RRC Group D Previous Year Paper 24 (Held On: 20 Sept 2018 Shift 2)

The least possible Venn diagram is as follows,

Since they are playing chess in the morning, sun is towards the east.

DIAGRAM

Mamatha is facing west.

Hence, “west” is the correct answer

The Correct Answer is Option 3 i.e Urjit Patel.

• Urjit Patel:
• As of 2018 Governor of Reserve Bank of India is Urjit Patel.
• He is the 24th Governor of RBI.
• He also served as the deputy governor of RBI prior to working as governor of RBI.
• But at present, as of May 2020, Governor of Reserve Bank of India is Shaktikanta Das.
• Shaktikanta Das is the 25th governor of RBI.
• Raghuram Rajan:
• He was the 23rd Governor of the Reserve Bank of India.
• He also served as the 15th Chief Economic Advisor, Ministry of Finance, Government of India.
• He also served as the Chief Economist and Director of Research at the International Monetary Fund.
• He has been named as Time magazine's 100 most influential people in 2016.
• Manmohan Singh:
• He served as the 13th Prime Minister of India from 2004 to 2014.
• He was the 15th governor of RBI.
• He also served as the 5th Chief Economic Advisor to the Government of India.
• Arvind Subramanian:
• He was the 16th Chief Economic Advisor to the Government of India.
• Foreign Policy magazine named him one of the world's top 100 global thinkers in 2011.

Follow the BODMAS rule to solve this question, as per the order given below.

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Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first and following the BODMAS rule in the bracket -

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Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

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Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

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Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

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Given expression is

20% of 60 is 25% of _______

⇒ (20/100) × 60 is 25% of _______

⇒ 12 is 25% of _______

⇒ 12 = 25% of x

∴ x = 12 × (100/25) = 48

CONCEPT**:**

Frequency:

• The number of vibrations at which sound waves travel per second is called the frequency of the sound wave.
• It is denoted by f or ν.
• The SI unit of frequency is Hertz (Hz).

 

EXPLANATION:

• The standard unit for measuring the frequency of a sound wave is Hertz (Hz). So option 4 is correct.

The Correct Answer is Option 1 i.e Bhubaneswar.

• The 2018 Men's Hockey World Cup:
• It was held from 28th November to 16th December 2018 at the Kalinga Stadium in Bhubaneswar, India.
• The Final match was played between Belgium and the Netherlands.
• Belgium won the world cup after defeating the Netherlands in the penalty shootout.
• Bengaluru:
• Bangaluru is the capital of Karnataka.
• It is commonly referred to as the “Silicon Valley of India”.
• Ranchi:
• Ranchi is the capital of Jharkhand.
• It is popularly known as a “City of Water Falls”.
• Patna:
• Patna is the capital Bihar.
• It is located on the south bank of the river Ganga.

The Correct Answer is Option 3 i.e Kailash Satyarthi.

• Santokbaa Humanitarian Award 2018:
• Santokbaa Humanitarian Award 2018 was presented to Child rights activist and Noble Laureate Kailash Satyarthi and ISRO chief A S Kiran Kumar.
• The award was instituted by Shree Ramkrishna Knowledge Foundation (SRKKF) and led by diamond baron Govind Dholakia.
• SRKKF confers the award every year for humanitarian contributions by individuals whose life and work are characterized by their selfless and inspiring service.
• Kailash Satyarthi:
• He is from Madhya Pradesh in India.
• He was the founder of social activist organization Bachpan Bachao Andolan.
• He also received the Robert F. Kennedy Human Rights Award in the year 1995.
• The Nobel Peace Prize 2014 was awarded jointly to Kailash Satyarthi and Malala Yousafzai "for their struggle against the suppression of children and young people and for the right of all children to education".
• He won the 2018 Santokbaa Humanitarian Award.
• Rajkumari Banerji:
• She was an Indian social worker from Bengal.
• She was the first Indian woman to visit England in 1871 AD.
• Daya Bhai:
• She is an Indian social worker from Kerala, working for the upliftment of tribes in Central India.
• In January 2012, she was awarded the Good Samaritan National Award.
• Sabitha Beegam:
• She is the first mayor of Kollam City.
• She is also a social worker from Kollam, Kerala.

CONCEPT:

• Electrical energy: The energy that is derived from the flow of electric charge is called electrical energy.
• The SI unit of electrical energy is Joule.
• Kilowatt-hour: It is the unit of energy and is equal to the energy consumed in the circuit at the rate of 1 kilowatt for 1 hour.
• The commercial unit of electrical energy is a kilowatt-hour (kWh).
• 1 kilowatt hour = 3.6 x 10⁶ joule.
• Electric Power: The rate at which electrical energy is consumed in a circuit is called electric power.
• SI unit is the watt.
• One Kilowatt is equal to 1000 watts.

EXPLANATION:

• The commercial unit of electrical energy is a kilowatt-hour (kWh). So option 1 is correct.

The number of triangles in the given figure is,

Hence, “12” is the correct answer

The Correct Answer is Option 3 i.e Carbon.

• Carbon (C):
• Atomic Number is 6.
• Carbon occurs naturally as anthracite, graphite, and diamond.
• It is used in the production of steel.
• Carbon has two stable, naturally occurring isotopes: carbon-12 and carbon-13.
• It has the highest melting and boiling point.
• Lithium (Li):
• Atomic Number is 3.
• Lithium is the lightest metal in the periodic table.
• It is widely used in rechargeable batteries for mobile phones, laptops, digital cameras, etc.
• Phosphorus (P):
• Atomic Number is 15.
• White phosphorus and Red phosphorus are the two main forms of phosphorus.
• It is mostly used in plant fertilizer, chemical pesticides, etc. and the most common use of this is in safety matches
• Argon (Ar):
• Atomic Number is 18.
• Argon is a colourless, odourless gas.
• It is an inert gas of Group 18 (noble gases).
• It is commonly used as an inert shielding gas​.

The Correct Answer is Option 1 i.e baking soda solution.

• Baking soda:
• It is a natural source of antacid.
• Sodium bicarbonate (NaHCO₃) in baking soda quickly neutralizes stomach acid.
• Sodium bicarbonate is a white crystalline  solid.
• It is used in baking products like cakes, cookies, etc.
• Washing Soda:
• It is commonly known as Na2CO3 or sodium carbonate.
• It is used in the softening of hard water.
• It is commonly used as a cleaning agent for domestic purposes.
• It is also used in the manufacturing of paper, soap, textiles, paints, etc.
• Vinegar:
• Vinegar is produced from the fermentation of alcohol.
• Vinegar is the natural source of acetic acid.
• It is widely used as a flavouring agent in most of the cuisines.
• Lemon juice is a rich natural source of citric acid.
• Buttermilk is a good source of probiotics.

The Correct Answer is Option 2 i.e Cartilages.

Key Points

• Cartilages:
• It is a type of connective tissue in the body.
• It is a strong, flexible tissue that is the main type of connective tissue in the body.
• Due to the presence of Cartilages in our ears, the ears can be folded.
• Elastic cartilage is a type of cartilage present in the outer ear.
• It doesn’t h ave blood vessels or nerves.
• This tissue is present in joints, ears, nose, rib cage, and in many other areas of the body.
• Bones:
• Bones in our bodies are living tissues that make up the skeleton.
• It provides shape and support to the body, as well as protection for some organs in the body.
• The Femur is the strongest bones of the human body.
• Ligaments:
• It is a short, fibrous, and elastic connective tissue.
• It attaches bone to bone, gives support to the joints.
• Tendons:
• Tendons are fibrous connective tissue.
• These attach muscle to bone.

Drawing the Venn diagram,

Conclusion 1: Some brown are rust → True (This is definitely true)

Conclusion 2: Some iron are brown → True (This is definitely true)

Hence, “all conclusions” follow.

The Correct Answer is Option 3 i.e Shubhangi Swaroop.

• Shubhangi Swaroop:
• She hails from Bareilly, Uttar Pradesh will soon fly the Maritime Reconnaissance aircraft.
• She became the first-ever female pilot to be inducted into the Indian Navy.
• Beside Swaroop, three other female cadets became the country's first women officers -- namely, Astha Segal from New Delhi, Roopa A from Puducherry, and Sakthi Maya S from Kerala, at the Naval Armament Inspectorate (NAI) branch.

43/140 = 0.307142857……

57/120 = 19/40 = 0.475

47/150 = 0.3133……

61/110 = 0.5545……

∴ 57/120 is a terminating decimal

Banana, Litchi and Kiwi are fruits.

Whereas,

Lettuce is a vegetable.

Hence, “lettuce” does not belong to the group.

The Correct Answer is Option 2 i.e Ekta Kapoor.

• Ekta Kapoor:
• The 17th edition of the Indian Television Academy Awards function was held in Mumbai.
• She won the ITA Sterling Icon of Indian Entertainment award 2017.
• She was honoured with the Padma Shri in 2020.
• She also won the 2012 Screen Award for Best Film - The Dirty Picture.
• Siddharth Roy Kapur:
• He won the 2017 Best Film for Dangal at Filmfare Awards.
• He won the Society Young Achievers Awards 2013 in the Business category.
• Shobha Kapoor:
• She won the 2001 ITA award for the best star cast.
• She won the 2012 Screen Award for Best Film - The Dirty Picture.
• Jitendra:
• He won the 2003 Filmfare Lifetime Achievement Award.
• He won the ITA Scroll of Honour (Entertainment) Award 2003.

The Correct Answer is Option 2 i.e Sieve tubes.

• Xylem:
• It is plant tissue that transports food water and other dissolved minerals from roots to other parts of the plant.
• It also provides mechanical strength to the plant body.
• Xylem consists of Tracheids, Vessels, Xylem Fibres, Xylem Parenchyma.
• Tracheids and vessels are the conducting elements of Xylem.
• Xylem fibres provide strength to the tracheids and vessels.
• The xylem parenchyma cells are mainly involved in the storage of carbohydrate, fats and water conduction.
• Phloem:
• The main function of the phloem is to transport food materials from the leaf to other parts of the plant.
• Phloem consists of Sieve tubes, Companion cells, Phloem Parenchyma, Phloem fibres.
• Sieve tubes: These are elongated living cells of the phloem.
• Companion cells: The companion cells regulate the activities related to sieve tubes.
• Phloem Parenchyma: These are living and thin-walled cells.
• It stores various materials like Resin, Latex etc.
• Phloem fibres: The sclerenchyma fibres associated with phloem are called phloem fibres.

CONCEPT:

Different positions of the object and their image by a concave mirror: 

EXPLANATION:

• The position of the image formed by a concave mirror when the object is placed at the centre of the curvature of that spherical mirror is at the centre of curvature. So option 4 is correct.

Important Points

The Correct Answer is Option 1 i.e ICICI Bank.

• ICICI Bank:
• The government has engaged private lender ICICI Bank to enable online payments at 470 mandis integrated with the national portal of electronic National Agriculture Market (e-NAM).
• ICICI Bank launched the country’s first contactless mobile payment solution to enable its credit and debit customers make in-store contactless payments by just waving their smartphones near an NFC-enabled merchant terminal.
• ICICI Bank also became the first to enable its customers to make electronic payments by just waving the cards near the merchant terminal.
• ICICI Bank Chairman is Girish Chandra Chaturvedi.
• Tagline: "Hum Hai Na, Khyal Apka".
• Headquarters: Mumbai.
• Dhanlakshmi Bank:
• It is a private sector bank.
• It is headquartered in Thrissur City, Kerala.
• Sunil Gurbaxani is the current MD & CEO of the bank.
• Its tagline is Tann. Mann. Dhan.
• Bandhan Bank:
• It is a private sector bank.
• Chandra Shekhar Ghosh is the current MD and CEO of the bank.
• It is headquartered in Kolkata, West Bengal.
• Its tagline is Aapka Bhala, Sabki Bhalai.
• Yes Bank:
• It is a private sector bank.
• Prasanth Kumar is the current MD & CEO of the bank.
• It is headquartered in Mumbai.
• Its tagline is Experience our Expertise.

The Correct Answer is Option 1 i.e Odisha.

• Odisha:
• The Odisha government has launched the Ama Gaon, Ama Vikas (Our Village, our development) a programme to reach out to the people in rural areas and involve themselves in developmental activities.
• The programme was launched in March 2018.
• Odisha Chief Minister Naveen Patnaik has launched the programme.
• Raghubar Das is the current governor of Odisha.
• Meghalaya:
• Conrad Sangma is the current CM of Meghalaya.
• Shillong is the capital of Meghalaya.
• Assam and Bangladesh are the borders of Meghalaya.
• Phagu Chauhan is the current governor of Meghalaya.
• West Bengal:
• Mamata Banerjee is the current CM of West Bengal.
• C. V. Ananda Bose is the current governor of West Bengal.
• Jharkhand, Odisha  Bihar, Bangladesh, Assam, Sikkim and Bhutan and Nepal are the boundaries of West Bengal.
• Kolkata is the capital of West Bengal.
• Assam:
• Himanta Biswa Sarma is the current CM of Assam.
• Gulab Chand Kataria is the current governor of Assam.
• Bangladesh, Bhutan, Nagaland, Arunachal Pradesh, Manipur, Mizoram, Tripura, Meghalaya and West Bengal are the boundaries of Assam.
• Dispur is the capital of Assam.

The least possible Venn diagram is as follows,

Conclusion 1: All biscuits are grains → True (This is definitely true)

Conclusion 2: All grains are millets → False (This is definitely false)

Hence, “only conclusion 1” follow.

The Correct Answer is Option 3 i.e Sachin Tendulkar.

• Sachin Tendulkar:
• "Playing It My Way" is the autobiography of former Indian cricketer Sachin Tendulkar. 
• It was launched in Mumbai on 5 November 2014.
• The book was authored by Boria Majumdar and Sachin Tendulkar.
• Vinod Kambli:
• "Vinod Kambli: The Lost Hero" is a book on the biography of former Indian cricketer Vinod Kambli.
• The book was authored by Kunal Purandare.
• Rahul Dravid:
• "The Nice Guy Who Finished First" is a biography of Rahul Dravid.
• The book was authored by Devendra Prabhudesai.
• Kapil Dev:
• "Kapil: The Autobiography of Kapil Dev" is a book on autobiography of former cricketer Kapil Dev.
• The book was authored by Kapil Dev.
• "Straight from the Heart: An Autobiography" is also the book authored by former cricketer Kapil Dev.

The Correct Answer is Option 4 i.e Krishna.

*** Equivalent fractions** can be defined as fractions with different Numerators and Denominators that represent the same value or proportion of the whole.

* Improper fractions is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).

* An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisor than 1.

* Like fractions are fractions that have the exact same denominator.

Now, According to the question,

2/3, 4/6 and 6/9 having the same value i.e., 2/3

∴ The fractions are Equivalent Fractions.

The Correct Answer is Option 1 i.e Akbar.

• Akbar (1556-1605):
• Emperor Akbar founded the city in by the name of “ILLAHABAS” which later became ALLAHABAD.
• He introduced the new religion as Din-i-Ilahi.
• He introduced the Mansabdari system.
• Akbar defeated Hemu in the second battle of Panipat.
• He built Ibadat Khana in Fatehpur Sikri.
• He followed the policy of Sulh-i-Kul.
• Babar(1526-1530):
• He declared himself as Badshah.
• He was the founder of the Mughal Empire in India.
• Baburnama, also known as Tuzk-e Babri is the biography of Babar written by him.
• Shah Jahan (1628 to 1658 AD):
• He built Red Fort in Delhi.
• He also built the Taj Mahal in Agra.
• He built Moti Masjid in Agra.
• He also built Jama Masjid in Delhi.
• Jahangir (1605–1627 AD):
• He built Begum Shahi Mosque in Lahore, Pakistan.

Important Points

Mughals:

• The Mughals were descendants of two great lineages of rulers.
• From their mother’s side, they were descendants of Genghis Khan (died 1227), the Mongol ruler who ruled over parts of China and Central Asia.
• From their father’s side, they were the successors of Timur (died 1404), the ruler of Iran, Iraq and modern-day Turkey.
• However, the Mughals did not like to be called Mughal or Mongol. This was because Genghis Khan’s memory was associated with the massacre of innumerable people.
• It was also linked with the Uzbeks, their Mongol competitors.
• On the other hand, the Mughals were proud of their Timurid ancestry, not least of all because their great ancestor had captured Delhi in 1398.

Shortcut Trick

Area of a parallelogram = Base × Height

Area = 20 × 5.4 = 108 m²

∴ The correct answer is 108 sq. m.

Alternate Method

Given:

Base (b) of the parallelogram = 20 m

Height (h) of the parallelogram = 5.4 m

Formula Used:

Area of Parallelogram = Base × Height

Calculations:

⇒ Area = 20 m × 5.4 m

⇒ Area = 20 × (54/10) m²

⇒ Area = 2 × 54 m²

⇒ Area = 108 m²

∴ The correct answer is 108 sq. m.

Additional Information

Properties of a Parallelogram

Opposite sides are equal and parallel. Opposite angles are equal, and diagonals bisect each other.

Perimeter of Parallelogram

Perimeter = 2 × (Sum of adjacent sides) = 2(a + b).

Relation with Diagonals

2(a² + b²) = d₁² + d₂², where d₁ and d₂ are the lengths of the diagonals.

? = (-5) {20 – (-2) × (-8)}

⇒ (-5) {20 – (16)}

⇒ (-5) {4}

∴ ? = − 20

In the case of the repeating year, we add 6 with the given year if the given year is a leap year + 1.

2004 is a leap year.

2005 = leap year + 1

so we add 6. 2005 + 6= 2011

The trick to remember:

 

 

 

 

 

 

2011 has the same calendar as that of 2005.

Hence, “2011” is the correct answer

Shortcut Trick

When the distance traveled is the same for both parts of the journey, use the Harmonic Mean formula.

Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂)

Average Speed = (2 × 40 × 60) ÷ (40 + 60) = 4800 ÷ 100 = 48 km/hr.

∴ The correct answer is 48 km/hr.

Alternate Method

Given:

Speed from A to B (S₁) = 40 km/hr

Speed from B to A (S₂) = 60 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Let the Distance between A and B be the LCM of 40 and 60 = 120 km.

⇒ Time taken from A to B (T₁) = 120 ÷ 40 = 3 hours.

⇒ Time taken from B to A (T₂) = 120 ÷ 60 = 2 hours.

⇒ Total Distance = 120 + 120 = 240 km.

⇒ Total Time = 3 + 2 = 5 hours.

⇒ Average Speed = 240 ÷ 5 = 48 km/hr.

∴ The correct answer is 48 km/hr.

Additional Information

Average Speed for Equal Time Intervals

If a person travels at speed S₁ and S₂ for equal time intervals, Average Speed = (S₁ + S₂) ÷ 2.

Three Equal Distances

If three equal distances are covered at speeds u, v, and w, Average Speed = (3uvw) ÷ (uv + vw + wu).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Co-prime numbers have no common factor other than 1.

Check pairs: (2) Even numbers (common factor 2), (3) Ends in 5 and 0 (common factor 5), (4) Sum of digits divisible by 3 (common factor 3).

Both 59 and 97 are prime numbers; hence they are always co-prime.

∴ The correct answer is 59, 97.

Alternate Method

Given: Pairs of numbers to identify co-primes.

Formula Used: If HCF(a, b) = 1, then a and b are co-primes.

Calculations:

⇒ For (1) 59 and 97: Both are prime numbers. HCF(59, 97) = 1.

⇒ For (2) 348 and 296: Both are even. HCF is at least 4. (348 = 4 × 87, 296 = 4 × 74).

⇒ For (3) 3025 and 4920: Both divisible by 5 (units digit 5 and 0). HCF is at least 5.

⇒ For (4) 114 and 213: Sum of digits of 114 (1+1+4=6) and 213 (2+1+3=6) are divisible by 3. HCF is at least 3.

⇒ Only the pair (59, 97) satisfies the condition HCF = 1.

∴ The correct answer is 59, 97.

Additional Information

Definition of Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime themselves.

Consecutive Numbers

Any two consecutive natural numbers (e.g., 14 and 15) are always co-prime.

Prime Pair Property

Any two distinct prime numbers are always co-prime to each other.

Shortcut Trick

Total Capacity (LCM of 1.8, 2.7, 4.5) = 27 units.

Efficiencies: A = +15, B = +10, C = −6.

Let Pipe B be on for x hours. Then Pipe A was on for (5.5 − x) hours. Pipe C was on for all 5.5 hours.

Net Work: (15 − 6) × (5.5 − x) + (10 − 6) × x = 27 ⇒ 9(5.5 − x) + 4x = 27 ⇒ 49.5 − 5x = 27 ⇒ 5x = 22.5 ⇒ x = 4.5 hours.

∴ The correct answer is 4.5 hours.

Alternate Method

⇒ Total time taken = 5.5 hours.

⇒ Let Pipe B be open for t hours. Then Pipe A was open for (5.5 − t) hours.

⇒ Pipe C was open for the entire duration of 5.5 hours because it was never turned off.

⇒ Work done by (A + C) for (5.5 − t) hours + Work done by (B + C) for t hours = 27

⇒ (15 − 6) × (5.5 − t) + (10 − 6) × t = 27

⇒ 9 × (5.5 − t) + 4 × t = 27

⇒ 49.5 − 9t + 4t = 27

⇒ 49.5 − 5t = 27

⇒ 5t = 22.5

⇒ t = 4.5 hours

∴ The correct answer is 4.5 hours.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency), while outlet/drain pipes remove water (negative efficiency).

Total Work Formula

Total Work = Efficiency × Time. For multiple pipes, Total Work = (Σ Efficiencies) × Time.

LCM Method

Always take the LCM of the individual times to assume a convenient Total Capacity for the cistern.

The least possible Venn diagram is as follows,

Conclusion 1: Some Hyena are Foxes → True (This is definitely true)

Conclusion 2: Some Foxes are Raccoons → False (This is definitely false)

Conclusion 3: No Raccoon is Hyena → False (This is definitely false)

Hence, “only conclusion 1” follow.

Shortcut Trick

Ratio of Procurement : Rent/Electricity = 90 : 10 = 9 : 1

Given: 1 unit = ₹15,000

Procurement (9 units) = 9 × 15,000 = ₹1,35,000

₹1,35,000 = ₹1.35 lakh

∴ The correct answer is ₹1.35 lakh.

Alternate Method

Given:

Expenditure on Rent and Electricity = 10% = ₹15,000

Expenditure on Procurement = 90%

Calculations:

⇒ Let the total monthly expenditure be X.

⇒ 10% of X = 15,000

⇒ (10 ÷ 100) × X = 15,000

⇒ X = 15,000 × 10 = ₹1,50,000

⇒ Procurement expenditure = 90% of 1,50,000

⇒ (90 ÷ 100) × 1,50,000 = 9 × 15,000

⇒ Procurement = ₹1,35,000

⇒ In lakhs: 1,35,000 ÷ 1,00,000 = 1.35 lakh

∴ The correct answer is ₹1.35 lakh.

Additional Information

Percentage Base Change

To find a value based on another percentage of the same base: (Value 1 ÷ % 1) × % 2.

Conversion to Lakhs

1 Lakh = 1,00,000. To convert a value to lakhs, divide the numerical amount by 10⁵.

Ratio Distribution

If a total is divided into parts a and b, then Value of part a = [a ÷ (a + b)] × Total.

Drawing the family tree,

Akhil’s father mother is the paternal grandmother to Supriya.

Hence, “Paternal grandmother” is the correct answer

The pattern followed here is,

7 + 3 = 10;

10 + 4 = 14;

14 + 5 = 19;

19 + 6 = 25;

25 + 7 = 32

Hence, “19” is the correct answer

CONCEPT:

• Power: The rate of work done by an electric current is called power. It is denoted by P. The SI unit of power is the watt (W).

Power dissipation is given by:

Power (P) = V I = V2/R = I2 R

Where V is the potential difference across resistance, I is current flowing and R is resistance.

CALCULATION:

Given that: 

Voltage (V) = 220 V

Power (W) = 1100 W

Electric power (P) = voltage (V) × current (I)

1100 = 220 × current

current (I) = 1100/220

current (I) = 5 A

• Therefore the current drawn from a generator is 5 A. So option 1 is correct.

The least possible Venn diagram is as follows,

DIAGRAM

Conclusion 1: All vessels are mud → True (This is definitely true)

Conclusion 2: Some mud are pot → True (This is definitely true)

Hence, “all conclusions” follow.

The correct answer is option 4 i.e heat.

Key Points

• The work done by friction is not lost but is transferred as heat energy.
• The Law of Conservation of Energy states that energy cannot be created or destroyed. It can only be transferred from one type to another.
• Energy is not lost when frictional forces occur. For example, when a bike applies its brakes and slows down, the kinetic energy of the bike is transformed into heat energy in the brakes.

The pattern followed is,

The symbols are moving clock- wise and the symbol in the previous block is added to the block which has two symbols.

In the second image the triangle from the first image is added to the second block.

In the third image the ‘*’ image is added to the bloc in the north – west direction.

The image which will come next in the series is,

Hence, “C” is the correct answer.

Shortcut Trick

Area of a Rhombus when side (a) and one diagonal (d₁) are given:

Area = d₁ × √(a² − (d₁/2)²)

Area = 2.8 × √(5² − (2.8/2)²) = 2.8 × √(25 − 1.96)

Area = 2.8 × √23.04 = 2.8 × 4.8 = 13.44 m²

∴ The correct answer is 13.44 m².

Alternate Method

Given:

Length of each side (a) = 5 m

Length of first diagonal (d₁) = 2.8 m

Formula Used:

1. Diagonals of a rhombus bisect each other at 90°.
2. a² = (d₁/2)² + (d₂/2)²
3. Area of Rhombus = (1/2) × d₁ × d₂

Calculations:

⇒ Let the second diagonal be d₂.

⇒ Half of first diagonal = 2.8 ÷ 2 = 1.4 m.

⇒ In the right-angled triangle formed by the side and half-diagonals:

⇒ 5² = (1.4)² + (d₂/2)²

⇒ 25 = 1.96 + (d₂/2)²

⇒ (d₂/2)² = 25 − 1.96 = 23.04

⇒ d₂/2 = √23.04 = 4.8 m

⇒ Second diagonal d₂ = 4.8 × 2 = 9.6 m

⇒ Area = (1/2) × 2.8 × 9.6

⇒ Area = 1.4 × 9.6 = 13.44 m²

Thus, the area of the rhombus is 13.44 m², which corresponds to Option (2).

∴ The correct answer is 13.44 m².

Additional Information

Properties of Rhombus

All sides are equal, and opposite angles are equal. Diagonals bisect each other at right angles (90°) and bisect the vertex angles.

Relation between Side and Diagonals

The side a and diagonals d₁, d₂ are related by 4a² = d₁² + d₂².

Perimeter of Rhombus

Perimeter = 4 × side = 4a. It is the total length of the boundary of the rhombus.

Alternative Area Formula

Area = Base × Height. Also, Area = a² × sin(θ), where θ is any interior angle.

The Correct Answer is Option 1 i.e NPCI.

• HDFC Bank:
• It is India's private sector bank.
• CEO: Aditya Puri
• Tagline: We Understand Your World
• Headquarters: Mumbai
• SBI Bank:
• It is the largest public sector banks in India.
• It began with the establishment of the Bank of Calcutta in Calcutta, on 2 June 1806.
• It was the first-ever joint-stock bank of British India, established under the sponsorship of the Government of Bengal.
• Rajnish Kumar is the chairman of SBI
• Tagline: The banker to every Indian.
• ICICI Bank:
• It is the private sector bank in India.
• ICICI Bank became the first to enable its customers to make electronic payments by just waving the cards near the merchant terminal.
• ICICI Bank Chairman is Girish Chandra Chaturvedi.
• Tagline: Hum Hai Na, Khyal Apka
• Headquarters: Mumbai.
• NPCI:
• It is an acronym for the National Payments Corporation of India.
• It is an umbrella organization for all retail payments and settlement systems in India.
• It is an initiative of the Reserve Bank of India (RBI) and the Indian Banks’ Association (IBA).
• It was formed as a “Not for Profit” Company under the provisions of Section 25 of Companies Act 1956.
• Its Headquarters‎ is in ‎Mumbai.
• BHIM App, an Indian mobile payment app has been developed by the National Payments Corporation of India.
• The National Payments Corporation of India (NPCI) has launched the Unified Payments Interface (UPI) 2.0 in 2018.
• UPI version 1 was launched in April 2016.
• UPI is a system that powers multiple bank accounts into a single mobile application.

The Correct Answer is Option 2 i.e Perini thandavam.

Key Points

• Bharatanatyam:
• It is an Indian classical dance that originated in Tamil Nadu.
• The three important features of Bharatanatyam are Nritta, Natya, and Nritya.
• This dance form is performed by both men and women.
• Sattriya:
• The Sattriya dance form was introduced in the 15th century A.D by the great Vaishnava saint and reformer of Assam, Sankaradeva.
• It was originated in the eastern state of Assam.
• It is one of the eight classical Indian dances
• Mohiniyattam:
• It is one of the eight classical dance forms of India.
• It is a classical solo dance form of Kerala.
• It is performed exclusively by women.
• Perini thandavam:
• It is a dance form performed by men.
• It is an ancient dance form of the state of Telangana.
• It was originated during the rule of Kakatiya dynasty

The Correct Answer is Option 3 i.e 20.

• The number of neutrons within the nucleus of a given atom can be found by subtracting the atomic number from the atomic mass i.e difference between the mass number of the atom and the atomic number.
• Number of neutrons in Potassium is the mass number of Potassium minus the atomic number of Potassium
• Number of neutrons = 39 - 19 = 20.

Shortcut Trick Total score for 5 students = 5 × 20 = 100 Total score for 3 students = 3 × 18 = 54 Combined score of 2 new students = 100 − 54 = 46 To minimize one score, maximize the other to the limit of 25 marks. Lowest marks possible = 46 − 25 = 21 ∴ The correct answer is 21.

Alternate Method Given: Initial students = 3, Initial Mean = 18 Final students = 5, Final Mean = 20 Maximum marks per student = 25 Formula Used: Total = Average × Number of observations

Calculations: ⇒ Total marks of first 3 students = 3 × 18 = 54 ⇒ Total marks of all 5 students = 5 × 20 = 100 ⇒ Sum of marks of 2 new students = 100 − 54 = 46 ⇒ Let the marks of new students be x and y (where x < y) ⇒ x + y = 46 ⇒ To find the lowest value for x, we take the maximum possible value for y ⇒ Since the test is out of 25, Max(y) = 25 ⇒ x + 25 = 46 ⇒ x = 46 − 25 ⇒ x = 21 ∴ The correct answer is 21.

Additional Information Average (Mean) Formula The mean is calculated as the Sum of all observations ÷ Total number of observations. Extremum Values in Averages To minimize a specific value in a set with a fixed sum, all other values must be maximized to their upper limit. Weighted Average New Average = (n1x1 + n2x2) ÷ (n1 + n2), where n is the count and x is the average of each group.

CONCEPT:

• Power: The rate of work done is called power. It is denoted by P.
• Average power: The total work done divided by the total time taken is called average power.

Average power = Total work done (W)/Time taken (t)

• Work-energy theorem: It states that work done by a force acting on a body is equal to the change in the kinetic energy of the body i.e.,

W = Kf - Ki

$W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = {\bf{\Delta }}K$

Where v = final velocity, u = initial velocity and m = mass of the body

CALCULATION:

Given that: 

Initial velocity (u) = 0 m/s (Becasue the block was in rest)

Final velocity (v) = 2 m/s

Total time (t) = 20 sec

Mass (m) = 10 kg

$W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = \frac{1}{2}\times10\times{2^2} - \frac{1}{2}\times 10\times{0^2}$

Total Work done (W) = 20 J

Average power = Total work done (W)/Time taken (t) = 20/20 = 1 W

The correct answer is inertia.

CONCEPT:

• Inertia: It is the property of a body by virtue of which the body resists the change in its initial state of rest or motion with uniform speed on a straight line.
• when a car or train starts suddenly, the passengers bends backwards is an example of inertia.
• momentum: It is the property of a moving body and is defined as the product of mass and velocity of the body.
• SI unit is kg.m/s
• Force: The interaction which when acts on a body changes or stories to change the initial state of rest or motion with a uniform velocity of the body is called force.
• SI unit of force is Newton.
• Velocity: The displacement of the object in a unit time interval is called velocity. It is denoted by V. 
• SI unit is meter/second.

EXPLANATION:

• The tendency of a body to resist change in a state of rest or state of motion is called inertia. So option 2 is correct.

The Correct Answer is Option 4 i.e 8 Nm.

CONCEPT:

Lever:

• An ideal lever is essentially a light (i.e. of negligible mass) rod pivoted at a point along its length. This point is called the fulcrum.
• Levers are the most basic machines that are used to do some work with minimal effort.
• If two forces F1 and F2 are acting on the lever as shown in the figure at distances d1 and d2 respectively from the fulcrum, then from the rotational equilibrium,

⇒ F1d1 = F2d2

⇒ (load arm) × load = (effort arm)×effort

CALCULATION:

• The moment of the couple is the product of the force and the perpendicular distance between them.

⇒ Moment of the couple at the new position = Moment on the heavier side - Moment on the light side

 = 5 N x 2 m (since the pivot is shifted 3 m left) - 0.25 N x 8 m (5m + 3m) 

⇒ Moment of the couple at the new position = 10 - 2 = 8 Nm.

Shortcut Trick

Apply the Tangent-Secant Theorem: DE² = BD × DA

Given: BD = 3 cm and AB = 9 cm

⇒ DA = AB + BD = 9 + 3 = 12 cm

⇒ DE² = 3 × 12 = 36

⇒ DE = √36 = 6 cm

∴ The correct answer is 6 cm.

Alternate Method

Given:

Length of chord AB = 9 cm

Length of external segment BD = 3 cm

Formula Used:

According to the Tangent-Secant Theorem, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external part.

DE² = BD × DA

D B A E O 3 cm

The Correct Answer is Option 2 i.e Divya Deskmukh.

The Correct Answer is Option 3 i.e Mani Vajipey.

• Priyanka Bakaya:
• She is an Australian - American entrepreneurial environmental leader.
• She founded Renewlogy, a clean energy company that converts plastic waste into fuel.
• Pronita Saxena:
• She is the Founder & CEO at Citizengage, a startup building mobile tools for communities to self-manage their civic behaviour.
• Mani Vajipey:
• He is the co-founder and CEO of Hyderabad based startup Banyan Nation, a technology-driven  company.
• Banyan Nation has won the Dell People’s Choice Award for Circular Economy Entrepreneur as part of the Circulars Awards at the World Economic Forum at Davos.
• It is the first-ever Indian firm to be shortlisted for and to win the Circular Economy awards.

The Correct Answer is Option 1 i.e the tailfin of a lobster and the flukes of a whale.

• Analogous organs:
• These are defined as the organs of different animals having different structures but perform the same functions.
• Examples:
• wings of insects and birds.
• Sweet potatoes and potatoes.
• the tailfin of a lobster and the flukes of a whale.
• Homologous organs:
• These are defined as the organs of different animals having similar structure but differ in their functions.
• Examples:
• forelimbs of frog, man, and the flippers of the whale
• The arm of a human and the leg of dogs, bulls.
• A bat's wing and a whale's flipper.
• the leg of a dog and the flipper of a dolphin or whale.

The Correct Answer is Option 1 i.e Afghanistan.

The Correct Answer is Option 1 i.e Calcium.

In the given image, there are two arrows pointing to different directions and a star symbol.

In image C also there are two arrows and a star symbol.

Hence, “C” is the correct answer.

The pattern followed here is,

837659 - 1 = 837658,

837658 - 2 = 837656;

837656 - 3 = 837653;

837653 - 4 = 837649;

837649 - 5 = 837644

Hence, “837656, 837644” is the correct answer.

Shortcut Trick

Difference in number of entries = 300 − 200 = 100 entries

Entry fee per head = ₹200

Less money received = 100 × ₹200 = ₹20,000

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Expected entries = 300

Actual entries = 200

Entry fee = ₹200

⇒ Total expected collection = 300 × 200 = ₹60,000

⇒ Total actual collection = 200 × 200 = ₹40,000

⇒ Difference in amount = ₹60,000 − ₹40,000 = ₹20,000

∴ The correct answer is ₹20,000.

Additional Information

Revenue Calculation

Total Revenue = Price per unit × Number of units sold.

Percentage Decrease

Percentage change in revenue = ((Initial − Final) ÷ Initial) × 100.

$\frac{3}{{15}} + \frac{{13}}{{14}} - \frac{{19}}{{21}} + \frac{{31}}{{35}} - \frac{{23}}{{30}}$

$\Rightarrow \frac{1}{5} + \frac{{13}}{{14}} - \frac{{19}}{{21}} + \frac{{31}}{{35}} - \frac{{23}}{{30}}$

$\Rightarrow \frac{{42; + ;13; \times ;15; - ;19; \times ;10; + ;31; \times ;6; - ;23; \times ;7}}{{210}}$

$\Rightarrow \frac{{42; + ;195; - ;190; + ;186; - ;161}}{{210}}$

⇒ 72/210

⇒ 12/35

The Correct Answer is Option 3 i.e India.

• World Customs Organization (WCO):
• It is intergovernmental organization and is headquartered in Brussels, Belgium.
• India has become the Vice-Chair (Regional Head) of the Asia Pacific Region of World Customs Organisation (WCO) for a period of two years, from July 2018 to June 2020.
• India is a member nation of WCO.
• China:
• China is the world's most populous country.
• Xi Jinping is the current president of China.
• Beijing is the capital of China.
• China is also a member nation of WCO.
• Australia:
• Canberra is the capital of Australia.
• Scott Morrison is the current PM of Australia.
• It is also a member nation of WCO.
• Japan:
• It is the 62nd largest country in terms of area.
• It is an island country in East Asia.
• Tokyo is the capital city of Japan.
• Shinzo Abe is the current PM of Japan.
• It is also a member nation of WCO.

The Correct Answer is Option 1 i.e Methylene.

• A homologous series is a group of similar constituted compounds in which members possess the same functional group and have similar chemical characteristics and two consecutive members differ in their molecular formula by -CH₂.
• All members of a homologous series differ by a CH_2​ group known as the methylene group.
• Each consecutive member of the family of hydrocarbons differs from the previous member by the methylene group.
• Example: methane (CH₄), ethane (C₂H₆), and propane (C₃H₈).
• The Methyl group is CH₃.
• An ethyl group is CH₃CH₂.
• An Ethylene group is C₂H₄.

Shortcut Trick

Let the tower height be h = 18 m. In the depression triangle (60°), the base x = h/√3 = 18/√3 = 6√3 m.

In the elevation triangle (45°), the additional height above the tower is equal to the base, so p = x = 6√3 m.

Total building height = h + p = 18 + 6√3 = 6(3 + √3) m.

∴ The correct answer is 6(3 + √3) m.

Alternate Method

Given: Height of tower (AB) = 18 m, Elevation angle (θ₁) = 45°, Depression angle (θ₂) = 60°.

Formula Used: tan θ = Perpendicular / Base

⇒ In ΔBCD (depression triangle), tan 60° = 18 / x

⇒ √3 = 18 / x

⇒ x = 18 / √3 = 6√3 m

⇒ In ΔADE (elevation triangle), tan 45° = p / x

⇒ 1 = p / 6√3

⇒ p = 6√3 m

⇒ Total Height of building = 18 + p = 18 + 6√3

⇒ Total Height = 6(3 + √3) m

∴ The correct answer is 6(3 + √3) m.

Additional Information

Angle of Elevation and Depression

The angle of elevation is measured upward from the horizontal, while the angle of depression is measured downward. They are alternate interior angles when considering the horizontal lines.

Standard Trigonometric Ratios

For height and distance: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3 are the most frequently used values.

Rationalization

To simplify 18/√3, multiply numerator and denominator by √3 to get (18×√3)/3 = 6√3.

According to the given figure,

In all the given options, except figure B the letters placed to the side of the original letter are the mirror images of the given alphabets.

Whereas, in figure B the reverse form of the alphabet is given.

Hence, “B” is the odd one out.

Shortcut Trick Ratio of Cost Price (CP) to Selling Price (SP) is inversely proportional to the quantity of items. Quantity ratio (CP : SP) = 15 : 20 ⇒ Price ratio (CP : SP) = 20 : 15. Simplifying the price ratio: 4 : 3. Loss = 4 − 3 = 1 unit. Loss% = (1 ÷ 4) × 100 = 25%. ∴ The correct answer is 25%.

Alternate Method Given: CP of 15 oranges = SP of 20 oranges. Formulas: Loss = CP − SP | Loss% = (Loss ÷ CP) × 100

⇒ Let the CP of 1 orange be Re. 1. ⇒ CP of 20 oranges = Rs. 20. ⇒ Given, SP of 20 oranges = CP of 15 oranges = Rs. 15. ⇒ Loss = 20 − 15 = Rs. 5. ⇒ Loss% = (5 ÷ 20) × 100 = 25%. ∴ The correct answer is 25%.

Additional Information Loss and Gain Concepts When SP < CP, a Loss occurs. It is always calculated on the Cost Price unless otherwise specified. Ratio Method for Quantity If CP of 'x' articles = SP of 'y' articles, then Profit or Loss% = (x − y) ÷ y × 100. Positive result denotes Profit, negative denotes Loss.

The Correct Answer is Option 2 i.e Papaya.

• Vegetative propagation is a form of asexual reproduction of a plant wherein a new plant grows from stems, roots, and leaves.
• Vegetative propagation can be natural and also can be done artificially.
• Example: Rose, Banana, Orange, Mango, Sugarcane, etc.
• Papaya is commercially propagated by seed and tissue culture plants. It is not grown through vegetative propagation.

The Correct Answer is Option 4 i.e Calcium Sulphate Hemihydrate.

• Calcium Sulphate Hemihydrate (CaSO₄· 1/2 H₂O):
• Calcium Sulphate Hemihydrate (CaSO₄· 1/2 H₂O)​ is the chemical name of plaster of Paris
• The plaster of Paris on mixing with water produces gypsum.
• Calcium Sulphate Hemihydrate (CaSO₄·1/2 H₂O) on hydration leads to the crystallization of gypsum calcium sulphate dihydrate (CaSO₄·2H₂O).
• Gypsum is a common sulfate mineral composed of calcium sulfate dihydrate.
• Gypsum is widely used in the manufacture of wallboard, cement, plaster of Paris, etc.
• Sodium hydrogen carbonate (NaHCO₃) or sodium bicarbonate:
• Sodium bicarbonate is commonly known as baking soda
• Sodium bicarbonate in baking soda quickly neutralizes stomach acid.
• Sodium bicarbonate is a white crystalline solid.
• It is used in baking products like cakes, cookies, etc.
• Calcium phosphate (Ca₃(PO₄)₂):
• Calcium Phosphate is a mineral composed of calcium cations and phosphate anions.
• Calcium phosphate is used to treat calcium deficiencies.

Shortcut Trick

Multiplier Method: Selling Price = Cost Price × (100 + Profit%) ÷ 100.

Selling Price = 1,500 × (100 + 21) ÷ 100 = 1,500 × 121 ÷ 100.

Selling Price = 15 × 121 = 1,815.

∴ The correct answer is Rs. 1,815.

Alternate Method

Given: Cost Price (CP) = Rs. 1,500, Profit Percentage = 21%.

Formulas: Profit = (Profit% ÷ 100) × CP | SP = CP + Profit.

⇒ Step 1: Calculate the absolute Profit amount.

⇒ Profit = 21% of 1,500 = (21 ÷ 100) × 1,500 = 21 × 15 = Rs. 315.

⇒ Step 2: Calculate the Selling Price (SP).

⇒ SP = CP + Profit = 1,500 + 315 = Rs. 1,815.

∴ The correct answer is Rs. 1,815.

Additional Information

Profit and Loss Basics

Profit occurs when the Selling Price is greater than the Cost Price. Formula: Profit = SP − CP.

Percentage Calculation

To find the result of a percentage increase, multiply the original value by (1 + r/100), where r is the percentage rate.

The Correct Answer is Option 2 i.e 14.

• Alcohols contain the hydroxyl functional group (-OH)
• C₂H₅OH is the molecular formula of Ethyl alcohol.
• The molecular mass of ethyl alcohol is 46.07
• CH₃OH is the molecular formula of Methyl alcohol.
• Methyl alcohol is also known as Methanol.
• The Molecular mass of Methyl alcohol is 32.04
• Methyl alcohol and Ethyl alcohol differ in molecular mass by 14 units.

The pattern followed here is,

For KITE,

The place value of K is 11, 11 - 1 = 10

The place value of I is 9, 9 - 1 = 8

The place value of T is 20, 20 - 1 = 19

The place value of E is 5, 5 - 1 = 4

So,

KITE is coded as 108194

Similarly,

For TEAR,

The place value of T is 20, 20 - 1 = 19

The place value of E is 5, 5 - 1 = 4

The place value of A is 1, 1 - 1 = 0

The place value of R is 18, 18 - 1 = 17

TEAR is coded as 194017

Hence, “194017” is the correct answer

According to the given statement,

Argument 1: This is strong, because gymnastics will help in the overall development of the child.

Argument 2: This is not strong, because they are not the things which are waste of time and energy, but they help in the development of the child.

Hence, “Only argument 1" is strong.

2 – [3 – {6 – (5 – 4 – 3 + 10)}]

⇒ 2 – [3 – {6 – (15 – 4 – 3)}]

⇒ 2 – [3 – {6 – (15 – 7)}]

⇒ 2 – [3 – {6 – 8}]

⇒ 2 – [3 + 2]

⇒ 2 – 5

⇒ – 3

The correct answer is option 4 i.e Maruti Suzuki.

Maruti Suzuki:

• It is an automobile manufacturer company in India.
• It is headquartered in New Delhi, India.
• Kenichi Ayukawa is the current CEO of the company.
• Ministry of Skill Development, Government of India and Maruti Suzuki enters into an agreement to support Skill India in the automobile industry in December 2017.

Tata Motors:

• It is an Indian multinational automotive manufacturing company.
• It is headquartered in Maharashtra.
• Guenter Butschek is the current CEO and Managing Director of Tata Motors.

Mahindra & Mahindra Ltd:

• It is an Indian multinational car manufacturing company.
• It is headquartered in Mumbai, Maharashtra.
• Anand Mahindra is the current CEO of Mahindra  & Mahindra Ltd.

Ashok Leyland:

• It is an Indian automobile company.
• It is headquartered in Chennai, India.
• Vipin Sondhi is the current CEO of the company.

CONCEPT:

• Kinetic energy (KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

$KE = \frac{1}{2}m{v^2}$

Where m = mass of the body and v = velocity of the body

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

$PE = mgh$

Where, m = mass of the body, g = acceleration due to gravity and h = height of the body

• Conservation of energy: According to the conservation of energy, energy can’t be created or destroyed, it can only transform from one form to another.
• The total energy of the system remains constant i.e. the sum of kinetic energy + potential energy remains constant.

EXPLANATION:

• When the body will be thrown upward the initial kinetic energy will slowly get converted into potential energy. but the total energy will remain constant.
• Thus the potential energy will increase and the kinetic energy will decrease until the body reached the top. So option 2 is correct.

Shortcut Trick

Area of rhombus = (d₁ × d₂) ÷ 2

216 = (24 × d₂) ÷ 2 ⇒ d₂ = 18 cm

Side = √((d₁/2)² + (d₂/2)²)

Side = √(12² + 9²) = √(144 + 81) = √225 = 15 cm

∴ The correct answer is 15 cm.

Alternate Method

Given:

Area of rhombus = 216 cm²

Diagonal 1 (d₁) = 24 cm

Formula Used:

Area = (1/2) × d₁ × d₂

Side (a) = √[(d₁/2)² + (d₂/2)²]

Calculations:

⇒ 216 = 1/2 × 24 × d₂

⇒ 216 = 12 × d₂

⇒ d₂ = 216 ÷ 12 = 18 cm

⇒ In a rhombus, diagonals bisect each other at 90°.

⇒ Half-diagonals are 12 cm and 9 cm.

⇒ Side = √(12² + 9²)

⇒ Side = √(144 + 81) = √225

⇒ Side = 15 cm

∴ The correct answer is 15 cm.

Additional Information

Properties of Rhombus

All sides are equal and diagonals bisect each other at right angles (90°).

Perimeter of Rhombus

Perimeter = 4 × Side (a). Also 4a² = d₁² + d₂².

Pythagorean Triplet

The values 9, 12, and 15 form a Pythagorean triplet, where 9² + 12² = 15².

Shortcut Trick

In Time and Work, if the number of workers is reduced by a factor, the time taken increases by the same factor (Inverse Proportion).

Number of workers (3 boys + 3 girls) → (1 boy + 1 girl) is a reduction by 3 times.

Time required = Original Time × 3

⇒ 6/5 × 3 = 18/5 hours.

∴ The correct answer is 18/5 hours.

Alternate Method

Given: Efficiency of (3B + 3G) = 5 units/hr.

⇒ 3 × (Efficiency of 1B + 1G) = 5

⇒ Efficiency of (1B + 1G) = 5/3 units/hr.

⇒ Time required (H) = Total Work ÷ Efficiency

⇒ H = 6 ÷ (5/3) = 6 × 3/5

⇒ H = 18/5 hours.

∴ The correct answer is 18/5 hours.

Additional Information

Work-Efficiency Relation

Total Work = Efficiency × Time. If work is constant, Efficiency is inversely proportional to Time (E₁T₁ = E₂T₂).

Man-Days Formula

M₁D₁H₁/W₁ = M₂D₂H₂/W₂ where M is workers, D is days, H is hours, and W is work done.

According to the given statement,

The statement says that winning a medal at the Olympics is a matter of pride for our country. 

Thus, it suggests that participating and winning an Olympics medal is a huge opportunity for a sportsperson of our country.

This implies that the Olympics offers a pedestal (platform or a position of esteem) for sportspersons to showcase their talents.

The given statement only talks about the Olympics. Thus, assumption II which is a generalization for any sports is not implicit.

Hence, “only assumption 1” is implicit.

By decoding given information,

 

125 ÷ 5 + 15 × 2 - 4 × 3

Using BODMAS rule,

= 25 + 15 × 2 - 4 × 3

= 25 + 30 - 12

= 55 - 12

= 43

Hence, “43” is the correct answer.

<br>

The pattern followed here is,

Hence, “6U” is the correct answer.

The Correct Answer is option 4 i.e Amitabh Bachchan.

• The Union government has roped in actor Amitabh Bachchan to promote the Goods and Services Tax (GST) in June 2017.
• Salman Khan:
• He received the IIFA Habitat Humanity Ambassadorship Award in the year 2010.
• He also won the Airtel Superstar Hero Award 2011 for the film Bodyguard.
• Sachin Tendulkar:
• He won the Bharat Ratna in the year 2014.
• He won the Padma Vibhushan in the year 2008.
• He won the BCCI cricketer of the year 2011.
• Aishwarya Rai Bachchan:
• She won the Padma Shri in the year 2009.
• She won the female Stardust Award for Actor of the Year 2007.
• Amitabh Bachchan:
• He won the Padma Vibhushan award in the year 2015.
• He also won the Padma Bhushan award in the year 2001.
• He won the 2019 Dadasaheb Phalke Award.
• He was appointed as the GST brand ambassador in June 2017.

According to the given information,

In 30 seconds the toy turns 45°

In 60 seconds the toy turns 45° + 45° = 90°

Initially the toy is facing in the west direction after rotating 45° + 45° in the clockwise direction, it is facing in the north direction.

Hence, “north” is the correct answer.

The correct answer is option 3 i.e atoms.

Oxygen (O)

• Two "O" represents two atoms of oxygen.
• The number of electrons in an atom is equal to the number of protons.
• The oxygen atomic number is eight and has eight electrons.
• Two or more atoms held together by chemical bonds is called a molecule.
• An ion is a charged atom or molecule with the net electrical charge.

According to the given statement,

Argument 1: This is not strong, because only apple will not provide all the nutrients to the body.

Argument 2: This is strong, every fruit is important for the healthy functioning of the body.

Hence, “only argument 2” is strong.

Shortcut Trick

Apply Remainder Theorem: Substitute x = 2 into the expression and equate to the given remainder.

2(2)^m + 2³ − 3(2)² − 26 = 994

2^m+1 + 8 − 12 − 26 = 994 ⇒ 2^m+1 − 30 = 994

2^m+1 = 1024 ⇒ 2^m+1 = 2¹⁰ ⇒ m + 1 = 10

∴ The correct answer is 9.

Alternate Method

Given:

Polynomial f(x) = 2x^m + x³ − 3x² − 26

Divisor = (x − 2)

Remainder (R) = 994

Formula Used:

According to the Remainder Theorem, when a polynomial f(x) is divided by (x − a), the remainder is f(a).

Calculations:

⇒ f(2) = 994

⇒ 2(2)^m + (2)³ − 3(2)² − 26 = 994

⇒ 2 × 2^m + 8 − 3(4) − 26 = 994

⇒ 2^m+1 + 8 − 12 − 26 = 994

⇒ 2^m+1 − 30 = 994

⇒ 2^m+1 = 994 + 30

⇒ 2^m+1 = 1024

⇒ 2^m+1 = 2¹⁰ (Since 2¹⁰ = 1024)

⇒ m + 1 = 10

⇒ m = 10 − 1

⇒ m = 9

∴ The correct answer is 9.

Additional Information

Remainder Theorem

It states that if a polynomial f(x) is divided by a linear factor (x − a), the remainder is always equal to f(a).

Factor Theorem

A special case of the remainder theorem where if f(a) = 0, then (x − a) is a factor of the polynomial f(x).

Laws of Exponents

When bases are the same, we can equate the exponents: If a^x = a^y, then x = y (where a ≠ 0, 1, −1).

CONCEPT:

• Force: According to Newton, a force can never occur singly in nature. 
• It is the mutual interaction between the two bodies.
• It is that external energy which when acts on a body changes or stories to change the initial state of rest or motion with a uniform velocity of the body.
• Newton is the SI unit of force.
• Momentum : It is the property of a moving body and is defined as the product of mass and velocity of the body.
• SI unit is kgm/s.
• Velocity: The displacement of the object in a unit time interval is called velocity. It is denoted by V. 
• SI unit is meter/second.
• Pressure: It is the force applied per unit area in a direction perpendicular to the surface of the object.
• SI unit of pressure is the pascal.

EXPLANATION:

• Since the force can never occur singly. It is a mutual interaction between two bodies. So option 1 is correct.

The given image has a rectangle along with two lines and the rectangle is surrounded by two circles.

Image D resembles the given figure.

Hence, “D” is the correct answer.

The correct answer is option 2 i.e 3.

• Dobereiner’s law of triads states that when elements are arranged in the order of increasing atomic masses, the atomic mass of the middle element of the triad is approximately the average of the atomic masses of the other two elements.
• Each of Dobereiner's triads was a group of three elements.
• Dobereiner could identify only 3 triads from the elements known at that time.
• Example: 
• In the triad of lithium, sodium, and potassium.
• The atomic mass of:
• Lithium =7
• Potassium = 39.
• The average of masses of lithium and potassium gives the atomic mass of sodium 23.

Another example:-

The atomic weight of:

• Nitrogen (N) = 14 u
• Phosphorus (P) = 30 u
• Gold (Au) = 196 u

Hence, (N, P, Au ) is not a Dobereiner triad as the atomic weight of Phosphorus (P) is not the average of the atomic weight of Nitrogen (N) and Gold (Au)

The correct answer is option 1 i.e Karun Nair.

Karun Nair:

• He is an Indian international cricketer.
• He plays for Karnataka in domestic cricket.
• He is a right-handed batsman and occasional off-break bowler.
• In December 2016, he became only the second Indian batsman to hit a triple hundred in Test Matches after Virender Sehwag.

​K.L. Rahul:

• He is an Indian international cricketer.
• He became the first Indian player to score a hundred on ODI debut in first of the three ODIs against Zimbabwe.
• He is a right-handed batsman and a wicket-keeper.

Virat Kohli:

• He is the former captain of the Indian cricket team.
• He was awarded the Padma Shri in the year 2017.
• He was awarded the Wisden's leading cricketer in the world for the year 2016, 2017 and 2018.

Rahul Dravid:

• He won the Padma Bhushan award in the year 2013.
• He also won the Padma Shri in the year 2004.
• He also won the ICC Test Player of the Year 2004.

According to the given statement,

Assumption 1: This is implicit, because protection of environment from pollution is necessary to maintain the ecosystem.

Assumption 2: This is not implicit, because nothing is mentioned about working environment in the statement.

Hence, “only assumption 1” is implicit.