RRC Group D Previous Year Paper 28 (Held On: 26 Sept 2018 Shift 2)

$\frac{5}{{11}} + \frac{{11}}{5}$

= $\frac{{25; + ;121}}{{55}}$

= $\frac{{146}}{{55}}$

The Correct Answer is Option 3 i.e Chetan Bhagat.

The Correct Answer is Option 1 i.e Baking powder.

• Baking powder:
• Baking powder is a mixture of baking soda and tartaric acid .
• Tartaric acid has been added to baking powder to neutralize the bitterness produced by sodium bicarbonate (NaHCO₃) .
• Baking soda:
• It is commonly known as sodium bicarbonate.
• 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 softening of hard water.
• It is commonly used as a  agent for domestic purposes.It is also used in the manufacturing of paper, soap, textiles, paints, etc.
• Vinegar:
• Vinegar is produced from fermentation of alcohol.
• Vinegar is the natural source for acetic acid.
• It is widely used as a flavouring agent in most of the cuisines.

Shortcut Trick

Given that 63% of a number is 315.

Using Unitary Method: 1% → 315 ÷ 63 = 5.

Total number (100%) → 5 × 100 = 500.

∴ The correct answer is 500.

Alternate Method

Given:

Percentage value = 63%

Resulting value = 315

Formula Used:

Number = (Value ÷ Percentage) × 100

Calculations:

Let the number be x.

⇒ 63% of x = 315

⇒ (63 ÷ 100) × x = 315

⇒ x = (315 × 100) ÷ 63

⇒ x = 5 × 100

⇒ x = 500

∴ The correct answer is 500.

Additional Information

Percentage Change

Percentage change is calculated as (Difference ÷ Original Value) × 100.

Fraction to Percentage

To convert a fraction to a percentage, multiply the fraction by 100 and add the % symbol.

Base Value Concept

In percentage problems, the original number is always considered as the 100% base.

The pattern followed here is:

2 × 9 = 18

18 × 9 = 162

162 × 9 = 1458

Hence, ‘1458’ is the correct answer.

The Correct Answer is Option 1 i.e Germanium.

• Germanium (Ge):
• Atomic number is 32.
• Germanium is most widely used as a Semiconductor.
• Germanium is used in transistors and in integrated circuits.
• Germanium is also used as an alloying agent.
• Eka-silicon is known as Germanium.
• Gallium (Ga):
• Atomic number is 31.
• It is used in electronic circuits, semiconductors and light-emitting diodes (LEDs).
• Eka aluminium is known as gallium.
• Silicon (Si):
• Atomic number is 14.
• It is widely used as a semiconductor.
• It is the second most abundant element in the crust.
• Aluminium (Al):
• Atomic number is 13.
• It is soft, malleable and ductile.
• It has high thermal and electrical conductivity
• It has excellent corrosion resistance.
• It is the most abundant metal in the Earth’s crust.
• It is widely used for foil, kitchen utensils and conductor cables etc.

The Correct Answer is Option 1 i.e Delhi Acers.

• Delhi Acers team won the 2016 Premier Badminton League (PBL) title against Mumbai Rockets.
• The season was held from 2–17 January 2016.
• This is the second edition of the Premier Badminton League.
• The second edition was renamed from the Indian Badminton League to the Premier Badminton League.
• Chennai Smashers won the 2017 Premier Badminton League (PBL) against Mumbai Rockets.
• Hyderabad Hunters won the 2017-18 edition of PBL against Bangalore blasters.
• Bangalore Raptors won the 2020 edition of PBL against Northeastern Warriors.

Shortcut Trick

Let radius of cone (r_c) = 5 and altitude (h) = 9.

Volume of cone = (1/3) × π × 5² × 9 = 75π.

Volume of sphere = (4/3) × π × r_s³ = 75π ⇒ r_s³ = 225/4.

Ratio r_c³ : r_s³ = 5³ : (225/4) = 125 : 56.25 = 500 : 225 = 20 : 9.

Ratio r_c : r_s = √³20 : √³9 = √³(20 × 3) : √³(9 × 3) = √³60 : 3.

∴ The correct answer is √³60 : 3.

Alternate Method

Given:

Radius of cone (r_c) = (5/9) × Height of cone (h)

Volume of Cone = Volume of Sphere

Formula Used:

Volume of Cone = (1/3)πr_c²h

Volume of Sphere = (4/3)πr_s³

Calculations:

⇒ From given, h = (9/5)r_c

⇒ (1/3)πr_c²h = (4/3)πr_s³

⇒ r_c² × (9/5)r_c = 4r_s³

⇒ (9/5)r_c³ = 4r_s³

⇒ r_c³ / r_s³ = (4 × 5) / 9 = 20 / 9

⇒ r_c / r_s = √³(20/9)

⇒ Multiply numerator and denominator by √³3 to rationalize

⇒ r_c / r_s = (√³20 × √³3) / (√³9 × √³3) = √³60 / √³27

⇒ r_c / r_s = √³60 / 3

∴ The correct answer is √³60 : 3.

Additional Information

Right Circular Cone Properties

Slant height (l) = √(r² + h²). Total Surface Area = πr(l + r).

Sphere Properties

Surface Area of a sphere = 4πr². Volume = (4/3)πr³.

Ratio of Volumes

When comparing volumes of different 3D shapes, ensure all dimensions are in the same units and express heights in terms of radii where possible.

The Correct Answer is Option 2 i.e Mirabai Chanu.

• Mirabai Chanu:
• She is an Indian weight lifter from Manipur.
• She was the only second Indian after Karnam Malleswari to win a gold medal at the World Weightlifting Championships.
• She won the gold medal in women's 48 kg category at the 2017 World Championship being held in Anaheim, USA.
• Thunya Sukcharoen:
• She is an Thai weightlifter.
• Thailand’s Sukcharoen Thunya won the silver medal at the  2017 World Championship being held in Anaheim, USA.
• Segura Ana Iris:
• She is from Colombia.
• Segura Ana Iris bagged the bronze medal at the 2017 World Championship being held in Anaheim, USA.
• Karnam Malleswari: 
• She is a retired Indian weightlifter.
• She became the first Indian woman to win a medal at the Olympics in Sydney 2000.
• She also became the first Indian woman to become a weightlifting World Champion in 1994 in Istanbul.

All options except ‘rack’ are things which can be opened and closed.

 

Hence, ‘rack’ is the correct answer.

CONCEPT:

• Refractive index/Absolute refractive index: The ratio of the speed of light in air/vacuum to the speed of light in the medium is called the refractive index of that medium. 
• It is generally denoted by μ or n. It is a dimensionless quantity.

$Refractive; index = \frac{{speed;of;light;in;air}}{{speed;of;light;in;medium}}$

• The absolute refractive index can never be less than 1.

EXPLANATION:

• The absolute refraction index of the diamond is 2.42. It is the experimental data. So option 3 is correct.

The Correct Answer is Option 4 i.e Banabhatta.

• Fa-Hien:
• He is a Chinese traveler who visited India during the reign of Chandra Gupta II.
• He didn't mention the name of the king in his accounts.
• Fa-Hien provides valuable information on the socio, economic, and religious conditions of the Gupta empire.
• Ramcharitmanas:
• Tulsidas is the author of an epic Ramcharitmanas (a story of Lord Rama)
• It was written in Awadhi language.
• Rajatarangini:
• Rajatarangini is a book written by Kalhana.
• It gives an account of the history of Kashmir.
• It was written in the Sanskrit language.
• Harshacharita:
• Harshacharita is a book written by Banabhatta.
• It was written in the Sanskrit language.
• It gives us accurate information about Harsha and his administration.

The pattern followed here is:

1³ = 1

2³ = 8

3³ = 27

5³ = 125

7³ = 343

11³ = 1331

Here, the prime numbers have been cubed in an increasing order.

Hence, ‘342’ is the correct answer.

The Correct Answer is Option 2 i.e Radha Mohan Singh.

• Piyush Goyal:
• As of May 2020, he is the current Minister of Railways and Minister of Commerce & Industry in the Government of India.
• He is a Member of the Upper House of the Parliament of India (Rajya Sabha) and the Deputy Leader of Rajya Sabha.
• He received the 4th Annual Carnot Prize in 2018 recognising the pathbreaking transformations in India’s energy sector.
• Arun Jaitley:
• He was the former Ministry of Finance, and the Ministry of Corporate Affairs, Government of India (2014-2019).
• He was also the Minister of Defence (2014 & 2017) and the Minister of Information and Broadcasting, Government of India (2014-2016).
• He was posthumously awarded the Padma Vibhushan in 2020 in the field of Public Affairs.
• Radha Mohan Singh:
• As of August 2018, he is the union minister of Agriculture and Farmers Welfare.
• He was currently the chairperson for Parliamentary Standing committee on Railways.
• As of May 2020, Narendra Singh Tomar is the union minister of Agriculture & Farmers Welfare.
• J.P. Nadda:
• As of May 2019,  Nadda is the Union Minister of Health and Family Welfare.
• He is the National President of the Bharatiya Janata Party since 20th January 2020.
• As of May 2020, Dr. Harsh Vardhan is the Union Minister of Health and Family Welfare.

The Correct Answer is Option 3 i.e Pokhran.

• Pokhran:
• India tested its first nuclear device in Pokhran, Rajasthan in the year 1974.
• 'Smiling Buddha' was the code name of India's first successful nuclear bomb test.
• With the Smiling Buddha, India became the sixth nuclear power in the world after the United States, Soviet Union, Britain, France, and China to successfully test out a nuclear bomb.
• Sriharikota:
• It is located in the Nellore district in Andhra Pradesh.
• Satish  Dhawan  Space  Centre  (SDSC) SHAR in Sriharikota is the Spaceport of  India.
• It is one of the two satellite launch centers in India
• Kalpakkam:
• It is situated on the Coromandel Coast of Chennai, Tamil Nadu.
• Kalpakkam Nuclear Power Plant in Tamil Nadu first began operating in 1984
• Tarapur:
• It is located in the state of Maharashtra:
• Tarapur Atomic Power Station was the first commercial nuclear power station built in India, commissioned in 1969.

Let us observe the pattern of 1^st and 2^nd figure.

Here, the second figure is the mirror image of the first figure when a mirror is placed to the right of the first figure. 

Similarly, the fourth figure will be the mirror image of the third figure when a mirror will be placed to the right of the third figure.

 Hence, figure ‘C’ is the correct answer.

√4.2436

Since

4.0000 < 4.2436 < 4.4100

So,

2.00 < $\sqrt {4.2436}$ < 2.10

So, option 2 and 4 are eliminated.

Now, we can get the correct option by simply squaring it

(2.06)² = 4.2436

And, (2.04)² = 4.1616

Hence, option 3 is correct.

Shortcut Trick

Mass of solution = Solute + Solvent = 60 + 340 = 400 g.

Concentration % = (Solute / Solution) × 100.

⇒ (60 / 400) × 100 = 60 / 4 = 15%.

∴ The correct answer is 15%.

Alternate Method

Given:

Mass of solute (common salt) = 60 g

Mass of solvent (water) = 340 g

Formula Used:

Mass percentage = [Mass of solute / (Mass of solute + Mass of solvent)] × 100

Calculations:

⇒ Total mass of solution = 60 g + 340 g = 400 g

⇒ Mass percentage = (60 / 400) × 100

⇒ Mass percentage = 60 / 4

⇒ Mass percentage = 15%

∴ The correct answer is 15%.

Additional Information

Mass by Volume Percentage

It is defined as the mass of solute in grams present in 100 mL of solution. Formula: (Mass of solute / Volume of solution) × 100.

Solute and Solvent

The component present in smaller amount is the solute, and the component present in larger amount is the solvent.

Saturated Solution

A solution in which no more solute can be dissolved at a particular temperature is called a saturated solution.

The correct answer is 3.

Key Points

• Benzene is an aromatic compound with molecular formula C₆H₆.
• It is planar hexagonal in shape with bond angles of 120º.
• Three double bonds and nine single bonds are present in one molecule of benzene.

​

The Correct Answer is Option 1 i.e Kalanithi Maran.

• Kalanithi Maran:
• He is the chairman and founder of the Sun Group.
• Sun TV Network was launched by Kalanithi Maran in 1993.
• Sun TV Network is an Indian media company headquartered in Chennai, Tamil Nadu.
• Sun TV Network operates satellite television channels in Tamil, Telugu, Kannada, and Malayalam, airs FM stations across India and owns the SunRisers Hyderabad cricket franchise of IPL
• He started a monthly magazine Poomalai in the year 1990.
• Forbes magazine named him the "Television king of southern India".
• Rakesh Jhunjhunwala:
• He is often referred to as India’s own Warren Buffet.
• He is an Indian investor, trader, and chartered accountant.
• He is the chairman of Hungama Media and Aptech ltd.
• Vikas Oberoi:
• He is Chairman/Managing Director at Oberoi Realty Ltd.
• Dr. Ranjan Pai:
• He is the Chairman of the Manipal Education and Medical Group (MEMG).
• He received the Padma Bhushan in the year 2011.
• He received the Golden Peacock Lifetime Achievement Award for the Year 2011.

1. M is 25 years old today.

Here, there is no reference to S.

Therefore, Statement 1 alone is not sufficient.

2. S is younger to M by 10 years

Here, we need to know the age of M to deduce the age of S.

Therefore, Statement 2 alone is not sufficient.

Combining 1 and 2, we get:

S = M – 10 and M = 25 years.

So, S’s age = 25 – 10 = 15 years.

So, both 1 and 2 statements are required to answer the question.

Hence, ‘statements 1 and 2 together are necessary’ is the correct answer.

Shortcut Trick

एक पूर्ण वर्ग संख्या (perfect square) जिसका इकाई अंक 5 है, उसके दहाई का अंक हमेशा 2 होना चाहिए (अर्थात संख्या 25 पर समाप्त होनी चाहिए)।

साथ ही, 25 से पहले के अंक दो क्रमागत संख्याओं (consecutive numbers) n × (n+1) का गुणनफल होने चाहिए।

विकल्प (2) में 18025 में, 180 को दो क्रमागत पूर्णांकों के गुणनफल के रूप में नहीं लिखा जा सकता है (13 × 14 = 182 और 12 × 13 = 156)।

इसलिए, 18025 एक पूर्ण वर्ग नहीं है और इसका वर्गमूल अपरिमेय होगा।

∴ The correct answer is 18025.

Alternate Method

दिया गया है: संख्याएँ 13225, 18025, 15625, 21025

सिद्धांत: यदि कोई संख्या पूर्ण वर्ग नहीं है, तो उसका वर्गमूल एक अपरिमेय संख्या (irrational number) होती है।

⇒ विकल्प (1): 13225 = 115² (पूर्ण वर्ग)

⇒ विकल्प (3): 15625 = 125² (पूर्ण वर्ग)

⇒ विकल्प (4): 21025 = 145² (पूर्ण वर्ग)

⇒ विकल्प (2): 18025, 134² (17956) और 135² (18225) के बीच स्थित है।

⇒ चूंकि 18025 एक पूर्ण वर्ग नहीं है, √18025 एक अपरिमेय संख्या है।

∴ The correct answer is 18025.

Additional Information

पूर्ण वर्ग के गुण (Properties of Perfect Squares)

किसी भी पूर्ण वर्ग संख्या का इकाई अंक कभी भी 2, 3, 7, या 8 नहीं हो सकता है।

अपरिमेय संख्या (Irrational Numbers)

वे संख्याएँ जिन्हें p/q के रूप में नहीं लिखा जा सकता और जिनका दशमलव प्रसार अशांत अनावर्ती (non-terminating non-recurring) होता है।

डिजिटल सम (Digital Sum)

एक पूर्ण वर्ग का डिजिटल सम (अंकों का योग) हमेशा 1, 4, 7, या 9 होता है।

Combining statements 1 and 3, we can arrange in the shortest to tallest order”

T < _ < _ < F

Remaining- K and M

Since there is no given relationship between K and M, we get two cases:

Case 1:

T < K < M < F

Case 2:

T < M < K < F

Thus, there is no way of concluding who is standing in the second place if we arrange shortest to tallest. Hence, the statements are insufficient.

Hence, ‘The statements are insufficient’ is the correct answer.

Let the number of red balls be 15x

Let the number of green balls be 26x

When 12 more green balls are added, the number of green balls become = 26x + 12

The new ratio of red balls to green balls = 1 : 2

$\frac{{15x}}{{26x + 12}} = \frac{1}{2}$

2 × 15x = 1 × (26x + 12)

30x = 26x + 12

30x – 26x = 12

4x = 12

x = 3

Therefore, the number of red balls in the bag = 15x = 15 × 3 = 45

Hence, ‘45’ is the correct answer.

The Correct Answer is Option 4 i.e Self-pollination.

• Self-pollination:
• The transfer of pollen grains from anther to the stigma of the same flower is called self pollination.
• Mendel obtained F2 progeny from F1 generation plants by the method of self pollination.
• Cross pollination:
• The transfer of pollen grains from anther of one flower to the stigma of another flower is called cross pollination.
• Vegetative propagation:
• It is a form of asexual reproduction of a plant where in new plant grows from a fragment of the parent plant.
• Asexual reproduction:
• Asexual reproduction produces plants that are genetically identical to the parent plant.
• In asexual reproduction there is no fusion of male and female gametes takes place.

From the graph:

CO₂ concentration in the year 1995 = 360

CO₂ concentration in the year 2015 = 400

Hence,

Percentage change = [(400 – 360)/360] × 100

⇒ 40/360 × 100

⇒ 1/9 × 100 = 11.11%

∴ The percentage change in CO2 concentration is 11.11%.

The Correct Answer is Option 1 i.e more reactive than copper.

• Zinc is more reactive than copper metal and so it can displace copper from copper sulphate solution.
• Zinc displaces the metals present below it in the series.
• Reactivity of an element decreases from top to bottom in the given reactivity series.
• Potassium (K)
• Sodium (Na)
• Calcium (Ca)
• Magnesium (Mg)
• Aluminium (Al)
• Zinc (Zn)
• Chromium (Cr)
• Iron (Fe)
• Lead (Pb)
• Hydrogen (H)
• Copper (Cu)
• Silver (Ag)
• Gold (Au)

The Correct Answer is Option 4 i.e Jhulan Goswami.

• Charlotte Edwards:
• She was an English former professional cricketer who was captain of the England women's team.
• She has won the ICC Women's player of the year 2008.
• She was also named as one of Wisden's five Cricketers of the Year 2014.
• Dane van Niekerk:
• She is a South African cricketer.
• She has been the South Africa's Women's team captain in all three forms since June 2016.
• Meg Lanning:
• She is the current captain of the Australian women's national cricket team.
• She became the first Australian, male or female, to score 2,000 runs in Twenty20 Internationals.
• Jhulan Goswami:
• She is the former captain of India's national women's cricket team.
• She was awarded the ICC Women's Player of the Year award in 2007.
• She became the first bowler to take 200 wickets in WODIs.
• She was also awarded the Padma Shri in the year 2012.
• She was also awarded the Arjuna Award in the year 2010.

The Correct Answer is Option 3 i.e BrahMos.

• BrahMos:
• Indian Navy in 2017 successfully test-fired the 290-km strike range Brahmos supersonic cruise missile.
• BrahMos is a medium-range supersonic cruise missile.
• It can be launched from ships, aircraft, or land.
• It is being developed through a collaboration between India and Russia.
• Agni:
• Agni missiles are a series of medium to intercontinental range ballistic missiles developed by India.
• Agni missiles are nuclear weapons capable missiles.
• These are surface to surface ballistic missiles.
• K9 vajra:
• It is a tracked self-propelled howitzer gun.
• It can turn around at zero radii.
• GSAT 17:
• It is an Indian geostationary communications satellite.
• It was launched on June 29, 2017 from Kourou, French Guiana by Ariane-5 VA-238.
• GSAT-17 was launched into a Geosynchronous Transfer Orbit (GTO) by Ariane-5 VA-238 launch vehicle.

The Correct Answer is Option 4 i.e Kerala.

• The pre-monsoon rains are also known as April rains or summer rains.
• Mango showers are the name of the pre-monsoon showers in Kerala and some parts of Karnataka, these rains help in the early ripening of mangoes.
• They are also known as 'Kaal Baisakhi' in Bengal, as Bardolli Chhera in Assam and as Cherry Blossom showers or Coffee Showers in Kerala.
• Odisha:
• Jharkhand, West Bengal, Andhra Pradesh and Chhattisgarh are the boundaries of Odisha.
• Bhubaneswar is the capital of Odisha.
• Mohan Charan Majhi is the CM of Odisha.
• Uttar Pradesh:
• It shares a boundary with a maximum number of Indian states.
• It shares its border with Uttarakhand, Himachal Pradesh, Haryana, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, Bihar as well as Delhi.
• Yogi Adityanath is the CM of Uttar Pradesh.
• Gujarat:
• Gandhinagar is the capital city of Gujarat.
• It has the longest Coastline in India.
• The city of Anand, located in Gujarat is commonly known as the Milk Capital of India.
• Bhupendra Patel is the current Chief Minister of the state.

Shortcut Trick

Put x = 1 in first expression: 2(1)² + a(1) + 2b = 16 → a + 2b = 14.

Put x = −1 in second expression: (−1)² + b(−1) + 2a = −1 → 2a − b = −2.

Multiply second by 2 and add: (a + 2b) + (4a − 2b) = 14 + (−4) → 5a = 10 → a = 2.

Substitute a = 2 in first: 2 + 2b = 14 → 2b = 12 → b = 6.

Required sum a + b = 2 + 6 = 8.

∴ The correct answer is 8.

Alternate Method

Given:

P(x) = 2x² + ax + 2b, divisor = (x − 1), remainder = 16

Q(x) = x² + bx + 2a, divisor = (x + 1), remainder = −1

Formula Used:

Remainder Theorem: If a polynomial f(x) is divided by (x − k), then the remainder is f(k).

Calculations:

⇒ For P(x), remainder = P(1) = 16

⇒ 2(1)² + a(1) + 2b = 16

⇒ 2 + a + 2b = 16

⇒ a + 2b = 14 --- (Eqn 1)

⇒ For Q(x), remainder = Q(−1) = −1

⇒ (−1)² + b(−1) + 2a = −1

⇒ 1 − b + 2a = −1

⇒ 2a − b = −2 --- (Eqn 2)

⇒ Multiplying (Eqn 2) by 2: 4a − 2b = −4

⇒ Adding (Eqn 1) and modified (Eqn 2): (a + 2b) + (4a − 2b) = 14 − 4

⇒ 5a = 10

⇒ a = 2

⇒ Substituting a = 2 in (Eqn 1): 2 + 2b = 14 ⇒ 2b = 12 ⇒ b = 6

⇒ a + b = 2 + 6 = 8

∴ The correct answer is 8.

Additional Information

Remainder Theorem

It states that the remainder of the division of a polynomial f(x) by a linear polynomial (x − a) is 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).

Linear Equations in Two Variables

System of equations like a₁x + b₁y = c₁ can be solved using substitution, elimination, or cross-multiplication methods.

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

**Step-1-**Parts of an equation enclosed in 'Brackets' must be solved first,

**Step-2-**Any mathematical 'Of' or 'Exponent' must be solved next,

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

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

104 ÷ [68 – {29 – (45 – 56 ÷ 7 × 4)}] = ?

⇒ ? = 104 ÷ [68 – {29 – (45 – 8 × 4)}]

⇒ ? = 104 ÷ [68 – {29 – 13}]

⇒ ? = 104 ÷ [68 – 16]

⇒ ? = 104 ÷ 52

⇒ ? = 2

The Correct Answer is Option 1 i.e 4. 

• In the modern periodic table, elements having atomic numbers 19 to 36 are placed in the period 4.
• They are K(19), Ca(20), Sc(21), Ti(22), V(23), Cr(24), Mn(25), Fe(26), Co(27), Ni(28), Cu(29), Zn(30), Ga(31), Ge(32), As(33), Se(34), Br(35), Kr(36)
• In the modern periodic table, elements having atomic numbers 55 to 86 are placed in the period 6.
• In the modern periodic table, elements having atomic numbers 37 to 54 are placed in the period 5.
• In the modern periodic table, elements having atomic numbers 11 to 18 are placed in the period 3.

Shortcut Trick

If a + 1/a = k, then the value of a³ + 1/a³ is calculated using the shortcut formula: k³ − 3k.

Given: k = −6.

Value = (−6)³ − 3 × (−6) = −216 + 18 = −198.

∴ The correct answer is −198.

Alternate Method

Given: a + 1/a = −6

Formula used: (x + y)³ = x³ + y³ + 3xy(x + y)

⇒ (a + 1/a)³ = (−6)³

⇒ a³ + (1/a)³ + 3 × a × (1/a) × (a + 1/a) = −216

⇒ a³ + 1/a³ + 3 × (−6) = −216

⇒ a³ + 1/a³ − 18 = −216

⇒ a³ + 1/a³ = −216 + 18

⇒ a³ + 1/a³ = −198

∴ The correct answer is −198.

Additional Information

Algebraic Cubing Identity

The basic algebraic expansion for sum of cubes is derived from (x + y)³ = x³ + y³ + 3xy(x + y).

Square Relation

If a + 1/a = k, then a² + 1/a² = k² − 2. This is often used as a prerequisite for higher power questions.

Subtraction Identity

If a − 1/a = k, then a³ − 1/a³ = k³ + 3k. Note the sign change in the 3k term.

The option figure that bears the closest resemblance to the question figure is shown below:

The answer figure A is like mirror image of the question. Also, it is the only figure among the answer figures that has three intersecting lines in it, similar to that of question figure.

Hence, ‘figure A’ is the correct answer.

Shortcut Trick

Total Work (LCM of 50, 37.5, 30) = 150 units.

2 × (A + B + C) efficiency = 3 + 4 + 5 = 12 ⇒ A + B + C = 6.

Efficiency: A = 6 − 4 = 2; B = 6 − 5 = 1; C = 6 − 3 = 3.

Time: A = 150/2 = 75; B = 150/1 = 150; C = 150/3 = 50.

∴ The correct answer is 75, 150 and 50 days.

Alternate Method

Given: Time taken by (A+B) = 50 days, (B+C) = 37.5 days (or 75/2 days), and (C+A) = 30 days.

Formula Used: Total Work = Time × Efficiency

⇒ Total efficiency of 2(A + B + C) = 3 + 4 + 5 = 12

⇒ Efficiency of (A + B + C) = 12 ÷ 2 = 6

⇒ Efficiency of A = (A + B + C) − (B + C) = 6 − 4 = 2

⇒ Efficiency of B = (A + B + C) − (C + A) = 6 − 5 = 1

⇒ Efficiency of C = (A + B + C) − (A + B) = 6 − 3 = 3

⇒ Time for A = 150 ÷ 2 = 75 days

⇒ Time for B = 150 ÷ 1 = 150 days

⇒ Time for C = 150 ÷ 3 = 50 days

∴ The correct answer is 75, 150 and 50 days.

Additional Information

Combined Work Formula

When pairs are given, the efficiency of individuals is found by (Sum of all pairs ÷ 2) − efficiency of the pair without that individual.

Pipes and Cisterns

The same logic applies to pipes filling a tank, where efficiency represents the rate of flow per unit time.

The correct answer is Option 3, i.e 9 × 108 J

• 1 unit of energy is equal to 1 kilowatt hour (kWh)
• We also know that
• 1 kWh = 3.6 × 10⁶ J
• Therefore, 250 units of energy = 250 × 3.6 × 10⁶ = 9 × 10⁸ J.

Shortcut Trick

Convert the given roots directly into linear factors: if root x = a/b, then factor is (bx − a) = 0.

For root x = 4/3 ⇒ (3x − 4) = 0.

For root x = −3/7 ⇒ (7x + 3) = 0.

The required quadratic equation is the product of these factors: (7x + 3)(3x − 4) = 0.

∴ The correct answer is (7x + 3)(3x − 4) = 0.

Alternate Method

Given: The roots of the equation are α = 4/3 and β = −3/7.

Formula: A quadratic equation with roots α and β is given by (x − α)(x − β) = 0.

⇒ (x − 4/3)(x − (−3/7)) = 0

⇒ (x − 4/3)(x + 3/7) = 0

⇒ ((3x − 4)/3) × ((7x + 3)/7) = 0

⇒ (3x − 4)(7x + 3) / 21 = 0

⇒ (3x − 4)(7x + 3) = 0 × 21

⇒ (7x + 3)(3x − 4) = 0

∴ The correct answer is (7x + 3)(3x − 4) = 0.

Additional Information

Standard Form of Quadratic Equation

The equation can also be written as x² − (Sum of Roots)x + (Product of Roots) = 0.

Sum and Product Properties

For ax² + bx + c = 0, Sum (α+β) = −b/a and Product (αβ) = c/a.

Discriminant and Nature of Roots

The value D = b² − 4ac determines the nature: D > 0 (Real & Distinct), D = 0 (Real & Equal), D < 0 (Imaginary).

The Correct Answer is Option 3 i.e Arts.

• Usha Uthup:
• She is a famous Indian pop and playback singer, currently a resident of West Bengal.
• She won the Padma Shri Award in the field of Arts in the year 2011.
• She also received the Rajiv Gandhi Purashkar for national integration for quality music.

The Correct Answer is Option 4 i.e Odisha.

• Pyarimohan Mohapatra:
• He was a former member of Parliament from Odisha.
• He died at a Mumbai hospital in the year 2017.
• Once upon a time, he was considered as the mastermind and the proxy leader of the Biju Janata Dal for more than two decades.
• Naveen Patnaik is the current CM of Odisha.
• Assam:
• Bangladesh, Bhutan, Nagaland, Arunachal Pradesh, Manipur, Mizoram, Tripura, Meghalaya and West Bengal are the boundaries of the state Assam.
• Dispur is the capital of Assam.
• Himanta Biswa Sarma is the CM of Assam.
• West Bengal:
• Kolkata is the capital of West Bengal.
• Jharkhand, Odisha  Bihar, Bangladesh, Assam, Sikkim and Bhutan and Nepal are boundaries of West Bengal.
• Mamata Banerjee is the CM of West Bengal.
• Bihar:
• It is bordered by Nepal, Uttar Pradesh, Jharkhand and West Bengal.
• Patna is the capital of Bihar.
• Nitish Kumar is the present CM of Bihar.

The Correct Answer is Option 4 i.e Ca and P.

• The bone cells are known as osteocytes which are embedded in a hard matrix that is composed of Calcium (Ca) and phosphorus (P) compounds.
• Calcium (Ca):
• It provides strength to bones and teeth with vitamins.
• It also plays an important role in blood formation, muscle contraction, clotting of blood, etc.
• Milk, eggs, fish, etc. are the main sources of calcium.
• Phosphorous (P):
• It provides strength to bones and teeth, in coordination with calcium.
• Milk, cheese, green leafy vegetables, etc. are the main sources of Phosphorus.
• Sodium (Na):
• It is normally found in the external fluid of a cell.
• It helps in the functioning of contraction of muscles, in the transmission of nerve impulses in nerve fiber, etc.
• Normal salt, meat, eggs, etc. are the main sources of sodium.
• Fluorine (F):
• It is the most electronegative element.
• Fluorine protects us from dental decay.
• Food, together with drinking water, is the main source of fluorine for human beings.
• Fluorine is essential for the maintenance of solidity of our bones.

 

Thus, ([(25 < 15)] × 4) < 1 will be decoded as ([(25 + 15)] ÷ 4) + 1

Solving

([(25 + 15)] ÷ 4) + 1)

= ([(40)] ÷ 4) + 1

= (10) + 1

= 11

Hence, ‘11’ is the correct answer.

Shortcut Trick

Initial Capital = ₹ 20,000

Increase = 30% of 20,000 = 6,000

New Investment = 130% of ₹ 20,000

New Investment = 1.3 × 20,000 = 26,000

∴ The correct answer is ₹ 26,000.

Alternate Method

Given:

Last year investment (Principal) = ₹ 20,000

Increase percentage = 30%

Formula:

New Value = Original Value × (1 + Increase%/100)

Calculations:

⇒ Increase Amount = (30/100) × 20,000

⇒ Increase Amount = 0.3 × 20,000 = 6,000

⇒ Total New Investment = 20,000 + 6,000

⇒ Total New Investment = 26,000

∴ The correct answer is ₹ 26,000.

Additional Information

Percentage Increase

To increase a number by x%, multiply the number by (1 + x/100).

Percentage Decrease

To decrease a number by x%, multiply the number by (1 − x/100).

Base Value Identification

Always identify the base (100%) on which the percentage change is applied; here, it is last year's investment.

The Correct Answer is Option 4 i.e 2.5.

• Power:
• The rate of doing work is called power.
• Its SI unit is watt.
• 1 kilowatt (kW) is equal to 1000 Watts.
• 1 megawatt is equal to 1000000 Watts
• 2.5 kilowatt (kW) is equal to 2500 Watts.

The Correct Answer is Option 2 i.e Nichrome.

• Aluminium:
• Atomic number is 13.
• It is soft, malleable, and ductile.
• It has high thermal and electrical conductivity
• It has excellent corrosion resistance.
• It is the most abundant metal in the Earth’s crust.
• It is widely used for foil, kitchen utensils, and conductor cables, etc.
• Nichrome:
• It is also known as nickel chrome.
• It is an alloy produced by mixing nickel, chromium.
• It is widely known for its heat resistance.
• It is also well resistant to both corrosion and oxidation.
• It is commonly used in electrical heating devices.
• Copper:
• It   is a soft, malleable, and ductile metal.
• It has a very high thermal and electrical conductivity.
• The copper metal turns green in color because of an oxidation reaction.
• Atomic number: 29.
• Iron:
• It is a silvery-white or grayish metal.
• It is ductile and malleable.
• Wrought Iron is the purest form of iron.
• Iron is the fourth most abundant element in the Earth's crust.
• The atomic number is 26.

Shortcut Trick

When the angle of elevation changes from 60° to 30° for a constant height (h), the horizontal distance (d) moved is given by: d = h(cot 30° − cot 60°).

d = 692 × (√3 − 1/√3) = 692 × (2/√3) = 692 × (2/1.73).

d = 1384 ÷ 1.73 = 800 m.

∴ The correct answer is 800 m.

Alternate Method

Given: Height (h) = 692 m, θ₁ = 60°, θ₂ = 30°.

Formula Used: tan θ = Perpendicular / Base

⇒ In first position: tan 60° = 692 / x₁

⇒ √3 = 692 / x₁ ⇒ x₁ = 692 / √3

⇒ In second position: tan 30° = 692 / x₂

⇒ 1/√3 = 692 / x₂ ⇒ x₂ = 692√3

⇒ Distance (d) = x₂ − x₁ = 692√3 − 692/√3

⇒ d = 692 × (√3 − 1/√3) = 692 × (2/√3)

⇒ d = (692 × 2) / 1.73 = 1384 / 1.73 = 800 m

∴ The correct answer is 800 m.

Additional Information

Angle of Elevation

The angle formed by the line of sight with the horizontal when looking up at an object.

Trigonometric Ratios for Heights

For standard angles: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Horizontal Movement Formula

Distance moved = Height × (cot θ_smaller − cot θ_larger) for an object moving away at a constant altitude.

Shortcut Trick Look at the unit digit of 4356, which is 6. The square root must end in 4 or 6. Check the range: 602 = 3600 and 702 = 4900. Since 4356 is between 3600 and 4900, the root is in the 60s. Possibilities are 64 or 66. Check 652 = 4225. Since 4356 > 4225, the answer must be 66. ∴ The correct answer is 66.

Alternate Method Given: Number = 4356 Method: Prime Factorisation ⇒ 4356 = 2 × 2178 ⇒ 4356 = 2 × 2 × 1089 ⇒ 4356 = 2 × 2 × 3 × 363 ⇒ 4356 = 2 × 2 × 3 × 3 × 121 ⇒ 4356 = 2 × 2 × 3 × 3 × 11 × 11 ⇒ √4356 = √(22 × 32 × 112) ⇒ √4356 = 2 × 3 × 11 = 66 ∴ The correct answer is 66.

Additional Information Unit Digit Property If a perfect square ends in 6, its square root must end in either 4 or 6. Square of numbers ending in 5 To find (n5)2, multiply n by (n+1) and suffix 25. Example: 652 = (6×7)25 = 4225. Perfect Square Identification A perfect square never ends with the digits 2, 3, 7, or 8.

The required number will lie in the shaded part: 

Therefore, Only hardworking but not honest or efficient → c – (v + s + t)

Hence, ‘c – (v + s + t)’ is the correct answer.

Trees are a type of plant. Similarly, desert is a type of land.

Hence, ‘Land’ is the correct answer.

The Correct Answer is Option 1.

• The Insolvency and Bankruptcy Code, 2016 provides a time-bound process to resolve insolvency among companies and individuals.
• Insolvency is a situation where an individual or company is unable to repay their outstanding debt.
• Features of Insolvency and Bankruptcy Code (Amendment) Ordinance, 2018:
• The Ordinance provides significant relief to home buyers by recognizing their status as financial creditors.
• The Ordinance empowers the Government to provide MSMEs with a special dispensation under the Code.
• The Ordinance also provides for a mechanism to allow participation of security holders, deposit holders, and all other classes of financial creditors that exceed a certain number, in meetings of the Committee of Creditors, through the authorized representation.
• The voting threshold for decisions of the committee of creditors has been lowered from 75% to 51%.

The logic is:

 

 Similarly,

 

Hence, ‘2312038’ is the correct answer.

The correct answer is 2.

• The maximum number of electrons present in the orbit can be calculated by using the following formula: 2n², where n is the principal quantum number.
• The maximum number of electrons that can be accommodated in k shell is 2.

The Correct Answer is Option 3 i.e Maharashtra.

• Bihar:
• Nitish Kumar is the present CM of Bihar.
• Phagu Chauhan is the present Governor of Bihar.
• Bihar is bordered by Nepal, Uttar Pradesh, Jharkhand, and West Bengal.
• Patna is the capital of Bihar.
• Jharkhand:
• The state is bordered  by Bihar, West Bengal, Odisha, Chhattisgarh, and Uttar Pradesh.
• Hemant Soren is the CM of  Jharkhand.
• Ranchi is the capital of Jharkhand.
• Gujarat:
• Gandhinagar is the capital city of Gujarat.
• It has the longest Coastline in India.
• The city of Anand, located in Gujarat is commonly known as the Milk Capital of India.
• Acharya Devvrat is the current Governor of the state.
• Bhupendrabhai Patel is the current Chief Minister of the state.
• Kakrapar nuclear power station is located in Gujarat.
• Maharashtra:
• Mumbai is the capital city of Maharashtra.
• The Gateway of India is the most famous monument and Iconic landmark located in Mumbai.
• Eknath Shinde is the current CM of Maharashtra.
• Bhagat Singh Koshyari is the governor of Maharashtra.
• Ministry of External Affairs (MEA) launched the country's first Videsh Bhavan on 27 August 2017.
• Four offices of MEA in Mumbai, namely, (i) Passport Office, (ii) Office of the Protector of Emigrants, (iii) Office of the Regional Director of ICCR, and (iv) Branch Secretariat of MEA, will be integrated and functioning from the newly constructed "Videsh Bhavan”.
• The "Videsh Bhavan’ is located at the Bandra Kurla Complex (BKC) in Mumbai.
• “Videsh Bhavan” at Mumbai is the first integrated office complex of the Ministry of External Affairs established in any State of India.

The Correct Answer is Option 4 i.e Planaria.

• Planaria:
• It is a flatworm with very simple ‘eyes’ that are really just eye-spots that detect light.
• Flatworms are also called planarians.
• They belong to the phylum Platyhelminthes.
• They are characterized by flat bodies, they have no skeleton, no circulatory or respiratory organs, etc.
• Ascaris:
• They belong to phylum Aschelminthes.
• They are bilaterally symmetrical and triploblastic animals
• It is a type of parasitic worm
• Ascariasis is the most common type of roundworm infection in humans.
• Tapeworm:
• They also belong to the phylum Platyhelminthes
• They are triploblastic animals.
• They are characterized by flat bodies, they have no skeleton, no circulatory or respiratory organs, etc.
• Liverfluke:
• They also belong to  the phylum Platyhelminthes.
• They are triploblastic  animals.
• They are characterized by flat bodies, they have no skeleton, no circulatory or respiratory organs, etc.

The pattern followed here is:

343 + 40 = 383

383 + 60 = 443

443 + 40 = 483

483 + 60 = 543

Hence, ‘543’ is the correct answer

The statement says that Leela is considering recommending the movie to her friends.

Therefore, we can conclude that Leela liked the movie and wants her friends to watch it.

Hence, both the conclusions follow.

The logic is:

 

Similarly,

 

Hence, ‘4151518’ is the correct answer.

Argument I highlights one of the disadvantages of using smart phones.

It says that one tends to spend more time on smart phones after a point of time and ignore personal time.

On the other hand, argument II states that the additional features offered by smart phones are necessary.

Hence, both the arguments are strong.

The Correct Answer is Option 3 i.e C2H5OH.

• Ethanol:
• It is also known as ethyl alcohol.
• It is a colorless, volatile, and flammable liquid that is soluble in water.
• It is most commonly found in alcoholic beverages.
• It is also used as an antiseptic and as a disinfectant.
• Its molecular formula is C2H5OH.

The triangles in the figure are shown below:

ABC, BCD, CDE, EDF,GFH, ACD and CDF

Hence, ‘7’ is the correct answer.

The Venn diagrams that correctly represents the relationship between:

A) Walking     

B) Swimming

C) Exercise

Is shown below:

Both walking and swimming are exercises.

Hence, ‘option 2’ is the correct answer.

Shortcut Trick

Assume Total Work = LCM(22, 33) = 66 units.

Efficiency of A = 3 units/hr, B = 2 units/hr.

If pipe A is closed 5.5 hours early, add the work A would have done: 5.5 × 3 = 16.5 units.

Total adjusted work = 66 + 16.5 = 82.5 units.

Total time = Total adjusted work ÷ Combined efficiency = 82.5 ÷ (3 + 2) = 16.5 hours.

∴ The correct answer is 16.5 hours.

Alternate Method

Given: Filling time of Pipe A = 22 hours, Pipe B = 33 hours. Pipe A closed 5.5 hours before completion.

Formula Used: Total Work = Efficiency × Time

Let the total time taken to fill the cistern be T hours.

⇒ Work done by Pipe A + Work done by Pipe B = Total Work

⇒ 3 × (T − 5.5) + 2 × T = 66

⇒ 3T − 16.5 + 2T = 66

⇒ 5T = 66 + 16.5

⇒ 5T = 82.5

⇒ T = 82.5 ÷ 5

⇒ T = 16.5 hours

∴ The correct answer is 16.5 hours.

Additional Information

Pipes & Cisterns Logic

Inlet pipes contribute positive work while outlet pipes (leaks) contribute negative work towards filling the tank.

Leaving Early Concept

When a person/pipe leaves 'n' hours before completion, add their potential work (efficiency × n) to the total work and divide by total efficiency.

Work and Wages

Wages are distributed based on the ratio of work done, which is the product of efficiency and the time worked by each pipe/person.

Given: 

Let us observe the pattern of the figure.

We can observe that the half circle is moving 90° anticlockwise on alternate steps while the upper circle does not move at all.

Thus, figure C and D will be eliminated as they did not follow the anticlockwise rotation rule.

Figure B will be eliminated as it does not follow the 90° rule.

Figure ‘A’ fulfills the above condition.

Hence, ‘Figure A’ is the correct answer.

The Correct Answer is Option 4 i.e Meghalaya.

Meghalaya is not the neighbouring state of West Bengal.

The Correct Answer is Option 2 i.e Coordination of muscular movement.

• Cerebrum:
• This is the most developed part of the brain.
• It is the largest part of the brain.
• Functions of the cerebrum include thinking, memory, knowledge, etc.
• Cerebellum: 
• Functions of cereb ellum include coordination of muscular body movements and maintenance of posture.
• The cerebellum is known as the little brain.

The Correct Answer is Option 1 i.e Uttam Singh.

• Lata Mangeshkar Award for Lifetime Achievement is given by the Maharashtra government for the contributions in the field of music.
• The Maharashtra government instituted this award in the year 1992 in the honour of Bharat Ratna Lata Mangeshkar.
• Noted music director and violinist Uttam Singh has won the 2016 Lata Mangeshkar Award for Lifetime Achievement.
• Uttam Singh is a well-known Indian violinist and music director.
• Arijit Singh:
• He is an Indian playback singer.
• He received the 2018 and 2019 IIFA Award for Best Male Playback Singer.
• He also received the Stardust Award for Best Playback Singer Male 2016.
• Bappi Lahiri:
• He is often known as the "Disco King" in India.
• He was an Indian singer, disco musician, and record producer.
• He received the Filmfare Lifetime Achievement Award 2018.

CONCEPT:

• Momentum: The  product of mass and velocity of the body is called momentum.
• It is a vector quantity. It is denoted by P.
• Its SI unit is kg ms-1

Momentum (P) = mass (m) x velocity (v)

CALCULATION:

Given that:

Mass (m) = 10 kg

Velocity (v) = 2 ms^-1

So momentum (P) = m v = 10 x 2 = 20 kgms^-1.

The Correct Answer is Option 2 i.e European.

• Arab traders shipped Indian goods to European countries through the Red Sea and the Mediterranean ports.
• Trade was also conducted through overland routes with Afghanistan, Central Asia, and Persia.
• Australia:
• Canberra is the capital of Australia.
• Scott Morrison is the PM of Australia.
• Great Victoria Desert is located in Australia.
• Africa:
• Africa is the world's second-largest continent and second-most-populous continent, after Asia.
• The continent is bounded by the Atlantic Ocean, the Mediterranean Sea, the Red Sea, and the Indian Ocean.
• America:
• The American comprises the continents of North and South America.
• Joe Biden is the current president of America.
• The continent is bounded by the Pacific Ocean, the Atlantic Ocean, the Arctic Ocean, and the Antarctic Ocean.

All options except ‘towel’ are used to hold things in place.

 

Hence, ‘Towel’ is the odd one out.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 25 m + 15 m = 40 m

Total Time = 4 s + 2 s = 6 s

Average Speed = 40 ÷ 6 = 6.67 ms⁻¹

∴ The correct answer is 6.67 ms⁻¹.

Alternate Method

Given:

Distance 1 (d₁) = 25 m, Time 1 (t₁) = 4 s

Distance 2 (d₂) = 15 m, Time 2 (t₂) = 2 s

Formula Used:

Average Speed = (Total Distance Covered) ÷ (Total Time Taken)

Calculations:

⇒ Total Distance = d₁ + d₂ = 25 + 15 = 40 m

⇒ Total Time = t₁ + t₂ = 4 + 2 = 6 s

⇒ Average Speed = 40 / 6

⇒ Average Speed = 6.666...

⇒ Average Speed ≈ 6.67 ms⁻¹

∴ The correct answer is 6.67 ms⁻¹.

Additional Information

Average Speed Formula

It is the total path length traveled divided by the total time interval. It is a scalar quantity.

SI Unit of Speed

The standard unit is metres per second (m/s or ms⁻¹). Ensure units are consistent before calculation.

Average Velocity

Unlike speed, average velocity is Total Displacement divided by total time. It includes direction.

Let Raghav’s present age be x.

Raghav’s age after 11 years = x + 11

Raghav’s age 5 years back = x – 5

Applying the condition,

x + 11 = 5(x – 5)

x + 11 = 5x – 25

5x – x = 25 + 11

4x = 36

x = 9

Thus, Raghav’s present age is 9 years.

Hence, ‘9 years’ is the correct answer.

The mirror image for the following figure when the mirror is kept horizontally is shown below:

Hence, figure ‘C’ is the correct answer.

The Correct Answer is Option 1 i.e Dobereiner’s law of traids.

• 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.
• For example in the triad of lithium, sodium, and potassium, the atomic mass of lithium is 7 and the atomic mass of potassium is 39.
• The average of masses of lithium and potassium gives the atomic mass of sodium 23.
• Newland’s law of octaves: 
• It states that when elements are arranged in order to increasing atomic masses, every eighth element has properties similar to the first.
• Mendeleev’s law:
• The law states that the physical and chemical properties of the elements are the periodic function of their atomic masses.
• Newton's law:
• Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless an external force acts on it.
• Newton's second law states that the rate of change in the momentum of a body is directly proportional to the applied force on the body.
• Newton's third law states that for every action there is an equal and opposite reaction.

Shortcut Trick

Simplify ratios by cross-multiplication: a : b = (3×3) : (7×2) = 9 : 14.

Simplify second ratio: b : c = (1×7) : (1×5) = 7 : 5.

Multiply b : c by 2 to make b common: b : c = 14 : 10.

Combine: a : b : c = 9 : 14 : 10.

∴ The correct answer is 9 : 14 : 10.

Alternate Method

Given:

a : b = 3/2 : 7/3

b : c = 1/5 : 1/7

Calculations:

⇒ a : b = (3/2) × 6 : (7/3) × 6 (LCM of 2 and 3 is 6)

⇒ a : b = 9 : 14

⇒ b : c = (1/5) × 35 : (1/7) × 35 (LCM of 5 and 7 is 35)

⇒ b : c = 7 : 5

⇒ To equate b, multiply b : c by 2 ⇒ b : c = 14 : 10

⇒ a : b : c = 9 : 14 : 10

∴ The correct answer is 9 : 14 : 10.

Additional Information

Compounding Ratios

To combine ratios like a:b and b:c, the common term b must have the same numerical value in both sets. Use the LCM of the two different values of b to scale the ratios.

Fractional Ratios

A ratio of fractions (x/y : p/q) can always be simplified to an integer ratio by multiplying both sides by the LCM of the denominators (y and q), or simply by cross-multiplication (xq : py).

Proportion Rule

If a/b = c/d, then they are in proportion. The product of means equals the product of extremes (b×c = a×d).

The triangle shaped figure flips 90° anticlockwise in each step and also moves clockwise to the next block in each step.

Therefore, Figure A, B and D are eliminated

Hence, figure C is the correct answer.

The Correct Answer is Option 1 i.e Is a member of Rajya sabha.

• Non-confidence motion:
• It has been mentioned under Rule 198 of the Rules of Procedure and conduct of Lok Sabha.
• The motion of No-confidence can be moved only in Lok Sabha.
• Rajya Sabha does not have the power to move such motion.
• It is moved against the entire Council of Ministers and not on individual ministers or private members.
• The motion has to be passed by a simple majority.
• When a no-confidence motion has been passed in the house then the Union council of ministers needs to resign and the union government collapses.
• The Prime Minister of India cannot participate in voting on a non-confidence motion against her/his government if she/he is a member of Rajya Sabha.

The Correct Answer is Option 4 i.e NITI Aayog.

• Niti Aayog:
• It is a policy think tank of the Government of India.
• It is neither a constitutional body nor a statutory body
• The Chairperson is the Prime Minister of India.
• Amitabh Kant is the present CEO of Niti Aayog.
• NITI Aayog has launched Move Hack, a global mobility hackathon to crowdsource solutions aimed at the future of mobility in India.
• MoveHack aims to bring about innovative, dynamic, and scalable solutions to problems pertaining to mobility.​
• Startup India:
• It is an initiative taken by the government of  India to promote and encourage the entrepreneurial spirit amongst its citizens.
• It was launched on 16th January 2016.
• Standup India:
• The Standup India scheme was launched on 5th April 2016:
• It was launched to promote entrepreneurship among Scheduled Caste/Schedule Tribe and Women for loans in the range of Rs 10 Lakhs to Rs 100 Lakhs.
• Startup Village Entrepreneurship Programme:
• The scheme was launched in the year 2018.
• It is a sub-scheme of Deendayal Antyodaya Yojana - National Rural Livelihoods Mission (DAY-NRLM).
• It has been launched to stimulate economic growth and reduce poverty and unemployment in villages by creating self-sustainable self-employment opportunities for youths located in selected villages.

Z and L travel in opposite directions (East-West)

To meet again, they must travel the opposite of their original directions.

Thus, the person who is traveling east must travel west. And the person who was traveling west must travel east.

So, both the person are meet at the middle point facing East and West.

Hence, ‘East-West’ is the correct answer.

The Correct Answer is Option 1 i.e Shahid Kapoor.

• The 18th edition of the International Indian Film Academy Awards was held in New York in 2017.
• Shahid Kapoor:
• He is an Indian bollywood actor.
• He been awarded with Best Actor (Male) award for Udta Punjab at the 18th IIFA Awards held in 2017.
• He also received the 2015 Filmfare Award for Best Actor for the film Haider.
• Arjun Kapoor:
• He is an Indian bollywood actor.
• He received the Zee Cine Award Best Male Debut for the year 2013.
• He received the Superstar of Tomorrow (Male) of Stardust Award  for Ishaqzaad In the year 2013.
• Aamir Khan:
• He received the Deenanath Mangeshkar Award 2017 for Dangal movie.
• He received Padma Shri in the year 2003.
• He also received Padma Bhushan in the year 2010.
• He received the 2002 IIFA Award for Best Actor for the film Lagaan.
• 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 Bodygaurd.

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

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first,

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

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

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

{(99 – 1)/7²} × 2 + 8 = ?

⇒ ? = {98/49} × 2 + 8

⇒ ? = 2 × 2 + 8

⇒ ? = 4 + 8 = 12

The Correct Answer is Option 4 i.e 

• Azim Premji:
• Azim Premji has been honoured with the 2017 Carnegie Medal of Philanthropy for his efforts to reform India’s public school system.
• He is the chairman of Wipro Limited.
• He is an Indian engineer, investor and philanthropist.
• He is informally known as the Czar of the Indian IT Industry.
• He was awarded with Padma Vibhushan in the year 2011.
• Ness Wadia:
• He is an Indian businessman.
• He is the co-owner of the Indian Premier League cricket team Kings XI Punjab.
• Ratan Tata:
• He is an Indian businessman, philanthropist, and a former chairman of Tata Sons.
• He received the Padma Vibhushan in the year 2008.
• He also received the Padma Bhushan in the year 2000.
• Anil Ambani:
• Anil Ambani is the Chairman of  Reliance Group.
• He was conferred with the ‘Entrepreneur of the Decade Award’ by the Bombay Management Association, 2002.

The Correct Answer is Option 4 i.e Aluminium.

• Sound waves are longitudinal waves.
• The speed of sound is different in different mediums.
• The speed of sound is maximum in solids and minimum in gases.
• In a medium, the speed of sound basically depends upon the elasticity and density of the medium.
• The speed of sound is independent of frequency.
• The speed of sound is independent of pressure.
• The speed of sound increases with the increase of temperature of the medium.
• When sound enters from one medium to another medium, its speed and wavelength changes but the frequency remains unchanged.

 

The family tree diagram is shown below:

Given: Pointing to a photograph, Neel says he is the son of the only daughter of the father of my sister.

1. Father of Neel’s sister is the father of Neel.

2. Son of the only daughter implies that the person in the photograph is the son of Neel’s sister.

Hence, Neel is pointing at his ‘Nephew’.

Hence, ‘Nephew’ is the correct answer.

The statement does not talk or suggest anything about the newspaper in general.

Therefore, assumption II is not implicit.

The meaning of the title is that our sufferings are a product of our thoughts.

Thus, it can be safely assumed that our actions depend on our thoughts.

Hence, only assumption I is implicit.

CONCEPT:

• Thrust: The force acting perpendicular to the surface of the object is called thrust. 
• It is a type of force so the SI unit of thrust is Newton (N).
• The effect of thrust is more on the smaller surface area than the thrust acting on a larger surface area.

EXPLANATION:

• The effect of thrust depends on the area of the surface on which it acts. So option 1 is correct.

​

• The normal force exerted by liquid at rest on a given surface in contact with it is called the thrust of liquid on that surface.
• The normal force (or thrust) exerted by liquid at rest per unit area of the surface in contact with it, is called pressure of liquid or hydrostatic pressure.

Shortcut Trick

For any two consecutive natural numbers n and (n+1), the number of non-perfect square numbers between their squares is always 2n.

Here, n = 5 and n + 1 = 6.

Number of non-perfect square numbers = 2 × 5 = 10.

∴ The correct answer is 10.

Alternate Method

Given: Two consecutive squares 5² and 6².

Formula Used: Count = (Higher Square − Lower Square) − 1

⇒ Lower perfect square = 5² = 25

⇒ Higher perfect square = 6² = 36

⇒ Numbers between them = 26, 27, 28, 29, 30, 31, 32, 33, 34, 35

⇒ Total count = 36 − 25 − 1

⇒ Total count = 11 − 1 = 10

∴ The correct answer is 10.

Additional Information

Property of Consecutive Squares

Between n² and (n+1)², there are 2n non-perfect square numbers. This is because (n+1)² − n² = n² + 2n + 1 − n² = 2n + 1. Excluding the endpoint gives (2n+1) − 1 = 2n.

Perfect Square Definition

A perfect square is a number that can be expressed as the product of an integer with itself (e.g., 1, 4, 9, 16, 25...).

Sum of Odd Numbers

The square of a number n is equal to the sum of the first n odd natural numbers. For example, 5² = 1 + 3 + 5 + 7 + 9 = 25.

Shortcut Trick

Pass Marks = Marks Obtained + Failing Marks

Pass Marks = 40 + 40 = 80 marks

As per question, 40% of Maximum Marks = 80

100% of Maximum Marks = (80 ÷ 40) × 100 = 200

∴ The correct answer is 200 marks.

Alternate Method

Given:

Passing Percentage = 40%

Marks Obtained = 40

Failing Margin = 40

Formula Used:

Maximum Marks = (Passing Marks ÷ Passing Percentage) × 100

Calculations:

⇒ Passing Marks = 40 + 40 = 80

⇒ Let Maximum Marks be x

⇒ 40% of x = 80

⇒ (40 ÷ 100) × x = 80

⇒ x = (80 × 100) ÷ 40

⇒ x = 2 × 100

⇒ x = 200

∴ The correct answer is 200 marks.

Additional Information

Percentage Change

Percentage change = (New Value − Old Value) ÷ Old Value × 100. Always use the original value as the base.

Pass/Fail Case Logic

If two candidates are given, use the difference in their percentage to find the difference in their marks: (Diff in %) × Total = Diff in Marks.

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

Shortcut Trick

Total Capacity (LCM of 6.8 and 10.2) = 20.4 units.

Efficiency: A = 20.4 ÷ 6.8 = 3 units/hr; B = 20.4 ÷ 10.2 = 2 units/hr.

Work by B in 1.7 hours = 2 × 1.7 = 3.4 units.

Remaining work = 20.4 − 3.4 = 17 units; Time for both = 17 ÷ (3 + 2) = 3.4 hours.

Total time = 1.7 + 3.4 = 5.1 hours = 5 hours 6 minutes.

∴ The correct answer is 5 hr 6 min.

Alternate Method

Given: Filling time of Pipe A = 6.8 hours, Pipe B = 10.2 hours. Pipe B runs alone for 1.7 hours.

Formula Used: Total Work = Efficiency × Time; Total Time = Initial Time + Remaining Time.

⇒ Work done by Pipe B in 1.7 hours = 2 × 1.7 = 3.4 units

⇒ Remaining work to be filled by (A + B) = 20.4 − 3.4 = 17 units

⇒ Efficiency of (A + B) = 3 + 2 = 5 units/hr

⇒ Time taken by (A + B) = 17 ÷ 5 = 3.4 hours

⇒ Total time taken = 1.7 + 3.4 = 5.1 hours

⇒ Conversion: 0.1 hours = 0.1 × 60 = 6 minutes

⇒ Total time = 5 hours 6 minutes

∴ The correct answer is 5 hr 6 min.

Additional Information

Pipes and Cisterns Efficiency

Efficiency is inversely proportional to the time taken. If a pipe fills a tank in x hours, its 1-hour work is 1/x.

Inlet and Outlet Pipes

Inlet pipes have positive efficiency (+), while outlet pipes (leaks) have negative efficiency (−).

Decimal to Time Conversion

To convert decimal hours to minutes, multiply the decimal part by 60 (e.g., 0.1 hr × 60 = 6 min).