DSSSB Junior Secretariat Assistant Official paper (Held on: 3 April 2022 Shift 1 ) (Previous Year Paper)

The logic followed here is :-

Logic: First number^1/2 - 2 = Second number.

In 576 : 22

= 576^1/2 - 2

= 24 - 2

= 22

and

In 225 : 13

= 225^1/2 - 2

= 15 - 2 

= 13

Similarly,

In  324 : ?

= 324^1/2 - 2

= 18 - 2

= 16

Hence, the correct answer is "16".

Family chart :-

Family Tree :-

1) Jyoti is Ansh's sister and Anmol is Ansh's father.

2) Isha is Jyoti's aunt and Isha is Roshni's daughter.

3) Kajal is the daughter-in-law of Roshni and Roshni is Yash's maternal grandmother.

∴ Here, Anmol is 'maternal uncle' of Yash.

Hence, the correct answer is "maternal uncle".

The logic followed here is:

EXPAND is written as XPNEDA.

Similarly,

WEALTH will be written as :

Hence, the correct answer is "WTLHEA".

The logic followed here is :-

By using BODMAS RULE :

Calculation :

36 - 2(19.75 + 12 ÷ 4.02 × 3.05 - 22) + 20 = ?

⇒ 36 - 2(20 + 12 ÷ 4 × 3 - 4) + 20 = ?

⇒ 36 - 2(20 + 3 × 3 - 4) + 20 = ?

⇒ 36 - 2(20 + 9 - 4) + 20 = ?

⇒ 36 - 2**(29** - 4) + 20 = ?

⇒ 36 - 2(25) + 20 = ?

⇒ 36 - 50 + 20 = ?

⇒ 56 - 50 = ?

⇒ 6 = ?

∴ Here, the value of '?' is 6.

Hence, the correct answer is "6".

Preparing the family tree using the following symbol:

Family Tree :-

∴ Here, Nikhil is uncle of Nihal or Nikhil is Nihal's mother's brother.

Hence, the correct answer is "mother's brother".

The logic followed here is :-

∴ Here, 'Away' is coded as 'ij'.

Hence, the correct answer is "ij".

Given statements : C = H > M ≥ R = W

Conclusions

I) C = R → False (As C = H > M ≥ R = W → C > R)

II) C = W → False (As C = H > M ≥ R = W → C > W)

Hence, the correct answer is "Neither I nor II is true".

The logic followed here is :-

By using BODMAS RULE :

and

Given equation : 14 ÷ 7 – 2 × 4 + 3

After replacing the numbers and symbols in given equation the equation is as follows : 14 ÷ 7 × 5 × 9 ÷ 3

= 14 ÷ 7 × 5 × 9 ÷ 3

= 2 × 5 × 3

= 30

Hence, the correct answer is "30".

Given statement : M = P < J < X = T < F

Conclusions:

I. P > X → False (As P < J < X → P < X)

II. F > J → True (As J < X = T < F → F > J)

∴ Here, Conclusion II is true.

Hence, the correct answer is "Only II".

The logic followed here is :-

Ten's digit × One's digit of 1^st number = Second number.

• 78 : 56 → 7 × 8 = 56

and

• 64 : 24 → 6 × 4 = 24

Similarly,

• 97 : ? → 9 × 7 = 63

Hence, the correct answer is "63".

Given series :

(Left) B % 7 K & 4 D π M 6 R Z Ω S Q 2 @ 3 ∞ E (Right)

The pattern followed here is :

• DM& → D + 2 = M and M - 4 = &
• 23S → 2 + 2 = 3 and 3 - 4 = S
• K4% → K + 2 = 4 and 4 - 4 = %
• RSπ → R + 3 = S and S - 6 = π

∴ Here, RSπ is different from other three alternatives.

Hence, the correct answer is "RSπ".

The logic followed here is :-

Starting from a place V, Anuj walks 10 km towards the east, then turns left and walks 10 km, and then turns left again and walks 10 km.

∴ Here, Anuj is walking towards 'West'.

Hence, the correct answer is "West".

The logic followed here is :-

ZS – VO – RK

1) MK – OL – PN

2) ZJ – XK – VL

3) YJ – WL – UM

4) YI – UE – QA

Hence, the correct answer is "YI – UE – QA".

Given statement : R < A ≤ M < X > Z > I = L ≥ E

Conclusions:

I: X > L → True (As X > Z > I = L → X > L)

II: E < M → False (As M < X > Z > I = L ≥ E → No relation given between E and M)

∴ Here, Only conclusion I is true.

Hence, the correct answer is "Only I".

The logic followed here is :-

In English alphabet order, a letter located at 7^th place from left is : G

The second letter is located at the 14^th place towards the right from this 7^th place letter → 7 + 14 = 21^st alphabet

21^st alphabet is 'U'.

First and second letters of word is "GU".

∴ The Second letter is "U".

Hence, the correct answer is "U".

Preparing the family tree using the following symbols:

According to the given information,

The given expression is :

‘E + D – M × Q – R’ → E is daughter of D, D is wife of M, M is son of Q, Q is the wife of R.

∴ Here, E is R's son daughter (granddaughter) or R is paternal grand father of E.

Hence, the correct answer is "Son’s daughter".

The logic followed here is :-

By using BODMAS RULE :

Calculations :

49.8 - [20.07 + {30.18 - (19.75 - 4.98)}] = ?

⇒ 50 - [20 + {30 - (20 - 5)}] = ?

⇒ 50 - [20 + {30 - 15}] = ?

⇒ 50 - [20 + 15] = ?

⇒ 50 - 35 = ?

⇒ 15 = ?

∴ Here, the value of '?' is 15.

Hence, the correct answer is "15".

Given words are :

HAZE MANY TINY SAME

1. Fist letter of HAZE and MANY are interchanged :

MAZE HANY

Maze → A network of paths and hedges designed as a puzzle through which one has to find a way.

2) Fist letter of TINY and SAME are interchanged :

SINY TAME

Tame → Domestic animals.

∴ Here, 'Haze and Same' form a meaningful English word after interchanging there first letters HAZE and MANY, TINY and SAME.

Hence, the correct answer is "Haze and Same".

The logic followed here is :-

Given - FP – IM – LJ

1) CR – FP – HQ

2) AZ – EY – FW

3) BX – EU – HR

4) ML – PF – RE 

∴ Here, 'BX – EU – HR' is similar and follow same relation of 'FP – IM – LJ'.

Hence, the correct answer is "BX – EU – HR".

The logic followed here is :-

Ramesh is facing south. He goes straight for 65 metres, turns left and walks 50 metres, then turns right and goes 55 metres, and then turns right again and covers a distance of 60 metres.

∴ Here, Ramesh is facing in 'West' direction.

Hence, the correct answer is "West".

The pattern followed here is:

 

Hence, '169' is the correct answer.

Alternate MethodThe pattern followed is:

Hence, the correct answer is "169".

The table is alphabets place value:

The pattern followed here is:

EBC is related to DAB

And,

MJK is related to LIJ

Similarly,

Hence, 'SPQ' is coded as "ROP".

The least possible diagram for the given statements is as follows

Conclusions:

(I) Some tigers are baddies → True (because some goodies are baddies and all goodies are tigers so some tigers are also baddies)

(II) Some wolves are baddies → True (because statement given some baddies are wolves so some wolves are also baddies)

Hence, “Both Conclusion (I) and Conclusion (II) definitely follow".

Given:

1. One of the two persons at the extreme ends is a doctor and the other is a teacher.

2. A student is to the left of the teacher.

3. The advocate is standing between the doctor and the businessman.

4. A businessman is standing to the right of an advocate.

Hence, Starting from the right, the student is at "2^nd" position.

Table show alphabet serial number –

The pattern followed is,

Hence, “NO(19)Q” will replace the question mark (?) in the given series.

The logic followed here is:

number of concentric figures = (sides of concentric figures -1)

number of concentric figures in hexagon = 6 - 1 = 5; There are 5 concentric hexagon in figure 1.

number of concentric figures in triangle = 3 - 1 = 2; There are 2 concentric triangles in figure 2.

number of concentric figures in square = 4 - 1 = 3 and not 4. There are 4 concentric square in figure 3.

number of concentric figures in pentagon = 5 - 1 = 4. There are 4 concentric pentagon in figure 4.

Hence, 'square/rectangle' is the odd one among the given figure.

Table show alphabet serial number –

The pattern followed is,

Hence, “80QR” is complete the series.

The pattern followed here is:

Hence, '425' is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

Middle figure rotate 90 degree a clockwise direction and the arrow increase by one in each term. Dark arrow and light arrow are added alternatively.

Final series is

Hence, ‘option 3’ is the correct answer.

Table show alphabet serial number –

The pattern followed is,

Hence, “R42S” is the complete series.

Given:

A certain number of people are sitting in a row, facing North.

1. T sits fourth to the right of R.

2. Only three persons sit between R and Q.

3. S sits third to the left of Q.

4. Only two persons sit between P and R.

Case I:

Case II:

In both case total 12 people are sitting in the row.

Hence, Total "12" people are sitting in the row.

Given:

• Five children Rima, Kriss, Somya, Tony and Nitin are standing in a queue facing towards the East.

1. Rima is not standing at the last position.

2. Kriss is standing just behind Tony and just in front of Somya.

3. There are only two children between Rima and Somya.

4. If Nitin is not standing at the first position.

Hence, "4" children are standing in front of Nitin.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'TVX’.

Hence, “TVX” is the odd one.

In figure A and B

In figure C and D

Hence, "Option 4" is the correct answer.

The logic followed here is:

i ) increase in number of black squares.(alternate series)

So, the next image will have 7 black squares.

ii) Increase in gap

Hence, 

 will be the next image in the given series.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'OMPJ’.

Hence, “OMPJ” is the odd one.

The image obtained when the paper is unfolded is,

Hence, option 1 is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

Hence, ‘option 1’ is the correct answer.

The shaded part represents 'Advocates but neither Politicians nor Industrialists'

 

The letter represents Advocates but neither Politicians nor Industrialists is I and J.

Hence, ‘I and J’ is the correct answer.

The shaded part represents 'Industrialists and Advocates but NOT Politicians'

 

The letter represents Industrialists and Advocates but NOT Politicians is G.

Hence, ‘G’ is the correct answer.

The correct answer is Tabla, Dholak, Damru, Naggada

Key Points

• A membranophone is one of a class of musical instruments in which a stretched membrane vibrates to produce sound.
• Example: Tabla, Dholak, Damru, Naggada
• In addition to drums, basic types include the mirliton, or kazoo, and friction drums.
• Musical instruments in which the sound-producing medium is a vibrating membrane fall into four main groups:
• Kettledrums
• Tubular drums
• Rattle drums
• Mirlitons​

Additional Information

• Sitar, rebab, banjo, mandolin, ukulele, and bouzouki are examples of Chordophones. Chordophones are stringed instruments.
• An Aerophone is a musical instrument that produces sound primarily by vibrating a body of air without the use of strings or membranes. Example: Trumpet, Flute.
• An Idiophone is any musical instrument that produces sound primarily from the vibration of the instrument. Examples include bells, clappers, and rattles.

The correct answer is Eighth 

Key Points

• Muthuvel Karunanidhi Stalin is an Indian politician who took oath as the 21^st Chief Minister of Tamil Nadu, the 8^th person to hold the position.
• Stalin along with the rest of his cabinet took oath as the Chief Minister on 7 May 2021.
• They won 159 seats out 234, with the Dravida Munnetra Kazhagam (DMK) itself winning an absolute majority with 132 seats.
• In the 2021 Assembly elections, Stalin led the campaign for the Secular Progressive Alliance.
• Kanjeevaram Natarajan Annadurai served as the fourth and last Chief Minister of Madras State from 1967 to 1969 and was the first Chief Minister of Tamil Nadu (Madras State renamed as Tamil Nadu) for 20 days before his death.
• Janaki Ramachandran was the first woman Chief Minister of Tamil Nadu. She was commonly known as VN Janaki who was a famous actress.​

Additional Information

• New Appointments of Chief Minister of India 2021 and 2022
• 2021  
• ​Pushkar Singh Dhami - Uttarakhand
• M.K. Stalin - Tamil Nadu
• Natesan Krishnasamy Rangasamy - Puducherry
• Basavaraj Somappa Bommai - Karnataka
• Himanta Biswa Sarma - Assam
• Bhupendrabhai Rajnikantbhai Patel - Gujrat
• 2022
• Manik Saha - Tripura
• ​Pushkar Singh Dhami - Uttarakhand
• Bhagwant Mann - Punjab
• Shri Sukhvinder Singh Sukhu - Himachal Pradesh

The correct answer is Shahjahan.

Key Points

• Red Fort, also called Lal Qila is located in Old Delhi, India.
• It was built by Shah Jahan in the mid-17^th century and remains a major tourist attraction.
• The fort was designated as a UNESCO World Heritage site in 2007.
• Emperor Shah Jahan began the construction of the Red Fort on 12 May 1638, when he decided to shift his capital from Agra to Delhi.
• Originally red and white, the Shah's favourite colours, the credit for its design goes to architect Ustad Ahmad Lahori, who also built the Taj Mahal.

Additional Information

• The famous monuments built by Alauddin Khilji include the Alai Darwaza, the Siri Fort, Hauz Khas and the Zamat Khana Masjid in Delhi.
• Famous monuments built by Aurangzeb include Badshahi Masjid, Bibi Ka Maqbara, Moti Masjid etc.
• Firoz Shah Tughlaq mainly worked for the development of infrastructure like schools, hospitals, river canals, and reservoirs in his state.
• He also repaired the Qutub Minar, which was damaged by the earthquake. He is known to have established four new towns- Firozabad, Fatebabad, Jaunpur and Hissar.

The correct answer is Crust.

Key Points

• The crust is the solid, hard part of our planet that floats on top of the asthenosphere.
• The crust is a cool layer of rigid rock, which has a thickness that varies from 5 to 80 km in depth.
• The lithosphere consists of the crust and the cool, rigid, outer 80-100 km of the mantle.
• The temperature of the crust closest to the mantle is about 500°C.
• The thinnest portions of the crust are found on the ocean floor and form the ocean crust, which can be less than 5 km thick.
• NOTE: The uppermost part of the upper mantle is called the asthenosphere. The asthenosphere (from the Greek words “a” + “sthenos” meaning without strength and “sphaira” meaning ball) is made of soft, flowing rock.

Additional Information

• The Earth's interior is made up of several concentric layers, of which the crust, mantle, outer core, and inner core are important because of their unique physical and chemical properties.
• The crust is a silicate solid, the mantle is a viscous molten rock, the outer core is a viscous liquid, and the inner core is a denser solid.
• Earth Core:
• The innermost layer of the earth is known as the core.
• It is divided into the inner core and the outer core.
• It comprises a high concentration of nickel and iron.
• The mantle is the widest section of the Earth. Its thickness is approximately 2,900 km.
• The mantle is mainly made up of semi-molten rock known as magma.
• The rock is hard in the upper part of the mantle, but lower down the rock is softer and begins to melt.
• The mantle is located directly under the Sima
• The crust is the outer layer where we live.
• It is a solid rock layer divided into two types:

1. Continental crust covers the land
2. Oceanic crust covers water

• Sima is an antiquated blended term for the lower layer of Earth's crust. This layer is made of rocks rich in magnesium silicate minerals.

The correct answer is Value Additions.

Key Points

• The term that is used to denote the net contribution made by a firm is called Value Additions.
• In economics, factor payments are the income people receive for supplying the factors of production: land, labor, capital or entrepreneurship. Payments made of scarce resources, or the factors of production in return for productive services.
• Double counting in accounting is an error whereby a transaction is counted more than once, for whatever reason. But in social accounting it also refers to a conceptual problem in social accounting practice, when the attempt is made to estimate the new value added by Gross Output, or the value of total investments.
• Intermediate goods, producer goods or semi-finished products are goods, such as partly finished goods, used as inputs in the production of other goods including final goods. A firm may make and then use intermediate goods, or make and then sell, or buy then use them.

The correct answer is I and II both are correct.

Key Points

• Ribosomes are made up of RNA and proteins.
• Ribosomes are present in both prokaryotic and eukaryotic cells.
• The prokaryotic cell contains 70S ribosomes and eukaryotic cells contain 80S ribosomes
• It doesn't have any membrane around him.
• Cells have many organelles.
• The primary function of RNA is to create proteins via translation.
• RNA carries genetic information that is translated by ribosomes into various proteins necessary for cellular processes. mRNA, rRNA, and tRNA are the three main types of RNA involved in protein synthesis.
• Thus, statement I and II both are correct.

The correct answer is Lemon.

Key Points

• Lemons contain about 31 grams of Vitamin C.
• It is also known as ascorbic acid and is found in citrus fruits (like orange, and lemon), kiwifruit, guava, broccoli, strawberries, etc.
• It is an essential nutrient and is not synthesized by the human body. It is a water-soluble vitamin.
• Functions - Repair of tissues, acts as a co-factor in many enzymatic reactions, important for the Immune system, acts as an antioxidant.
• C₆H₈O₆ is the chemical formula of Vitamin C.

Additional Information

• It is on the List of Essential Medicines of the World Health Organization.
• Deficiency Disease - The deficiency of Vitamin C causes scurvy.
• Discovery - It was discovered in 1912 and first isolated in 1928.

The correct answer is Oxygen.

Key Points

• Oxygen is an element that is highly reactive and readily combines with other elements.
• Oxygen is the most abundant element in the Earth's crust. The crust is 46.6% Oxygen by weight.
• The second most abundant element in Silicon is at 27.7% by weight.
• In the Earth's crust, there is a great deal of silicate, which is formed from silicon and oxygen.
• Other elements in decreasing order of abundance are aluminium (8.1), iron (5.0), calcium (3.6), potassium (2.8), sodium (2.6), magnesium (2.1), manganese (0.10), nickel (trace).
• The Earth's core is believed to consist primarily of a nickel-iron alloy.

The correct answer is Animals.

Key Points

• Pillars are the best examples of Mauryan-era architecture.
• There are animal figures on the top of the Ashoka pillars while human figures are on the Iranian pillars.
• Various animal figures on top of Ashoka Pillars:
• Basarh pillar – lion
• Sankisa pillar – elephant
• Rampurva Pillar – Taurus
• Lauria Nandgarh – Singh
• Sanchi and Sarnath – together with the figures of four lions.
• All these pillars are completely independent in themselves and stand without any support.
• All are made of Chunar sandstone.
• It seems that there may have been a pillar manufacturing factory in Chunar (Mirzapur).

Additional Information

• There are two types of pillars of Ashoka –
• The pillars on which the Dhamma scripts are inscribed.
• Absolutely plain column.
• In the first type, the pillars of Delhi-Meerut, Allahabad (now Prayagraj), Lauria Nandgarh, Lauria Arraj, Rampurwa (Lion Shirsha, Sankisa, Sanchi, Sarnath, Lumbini, Nigali Sagar etc.) are included.
• In the second type, Rampurva (bullhead), Basadh, Kosam etc. are prominent.
• All the pillars are shiny, tall, shapely and monolithic (made of a single stone)
• The Bodhi tree, also known as the Bodhi fig tree or the bow tree, is a large sacred fig tree located in Bodh Gaya, Bihar, India.

The correct answer is Mariculture

Key Points

• Marine agriculture or marine farming is a specialized branch of aquaculture and the cultivation of aquatic, marine life forms for food in the open ocean, ponds, or raceways filled with seawater.
• An example of the latter is the farming of marine fish, including finfish and shellfish such as prawns, or oysters and seashells in saltwater ponds.
• Non-food products produced by mariculture include fish meal, nutritional agar, and ornaments.
• Aquaculture is the cultivation of saltwater and freshwater organisms such as finfish, crustaceans, molluscs, and aquatic plants.

Additional Information 

• Viticulture:- Viticulture (from the Latin word for vine) or winegrowing (growing wine) is the cultivation and harvesting of grapes. It is a branch of Horticulture Science.
• Pisciculture:- Breeding of fish on a large scale (commercial) for the production of fish for sale in the market.
• Pisciculture is related to the Blue Revolution (Blue Revolution), an initiative was taken by the government for the development of the aquaculture industry and was started in 1985-1900 during the 7^th Five Year Plan.
• Sericulture:- The process of breeding, growing, and management of silkworms to get pure raw silk is sericulture. It is an agro-based industry.

The correct answer is Kathak.

Key Points

• Durga Arya is a Kathak dancer, choreographer and teacher. She lives in Germany and comes to India every year.
• Durga Arya was introduced to the Lucknow Gharana of Kathak at a tender age under the tutelage of Smt. Guru Reba Vidyarthi.
• She later continued her training under the leadership of Shri Munna Shukla and flourished under the guidance of the great Kathak maestro Pandit Birju Maharaj.
• In India, she performed in respected festivals like Khajuraho Dance Festival, Kalakshetra Dance Festival, Surya Dance Festival, etc.

Additional Information

• Kathak, a north Indian dance form, is a mixture of dance and drama which is usually performed by both men and women.
• Kathak is found in three distinct forms, called "Gharanas", named after the cities where the Kathak dance tradition evolved – Jaipur, Banaras and Lucknow.
• Manipuri is an ancient classical dance that originated in the northeastern state of Manipur, India. Lai Haraoba is the earliest form of dance in Manipur.
• Kuchipudi is one of the eight major Indian classical dances that originated from a village called Kuchipudi in Andhra Pradesh. Kuchipudi is known for its impressive, quick footwork, dramatic characterization, expressive eye movements and spirited narrative.
• Odissi or Odissi is one of the pre-eminent classical dance forms of India, originating from Odisha in India. The Natya Shastra refers to this dance as Odar Magadha. It is considered to be one of the oldest dances in the world.

The correct answer is Chhattisgarh.

 

Key Points

• Indira Kala Sangeet Vishwavidyalaya (IKSV), also Indira Kala Sangeet Vishwavidyalaya, is a public university located in Khairagarh, Rajnandgaon district, Chhattisgarh, India.
• It was established in 1956.
• It claims to be the first musical university in Asia.
• This institute was run under the Government of Madhya Pradesh till the creation of the new state of Chhattisgarh in 2000. Thereafter, it is run under the Government of Chhattisgarh.
• The university has a museum inside it which is under the Department of Ancient Indian History Culture & Archeology.

The correct answer is 273 °K

Key Points

• For ice, the melting point is 0°C or 273K.
• 0°C is equivalent to 273 kelvins and 32 Fahrenheit.
• The melting point at which ice a solid turns to water a liquid is 32 F (0°C).
• The melting point is the temperature at which a solid turns into a liquid.
• The temperature of the reverse change from liquid to solid is called the freezing point or crystallization point.

Additional Information 

• Melting points of some common substances:

The correct answer is Hockey.

Key Points

• Rani Rampal is an Indian Hockey player. She was born on 4^th December 1994 in Shahbad Markanda Village in Kurukshetra district in Haryana.
• She was conferred with the Rajiv Gandhi Khel Ratna 2020 and she is the first woman hockey player to get this award.
• Rani Rampal captained India and was the Flag-Bearer in Asian Games 2018 and won the Silver Medals for the country in Women's Hockey.
• About Rajiv Gandhi Khel Ratna Award:
• This award was started in 1991. It is the most prestigious and highest award in Sports Fraternity in India.
• This Award has now been renamed to Dhyan Chand Khel Ratna Award, in tribute to Major Dhyan Chand.
• Dhyan Chand, whose birthday is celebrated as National Sports Day.

Additional Information

• All other winners of the Rajiv Gandhi Khel Ratna award 2020 are:
• Rohit Sharma (Cricket),
• Manika Batra (Table Tennis),
• Vinesh Phogat (Wrestling),
• Mariyappam Thangavelu (Paraolympic High Jumper)
• Indian women's hockey team fought tooth and nail against some of the top teams in the world at the Tokyo Olympics in July-August 2021. They made history when they defeated the three-time Olympic gold medallists Australia 1-0 in the quarter-final and played in their first-ever Olympic semi-final against Argentina.

The answer is Option 3.

Key Points

• Mercury is a NOT fair it is good conductor of heat, but a poor conductor of electricity.
• Thus, option 3 is incorrect.
• Mercury is the only metal that is liquid under standard conditions for temperature and pressure.
• Thus, option 2 is correct.
• Mercury has a single electron configuration that strongly opposes the removal of an electron, making it behave similarly to the noble gas elements.
• Thus, option 4 is correct.
• Mercury dissolves to form amalgams with gold, zinc, and many other metals. Iron is an exception, and iron flasks have been traditionally used to trade mercury. Sodium amalgam is a common reducing agent in organic synthesis, and it is also used in high-pressure sodium lamps.
• Thus, option 1 is correct.

Additional Information

• Mercury is a dense, silvery d-block element.
• The element other than mercury that is liquid under standard temperature and pressure is bromine, though metals such as caesium, gallium, and rubidium melt just above room temperature.

The correct answer is Brown algae.

Key Points

• Members of the Phaeophyceae are brown algae as the yellowish-brown pigments predominate in xanthophylls.
• Brown algae are mostly marine.
• They are found in cold waters along the coast.
• They are either free-floating or found to be attached to the substratum.
• Ectocarpus is an epiphyte, Fucus is found attached to rocks and Sargassum is an example of free-floating brown algae.

Additional Information 

• Some brown algae have special gas-filled bladders called pneumatocysts. They are mostly present near the lamina.
• It provides buoyancy to the algae and helps to keep the algae part close to the surface for photosynthesis.

The correct answer is Mass.

Key Points

• A scalar quantity is defined as the physical quantity with magnitude and no direction.
• The mass has only magnitude, not direction. If we consider the weight, then it is the force experienced by the object due to its mass.
• Mass, Speed, Distance, Time, Area, Volume, Density, and Temperature are examples of Scalar Quantity.
• A vector quantity is defined as the physical quantity that has both directions as well as magnitude.
• Linear momentum, Acceleration, Displacement, Momentum, Angular velocity, Force, Electric field, and Polarization are examples of vector quantity.

Additional Information

• Electric Current has a definite direction yet it is a scalar quantity.
• Unit vectors are vectors with a magnitude of 1, they are used to define direction.
• William Rowan Hamilton is given credit for inventing vectors.
• A zero vector is a vector with zero magnitudes and an arbitrary direction.

The correct answer is the Caspian Sea.

Key Points

• The Caspian Sea is the largest inland body of water on the earth's surface.
• A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake.
• Lakes lie on land and are not part of the ocean, although, like the much larger oceans, they do form part of the Earth's water cycle.
• The Caspian Sea lies at the junction of Europe and Asia.
• It has the greatest surface area of any lake at 143,200 square miles (370,886 square kilometres).
• It accounts for 40 to 44% of the total lacustrine waters of the world.
• The Caspian Sea is best known for its caviar and oil industries.
• The Caspian Sea is bounded by: 
• Iran to the south and adjacent corners.
• Russia from mid-north to mid-west.
• Kazakhstan from mid-north to mid-east.
• Azerbaijan to the southwest.
• The Caspian Sea is bordered by five countries: Russia, Kazakhstan, Turkmenistan, Iran, and Azerbaijan.

Additional Information

• Lake Superior: Lake Superior is the largest of the Great Lakes of North America, and among freshwater lakes, it is the world's largest in surface area and third-largest by volume.
• Lake Van: Lake Van is the largest lake in Turkey. It is a saline soda lake and one of the few endorheic lakes in the world (a lake that has no outlet).
• Dal Lake: Dal Lake is an urban lake located in Srinagar, the summer capital of Jammu and Kashmir. It is integral to tourism and recreation in the Kashmir valley and is variously known as the "Lake of Flowers", "Jewel in the crown of Kashmir" or "Srinagar's Jewel".

Confusion Points

There are two lakes that can be considered the world's largest freshwater lake, depending on whether we measure by surface area or volume:

1. Lake Superior

• The world's largest freshwater lake by surface area, Lake Superior is located on the border of the United States and Canada. It has a surface area of around 82,103 square kilometers.

2. Lake Baikal

• The world's largest freshwater lake by volume and depth, Lake Baikal is located in the southern region of Siberia in Russia
• Thus, Caspian Sea is the correct answer.

The correct answer is Tamil Nadu

Key Points

• Syed Mushtaq Ali Trophy is related to Cricket.
• The 2020–21 Syed Mushtaq Ali Trophy was the thirteenth edition of the Syed Mushtaq Ali Trophy, a Twenty20 competition played in India.
• It started on 10 January 2021, with the final on 31 January 2021.
• Tamil Nadu won the tournament by defeating Baroda by seven wickets in the final.
• Karnataka were the defending champions.
• The Board of Control for Cricket in India (BCCI) was the administrator of this tournament.

 

Additional Information 

• The Tamil Nadu cricket team is a domestic cricket team run by the Tamil Nadu Cricket Association, representing the Indian state of Tamil Nadu.
• It has been one of the most influential teams in white-ball cricket in the domestic circuit.
• They have won the Ranji Trophy twice and have been runner-up nine times.
• The Board of Control for Cricket in India (BCCI) is the governing body of cricket in India.
• Its headquarter is located at Wankhede Stadium in Mumbai, Maharashtra.

The correct answer is Option 1.

Key Points

• Tropical cyclones, also known as typhoons or hurricanes, are among the most destructive weather phenomena.
• They are intense circular storms that originate over warm tropical oceans and have maximum sustained wind speeds exceeding 119 kilometres per hour and heavy rains.

 

Important Points 

• Tropical cyclones are referred to by different names depending on where they originate in the world.
• Hurricanes occur in the Atlantic Ocean and the eastern north Pacific Ocean.
• Typhoons occur in the western Pacific Ocean and the northern Indian Ocean.
• Tropical cyclones occur in the south Pacific Ocean and the Indian Ocean.
• They have different names in different regions as below:
• Australia - Willy-Willy
• China Sea - Typhoons
• Coastal US - Tornadoes
• Caribbean Sea - Hurricanes

The correct answer is 2007.

Key Points 

• The Centre-State Relations Commission was constituted by the Government of India on 27 April 2007 under the chairmanship of Justice Madan Mohan Punchhi.
• Highlights of the commission:
• To examine what could be the role, responsibility, and jurisdiction of the Centre during major and prolonged outbreaks of communal violence, caste violence, or any other social conflicts.
• To review other aspects of Centre-States relations including taxes and linking of rivers.
• To study the role, responsibility, and jurisdiction of the Centre vis-à-vis States in promoting effective devolution of powers and autonomy to Panchayati Raj institutions and local bodies.
• To study the need and relevance of separate taxes for freeing inter-state trade to establish a unified domestic market.

Additional Information

• Madan Mohan Punchhi was the former Chief Justice of India, appointed on 18-1-1998 and retired on 9-10-1998.
• He was born on 10^th October 1933 at Pakpattan, District, Montgomery (now in Pakistan).

The correct answer is 1990-1991.

Key Points

• The period from 14 April 1990 to 14 April 1991 was observed as the "Year of Social Justice" in the memory of B. R. Ambedkar.
• He is known as the father of the Indian Constitution. He was the then Law Minister who presented the final draft of the Constitution in the Constituent Assembly.
• B.R Ambedkar is known as the "Modern Manu of India". He is called by this name because he drafted the Hindu code bill.

 

Important Points

• B.R. Ambedkar's birthday is celebrated as 'Equality Day' in India, and the demand to declare this day as "International Equality Day" goes to the United Nations.
• On 6 April 2020, in Canada, it was decided to observe 14 April as "Dr. BR Ambedkar Day of Equality". This decision was taken by the Canadian City Council of Burnaby.
• On 14 April 1990, Ambedkar was bestowed with the Bharat Ratna award.

The correct answer is Kerala.

Key Points

• The sex ratio refers to the number of females per 1000 males. According to the 2011 census, Kerala has the highest sex ratio, i.e. 1084 females per 1000 males.
• As per the 2011 census, Haryana has the lowest sex ratio in India, with only 877 females per 1000 males.
• According to the 2011 census, the sex ratio of India is 940 females per 1000 males.
• As per the 2011 census, Mizoram has the highest child sex ratio recorded at 971 girls per 1000 boys.

Additional Information

• The decadal census of India has been conducted 15 times (7 times after independence) as of 2011.
• While it has been introduced every 10 years, the first "full census" took place in 1881, under the British Viceroy Lord Ripon 1881, but 1^st census took place during the tenure of Lord Mayo in 1872

The correct answer is 1843.

Key Points

• The Indian Slavery Act, of 1843, also known as Act V of 1843, was an act passed on 7 April 1843 in British India under the rule of the East India Company.
• The Act stated that the sale of any person as a slave was banned and anyone who bought or sold slaves would be booked under the Indian Penal Code with the offense of severe punishment

Additional Information

• Lord Ellenborough was the Governor-General of India during the implementation of the Indian Slavery Act, 1843.
• He was the Chairman of the Board of Control for four terms and also served as the Governor-General of India between 1842 and 1844.

The correct answer is Smt. Indira Gandhi.

Key Points

 

• In India, a privy purse was paid to ruling families of erstwhile princely states after India's independence, first in 1947, as part of their agreements to integrate with India.
• In 1949, there was a discussion about dissolving privy purses but the issue was not taken up further.
• It was again proposed before the Parliament in 1971 and was successfully passed as the 26^th Amendment to the Constitution of India 1971 and extra amounts paid to princely states were stopped.
• The then Prime Minister Indira Gandhi argued that abolition was based on equal rights for all citizens and the need to reduce the government's revenue deficit.

 

Additional Information

• Indira Gandhi was the 3^rd Prime Minister of India and served as prime minister from January 1966 to March 1977 and again from January 1980 until her assassination in October 1984.
• Vishwanath Pratap Singh (25 June 1931 – 27 November 2008), V.P. Singh, abbreviated as Singh, was an Indian politician who was the 7^th Prime Minister of India from 1989 to 1990. He is the only Prime Minister of India who has been a member of the former royal family.
• Chaudhary Charan Singh (23 December 1902 – 29 May 1987) served as the 5^th Prime Minister of India between 28 July 1979 and 14 January 1980. He is also known as the 'champion of India's peasants.'
• Lal Bahadur Shastri (2 October 1904 – 11 January 1966) was an Indian politician who served as the second Prime Minister of India.

The correct answer is Tabaqat-i-Nasiri.

Key Points

• Minhaj-i Siraj was a 13^th centurion Persian historian.
• He wrote Tabaqat-i-Nasiri which contained the history of the Islamic world.
• Razia Sultan (1236-40) summoned him to Delhi and appointed him the head of Madrassa-i Nasiri in Delhi.
• His work describes Razia Sultan.

Additional Information

• The Baharistan-i-Ghaibi written by Mirza Nathan, is a 17^th-century chronicle on the history of Bengal, Cooch Behar, Assam, and Bihar under the reign of Mughal emperor Jahangir (1605-1627).
• Fathiya-i-Ibriyya also known as Tarikh-i-Assam was written by Ibn Muhammad Wali Ahmad, better known as Shihabuddin Talish, which was his poetical name.
• Tarikh-i Firoz Shahi is a book on Indo-Persian historiography during the Delhi Sultanate period in India. It was written by Ziauddin Barani. Ziauddin Barani was a Muslim political thinker who lived during the reign of Muhammad bin Tughlaq and Firuz Shah Tughlaq. The book covers the data from the reign of Ghiyas ud din Balban to the first six years of the reign of Firoz Shah Tughluq. The book was completed in 1357 CE.

The correct answer is Ireland.

Key Points

• Constitutional Provisions: Part IV of the Constitution of India (Article 36–51) contains the Directive Principles of State Policy (DPSP).
• They are borrowed from the Constitution of Ireland, which copied it from the Spanish Constitution.
• Article 37 of the Indian Constitution states the application of the Directive Principles.
• These principles aim at ensuring socio-economic justice to the people and establishing India as a welfare state whereas fundamental rights ensure political justice.​

Additional Information

• Borrowed Features of the Indian Constitution:
• Irish Constitution - Directive Principles of State Policy, Nomination of Rajya Sabha members & Method of the election of the President.
• US Constitution - Fundamental rights, Independent judiciary and judicial review, Impeachment of the President, Removal of Supreme Court and High Court judges & Post of Vice-President.
• France Constitution  - Republic, Ideals of liberty, equality, and fraternity in the Preamble.
• Britain (UK) Constitution - Parliamentary government, Rule of Law, Legislative procedure, Single Citizenship, Cabinet system, Prerogative writs, Parliamentary privileges, Bicameralism.

The correct answer is the Reserve Bank of India.

Key Points

• Non-Banking Financial Companies operate under the Companies Act, 2013, and are regulated by RBI under the RBI Act, 1934.
• It is typically associated with services related to lending, credits and advances, savings, and investment products, and also performs functions such as trading in the money market, handling a portfolio of stocks, and transferring funds.
• Under Section 8, Micro-finance Institutions are financial companies that provide small loans to people who do not have any access to banking facilities.
• Types of Committees to Review the existing framework of NBFCs - James S. Raj Committee and Chakravarty Committee.
• NBFC reserves the right to accept a deposit (only term deposit). They are not eligible to accept deposits repayable on demand.

Additional Information 

• State Bank of India, earlier known as “The Imperial Bank of India” became the State Bank of India on 1 July 1955. It is the 43^rd largest bank in the world. The current chairman of SBI is Dinesh Kumar Khara (as of June 2022).
• National Bank for Agriculture and Rural Development (NABARD) was established on the recommendations of the B.Sivaraman Committee on 12 July 1982 to implement the National Bank for Agriculture and Rural Development Act 1981.

Important Points

• Challa Sreenivasulu Setty became the 27^th chairman of SBI on August 28, 2024.

The correct answer is Wardha.

Key Points

• The Congress Working Committee (CWC) was formed in December 1920 at the Nagpur session of the Congress, headed by **C. Vijayaraghavacharya.**​
• The Congress Working Committee meeting held at Wardha on 14 July 1942 passed a resolution demanding Complete Independence from the British Government.
• It passed the historic ‘Quit India’ resolution.
• The Indian National Congress session held on 7 August 1942 at Gowalia Tank (Kranti Maidan) in Mumbai gave a call for Quit India Movement.
• Maulana Abul Kalam Azad was the President of this session.
• Gandhiji gave a call for 'Do-or-die' during Quit India Movement
• Lord Linlithgow was the Viceroy of India when the Quit India Movement started in 1942.

The correct answer is Nine.

Key Points

• The Andaman Islands and the Nicobar Islands separate the Andaman Sea to the east from the Indian Ocean. These two groups are separated by the 10° N parallel (also known as the Ten Degree Channel), the Andamans lying to the north of this latitude, and the Nicobars to the south.
• It is made up of 3 Districts only.
• Andaman and Nicobar Administration has jurisdiction over 9 Tehsils.
• The Lieutenant Governor of Andaman and Nicobar Islands (UT) is Admiral DK Joshi (as of June 2022).​

Additional Information

• Union Territory of the Andaman and Nicobar Islands comes under the jurisdiction of the Calcutta High Court.
• Major tribes: Great Andamanese, Onges, Jarwas, Sentinelese.
• Barren Island Volcano, 140 km northeast of Port Blair, is the only confirmed active volcano in the Indian subcontinent.

The correct answer is English.

Key Points

• The Eighth Schedule to the Constitution of India lists the official languages of the Republic of India.
• As per Articles 344 (1) and 351 of the Indian Constitution, the 8^th schedule includes 22 languages: Assamese, Bengali, Gujarati, Hindi, Kannada, Kashmiri, Konkani, Malayalam, Manipuri, Marathi, Nepali, Oriya, Punjabi, Sanskrit, Sindhi, Tamil, Telugu, Urdu, Bodo, Santhali, Maithili, and Dogri.
• Surprisingly these 22 languages do not include “English” which is widely spoken in India.​

Mistake Points

• Many students confuse these languages with “Classical language” which includes only 11 languages of India and are recognized for their historical significance and rich literary heritage. They include:

Sanskrit, Tamil, Telugu, Kannada, Malayalam, Odia, Prakrit, Pali, Bengali, Assamese, Marathi and Persian.

Additional Information

• Nepali was originally not present in the 8^th schedule of the constitution but later added with the 71^st amendment act along with Konkani & Manipuri.
• Bodo, Dogri, Maithili, and Santhali were added by the 92^nd Amendment Act of 2003.

The correct answer is Heliodorus.

 

Key Points

• The Heliodorus pillar is a stone column that was erected around 110 BCE in central India in Vidisha near modern Besnagar, by Heliodorus, a Greek ambassador of the Indo-Greek king Antialcidas to the court of the Sunga king Bhagabhadra.
• The pillar was discovered by Alexander Cunningham in 1877.
• The pillar also glorifies the Indian ruler as "Bhagabhadra the saviour".
• The pillar was called Garuda-manaka by Heliodorus, referring to Garuda.
• The pillar is also one of the earliest surviving records of a foreign convert into “Vaishnavism”.
• The locals at the time called the pillar the Khamba Baba or Kham Baba.

Additional Information

• Alexander the Great overthrew the Persian Empire, carried the arms of Macedonian to India, and laid the foundation for the Hellenistic world of regional empires.
• Megasthenes was a Greek historian who was the first to describe ancient India, and is therefore called the "father of Indian history".
• He was the Greek ambassador of Seleucus I Nicator in the court of King Chandragupta Maurya.

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi was not a member of the Constituent Assembly of India.
• The members were elected by indirect election by the members of the provincial legislative assemblies according to the scheme recommended by the Cabinet Mission.
• The Assembly consisted of 292 representatives among which 15 were women.
• There were a total of 22 committees of which some important members were - B.R. Ambedkar, Jawaharlal Nehru, Vallabhbhai Patel, J.B. Kriplani, etc., but Mahatma Gandhi was not included in the list.

Important Points

• The idea of ​​establishing a Constituent Assembly was given by M.N. Roy in the year 1934.
• It was finally accepted by the British in 1940 when C. Rajagopalachari raised his voice in the Constituent Assembly held on 15 November 1939.
• It was proposed via Cabinet Mission Plan to form a Constituent Assembly.​

Additional Information

• On 26^th November 1949, 3 provisions -  Elections, citizenship and provisional Parliament came into force and rest of the provisions only on 26^th January 1950.
• The first speaker of the Constituent assembly was Ganesh Vasudev Mavalankar, popularly known as Dadasaheb.
• The National Flag of India was adopted on 22 July 1947.

The correct answer is Reserved Forests

Key Points

• Permanent Forests: Reserved and protected forests are also referred to as permanent forest estates maintained for the purpose of production of wood and other forest products and for protective reasons. Madhya Pradesh has the largest area under permanent forests.
• Reserved Forest: More than half of the total forest land has been declared as Reserved Forest. As far as the conservation of forest and wildlife resources is concerned, reserve forests are considered to be the most valuable.
• The first Reserve Forest of India was Satpura National Park. It is located in the Hoshangabad district of Madhya Pradesh.​

Additional Information

• Protected Forest: A protected forest is a land that is a reserved forest, and over which the government has property rights, as declared by the state government under section 29 of the Indian Forest Act 1927.
• Unclassed Forest: Unclassed Forests are forests and wastelands belonging to both government and private individuals and communities. All North-eastern states and parts of Gujarat have a very high percentage of their forests as unclassed forests managed by local communities.
• Community Forest: A community forest provides local community value and benefits from land, access to and rights to forest resources, and participation in management decisions. These forests can be managed for timber production, agroforestry, recreation, and/or watershed conservation.

The correct answer is Atal Tunnel.

Key Points

• The Atal Tunnel is a highway tunnel built under the Rohtang Pass in the eastern Pir Panjal Range of the Himalayas on the Leh–Manali highway in Himachal Pradesh, India.
• It is now the longest highway tunnel in the world at over 10,000 feet and 9.02 km (5.6 mi) long.
• Atal Tunnel is also known as Rohtang Tunnel and it was inaugurated by Prime Minister Narendra Modi on 3 October 2020.
• Prime Minister Narendra Modi changed the name of the tunnel to Atal Tunnel in honour of Shri Atal Bihari Vajpayee on Vajpayee's birthday on 25 December 2019.

Additional Information

• The project was announced by the then Prime Minister Atal Bihari Vajpayee on 3 June 2000 and built by Border Roads Organisation (BRO).
• The Maliguda Tunnel of Odisha is the fourth largest broad-gauge railway tunnel.
• The Dr Shyama Prasad Mukherjee Tunnel is a road tunnel in Jammu and Kashmir, India.
• The Pir Panjal Railway Tunnel or Qazigund Railway Tunnel is an 11.215 km long railway tunnel located in the Pir Panjal Range of the Central Himalayas in Jammu and Kashmir.

​

The correct answer is Equal to the aggregate supply

Key Points

• According to Keynesian theory, the equilibrium level of income in an economy is determined when aggregate demand as represented by the C + I curve is equal to aggregate output (aggregate supply or AS).
• The Aggregate Demand and Aggregate Supply Equilibrium provides information on price levels, real GDP, and changes in unemployment, inflation, and growth as a result of new economic policy.

 

Additional Information

• When aggregate demand exceeds aggregate supply, planned inventory will fall below the desired level. To bring inventory back to the desired level, producers expand output. More output means more income.
• Investment is everything that is left of total expenditure after consumption, government spending, and net exports are subtracted (i.e. I = GDP - C - G - Nx).
• When aggregate demand is less than aggregate supply at the absolute level of employment, there is a decrease in demand in the economy leading to deflation.

The correct answer is Chhota Nagpur plateau.

 

Key Points

• Chhota Nagpur plateau is called the “Heart of industrial India” because it is rich in minerals and power fuels.
• It is also called the "Ruhr of India".
• The Chota Nagpur region has the most valuable concentration of mineral resources in India. Its largest division is the Ranchi Plateau.
• The Damodar Valley has vast deposits of coal, and the Hazaribagh area is one of the major sources of mica in the world.

Additional Information

• Chota Nagpur plateau is located in eastern India, in northwestern Chhattisgarh and central Jharkhand states.
• Malwa plateau region, made up of volcanic origin is situated in the central-western part of India. Agriculture is the main occupation of the people of Malwa. The region has been one of the important producers of opium in the world.
• The Deccan Plateau is a very large plateau located in the southwestern part of India. It is very rich in minerals and precious stones. Tiruvannamalai in Tamil Nadu is often regarded as the Southern gateway of the Deccan plateau.
• The Bundelkhand region of central India, now included in the northern state of Madhya Pradesh, includes the hilly Vindhya region, cut by valleys, and the northeastern plain.

The correct answer is NCT of Delhi and Chandigarh.

Key Points

• In India, Delhi is the highest populated union territory of India.
• Delhi has a population density of 11,320​ per square kilometer as per census-2011.
• Among the Union Territories, Delhi is followed by Chandigarh and then Puducherry.
• Bihar is the most thickly populated state (1106 persons/sq km.) followed by West Bengal - 1028 and Kerala - 860 as per census 2011.

Additional Information

• Other union territorys' population density:
• Lakshadweep - 2,149 people per square km
• Dadra and Nagar Haveli - 700 persons per square km
• Daman and Diu - 2,191 persons per square km
• Chandigarh - 9,258 people per square km
• Puducherry - 2,547 person per square km

The correct answer is Seismic disturbances

Key Points

• Seismic disturbances are shaking and vibration at the surface of the earth resulting from underground movement along a fault plane or from volcanic activity.
• Thus they do not play a role in determining the climate conditions on the earth.
• The elements affecting the climate are latitude, altitude and pressure and winds, distance from the sea (continentality), ocean currents, and relief features.

Additional Information

• Surface winds and air masses blow over the oceans and move from the coast to the mainland and affect the climate.
• Upper air circulation occurs when the Sun heats the Earth more at the equator than at the poles. It is also affected by the rotation of the earth.
• Tropical cyclones, also known as typhoons or hurricanes, are intense circular storms that originate from warm tropical oceans and have maximum sustained wind speeds and heavy rainfall.

The correct answer is Wheat

 

Key Points

• The Harappans grew wheat, barley, pulses, peas, rice, sesame, linseed, and mustard.
• Their staple food was wheat and barley, which were probably made into bread and probably cooked with water as porridge.
• There is evidence that the Harappans cultivated Italian millet, ragi, and amaranth, as well as sorghum and rice.

Additional Information

• Millets (Bajra) are found from sites in Gujarat.
• The first South Asian evidence of Rice cultivation is found in Lothal and Rangpur.
• Many varieties of wheat have been found at Harappan sites.
• A good quantity of barley has been discovered at Banawali.

Given:

Average income of 30 persons = Rs. 5600.

Average income of 25 persons = Rs. 5000.

Formula used:

If average of x entities is 'a' and average of y entities is 'b' then

Weighted average = (xa + yb) / (x + y)

Calculation:

Average income of the whole group is calculated using the above formula.

For x = 30, y = 25, a = 5600 and b = 5000, we get

Average income

= (xa + yb) / (x + y)

= \(\dfrac{30\times 5600 + 25 \times 5000 }{30 + 25}\)

= \(\dfrac{168000 + 125000 }{30 + 25} \)

= \(\dfrac{293000 }{55} \)

= 5327.27.

∴ Average income of the whole group is Rs. 5327.27.

Given: 

A's salary is 100% more than B's salary.

Concept used:

For two numbers a and b, the percentage by which b is less than 'a' is found by

= [(a - b) / a] × 100

Calculation:

Let B's salary be x.

Then A's salary 

= x + 100% of x

= \(x + \dfrac{100}{100} \times x \)

= x + x

= 2x.

Percentage by which B's salary is less than A's salary

= [(A - B) / A] × 100

= \(\dfrac{2x - x}{2x} \times 100 \)

= (1 / 2) × 100

= 50%.

∴ B's salary is less than A's salary by 50%.

Given:

Principal (P) = Rs. 14000.

Rate percent per annum (R) = 16%.

Time (T) = 6 months.

Interest is compounded quarterly.

Formula used:

Amount in compound interest (A)

A = P(1 + R/100)^T

For finding C.I. (Compound interest),

A = P + C.I.

where

P = principal.

R = rate percent per annum.

T = time.

When compounded quarterly, the time becomes 4 times and the rate becomes (1 / 4) times.

Calculation:

Rate and time for compound interest compounded quarterly, 

R = 16/4 = 4% and T = 4 × 6 months = 24 months = 2 years.

Putting these in the formula for amount

A = P(1 + R / 100)^T

A = 14000 × (1 + 4 / 100)²

A = 14000 × (1 + 1 / 25)²

\(A = 14000 \times \dfrac{26}{25} \times \dfrac{26}{25} \)

\(A = 560 \times 26 \times \dfrac{26}{25} \)

A = 22.4 × 26 × 26

A = 15142.4.

Now, C.I. will be as follows

A = P + C.I.

15142.4 = 14000 + C.I.

C.I. = 15142.4 - 14000

C.I. = 1142.40

∴ Compound interest is Rs. 1142.40.

Shortcut Trick

Number of times (n) = Volume of Sphere ÷ Volume of Cylinder

n = [(4/3) × π × R³] ÷ [π × r² × h]

n = [4/3 × 12 × 12 × 12] ÷ [4 × 4 × 16]

n = [4 × 4 × 12 × 12] ÷ [16 × 16] = 2304 ÷ 256 = 9

∴ The correct answer is 9.

Alternate Method

Given:

Cylindrical container: Height (h) = 16 cm, Diameter = 8 cm ⇒ Radius (r) = 4 cm

Spherical bowl: Inner Radius (R) = 12 cm

Formula Used:

Volume of Cylinder = πr²h

Volume of Sphere = (4/3)πR³

Calculations:

⇒ Volume of Cylindrical container = π × 4 × 4 × 16 = 256π cm³

⇒ Volume of Spherical bowl = (4/3) × π × 12 × 12 × 12

⇒ Volume of Spherical bowl = 4 × π × 4 × 12 × 12 = 2304π cm³

⇒ Number of times (n) = Volume of Bowl ÷ Volume of Container

⇒ n = 2304π ÷ 256π

⇒ n = 9

∴ The correct answer is 9.

Additional Information

Volume of Hemisphere

If the bowl is a hemisphere, the volume is (2/3)πR³. Always check if the question specifies a full sphere or a hemisphere.

Surface Area of Sphere

The total surface area of a sphere is 4πR², while for a solid hemisphere, it is 3πR².

Cylinder Mensuration

Curved Surface Area (CSA) of a cylinder = 2πrh and Total Surface Area (TSA) = 2πr(h + r).

Given:

First 10 natural numbers are taken.

Formula used:

Sum of cubes of first n natural numbers is given by

\(= \left(\dfrac {n(n+1)}{2}\right)^2 \)

Average = Sum of numbers / Total numbers taken

Calculation:

Sum of cubes of first 10 natural numbers 

\(= \left(\dfrac {n(n+1)}{2}\right)^2 \)

\(= \left(\dfrac {10(10+1)}{2}\right)^2 \)

\(= (5 \times 11)^2 \)

= 55²

= 3025.

Average of cubes of first 10 natural numbers

= Sum / Total numbers taken

= 3025 / 10

= 302.5

∴ Average of first 10 natural numbers is 302.5.

Given:

\(\rm \begin{array}{l} ,,,,,B,9\ + ,4,A\ _____\ ,,,,,6,5 \end{array} \)

Concept:

In Cryptarithms, we can find the values of letters in place of digits by using hit and trial method or by forming equations.

Calculation:

As 9 is the largest single digit number,

\(9 + A \neq 5\)

9 + A = 15

A = 15 - 9

A = 6.

1 gets carried over B and we get,

1 + B + 4 = 6

B = 6 - 5

B = 1.

∴ A = 6 and B = 1.

Given:

Amount of invoice = ₹50,000.

Conditions of invoice = [5/15, n/30].

Invoice dated = 31 August 2021.

Date on which amount paid = 8 September 2021.

Concept:

The condition [5/15, n/30] is read as the person would get 5% discount if he pays within the first 15 days of the month.

Calculation:

As the person paid the amount on the 8^th day after the invoice was issued, he will get a discount of 5%.

5% discount on 50000 is calculated as:

= 50000 - 5% of 50000

= 50000 - (5 / 100) × 50000

= 50000 - 2500

= 47500.

∴₹47,500 was effectively paid by the person.

Given:

3 + 3.33 + 33.3 + 3.03 + 333

Concept used:

Number of decimals before and after addition is constant.

Calculation:

We have to find the sum of

3 + 3.33 + 33.3 + 3.03 + 333

We add the numbers in pair of two at a time

⇒ (3 + 3.33) + 33.3 + 3.03 + 333

⇒ (6.33 + 33.3) + 3.03 + 333

⇒ (39.63 + 3.03) + 333

⇒ 42.66 + 333

⇒ 375.66.

∴ 3 + 3.33 + 33.3 + 3.03 + 333 = 375.66.

Shortcut Trick⇒ 3 + 3.33 + 33.3 + 3.03 + 333

We has 0.33, 0.03 and 0.3 in decimal places

If we add 0.33 + 0.3 + 0.03 = 0.66

we see only one option having 0.66 as a decimal place

∴ 3 + 3.33 + 33.3 + 3.03 + 333 = 375.66.

Given:

Radius of cylinder (r) = 6 cm.

Height of cylinder = 128 cm.

Cylinder is sliced across its diameter and two parts are cast into a sphere and a cone.

Height of the cone = 48 cm

Concept used:

When the cylinder is sliced across its diameter, its height will be divided into two equal parts.

Volume of cylinder = π × r² × h

where 

r = radius of cylinder

h = height of cylinder

Volume of cone = (1 / 3) × π × r₁2 × h₁ 

where 

r₁ = radius of cone

h₁ = height of cone

Volume of sphere = (4 / 3) × π × r₂3 

where

r₂ = radius of sphere.

Calculation:

Volume of cylinder for each part:

v' = (π × r2 × h)/2 = (π × 36 × 128)  / 2 = 36 × 64 π cm².

For cone part,

Volume of cone = Volume of first part of sliced cylinder

(1 / 3) × π × r12 × 48 =  36 × 64 π cm2.

\(\dfrac{1}{3} \times r_1^2 \times 48 = 6^2 \times 64 \)

\(r_1^2 = \dfrac{36 \times 64 \times 3}{48} \)

r₁² = 144

r₁ = 12 cm.

For sphere part,

Volume of sphere = Volume of second part sliced cylinder

(4 / 3) × π × r23  = (π × r2 × h)/2

\(\dfrac{4}{3} \times r_2^3 = 6^2 \times 64 \)

\(r_2^3 = \dfrac{36 \times 64 \times 3}{4} \)

r₂³ = 27 × 64

r₂ = 3 × 4

r₂ = 12 cm.

Sum of radii of cone and sphere

= r₁ + r₂

= 12 + 12

= 24 cm.

∴ Sum of radii of cone and sphere is 24 cm.

Given:

We have to simplify

\( (\sqrt{81} + \sqrt{0.81} + \sqrt{0.0081}) \sqrt{10000} \)  

Concept used:

\(\sqrt{81} = 9\)

\(\sqrt {100} = 10 \)

\(\sqrt {10000} = 100 \)

Calculation:

Simplifying the given equation we get

\( (\sqrt{81} + \sqrt{0.81} + \sqrt{0.0081}) \sqrt{10000} \)

\(= (\sqrt{81} + \sqrt{\dfrac{81}{100}} + \sqrt{\dfrac{81}{10000}}) \sqrt{10000} \)   

\(= \left(9 + {\dfrac{9}{10}} + {\dfrac{9}{100}}\right) \times {100} \)

\(= \left(\dfrac{900 + 90 + 9}{100}\right) \times {100} \)

= 999.

∴ Simplification of \( (\sqrt{81} + \sqrt{0.81} + \sqrt{0.0081}) \sqrt{10000} \) gives 999.

Given:

We have to find which one from the given options is not a square of a natural number.

Concept used:

The unit digit of a square of a natural number can only be 1, 4, 5, 6, 7 or 9.

Solution:

√ 8836 = 94;

√ 60025 = 245;

√ 13225 = 115;

From the given options we see that the unit digit of 14762 is 2, which is not equal to 1, 4, 5, 6 or 9 and hence it cannot be the square of a natural number.

∴14762 is not the square of a natural number.

Given:

42x-1 = (128)2

Concept used:

In such questions we try to make the base of terms on both the sides of the equation equal, then use the properties:

If a^x = a^y, then x = y.

Also (b^m)ⁿ = b^mn.

Calculation:

42x-1 = (128)2

(2²)^2x-1 = (2⁷)²

2^{2(2x - 1)} = 2⁷⁽²⁾

2^{4x - 2}  = 2¹⁴

Using the property above,

4x - 2 = 14

4x  = 16

x = 4.

∴ The value of x is 4.

Given:

Outer radius (R) of hemispherical bowl = 45 cm.

Inner radius (r) of hemispherical bowl = 41 cm.

Formula used:

Total surface area (T.S.A) of hemispherical shell 

= 2πR² + 2πr² + π(R² - r²)  

= 2πR2 + 2πr2  + πR2 - πr2 

= 3πR² + πr²

Calculation:

Using the above formula we get:

T.S.A = 3πR2 + πr2

T.S.A = 3 × π × (45)² + π × (41)²

T.S.A = 3 × π × 2025 + π × 1681

T.S.A = 6075π + 1681π

T.S.A = 7756π cm² 

∴Total surface area of the bowl is 7756π cm².

Given:

A sum is invested at 10% rate per annum.

The same sum is now invested at 10% rate per annum, compounded half-yearly.

Time (T) = 1 year.

Difference in interest obtained = Rs. 40.

Formula used:

Amount in compound interest (A)

A = P(1 + R / 100)^T

For finding C.I. (Compound interest),

A = P + C.I.

where

P = principal.

R = rate percent per annum.

T = time.

When compounded half-yearly, the time becomes 2 times and the rate becomes (1 / 2) times.

Calculation:

Let the sum be Rs. x.

Amount when compounded yearly,

A = P(1 + R / 100)^T

A = x(1 + 10 / 100)¹

A = x(1 + 1 / 10)

A = 11x / 10.

Compound interest (C.I.),

A = P + C.I.

11x / 10 = x + C.I.

C.I. = (11x /10) - x

C.I. = x / 10.

Rate and time for compound interest compounded half-yearly,

R' = 10 / 2 = 5% and T' = 2 × 1 year = 2 years.

Putting these in the formula for amount

A' = P(1 + R' / 100)^T'

A' = x(1 + 5 / 100)²

A' = x(1 + 1 / 20)²

\(A' = x \times \dfrac{21}{20} \times \dfrac{21}{20} \)

A' = 441x / 400

The compound interest when compounded half-yearly,

A' = P + (C.I.)'

(C.I.)' = A - P

(C.I.)' = (441x / 400) - x

(C.I.)' = 41x / 400

Difference between the two compound interests

(C.I.)'  - (C.I.) = Rs. 40

\(\dfrac{41x}{400} - \dfrac{x}{10} = 40 \)

\(\dfrac{41x}{400} - \dfrac{40x}{400} = 40 \)

x / 400 = 40

x = 40 × 400

x = 16000.

∴ The sum invested is Rs. 16000.