DSSSB Junior Secretariat Assistant Official paper (Held on: 2 April 2022 Shift 1 ) (Previous Year Paper)

According to the given information:

By using the BODMAS rule:

The numbers 9 and 24 are interchanged.

The equation becomes as follows;

24 ÷ 3 + 8 × 14 − 9

​Solving the given equation,

= 24 ÷ 3 + 8 × 14 − 9

= 8 + 8 × 14 − 9

= 8 + 112 − 9

= 120 - 9

= 111

Hence, the correct answer is "111".

According to the given information:

• Ravi walks toward the north
• Then turns right,
• Then left,
• Then right,
• And then left.

​So from the following, this diagram can be deduced,

 

As we can see from the diagram he is currently walking in the north direction.

Hence, the correct answer is "North*"*

By using the BODMAS rule:

Option 1) 9 and 4; × and −

Given equation - 43 × 16 − 7 + 91 ÷ 18 = −57

After changing the signs and digits in the given equation the equation is followed as, 

93 - 16 × 7 + 41 ÷ 18 = −57

=> 93 - 16 × 7 + 41 ÷ 18 = −57.

=> 93 - 16 × 7 + 2.27 = −57.

=> 93 - 112 ​+ 2.27 = −57.

=> 95.27 - 112 = -57

=> -16.73 ≠ -57

LHS ≠  RHS

Option 2) 9 and 6; ÷ and +

Given equation - 43 × 16 − 7 + 91 ÷ 18 = −57

After changing the signs and digits in the given equation the equation is followed as, 

43 × 19 − 7 ÷  61 + 18 = −57

=> 43 × 19 − 7 ÷ 61 + 18 = −57

=> 43 × 19 − 0.11 + 18 = −57

=> 817 - 0.11 + 18 = −57

=> 835 - 0.11

=> 834.89 ≠ -57

LHS ≠ RHS

Option 3) 8 and 3; × and − 

Given equation - 43 × 16 − 7 + 91 ÷ 18 = −57

After changing the signs and digits in the given equation the equation is followed as, 

48 - 16 × 7 + 91 ÷ 13 = −57

=> 48 - 16 × 7 + 91 ÷ 13 = −57

=> 48 - 16 × 7 + 7 = −57

=> 48 - 112 + 7 = −57

=> 55 - 112 = -57

=> -57 = -57

LHS = RHS

Option 4) 8 and 6; ÷ and ×

Given equation - 43 × 16 − 7 + 91 ÷ 18 = −57

After changing the signs and digits in the given equation the equation is followed as, 

43 ÷ 18 − 7 + 91 × 16 = −57

=> 43 ÷ 18 − 7 + 91 × 16 = −57

=> 2.38 − 7 + 91 × 16 = −57

=>  2.38 − 7 + 1456 = −57

=> 1458.38 - 7 = −57

=> 1451.38 ≠ −57

LHS ≠ RHS

Hence, the correct answer is "8 and 3; × and −".

According to the given information:

1. T is the daughter of P, who is the son of H.

• T is the daughter of P,
• P is the son of H.

​

2. F is the daughter of Q, who is married to P.

3. C is the brother of E.

• F is the daughter of Q,
• Q is married to P.
• Thus C is the husband of H.

​

​This is the final diagram that can be deduced,

As we can see C is the father of P, who is the father of T.

Thus, C is T's father's father.

​Hence, the correct answer is "Father's father".

The logic followed here is:

MNQT is related to STWZ.

KLOR is related to FGJM.

All the alphabets share a common difference among them,

Similarly, 

JKNQ related to,

Hence, the correct answer is "GHKN".

The logic followed here is:

+7 is added to the initial number to get the related next number.

9761 is related to 9768.

• ​9761 + 7 = 9768

6357 is related to 6364. 

• 6357 + 7 = 6364​​

Similarly,

5349 is related ?

• 5349 + 7 = 5356

​Hence, the correct answer is "5356".

The logic followed here is:

• The related number is the square of the **initial number.**​
• ​4² = 16
• ​92 = 81

Similarly,

• ​162 = 256

​Hence, the correct answer is "256"

According to the given information:

• Parth is Aanya's maternal uncle.
• Poonam is the mother of Aanya.
• Varun is Poonam's husband.

• Alok is the paternal grandfather of Aanya.

• Varun is the son-in-law of Rina.
• Luv is the husband of Rina.
• Luv has two children.

​This is the final diagram that can be deduced

From the diagram, we can see Luv is Varun's wife's father.

Thus, Varun is Luv's Son-in-law.

​Hence, the correct answer is "Son-in-law".

According to the given information:

 

Option 1)  P − Q ÷ M × R → P is the brother of Q, Q is the wife of M, and R is the daughter of M.

 

P is R's mother's brother.

Option 2) P − Q × R → P is the brother of Q and R is the daughter of Q.

P is the uncle of R, but Q's gender is not defined.

Option 3) P + Q × R ÷ M → P is the sister of Q, R is the daughter of Q, and R is the wife of M.

P is the uncle of R, but Q's gender is not defined.

Option 4) P − Q ÷ R × M → P is the brother of Q, Q is the wife of R, and M is the daughter of R.

R is p's brother in law.

From the above diagram, only option 1 satisfies the condition of P being R's mother's brother.

In options 2 and 3, the gender of Q is not definite.

Hence, the correct answer is "P − Q ÷ M × R"

Confusion Points'A × B' means 'B is the daughter of A' this is a reverse relation.

The alphabets are positioned in the following order:

Given word - RAVISHING

The word can be represented as follows.

So, in the forward direction "HI".

In the backward direction " GI".

Thus, there are 2 pairs of letters in the word RAVISHING according to the English alphabetical series in both forward and backward directions.

Hence, the correct answer is "Two".

As per the given condition, let the baby crawls from point O towards east direction, then she turns left and right;

The diagram according to the given condition is,

Now, after crawling for sometime she turns towards left and again turns left.

Therefore the diagram is,

Here,the direction in which the baby is facing now is West.

Hence, the correct answer is "West".

The logic followed here is:

As per the given condition the word PUNCTUATION is coded as;

Similarly, 

As per the given logic, PACT can be coded as;

Hence the correct answer is "8491".

Given:

A * Z means A is greater than Z

A # Z means A equal to Z

A + Z means A is less than or equal to Z

A − Z means A is neither greater than nor equal to Z,

Let us first decode the given symbols and then draw a family tree.

Given expression: Z # P + T − U * C # M

Now break the code Z = P ≤ T < U > C = M

Conclusions:

I. Z < U → True (as Z = P ≤ T < U gives; as Z ≤ T and T < U so Z < U; True).

II. M > U → False (as U > C = M gives; as U > M so M > U; False).

Hence, the correct answer is “Only I”.

Given statement : B < M = R ≤ T; R > C > W

On combining : B < M = R > C > W; B < M = R ≤ T

Conclusions :

I. B < C →  FALSE (as B < M = R > C > W gives; B < R and R > C → clear relationship between B and C cannot be determined).

II. B < T → TRUE (as B < M = R ≤ T gives; B < T → clear relationship between B and T can be determined).

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

As per the given question the last three letters of the word BASKET are written at the starting and the first three letters of the word are written at the end as;

Thus, the word BASKET is written as EKTABS.

Similarly,

By applying the same logic, the last three letters of the word PENCIL are written at the starting and the first three letters of the word are written at the end as;

Thus, the word PENCIL is written as ICLEPN.

Hence, the correct answer is ICLEPN.

Decoding the information,

 

Given equation: 6 × 16 + 2 ÷ 4 − 3 = 14 + 7 ÷ ? − 2       

After replacing the sign from left to right and using BODMAS rule, we get  

⇒ 6 - 16 ÷ 2 + 4 × 3 = 14 ÷ 7 + ? × 2

⇒ 6 - 8 + 4 × 3 = 2 + ? × 2

⇒ 6 - 8 + 12 = 2 + ? × 2

⇒ 18 - 8 = 2 + ? × 2

⇒ 10 = 2 + ? × 2

⇒ 10 - 2 = ? × 2

⇒ 8 = ? × 2

⇒ 8 ÷ 2 = ?

⇒ ? = 4

Hence, the correct answer is "4".

Given:

WALK             MINT            TALL               BARE

The second letter of the third word from right:

WALK             MINT            TALL               BARE

The third letter of the first word from left:

WALK             MINT            TALL               BARE

The letters are there between I and L is:

I           J          K         L

Hence, “Two” is the correct answer.

The table is alphabets place value:

Given:

CAE : GEI 

Similarly,

Option(1): FDH : LJN

Hence, "Option (1)" is the correct answer.

Given:

WALK        MONK       TALL        DARE

If the last letter of each word is replaced by the next letter:

WALL        MONL       TALM        DARF

And all the vowels in each word are replaced by 'E'

WELL         MENL       TELM       DERF

WELL → A well is a hole that is dug, drilled, or cut into the earth in order to reach a supply of water, oil, or gas.

MENL → Not a meaningful word.

TELM → Not a meaningful word.

DERF → Not a meaningful word.

There are one meaningful English words that will be formed.

Hence, “Walk” is the correct answer.

Given statements: A = F < K ≥ P = U

Conclusions:

I) A > P → False (as A = F < K ≥ P; gives A < K and K ≥ P → clear relationship between A and P cannot be determined).

II) A = P → False (as A = F < K ≥ P; gives A < K and K ≥ P → clear relationship between A and P cannot be determined).

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

The pattern followed here is:

Hence, '50' is the correct answer.

The pattern followed here is:

 

Hence, the correct answer is "CD13".

The pattern followed here is:

Hence, '110' is the correct answer.

The table is alphabets place value:

Given:

DEAF - WVZU - VUYT

Similarly,

Option (4): ORANGE - LIZMTV - KHYLSU

Hence, "Option (4)" is the correct answer.

Table show alphabet serial number –

The pattern followed is,

1)  LKP : NPQ

2)  HJV : JQW

3)  KST : MHV

4)  QDY : SWZ

All follow the same pattern, except 'KST : MHV’.

Hence, “KST : MHV” is the odd one.

The image obtained when the paper is unfolded is,

Hence, option 1 is the correct answer.

The logic followed here is:

• If we rotate figure 45⁰ anticlockwise direction we get all the figures.

Now check all the options,

After following this pattern we get options (1), (2) and (3) but option (4) doesn't get..

Hence, "Option (4)" is different.

Given:

1. Navya's rank is 8th from the top and Dharitri's rank is 12th from the bottom. Shivalika's rank is exactly at the middle of Navya's and Dharitri's ranks.

2. Shivalika's rank is 15th from the bottom

Number of students between Shivalika and Dharitri:

=> Number of students between Shivalika and Dharitri = Shivalika rank from bottom - Dharitri rank from the bottom - 1

=> Number of students between Shivalika and Dharitri = 15 - 12 - 1 = 3 - 1 = 2

Because Shivalika's rank is exactly at the middle of Navya's and Dharitri's ranks;

• So, the number of students between Shivalika and Navya's = the number of students between Shivalika and Dharitri = 2
• The number of students between Navya and Dharitri = students between Shivalika and Navya's + students between Shivalika and Dharitri + 1
• The number of students between Navya and Dharitri = 2 + 2 + 1 = 5

Dharitri rank from the top:

=> Dharitri rank from the top = Navya rank from the top +  Number of students between Navya and Dharitri + 1

=> Dharitri rank from the top = 8 + 5 + 1 = 14

Total number of students in the class:

=> Total number of students = Dharitri rank from the top + Dharitri rank from the bottom - 1

=> Total number of students = 14 + 12 - 1 = 26 - 1 = 25

Hence, "25" total number of students in the class.

Six Persons: S, T, U, V, W and X

Facing: North

1. W and T are sitting at the fourth position from the left end and the right end, respectively.

2. U and X are not the immediate neighbours of T and W.

3. S is sitting at the fifth position from the right end.

So, final sitting arrangement:

Hence, “V” is sitting at the second position from the right end.

Statements:

All fruits are flowers.

All flowers are buds.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some buds are fruits → True (because all fruits are flowers and all flowers are buds so all fruits are buds so some buds are also fruits)

II. Some buds are flowers → True (because all flowers are buds so some buds are also flowers)

Hence, “Both the conclusions follow".

The logic followed here is:

In figure A and B:

• Alphabet change into next alphabets.
• Then it is change into mirror image.

Similarly, 

In figure C and D:

• Alphabet change into next alphabets.
• Then it is change into mirror image.

Hence, "Option 3" is the correct answer.

The embedded part of this image is:

Hence, option (2) is the correct answer.

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

1) The triangle rotates clockwise direction corner to corner.

• Triangle is divided into four parts one by one, one part becomes dark.

2) The heart rotates clockwise direction corner to corner.

• Every time it is flipped horizontally.

3) The middle letter replaces by the following alphabet letter.

Final series is:

Hence, ‘option 3’ is the correct answer.

1. Kashi is standing fourteenth from the right. Sana is fifth to the right of Kashi

So, Sana is from right,

Sana position from the right = Kashi position from the right - Sana position from to the right of Kashi

Sana position from the right = 14 - 5 = 9th

2. Sana is thirteenth from the left.

=> The number of students in the row = Sana position from the left + Sana position from the right - 1

=> The number of students in the row = 13 + 9 - 1 = 22 - 1 = 21

Hence, total “21” students in the row.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘RPM’.

Hence, “RPM” is the odd one

Table show alphabet serial number –

The pattern followed here is,

Hence, “GH64” is the complete series.

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

• 1st to 2nd figure triangle shifted to second next part of square.
• 2nd to 3rd figure triangle shifted to next part of square.
• 3rd to 4th figure triangle shifted to second next part of square.

​

​

Note:- 3rd image is the mirror image of 2nd image similarly 4th image is the mirror image of 1st image.

Hence, ‘Option 1’ is the correct answer.

The pattern followed here is:

 

Hence, the correct answer is "13J".

The shaded part represents the total number of people who are taking Singing classes.

The total number of people who are taking Singing classes = 18 + 11 + 47 + 45 = 121

Hence, ‘121’ is the correct answer.

The shaded part represents the number of people taking classes only Dancing and those taking all three classes.

The number of people taking classes only Dancing = 11

The number of people taking all three classes = 51

The difference between the number of people taking classes of only Dancing and those taking all the three classes = 51 - 11 = 40

Hence, ‘40’ is the correct answer.

The correct answer is Aditya L1.

Key Points

• Aditya L 1 is a planned coronagraphy spacecraft to study the solar atmosphere.
• It will be inserted in a halo orbit around the L1 point between Earth and Sun where it will study the solar atmosphere, solar magnetic storms, and its impact on the environment around Earth.
• It is the first dedicated Indian mission to observe Sun, it is planned to be launched in January 2023 aboard a PSLV-XL launch vehicle.

Additional Information

• Indian Space Research Organization is the national space agency of India, headquartered in Bangalore.
• Solar Orbiter is an international cooperative mission between ESA (the European Space Agency) and NASA that addresses a central question of heliophysics.
• Gaganyaan mission, the country's first manned space flight by ISRO. The objective of the Gaganyaan program is to demonstrate the indigenous capability to undertake human space flight missions to LEO.
• Chandrayaan-3 is a planned third lunar exploration mission by the Indian Space Research Organisation.

The correct answer is 30

Key Points

• The 2021 ISSF World Cup is the annual edition of the ISSF World Cup in the Olympic shooting events, governed by the International Shooting Sport Federation.
• 2021 ISSF World Cup New Delhi was held from 18 to 29 March 2021 at the Dr. Karni Singh Shooting Range in New Delhi.
• India secured 30 medals which included 15 gold, 9 silver, and 6 bronze.
• The USA stands at the second position preceded by India at the1st Position.

Additional Information

• The ISSF World Cup was introduced by the International Shooting Sport Federation in 1986 to provide a homogeneous system for qualification to the Olympic shooting competitions.
• It still is carried out in the Olympic shooting events, with four competitions per year in each event.

The correct answer is Albert Einstein

Key Points

• The equation E = mc² states that the amount of energy possessed by an object is equal to its mass multiplied by the square of the speed of light.
• The mass-energy relation, moreover, implies that, if energy is released from the body as a result of such a conversion, then the rest mass of the body will decrease.

Additional Information

Concept:

Mass-Energy:

• Einstein showed from his theory of special relativity that it is necessary to treat mass as another form of energy.
• Before the advent of this theory of special relativity, it was presumed that mass and energy were conserved separately in a reaction.
• However, Einstein showed that mass is another form of energy and one can convert mass-energy into other forms of energy, say kinetic energy and vice-versa.
• Einstein gave the famous mass-energy equivalence relation ⇒ E = mc2
• Where E = energy, m = mass and c = 3 × 108 m/sec = velocity of light in vacuum

According to the Theory of Special Relativity:

1. The Laws of physics remain the same for all observers who are non-accelerating (i.e. not in motion).
2. The speed of light in the vacuum is completely independent of the observer's motion.
3. No particle which carries energy and has a mass can travel at the speed of light.
4. And the most amazing idea is that the perception of time will change in every frame of reference.

• Ernest Rutherford was a New Zealand physicist who came to be known as the father of nuclear physics.
• Sir Joseph John Thomson was a British physicist and Nobel Laureate in Physics, credited with the discovery of the electron, the first subatomic particle to be discovered.
• Sir James Chadwick, was an English physicist who was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron in 1932.

The correct answer is Dholavira

Key Points

• Dholavira is one of the two largest Harappan sites in India and 5th largest in the subcontinent.
• It is located in Rann of Kutch, Gujarat.
• The site was unearthed by the Archeological Survey of India (ASI) in 1967.
• Dholavira has one of the world’s earliest water conservation systems ever excavated.
• The inhabitants of Dholavira were master water conservationists.
• No significant rivers were flowing by, just two rivulets — Mansar and Manhar.
• Nine reservoirs were built around the city to store water.
• The city itself was divided into three parts — the Citadel, the Middletown, and the Lower town.

Additional Information

• UNESCO has included Dholavira of Kutch in the list of World Heritage Sites in 2021. It has become the 40th World Heritage Site of India.
• Harappa is an archaeological site in Punjab, Pakistan, and the first Indus site to be discovered.
• Mohenjo-Daro is an archaeological site in the province of Sindh, Pakistan. It is a designated UNESCO World Heritage Site.
• Surkotada is an archaeological site located in Rapar Taluka of Kutch district, Gujarat, India which belongs to the Indus Valley civilization.

The correct answer is Bhupendra Patel

Key Points

• The Chief Minister of Gujarat is the chief executive of the government of the Indian state of Gujarat.
• Bhupendra Patel became the Chief Minister of Gujarat in September 2021.
• The chief minister's term is for five years and is subject to no term limits, given that he has the confidence of the assembly.

Additional Information 

• The state of Gujarat was created on 1 May 1960, composed of the Gujarati-speaking districts of Bombay State following the Mahagujarat Movement.
• Jivraj Narayan Mehta of the INC was the inaugural chief minister.
• Narendra Modi of the BJP is the longest serving chief minister for twelve and a half years from 2001 to 2014.
• Anandiben Patel was the first woman Chief Minister of Gujarat state.

The correct answer is Atal Bihari Vajpayee.

Key Points

• Atal Bihari Vajpayee was an Indian politician and diplomat who served three terms as the prime minister of India.
• First for a term of 13 days in 1996, then for a period of 13 months from 1998 to 1999, followed by a full term from 1999 to 2004.
• Vajpayee was one of the co-founders and a senior leader of the Bharatiya Janata Party (BJP).
• He was the first Indian prime minister not of the Indian National Congress to serve a full term in office. He was also a renowned poet and writer.
• Among the given options, Atal Bihari Vajpayee was the prime minister who never presented the budget of India.

Additional Information

• Indira Gandhi: Indira Priyadarshini Gandhi was an Indian politician and a central figure of the Indian National Congress. **She was elected as 3rd prime minister of India in 1966 and was also the first and, to date, only female prime minister of India.**She served as Prime Minister from 1966 to 1977 and 1980 to 1984. She held the Finance portfolio in 1969 and presented the 1969-70 budget.
• Manmohan Singh - He was Prime Minister from 2004 to 2014. He had previously served as Finance Minister from 1991 to 1996 and presented several budgets during this period.
• Jawaharlal Nehru was an Indian anti-colonial nationalist, secular humanist, social democrat, and author who was a central figure in India during the middle of the 20th century. He was the first prime minister of India from **15 August 1947 to 26 January 1950.**He was the first Prime Minister and Finance Minister of independent India. He presented the budget from 1947 to 1958.

The correct answer is Buddhism

Key Points

• A stupa is a mound-like or hemispherical structure containing relics that is used as a place of meditation. A related architectural term is a chaitya, which is a prayer hall or temple containing a stupa.
• In the post-Mauryan period, the 'Stupa' architecture is associated with Buddhism.
• Buddhism is one of the world's largest religions and originated 2,500 years ago in India.
• Buddhism is an Indian religion founded on the teachings of Gautama Buddha, a Śramaṇa also called Shakyamuni.
• Buddhists believe that human life is one of suffering and that meditation, spiritual and physical labour and good behaviour are the ways to achieve enlightenment or nirvana.

Additional Information

• Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest religion, with about 2.8 billion followers, representing one-third of the global population.
• Jain Dharma is an ancient Indian religion. The three main pillars of Jainism are ahiṃsā (non-violence), anekāntavāda (non-absolutism), and aparigraha (asceticism).
• Hinduism is the world's oldest religion, It is the world's third-largest religion, with over 1.2 billion followers, or 15–16% of the global population, known as Hindus.

The correct answer is Guwahati

Key Points

• The 36th National Junior Athletics Championships 2021 was held at Guwahati from 6th to 10th February.
• Haryana (21 gold, 20 silver, 14 bronze) finished on top of the medals tally while Tamil Nadu (13 gold, 12 silver, 12 bronze) and Uttar Pradesh (13 gold, 8 silver, 14 bronze) finished second and third respectively.

Additional Information

• Bhubaneswar is the capital and largest city of the Indian state of Odisha. Bhubaneswar's major sporting arena is the Kalinga Stadium, having facilities for athletics, football, hockey, basketball, tennis, table tennis, and swimming.
• Major sporting venues in New Delhi include the Jawaharlal Nehru Stadium, Ambedkar Stadium, Indira Gandhi Indoor Stadium, Arun Jaitley Stadium, R.K. Khanna Tennis Complex, Dhyan Chand National Stadium, and Siri Fort Sports Complex.

The correct answer is Value of Gravitational Constant

Key Points

• The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), is denoted by G.
• Henry Cavendish gave the value of this constant G.
• In SI units, its value is approximately 6.674 × 10⁻¹¹ m³kg⁻¹s⁻².
• Henry Cavendish was an English natural philosopher and scientist who was an important experimental and theoretical chemist and physicist.

Additional Information

• Mass-energy equivalence entails that the total mass of a system may change, although the total energy and momentum remain constant.
• According to the quantum theory, energy is held to be emitted and absorbed in tiny, discrete amounts.
• The first evidence of radioactivity was a photographic plate, wrapped in black paper and placed under a piece of uranium salt by Henri Becquerel on February 26, 1896.

The correct answer is Karnataka

Key Points

• Karaga is a folk dance of Karnataka and parts of Karnataka which originated as a ritual dedicated to Draupadi as known in these parts as Droupadmma.
• The garage itself is a mud pot, on which stands a tall floral pyramid that is balanced on the carrier's head.
• This festival that takes place in the central part of the city is called Bangalore Karaga.

Additional Information

• Makar Sakranti is the top harvest festival in Uttar Pradesh.
• Onam is the most important and popular festival in Kerala. Celebrated with much pomp and fervor, Onam is a harvest festival. Onam is also called Thiruonam.
• Jagannath Ratha Yatra is the famous festival of Odisha.

The correct answer is John A Wheeler.

Key Points

• The term “black hole“ was itself coined in 1968 by the Princeton physicist John Wheeler.
• A black hole is a place in space where gravity pulls so much that even light can not get out.
• The gravity is so strong because matter has been squeezed into a tiny space.
• The most common black holes are probably formed by the collapse of massive stars.

Additional Information

• Sir Chandrasekhara Venkata Raman was an Indian physicist known for his work in the field of light scattering. Raman received the 1930 Nobel Prize in Physics for the discovery and was the first Asian to receive a Nobel Prize in any branch of science.
• Kip Stephen Thorne is an American theoretical physicist known for his contributions to gravitational physics and astrophysics. Thorne was awarded the 2017 Nobel Prize in Physics.
• Homi Jehangir Bhabha, was an Indian nuclear physicist, founding director, and professor of physics at the Tata Institute of Fundamental Research. He was known as the "Father of the Indian nuclear programme", Bhabha was also the founding director of the Atomic Energy Establishment, Trombay (AEET) which is now named the Bhabha Atomic Research Centre in his honour.

The correct answer is Gene

Key Points

• Gene is a basic unit of heredity and a sequence of nucleotides in DNA that encodes the synthesis of a gene product, either RNA or protein.
• Thus**, Gene is the basic unit of inheritance.**
• The transmission of genes to an organism's offspring is the basis of the inheritance of phenotypic traits.
• These genes make up different DNA sequences called genotypes.

Concept:

• Genes are hereditary markers from which derive various characteristics like skin colour, height, etc.
• Each DNA molecule consists of sequences of Genes.
• Each gene is a particular set of instructions for specific functions.
• Each gene naturally consists of a sequence of nucleotides and base pairs.

Additional Information

The correct answer is Microorganisms cannot grow in the high salt concentration of Pickles

Key Points

• All pickles have an extended shelf life because both brine and vinegar belong to natural preservatives.
• Preservatives are chemical substances that are added to food to help: prevent spoiling. improve the appearance and/or maintain the food's nutritional quality.
• Antimicrobials preservatives destroy or delay the growth of bacteria, yeast, and molds.
• Concept:
• Food preservation is the technique to prevent food spoilage, food poisoning, and microbial contamination in food.
• Food preservation is done to preserve food for a longer time.​
• Objectives of food preservation:
• To prevent microbial contamination.
• To kill pathogens.
• To minimize food spoilage and food poisoning.
• Explanation:
• Pickling:
• Salt and extra edible oils are two main preservatives that are used in pickling.
• It prevents microbial growth.
• Pickles can be made, stored, and enjoyed throughout the year.
• Example: Raw mango to mango pickle.

 

Additional Information 

• Other methods of food preservation:
• Drying:
• It is the process of removal of water from food.
• It is the simplest method and prevents food spoilage by removing water.
• Example: Potato to chips.
• Cooling:
• Cooling at very low temperatures prevents microbial growth.
• Microbes do not get the optimum temperature they need for growth, their growth is inhibited.
• Example: Fresh peas to frozen peas.
• Sugaring:
• Sugar is a good moisture absorbent.
• Reducing moisture content restrains microbial growth.
• Example: Apple to apple jam.
• Salting:  
• Preservation by salt is known as salting.
• Salting helps to preserve fruits for the long term.
• Example: Salting of meats and fish.
• Adding chemicals:
• Adding synthetic preservatives like vinegar, sodium benzoate, sodium metabisulphite, etc.
• Other methods:
• Sterilization, radiation, smoking, etc.

The correct answer is 1969.

Key Points

• Apollo 11 (July 16–24, 1969) was the American spaceflight that first landed humans on the Moon.
• Apollo 11 was launched by a Saturn V rocket from Kennedy Space Center on Merritt Island, Florida.
• Commander Neil Armstrong and lunar module pilot Buzz Aldrin landed the Apollo Lunar Module Eagle on July 20, 1969, and Armstrong became the first person to step onto the Moon's surface.

Additional Information

• Luna 1 (launched on Jan. 2, 1959) was the first spacecraft to escape Earth’s gravity. Luna, a series of 24 unmanned Soviet lunar probes launched between 1959 and 1976.
• In 1979, the first experimental remote-sensing satellite which was built in India was launched namely Bhaskara-I. The images sent by it are used to study hydrology and forestry and oceanographic studies.

The correct answer is Kuchipudi

Key Points

• Raja and Radha Reddy are an Indian Kuchipudi dancing couple, gurus, and choreographers.
• They founded and run the Natya Tarangini Institute of Kuchipudi Dance in New Delhi.
• For their services to the field of arts, the Government of India has conferred on them the Padma Shri and Padma Bhushan awards.
• Kuchipudi is indigenous to the state of Andhra Pradesh.

Additional Information

• Bharatanatyam is a major form of Indian classical dance that originated in Tamil Nadu. Rukmini Devi Arundale is a famous personality of this form of dance.
• Kathak is one of the eight major forms of Indian classical dance. It is the classical dance form of Uttar Pradesh. Birju Maharaj is a famous personality of this form.
• Odissi is a dance form from the state of Odisha in eastern India. Madhavi Mudgal is famous for this dance form.

The correct answer is the Lithosphere

Key Points

• The lithosphere is the rigid, outermost rocky shell of a terrestrial planet or natural satellite.
• On Earth, it is composed of the crust and the portion of the upper mantle.
• It is bounded by the atmosphere above and the asthenosphere (another part of the upper mantle) below.
• The lithosphere can be divided into the oceanic and continental lithosphere.

Additional Information

• The innermost layer of the earth is called the “Core or Barysphere”. It is otherwise known as NIFE, because of the presence of Nickel and Ferrous (iron). This layer produces the earth's magnetic field.
• Earth's mantle is a layer of silicate rock between the crust and the outer core.
• The biosphere is made up of the parts of Earth where life exists. The biosphere extends from the deepest root systems of trees to the dark environment of ocean trenches, to lush rain forests and high mountaintops.

The correct answer is Option 2.

Key Points

• Jovian planets refer to a group of four planets in the solar system.
• They are also known as gas giants. The four Jovian planets are: Jupiter, Saturn, Uranus, and Neptune.
• The term 'Jovian' comes from the name of the planet 'Jupiter', thereby describing other gas planets in the solar system as Jupiter-like.
• They are massive planets, usually with a primary composition of gases or ice instead of solid matter such as rocks.
• The Jovian planets are larger than all other planets within the solar system and have many moons.
• Thus, option 2 is correct.

Additional Information

• Terrestrial planets are those like Earth which are characterized by solid surfaces, compact size, and closer proximity to the Sun.
• Terrestrial planets include Mercury, Venus, Earth, and Mars. These planets are relatively small in size and in mass.

The correct answer is New Delhi.

Key Points

• National Institute of Indian Classical Dance (NIICD)​ is an Indian classical dance institution situated in New Delhi. It is well-known and renowned all across the nation.
• NIICD​ is an open-for-all-ages dance institute formed to spread the love for Indian classical dances around the world.
• NIICD offers classes for Bharatanatyam and Kathak.

Additional Information

• International Dance Day is a global celebration of dance, is celebrated every year on 29 April, which is the anniversary of the birth of Jean-Georges Noverre, the creator of modern ballet.
• Classical Dances in India:
• Bharatnatyam - Tamil Nadu
• Kathak Uttar - Pradesh
• Kuchipudi Andhra - Pradesh
• Odissi - Odisha
• Kathakali - Kerala
• Sattriya - Assam
• Manipuri - Manipur
• Mohiniyattam - Kerala

The correct answer is Cnidoblasts

Key Points

• Cnidoblasts or nematoblasts are stinging cells found in cnidaria or Coelenterata.
• Each of them bears a stinging cell organelle called nematocyst which is used in the offence, defence, and attachment of the animal.
• These are present on the body surface and tentacles.

Additional Information

• Ostia are the tiny pores present on the surface of sponges, from where water enters and goes to the spongocoel.
• Choanocytes are specialized cells that have a single flagellum surrounded by a net-like collar of microvilli.
• Spongocoel is the large, central cavity of sponges. Water enters the spongocoel through hundreds of tiny pores (ostia) and exits through the larger opening (osculum).

The correct answer is 1.2 m.

Key Points

Given that,

The person can't see objects beyond 1.2 m directly

So, in order to view the distances beyond 1.2 m, the focal length of the lens should be 1.2 m.

Now, the power

P = 1/f

P = 1/1.2

P = 0.83 Dioptre(D)

So, if a person suffers from Myopia, the corrective lens will be the concave or diverging lens.

Additional Information

• A concave lens is a type of lens that diverges a straight light beam from the source into a diminished, upright, virtual image.
• According to the sign convention, the focal length of a concave lens is always negative.
• It has the ability to create only Virtual and erect images.
• They’re used to treating myopia because they make faraway items appear smaller than they are.

The Correct answer is Speaker.

Key Points

   Money Bill.

• A Money Bill is a Specific Kind of Bill, defined Very Precisely, It must deal only with Matters Specified in Article 110(1)(a) to (g).
• A Money Bill is Certified by Speaker.
• Only those Bill that Carry the Speaker's Certification is Money Bills.
• Money Bill was only Introduced in Loksabha, not Rajya Sabha.
• The Rajya Sabha can neither reject a Money Bill nor Amend it.
• If a Money Bill is not returned by the Rajya Sabha within 14 days, it shall be deemed to have been passed by both Houses in the form in which it was passed by the Look Sabha.

Additional Information

      Speaker of the Lok Sabha 

• The Speaker and the Deputy Speaker are Chosen by the Lok Sabha from among its Members.
• The Speaker Presides Over the Lok Sabha.
• The Speaker Presides over a Joint Sitting of the Two Houses of Parliament.
• The Speaker normally Holds Office during the Life of the House.

The Correct answer is 2011.

Key Points

• RBI Constituted a panel in 2010 to study issues and concerns in the microfinance sector.
• This Committee was headed by YH Malegam.
• The Malegam Committee submitted its report to the RBI in January 2011.

       Recommendations of the Malegam Committee,

• Recommend that a separate category be created for NBFCs operating in the Microfinance Sector, such as NBFCs being designated as NBFC-MFI.
• NBFC-MFI Should Satisfy the Following Conditions -

          – Not less than 90% of its total assets are in the nature of "qualifying assets“

• NBFC which does not qualify as an NBFC-MFI should not be permitted to give loans to the microfinance sector.

The Correct answer is Naujawan Bharat Sabha.

Key Points

• Bhagat Singh Founded Naujawan Bharat Sabha in March 1926.
• The objective of this organisation was to encourage revolution against British rule by rallying the peasants and workers.
• Bhagat Singh established contact with Sohan Singh Josh and through him ‘the worker and peasants party’ which brought out the monthly magazine Kirti in Punjabi.
• Bhagat Singh:
• Bhagat Singh was born on September 1907, in Lyallpur western Punjab, India ( Now in Pakistan)
• In 1923, he joined National College in Lahore founded by Lala Lajpat Rai.
• Bhagat Singh was deeply affected by the Jallianwala Bagh massacre.
• In 1928, He established the Hindustan Socialist Republican Association (HSRA) along with Chandrashekhar and others.
• Bhagat Singh and Batukeshwar Dutt, on April 8th,1929, threw a bomb in the Central Legislative Assembly.
• On 23 March 1931 Bhagat Singh, Rajguru and Sukhdev were Hanged by the British Government.
• At that time his age was a little more than 23 years.

The Correct answer is 14 years. 

Key Points     Fundamental Rights 

• Part lll Constitution of India and **Article (12-35) known as the **Magna Carta of India.
• This is called Fundamental because it is Guaranteed and protected by the constitution.
• Article 24 of the Indian Constitution,
• Prohibition of child labour in Factories and Hazardous Industries.
• It is a Special Provision made for the Protection of Children.
• Under this Article, no child below the age of  14 years can be Employed to Work in any Factory or Mine Or Engaged in any other Hazardous Employment.
• Punishment 6 months to 2 years Or 5000 rupees Or Both.

The Correct answer is Nandas.

Key Points

• Mahapadma overthrew the Shishunag Dynasty and established a new dynasty known as Nanda Dynasty
• Mahapadma is known as Sarvakshatrantak i.e, Uprooter of all the Kshatriyas.
• Mahapadma was Succeeded by His eight sons. Dhanananda was the last one.
• The Nanda Dynasty was Overthrown by another Dynasty Known as the Muaryas Dynasty, with Chandragupta Maurya as the Founder.

Additional Information 

Huns:

• During the Skandagupta, the last Ruler of the Gupta Dynasty was Invaded by Huns.
• The continuous attacks of the Huns Weakened the Gupta empire.

Shunga:

• The Sunga Dynasty was Established by Pushymitra Sunga.
• Pushyamitra was Succeeded by His Son Agnimitra.
• Agnimitra was the Hero of the Famous Kalidasa Drama Malvikagnimitra.

Sakas

• The Sakas, also known as Scythians.
• Sakas were nomadic tribes originally from central Asia.
• The most famous sakas ruler in India was Rudradaman.

The Correct answer is Cotton.

Key Points

• The crops grown in the rainy season i.e, from June to September are called Kharif crops. It is also called Monsoon crops.
• ​These crops require more temperature and humid conditions.​
• Cotton, Maize, Bajra, Red Gram, Paddy, Soyabean, Groundnut, Sugarcane, and Tea are examples of Kharif crops. Hence Option 4 is the correct answer.

 Additional Information

• The Crops grown in the winter season i.e, from October to March are called Rabi Crops.
• It Requires a low temperature at the time of sowing and more temperature at the time of harvesting.
• Wheat, Barley, Mustard, Pea, and Green gram are examples of Rabi Crops.

The correct answer is Russia.

Key Points

• The Anglo-Russian Convention of 1907 or Convention between the United Kingdom and Russia relating to Persia, Afghanistan, and Tibet was signed on August 31, 1907, in Saint Petersburg.
• The convention brought shaky British–Russian relations to the forefront by solidifying boundaries that identified respective control in Persia, Afghanistan, and Tibet.
• Thus, England had developed strained relations in Tibet with Russia which were later resolved through a convention.

Additional Information

• Currently, the Tibetan government in exile is working closely with the British government's foreign office to nullify the Communist Party of China's (CPC) stand that Tibet is a part of China.

The Correct answer is Integrated Judiciary.

Key PointsFederalism is an Institutional Mechanism to Accommodate two sets of Polities i.e first is at the Centre or National level and the Second is at the Provincial and Regional level. Both the set of Polities are Autonomous in their own Sphere.

Federal Features of Indian Constitution.

• Written Constitution
• Two Government Power Divisions (Centre and States)
• Supremacy of Constitution
• Independent Judiciary
• Bicameralism

Additional Information

• Unitary State,
• A state is unitary when governed by a single unit like the only Centre rule.
• Features of Unitary States,
• Single Citizenship.
• Single Constitution.
• Integrated Judiciary.

The Correct answer is Where all the factors of production are fully employed in the production process.

Key Points

• The Factor of production is a term used to categorize all of the resources and contributions that go into producing a good and services.
• Land, Labor, Capital, and Entrepreneurship are four factors of production.
• The above four create all the goods and services that make up an economy.
• If any of the Factors of production are scarce or high in demand, it affects and impacts the economy, because the product will then be sold for a higher price or consumed at a greater rate.

The Correct answer is Vasudeva.

Key Points

• ​​Vasudeva Founded Kanva Dynasty.
• He was Minister of Devbhuti(Last Ruler of Sunga Dynasty).
• The Kanva Dynasty's rule came to an end in 28 BC.

Additional Information

• Narayana, Susharman, and Bhumi Mitra were the others king of the Kanva Dynasty.
• The last Kanva Ruler Susharman was Overthrown by a successor of Simuka of the Satavahana Dynasty.

The correct answer is 1995.

Key Points

• The National Highways Authority of India or NHAI is an autonomous agency of the Government of India.
• It was set up in 1995 under the NHAI Act, 1988..

Additional Information

• NHAI is responsible for management of a network of over 50,000 km of National Highways out of 1,32,499 km in India.
• It is a nodal agency of the Ministry of Road Transport and Highways.

The correct answer is 12 members.

Key Points

• 12 out of the 250 members of the Rajya Sabha are nominated by the President.
• They are nominated for six-years term for their contributions towards arts, literature, sciences, and social services.

Additional Information

• The Rajya Sabha should consist of not more than 250 members.
• 238 members representing the States and Union Territories.
• 12 members nominated by the President.
• Rajya Sabha is a permanent body and is not subject to dissolution.

The correct answer is 1985.

Key Points

• The Supreme Court in Olga Tellis vs Bombay Municipal Corporation held that pavement dwellers are different from trespassers.
• The judgement from 1985 ruled that eviction of pavement dwellers using unreasonable force, without giving them a chance to explain is unconstitutional.

Additional Information

• The following fundamental rights were upheld in this ruling -
• Article 32 - The right to move the Supreme Court by appropriate proceedings for the enforcement of the rights.
• Article 21 - Right to personal liberty.
• Article 19(1) - The right to life and livelihood.

The correct answer is 1978-79.

Key Points

• The integrated Rural Development Programme (IRDP) was launched in 1978-79.
• Objective: to deal with the dimensions of rural poverty in the country.
• It continued till 1999.

Additional Information

• IRDP, along with 5 other schemes, was rebranded as the Swarnjayanti Gram Swarozgar Yojana.
• SGSY was launched on April 1, 1999.
• The following schemes were merged to form it -
• Integrated rural development programme (IRDP)
• Training of rural youth for self employment (TRYSEM)
• Development of Woman And Children In Rural Areas (DWCRA)
• the Ganga Kalyan Yojna (GKY)
• the million wells scheme (MWS)
• Objective: to bring every assisted family above the poverty line within three years by providing them income generating assets through a mix of bank credit and Government subsidy.

The correct answer is seasonal unemployment.

Key Points

• It is an unemployment that occurs during certain seasons of the year.
• For example, agriculture is seasonal and agricultural labourers only get work during those seasons.

Additional Information

• Cyclic Unemployment - During a business cycle, people are hired during high economic growth, but find themselves unemployed during recession.
• Under employment - In this, people are able to find employment only for shorter than normal periods, leading to high volatility.
• Disguised unemployment  - Primarily seen in agriculture and unorganized sectors, more people are employed than needed, leading to very low wages.

The correct answer decreases.

Key Points

• Atmospheric pressure is inversely proportional to the altitude.
• As altitude increases, atmospheric pressure decreases.
• Thus, as we go higher up the Himalayas, the atmospheric pressure will fall, making it harder to breathe.

Additional Information 

• Air pressure at sea level averages near 1013 hectopascals (millibars).
• It decreases at a rate of approximately 1 hectopascal per 10 meters (33 feet) of ascent.
• This is true up to an altitude of approximately 18,000 feet where the air pressure is near 500 hectopascals.
• From there and on it decreases at a slower rate.

The correct answer is Brahman.

Key Points

• The Kadambas were an ancient royal family of Karnataka.
• They ruled northern Karnataka and the Konkan from Banavasi in present-day Uttara Kannada district.
• The kingdom was founded by Mayurasharma in 345 CE and declined in 540 CE.

Additional Information

• The caste system divides Hindus into four main categories - Brahmins, Kshatriyas, Vaishyas and the Shudras.
• Brahmins - They are designated as the priestly class as they serve as priests and religious teachers.
• Kshatriyas - They are warriors and rulers ranking immediately below the Brahmans.
• Vaishyas - They are mainly people pursuing agriculture, taking care of cattle, trade and other business pursuits.
• Shudras - They are traditionally artisans and labourers.

The correct answer is Assam, Meghalaya, Mizoram,Tripura.

Key Points

• The Sixth Schedule consists of provisions for the administration of tribal areas in the states of Assam, Meghalaya, Tripura, and Mizoram.
• It is in accordance with Article 244(2) and Article 275(1) of the Indian Constitution.

Additional Information

• Objective: To safeguard the rights of the tribal population through the formation of Autonomous District Councils (ADC).
• In September 2019, the National Commission for Scheduled Tribes recommended the inclusion of Ladakh under the Sixth Schedule.

The correct answer is Number of live births per thousand persons in a year.

Key Points

• The birth rate in a period is the total number of live births per 1,000 population divided by the length of the period in years.
• As per the last census of 2011, birth rate in India stands at 21.8 infants born per 1000 people each year.

Additional Information

• The mortality rate or death rate is defined as the number of deaths in a particular population during a specific time.
• According to World Bank's data, the mortality rate or crude death rate in India is 7.30 per 1000 persons per year.
• In India, approximately 26789 deaths are reported per day.
• With the death rate much lower than the birth rate, the population of India is on an upward trajectory.

The correct answer is Puducherry.

Key Points

• Pondicherry or Puducherry has of four separate districts - Pondicherry, Karaikal, Yanam, and Mahé.
• Karaikal is a major port city of East Coast of India.
• This is the birthplace of Karaikal Ammaiyar.
• The major attraction in the area is Saneeswara Temple, Sri Kailasanathar Temple, Navagraha Temples and Ammaiyar Temple.
• Madras High Court has jurisdiction over Tamil Nadu and the Union Territory of Puducherry.

Additional Information

• The Lakshwadeep region forms a single Indian district with 10 subdivisions.
• Kavaratti serves as the capital of the Union Territory.
• The region comes under the jurisdiction of Kerala High Court.
• Andaman and Nicobar has 3 districts - Nicobar, North and Middle Andaman, and South Andaman.
• ​Port Blair serves as the capital city.
• The region comes under the jurisdiction of Calcutta High Court.
• Jammu and Kashmir is divided into 14 districts.
• Srinagar serves as the summer capital and Jammu as the winter capital.
• Their is a full-fledged High Court of Judicature for the Jammu and Kashmir.

Shortcut Trick

Solve brackets inside out: (6 − 5) = 1.

Small bracket: (1 − 4 × 1 + 4) = 1 − 4 + 4 = 1.

Square bracket: [4 + 2 × 1 − 8] = 4 + 2 − 8 = −2.

Final calculation: 12 − 3 × (−2) ÷ 3 = 12 − (−6) ÷ 3 = 12 + 2 = 14.

∴ The correct answer is 14.

Alternate Method

Given:

Expression = 12 − 3[4 + 2(1 − 4(6 − 5) + 4) − 8] ÷ 3

Formula Used:

BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction)

Calculations:

⇒ 12 − 3[4 + 2(1 − 4(1) + 4) − 8] ÷ 3

⇒ 12 − 3[4 + 2(1 − 4 + 4) − 8] ÷ 3

⇒ 12 − 3[4 + 2(1) − 8] ÷ 3

⇒ 12 − 3[4 + 2 − 8] ÷ 3

⇒ 12 − 3[−2] ÷ 3

⇒ 12 − (−6) ÷ 3

⇒ 12 + 6 ÷ 3

⇒ 12 + 2 = 14

∴ The correct answer is 14.

Additional Information

BODMAS Rule

BODMAS stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction. It defines the order in which operations should be performed.

Types of Brackets

The order of solving brackets is Parentheses ( ), then Braces { }, and finally Square Brackets [ ].

Sign Rules

(−) × (−) = (+), (+) × (−) = (−), and (−) ÷ (+) = (−).

Given:

M.P = 1850

Two discounts = 20% and 30%

Formula used:

Successive discount = D₁ + D₂ - $\frac{D1 × D2}{100}$

S.P =( 100 - D )% M.P

S.P = Selling Price

M.P = Marked Price

D = Discount

Calculation:

Successive discount = 20 + 30 - $\frac{20 × 30}{100}$

⇒ (50 - 6)% = 44%

S.P = (100 - 44 )% × 1850

⇒ 5.6 × 185

⇒ 1036

∴ The answer is 1036.

Alternate MethodGiven:

Marked Price = 1850

Two discounts = 20% and 30%

Formula used:

S.P =( 100 - D )% M.P

Calculation:

S.P =( 100 - 20 )%× ( 100 - 30 )%  1850

⇒ 0.8 × 0.7 × 1850

⇒ 1036

∴ The answer is 1036.

Given:

$\sqrt[3]{512}$

Calculation:

$\sqrt[3]{512}$

= $\sqrt[3]{256×2}$

= $\sqrt[3]{128×2×2}$

= $\sqrt[3]{64×2×2×2}$

= $\sqrt[3]{4×4×4×2×2×2}$

= $\sqrt[3]{8×8×8}$

=8

Answer is 8.

Given:

Principal = ₹10,933

Rate = 5%

Seema = 16 years

hassan = 18 years

Formula used:

Amount = Principal $(\frac{100+R}{100})^{time}$ [ where R is rate percentage]

Calculation:

let X and Y be the sums of seema and hassan by dividing 10,933

The amount payable on maturity to Seema after 16 years would be the same as the amount payable on maturity to Hassan after 18 years

X $(\frac{100+5}{100})^{16}$ = Y $(\frac{100+5}{100})^{18}$

X = Y $(\frac{105}{100})^{2}$

$\frac{X}{Y}$ = $(\frac{21}{20})^{2}$

X:Y = 441:400

if 441a and 400a are the sums of seema and hassan 

Total sum = 441a + 400a

= 841a

841a = 10933

a = 13

Seema share 441a = 441 × 13

= 5733

Answer is 5733.

Shortcut Trick

Convert terms to decimals: 2⁰ = 1 and 2⁻¹ = 0.5.

Substitute values: (1 + 0.5) ÷ (0.5 − 1).

Calculate: 1.5 ÷ (−0.5) = −3.

∴ The correct answer is −3.

Alternate Method

Given: (2⁰ + 2⁻¹) ÷ (2⁻¹ − 2⁰)

Formula used: a⁰ = 1 and a⁻ⁿ = 1/aⁿ

⇒ 2⁰ = 1

⇒ 2⁻¹ = 1/2

⇒ Numerator = 1 + 1/2 = 3/2

⇒ Denominator = 1/2 − 1 = −1/2

⇒ Expression = (3/2) ÷ (−1/2)

⇒ Expression = (3/2) × (−2/1) = −3

∴ The correct answer is −3.

Additional Information

Zero Exponent Rule

Any non-zero base raised to the power of 0 results in 1, formulated as a⁰ = 1.

Negative Exponent Rule

A negative exponent represents the reciprocal of the base raised to the positive exponent: a⁻ⁿ = 1/aⁿ.

Division of Fractions

To divide two fractions, multiply the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c).

Shortcut Trick

Perimeter of the shape = Sum of curved boundaries + Straight boundaries.

Two semi-circles make one full circle: Circumference = 2 × π × r.

Visible straight lines are only the two lengths of the rectangle (15 cm each).

Perimeter = (2 × 22/7 × 14) + (2 × 15) = 88 + 30 = 118 cm.

∴ The correct answer is 118 cm.

Alternate Method

Given:

Radius of the semi-circles (r) = 14 cm

Length of the rectangle (L) = 15 cm

Width of the rectangle (W) = Diameter of the circle = 2 × 14 = 28 cm

Formula Used:

Perimeter of a composite shape = Sum of all outer boundaries.

Circumference of a semi-circle = πr.

Calculations:

⇒ Boundary 1 (Left Semi-circle) = π × r = (22/7) × 14 = 44 cm

⇒ Boundary 2 (Right Semi-circle) = π × r = (22/7) × 14 = 44 cm

⇒ Top boundary of rectangle = 15 cm

⇒ Bottom boundary of rectangle = 15 cm

⇒ Total Perimeter = 44 + 44 + 15 + 15

⇒ Total Perimeter = 88 + 30 = 118 cm

∴ The correct answer is 118 cm.

Additional Information

Perimeter of a Semi-circle

The total perimeter of a closed semi-circle includes the arc and the diameter: P = πr + 2r. In composite shapes, internal boundaries are excluded.

Area of Composite Shape

Area = Area of rectangle + Area of circle = (L × W) + πr². Here, Area = (15 × 28) + (22/7 × 14 × 14).

Circle Constants

For a circle with radius 7, 14, 21: The circumferences are 44, 88, 132 respectively. This is a common pattern in quantitative aptitude exams.

Given:

0.25% of z = 0.04

Calculation:

Convert decimals into fraction

$\frac{25}{10000}$ × z = $\frac{4}{100}$

z = $\frac{4}{100}$ × $\frac{10000}{25}$

z = 16

Answer is 16.

Given:

Area of the circular field is 560 m²

Formula used:

Perimeter of square = 4 × side

Perimeter of circle = 2πr 

Area of a circle = πr²

Area of a square = side²

Calculation:

πr² = 560

r² = 560 / π 

r = $\sqrt{\frac{560}{π}}$

Perimeter of a square and a circular field are the same

 2πr  = 4 × side

2 × π × $\sqrt{\frac{560}{π}}$ = 4 × side

Side of a square = $\frac{\sqrt{560×π}}{2}$  

Area of the square = side²

= $\frac{\sqrt{560×π}}{2}$ × $\frac{\sqrt{560×π}}{2}$

= 560 × π / 4 

= 140 × π

= 140 × $\frac{22}{7}$

= 440

Area of the square is 440 m²

Answer is 440m².

Given:

Average of five consecutive odd numbers is 61

Formula used:

Average = $\frac{Total\ Sum}{Number\ Of\ Terms}$

Calculation:

let the 5 consecutive numbers be x , x+2 , x+4 , x+6 , x+8

Average = $\frac{Total\ Sum}{Number\ Of\ Terms}$

61 = $\frac{x+x+2+x+4+x+6+x+8}{5}$

305 = 5x + 20

5x = 285

x = 57

Highest number = x+8 = 65

Lowest number = x = 57

Difference between the numbers is 65 - 57 = 8

Answer is 8.

Alternate MethodGiven:

Average of five consecutive odd numbers is 61

Concept  used:

Middle term of a  consecutive series will always be the average of the series

Calculation:

let the 5 consecutive numbers be x , x+2 , x+4 , x+6 , x+8

x+4 is the average 

x+4 = 61

x = 57

Highest number = x+8 = 65

Lowest number = x = 57

Difference between the numbers is 65 - 57 = 8

Answer is 8.

Given:

Dividing a number by 26, we get 85 as the quotient and 14 as the remainder

Formula used:

Quotient × Divisor + Remainder = Dividend

Calculation:

Quotient = 85 , Divisor = 26 , Remainder = 14

Quotient × Divisor + Remainder = Dividend

85 × 26 + 14 = Dividend  

= 2210 + 14

= 2224

The Number is 2224

Answer is 2224.

Alternate MethodGiven:

Dividing a number by 26, we get 85 as the quotient and 14 as the remainder

Formula used:

Quotient × Divisor + Remainder = Dividend

Calculation:

Unit digit method:

5 × 6 + 4 = 0 + 4

= 4

From the options, 

Answer is 2224.

Given:

First 30 natural numbers

Formula used:

Average of n natural numbers = $\frac{n+1}{2}$ (where n is any natural number)

Calculation:

Average of n natural numbers = $\frac{n+1}{2}$ 

= $\frac{30+1}{2}$

= 15.5

Answer is 15.5

Additional InformationAverage of n even numbers = n+1

Average of n odd numbers = n

Average of squares of n natural numbers =$\frac{(n+1)(2n+1)}{6}$

Average of cubes of n natural numbers = $\frac{(n)(n+1)^2}{4}$

Given:

Marked price = 7500

First discount = 18%

He offers a further discount of 10% if the buyer returns his old vacuum cleaner

Formula used:

Marked Price (100-discount)% = Cost Price(100+profit)%

Calculation:

Cost price is 30% less than Marked price

Cost Price = 7500 × $\frac{70}{100}$

= 5250

Step 1:Profit With return(P1)

Marked Price (100 - discount)% = Cost Price (100 + profit)%

7500 (100 -18)% (100 -10)% = 5250 (100 + P1)%

7500 × $\frac{82}{100}$ × $\frac{90}{100}$ = 5250 $\frac{100+P1}{100}$

 5535= 5250 $\frac{100+P1}{100}$

$\dfrac{553500}{5250}$= 100 + P1

$\dfrac{553500 - 525000}{5250}$ = P1 = $\dfrac{28500}{5250}$

Profit% of the retailer with the return of the old vacuum cleaner scheme = 5.43%

Step 2:Profit Without return (P2)

Marked Price (100-discount)% = Cost Price(100+profit)%

7500 (100-18)% = 5250 (100+profit)%

7500 × $\frac{82}{100}$  = 5250 $\frac{100+profit}{100}$

6150 = 5250 $\frac{100+profit}{100}$

$\dfrac{615000}{5250}$ = 100 + profit 

$\dfrac{615000 - 525000}{5250}$ =  $\dfrac{90000}{5250}$

Profit% of the retailer with the return of the old vacuum cleaner scheme = 17.14%

*Step 3:*The profit of the retailer with the return  is what percentage of the profit without the return 

= $\frac{28500}{90000}$ × 100

= 31.66

Approximately 32%

Answer is 32%.

Alternate MethodGiven:

Marked price = 7500

First discount = 18%

He offers a further discount of 10% if the buyer returns his old vacuum cleaner

Formula used:

Successive discount = Discount 1 + Discount 2 - $\frac{Discount 1 × Discount 2}{100}$

Profit = $\frac{(Selling\ Price - Cost\ price)}{Cost\ Price}$ × 100

Selling Price =( 100 - Discount )% Marked Price

Calculation:

According to the question only percentage is asked so don't take the amount in consideration

Let 100 be the Marked Price and 70 be the Cost Price

Step 1:Profit With return

Successive discount = Discount 1 + Discount 2 - $\frac{Discount 1 × Discount 2}{100}$

= 18 + 10 - 180/100

= 26.2%

Selling Price =( 73.8 )% × 100

= 73.8

Profit = $\frac{(3.8)}{70}$ × 100

= $\dfrac{38}{7}$

Step 2:Profit Without return

Selling Price =( 100 - 18 )% × 100

= 82

Profit = $\frac{(12)}{70}$ × 100

= $\frac{120}{7}$

*Step 3:*The profit of the retailer with the return  is what percentage of the profit without the return 

= $\frac{38}{120}$ × 100

= 31.66

Approximately 32%

Answer is 32%.

Given:

Larger Metal cube side = 6cm

Smaller cubes sides 3cm and 4cm

Formula used:

Volume of the cube = side³

Concept used:

Volume of the larger cube is equal to the sum of the volume of the 3 smaller cubes

Formula used:

let x be the side of the third cube

6 × 6 × 6 = ( 3³ + 4³ + x³ )

216 = 27 + 64 + x³

125 = x³

x = 5

Side of the third cube is 5cm

Answer is 5cm.

Alternate MethodLateral surface area of the cube = 4 side²

Total Surface area of the cube = 6 side²

Given:

HCF of 75 and 125 is in the form of 75m-125

Concept used:

HCF is Highest Common divisor

Calculation:

HCF (75 , 125)

HCF ( 25 × 3 , 25 × 5 )

HCF of 75 and 125 is 25

HCF of 75 and 125 = 75m - 125

25 = 75m - 125

75 m = 150

m = 2

Answer is 2.

Given:

An amount of Rs. 4,000 is borrowed at the interest rate of 7.5% (compounded annually)

As a part of repayment, Rs. 1,500 is paid in three instalments

Time = 3 years

Formula used:

Amount = Principal $(1+\frac{R}{100})^{time}$

Calculation:

In compound interest the amount after 1 year is the principal for the second year

STEP 1:

Amount after the first year

Amount = 4000 $(\frac{107.5}{100})$

Amount = 4300

1500 is paid as a installment every year for three years

Amount = 4300 - 1500

= 2800(principal for second year)

STEP 2:

Amount after the second year

Amount = 2800 $(\frac{107.5}{100})$

Amount = 3010

1500 is paid as a installment in second year

Amount = 3010 - 1500

= 1510(principal for third year)

STEP 3:

Amount after the third year

Amount = 1510 $(\frac{107.5}{100})$

Amount = 1623.25

1500 is paid as a installment in second year

Amount = 1623.25 - 1500

= 123.25

Remaining amount to be paid is Rs. 123.25

Answer is 123.25.

 Alternate Method

Given:

An amount of Rs. 4,000 is borrowed at the interest rate of 7.5% (compounded annually)

As a part of repayment, Rs. 1,500 is paid in three instalments

Time = 3 years

Formula used:

Remaining amount = { [ (Principal × $(1+\frac{R}{100})$ - instalment 1 ) × $(1+\frac{R}{100})$ - installment 2  ] ×  $(1+\frac{R}{100})$ - installment 3}

Calculation:

Remaining amount = { [ (4000 × $\frac{43}{40}$ - 1500 ) × $\frac{43}{40}$ - 1500 ] ×  $\frac{43}{40}$ - 1500}

= { [ (4000 × $\frac{43}{40}$ - 1500 ) × $\frac{43}{40}$ - 1500 ] ×  $\frac{43}{40}$ - 1500}

= { [ (4300 - 1500 ) × $\frac{43}{40}$ - 1500 ] ×  $\frac{43}{40}$ - 1500}

= { [ 2800 × $\frac{43}{40}$ - 1500 ] ×  $\frac{43}{40}$ - 1500}

= { [ 3010 - 1500 ] ×  $\frac{43}{40}$ - 1500}

= { 1510 ×  $\frac{43}{40}$ - 1500 }

= 1623.5 - 1500

= 123.25

Answer is 123.25.

Given:

${\displaystyle \ [{\displaystyle \ {\displaystyle \ (\sqrt[4]{p^{-5/4}}),}^{-4/5}}]^{4}}$

Formula used:

(​xy​)​z​ = ​xyz

Calculation:

\({\displaystyle \ [{\displaystyle \ {\displaystyle \ (\sqrt[4]\frac{1}{p^{5/4}}),}^{-4/5}}]^{4}}\)

= ${\displaystyle \ [{\displaystyle \ {\displaystyle \ (\frac{1}{p^{5/16}}),}^{-4/5}}]^{4}}$

= ${\displaystyle \ [{\displaystyle \ {\displaystyle \ ({p^{5/16}}),}^{4/5}}]^{4}}$

= $(p)^{\frac{5}{16} × \frac {4}{5} × 4}$

= $(p)$

Answer is p.

Additional Information x^m​ × ​xⁿ = ​x^(m+n)

x^m ÷ ​xⁿ​ = ​x^(m-n)

(​x^y​)​^z​ = ​x^yz

Given:

The ratio between the curved surface area and the total surface area of a right circular cylinder is 15 : 22

Formula used:

let r and h be radius and height

Curved Surface area of cylinder = 2πrh

Total Surface area of cylinder = 2πr (h+r)

Calculation:

$\frac{2πrh}{2πr(r+h)}$ = $\frac{15}{22}$

$\frac{h}{r+h}$ = $\frac{15}{22}$

$\frac{r +h}{h} =\frac{22}{15}$

$\frac{r}{h} +1 =\frac{22}{15}$

$\frac{r}{h} =\frac{7}{15}$

$\frac{2r}{2h} = \frac{7}{15}$

$\frac{d}{h} = \frac{14}{15}$

Ratio of the height to the diameter of the cylinder = Height : Diameter

= 15 : 14

Answer is 15 : 14.

Shortcut Trick

Ratio of CSA to TSA = h : (r + h) = 2 : 3 ⇒ h = 2r.

Given TSA = 6πr² = 231 ⇒ r² = 231 × 7 ÷ (6 × 22) = 49/4 ⇒ r = 7/2 cm.

Height h = 2 × (7/2) = 7 cm.

Volume = πr²h = (22/7) × (49/4) × 7 = 269.5 cm³.

∴ The correct answer is 269.5 cm³.

Alternate Method

Given:

Total Surface Area (TSA) = 231 cm²

Curved Surface Area (CSA) = 2/3 of TSA

Formula Used:

TSA = 2πr(r + h)

CSA = 2πrh

Volume = πr²h

Calculations:

⇒ CSA = (2/3) × 231 = 154 cm²

⇒ We know that, TSA = CSA + 2 × Area of Base

⇒ 231 = 154 + 2πr²

⇒ 2πr² = 231 − 154 = 77

⇒ 2 × (22/7) × r² = 77

⇒ (44/7) × r² = 77

⇒ r² = (77 × 7) ÷ 44 = 49/4

⇒ r = 7/2 = 3.5 cm

⇒ Now, substitute r in the CSA formula:

⇒ 2πrh = 154

⇒ 2 × (22/7) × (7/2) × h = 154

⇒ 22 × h = 154

⇒ h = 154 ÷ 22 = 7 cm

⇒ Volume of cylinder = πr²h

⇒ Volume = (22/7) × (7/2) × (7/2) × 7

⇒ Volume = 11 × 7 × 7 ÷ 2 = 539 ÷ 2 = 269.5 cm³

∴ The correct answer is 269.5 cm³.

Additional Information

Cylinder Surface Areas

The Curved Surface Area (CSA) of a cylinder is 2πrh. The Total Surface Area (TSA) includes the two circular bases, calculated as 2πr(r + h).

Volume of a Cylinder

The volume represents the total 3D space enclosed and is given by πr²h, where r is the base radius and h is the height.

Relation to a Cone

A cone with the same base radius and height as a cylinder has exactly one-third the volume of the cylinder (Volume = 1/3 × πr²h).

Shortcut Trick

Expand the repeating decimals to a few terms and add them directly column by column.

First number = 0.23545454...

Second number = 0.24464646...

Sum = 0.23545454... + 0.24464646... = 0.48010101...

The digits '01' are repeating continuously, which is written as 0.4801.

∴ The correct answer is 0.4801.

Alternate Method

Given:

Expression = 0.2354 + 0.2446

Formula Used:

To convert a mixed recurring decimal to a fraction:

Fraction = (Complete number − Non-recurring part) ÷ (Number of 9s equal to recurring digits followed by 0s equal to non-recurring digits)

Calculations:

⇒ 0.2354 = (2354 − 23) ÷ 9900 = 2331 ÷ 9900

⇒ 0.2446 = (2446 − 24) ÷ 9900 = 2422 ÷ 9900

⇒ Sum = (2331 ÷ 9900) + (2422 ÷ 9900)

⇒ Sum = (2331 + 2422) ÷ 9900

⇒ Sum = 4753 ÷ 9900

Now, to convert the fraction back to a recurring decimal, we structure the numerator in the form (Complete number − Non-recurring part):

⇒ 4753 ÷ 9900 = (4801 − 48) ÷ 9900

⇒ Therefore, the matching decimal format is 0.4801

∴ The correct answer is 0.4801.

Additional Information

Pure Recurring Decimal

A decimal in which all the digits after the decimal point are repeated continuously is called a pure recurring decimal. Example: 0.7 = 7 ÷ 9.

Mixed Recurring Decimal

A decimal in which at least one digit after the decimal point is not repeated and then some digits are repeated is called a mixed recurring decimal. Example: 0.16 = (16 − 1) ÷ 90 = 15 ÷ 90 = 1 ÷ 6.

Fraction Rules

When adding fractions with the exact same denominator, directly add the numerators while keeping the denominator identical.

Given:

The average weight of 5 person's increases by 4.4 kg when a new person comes in place of one of them weighing 40 kg

Formula used:

Average = $\frac{Total\ Sum}{Numbr\ Of\ Terms}$

Calculation:

let x be the average of 5 person's

Let y be the new person's weigth

$\frac{5x-40+y}{5}$ = x + 4.4

5x - 40 + y = 5x + 22

y = 40 + 22

y = 62

Weight of the new person is 62kg

Answer is 62kg.

Alternate MethodGiven:

The average weight of 5 person's increases by 4.4 kg when a new person comes in place of one of them weighing 40 kg

Calculation:

if average is increased by 4.4kg when a new person replaced a person of 40kg,

Then the Total weight increased is = 5 × 4.4 

= 22kg

New person = 22kg + 40 Kg

= 62kg

Answer is 62kg.