SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 3) (Previous Year Paper)

The logic followed here is:

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

In the given figure, Opposite faces are :

∴ Here, the opposite side of face '1' is '2'.

Hence, the correct answer is "2".

The logic followed here is :-

1) Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90° anticlockwise.

2) Then she turns 45° clockwise, followed by a 135° anticlockwise turn.

∴ Here, At last Reeta is facing towards 'East'.

Hence, the correct answer is "East".

After unfolding the given paper the figure thus formed is as shown below :-

Hence, the correct answer is "Option 2".

The logic followed here is :-

1) YJB

Y(25) + 11 = 36 = 26 + 10 = J(10) 

J - 8 = B

2) UFQ

U(21) + 11 = 32 = 26 + 6 = F(6)

F + 11 = Q

3) RCN

R(18) + 11 = 29 = 26 + 3 = C(3)

C + 11 = N

4) EPA

P + 11 = 27 = (26 + 1) = A

∴ Here, 'YJB' is different from the other three alternatives.

Hence, the correct answer is "YJB".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : + and × 

Given equation : 32 + 24 × 4 ÷ 16 – 64 = 90

After interchanging the symbols in given equation the equation is as follows : 32 × 24 + 4 ÷ 16 - 64 = 90

⇒ 32 × 24 + 4 ÷ 16 - 64 = 90

⇒ 32 × 24 + 0.25 - 64 = 90

⇒ 768 + 0.25 - 64 = 90

⇒ 768.25 - 64 = 90

⇒ 704.25 ≠ 90

LHS ≠ RHS

Option 2) : ÷ and +

Given equation : 32 + 24 × 4 ÷ 16 – 64 = 90

After interchanging the symbols in given equation the equation is as follows : 32 ÷ 24 × 4 + 16 - 64 = 90

⇒ 32 ÷ 24 × 4 + 16 - 64 = 90

⇒ 1.333 × 4 + 16 - 64 = 90

⇒ 5.333 + 16 - 64 = 90

⇒ 21.333 - 64 = 90

⇒ - 42.666 ≠ 90

LHS ≠ RHS

Option 3) : ÷ and ×

Given equation : 32 + 24 × 4 ÷ 16 – 64 = 90

After interchanging the symbols in given equation the equation is as follows : 32 + 24 ÷ 4 × 16 - 64 = 90

⇒ 32 + 24 ÷ 4 × 16 - 64 = 90

⇒ 32 + 6 × 16 - 64 = 90

⇒ 32 + 96 - 64 = 90

⇒ 128 - 64 = 90

⇒ 64 ≠ 90

LHS ≠ RHS

Option 4) : + and –

Given equation : 32 + 24 × 4 ÷ 16 – 64 = 90

After interchanging the symbols in given equation the equation is as follows : 32 - 24 × 4 ÷ 16 + 64 = 90

⇒ 32 - 24 × 4 ÷ 16 + 64 = 90

⇒ 32 - 24 × 0.25 + 64 = 90

⇒ 32 - 6 + 64 = 90

⇒ 96 - 6 = 90

⇒ 90 = 90

LHS = RHS

Hence, the correct answer is "+ and –".

The logic followed here is :-

By using BODMAS RULE :

Given :-

Given expression is : 8 B (4 A 5) C (99 A 27) D 14 A 5 B (112 D 16)

After replacing the alphabets with symbols the expression is as follows : 8 × (4 + 5) - (99 + 27) ÷ 14 + 5 × (112 ÷ 16)

= 8 × (4 + 5) - (99 + 27) ÷ 14 + 5 × (112 ÷ 16)

= 8 × 9 - 126 ÷ 14 + 5 × 7

= 8 × 9 - 9 + 5 × 7

= 72 - 9 + 35

= 107 - 9

= 98

Hence, the correct answer is "98".

The logic followed here is :-

‘TURKEY’ is written as ‘76911525’.

Similarly,

‘BREATH’ will be written as :

Hence, the correct answer is "259221208".

Preparing the family tree using the following symbols:

 ‘A % B’ means ‘A is the sister of B’.

‘A $ B’ means ‘A is the brother of B’.

‘A @ B’ means ‘A is the son of B’.

‘A & B’ means ‘A is the mother of B’.

The given expression is :

‘R % T & Z $ S @ V @ C % Y’ → R is sister of T, T is mother of Z, Z is brother of S, S is son of V, V is the son of C, C is the sister of Y.

Option 1) : C is the paternal grandmother of Z → True (As T is mother of Z, Z is brother of S, S is son of V, V is the son of C so, C is the paternal grandmother of Z is true)

Option 2) : T is the mother of S → True (As T is mother of Z, Z is brother of S, S is son of V so, T is the mother of S is true)

Option 3) : T is the daughter of C → False (As T is mother of Z, Z is brother of S, S is son of V, V is the son of C so, T is daughter-in-law of C but given T is the daughter of C is false)

Option 4) : V is the father of Z → True (As T is mother of Z, Z is brother of S, S is son of V so, V is the father of Z is true)

∴ Here, 'T is the daughter of C' is not correct by following statements in given expression.

Hence, the correct answer is "T is the daughter of C".$

The image that replace the ? in the given series is as shown below :-

• The darken square moves left to right one step from figure 1 to figure 2, two steps from figure 2 to figure 3, three steps from figure 3 to figure 4 and four step left to right from figure 4 to figure 5.
• Darken triangle moves right to left two steps from figure to figure.
• × symbol moves 6 steps upwards in open boxes from figure to figure in clockwise.

Hence, the correct answer is "Option 2".

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

Conclusions:

I. Some printers are machines → False (As Some printers are coolers and All machines are telephones and No cooler is a telephone so, Some printers are machines is false)

II. No machine is a cooler → True (As All machines are telephones and No cooler is a telephone so, No machine is a cooler is true)

∴ Here, Only conclusion II is true.

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

The logic followed here is:-

Hence, the correct answer is "111".

The image embedded in given figure is as shown below :

 

∴ Here, Option figure 2 is embedded in given figure (X).

Hence, the correct answer is "Option 2".

The logic followed here is :-

Adding the alternate prime numbers: 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67.

Hence, the correct answer is "140".

Additional Information

Prime Numbers: The numbers which have only two factors one and the number itself.

Example: 2, 3, 5, 7 etc.

The logic followed here is:-

(First number + 1)² × 2 = Second Number

• 14 : 450

= (14 + 1)² × 2 = 450

= (15)² × 2 = 450

= 225 × 2 = 450

= 450 = 450

Similarly,

• 18 : 722

= (18 + 1)2 × 2 = 722

= (19)2 × 2 = 722

= 361 × 2 = 722

= 722 = 722

Hence, the correct answer is "Option 2".

Alternate Method

First number × ((First number + 2) × 2) + 2 = Second number.

By using BODMAS RULE :

• 14 : 450

= 14 × ((14 + 2) × 2) + 2

= 14 × (16 × 2) + 2

= 14 × 32 + 2

= 448 + 2

= 450

Similarly,

• 18 : 722

= 18 × ((18 + 2) × 2) + 2

= 18 × (20 × 2) + 2

= 18 × 40 + 2

= 720 + 2

= 722

Hence, the correct answer is "18 : 722".

The logic followed hers is :-

Code of or → ru

Code for do → ko

∴ Here, 'die' is coded as 'su'.

Hence, the correct answer is "su".

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

2. Junction
3. Junctures  
4. Junketeered
5. Junketeering
6. Junketers

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

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

Detailed Explanation:

• The line PQ is the mirror.
• The word "5gsdfncK" has last third letter 'n'. So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "5gsdfncK" has last fourth letter 'f'. So, the mirror image should be "

" ⇒ Option 3 is eliminated.

• The word "5gsdfncK" has second letter 'g'. So, the mirror image should be "

" ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option 1".

The logic followed here is :-

PDK : QFN

Similarly,

SJQ : ?

Hence, the correct answer is "TLT".

Given :- S P _ _ _ P S T S _ _ _ S P S _ 

By checking options and substituting accordingly.

1) T S S P T S S → S P T S - S P S T - S P T S - S P S S

2) P S S P P S S → S P P S - S P S T - S P P S - S P S S

3) P S T S P T T → S P P S - T P S T - S S P T - S P S T

4) S T S P S T T → S P S T - S P S T - S P S T - S P S T

• Here 'SPST' is repeated.
• Option (4) gives the pattern of :- S P S T - S P S T - S P S T - S P S T

Hence, the correct answer is "S T S P S T T".

The logic followed here is :-

Given 90% of a number is 621

Let us consider number as 'A'.

⇒ (90/100) × A = 621

⇒ 0.9A = 621

⇒ A = 690

∴ The number is '690'.

Then 50% of 20% of that number is :

⇒ 50% = 0.5, 20% = 0.2

= 0.5 × 0.2 × 690

= 0.1 × 690

= 69

Hence, the correct answer is "69".

The least possible Venn diagram for the given relation is a shown below :

• Some Doctors are Married.
• Some Females are Doctors.
• Some Doctors are female.

Hence, the correct answer is "Option2".

The logic followed here is :-

‘SANCTION’ is written as ‘TZOBUHPM’.

Similarly,

‘TELEVISE’ will be written as :

∴ Here, 'TELEVISE' is coded as 'UDMDWHTD'.

Hence, the correct answer is "UDMDWHTD".

The logic followed here is:

Logic used: {(First number)² + (Second number ÷ 3) = Third number}

Row 1:

⇒ 6² + (18 ÷ 3) = 42

⇒ 36 + 6 = 42

⇒ 42 = 42

Row 3:

⇒ 72 + (36 ÷ 3) = 61

⇒ 49 + 12 = 61

⇒ 61 = 61

Similarly,

Row 2:

⇒ 52 + (15 ÷ 3) = ?

⇒ 25 + 5 = ?

⇒ ? = 30

Hence, the correct answer is "30".

The logic followed here is :-

Hence, the correct answer is "SUBK".

The logic followed here is :-

Six houses, A, B, C, D, E and F, are situated in a colony.

D is 60 m south of E. F is 40 m south of B. A is 30 m north of E. F is 50 m east of A. C is 50 m west of B.

∴ Here, House C is located at 40m north with respect to A.

Hence, the correct answer is "40 m north".

The correct answer is 2025-26.

Key Points

• As per the Union Budget 2021-22, the government plans to continue on the path of fiscal consolidation, achieving a fiscal deficit level below 4.5% of GDP by 2025-26.
• "The fiscal deficit in 2022-23 is estimated to be 6.4 percent of GDP, which is consistent with the broad path of fiscal consolidation announced last year to achieve a fiscal deficit level below 4.5 percent by 2025-26," said Union Minister for Finance and Corporate Affairs Smt. Nirmala Sitharaman while presenting the Union Budget 2022-23 in Parliament.
• Furthermore, the Revised Fiscal Deficit for the current fiscal year is predicted to be 6.9% of GDP, up from 6.8% in the Budget Estimates.
• The government's fiscal deficit for 2022-23 is expected to be Rs. 16, 61,196 crores.

Important Points

• A fiscal deficit occurs when the government spends more than it earns.
• It is determined by subtracting total income from total expenditure and is expressed in either absolute or percentage terms of GDP (Gross Domestic Product).

The correct answer is 15.

Key Points

• The Constituent Assembly of India was chosen to draft the Indian Constitution.
• The 'Provincial Assembly' selected it. Its members served as the nation's first Parliament after India gained independence from the British government in 1947. The Indian Constituent Assembly had 389 members, 15 of them were women.
• The 15 women were: Ammu Swaminathan, Annie Mascarene, Dakshayani Velayudhan, Begum Aizaz Rasul, Durgabai Deshmukh, Hansa Jivraj Mehta, Kamla Chaudhry, Leela Roy, Malati Choudhury, Purnima Banerjee, Rajkumari Amrit Kaur, Renuka Ray, Sarojini Naidu, Sucheta Kriplani and Vijayalakshmi Pandit.

Important Points

• Following India's independence from the British government in 1947, its members formed the 'Provisional Parliament of India,' the country's first parliament.
• M. N. Roy, a pioneer of the Indian Communist movement and a proponent of radical democracy, suggested the notion of a Constituent Assembly in 1934.
• In 1935, the Indian National Congress made it a formal demand. Pt. Jawahar Lal Nehru presided over the Indian National Congress session at Lucknow in April 1936.

Additional Information

• The official demand for a Constituent Assembly was made, and the Government of India Act, of 1935 was rejected since it imposed the Constitution against Indians' choice. C. Rajagopalachari demanded a Constituent Assembly based on the adult franchise on November 15, 1939, and the British agreed in August 1940.
• 299 representatives from all castes, regions, religions, and genders crafted the constitution.
• These delegates met for 114 days over the course of three years (2 years 11 months and 17 days to be exact) to discuss what should be included in the constitution and what legislation should be included. B. R. Ambedkar was the chairman of the Constitutional Drafting Committee.

The correct answer is neonatal mortality rate.

Key Points

• The number of deaths during the first 28 completed days of life per 1000 live births in a given year or period is defined as the neonatal mortality rate.
• There are some concerns about the quality of neonatal mortality reporting both internationally and within states, particularly in terms of defining a live birth and/or reporting both birth and death certificates for newborns with very low birth weights.
• When neonatal death certificates are matched to corresponding birth certificates, much more additional and valuable data (birth weight, mother's smoking status, when prenatal care began, etc.) is obtained for neonatal mortality risk analysis.

Important Points

• The number of newborn deaths per 1,000 live births is known as the infant mortality rate.
• The infant mortality rate is an essential indicator of a society's general health, in addition to providing crucial information regarding maternal and baby health.
• The crude mortality rate is derived by dividing the number of fatalities in a particular time by the number of people who were at risk of dying during that period.
• A death rate that is limited to a certain age group is known as an age-specific mortality rate.

The correct answer is 2010.

Key Points

• The Right of Children to Free and Compulsory Education Act 2009 is an Act of Parliament that came into force in 2010.
• On August 4, 2009, the Indian Parliament passed the Right to Education Act 2009, popularly known as the RTE Act 2009.
• It explains the importance of free and compulsory education for children aged 6 to 14 years in India, as defined by Article 21 (A) of the Indian Constitution.
• On April 1, 2010, this act took effect, making India one of 135 countries to make education a fundamental right for all children.
• It establishes basic standards for elementary schools, forbids unrecognized schools from operating, and opposes donation fees and kid admission interviews.

Important Points

• Through frequent surveys, the Right to Education Act keeps tabs on all neighbourhoods and identifies children who are eligible for but lack the financial means to receive an education.
• For many years, India has had educational difficulties at both the national and state levels.
• The Right to Education Act of 2009 establishes roles and obligations for the national government, states, and local governments in order to close gaps in their educational systems and improve the country's educational quality.

The correct answer is Only I and II.

Key Points

• Mountains are sometimes organised in a line called a range. Many mountain ranges are made up of a series of parallel ranges that stretch for hundreds of kilometres sometimes such a line known as a mountain range. Hence statement 1 is correct.
• The Himalayas, Alps, and the Andes are Asian, European, and South American mountain ranges, respectively.
• The Aravallis in Northwestern India are one of the world's oldest fold mountains, forming remnant mountains with elevations ranging from 300 to 900 metres. Hence statement 2 is correct.
• They reach 800 kilometres from Gujarat's Himmatnagar to Delhi's 692 kilometres, encompassing Haryana, Rajasthan, Gujarat, and Delhi.
• At 5,895 metres, Mount Kilimanjaro is Africa's tallest mountain (19,340 feet).
• It is the world's tallest free-standing mountain rise, meaning it exists independently of any mountain range.
• Kilimanjaro, also known as a stratovolcano (a big volcano comprised of ash, lava, and rock), is made up of three cones: Kibo, Mawenzi, and Shira.
• Mt. Kilimanjaro is a volcanic mountain but it lies in Africa, not in South America.. Hence statement 3 is incorrect.
• The mountain's top and the tallest of the three volcanic structures is Kibo.

The correct answer is Narendra Modi.

Key Points

• Shri Narendra Modi's book 'Social Harmony' is a collection of writings on Dalits, Tribals, Women, and Family Relations that explains how to attain Social Harmony in our society.
• The title of the book in Hindi is "Samajik Samrasta." Narendra Modi has written numerous books.
• Exam warriors, Jyotipunj, Convenient Action: Continuity for Change, and others are some of the most popular novels.
• Narendra Damodardas Modi is an Indian politician who has been the country's 14^th and current Prime Minister since 2014.
• He is a Member of Parliament from Varanasi and was the Chief Minister of Gujarat from 2001 until 2014.
• He is the first prime minister to be born after India's independence in 1947, and the second prime minister to win two consecutive majorities in the Lok Sabha, or lower house of India's parliament, who is not a member of the Indian National Congress.
• He is also the longest-serving prime minister from a party other than the Democratic Party.

Important Points

• H.D Deve Gowda is a politician in the Indian state of Karnataka. From June 1, 1996, to April 21, 1997, he was India's 11^th Prime Minister.
• Manmohan Singh is an economist and statesman who served as India's 13^th Prime Minister from 2004 to 2014.
• Pamulaparthi Venkata Narasimha Rao, an Indian lawyer, and politician, was the country's ninth Prime Minister from 1991 until 1996. He is called the "Father of Indian Economic Reforms" by many.

The correct answer is British.

Key Points

• The idea of having a provision for a Bicameral Parliament in the Constitution of India was borrowed from the British Constitution.
• The Government of India Act of 1919, commonly known as the Montagu-Chelmsford Reforms, took effect in 1921.
• It was the first time in the country that bicameralism and direct elections were implemented.
• The Indian Legislative Council was therefore replaced with a bicameral legislature with an Upper House (Council of State) and a Lower House (Legislative Assembly).
• Direct election was used to elect the majority of members of both Houses.

Important Points

The correct answer is Kambala.

Key Points

• The roaring buffalos running through the plains are exciting to see, splashing through the mud.
• On the first day of Kambala, all of the buffalos participate in a run.
• Before the race, the buffalos are pitted against one another.
• The celebration is said to be held in honour of Lord Kadri Manjunatheshwara in order to seek blessings for a bountiful harvest.
• The festival is usually held over two days.
• The game is mostly run by farmers. This Karnataka native event may be worth seeing.
• Plan your journey to Mangalore during the Kambala race.

Important Points

• The Pattadakkal Dance Festival is an annual dance festival that takes place in Pattadakkal, a small town in Karnataka's southern state.
• Karaga festival celebrates Karnataka's rich cultural and religious heritage. It's a festival dedicated to the Goddess Shakti.
• Mahamastakabhisheka is one of the most important and important festivals for the Jain community, held every twelve years in Shravanabelagola, Karnataka.

The correct answer is 2023-24.

Key Points

• Odisha has set 2023-24 as the target year for providing 100% functional household tap water connections in every rural household.
• The Odisha government intends to reach 100% saturation of household tap water connections by 2024 in order to provide people with safe drinking water.
• The Jal Jeevan Mission (JJM) released its annual action plan (AAP), which outlines the State Government's plan of action for the fiscal year 2021-22 as well as the State's saturation plan.
• In particular, more than 27% of rural families in the state receive drinking water from the tap, up from 3.63 percent in 2019.
• In Odisha, there are 85.66 lakh rural homes, with 23.25 lakh of them having tap connections.

Additional Information

• Odisha:
• Statehood: 1 April 1936
• Capital and Largest city: Bhubaneswar
• Districts: 30
• Governor: Shri Raghubar Das
• Chief Minister: Naveen Patnaik

The correct answer is septic.

Key Points

• A septic tank is concrete, fibreglass, or plastic subterranean chamber through which domestic wastewater (sewage) flows for basic treatment.
• Anaerobic action occurs within the septic tank. The term "septic" refers to the anaerobic bacterial environment that forms in the tank and decomposes the waste that is expelled.
• Domestic sewage, as well as animal and poultry wastes, are examples of N-rich materials that supply nutrients for anaerobic organism development and multiplication.

Important Points

• A pressure/vacuum vent is installed in pressure tanks to avoid venting loss due to boiling and breathing loss due to daily temperature or barometric pressure variations.

The correct answer is Rani Rampal.

Key Points

• Rani Rampal is the first woman hockey player to receive the Rajiv Gandhi Khel Ratna Award.
• She was the youngest player in the national team that competed in the 2010 World Cup at the age of 15.
• She completed her education but was unable to obtain a graduate degree due to scheduled practice sessions and competitions. On her team, she is a forward.
• She has scored 134 goals in 212 international appearances.
• She is the captain of the Indian Women's Hockey Team at the moment.
• She is also recognised as a striker who frequently plays in the midfield. The Indian government awarded her the Padma Shri in 2020.

Important Points

• Vandana Katariya is an Indian field hockey player who represents her country as a forward. Vandana rose to attention after scoring the most goals for India in the Women's Hockey Junior World Cup in 2013.
• Nikki Pradhan is a professional field hockey player from India who also plays for the national squad. She was the first female athlete from Jharkhand to compete in the Olympics for India.
• Sharmila Devi is a field hockey player from India. In the 2019 Women's FIH Olympic Qualifiers, she made her international debut against the USA, scoring a goal.

The correct answer is Both A and D.

Key Points

• Hexoses, glucose, and fructose are the most common monosaccharides found in fruits and vegetables.
• Fructose is a monosaccharide, a form of sugar. Fructose, like other sugars, has four calories per gram.
• Fructose is often known as "fruit sugar" since it is found in many fruits naturally. Other plant foods that include it include honey, sugar beets, sugar cane, and vegetables.
• The main sugar in human blood is glucose. It is the human body's major source of energy and comes from the food you eat.
• Human blood transports glucose to all of the human body's cells for energy production. Diabetes is a condition in which blood sugar levels are abnormally high.​

Important Points

• Monosaccharides, often known as simple sugars, are the most basic sugar molecules (monomers) from which all carbohydrates are constructed.
• They are usually white, crystalline solids that are water-soluble. Only a few monosaccharides have a sweet flavour, despite their name (sugars).
• Disaccharides (such as sucrose and lactose) and polysaccharides are made up of monosaccharides (such as cellulose and starch).
• The common table sugar, sucrose, is a disaccharide that contains one molecule of each of the two monosaccharides D-glucose and D-fructose.

The correct answer is General MM Naravane.

Key Points

• General MM Naravane was conferred the honorary rank of General of the Nepali Army in November 2020.
• President Bidya Devi Bhandari bestowed the honorary rank of General of the Nepali Army to Indian Army Chief General M. M. Naravane during a special event, continuing a decades-old practice that highlights the strong links between the two militaries.
• During the function at the President's official house 'ShitalNiwas' in Kathmandu, he was also presented with a sword and scroll.
• The ceremony was attended by Prime Minister K. P. Sharma Oli, Indian Ambassador Vinay M Kwatra, and other top officials from both countries.
• The 1950 tradition demonstrates the strong ties that exist between the two militaries.

Important Points

• In 1950, Gen. K. M. Cariappa became the first Indian Army chief to be awarded the title.
• President Ram Nath Kovind made Nepali Army Chief General Purna Chandra Thapa an honorary General of the Indian Army at a ceremony in New Delhi in January last year.
• General Manoj Mukund Naravane is a retired Indian Army general who served as the 27^th Chief of the Army Staff (COAS) and the temporary Chairman of the Chiefs of Staff Committee from December 15, 2021, to April 30, 2022.
• On December 31, 2019, he took over as COAS from General Bipin Rawat, who had served his term.

The correct answer is Arthritis.

Key Points

• Poor sanitation conditions may NOT be the likely reason behind Arthritis.
• Arthritis is a condition in which one or more joints enlarge and become tender. Joint pain and stiffness are the most common symptoms of arthritis, which normally worsen with age.
• Osteoarthritis and rheumatoid arthritis are the two most frequent kinds of arthritis. Cartilage — the firm, slippery tissue that covers the ends of bones where they form a joint — breaks down as a result of osteoarthritis.
• Rheumatoid arthritis is an autoimmune illness in which the immune system destroys the joints, starting with the lining.
• Diarrhoeal disorders including cholera and dysentery, as well as typhoid, intestinal worm infections, and polio, are all connected to poor sanitation. Stunting is exacerbated by poor nutrition, which also leads to the spread of antibiotic resistance.
• Children are in danger of childhood infections and malnutrition as a result of poor sanitation, which can have a negative influence on their general development, learning, and, later in life, economic opportunities.

Additional Information

• The poliovirus causes polio, a debilitating and potentially fatal disease. The virus can infect a person's spinal cord, causing paralysis (the inability to move parts of the body).
• Typhoid fever is a bacterial infection that can infect multiple organs and spread throughout the body.
• Cholera is a bacterial infection that is spread by drinking contaminated water.

The correct answer is Alexander and Porus.

Key Points

• In 326 BC, Alexander the Great faced King Porus in the Battle of the Hydaspes, also known as the Battle of Jhelum.
• It took place on the banks of the Jhelum River (called as Hydaspes by the ancient Greeks) in the Punjab area of India (modern-day Punjab, Pakistan).
• The conflict ended with a Greek triumph and Porus' capitulation.
• Large swaths of Punjab were integrated into the Alexandrian Empire, and Alexander reinstalled the vanquished and dethroned Porus as a subordinate ruler.
• One of Alexander's "masterpieces" was his choice to cross the monsoon-swollen river despite intense Indian monitoring in order to catch Porus' army off-guard.

Important Points

• Alexander III of Macedon, also known as Alexander the Great, was the monarch of Macedon in ancient Greece.
• At the age of 20, he succeeded his father Philip II to the throne in 336 BC and spent the majority of his reign executing a lengthy military campaign across Western Asia and Northeastern Africa.
• He had built one of the biggest empires in history by the age of thirty, ranging from Greece to northwestern India.
• Porus was an ancient Indian king whose kingdom stretched between the Hydaspes (Jhelum River) and the Acesines (Chenab River) in the Punjab area of India.

The correct answer is Container-Based sanitation.

Key Points

• Container-based sanitation (CBS) is a sanitation method in which toilets collect human waste and transport it to treatment facilities in sealable, removable containers (also known as cartridges).
• This method of sanitation entails the use of a commercial service that offers specific types of portable toilets and distributes empty containers when full ones are picked up. The service carries excreta and carefully disposes of or reuses it.
• The users are normally responsible for the cost of excreta collection. CBS can be utilised to offer low-income urban areas safe collection, transportation, and treatment of faeces at a lesser cost than establishing and maintaining sewers with the right development, support, and collaborations.
• Sanitation systems based on containers are a low-cost option. They can be employed in quickly increasing cities, refugee camps, and disaster relief circumstances.
• They are in line with Sustainable Development Goal 6 of the United Nations, which is to "provide sanitation for all by 2030."

Important Points

• Ecological sanitation is a method of sanitation that tries to safely reuse human waste in agriculture.
• It is a concept, not a technology or a device, that is defined by a goal to "complete the loop" between sanitation and agriculture in a safe manner, primarily for nutrients and organic matter.
• The disposal of human waste without the use of water as a carrier is known as dry sanitation.
• CLTS (Community Led Total Sanitation) is an innovative approach to mobilizing communities to prevent open defecation (OD). Communities are given the tools they need to assess and analyze open defecation (OD) and take steps to achieve ODF (open defecation free).

The correct answer is Andhra Pradesh.

Key Points

• The current Chief Justice of India is Nuthalapati Venkata Ramana. He was born in Andhra Pradesh's Krishna district.
• He formerly served on the Supreme Court of India as a judge, the Delhi High Court as chief justice, and the Andhra Pradesh High Court as interim chief justice.
• He served as president of the Andhra Pradesh Judicial Academy.
• On June 27, 2000, Ramana was appointed to the Andhra Pradesh High Court as a permanent judge.
• He was appointed Chief Justice of the Delhi High Court on September 2, 2013, and a judge of the Supreme Court of India on February 17, 2014.
• President Ram Nath Kovind appointed Ramana as the 48^th Chief Justice on April 6, 2021, and he took his oath of office at Rashtrapati Bhavan on April 24, 2021.

Additional Information 

• President Droupadi Murmu has appointed Justice DY Chandrachud as the 50^th Chief Justice of India (CJI).

Important Points

• The chief justice of the Supreme Court of India is the highest-ranking officer of the Indian federal judiciary and the chief judge of the Supreme Court of India.
• The president of India is empowered by the Indian Constitution to nominate the next chief justice, in consultation with the departing chief justice, who will serve until they reach the age of 65 or are impeached.
• The name suggested by the current chief justice is nearly invariably the next most senior Supreme Court judge, as is customary.
• The first Chief Justice of India was Sir Hiralal Jekisundas Kania.

The correct answer is Godavari.

Key Points

• Trimbakeshwar Jyotirlinga Temple is situated on the Godavari River's banks.
• Maharashtra's Nashik district is home to the temple.
• In Andhra Pradesh's Krishna district, the Krishna River flows from Mahabaleshwar to the Bay of Bengal.
• The Sri Sita Ramachandra Swamy temple is a Hindu shrine dedicated to Rama, the god Vishnu's most famous avatar.
• It lies in the town of Bhadrachalam, Telangana, India, on the banks of the Godavari River.
• It's one among the country's 12 Jyotirlingas. After the Ganga, the Godavari is the longest river.
• Its source is in Trimbakeshwar, Nashik, Maharashtra.
• The rivers Narmada, Johila, and Son all emerge near Amarkantak in Madhya Pradesh.

Important Points

• The Krishna River is a river on India's Deccan plateau that is the country's third-longest river after the Ganges and Godavari, and the fourth-largest in terms of water inputs and basin area after the Ganges, Indus, and the Godavari.
• The Brahmaputra is a transboundary river that flows through Tibet, China, India, and Bangladesh. It is also known as the Yarlung Tsangpo in Tibet, the Siang/Dihang River in Arunachal Pradesh, and Luit in Assamese.
• The Narmada River, also known as the Reva and originally as Narbada or anglicized as Nerbudda, is India's 5^th longest river and overall biggest west-flowing river.

The correct answer is Central Bank.

Key Points

• The central bank is referred to as ‘The lender of last resort'.
• A lender of last resort (LoR) is a financial institution, usually, a country's central bank, that provides loans to banks and other qualifying entities that are in financial distress or are regarded as highly hazardous or on the verge of collapse.
• The lender of last resort serves to protect depositors and to prevent panicked clients from withdrawing funds from banks with temporary low liquidity.
• Commercial banks often avoid borrowing from lenders of last resort since doing so shows that the bank is in financial distress.

Important Points

• A central bank is a financial entity that administers a country's commercial banking system and regulates its currency and monetary policy. A central bank, unlike a commercial bank, has a monopoly on growing the monetary base.
• The State Bank of India is a multinational public sector bank and statutory organisation located in Mumbai, Maharashtra, India. SBI is the 43^rd largest bank in the world, and it is the only Indian bank in the Fortune Global 500 list of the world's largest enterprises for 2020.
• Dena Bank was a state-owned bank that merged with Bank of Baroda in 2019.

The correct answer is To prevent tooth decay.

Key Points

• Water fluoridation is the addition of fluoride to a public water supply with the express purpose of preventing tooth decay.
• Fluoridated water contains a sufficient amount of fluoride to prevent cavities; this can occur naturally or through the addition of fluoride.
• Fluoridated water works on dental surfaces by producing low levels of fluoride in saliva, which slows the demineralization of tooth enamel and speeds up the remineralization of tooth enamel in the early stages of cavities.
• In most industrialised countries, tooth decay is still a serious public health concern, impacting 60–90 percent of kids and the vast majority of adults.
• Fluoridation of drinking water decreases cavities in children, but its effectiveness in adults is unclear.​

Additional Information

• Damage to a tooth's surface, or enamel, is known as tooth decay.
• It occurs when oral bacteria produce acids that destroy the enamel.
• Cavities (dental caries) are holes in your teeth caused by tooth decay.
• If left untreated, dental decay can lead to discomfort, infection, and even tooth loss.

The correct answer is November 2020.

Key Points

• With global asset shifts towards equities and prospects of a faster recovery in emerging economies, India remained a preferred foreign investment destination in FY21, with Foreign Direct Investment (FDI) pouring in.
• As risk appetite began to recover, net FPI (Foreign Portfolio Investments) inflows reached an all-time monthly high of US$9.8 billion in November 2020.
• Furthermore, in 2020, India was the only major economy to attract equity Foreign Institutional Investments (FII).
• The economy's liquidity condition is solid, and the stock market has reached previously inconceivable heights in recent months.

Important Points

• Securities and other financial assets held by investors in another nation are referred to as foreign portfolio investments (FPI).
• It does not provide the investor's actual ownership of a company's assets and, depending on market volatility, is relatively liquid$.

The correct answer is Tomara Rajputs.

Key Points

• The Tomara Rajputs, who were vanquished by the Chauhans (also known as Chahamanas) of Ajmer in the middle of the twelfth century, established Delhi as the capital of a kingdom.
• Delhi grew in importance as a commercial centre during the Tomaras and Chauhans.
• The city was home to many wealthy Jaina merchants who built multiple temples.
• The Dehliwal coins, which were made here, were widely circulated.
• The creation of the Delhi Sultanate in the early thirteenth century began the transition of Delhi into a city that governed broad swaths of the subcontinent.

Important Points

• The Chauhans were the feudatories of the Gurjar-Pratiharas, who helped Nagabhatta I defeat and safeguard the boundaries from Arab invasions during the Battle of Rajasthan.
• Ajayaraj Chauhan, the Chauhan king of Sakambhari, founded the city of Ajayameru, which later became known as Ajmer.
• The Slave dynasty's third and greatest Delhi sultan was Iltutmish. Iltutmish was sold into slavery, but he married the daughter of his master, Qutub ud-din Aibak, in 1211.
• Between 1290 to 1320, the Khilji dynasty governed the Delhi Sultanate, which included significant swaths of the Indian subcontinent.

The correct answer is Kuchipudi.

Key Points

• Kuchipudi is one of India's eight primary classical dance forms. It comes from Kuchipudi, a village in the Indian state of Andhra Pradesh.
• It is a dance-drama genre that originated in the ancient Hindu Sanskrit scripture Natya Shastra.
• Like all of India's great classical dances, it began as a religious art form tied to itinerant bards, temples, and spiritual beliefs.
• Copper inscriptions from the 10^th century and books like the Machupalli Kaifat from the 15^th century show that Kuchipudi existed in an earlier iteration.
• According to Kuchipudi legend, in the 17^th century, Tirtha Narayana Yati, an Advaita Vedanta Sanyasin, and his disciple, an orphan named Siddhendra Yogi, developed and systematised the present style of Kuchipudi.

Important Points

• Mohiniyattam is an Indian traditional dance genre that originated in Kerala and has remained popular ever since. Mohiniyattam dance takes its name from Mohini, a historical enchantress avatar of the Hindu God Vishnu who uses her feminine skills to assist good triumph over evil.
• Kathakali is a popular genre of Indian classical dance. It's a "story play" kind of art, but it's differentiated by the traditionally male actor-dancer's lavishly colourful make-up, costumes, and face masks.
• Bharatanatyam is a significant Hindu form of Indian classical dance. The initial origins of Bharatanatyam are regarded to be Bharata Muni's Natya Shastra and Nandikeshvara's Abhinaya Darpana.

The correct answer is West Bengal.

Key Points

• Buxa Fort is located in the Buxa Tiger Reserve, in the Kalchini CD block of the Alipurduar subdivision of the Alipurduar district, West Bengal, at an elevation of 867 metres (2,844 feet).
• Alipurduar, the nearest town, is 30 kilometres (19 miles) away.
• The fort was utilised by the Bhutanese King to secure the section of the border between Tibet and India that passed through Bhutan.
• Hundreds of refugees arrived at the location afterwards, during the upheaval in Tibet's occupation, and used the abandoned fort as a haven.

Additional Information

• Buxa Tiger Reserve is a tiger reserve and national park in northern West Bengal, India, that spans 760 square kilometres.
• It varies in altitude from 60 metres in the Gangetic Plains to 1,750 metres on the Himalayan border in the north.
• The reserve is home to at least 284 different bird species.

The correct answer is Ahmedabad.

Key Points

• A new sports complex will be built in Naranpura, Ahmedabad, which will be recognised as "the sports city of India."
• It will be able to host any international sporting event, together with the Sardar Vallabhbhai Patel Sports Enclave and Narendra Modi Stadium in Motera.
• With funds of Rs 458 crore, an athletic Sports Complex would be built on a 17-acre plot of land.​

Important Points

• Before the third Test between India and England, the majestic Sardar Patel Stadium in Ahmedabad's Motera was christened Narendra Modi Cricket Stadium.
• The freshly restored stadium, which seats 1,10,000 people and is equipped with modern amenities, is the world's largest cricket arena.
• In what was a historic day for Indian cricket, President Ram Nath Kovind inaugurated the freshly restored stadium in the presence of Home Minister Amit Shah, Sports Minister Kiren Rijiju, and BCCI secretary Jay Shah.

Given:

The performance of 1800 students in grades has been shown in the following pie chart.

Calculation:

Total percentage of grades B and E = 27% + 8% = 35%

Here, (54/1800) × 100 = 3%

Then, 54 students of 1800 is 3% students

We have to find the sum of two groups in which the sum of percentage = 35% - 3% = 32%

The percentage of students in Grade C = 24%

The percentage of students in Grade E = 8%

The total percentage of Grade C and E = 24% + 8% = 32%

∴ The number of students is 54 less than the number of students in grades B and E taken together in Grade C and E

Given:

The given numbers are 156, 181 and 331

After dividing by the greatest number, the remainder in each case = 6

Concept used:

The greatest number that will divide a, b, and c and leaving the same remainder in each case is given by the HCF of |a - b|, |b - c|, and |c - a|

Calculation:

Here, |156 - 181| = |- 25| = 25

|181 - 331| = |- 150| = 150

|331 - 156| = 175

Prime factors of 25 = 5 × 5

Prime factors of 150 = 2 × 3 × 5 × 5

Prime factors of 175 = 5 × 5 × 7

So, HCF of 25, 150, and 175 = 5 × 5 = 25

∴ The greatest number is 25

Given:

The initial loss = 18%

Formula used:

S.P. = (Profit/C.P.) × 100

Where, S.P. = Selling price; C.P. = Cost price

Calculation:

Let, the cost price of the article = ₹ x

So, (82x/100) + 960 = (112x/100)

⇒ (112x/100) - (82x/100) = 960

⇒ (30x/100) = 960

⇒ x = (960 × 100)/30 = 3200

∴ The cost price of the article = ₹ 3200

Required selling price = ₹ 3840

Then, profit = 3840 - 3200 = ₹ 640

The profit percentage = (640/3200) × 100 = 20%

∴ The profit percentage is 20%

Given:

CD = 9 cm, BE = 6 cm, AB = 5 cm and ED = 2 cm

Calculation:

Here, BE || CD

So, AB/AC = BE/CD = AE/AD

Then, AB/AC = 6/9

⇒ 5/(5 + BC) = 6/9

⇒ 6BC + 30 = 45

⇒ 6BC = 45 - 30 = 15

⇒ BC = 15/6 = 2.5 cm

Also, AE/AD = 6/9

⇒ AE/(AE + 2) = 6/9

⇒ 9AE = 6AE + 12

⇒ 9AE - 6AE = 12

⇒ 3AE = 12

⇒ AE = 12/3 = 4 cm

∴ The measures of the lengths (in cm) of AE and BC are 4 cm and 2.5 cm

Given:

tan2A + 2tanA - 63 = 0

Formula used:

Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

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

Calculation:

tan2A + 2tanA - 63 = 0

Let, tan A = x

⇒ x2 + 2x - 63 = 0

⇒ x2 + 9x - 7x - 63 = 0

⇒ x (x + 9) - 7 (x + 9) = 0

⇒ (x + 9) (x - 7) = 0

⇒ x + 9 = 0 ⇒ x = - 9  ["-" will be neglected because 0 < A < π/2]

⇒ x - 7 = 0 ⇒ x = 7

So, tan A = $7\over1$ = $p\over b$ 

Using Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

⇒ h = $\sqrt{7^2+1^2}$ = √50

So, 2sinA + 5cosA

= [2 × $7\over{\sqrt50}$] + [5 × $1\over{\sqrt50}$]

= $14\over{\sqrt50}$ + $5\over{\sqrt50}$ = ${14+5}\over{\sqrt50}$ = $19\over{\sqrt50}$

∴ The value of (2sinA + 5cosA) is $19\over{\sqrt50}$.

Given:

The total number of students in 2019 = 2000

The total number of students in 2020 = 2400

Calculation:

The percentage of Engineering students in 2019 = 13%

The number of Engineering students in 2019 = (13/100) × 2000 = 260

The percentage of Engineering students in 2020 = 12%

The number of Engineering students in 2020 = (12/100) × 2400 = 288

The number of Engineering students increase from 2019 to 2020 = 288 - 260 = 28

The increase percentage = (28/260) × 100 = 10.769...% ≈ 10.77%

∴ The number of students of Engineering in 2020 as compared to 2019 increases 10.77%

Given:

The given expression = $\frac{{3\frac{1}{2}, + ,5\frac{1}{3}, \div ,1\frac{1}{3}, × ,5\frac{1}{4}, - ,5\frac{1}{2}}}{{1\frac{1}{2}, × ,1\frac{2}{3}, - ,6\frac{1}{2}}}, \div ,7, × ,2$

Calculation:

$\frac{{3\frac{1}{2}, + ,5\frac{1}{3}, \div ,1\frac{1}{3}, × ,5\frac{1}{4}, - ,5\frac{1}{2}}}{{1\frac{1}{2}, × ,1\frac{2}{3}, - ,6\frac{1}{2}}}, \div ,7, × ,2$

= $\frac{\frac{7}{2}+\frac{16}{3}\div\frac{4}{3}×\frac{21}{4}-\frac{11}{2}}{\frac{3}{2}×\frac{5}{3}-\frac{13}{2}}\div7×2$

= $\frac{\frac{7}{2}+\frac{16}{3}×\frac{3}{4}×\frac{21}{4}-\frac{11}{2}}{\frac{5}{2}-\frac{13}{2}}\div7×2$

= $\frac{\frac{7}{2}+21-\frac{11}{2}}{-4}\div7×2$

= $\frac{19}{-4}\div7×2$

= (19/- 4) × (1/7) × 2

= - 19/14

= $-1\frac{5}{14}$

∴ The value of the expression is $-1\frac{5}{14}$

Given:

p is the third proportional to 8, 20

q is the fourth proportional to 3, 5, 24

Concept used:

If x is the third proportional to a, b then x = b²/a

If x is the fourth proportional to a, b, c then a/b = c/x

Calculation:

Here, p = 20²/8 = 400/8 = 50

Also, 3/5 = 24/q

⇒ q = (5 × 24)/3 = 40

Then, (2p + q) = (2 × 50) + 40 = 100 + 40 = 140

∴ The value of (2p + q) is 140

Given:

x = 4 + √15

Formula used:

(a + b)² = a² + b² + 2ab

(a + b) (a - b) = a² - b²

Calculation:

x = 4 + √15

So, 1/x = 1/(4 + √15)

= (4 - √15)/[(4 + √15) (4 - √15)]

= (4 - √15)/(16 - 15)

= 4 - √15

Then, x + (1/x) = (4 + √15) + (4 - √15)

⇒ x + (1/x) = 8

⇒ [x + (1/x)]² = 8²  [Taking square on both sides]

⇒ x² + (1/x²) + [2 × x × (1/x)] = 64

⇒ x2 + (1/x2) + 2 = 64

⇒ x2 + (1/x2) = 64 - 2 = 62

∴ The value of x2 + (1/x2) is 62

Shortcut Trick

Initial Cost = 100 (RM) + 30 (Labour) = 130

New RM Price = 125 | New Labour = 38% of 125 = 47.5

New Total Cost = 125 + 47.5 = 172.5

Reduction required = (172.5 − 130) ÷ 172.5 × 100

Reduction % = 42.5 ÷ 172.5 × 100 ≈ 24.63%

∴ The correct answer is 24.6%.

Alternate Method

Let the initial Price of Raw Material be ₹100.

⇒ Initial Labour Cost = 30% of 100 = ₹30

⇒ Initial Total Cost = 100 + 30 = ₹130

⇒ New Price of Raw Material = 100 + 25% of 100 = ₹125

⇒ New Labour Cost = 38% of 125 = 0.38 × 125 = ₹47.5

⇒ New Total Cost (at same consumption) = 125 + 47.5 = ₹172.5

To keep the cost same as before (₹130), the Consumption must be reduced.

⇒ Reduction % = [(New Cost − Initial Cost) ÷ New Cost] × 100

⇒ Reduction % = [(172.5 − 130) ÷ 172.5] × 100

⇒ Reduction % = (42.5 ÷ 172.5) × 100 ≈ 24.637%

∴ The correct answer is 24.6%.

Additional Information

Expenditure Consistency Rule

If the price increases by r%, the consumption must be reduced by [r ÷ (100 + r)] × 100 to keep the expenditure constant.

Successive Percentage Change

When a value changes by a% and then by b%, the net change is given by [a + b + (a × b)/100]%.

Given:

The average of 52, 71, 43, 22, a, and b = 55

The average of 42, 45, 49, 51, 42, c, and d = 53

Concept used:

Sum of terms = Average × Number of terms

Calculation:

Here, (52 + 71 + 43 + 22 + a + b)/6 = 55

⇒ 188 + a + b = 6 × 55 = 330

⇒ a + b = 330 - 188

⇒ a + b = 142   .....(1)

Also, (42 + 45 + 49 + 51 + 42 + c + d)/7 = 53

⇒ 229 + c + d = 7 × 53 = 371

⇒ c + d = 371 - 229

⇒ c + d = 142

The average of a, b, c, and d = (142 + 142)/4 = 71

∴ The average of a, b, c, and d is 71

Given:

a2 + b2 + c2 = 6.25

(ab + bc + ca) = 0.52

(a + b + c) < 0

Formula used:

(a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)

Calculation:

(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)

⇒ (a + b + c)2 = 6.25 + (2 × 0.52)

⇒ (a + b + c)2 = 6.25 + 1.04

⇒ (a + b + c)2 = 7.29

⇒ (a + b + c) = √7.29

⇒ (a + b + c) = ± 2.7

But (a + b + c) < 0 So, a + b + c = -2.7

∴ The value of (a + b + c) is - 2.7

Hint

(a + b + c) = √7.29

Concept Used:

Use basic arithmetic to simplify the square root.

Formula Used:

√x is the principal square root of x.

Calculation:

√7.29

Recognize that 7.29 is a perfect square:

$7.29 = 2.7 \times 2.7$

√7.29 = ± 2.7

So, ( a + b + c = ± 2.7)

Given:

The following bar graph shows the total number of youth (in lakhs) and the number of employed youth (in lakhs) in 5 states A, B, C, D, and E.

Calculation:

The unemployed youth in state A (in lakhs) = 12 - 10.5 = 1.5

The unemployed youth in state B (in lakhs) = 8 - 7 = 1

The unemployed youth in state C (in lakhs) = 11.5 - 10 = 1.5

The unemployed youth in state D (in lakhs) = 10 - 7.5 = 2.5

The unemployed youth in state E (in lakhs) = 9 - 8 = 1

∴ The state D has the maximum number of unemployed youth.

Given:

The 7-digit number x8942y4 is divisible by 56

Concept used:

Divisibility of 7:

If twice the number at the unit place is subtracted from the rest of the digits and the remainder is divisible by 7 then the number is divisible by 7

Divisibility of 8:

If the last three digits of a number are divisible by 8, then the number is divisible by 8.

Calculation:

The 7-digit number x8942y4 is divisible by 56

So, the 7-digit number x8942y4 is divisible by 7 and 8

For divisible by 8, 2y4 should be divisible by 8

For greater value of y, put the values of y in a descending way, like 9, 8, 7, ...so on

If y = 6, then 264 is divisible by 8

⇒ y = 6

For divisible by 7,

⇒ [x894264] ÷ 7

⇒ If x = 7 then 7894264 is divisible by 7.

⇒ x = 7

Then, (x2 + y) = (72 + 6) = 49 + 6 = 55

∴ The value of (x2 + y) is 55

Shortcut Trick

The 7-digit number x8942y4 is divisible by 56

So, the 7-digit number x8942y4 is divisible by 7 and 8

For divisible by 8, 2y4 should be divisible by 8

For greater value of y, put the values of y in a descending way, like 9, 8, 7, ...so on

If y = 6, then 264 is divisible by 8

⇒ y = 6

Now check the options as we got y = 6, then the remaining number should be a perfect square,

hence options 2 & 4 are eliminated,

As 27 & 38 are not perfect squares.

now substitute values that come from options 1 & 3 ie.

from option 1 we will get x = 7 & from 3 we will get x = 8

By substituting we can say that,

Option 1 satisfies the condition.

∴ The correct answer is option 1.

Given:

∠TPQ = 42°

Concept used:

The sum of all three angles of a triangle = 180°

The sum of all angles on a straight line = 180°

Calculation:

Draw a tangent to the circles at T, intersecting QP

So, OT and OQ are two tangents to a common circle from the same external point O

Therefore, OQ = OT then ∠OQT = ∠OTQ

Also, OT and OP are two tangents to a common circle from the same external point O

Therefore, OP = OT then ∠OPT = ∠OTP

∠TPQ = 42°

Then, ∠TPQ = ∠OPT = ∠OTP = 42°

In ΔOPT, ∠OPT + ∠OTP + ∠POT = 180°

⇒ 42° + 42° + ∠POT = 180°

⇒ ∠POT = 180° - 42° - 42° = 96°

Also, ∠POT + ∠QOT = 180°

⇒ 96° + ∠QOT = 180°

⇒ ∠QOT = 180° - 96° = 84°

In ΔQOT, ∠OQT + ∠OTQ + ∠QOT = 180°

⇒ ∠OQT + ∠OQT + 84° = 180°  [∵ ∠OQT = ∠OTQ]

⇒ 2 ∠OQT = 180° - 84°

⇒ 2 ∠PQT = 96°

⇒ ∠PQT = 96°/2 = 48°

∴ The value of ∠PQT (in degrees) is 48°

Given:

sec A = $17 \over 8$, A < 90°

Formula used:

Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

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

Calculation:

sec A = $17 \over 8$ (secA = $1\over cosA$)

⇒ cos A = $8\over17$ = $b\over h$

Using Pythagoras Theorem,

h = $\sqrt{p^2+b^2}$

⇒ p = $\sqrt{h^2-b^2}$

⇒ $\sqrt{17^2-8^2}$= $\sqrt{289 - 64}$

⇒ √225 = 15 = p

$34 sin A+15 cot A \over 68 cos A-16 tan A$

⇒ ${{34{p\over h}}+{15{b\over p}}}\over{{68{b\over h}-{16{p\over b}}}}$ = ${{34{15\over 17}}+{15{8\over 15}}}\over{{68{8\over 17}-{16{15\over 8}}}}$

⇒ ${30+8}\over{32-30}$ = 19

∴ The value of $34 sin A+15 cot A \over 68 cos A-16 tan A$ is 19

Shortcut Trick

Total work = 240 (LCM of 48 and 60)

Efficiency = Work/Time

A and B complete in 12 days = 12 × (5 + 4) = 108 work

25% of the remaining work = (240 - 108)/4 = 33 work

Time is taken by B = 33/4 days

= (33/4) × 24 hours

= 198 hours

= 8 days 6 hours

∴ B will finish 25% of the remaining work in 8 days 6 hours

Alternate Method

Given:

A can finish a piece of work in 48 days

B can finish the same work in 60 days

Calculation:

A complete in 1 day = 1/48 work

B complete in 1 day = 1/60 work

A and B complete together in 1 day = (1/48) + (1/60) = 3/80 work

A and B complete together in 12 day = (3/80) × 12 = 9/20 work

The remaining work = 1 - (9/20) = 11/20

25% of the remaining work = (11/20) × (25/100) = 11/80 work

Time taken by B = (11/80) ÷ (1/60) = (11/80) × 60 = 33/4 days

= (33/4) × 24 hours

= 198 hours

= 8 days 6 hours

∴ B will finish 25% of the remaining work in 8 days 6 hours

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of the side opposite to 30° to the hypotenuse is always 1 : 2.

Given the side opposite to 30° (height) = 90 m.

Length of the string (hypotenuse) = 2 × Height = 2 × 90 m = 180 m.

∴ The correct answer is 180 m.

Alternate Method

Given:

Height of the kite (Opposite side) = 90 m

Angle of elevation (θ) = 30°

Formula Used:

sin θ = Perpendicular / Hypotenuse

Calculations:

⇒ sin 30° = Height / Length of string

⇒ 1 / 2 = 90 / Length of string

⇒ Length of string = 90 × 2

⇒ Length of string = 180 m

∴ The correct answer is 180 m.

Additional Information

Trigonometric Ratios in Right Triangles

Fundamental ratios: sin θ = P/H, cos θ = B/H, and tan θ = P/B where P=Perpendicular, B=Base, and H=Hypotenuse.

Standard Angle Values

For a 30° angle: sin 30° = 1/2, cos 30° = √3/2, and tan 30° = 1/√3.

Pythagoras Theorem

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: H² = P² + B².

Shortcut Trick

Let Speed of Boat (u) = 9 km/h and Speed of Stream = v km/h.

Downstream Speed (D) = 9 + v and Upstream Speed (U) = 9 − v.

Using 44/D + 35/U = 9: By Hit and Trial, if v = 2, D = 11 and U = 7.

⇒ 44/11 + 35/7 = 4 + 5 = 9 hours (Satisfied).

New Time = 33/11 + 28/7 = 3 + 4 = 7 hours.

∴ The correct answer is 7 hours.

Alternate Method

Given: Speed of boat in still water (u) = 9 km/h. Total time for 44 km downstream and 35 km upstream = 9 hours.

Formula: Time = Distance ÷ Speed; Downstream Speed (D) = u + v; Upstream Speed (U) = u − v.

⇒ 44/(9 + v) + 35/(9 − v) = 9

⇒ 44(9 − v) + 35(9 + v) = 9(81 − v²)

⇒ 396 − 44v + 315 + 35v = 729 − 9v²

⇒ 711 − 9v = 729 − 9v²

⇒ 9v² − 9v − 18 = 0 ⇒ v² − v − 2 = 0

⇒ (v − 2)(v + 1) = 0 ⇒ v = 2 km/h (speed cannot be negative).

⇒ Downstream Speed = 9 + 2 = 11 km/h; Upstream Speed = 9 − 2 = 7 km/h.

⇒ Required Time = 33/11 + 28/7 = 3 + 4 = 7 hours.

∴ The correct answer is 7 hours.

Additional Information

Speed of Boat and Stream

Speed of boat in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2.

Speed of Current

Speed of stream (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Average Speed in Boats

Average speed for a round trip = (Downstream Speed × Upstream Speed) ÷ Still water speed.

Given:

There is the histogram that shows the height (in cm) of 100 students in an athletic team

Calculation:

The number of students with a height of less than 170 cm = 6 + 12 + 20 =38

The number of students with a height of more than 160 cm = 20 + 24 + 18 + 16 + 4 = 82

The percentage = (38/82) × 100 = 46.34...% ≈ 46.3%

∴ The number of students with height less than 170 cm is 46.3% of the number of students with height more than 160 cm

Shortcut Trick

The reduction of price = 15%

A person can buy 2 kg more salt for ₹272.

The reduced price = (Price/Quantity) × (Reduction/100)

= (272/2) × (15/100) = 20.40

∴ The reduced price of salt per kg (in ₹) is ₹ 20.40

Alternate Method

Given:

The reduction of price = 15%

A person can buy 2 kg more salt for ₹272.

Calculation:

Let, the original price of the salt = ₹ x/kg

The person can buy = 272/x kg

The price of salt after reduced = x × (85/100) = 17x/20

So, $\frac{272}{17x/20}-\frac{272}{x}=2$

⇒ $\frac{(272×20)-(272×17)}{17x}=2$

⇒ 272 (20 - 17) = 34x

⇒ 272 × 3 = 34x

⇒ x = (272 × 3)/34 = 24

The original price of the salt = 24/kg

The reduced price = (85/100) × 24 = ₹ 20.40 per kg

∴ The reduced price of salt per kg (in ₹) is ₹ 20.40

Given:

The height of the frustum = 35 cm

The radius of the upper ends of the frustum = 12 cm

The radius of the lower ends of the frustum = 18 cm

The base radius of the cylindrical drum = 20 cm

Formula used:

The volume of the frustum = (πh/3) (R² + r² + Rr)

Where, h = The height of the frustum

R = Radius of the lower end

r = Radius of the upper end

The volume of a cylinder = πr²h

Where, r = Radius of the cylinder; h = Height of the cylinder

Calculation:

Let, the height of water = x cm

So, [(22/7 × 35)/3] (182 + 122 + 18 × 12) = (22/7) × 202 × x

⇒ (110/3) (324 + 144 + 216) = (22/7) × 400x

⇒ (110/3) × 684 = (22/7) × 400x

⇒ 25080 = (22/7) × 400x

⇒ x = (25080 × 7)/(22 × 400) = 19.95

∴ The height of water (in cm) in the drum is 19.95 cm