MP Police Constable : (6 Nov 2025, Shift 2) Memory-Based Paper (Previous Year Paper)

The correct answer is Article 109. 

Key Points

• Article 109 -  A Money Bill shall not be introduced in the Council of States.
• A money Bill is defined in Article 110 of the Indian Constitution.
• Money bills are concerned with financial matters like taxation, public expenditure, etc.
• The bill is significant for Indian Polity and governance as many important issues like Aadhar Bill, Insolvency, and Bankruptcy Bill are also related to it.

Additional Information

• Article 354: Application of provisions relating to the distribution of revenues while a proclamation of emergency is in operation.
• Article 193 speaks about the Penalty for sitting and voting before making an oath or affirmation under Article 188 or when not qualified or when disqualified.
• Article 298 of the Constitution deals with the power to carry on trade.

The correct answer is Atomic Number.

Key Points

• Atomic Number-
• Periodic Table- This is a table of chemical elements arranged in the order of atomic numbers in such a way that elements with the same atomic structure are displayed in the vertical column.
• Modern Periodic Law-  Modern Periodic Law states "The chemical and physical properties of elements are the recurring functions of their atomic numbers".
• Mass Number-
• The sum of the number of protons and neutrons located in the nucleus of an atom is called the mass number.
• The mass number is denoted by A. It is also called 'atomic mass number' or 'nucleon number'.

Additional Information

• In class 1, which is in the leftmost place, contains alkaline metals (Li, Na, K, Rb, Cs, and Fr).
• Alkaline soil metals are metallic elements found in class 2 of the periodic table.
• The elements found in squares 3–12 in the central part of the periodic table are called transition elements.
• In transition elements, valence electrons are present in more than one shell.
• In square 18, which is at the rightmost position, the ideal gases are (He, Ne, Ar, Kr, Xe, and Rn).
• Their outermost shells have 8 electrons, except He, because it has an outer shell K and can only hold a maximum of 2 electrons.

• In the statement, the chairman of the cricket board declares that they will be interviewing those who were former wicket-keepers for the coaching position.
• Thus, conclusion I clearly follows.
• Since the word "people" is used in the question statement, the possibility of more than one person being interviewed does exist. Thus, conclusion II also follows.

Hence the correct answer is option 2.

Shortcut Trick

When a larger sphere is melted to form smaller spheres, the number of spheres is the cube of the ratio of their radii.

Ratio of radii (R : r) = 35 : 5 = 7 : 1

Number of small spheres = (R ÷ r)³

Number of small spheres = 7³ = 343

∴ The correct answer is 343.

Alternate Method

Given:

Radius of metallic solid sphere (R) = 35 cm

Radius of small sphere (r) = 5 cm

Formula Used:

Volume of a sphere = (4/3) × π × r³

Number of small spheres = Volume of large sphere ÷ Volume of one small sphere

Calculations:

⇒ Let the number of small spheres be n.

⇒ n × (4/3) × π × r³ = (4/3) × π × R³

⇒ n × r³ = R³

⇒ n × 5³ = 35³

⇒ n = (35 × 35 × 35) ÷ (5 × 5 × 5)

⇒ n = 7 × 7 × 7

⇒ n = 343

∴ The correct answer is 343.

Additional Information

Volume Conservation

When one solid object is melted and recast into another shape, the total volume remains the same (Volume_initial = Volume_final).

Surface Area of Sphere

The total surface area of a sphere is given by the formula 4πr².

Hemisphere Formulas

Volume of hemisphere = (2/3)πr³ and Total Surface Area = 3πr².

• The correct answer is option(2)

• Qualities Projected in this situation:​ Situation Handling Ability

Key Points 

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information Officer qualities:

Shortcut Trick

Ratio of the number of coins = 2 : 3 : 5

Ratio of their values = (2 × 50) : (3 × 25) : (5 × 20) = 100 : 75 : 100

Simplified value ratio = 4 : 3 : 4

Total value parts = 4 + 3 + 4 = 11 parts → Rs. 550

Difference between 50 p and 20 p parts = 4 − 4 = 0 parts

∴ The correct answer is Rs. 0.

Alternate Method

Given:

Total amount in the bag = Rs. 550

Ratio of the number of 50 p, 25 p, and 20 p coins = 2 : 3 : 5

Total Amount = ₹550

4 Parts
3 Parts
4 Parts

50 p Coins
Amount = ₹200

25 p Coins
Amount = ₹150

20 p Coins
Amount = ₹200

Difference (50p - 20p) = ₹200 - ₹200 = ₹0

Calculations:

⇒ Let the number of 50 p, 25 p, and 20 p coins be 2x, 3x, and 5x respectively.

⇒ Value of 50 p coins = 2x × 0.50 = x Rupees

⇒ Value of 25 p coins = 3x × 0.25 = 0.75x Rupees

⇒ Value of 20 p coins = 5x × 0.20 = x Rupees

⇒ Total value = x + 0.75x + x = 2.75x Rupees

⇒ According to the question, 2.75x = 550

⇒ x = 550 ÷ 2.75 = 200

⇒ Amount contributed by 50 p coins = x = Rs. 200

⇒ Amount contributed by 20 p coins = x = Rs. 200

⇒ Difference in amounts = Rs. 200 − Rs. 200 = Rs. 0

∴ The correct answer is Rs. 0.

Additional Information

Total Value of Coins

The total amount is the sum of the products of the number of coins and their respective face values. Total Amount = Count × Denomination Value.

Equivalent Ratio Method

When working with mixed units (e.g., paise and rupees), always convert all values to a single unit (either all in paise or all in rupees) before setting up proportional equations.

The Correct answer is Ladakh.

Key Points

• Jabro is a traditional nomadic dance performed by the people of Ladakh, particularly by the Changpa nomads of the Changthang region.
• The dance is an integral part of the cultural heritage of the region and is typically performed during festivals and social gatherings.
• Jabro is not just a dance but also a way of expressing harmony and community bonding among the nomadic tribes.
• The dancers wear traditional Ladakhi attire, which includes colorful robes and headgear that reflect the unique culture and traditions of Ladakh.
• The dance is accompanied by traditional Ladakhi music and songs, which often narrate tales of nomadic life and the natural beauty of the region.
• The Jabro dance highlights the rich cultural diversity of India and emphasizes the importance of preserving indigenous traditions.

Additional Information

• Puducherry
• Puducherry, a Union Territory of India, is known for its French colonial heritage, serene beaches, and spiritual centers like the Aurobindo Ashram.
• It is not traditionally associated with the nomadic lifestyle or dances like Jabro.
• Assam
• Assam is renowned for its Bihu dance, which is performed during the Bihu festival to celebrate the Assamese New Year.
• Unlike the Jabro dance, Bihu is not related to nomadic traditions but is an agricultural dance celebrating the harvest season.
• Sikkim
• Sikkim is known for its Mask dances, such as the Cham dance, performed during Buddhist festivals.
• These dances reflect the Buddhist culture of the region and are not related to nomadic traditions like Jabro.

Concept:

• Refraction is the change in the direction of propagation of light (electromagnetic wave) as it travels from one medium to another.
• This occurs due to a change in the velocity as well as the wavelength of light.
• As the wave moves from one medium to another, depending upon the particles, state and physical properties of the media, there is a change in the velocity and wavelength of the wave because of which it suffers deflection and change in direction.
• It can be expressed as

\(\frac{{sini}}{{sinr}} = \frac{{{v_2}}}{{{v_1}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}}\)

Explanation:

• Refraction is the change in the direction of propagation of light (electromagnetic wave) as it travels from one medium to another.
• This occurs due to change in the velocity as well as the wavelength of light. As the wave moves from one medium to another, depending upon the particles, state and physical properties of the media, there is a change in the velocity and wavelength of the wave because of which it suffers deflection and change in direction.

Given:

Total number of boys in the row = 49

A is 27^th from the left end.

B is 27^th from the right side.

A's Position from Right End = Total boys - A's position from Left End + 1

=  49 - 27 + 1 

= 23

Boys between A and B = Position of B from Right End - Position of A from Right End - 1

= 27 - 23 - 1

= 3

= 3

Hence, the correct answer is "3".

Shortcut Trick

Sides of the given squares are 52 ÷ 4 = 13 cm and 20 ÷ 4 = 5 cm.

According to the question, Area₃ = Area₁ − Area₂

Side of the 3^rd square = √(13² − 5²) = √(169 − 25) = √144 = 12 cm.

Perimeter of the 3^rd square = 4 × 12 = 48 cm.

∴ The correct answer is 48 cm.

Alternate Method

Given:

Perimeter of 1^st square = 52 cm

Perimeter of 2^nd square = 20 cm

Formula Used:

Perimeter of a square = 4 × Side

Area of a square = Side²

Area = 169
a = 13
P = 52 cm

−

Area = 25
a = 5
P = 20 cm

=

Area = 144
a = 12
P = 48 cm

Calculations:

⇒ Side of 1^st square (a₁) = 52 ÷ 4 = 13 cm

⇒ Area of 1^st square (A₁) = 13² = 169 cm²

⇒ Side of 2^nd square (a₂) = 20 ÷ 4 = 5 cm

⇒ Area of 2^nd square (A₂) = 5² = 25 cm²

⇒ Area of 3^rd square (A₃) = A₁ − A₂

⇒ A₃ = 169 − 25 = 144 cm²

⇒ Side of 3^rd square (a₃) = √144 = 12 cm

⇒ Perimeter of 3^rd square = 4 × 12 = 48 cm

∴ The correct answer is 48 cm.

Additional Information

Diagonal of a Square

The length of the diagonal is given by d = a√2, where 'a' is the side length of the square.

Area using Perimeter

The area can be found directly from the perimeter using the formula Area = (P ÷ 4)².

Pythagorean Triplets

Numbers that satisfy a² + b² = c² form a Pythagorean triplet. In this question, 5, 12, and 13 perfectly represent this property as 5² + 12² = 13².

The logic followed here is:

Vowel - 2 = code 

Consonant  - 1 = code

For, 'MANAGE’ is written as ‘LYMYFC’.

For, ‘CREATE’ is written as ‘BQCYSC’.

Similarly, For, ‘BUILD’ be written as.

Thus, ‘BUILD’ be written as 'ASGKC'.

Hence, the correct answer is "Option 2",

Given:

A car covers a distance of 350 km in 5 hours and covers another 450 km at a speed of 90 km/h

Formula used:

Average speed = Total distance/ Total time

Calculation

Total distance covered = 350 km + 450 km = 800 km

Total time = 5 hour + 5 hour = 10 hours

Average speed = Total distance/ Total time

Average speed = 800/10 = 80 km/hr

His average speed for the whole journey is 80 km/hr.

The correct answer is Increase in groundwater level.

Key Points

• An increase in groundwater level is not a consequence of deforestation.
• Deforestation
• It is a very broad term, which consists of cutting of trees including repeated lopping, felling, and removal of forest litter, browsing, grazing, and trampling of seedlings. It can also be defined as the removal or damage of vegetation in a forest to the extent that it no longer supports its natural flora and fauna.
• Deforestation not only affects the climate by increasing the atmospheric level of carbon dioxide but also affects the environment by inhibiting water recycling, triggering severe flooding, aquifer depletion, soil degradation, and the extinction of plant and animal species.
• Deforestation leads to an increase in soil erosion and a decrease in rainfall and a decrease in biodiversity.
• Causes of Deforestation: The most common reason for deforestation is the cutting of wood for fuel, lumber, and paper. Another important cause relates to the clearing of forest land for agriculture, including conversion to cropland and pasture. The main causes of deforestation are:
• Agriculture
• Shifting cultivation
• Demand for firewood
• Wood for industry and commercial use
• Urbanization and developmental projects
• Overgrazing of forests

The correct answer is Concave.

Key Points

• Presbyopia:
• The power of accommodation of the eye decreases with aging.
• People with the defect can't see nearby as well as distant objects distinctly.
• Causes - (a) gradual weakening of ciliary muscles, (b) diminishing flexibility of the eye lens.
• Correction - bi-focal lenses, in which the upper portion consists of the concave lens (facilitates distant vision) and the lower portion consists of the convex lens (facilitates near vision).

Additional Information

• Prism:
• The splitting of a composite beam of light into its constituent colors is called dispersion of light.
• The dispersion of white light occurs because the colors of white light travel at different speeds through the glass prism.
• The dispersion was discovered by Sir Issac Newton.
• Newton discovered that light is made up of seven different colors.

Six Persons: P, Q, R, S, T, and U.

1) P is sitting towards the immediate left of Q and the immediate right of R.

2) R is sitting to the immediate right of U.

3) S is the immediate right of T who is to the left of U.

Hence, U and R are in the middle.

Shortcut Trick

Total capacity of the tank = LCM of 5, 15, and 7.5 = 15 units.

Efficiencies: P = 15 ÷ 5 = +3, Q = 15 ÷ 15 = +1, R = 15 ÷ 7.5 = −2.

Net combined efficiency of P, Q, and R = 3 + 1 − 2 = 2 units/hr.

Time taken to fill the tank = Total Capacity ÷ Net Efficiency = 15 ÷ 2 = 7.5 hours.

∴ The correct answer is 7.5 hours.

Alternate Method

Given:

Time taken by P to fill the tank = 5 hours

Time taken by Q to fill the tank = 15 hours

Time taken by R to empty the tank = 7.5 hours

Formula Used:

Total Work = LCM of given time periods

Efficiency = Total Work ÷ Time

Total Time = Total Work ÷ Combined Efficiency

Calculations:

⇒ Net efficiency of all three pipes together = (+3) + (+1) + (−2)

⇒ Net efficiency = 4 − 2 = +2 units/hr

⇒ Since the net efficiency is positive, the tank is being filled overall.

⇒ Time taken to fill the tank = Total Work ÷ Net Efficiency

⇒ Time taken = 15 ÷ 2

⇒ Time taken = 7.5 hours

∴ The correct answer is 7.5 hours.

Additional Information

Inlet vs Outlet Pipes

An inlet pipe fills the tank and has a positive efficiency, whereas an outlet pipe empties the tank and has a negative efficiency. If the net efficiency is positive, the tank fills up; if negative, the tank empties completely.

Combined Work Rule

If pipe A fills a tank in x hours and pipe B empties it in y hours (where y > x), then the total time taken to fill the tank when both are open is (x × y) ÷ (y − x) hours.

Leakage Problems

A leak in the bottom of a tank functions exactly like an outlet pipe. It continuously removes water, which reduces the effective filling rate and increases the overall time required to fill the tank.

The least possible diagram for the given statements is as follows,

Conclusions:

I. Some bad are stable. → False (It is possible but not definite)

II. No bad are stable. → False (It is possible but not definite)

Conclusions I and II are complementary pair.

Thus, either I or II follows.

Formula Used:

Standard deviation (SD): It indicates how far a value has varied from the mean value.

\(\bar{X}\) = Mean = Sum of observation / Total no. of observation

Calculation:

Using the above formula -

Mean = (7 + 9 + 11 + 13 + 15)/5 = 55/5 = 11

Standard deviation  σ = \(\sqrt {\dfrac{∑ ( X − μ ) ^2} n} \)

⇒ \(\sqrt {\dfrac{-4^2 + (-2)^2 + 0 + 2^2 + 4^2}{5} }= \sqrt {\dfrac{40}{5}} \)

⇒ \( \sqrt 8 = 2.82\)

∴ The correct answer is 2.82

The correct answer is four, eight.

Important Points

• The foundation of Buddhism is the four noble truths and the eight-fold path.
• The four Noble Truths are:
• The Truth of Suffering (Dukkha)
• The Truth of the Cause of Suffering (Samudhya)
• The Truth of the Cessation of Suffering (Nirodha)
• The Truth of the Path Cessation of Suffering (Magga)
• The eight-fold path is Ashtangika Marga - 
• Right View or Right Understanding
• Right Thoughts
• Right Speech
• Right Conduct
• Right Livelihood
• Right Effort
• Right Mindfulness
• Right Meditation or Right Contemplation​

Additional Information

• Mahayana Buddhism:
• After the death of Buddha, a group evolved who believed that compassion for all humanity was an important part of the path, and that teaching is fully available to all.
• Those who followed the newly expanded ideals called themselves Mahayana meaning the big raft.
• In Mahayana Buddhism, all practicing Buddhists are apprentice Bodhisattvas.
• In Mahayana countries, images of the Buddha are set up in the temples and homes as an object of worship.
• Hinayana Buddhism:
• From about 100 years after the death of the Buddha, there had been a movement towards embracing the style of Buddhism.
• The early monks concentrated on personal enlightenment, seeking spiritual answers for themselves, and teaching others the way of enlightenment.
• But the information was severely limited to the lay community as it was assumed only monks could achieve Buddhahood.
• This section came to be known as Hinayana or also known as Theravada.
• Theravada means the way of elders.
• Milindapanha:
• The Milindapanha, or "Milinda's Questions," is an important early Buddhist text that usually is not included in the Pali Canon.
• Even so, the Milindapanha is cherished because it addresses many of Buddhism's most difficult doctrines with wit and clarity.
• The Milindapanha presents a dialogue between King Menander I (Milinda in Pali) and an enlightened Buddhist monk named Nagasena.
• Menander- I was an Indo-Greek king thought to have ruled from about 160 to 130 BCE.
• He was a king of Bactria, an ancient kingdom that took in what is now Turkmenistan, Afghanistan, Uzbekistan, and Tajikistan, plus a small part of Pakistan.

EXPLANATION:

Snell's Law (Second Law of Refraction)

Snell's Law describes the relationship between the angles of incidence (i) and refraction (r) when a wave passes from one medium to another.

The law is mathematically expressed as:

n₁sinI = n₂sinr

Where n₁ and n₂ are the refractive indices of the two media.

Angle of incidence (I) is the angle the incident ray makes with the normal.

Angle of refraction (r) is the angle the refracted ray makes with the normal.

Additional Information

When light passes from a denser medium to a rarer medium (e.g., glass to air):

If the angle of incidence (I) is greater than the angle of refraction (r), the refracted ray bends towards the normal.

If the angle of incidence (I) is less than the angle of refraction (r), the refracted ray bends away from the normal.

In the given scenario, if I > r, the refracted ray bends towards the normal.

Therefore, the correct answer is Option 3: "If I > r, refracted ray bends towards the normal."

The sitting arrangement as per the given information is as:

1. Q is at the extreme right end of the row.
2. R is an immediate neighbour of Q.
3. S is an immediate neighbour of both T and R.

Here, 'U' is sitting at the extreme left end.

Hence, the correct answer is "U".

Calculation:     

 \(1\frac{2}{5} + 4\frac{3}{10} - 1\frac{7}{20}\)

\(\frac{7}{5} + \frac{43}{10} - \frac{27}{20}\)

LCM of 5, 10 and 20 is 20

\(\frac{7}{5} \times \frac{4}{4} = \frac{28}{20} \)

\(\frac{43}{10} \times \frac{2}{2} = \frac{86}{20} \)

\(\frac{27}{20} \times \frac{1}{1} = \frac{27}{20} \)

\(⇒ \frac{28}{20} + \frac{86}{20} - \frac{27}{20}\)

\(⇒ \frac{28 + 86 - 27 }{20}\)

\(⇒ \frac{87}{20}\)

\(∴ \frac{7}{5} + \frac{43}{10} - \frac{27}{20} = \frac{87}{20}\)

The correct option is 4 i.e. \(4\frac{7}{20}\)

From the given information:

Step 1: Rohini walked for 2 kilometres on a straight road, facing North.

Step 2: Then she took a right turn and walked for 1 kilometre.

Step 3: Then she again took a right turn and walked 2 kilometres.

From the diagram we can see that Rohini is facing towards south.

Hence the correct answer is " South ".

Solution:

\(\rm \frac{4}{12}\times \frac{3}{2}\div \frac{4}{8}-12+4\)

⇒ \(\rm \frac{4}{12}\times \frac{3}{2}\times \frac{8}{4}-12+4\)

⇒ \(\rm \frac{1}{12}\times 3\times \frac{4}{1}-12+4\)

⇒ \(1-12+4\)

⇒ -7

∴ The correct option is 2.

The correct answer is Electricity generation.

Key Points

The summary of the Index of Eight Core Industries is given below:

• Coal - Coal production (weight: 10.33 per cent) increased by 12.2 per cent in March, 2023 over March, 2022. Its cumulative index increased by 14.8 per cent during 2022-23 over corresponding period of the previous year.
• Crude Oil - Crude Oil production (weight: 8.98 per cent) declined by 2.8 per cent in March, 2023 over March, 2022. Natural Gas - Natural Gas production (weight: 6.88 per cent) increased by 2.8 per cent in March, 2023 over March, 2022.
• Petroleum Refinery Products - Petroleum Refinery production (weight: 28.04 per cent) increased by 1.5 per cent in March, 2023 over March, 2022. Its cumulative index increased by 4.8 per cent during 2022-23 over the corresponding period of previous year.
• Fertilizers - Fertilizers production (weight: 2.63 per cent) increased by 9.7 per cent in March, 2023 over March, 2022. Its cumulative index increased by 11.3 per cent during 2022-23 over the corresponding period of previous year.
• Steel - Steel production (weight: 17.92 per cent) increased by 8.8 per cent in March, 2023 over March, 2022. Its cumulative index increased by 8.6 per cent during 2022-23 over the corresponding period of previous year.
• Cement - Cement production (weight: 5.37 per cent) declined by 0.8 per cent in March, 2023 over March, 2022. Its cumulative index increased by 8.6 per cent during 2022-23 over the corresponding period of previous year.
• Electricity - Electricity generation (weight: 19.85 per cent) declined by 1.8 per cent in March, 2023 over March, 2022. Its cumulative index increased by 8.9 per cent during 2022-23 over the corresponding period of previous year.

Reflection formed by the plan mirror is called Lateral inversion. This means, upon reflection via a Plane mirror, right hand side of an objects appears to be on left in the image formed and left side of an object appears on the right hand side.

Given Input: but going for crept te light sir

First, we arrange the words with a maximum number of letters in decreasing order and also in alphabetical order. One word at a time.

Step-I: crept but going for te light sir

Crept has a number of letters 5 and come first place in alphabetical order.

Step-II: crept going but for te light sir

After crept, going has also a number of letters 5 and come second place in alphabetical order.

Step-III: crept going light but for te sir

After going, light has also a number of letters 5 and come third place in alphabetical order.

Step-IV: crept going light but for sir te

After light, but for are already arranged with a number of letters 3 so skip those two words then come to the word sir.

Step-IV is the last step for this input.

Similarly we can write all the steps of the given input as,

Input  -  true se veto be nuke my like

Step I  -  like true se veto be nuke my 

Step II  -  like nuke true se veto be my

Step III-    like nuke true veto se be my  

Step IV  -  like nuke true veto be se my 

Step V  -  like nuke true veto be my se

Step V is the final step of the given input.

Step IV is "like nuke true veto be se my".

Hence, "option 1" is the correct answer.

NOTE: There was a discrepancy in the original question so we modify it a little bit so that it can be solved.

Shortcut Trick

Base Area = πr² = (22/7) × 7 × 7 = 154 cm².

CSA + TSA = 2 × CSA + 2 × Base Area = 2068.

2 × CSA + 2(154) = 2068 ⇒ 2 × CSA = 1760 ⇒ CSA = 880 cm².

CSA = 2πrh = 880 ⇒ 44 × h = 880 ⇒ h = 20 cm.

Volume = Base Area × height = 154 × 20 = 3080 cm³.

∴ The correct answer is 3080 cm³.

Alternate Method

Given: Radius (r) = 7 cm, CSA + TSA = 2068 cm².

Formula Used: CSA = 2πrh | TSA = 2πr(h + r) | Volume = πr²h

⇒ CSA + TSA = 2068

⇒ 2πrh + 2πr(h + r) = 2068

⇒ 2πrh + 2πrh + 2πr² = 2068

⇒ 4πrh + 2πr² = 2068

⇒ 4 × (22/7) × 7 × h + 2 × (22/7) × 7 × 7 = 2068

⇒ 88h + 308 = 2068

⇒ 88h = 2068 − 308 = 1760

⇒ h = 1760 ÷ 88 = 20 cm

⇒ Volume of Cylinder = πr²h

⇒ Volume = (22/7) × 7 × 7 × 20

⇒ Volume = 22 × 7 × 20 = 154 × 20 = 3080 cm³

∴ The correct answer is 3080 cm³.

Additional Information

Curved Surface Area of Cylinder

The area of the curved part of the cylinder is CSA = 2πrh, where r is radius and h is height.

Total Surface Area of Cylinder

The sum of the area of the curved surface and the two circular bases: TSA = 2πr(h + r).

Volume of Cylinder

The capacity or space occupied by the cylinder: Volume = πr²h.

Hollow Cylinder Volume

The volume of material in a hollow cylinder is V = π(R² − r²)h, where R is outer and r is inner radius.

Given:

(i) There is a group of five persons - A, B, C, D and E.

(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate.

(iii) Three of them - A, C and the advocate prefer tea to coffee and two of them - B and the journalist - prefer coffee to tea. 

(iv) The industrialist and D and A are friends to one another but two of them prefer coffee to tea.

Because A is already like Tea means D and industrialists like coffee.

(v) The horticulturist is C's brother.

So, the final table will be as follows:

So, from the above table, it is clear that "C" is Physicst

Hence, the correct option is "Option 4".

Given:

CSA = 2200 cm²

C = 110 cm

Formula used:

CSA(Cylinder) = 2 x 22/7 x r x h

Circumference of circle = 2 x 22/7 x r

Calculation:

2 x 22/7 x r = 110

r = 70/4 = 35/2 cm

2 x 22/7 x 35/2 x h = 2200

h = 2200/110 = 20 cm

Height = 20 cm

Hence, the correct option is 3.

Alternate MethodBase of a solid cylinder = 2πr = 110cm

The curved surface area of cylinder = 2200cm2 

⇒ 2πrh = 2200

⇒ 110 × h = 2200

⇒ h = 2200/110 = 20cm

The correct answer is Kannauj.

• Lakh Bahosi Sanctuary is situated in Kannauj.
• Lakh Bahosi Sanctuary is one of India's largest bird sanctuaries in India.
• Jackal, blue bull, fishing cat, and monkeys are also found here.
• Mahavir Swami Sanctuary is situated in Lalitpur.
• National Chambal Wildlife Sanctuary is situated in Agra and Etawah districts.
• Parvati Arga Bird Sanctuary is situated in the Gonda district of Uttar Pradesh.

The correct answer is all mirrors irrespective of their shape.

Key Points

• The laws of reflection state that the angle of incidence is equal to the angle of reflection.
• These laws are applicable to all types of reflecting surfaces including plane, concave, and convex mirrors.
• The incident ray, the reflected ray, and the normal to the mirror at the point of incidence all lie in the same plane.
• These laws are fundamental principles of optics and do not depend on the shape of the mirror.

Additional Information

• Reflection of Light:
• Reflection is the phenomenon where light bounces back from a surface into the same medium.
• There are two types of reflection: specular (mirror-like) and diffuse (scattering).
• Normal Line:
• The normal line is an imaginary line perpendicular to the surface at the point of incidence.
• It is used as a reference to measure the angles of incidence and reflection.
• Angle of Incidence:
• The angle between the incident ray and the normal is called the angle of incidence.
• This angle is crucial in determining the angle of reflection.
• Angle of Reflection:
• The angle between the reflected ray and the normal is called the angle of reflection.
• According to the law of reflection, this angle is always equal to the angle of incidence.

Given : 7^th May 2000 was Sunday

Explanation :

The number of odd days from 7^th May 2000 to 15^th July 2010 :

∴ The number of odd days from 7^th May 2000 to 15^th July 2010 ⇒ 4

⇒So, Four odd day get added to Monday because day asked in future.

∴ Thursday was the day of the week on the 15^th July 2010.

Hence, "Thursday" is the correct answer.

Additional Information

• Number of odd days for the days of week.

​

• Number of odd days for the years.

Shortcut Trick

Given: LCM = 3 × HCF and LCM × HCF = 867

⇒ (3 × HCF) × HCF = 867 ⇒ 3 × HCF² = 867

⇒ HCF² = 289 ⇒ HCF = 17

⇒ LCM = 3 × 17 = 51

Since the numbers are factors of LCM and multiples of HCF, and HCF is 17 while LCM is 51, the numbers are 17 and 51.

∴ The correct answer is 17, 51.

Alternate Method

Given:

⇒ Let HCF be h and LCM be L.

⇒ L = 3h

⇒ L × h = 867

Formula Used:

⇒ Product of two numbers = HCF × LCM

Calculations:

⇒ Substituting L = 3h in the product equation:

⇒ 3h × h = 867

⇒ 3h² = 867

⇒ h² = 867 ÷ 3 = 289

⇒ h = √289 = 17

⇒ L = 3 × 17 = 51

⇒ Since LCM is a multiple of both numbers and HCF is a factor, and the product of numbers equals L × h,

⇒ The numbers must be 17 and 51 as 17 × 51 = 867 and HCF(17, 51) = 17.

∴ The correct answer is 17, 51.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, a × b = HCF(a, b) × LCM(a, b). Also, HCF is always a factor of LCM.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to the product of the two numbers.

HCF of Fractions

HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

The correct answer is "option(1)".

• Qualities projected in this situation: (Social Adaptability, Initiative, and Determination)

Key Points 

Checklist for attempting SRT Questions:

1. Read the question and options carefully

2. Look for an option that is optimistic, realistic, and reflects officer-like qualities.

3. Do not skip any questions.

4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, your thinking ability should be swift.

5. Read quickly and be logical.

Additional Information

Given:

Perimeter of triangle (P) = 36 cm.

One side (a) = 9 cm.

Difference between the other two sides = 3 cm.

Formula used:

Perimeter of a triangle(P) with sides a, b and c

P = a + b + c

Area of a triangle, 

A = (1/2) × b × h

where 

b = base of triangle

h = height of triangle

Calculation:

Let the second and third sides be b and c.

b - c = 3

b = c + 3.

Perimeter of triangle

P = a + b + c

36 = 9 + c + 3 + c

24 = 2c

c = 12 cm.

Thus, 

b = c + 3

b = 12 + 3

b = 15 cm.

Clearly, 9,12 and 15 are in the ratio 3 : 4 : 5 and hence form a Pythagorean triplet.

Thus, the triangle is a right angled triangle with hypotenuse 15 cm.

Area of triangle

A = (1/2) × b × h

A = (1/2) × 12 × 9

A = 54 cm² .

∴ Area of triangle is 54 cm².

The correct answer is Narmada.

• Major tributaries of the river Narmada are Banjar, Heran, Kolar, Tawa, Tendoni, Beda, Jobat, and Goi rivers.
• Banjar river is an important source of water for the thriving flora and fauna of the Kanha National Park.
• It originates in the Malajkhand region, along the state borders of Madhya Pradesh and Chhattisgarh.
• The Kanha Tiger Reserve is located on the banks of the Banjar River.

Important Points

• Yamuna and Chambal are the sub-sub basins of the Ganga Basin.
• Chambal River (938 km) originates from Indore District and meets the river Yamuna.
• Kali Sindh, Parvati, Kuno, Newaj, and Shipra are the main tributaries of the river Chambal.
• Kota city is located on the banks of the river Chambal.

The correct answer is Option 2 – Cerebellum

Key Points

• The Cerebellum is also called the “little brain.”
• It is located at the back of the brain, beneath the cerebrum.
• Functions of the cerebellum include:
• Maintaining balance and posture
• Coordinating voluntary movements
• Supporting motor learning and fine-tuning movements
• Medulla controls involuntary functions like heartbeat and breathing.
• Pons serves as a relay between different parts of the brain.
• Cerebrum is the largest part of the brain responsible for higher cognitive functions.

So, the “little brain” = Cerebellum.

The pattern followed here is-

Thus, 39 will replace the question mark.

Given 

The ages of Manu and Bharat are in the ratio = 6 : 5 

Total age = 44  years 

Calculation 

Let the ratio be x 

6x + 5x = 44

⇒ x = 4 

Manu's age after 8 years = 6x + 8 =  32 

Bharat's age after 8 years = 5x + 8 = 28 

Required ratio = 8 : 7

∴ The required answer is 8 : 7

As we know in the morning, sun will be in east thus the opposite direction to the east is west.

Following figure shows the travelling path of Nina.

Clearly Nina turned towards the east direction at last.

Hence, “east” is the correct answer.

Given:

 sin (θ + 30) = cos 5θ

Concept:

The sine of the complement of an angle is equal to the cosine of the angle.

Calculation:

⇒ sin (90 - 5θ) = cos 5θ

⇒ θ + 30 = 90 - 5θ

⇒ 6θ = 60

⇒ θ = 60/6

Therefore, θ = 10°

The correct answer is Article 253.

Key Points

• Article 253 of the Indian constitution empowers the Parliament to make laws on the State list subject.
• The article gives power to Parliament to form any law for the whole or any part of the territory of India.
• Such power is given for the implementation of any international treaty, agreement, and convention.

Important Points

• Article 249:
• If the Rajya Sabha proposes with a two-thirds majority of its members present and voting that it is necessary or beneficial in the national interest, the Parliament can legislate on any of the subjects listed in the State List.
• Article 250:
• ​If the Proclamation of Emergency is in force, Parliament will have the power to make laws with respect to the subject of the State List.
• Such law remains in force for the period of emergency and 6 months beyond that.
• Article 252:
• The Legislatures of two or more states can pass a resolution requesting Parliament to make laws regarding any subject in the State List.
• Such statutes can also be extended to other states provided the legislatures of the respective states pass resolutions to this effect.
• Articles 245 to 255 discuss the centre-state legislative relationship in Part-XI of the Constitution.

Option 1 is correct, i.e. Current/area.

• Current density:
• Current per unit area (taken normal to the current), I/A, is called current density.
• It is denoted by j.
• The SI units of the current density are A/m².
• E = j ρ (where, E= uniform electric field, j= current density, ρ= resistivity).

NOTE:

• Electric Current:
• It is defined as the net amount of electric charge flows through a cross-section of a conductor in an electric circuit in a per unit time.
• If the number of electrons traveling in any direction will be equal to the number of electrons traveling in the opposite direction. So, there will be no net electric current.
• S.I unit of electric current is Ampere(A).
• It is a scalar quantity.

The logic followed here is:

2^nd number = 1^st number + (Subtraction of digits of 1^st number)

3^rd number = 2^nd number + (Subtraction of digits of 2^nd number)

29 : 36 : 39

Second number = 29 + (9 - 2) = 29 + 7 = 36

Third number = 36 + (6 - 3) = 36 + 3 = 39

Similarly, 

48 : 52 : 55

Second number = 48 + (8 - 4) = 48 + 4 = 52

Third number = 52 + (5 - 2) = 52 + 3 = 55

Hence, the correct answer is "Option 3".

Given

Height = 15 cm 

Formula used:

The volume of the cylinder = π × r² × h  (Where, r = The radius of the cylinder and h = The height of the cylinder)

Circumference of the base of a right circular cylinder =  2πr

Calculation:

According to the question,

Circumference of the base of a right circular cylinder =  2πr

⇒ 44 = 2 × 22/7 × r

⇒ r = 7 cm

Now,

The volume of the cylinder = π × r2 × h

⇒ (22/7) × 7 × 7 × 15 = 2310 cm³

∴ The volume of the cylinder is 2310 cm³.

The least possible Venn diagram is,

Conclusion I: No nail is a pin → False (This is definitely false)

Conclusion II: Some pins are nails → True (This is definitely true)

Hence, “only conclusion II” follows.

Given:

Total time taken = 5 hours

He travels half of the distance with a speed of 42 km/hr and the other half at a speed of 48 km/hr

Formula used:

Time = Distance/Speed

Calculation:

Let the total distance of the journey be 2x km

Time taken to travel first half of the journey = x/42 hours

Time taken to complete other half = x/48 hours

Total time = x/42 + x/48 hours

⇒ 5 = (8x + 7x)/336

⇒ 15x = 1680

⇒ x = 1680/15

⇒ x = 112

Total distance = 2x = 2 × 112

∴ Total distance of the journey is 224 km

Formula used:

Average speed = 2xy/(x + y)

Where, x = Speed in 1^st half

y = Speed in 2^nd half

Distance = Average speed × Time taken

Calculation:

Average speed = 2 × 42 × 48/(42 + 48) km/hr

⇒ (84 × 48)/90 km/hr

⇒ 44.8 km/hr

Total distance = (44.8 × 5) km

⇒ 224 km

∴ The total distance of the journey is 224 km

The correct answer is Bhopal.

​

Key Points

• Kala Parishad is situated in the Bhopal district of Madhya Pradesh.
• It was set up in 1952.
• Objective: To promote activities related to folk music, dance, drama, and art.
• It organizes a 3-days divisional festival annually.
• Khajuraho festival, Bhedaghat festival, and Malwa Utsav are also organized by Kala Parishad.
• 'Kalavarta' is the monthly magazine of Kala Parishad.
• 'Raza Award' and 'Madhya Pradesh Art Exhibition Award' are conferred by Kala Parishad to distinguished art workers.
• In 2006, the Kala Parishad was merged with the name of Ustad Allauddin Khan.
• Since then it is known as Ustad Allauddin Khan Sangeet Evam Kala Academy.

Additional Information

• About Bhopal:
• Bhopal is the capital of the state of Madhya Pradesh.
• Bhopal is also called the City of lakes.
• Bhopal's ancient name is Bhupal.
• It was founded by Dost Mohammad Khan.
• Bharat Heavy Electricals Limited (BHEL) has a factory in Bhopal.
• The Indian Space Research Center has established its second 'master control facility' in Bhopal.
• Bhopal has the Indian Institute of Forest Management, which is the only institute of forest management in India.
• Madhya Sahitya Parishad is also situated here.

Key Points

• The male reproductive organs include a pair of testes (singular, testis), two sperm ducts, and a penis.
• The testes produce the male gametes called sperms. Millions of sperms are produced by the testes.
• Though sperms are very small in size, each has a head, a middle piece, and a tail.
• The male reproductive system does not include the cervix. Cervix is a part of the female reproductive tract.

• The cervix is located at the lowermost portion of the uterus and connects the vagina and uterus.
• The cervix along with the vagina forms the birth canal.

Additional Information

• The female reproductive organs are a pair of ovaries, oviducts (fallopian tubes), Cervix, Vagina, and uterus.
• Ovaries produce female gametes called ova (eggs).
• In human beings, a single matured egg is released into the oviduct by one of the ovaries every month.
• The uterus is the part where the development of the baby takes place. Like the sperm, an egg is also a single cell.

BODMAS Rule: 

According to the question:

Now,

Given equation: 64 ÷ 13 + 65 - 15 × 48 + 8 = ?

After replacing the symbols:

⇒ 64 + 13 ÷ 65 × 15 - 48 ÷ 8 = ?

⇒ 64 + 3 - 6 = ?

⇒ 67 - 6 = 61.

Hence, the correct answer is "61".

Given:

Length of rectangle : breadth of rectangle = 3 : 2

Area of rectangle = 150 cm²

Formula used:

Area of rectangle = L × B

Perimeter of rectangle = 2 × (L + B)

Where, L = length ; B = breadth

Calculation:

Let the length of the rectangle = 3x

Breadth of the rectangle = 2x

According to the question:

Area of rectangle = 150

⇒ L × B = 150

⇒ 3x × 2x = 150 

⇒ 6x² = 150

⇒ x² = 25 

⇒ x = 5

Length = 3x = 3 × 5 = 15 cm

Breadth = 2x = 2 × 5 = 10 cm

The perimeter of rectangle = 2 × (L + B)

⇒ 2 × (L + B) = 2 × (15 + 10)

⇒ 2 × 25 = 50 cm

∴ The correct answer is 50 cm.

Total student in class = 52

Bilal's rank is 11^th from the bottom

⇒ (Rank from Bottom = 11^th, Rank from Top = 42^nd)

Salman is 9 ranks above Bilal

⇒ (Rank from Bottom = 11^th + 9 rank = 20^th, Rank from Top = 33^rd)

Hence, Salman’s Rank from top will be 33^rd.

Given:

Ratio of Teena's income to Sheena's income = 2 ∶ 3

Ratio of Teena's expenditure to Sheena's expenditure = 3 ∶ 5

Each saves Rs. 1000

Concept:

Income = Expenditure + Savings

Solution:

Let 2x and 3x be the incomes of Teena and Sheena, respectively. Let 3y and 5y be their expenditures, respectively.

Using the fact that each saves Rs. 1000, we get two equations: 2x - 3y = 1000 and 3x - 5y = 1000.

Solving these two equations, we find x = 2000 and y = 1000.

Hence, Teena's income is 2x = 2 ×  2000 = Rs. 4000. Hence, Teena's income is Rs. 4000.

The Correct Answer is ​Operation Shiva.

In News

• Indian Army launches ‘Operation Shiva’ to ensure foolproof security for Amarnath Yatra 2025.

Key Points

• The Army launched Operation Shiva to ensure foolproof security for the Amarnath Yatra.
• The shrine is located at 3,888 meters in Jammu & Kashmir.
• Over 42,000 security personnel deployed, including CRPF, BSF, SSB, ITBP, and CISF.
• Two main pilgrimage routes: Pahalgam and Baltal.
• Security includes drone surveillance, CCTV monitoring, bulletproof vehicles, and route clearance.
• Includes anti-sabotage checks and three-tier security setup.
• Enhanced medical, transport, and accommodation facilities from Lakhanpur onward.
• RFID cards made mandatory for all pilgrims for tracking and safety.

• When we see the rainbow the sun remains behind us and we face raindrops.
• We see a rainbow when there are enough water particles in air and the sun is bright.
• The formation of a rainbow involves a series of physical phenomena - reflection, refraction, dispersion and total internal reflection.

Here, we need to find the pattern to get the odd one out.

The logic here is: The last term is cube root of a number. That number is subtracted by 2 and this number is added to the last term to get the first term of each row.

So, 14 : 512 \(\Rightarrow 512 = 8^3\) , 8 + (8 - 2) = 14

22 : 1728 \(\Rightarrow 1728 = 12^3\), 12 + (12 - 2) = 22

46 : 23 \(\Rightarrow 12167 = 23^3\) , 23 + (23 - 2) = 44, But they have given 46 as the 1^st term

38 : 8000 \(\Rightarrow 8000 = 20^3\) , 20 + (20 - 2) = 38

Thus, all except option 3 does not follow the pattern.

Hence, the number pair '46 : 12167' is the odd one out.

Alternate Method14 : 512 → (14 ÷ 2 + 1)³ = 512

22 : 1728 → (22 ÷ 2 + 1)³ = 1728

46 : 12167 → (46 ÷ 2 + 1)³ = 13824 ≠ 12167

38 : 8000 → (38 ÷ 2 + 1)³ = 8000

Hence, the correct answer is "Option 3".

Given:

The height of the right circular cylinder = 14 cm

The curved surface area of the right circular cylinder = 704 sq cm

Formula used:

The curved surface area of the right circular cylinder = 2 × π × R × h

The volume of the right circular cylinder = π × R² × h     Where, R = The radius of the cylinder, and h = The height of the cylinder

Calculation:

Let us assume the volume of the cylinder be V and radius be R

⇒ 704 = 2 × (22/7) × R × 14

⇒ R = 8 cm

⇒ The volume V = (22/7) × 8² × 14 = 2816 cm³

∴ The required result will be 2816 cm³.

Kidney, Liver and Lungs are the internal organs of the body.

Whereas,

Nose is not an internal organ.

Hence, “nose” is the odd one out.

Shortcut Trick

Volume of cylinder V = π × r² × h

Given r = h, ∴ V = π × h³

814 = (22/7) × h³

h³ = 814 × (7/22) = 37 × 7 = 259

h = ³√259 cm

∴ The correct option is C.

Alternate Method

Given:

Volume of cylinder (V) = 814 cm³

Radius (r) = Height (h)

Value of π = 22/7

Formula Used:

Volume of a right circular cylinder = πr²h

 r    h Condition: r = h Volume = 814 cm³

Calculations:

⇒ Volume = π × r² × h

⇒ 814 = (22/7) × h² × h (since r = h)

⇒ 814 = (22/7) × h³

⇒ h³ = (814 × 7) ÷ 22

⇒ h³ = 37 × 7

⇒ h³ = 259

⇒ h = ³√259 cm

∴ The correct option is C.

Additional Information

Curved Surface Area (CSA) of Cylinder

The area of the curved surface is given by the formula 2πrh.

Total Surface Area (TSA) of Cylinder

The total area including the two circular bases is 2πr(r + h).

Hollow Cylinder Volume

Volume of a hollow cylinder with external radius R and internal radius r is π(R² − r²)h.

Cheraw dance is the traditional dance form of Mizoram.

• It consists of usually six to eight people holding a pair of bamboo staves onto another bamboo positioned horizontally on the ground.
• It is an attractive hub during festive occasions.
• In 2010, A Guinness World Record was made in which the highest number of Cheraw dancers performed at the same time.
• It also recognized as the oldest dance form of Mizoram.

The correct answer is phototropism.

Key Points

• Phototropism is a directed response in plants that permits them to grow towards, or away from, a light source.
• The modulation of physiology or development in relation to day length is known as photoperiodism.
• Positive phototropism is the plant's reaction to the light source.
• Sunflower is an example.
• Negative phototropism occurs when a plant grows in the opposite direction of the light source.

Important Points

• In 1880, Charles Darwin studied phototropism in canary grass and oat coleoptiles with the help of his son, and published his findings in the book 'The Power of Movement in Plants.' They noticed seedlings bending towards the light.
• They showed this by covering the tops of the oat coleoptiles, preventing photosynthesis.
• They became phototropic when they covered the lower portion of these coleoptiles. From this and other trials, he determined that the grass's tip (called coleoptiles) has a strong perception of light and bends towards it, but the central region activates protons, lowering the pH in the cells.

Here pair of ‘Purpose and Place’ is given in all options except Court – Justice (option 1).It might be  Justice - court

Hence, the odd word pair is ‘Court - Justice’.

Given:

40% of the students in a class are from India and 50% are girls.

Calculation:

40% of the students in the class are from India.

That mean, Non-Indian student = 100 - 40 = 60%

Let the total number of students be 100.

Total number of Indian students = 100 × 4010040100

 = 40

Total number of girls in Indian students = 40 × 2510025100

 = 10

Total number of Indian boys = 40 - 10 = 30

Total number of boys = 50 (Because 50% are girls)

So, number of non-Indian Boys = 50 - 30 = 20

Required % = 20602060

 × 100 = 33.33%

∴ 33.33% percentage of non-Indian students are boys.

The logic followed here is:-

HDLS

GCKT

DZHW

PLSK

Hence, PLSK is different from other three alternatives.

Hence, the correct answer is "PLSK".

Alternate Method

The logic followed here is:

Sum of positional value of the all letters = prime number.

1. HDLS → 8 + 4 + 12 + 19 = 43

2. GCKT → 7 + 3 + 11 + 20 = 41

3. DZHW → 4 + 26 + 8 + 23 = 61

4) PLSK → 16 + 12 + 19 + 11 = 58

Hence, the correct answer is "PLSK".

Shortcut Trick

Calculate the Total Interest Percentage: (Interest ÷ Principal) × 100

Total Interest % = (1260 ÷ 18000) × 100 = 7%

Given the Annual Rate of Interest is 7% per annum.

Since the total interest percentage (7%) matches the annual rate (7%), the Time Period must be exactly 1 year.

∴ The correct answer is 1 year.

Alternate Method

Given:

Principal (P) = ₹18,000

Compound Interest (CI) = ₹1,260

Rate (R) = 7% per annum

Formula: Amount (A) = Principal (P) + Compound Interest (CI)

Calculation:

⇒ Amount (A) = 18000 + 1260 = ₹19,260

⇒ Formula for Compound Interest: A = P(1 + R/100)ⁿ

⇒ 19260 = 18000(1 + 7/100)ⁿ

⇒ 19260 ÷ 18000 = (107/100)ⁿ

⇒ 1.07 = (1.07)ⁿ

⇒ (1.07)¹ = (1.07)ⁿ

⇒ n = 1

∴ The correct answer is 1 year.

Additional Information

Compound Interest Formula

The formula for the total amount is A = P(1 + r/n)^nt, where n is the number of times interest is compounded per year.

CI vs SI for the First Year

For the first year (or the first compounding period), Simple Interest and Compound Interest are always equal on the same principal and rate.

Effective Interest Rate

When interest is compounded more than once a year, the Effective Annual Rate (EAR) is higher than the nominal rate, calculated as [(1 + r/n)ⁿ − 1] × 100.

The correct answer is "Harda".

Key Points:

• A total of 9 districts of M.P. share border with Maharashtra. They are:
• Khargone.
• Badwani.
• Betul.
• Khandwa.
• Chhindwara.
• Seoni.
• Balaghat.
• Alirajpur.
• Burhanpur.

Additional Information: Districts of M.P. sharing border with neighbouring states:

An inert gas is a gas that has extremely low reactivity with other substances. The noble gases—helium, argon, neon, xenon, krypton, radon, and element 118 (Uuo)—exist in their elemental form and are found in Group 18 of the periodic table.

The pattern followed here is:

According to the alphabetical positions of the letters,

In numerical series, the difference is consecutive multiples of 12.

Hence, ‘T126C’ is the correct answer.

Given:

The average weight of 12 persons increased by 3.5 when a new person replaced a 58 kg person

Formula used:

Weight of new person = previous person weight + Increased × number of persons

Calculation:

According to the formula, 

⇒ Weight of new person = 58 + 3.5 × 12

⇒ Weight = 58 + 42 =100

⇒ Hence, The weight of the new person is 100 kg

Alternate Method

 Let average weight of 12 persons be x.

Total weight of 12 persons = 12x

If a person with 58 kg weight is replaced by a new person of y kg weight,

Average weight increases by 3.5 kg.

Then, 12x – 58 + y = 12(x + 3.5)

⇒ 12x – 58 + y = 12x + 42

∴ y = 58 + 42 = 100 kg

Therefore, the weight of new person is 100 kg.

According to given conditions:

Distance is he now from his house \(= \sqrt {{6^2} + {8^2}} = \sqrt {36 + 64} = \sqrt {100} = 10\;km\)

Hence, ’10 km’ is the correct answer.