on 4 June 1946 in Nellore, Madras Presidency, British India.
• Balasubrahmanyam made his debut as a playback singer on 15 December 1966 with Sri Sri Sri Maryada Ramanna, a Telugu film scored by his mentor, S. P. Kodandapani.

Additional Information

• SP Balasubramaniam awards are:
• Padma Vibhushan in 2021
• Padma Shri in 2001
• Best Devotional Album in 2016
• Chevalier Sivaji Ganesan Award for Excellence in Indian Cinema in 2012

The correct answer is Nikolai Snesarev.

• Nikolai Snesarev was appointed as the middle and long-distance coach of the Indian athletics team in January 2021.

Key Points

• Snesarev was coaching 3000m steeplechaser Avinash Sable, who has qualified for the Olympics, and other middle and long-distance runners in their bid to qualify for the Tokyo Games.
• He had quit as Indian athletics’ long and middle distance coach in February 2019 after Sable opted to leave him and train under Army coach Amrish Kumar.
• Snesarev coached 10,000m runners Preeja Sreedharan and Kavita Raut to a 1-2 finish in the 2010 Asian Games and steeplechaser Sudha Singh to gold.
• Later, he advised Lalita Babar to try the steeplechase, an event where she reached the Olympic final in 2016 in Rio.

Additional Information

The correct answer is Population.

• According to Malthusian theory, the population grows in geometric progression.
• The Malthusian Theory of Population is the theory of exponential population and arithmetic food supply growth.
• The theory was proposed by Thomas Robert Malthus. He believed that a balance between population growth and food supply can be established through preventive and positive checks.

Key Points

• Malthusian Theory of Population Growth:
• Among the most famous theories of demography is the one associated with the English political economist Thomas Robert Malthus (1766-1834).
• Malthus's theory of population growth - outlined in his Essay on Population (1798) - was a rather pessimistic one.
• He argued that human populations tend to grow at a much faster rate than the rate at which the means of human subsistence (especially food, but also clothing and other agriculture-based products) can grow. Therefore humanity is condemned to live in poverty forever because the growth of agricultural production will always be overtaken by population growth.
• While population rises in geometric progression (i.e., like 2, 4, 8, 16, 32 etc.), agricultural production can only grow in arithmetic progression (i.e., like 2, 4, 6, 8, 10 etc.).
• Because population growth always outstrips growth in the production of subsistence resources, the only way to increase prosperity is by controlling the growth of the population.
• Unfortunately, humanity has only a limited ability to voluntarily reduce the growth of its population (through 'preventive checks' such as postponing marriage or practicing sexual abstinence or celibacy).
• Malthus believed therefore that positive checks' to population growth - in the form of famines and diseases - were inevitable because they were nature's way of dealing with the imbalance between food supply and increasing population.

The correct answer is RK Shanmukham Chetty.

• RK Shanmukham Chetty was the first Finance Minister of Independent India.

Key Points

• R.K. Shanmukham Chetty was born in Coimbatore on 17th October 1892.
• Independent India's first Budget was presented by the country's first finance minister, RK Shanmukham Chetty, on November 26, 1947, which was an interim Budget.
• The Budget statement presented by Mr. Chetty covered a period of seven and half months from August 15, 1947, to March 31, 1948, according to the Department of Economic Affairs website.

Additional Information

The correct answer is 19 January.

Key Points

• The National Disaster Response Force (NDRF) Raising Day is celebrated on January 19 to mark its formation.
• In 2021, the NDRF observed its 16th NDRF Raising Day.
• The NDRF came into existence on January 19, 2006. The specialized task force has been constituted for special response to a threatening disaster situation or a disaster.
• National Disaster Management Authority is the parent body of the NDRF.

Additional Information

• Last year when the NDRF Raising Day was observed, it was reported that the response force had saved 4,000 lives from the disasters.
• In 2020, NDRF personnel were deployed to respond to floods in Odisha during the Covid-19 crisis in the country.

The correct answer is Kerala.

• Kerala states’ tourism ministry announced the launch of India’s first Labour Movement Museum in January 2021.

Additional Information

The correct answer is Adil Hussain.

Key Points

• Actor Adil Hussain has bagged the Best Actor award at the Indo German Film Week in Berlin, for two of his recent performances - Pareeksha and Nirvana Inn.
• Prakash Jha directed Pareeksha while Vijay Jayapal had helmed Nirvana Inn.
• Adil was most recently seen as Buchchi a rickshaw-puller making all efforts to ensure the best education for his child in Prakash Jha's film.

Additional Information

• The Dadasaheb Phalke Award is India's highest award in cinema.
• It is presented annually at the ceremony by the Directorate of Film Festivals, an organization set up by the Ministry of Information and Broadcasting.
• The recipient is honored for their outstanding contribution to the growth and development of Indian cinema.
• Dadasaheb Phalke Award winners:
• 2017 - Vinod Khanna
• 2018 - Amitabh Bachchan
• 2019 - Rajinikanth

The correct answer is Bihar.

• Bihar states inaugurated its first bird festival ‘Kalrav’ in January 2021.

Key Points

• Bird sanctuaries in Bihar are:
• Salim Ali-Jubba Sahni Bird Sanctuary.
• Pant Wildlife Sanctuary.
• Kanwar Lake Bird Sanctuary.
• Nagi Bird Sanctuary.

Additional Information

The correct answer is Odisha.

• Odisha states launched the scheme ‘Sujal - Drink from Tap Mission’ that aims to provide quality drinking water directly from tap to all households in urban areas.

Key Points

• Odisha government launched the 'Sujal- Drink From Tap Mission' on October 13, 2020, to supply tap drinking water throughout the state.
• With the program, Odisha became the first state in India to implement a scheme of providing water fit for direct consumption in urban areas.
• A fund of Rs1300 crore was granted to provide quality tap water to over 15 lakh people in 15 towns in a phased manner.

Additional Information

The correct answer is 1947.

• In 1947 the Indian Independence Act passed by the British Parliament.

Key Points

• The Indian Independence Act, 1947 received royal assent and entered into force on 18th July 1947.
• The Indian Independence Act, 1947 was an act of the British Parliament that partitioned India into two independent dominions of India and Pakistan.
• The Act decided to grant independence to India and Pakistan with effect from 15th August 1947.
• British suzerainty over the princely states was to end. These states could decide to join either India or Pakistan or remain independent. Over 560 states decided to merge with India.

Additional Information

• According to this act, Pakistan became independent on 14 August and India on 15 August 1947. Muhammad Ali Jinnah was appointed Governor-General of Pakistan and Lord Mountbatten became of India.

The correct answer is Switzerland.

• Switzerland was the headquarters of the International Olympic Committee located as of February 2021.

Key Points

• The International Olympic Committee is a non-governmental sports organization based in Lausanne, Switzerland.
• It is formed as a federation under the Swiss Civil Code (Articles 60–79).
• Founded in 1894 by Pierre de Coubertin and Demetrios Viquelas, it is the authority responsible for organizing the modern (summer, winter and youth) Olympic Games.
• The IOC is the governing body of the National Olympic Committees (NOCs) and the worldwide Olympic movement, the term IOC for all entities and individuals involved in the Olympic Games.

Additional Information

The correct answer is Kerala.

• Makaravilakku is an annual festival held on Makar Sankranti in the Kerala states.

Key Points

• Makaravilakku is an annual festival held on Makara Sankranti at the Sabarimala Ayyappa temple in Kerala.
• Makara Jyothi is a star that appears in the sky on Makara Samkramam, when the Sun moves from dhanu Rasi (Sagittarius) to Makaram Rasi (Capricorn) on the first day of the Malayalam month of Makaram, January 14 (Makara Sankranti) this year.
• Onam is the most important and popular festival in Kerala. Celebrated with much pomp and fervor, Onam is a harvest festival.

Additional Information

The correct answer is Dantidurga.

• Dantidurga established the Rashtrakuta kingdom.

Key Points

• Dantidurga, also known as Dantivarman, was the founder of the Rashtrakuta kingdom of Manyakheta.
• His capital was located in the Gulbarga region of Karnataka.
• The Elichpur clan was a feudatory of the Badami Chalukyas, and during the rule of Dantidurga, it overthrew the Chalukya Kirtivarman II and created an empire with the Gulbarga region.
• This clan came to be known as the Rashtrakutas of Manyakheta, who came to power in South India.​

Important Points

The correct answer is Vishwavir Ahuja.

Mistake Points

• As per the March 2022,Rajeev Ahuja was appointed as interim MD & CEO on December 25, 2021 after its regular MD & CEO Vishwavir Ahuja proceeded on medical leave

Key Points

• Vishwavir Ahuja has been re-appointed as the MD and CEO of the RBL Bank in January 2021 for three years.
• RBL Bank, also known as Ratnakar Bank, is an Indian private sector bank and its headquarter is located in Mumbai.
• RBL Bank was established in 1943.
• In 2016, RBL Bank launched a financial literacy program called Saksham in collaboration with the CDC to provide education to 25,000 individuals and 300 villages in four districts of Madhya Pradesh.​

Additional Information

• Rajeev Ahuja has been appointed as interim MD & CEO of RBI
• On August 6, 1943, Ratnakar Bank was founded as a regional bank in Maharashtra with two branches in Kolhapur and Sangli founded by Babgonda Bhujgonda Patil from Sangli & Gangappa Siddappa Chougule from Kolhapur.
• In 1959, the bank was categorized as a scheduled commercial bank as per the Reserve Bank of India Act, 1934.
• In July 2010, Vishwavir Ahuja became managing director and CEO of the bank. In August 2014 the name of the bank was changed to RBL Bank Limited.

The correct answer is Andhra Pradesh.

• Kolleru Lake is located in the state of Andhra Pradesh.

Key Points

• Kolleru Lake is one of the largest freshwater lakes in India located in the state of Andhra Pradesh, 15 km from the city of Eluru.
• Kolleru is situated between the Krishna and Godavari deltas. Kolleru is spread over two districts - Krishna and West Godavari.
• The lake serves as a natural flood-balancing reservoir for these two rivers.
• The RAMSAR site of Kolleru Sanctuary is facing pollution and degradation due to large-scale shrimp cultivation for export.

Important Points

The correct answer is Nitric acid.

• Nitric acid is used in the purification of gold and silver.

Key Points

• Nitric acid is used in the purification of gold. The acid mixture aqua regia, or royal water, dissolves gold and is used to purify scrap alloy containing gold.
• Aqua regia is a mixture of hydrochloric acid and nitric acid in a 3:1 ratio.
• Nitric acid is a nitrogen oxoacid of formula HNO3 in which the nitrogen atom is bonded to a hydroxy group and by equivalent bonds to the remaining two oxygen atoms.

Important Points

The correct answer is Venation.

• Venation is the pattern of veins in the blade of a leaf.

Key Points

• The arrangement of veins in a leaf is called venation. In monocots, the veins show parallel venation, while in dicots, the veins show reticulate venation.
• Within each leaf, the vascular tissue forms veins. The arrangement of veins in a leaf is called the venation pattern.
• In monocot leaves, the veins run parallel to each other. Such leaves are said to have parallel venation.
• Example: banana, grass, and wheat.
• In dicot leaves, the veins, and veinlets are irregularly distributed over the entire lamina, forming a network.
• Example: mango and peepal.

Additional Information

• Morphology:
• ​Morphology is a branch of biology dealing with the study of the form and structure of organisms and their specific structural features.
• Cytology:
• ​Cytology is the exam of a single cell type, as often found in fluid specimens. It's mainly used to diagnose or screen for cancer.
• Anthology:
• ​The meaning of Anthology is a collection of selected literary pieces or passages or works of art or music.

The correct answer is Granite.

• Granite is is a coarse-grained igneous rock that contains quartz and feldspar.

Key Points

• Granite is a coarse-grained, light-colored, intrusive igneous rock that contains mainly quartz, feldspar, and mica minerals.
• Granite is a light-colored igneous rock with grains large enough to be visible with the unaided eye.
• It forms from the slow crystallization of magma below Earth's surface.
• Granite is composed mainly of quartz and feldspar with minor amounts of mica, amphiboles, and other minerals.
• ​Major production of granite in raw as well as processed form is generally from Andhra Pradesh, Rajasthan, Karnataka, Tamil Nadu, and Gujarat.

Additional Information

The correct answer is Rani of Jhansi Regiment.

• Rani of Jhansi Regiment is the name of the women's regiment in the Indian National Army founded by Subhash Chandra Bose.

Key Points

• The Rani of Jhansi Regiment was the women's regiment of the Indian National Army, the armed force formed by Indian nationalists in 1942 in Southeast Asia.
• It was one of the all-female combat regiments of the Second World War on all sides.
• It was Led by Captain Lakshmi Swaminathan, the unit was raised in July 1943 with volunteers from the expatriate Indian population in Southeast Asia.
• The announcement of this regiment was done by Bose on 12 July 1943.

Additional Information

• Subhash Chandra Bose was born on January 23, 1897, in Cuttack, Orissa.
• Azad Hind Radio station in Germany was established by Netaji.
• In 1923, Bose became the President of the All India Youth Congress and then eventually became the Congress President in 1938.
• Subash Chandra Bose authored the book The Indian Struggle which covers the Indian independence movement from 1920 to 1942.

The correct answer is Karnataka.

• The Kunchikal falls located in the state of Karnataka.

Key Points

• Kunchikal Falls is located in Nidagodu village near Masthikatte in Shimoga district of state Karnataka.
• Kunchikal falls is formed by the Varahi River.
• Kunchikal falls cascade down rocky boulders and the total height of the fall is 455 meters.

Additional Information

Given:

BO and CO is the angle bisector of ∠CBD and ∠BCE respectively.

∠BOC = 63° 

Concept used:

BO and CO is the angle bisector of ∠CBD and ∠BCE respectively.

Then, ∠BOC = 90° – (∠BAC/2)

Calculation:

According to the question

∠BOC = 63° 

⇒ ∠BOC = 90° – (∠BAC/2)

⇒ ∠BAC/2 = (90° – 63°)

⇒ ∠BAC/2 = 27° 

⇒ ∠BAC = (27 × 2)

⇒ ∠BAC = 54° 

∴ The required value is 54°

Given:

 sin6θ + cos6θ = $\frac{1}{3}$

Formula used:

a³ + b³ = (a + b) (a² + b² – ab)

a² + b² = (a + b)² – 2ab

Calculation:

a3 + b3 = (a + b) (a2 + b2 – ab)

sin6θ + cos6θ = (sin²θ)³ + (cos²θ)³ = 1/3

⇒ (sin2θ)3 + (cos2θ)³ = (sin²θ + cos²θ) (sin⁴θ + cos⁴θ – sin²θ × cos²θ) = 1/3

⇒ 1 × (sin4θ + cos4θ – sin2θ × cos2θ) = 1/3

⇒ (sin4θ + cos4θ – sin2θ × cos2θ) = 1/3

Now,

a2 + b2 = (a + b)2 – 2ab

⇒ (sin²θ + cos²θ)² – 2 × sin²θ × cos²θ – sin²θ × cos²θ = 1/3

⇒ (1)² - 3sin²θ × cos²θ = 1/3

⇒ 1 - 3sin²θ × cos²θ = 1/3

⇒ 3sin²θ × cos²θ = (1 – 1/3)

⇒ 3sin²θ × cos²θ = (2/3)

⇒ sin²θ × cos²θ = [2/(3 × 3)]

⇒ sin²θ × cos²θ = 2/9

⇒ sinθ × cosθ = √2/3

∴ The required value is $\frac{\sqrt{2}}{3}$

Given:

∠OAC = 35° 

∠OBC = 45° 

Concept used:

If two sides of a triangle are equal, then, the opposite angle will also be equal.

In circle, the length of each of the radius is same.

The sum of all interior angle of a triangle is 180°.

Sum of all the point around the circle is 360° 

Calculation:

In ΔOAC

⇒ OA = OC [radius]

So, ∠OAC = ∠OCA = 35° 

Now,

∠OAC + ∠OCA + ∠AOC = 180° 

⇒ 35° + 35° + ∠AOC = 180° 

⇒ 70° + ∠AOC = 180° 

⇒ ∠AOC = (180° – 70°)

⇒ ∠AOC = 110° 

In ΔOBC

⇒ OB = OC [radius]

So, ∠OBC = ∠OCB = 45° 

Now,

∠OBC + ∠OCB + ∠BOC = 180° 

⇒ 45° + 45° + ∠BOC = 180° 

⇒ 90° + ∠BOC = 180° 

⇒ ∠BOC = (180° – 90°)

⇒ ∠BOC = 90° 

Now,

∠AOB + ∠AOC + ∠BOC = 360° 

⇒ ∠AOB + 110° + 90° = 360° 

⇒ ∠AOB + 200° = 360° 

⇒ ∠AOB = (360° – 200°)

⇒ ∠AOB = 160° 

∴ The required value is 160°

Alternate Method 

In ΔOAC

⇒ OA = OC [radius]

So, ∠OAC = ∠OCA = 35° 

Also, In ΔOBC

⇒ OB = OC [radius]

So, ∠OBC = ∠OCB = 45°

⇒ ∠ACB =  ∠OCA + ∠OCB = 35° + 45° = 80° 

We know that angle subtended by an arc on the center of the circle is twice the angle subtended by it on any other part of the circle.

⇒ ∠AOB = 2 × ∠ACB = 2 × 80° = 160° 

∴ The required value is 160°

Calculation:

Number of students studying commerce in institute D = 55

Total number of students in Arts = (36 + 45 + 55 + 45 + 48) = 229

Total number of students in Science = (48 + 54 + 36 + 48 + 44) = 230

Total number of students in Commerce = (59 + 55 + 56 + 55 + 52) = 277

Total number of students in Computer science = (57 + 48 + 51 + 53 + 55) = 264

Total number of students of the 5 institutes = (229 + 230 + 277 + 264) = 1000

Required percentage = (55/1000 ×100)

⇒ (55/10)

⇒ 5.5

The required percentage is 5.5

Given:

Sides of the triangle = 5cm, 12cm and 13 cm

Formula used:

Area of triangle = √s(s – a)(s – b) (s – c)

Semi perimeter (s) = (a + b + c)/2

Area of right angle triangle = 1/2 × base × height

Concept used:

Any triangle have three altitude, each altitude is from vertex to the opposite side.

Calculation:

The semi perimeter of triangle = (5 + 12 + 13)/2

⇒ (30/2)

⇒ 15 cm

Area of triangle = √s(s – a)(s – b) (s – c)

⇒ √15(15 – 5)(15 – 12)(15 – 13)

⇒ √15 × 10 × 3 × 2

⇒ √900

⇒ 30 cm²

As we know 5, 12 and 13 are triplets and form a right angle triangle.

The smallest altitude will be on Hypotenuse

Area of right angle triangle = 1/2 × base × height

⇒ 30 = 1/2 × 13 × height

⇒ 60 = 13 × height

⇒ height = (60/13)

⇒ height = 4.6 cm

∴ The length of the smallest altitude of the triangle is 4.6 cm

Shortcut Trick 

The length of smallest altitude is always perpendicular to the largest side of the triangle

So BO is the smallest altitude 

Now, BO = (AB × BC)/AC

⇒ BO = (5 × 12)/13 = 60/13 = 4.6 cm

∴ The correct answer is 4.6 cm

Given:

Time taken by 5 men to complete a work = 20 days

Time taken by 10 women to complete a work = 15 days

Formula used:

Work = Efficiency × Time

Calculation:

Five men can complete a work in 20 days = (20 × 5) = 100 

Ten women can complete the same work = (15 × 10) = 150 

LCM of 100 and 150 is 300

Efficiency of 1 man = (300/100) = 3 units/day

Efficiency of 1 woman = (300/150) = 2 units/day

2 men and 6 women worked together for five days

⇒ (2 × 3 + 6 × 2) × 5

⇒ (6 + 12) × 5

⇒ (18 × 5) = 90 days

Remaining work = (300 – 90) = 210 units 

Now,

After 5 days, 3 women left the work =  (6women – 3women) = 3women

And 1 man joined the work = (1man + 2man) = 3man

Time taken to complete the remaining work by 3 women and 3 men is

⇒ [210/(3 women + 3 men)]

⇒ [210/(3 × 2 + 3 × 3)] 

⇒ [210/(6 + 9)] 

⇒ (210/15) days

⇒ 14 days

∴ The required time is 14 days

Shortcut TrickHere we need to equal number of men and women,

Ten women can complete the work in 15 days

So, five women can complete the work in 30 days

Now,

Total work 60 × 5 [∵ 5 men or women are also working]

2 men and 6 women together = (2 × 3 + 6 × 2) × 5 = 90 units in five days

Remaining = 300 - 90 = 210 units

Now,

Time taken by 3 men and 3 women to complete the remaining work = [210/(3 × 2 + 3 × 3)] = 14 days

Given:

AB = 12 cm

CD = 18 cm

Distance between the chords AB and CD = 15 cm

Formula used:

AB² + BC² = AC²

Calculation:

The distance between the centre O and chord AB be x.

Then, The distance between the centre O and chord CD be (15 – x).

Now,

From ΔAMO,

AM² + OM² = OA²

⇒ (6)² + x² = r² ....(1)

Similarly from ΔOCN,

ON² + CN² = OC²

⇒ (15 – x)² + (9)² = r² ....(2)

From equation (1) and (2)

⇒ (6)2 + x2 = (15 – x)2 + (9)2 

⇒ 36 + x² = 225 + x² – 30x + 81

⇒ 30x = (225 – 36) + 81

⇒ 30x = (189 + 81)

⇒ 30x = 270

⇒ x = 9

Now, putting the value of x in equation (1), we get

⇒ (6)² + (9)² = r²

⇒ 36 + 81 = r²

⇒ 117 = r²

⇒ 3√13 = r

∴ The value of radius is 3√13

Calculation:

The number of seat remained vacant in 2nd class Non-AC on Wednesday = (900 – 830) = 70

The number of seat remained vacant in 2nd class Non-AC on Thursday = (900 – 790) = 110

The number of seat remained vacant in 1st class Non-AC on Wednesday = (500 – 390) = 110

The number of seat remained vacant in 1st class Non-AC on Thursday = (500 – 480) = 20

Total number of vacant seat in all the Non-AC classes on Wednesday and Thursday = (70 + 110 + 110 + 20)

⇒ 310

The number of seat remained vacant in AC III tier on Monday = (500 – 480) = 20

The number of seat remained vacant in AC III tier on Tuesday = (500 – 450) = 50

The number of seat remained vacant in AC II tier on Monday = (250 – 240) = 10

The number of seat remained vacant in AC II tier on Tuesday = (250 – 230) = 20

The number of seat remained vacant in AC II tier on Friday = (250 – 210) = 40

The number of seat remained vacant in AC 1st class on Monday = (150 – 145) = 5

The number of seat remained vacant in AC 1st class on Tuesday = (150 – 120) = 30

The number of seat remained vacant in AC 1st class on Friday = (150 – 130) = 20

Total number of vacant seat in all the AC classes on Monday, Tuesday and Friday = (20 + 50 + 10 + 20 + 40 + 5 + 30 + 20)

⇒ 195

The ratio of number of seats that remained vacant in all the Non-AC classes on Wednesday and Thursday taken together to number of seats remained vacant in AC classes on Monday, Tuesday and Friday = (310 : 195)

⇒ 62 : 39

∴ The required ratio is 62 : 39

Given:

(secθ + tanθ)2 + $\frac{1 + cosec θ}{1 - cosec θ}$ , 0° < θ < 90°

Formula used:

cosec²θ  = 1 + cot²θ 

1 – cosec²θ = - cot²θ 

Calculation:

(secθ + tanθ)2 + $\frac{1 + cosec θ}{1 - cosec θ}$

Multiplying $\frac{1 + cosec θ}{1 - cosec θ}$ by the conjugate of 1 – cosecθ, i.e. by 1 + cosecθ

⇒ (secθ + tanθ)² + (1 + cosecθ/1 – cosecθ) × (1 + cosecθ/1 + cosecθ)

⇒ (secθ + tanθ)2 + (1 + cosecθ)²/(1 – cosec²θ)

⇒ (secθ + tanθ)2 + (1 + cosecθ)²/(-cot²θ)

⇒ (secθ + tanθ)2 – ((1 + cosecθ)/cotθ)²

⇒ (secθ + tanθ)² – (1/cotθ + cosecθ/cotθ)²

⇒ (secθ + tanθ)2 – (tanθ + secθ)²

⇒ 0

So, the required value is 0.

Shortcut Trick

we can also put θ = 30° 

⇒ (sec30° + tan30°)² + (1 + cosec30°/1 - cosec30°)

⇒ (2/√3 + 1/√3)² + (1 + 2/1 - 2)

⇒ 9/3 - 3/1

⇒ 3 - 3 

⇒ 0

So, the required value is 0.

Calculation:

Number of persons income less than 250 = 26

Number of persons less than 350 = 40

According to the question

Person earn Rs. 250 or more but less than Rs. 350 daily = (40 – 26)

⇒ 14

∴ The required persons is 14

Given:

The ratio of sum of money = 4 : 5

T₁ = 4 years

T₂ = 5 years

Rate = 8%

Difference between the interests earned from the two parts = Rs. 4680

Formula used:

SI = (P × R × T)/100

Calculation:

Let the ratio of sum of money be 4x and 5x respectively

Total ratio of sum of money = (4x + 5x) = 9x

According to the question

SI on first part = (4x × 8 × 4)/100

⇒ 128x/100

SI on second part = (5x × 8 × 5)/100

⇒ 200x/100

Difference between the interests = (200x/100 – 128x/100)

⇒ 72x/100

Now,

⇒ 72x/100 = 4680

⇒ 72x = (4680 × 100)

⇒ 72x = 468000

⇒ x = (468000/72)

⇒ x = Rs. 6500

The total sum lent = 9x = Rs. (9 × 6500)

⇒ Rs. 58500

∴ The required total sum lent is Rs. 58500

Given:

The ratio of x and y in alloy A = 5 : 2

The ratio of x and y in alloy B = 3 : 4

The ratio of A and B in the alloy C = 4 : 5

Calculation:

Let the quantity of y in alloy C be x.

⇒ Quantity of metal x in alloy A = 5/7

⇒ Quantity of metal y in alloy A = 2/7

⇒ Quantity of metal x in alloy B = 3/7

⇒ Quantity of metal y in alloy B = 4/7

According to the question

The ratio of x and y in alloy C = (5/7 × 4 + 3/7 × 5)/(2/7 × 4 + 4/7 × 5)

⇒ (20/7 + 15/7)/(8/7 + 20/7)

⇒ (35/7)/(28/7)

⇒ 5/4

The ratio of x and y in alloy C = 5 : 4

⇒ Quantity of y in alloy C = 4/9

Percentage of y in alloy C = (4/9 × 100)

⇒ (400/9)

⇒ $44\frac{4}{9}\%$%

∴ The percentage of y in alloy C is $44\frac{4}{9}\%$%

Given:

Ratio of investment of Keshav, Surjeet and Thomas = 2 : 3 : 4

The ratio of their period of investments = 5 : 6 : 9

Profit spent on rent and maintenance = 20%

The difference in the shares of profit of Keshav and Surjeet = Rs. 7264

Formula used:

Profit = Investment × Time

Calculation:

Let the ratio of their period of investments be 5x, 6x and 9x respectively

Profit of Keshav = (5x × 2) = 10x

Profit of Surjeet = (6x × 3) = 18x

Profit of Thomas = (9x × 4) = 36x

According to the question 

18x - 10x = 7264

⇒ x = 908

So, Profit of Keshav + Surjeet + Thomas = 64x 

⇒ 64 × 908 = 58112

But it is the 80% of the actual profit 

So, 80% is equivalent to 58112

So, 100% is equivalent to 58112 × 5/4 = 72640

∴ The required total profit is Rs. 72640

Given:

The sides of a right angle triangle = 5 cm and 12 cm

Formula used:

Area of triangle = 1/2 × base × height

BC² = AC² + AB²

Calculation:

Let the radius be r

According to the question

Area of triangle = 1/2 × base × height

⇒ (1/2 × 5 × 12) cm²

⇒ 30 cm²

By Pythagoras theorem

BC2 = AC2 + AB²

⇒ BC² = (5)² + (12)²

⇒ BC² = (25 + 144)

⇒ BC² = 169

⇒ BC = 13 cm

Area of ΔABC = Area of ΔOAB + Area of ΔOBC + Area of ΔOCA

⇒ 30 = 1/2 × r × AB + 1/2 × r × BC + 1/2 × r × AC

⇒ 30 = 1/2r(AB + BC + AC)

⇒ 30 = 1/2r(12 + 13 + 5)

⇒ 60 = r(30)

⇒ r = (60/30)

⇒ r = 2 cm

∴ The required radius is 2 cm

Alternate MethodBy Pythagoras's theorem

BC2 = AC2 + AB2

⇒ BC2 = (5)2 + (12)2

⇒ BC2 = (25 + 144)

⇒ BC2 = 169

⇒ BC = 13 cm

Radius of circle = (AC + AB - BC)/2 

⇒ (12 + 5 - 13)/2

⇒ 4/2

⇒ 2 

So, the required radius is 2 cm

Calculation:

Expenditure on food = 105

Expenditure on rent = 70

Required percentage = [(105 – 70)/70 × 100]

⇒ (35/70 × 100)

⇒ 50%

∴ The required percentage is 50%

Given:

a3 –  b3 = 2349 and (a – b) = 9

Formula used:

(a + b)² = a² + b² + 2ab

(a³ – b³) = (a – b) (a² + ab + b²)

Calculation:

According to the question

(a + b)2 –  ab

⇒ a² + b² + 2ab – ab

⇒ a² + b² + ab

Now,

(a3 – b3) = (a – b) (a2 + ab + b2)

⇒ 2349 = 9 (a² + ab + b²)

⇒ (a2 + ab + b²) = (2349/9)

⇒ (a2 + ab + b²) = 261

∴ The required value is 261

Given:

CP of a machine = Rs. 4600

Money spent on repairs and transport = Rs. 500

He marked the machine at 8% above the price overall cost price

SP of a machine = Rs. 4681.80

Formula used:

Loss = CP – SP

Loss% = Loss/CP × 100

Calculation:

CP of a machine = Rs. (4600 + 500)

Rs. 5100

He marked the machine at 8% above the price overall cost price

⇒ (5100 × 8/100)

⇒ Rs. 408

New CP = Rs. (5100 + 408) = Rs. 5508

Now,

Loss = SP – CP

⇒ (5508 – 4681.80)

⇒ Rs. 826.20

Loss% = (826.20/5508 × 100)

⇒ (82620/5508)

⇒ 15%

∴ The value of x is 15

Given:

sin(A + B) = 1 and cos(A - B) = √3/2

A + B = 90° and A > B 

Formula used:

sin90° = 1

cos30° = √3/2

sin30° = 1/2

tan60° = √3

cos60° = 1/2

Calculation:

sin(A + B) = 1

⇒ sin(A + B) = 90° 

⇒ A + B = 90° ....(1)

Again, 

cos(A – B) = √3/2

⇒ cos(A – B) = 30° 

⇒ A – B = 30° .....(2)

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

⇒ A + B + A – B = (90° + 30°)

⇒ 2A = 120° 

⇒ A = (120/2)

⇒ A = 60° 

Putting the value of A in equation(2), we get

⇒ 60° – B = 30° 

⇒ B = 30° 

Now,

$\frac{5 \sin^2 B + 4 \tan^2 A}{2 \sin B\cos A}$ = (5 × sin²30° + 4 tan²60°)/(2 × sin30° × cos60°)

⇒ [5 × (1/2)² + 4 × (√3)²]/(2 × 1/2 × 1/2)

⇒ [(5 × 1/4) + (4 × 3)/1/2]

⇒ [(5/4 + 12)/1/2] 

⇒ [(5 + 48)/4/(1/2)]

⇒ (53/4)/(1/2)

⇒ 53/2

⇒ 26$\frac{1}{2}$

So, the required value is $26\frac{1}{2}$

Given:

A.T.V. is sold at 8% gain. Had it been sold for Rs.2553 less

Loss = 15%

Formula used:

SP = (100 + gain) × CP/100

Calculation:

Let the cost price be 100x.

⇒ Selling price = (100x + 8x) = 108x

A TV sold = Rs. 2553 less, there would have been loss of 15%

⇒ (108 – 85)x = 2553

⇒ 23x = 2553

⇒ x = 2553/23

⇒ x = Rs 111

Cost price = 100x = (100 × 111)

⇒ Rs. 11100

Now, to gain = 18%

SP = Rs. (11100 × 118/100). 

⇒ Rs. (111 × 118)

⇒ Rs. 13098

∴ The selling price of T.V. is Rs. 13098

Given:

a + b + c = 0

Formula used:

(a + b)² = (a² + b² + 2ab)

Calculation:

a + b + c = 0

a + b = -c ..(1)

b + c = -a ...(2)

c + a = -b ...(3)

Now,

$\frac{(b + c)^2}{bc} + \frac{(c + a)^2}{ca}+\frac{(a + b)^2}{ab}$

⇒ (b² + c² + 2bc)/bc + (c² + a² + 2ca)/ca + (a² + b² + 2ab)/ab

⇒ (b²/bc + c²/bc + 2bc/bc) + (c²/ca + a²/ca + 2ca/ca) + (a²/ab + b²/ab + 2ab/ab)

⇒ (b/c + c/b + 2) + (c/a + a/c + 2) + (a/b + b/a + 2)

⇒ (b + c)/a + (c + a)/b + (a + b)/c + 2 + 2 + 2

Using equations (1), (2), and (3)

⇒ (-b/b) + (-c/c) + (-a/a) + 6

⇒ (-1) + (-1) + (-1) + 6

⇒ 6 – 3

⇒ 3

∴ The required value is 3.

Shortcut Trick$\frac{(b + c)^2}{bc} + \frac{(c + a)^2}{ca}+\frac{(a + b)^2}{ab}$

a + b + c = 0

a + b = -c ..(1)

b + c = -a ...(2)

c + a = -b ...(3)

Using the above values, 

⇒ $\frac{(- a)^2}{bc} + \frac{( - b)^2}{ca}+\frac{(- c)^2}{ab}$

⇒ $\frac{a^2}{bc} + \frac{ b^2}{ca}+\frac{ c^2}{ab}$

⇒ $\frac{a^3}{abc} + \frac{b^3}{bca}+\frac{ c^3}{cab}$

We know that, if a + b + c = 0 then a³ + b³ + c³ = 3abc

Using the above result, we get,

⇒ 3abc/abc = 3

∴ The required value is 3.

Given:

$x - \frac{1}{x}= √{77}$

Formula used:

(x + 1/x)² = (x)² + (1/x)² + 2 × x × 1/x

Calculation:

$x - \frac{1}{x}= √{77}$

Squaring both sides, we get

(x – 1/x)² = (√77)²

⇒ (x)² + (1/x)² – 2 × x × 1/x = 77

⇒ x² + 1/x² – 2 = 77

⇒ x² + 1/x² = (77 + 2)

⇒ x² + 1/x² = 79

Now,

(x + 1/x)² = x² + 1/x² + 2 × x × 1/x

⇒ x² + 1/x² + 2 

⇒ 79 + 2

⇒ 81

⇒ (x + 1/x) = 9

Now,

(x³ + 1/x³) = (x + 1/x)³ – 3 × x × 1/x × (x + 1/x)

⇒ (9)³ – 3 × 9

⇒ 729 – 27

⇒ 702

We know that when we find a square root of any number there is a two value coming i.e. positive value or negative value

So,

⇒ 702 is not given, it means the right value of the given question is -702

∴ The required value is -702

Confusion Points(x + 1/x) = - 9

Now,

(x3 + 1/x3) = (x + 1/x)3 – 3 × x × 1/x × (x + 1/x)

⇒ - 9³ - 3(- 9)

⇒ -729 + 27

⇒ - 702

∴ The required value is -702

Concept Used:     

Follow the BODMAS rule according to the table given below:

Calculation:

441 ÷ $\left[270 ÷ \frac{3}{7}+\left(17÷ \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]$

⇒ 441 ÷ [270 ÷ 3/7 + (17 × 3) – (17/2 – 5/2)]

⇒ 441 ÷ [270 ÷ 3/7 + 51 – (17/2 – 5/2)]

⇒ 441 ÷ [270 ÷ 3/7 + 51 – (12/2)]

⇒ 441 ÷ [270 ÷ 3/7 + 51 – 6]

⇒ 441 ÷ [270 × 7/3 + 51 – 6]

⇒ 441 ÷ [(90 × 7) + 51 – 6]

⇒ 441 ÷ [630 + 51 – 6]

⇒ 441 ÷ [681 – 6]

⇒ 441 ÷ 675

⇒ 49/75

∴ The required value is 49/75

Given:

A train runs with the speed of 72 km/h, it reaches its destination late = 15 minutes

A train runs with the speed of 90 km/h, it reaches its destination late = 5 minutes

Formula used:

Distance = Speed × Time

Concept used:

Distance is same

Calculation:

Let the correct time to covers its journey be x min

According to the question

⇒ 72 × (x + 15)/60 = 90 × (x + 5)/60

⇒ 4 × (x + 15) = 5 × (x + 5)

⇒ 4x + 60 = 5x + 25

⇒ (5x – 4x) = (60 – 25)

⇒ x = 35 min

∴ The correct time to covers its journey is 35 min

Given:

The average daily production of toys in a factory in the month of December = 512

The average production during first 20 days = 515 

The last 13 days = 510

Concept used:

Total number of days in December = 31 

Formula used:

Average = sum of observations/Number of observations

Calculation:

The average daily production of toys in a factory in the month of December = 512

⇒ (31 × 512)

⇒ 15872

The average production during first 20 days = 515 

⇒ (20 × 515)

⇒ 10300

The last 13 days = 510

⇒ (13 × 510)

⇒ 6630

The average of production on 19 and 20 December = [(The average production during first 20 days + The last 13 days) – (The total average production in December)]/2

⇒ [(10300 + 6630) – 15872]/2

⇒ (16930 – 15872)/2

⇒ 1058/2

⇒ 529

∴ The required average is 529

Given:

A number P is divisible by 2 and another number Q is divisible by 3

Concept used:

Divisibility rule of 2 - All whole number that ends in 0, 2, 4, 6, 8 will be divisible by 2.

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

Calculation:

If a number is divisible by 2 and another number is divisible by 3 then that number satisfy the divisibility rule of 6.

Let us take the number i.e. 306 which is divisible by both 2 and 3.

⇒ The last digit of number is 6, which is an even number.

Hence, it is divisible by 2

⇒ The sum of digits = (3 + 0 + 6) = 9, which is multiple of 3.

Hence, it is divisible by 3.

∴ P × Q is divisible by 6

Note:

P + Q is divisible by 5

Some condition is satisfied like P = 2, Q = 3 = 5 divisible by 5

P = 10, Q = 15. 

⇒ 10 + 15 = 25, 25 is divisible by 5

Not satisfied condition like P = 4, Q = 9 

⇒ 4 + 9 = 13, 13 is not divisible by 5

That's why we have not considered Option 2 as the correct answer.

Option 4 is satisfied all conditions.