RRB Group D Previous Year Paper (Held on: 1 Sept 2022 Shift 1)

The correct answer is Mizoram.

Key Points

• Anthurium festival of Mizoram is one of the most popular festivals celebrated in the state.
• This festival is celebrated to promote tourism.
• The Anthurium Festival is organized annually by the Tourism Department in collaboration with the Horticulture Department.
• The Chapchar Kut is also regarded as the most popular spring festival for the people of the state.
• This festival is a public holiday in the state.
• Traditional bamboo dance - Cheraw and other dances were performed at the main event, attracting thousands of people.
• Mizoram:
• State Animal - Sumatran serow.
• State Bird - Mrs. Hume's pheasant.
• National Parks - Murlen National Park, Phawngpui National Park.

Additional Information

• Festivals of Assam:
• ​Bihu is the harvest festival of Assam.
• Bihu marks the end of the harvesting season.
• Bihu is a set of three important Assamese festivals.
• Rongali or Bohag Bihu in April.
• Kongali or Kati Bihu in October.
• Bhogali or Magh Bihu in January.
• Festivals of Manipur:
• ​Lai Haraoba.
• Kang Festival.
• Sangai Festival.
• Kut Festival.
• Cheiraoba Festival
• Festivals of Nagaland:
• ​Hornbill Festival.
• Sekrenyi.
• Tsukheneye.
• Aoleang.
• Naknyulem

Given:

25 ÷ 5 × 2 + 25 - 11 = 24

Calculation:

By option Method:

Option I: After interchanging 11, 24

⇒ 25 ÷ 5 × 2 + 25 - 24 = 11

⇒ 5 × 2 + 25 - 24

⇒ 10 + 1

⇒ 11 = 11

This is correct the equation.

Option II: After interchanging  2, 5

⇒ 25 ÷ 2 × 5 + 25 - 11 = 24

⇒ 12.5 x 5 + 25 -11 = 24

⇒ 76.5  ≠ 24

This is not correct the equation.

Option III: After interchanging 5, 25

⇒ 25 ÷ 25 × 2 + 5 - 11 = 24

⇒ 1 × 2 + 5 - 11 = 24

⇒ - 5 ≠ 11

This is not correct the equation.

Option IV: After interchanging 24, 25

⇒ 25 ÷ 5 × 2 + 24 - 11 = 25

⇒ 5 × 2 + 24 -11 = 25

⇒ 23 ≠ 25

This is not correct the equation.

∴ Interchanges (11,24) would make the given equation correct.

The correct answer is Sindhi.

Key Points

• The Sindhi language was added to the list of languages in the Indian Constitution by the 21st Amendment in 1967.
• It was added to the 8th schedule by the 21st Amendment Act of 1967.

Additional Information

• There are 22 languages that have been recognized in the eighth schedule of the Indian constitution.
• Part XVII of the Indian constitution deals with the official languages of India from articles 343 to 351.
• Originally, only 14 languages were mentioned and later, after several amendments, the other languages were added.
• The Sindhi language was added to the 8th schedule by the 21st Amendment Act of 1967.
• Konkani, Manipuri and Nepali were added by the 71st Amendment Act of 1992.
• Bodo, Dongri, Maithili and Santhali were added by the 92nd Amendment Act of 2003.
• Of all the 22 official languages the Hindi language is spoken by most of Indians.

Shortcut Trick

Product of LCM and HCF = Product of the two numbers.

Product = 48 and Difference = 13.

Check options: 3 × 16 = 48 and 16 − 3 = 13. This satisfies both conditions.

∴ The correct answer is 3 and 16.

Alternate Method

Given:

LCM × HCF = 48

Difference (x − y) = 13

Formula Used:

Product of two numbers = LCM × HCF

Calculations:

⇒ Let the numbers be x and y.

⇒ x × y = 48

⇒ x − y = 13 ⇒ x = 13 + y

⇒ (13 + y) × y = 48

⇒ y² + 13y − 48 = 0

⇒ y² + 16y − 3y − 48 = 0

⇒ y(y + 16) − 3(y + 16) = 0

⇒ (y − 3)(y + 16) = 0

⇒ y = 3 (since numbers are positive)

⇒ x = 13 + 3 = 16

∴ The correct answer is 3 and 16.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF as a Factor

The HCF of two or more numbers is always a factor of their LCM.

Co-prime Numbers

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

Shortcut Trick

Work done by Rani in 1 day (6 hours) = 6 ÷ 3 = 2 gowns.

Work done by Padma in 1 day (6 hours) = 6 ÷ 2 = 3 gowns.

Alternate days cycle (2 days): 2 + 3 = 5 gowns.

In 10 cycles (20 days), work done = 10 × 5 = 50 gowns.

Remaining 2 gowns are stitched by Rani on the 21^st day.

∴ The correct answer is 21 days.

Alternate Method

Given:

Time taken by Rani per gown = 3 hours.

Time taken by Padma per gown = 2 hours.

Daily working hours = 6 hours.

Total gowns to be stitched = 52 gowns.

Calculations:

⇒ Day 1 (Rani) = 2 gowns.

⇒ Day 2 (Padma) = 3 gowns.

⇒ Total gowns in 2 days = 2 + 3 = 5 gowns.

⇒ Total cycles of 2 days needed = 52 ÷ 5 = 10 cycles with 2 gowns remainder.

⇒ Days for 10 cycles = 10 × 2 = 20 days.

⇒ Gowns completed in 20 days = 10 × 5 = 50 gowns.

⇒ Remaining gowns = 52 − 50 = 2 gowns.

⇒ On 21^st day, Rani stitches the remaining 2 gowns (since her capacity is 2 gowns/day).

⇒ Total time = 20 + 1 = 21 days.

∴ The correct answer is 21 days.

Additional Information

Alternate Day Work

In alternate work, tasks are solved in cycles. If A and B work alternately, 1 cycle = 2 days, and work done per cycle = Efficiency(A) + Efficiency(B).

Work and Efficiency

Efficiency is inversely proportional to time. Total Work = Efficiency × Time. In this problem, efficiency is converted to gowns per day based on a 6-hour shift.

Shortcut Trick

Sum of ages 3 years ago = 26 − (3 × 2) = 20 years.

Ratio of Kishore to Sarala (3 years ago) = 3 : 2.

Total units = 3 + 2 = 5 units → 20 years.

1 unit = 4 years ∴ Sarala's age (3 years ago) = 2 × 4 = 8 years.

Present age of Sarala = 8 + 3 = 11 years.

∴ The correct answer is 11 years.

Alternate Method

Given: Sum of Sarala (S) and Kishore (K) is 26. 3 years ago, K was 3/2 of S.

Formula: Ratio = Age₁ / Age₂

⇒ Let Sarala's present age be S.

⇒ Kishore's present age K = 26 − S.

⇒ 3 years ago: (K − 3) = 3/2 × (S − 3).

⇒ (26 − S − 3) = 3/2 × (S − 3).

⇒ 2 × (23 − S) = 3 × (S − 3).

⇒ 46 − 2S = 3S − 9.

⇒ 5S = 55.

⇒ S = 11.

∴ The correct answer is 11 years.

Additional Information

Age Sum Property

If the sum of ages of 'n' persons is S now, then 't' years ago, the sum was S − (n × t).

Ratio of Ages

The difference between the ages of two people remains constant regardless of the number of years passed.

Linear Equations

For age problems, always define variables based on the Present Age to avoid calculation errors in final steps.

The logic is follows here is as,

Hence, 'option 3' is the correct answer.

The correct answer is Ministry of Minority Affairs.

Key Points

• The revised PMJVK will be implemented in all districts of the country including all the Aspirational Districts.
• The projects under PMJVK will be proposed in any area where the concentration of the minority population is more than 25% in the catchment area (15 KM radius).
• The revised PMJVK has been approved by the Government for continuation over the 15th Finance Commission Cycle i.e., during FY 2021-22 to 2025-26.
• PMJVK will support the State/UTs in creating infrastructure to improve the quality of life of people and reduce the imbalances in the identified minority concentration areas to be at par with the rest of the country.

Additional Information

• The Cabinet Committee on Economic Affairs chaired by Prime Minister Narendra Modi on May 2, 2018, approved the proposal for renaming and restructuring of the Multi-sectoral Development Programme (MsDP) as Pradhan Mantri Jan Vikas Karyakram (PMJVK).
• The restructured program would provide better socio-economic infrastructure facilities to the minority communities, particularly in the field of education, health & skill development.
• The area to be covered under PMJVK would be 57% more as compared to the existing MsDP.
• The MsDP covered 196 districts of the country whereas PMJVK will cover 308 districts of the country.

Given:

x = 18% of 200

Calculation:

⇒x = 18% of 200

⇒ x = $200 \times {18 \over 100}$

⇒ x = 36

The value of x is 36.

Shortcut Trick

Let the cost of production be x.

Final Price = x × (112 ÷ 100) × (115 ÷ 100) × (120 ÷ 100) = 15,456.

x × (28 ÷ 25) × (23 ÷ 20) × (6 ÷ 5) = 15,456.

x = (15,456 × 25 × 20 × 5) ÷ (28 × 23 × 6).

x = 10,000.

∴ The correct answer is ₹10,000.

Alternate Method

Given: Retail Price = ₹15,456, Manufacturer Gain = 12%, Wholesale Gain = 15%, Retailer Gain = 20%. Formulas: SP = CP × (100 + P%) ÷ 100.

⇒ Let Cost of Production = C. ⇒ Price after Manufacturer = C × 1.12. ⇒ Price after Wholesaler = (C × 1.12) × 1.15. ⇒ Price after Retailer (Retail Price) = (C × 1.12 × 1.15) × 1.20 = 15,456. ⇒ C × 1.5456 = 15,456. ⇒ C = 15,456 ÷ 1.5456 = 10,000.

∴ The correct answer is ₹10,000.

Additional Information

Successive Percentage Changes

When a value changes by a%, then b%, then c% successively, the Effective Multiplier is (1 + a/100) × (1 + b/100) × (1 + c/100).

Chain Rule in Profit and Loss

In a chain of transactions, the Selling Price for one becomes the Cost Price for the next buyer in the sequence.

Shortcut Trick

Check for divisibility by 11 (since π = 22/7 involves a multiple of 11).

Volume = πr²h = (22/7) × 6 × 6 × 10.5

Volume = 11 × 2 × 6 × 6 × 1.5 = 11 × 108 = 1188 cm³.

∴ The correct answer is 1188 cm³.

Alternate Method

Given:

Diameter (d) = 12 cm ⇒ Radius (r) = 12 ÷ 2 = 6 cm

Height (h) = 10.5 cm

Formula Used:

Volume of a Cylinder = πr²h

Calculations:

⇒ Volume = (22 ÷ 7) × 6 × 6 × 10.5

⇒ Volume = (22 ÷ 7) × 36 × (21 ÷ 2)

⇒ Volume = 22 × 36 × (3 ÷ 2)

⇒ Volume = 11 × 36 × 3

⇒ Volume = 11 × 108

⇒ Volume = 1188 cm³

∴ The correct answer is 1188 cm³.

Additional Information

Curved Surface Area (CSA)

The area of the side surface of a cylinder is given by 2πrh.

Total Surface Area (TSA)

The sum of CSA and the area of two circular bases: 2πr(h + r).

Hollow Cylinder Volume

If R is outer radius and r is inner radius, Volume = π(R² − r²)h.

Given:

$x=\left(-\frac{5}{3}\right) \times\left(\frac{9}{25}\right)+\left(\frac{1}{5}-2\right)$

Calculation:

⇒$\left(-\frac{5}{3}\right) \times\left(\frac{9}{25}\right)+\left(\frac{1}{5}-2\right)= x$

⇒$x=\left(-\frac{3}{5}\right)+\left(\frac{1-10}{5}\right)$

⇒$x=\left(\frac{-3+1-10}{5}\right) ::$

⇒$x=\left(\frac{-12}{5}\right)::$

The value of $\bf \left(-\frac{5}{3}\right) \times\left(\frac{9}{25}\right)+\left(\frac{1}{5}-2\right)=\left(\frac{-12}{5}\right) : :$.

Shortcut Trick

To find the LCM of 24, 42, and 56, pick the largest number and check its multiples.

Largest number = 56

Multiples of 56: 56 (not div by 24, 42), 112 (not div by 24, 42), 168.

Check 168: 168 ÷ 24 = 7 and 168 ÷ 42 = 4.

∴ The correct answer is 168.

Alternate Method

Given: Numbers are 24, 42, and 56.

Formula Used: Prime Factorization Method for finding LCM.

⇒ Prime factors of 24 = 2 × 2 × 2 × 3 = 2³ × 3¹

⇒ Prime factors of 42 = 2 × 3 × 7 = 2¹ × 3¹ × 7¹

⇒ Prime factors of 56 = 2 × 2 × 2 × 7 = 2³ × 7¹

⇒ LCM = Product of the highest powers of all prime factors involved

⇒ LCM = 2³ × 3¹ × 7¹

⇒ LCM = 8 × 3 × 7

⇒ LCM = 168

∴ The correct answer is 168.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers without leaving a remainder.

HCF and LCM Relation

For two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Division Method

A method where numbers are divided by common prime factors simultaneously until no further division is possible by a prime other than 1.

Given:

A, B, C, D, E, F and G were seven kings, sitting around a circular table, facing the centre.

Solution :

(1) Only E was sitting between F and C.

 

(2) G was sitting to the immediate left of C. Case 2 is eliminated and only case 1 is possible.

(3) A was third to the left of G.

(4) Only D was sitting between A and B.

Here, king B was sitting to the immediate left of G.

Hence, 'option 2' is the correct answer.

Given: 

P, Q, R, S, T and U are six siblings who passed their class tenth exam in different years viz. 2001, 2003, 2005, 2007, 2010 and 2012 but not necessarily in the same order.

Solution: 

(1) Only Q passed before R.

(2) P passed in one of the years before S and after R. 

(3) U passed in one of the years before P.

(4) T passed in the year immediately after S. 

Here, 'P' passed their class tenth exam in the year 2007.

Hence, 'option 3' is the correct answer.

Shortcut Trick

Substitute a standard angle value, say A = 60°.

LHS = sin² 60° ÷ (1 − cos 60°) = (3/4) ÷ (1 − 1/2) = (3/4) ÷ (1/2) = 1.5.

Now check the options: cos 60° + 1 = 0.5 + 1 = 1.5.

Since the values match, the expression simplifies to cos A + 1.

∴ The correct answer is cos A + 1.

Alternate Method

Given: The trigonometric expression is (sin² A) ÷ (1 − cos A).

Formula Used: Standard trigonometric identity sin² A + cos² A = 1 and algebraic identity a² − b² = (a − b)(a + b).

⇒ From the identity, we know: sin² A = 1 − cos² A

⇒ The given expression becomes: (1 − cos² A) ÷ (1 − cos A)

⇒ Using (a² − b²) formula: [(1 − cos A) × (1 + cos A)] ÷ (1 − cos A)

⇒ Cancelling the common term (1 − cos A) from numerator and denominator:

⇒ Result = 1 + cos A

∴ The correct answer is cos A + 1.

Additional Information

Pythagorean Identities

The three main identities are sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

Always keep in mind that sec A = 1/cos A and cosec A = 1/sin A for quick simplifications.

Factorization in Trigonometry

Expressions like 1 − sin² A or sec² A − 1 can often be factored as a difference of squares to cancel terms in fractions.

The correct option is 'H2S' .

Key Points

• Na₂S+2HCl→2NaCl+H₂S↑
• H₂S
• ​Hydrogen sulfide is slightly denser or heavier than air but fairly soluble in water.
• Hydrogen sulphide is a colourless, poisonous gas that can lead to headaches even if it is inhaled in small quantities.
• It has a distinct rotten egg smell.
• Hydrogen sulfide is a flammable gas.​

The correct answer is Only (i).

Key-points

• According to Dobereiner, when Elements are arranged in Order of Increasing Atomic Mass, groups of three Elements (known as triads) that have Similar Chemical Properties are Obtained.
• The Atomic mass of the Middle Element was nearly equal to the Arithmetic Mean of the Other.
• Examples of triads of elements are as follows-

• This classification was not widely accepted since only a few elements could be arranged into triads.

Additional Information

• Moseley's Modern periodic law
• According to Moseley's Modern periodic law, Elements are Arranged in a Tabular form based on their Atomic Numbers.
• it states that the Chemical and Physical Properties of Elements is a Periodic Function of their Atomic Number.
• Newland 
• Newland arranged the Elements in the Order of Increasing Atomic Masses and found that the Properties of Every 8th Element are Similar to that of the 1st Element, Just like musical notes.
• Mendeleev
• Mendeleev arranged the Elements in the Increasing Order of their Atomic Mass.
• Mendeleev's Periodic table is based on the Chemical Properties of the Elements.
• It contains 7 Periods(horizontal rows) and 8 Groups (vertical columns).

The correct answer is $\frac{u v}{u+v}$.

Key Points

• Mirror Formula: The following formula is known as the mirror formula, which provided a relationship between focal length (f), image distance (v), and objects distant (u) as shown below

 

 

Since the plane mirror is a part of an infinitely large spherical mirror, therefore the radius of curvature and focal length of the plane mirror is Infinity. Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when focal length goes to infinity. 

$\Rightarrow \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

so f =  $\frac{u v}{u+v}$

​EXPLANATION:

Plane Mirror is a part of the infinitely large spherical mirror:

Additional Information

Sign convention in mirrors

• All distances are measured from the pole of the mirror.
• The distance measured from the pole (p) to the left side of the mirror is taken as negative.
• The distance measured from the pole (p) to the right side of the mirror is taken as positive.
• The heights measured upwards and perpendicular to the principal axis of the mirror is taken as positive.
• The heights measured downwards and perpendicular to the principal axis of the mirror is taken as negative.

The correct answer is reducing agent.

Key-points

• a reducing agent (also known as a reductant, reducer, or electron donor) is a chemical species that "donate" an electron to an electron recipient (called the oxidizing agent, oxidant, oxidizer, or electron acceptor).
• CuII + 2 e- → Cu0 (reduction)
• Mg0 - 2 e- → MgII (oxidation)
• Reduction is the gain of electrons or a reduction in the oxidation state of an atom, ion, or certain atoms in a molecule.
• Mg + CuSO4 = Cu + MgSO4 is a redox reaction where Mg is oxidized and Cu is reduced.
• Mg is a reducing agent (i.e. it lost electrons) and CuSO4 is an oxidizing agent (i.e. it gained electrons).

​

Additional information

• Oxidizing agent
• ​An oxidizing agent (often referred to as an oxidizer or an oxidant) is a chemical species that tends to oxidize other substances, i.e. cause an increase in the oxidation state of the substance by making it lose electrons.
• ​Dissolving agent
• ​A solvent is a dissolving agent and is the liquid portion of a solution.
• The molecules that dissolve in the solvent are called solutes.
• ​Catalyst
• ​A catalyst is a substance that speeds up a chemical reaction or lowers the temperature or pressure needed to start one, without itself being consumed during the reaction.
• Catalysis is the process of adding a catalyst to facilitate a reaction.

Drawing figure as per given information,

• To reach house B from house A, a person has to walk 30 m towards the south.
• Then he must take a left turn and walk 15 m.
• Then he must take a left turn again and walk 20 m.
• Again, he must take a left turn and walk 25 m.
• Then he must take a right turn and walk 10 m.
• Then he must take a left turn and walk 17 m to finally reach house B.

Here, 27 m, East direction is house A from house B.

Hence, 'option 2' is the correct answer.

The correct answer is Male germ cell - small and motile, Female - large with food store.

Key-points 

Here's a table that explains the characteristics of male germ cells (sperm cells) and female germ cells (oocytes):

• Explanation:
• Size:
• Male germ cells, or sperm cells, are generally small in size.
• They are specialized for mobility and reaching the egg for fertilization.
• In contrast, female germ cells, known as oocytes or eggs, are comparatively larger due to the presence of abundant cytoplasm to support the developing embryo.
• Motility:
• Sperm cells are highly motile, equipped with a whip-like tail called a flagellum, which propels them toward the egg.
• Their motility allows them to swim through the female reproductive tract to reach the site of fertilization.
• On the other hand, oocytes are non-motile and remain stationary within the ovaries until they are released during ovulation.
• Food Store:
• Male germ cells (sperm cells) have a limited food store.
• They primarily carry genetic material necessary for fertilization but rely on the female reproductive tract for nourishment.
• In contrast, female germ cells (oocytes) possess a substantial food store in the form of yolk or nutrient-rich cytoplasm.
• This food supply is crucial for supporting the early stages of embryo development until it can establish its own nutrient supply.

Given :  I _ L O _ R U V X _ B _ G

By checking options and substituting accordingly.

(1): JPAD   → I J L / O P R / U V X / A B D / G

Here, each word is formed with three alphabets. In which gap between 2nd and 3rd alphabet is one alphabet while gap between last alphabet and first alphabet of next word is two alphabets .As given in below figure,

(2): JPAG  →  I J L / O P R / U V X / A B G / G (No pattern Followed)

(3): JPXD  →  I J L / O P R / U V X / X B D / G (No pattern Followed)

(4): JRAD  →  I J L /O R R / U V X / A B D / G  (No pattern Followed) ​

Hence, ‘JPAD ’ is the correct answer.

Given: 

Eight classmates D, E, F, G, H, I, J and K are sitting in a straight row, facing north. 

Solution:

(1) There are only two classmates sitting between H and D.

(2) K sits to the immediate left of D.

(3)  D and I are immediate neighbours.

(4)  J is at the extreme right end of the row.

(5) Only E sits between I and G.

• Only case 1 is possible.

(6) unoccupied seat will be filled by F.

Here, F sits at the second position from the left end of the row.

Hence, 'option 2' is the correct answer.

The correct answer is History.

Key Points

• Temporal synthesis is defined as the automated construction of a system whereby we develop a temporary specification and then try to prove it.
• It is done in history as a discipline.
• It refers to the comparisons made with respect to the passage of time.
• Here, if a process is temporally extended, it means that it happens over a period of time.
• If the occurrence of two events differs temporally, then they happened at different points in time.

Additional Information

• Spatial synthesis is attempted by Geography.
• It includes any of the formal techniques which study entities using their topological, geometric, or geographic properties.
• Geomorphology:
• ​Geomorphology is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or near Earth's surface.
• Spatial synthesis is the subject matter in Geomorphology.
• Anthropology:
• ​Anthropology is the study of the origin and development of human societies and cultures.
• Culture is the learned behaviour of people, including their languages, belief systems, social structures, institutions, and material goods.
• Both Spatial and temporal synthesis are the subject matter in Anthropology.
• Philosophy:
• ​Philosophy is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.
• Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation.
• Existential synthesis is the subject matter in Philosophy.

The correct answer is Swaran Singh Committee.

Key Points

• The Fundamental Duties were incorporated in Part IV-A of the Indian Constitution through the 42nd Constitutional Amendment Act, 1976.
• At present, there are eleven fundamental duties under Article 51 A of the constitution.
• The idea of Fundamental Duties has been borrowed from the erstwhile USSR.
• Originally the duties were ten in number, later on through 86th Amendment Act, 2002, the eleventh Fundamental duty was added.
• Fundamental duties are non-enforceable in nature.
• Swaran Singh Committee recommended the inclusion of Fundamental Duties in the Indian Constitution.

Additional Information

• JB Kripalani Committee:
• This was the Fundamental Rights sub-committee. It was headed by J.B. Kriplani.
• He suggested that:
• ​Fundamental Rights are the basic human rights guaranteed to the citizens of India by the Constitution.
• There are six fundamental rights Nine major committees were appointed by the Constituent Assembly to deal with different tasks of constitution-making.
• The advisory committee on Fundamental Rights, Minorities, and Tribal and Excluded Areas had a subcommittee.
• HC Mookherjee Committee:
• The Chairman of Minorities Sub Committee was H.C Mookherjee during 1946.
• He was the VicePresident of the Constituent Assembly of India for drafting the Constitution of India before the partition of India.
• AV Thakkar Committee:
• ​He was appointed the chairman of "Excluded and Partially Excluded Areas (Other than Assam), a sub committee of the constituent assembly.
• Mahatma Gandhi would call him 'bapa'.
• In one of his appeals in 1939 Mahatma Gandhi called him "Father of Harijans".

The correct answer is strong, high.

Key-points

• Tungsten metal is used for making the filament of electric bulbs.
• Tungsten is used to making an electrical bulb filament for the following properties:
• It has a very high melting point being an alloy.
• It has very high resistance, so it does not burn easily at room temperature.
• The lamp glows at high temperatures.
• Tungsten filament does not melt even though a significant amount of heat is generated due to the passing of the current through the filament (through the heating effect of the current).

Additional Information

• An incandescent light bulb is an electrical light with a wire filament that is heated until it glows.
• The filament is wrapped in a bulb of glass to shield the filament from oxidation. Current is supplied to the filament by means of terminals or wires inserted in the glass.
• The incandescent bulb has been commonly used in household and commercial lighting, for portable lightings such as car headlamps, table lamps and flashlights, and for decorative and advertisement lighting.

• The shaded part represents  types of juices does the company make that contain both Apple and Strawberry flavours

 

• The number representing types of juices does the company make that contain both Apple and Strawberry flavours = 10 + 8 = 18

Hence, ‘18’ is the correct answer.

Shortcut Trick

Observe the x³ terms: (3 × 9x³) − (9 × 3x³) = 27x³ − 27x³ = 0.

Combine the x² and x terms: 3(−6x²) + (−9 × −2x) = −18x² + 18x.

Combine the constants: (3 × 30) − (9 × 30) = 90 − 270 = −180.

The resulting expression is −18x² + 18x − 180.

Factor out −18: −18(x² − x + 10).

∴ The correct answer is -18(x² − x + 10).

Alternate Method

Given: 3(9x³ − 6x² + 30) − 9(3x³ − 2x + 30)

Method: Apply the Distributive Law a(b + c) = ab + ac and then group like terms.

⇒ (3 × 9x³ + 3 × (−6x²) + 3 × 30) − (9 × 3x³ + 9 × (−2x) + 9 × 30)

⇒ (27x³ − 18x² + 90) − (27x³ − 18x + 270)

⇒ 27x³ − 18x² + 90 − 27x³ + 18x − 270

⇒ (27x³ − 27x³) − 18x² + 18x + (90 − 270)

⇒ −18x² + 18x − 180

⇒ −18(x² − x + 10)

∴ The correct answer is -18(x² − x + 10).

Additional Information

Distributive Property

This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products: a(b + c) = ab + ac.

Combining Like Terms

To simplify algebraic expressions, we group terms with the same variables and exponents together (e.g., all x³ terms together).

BODMAS Rule

Always simplify expressions following the BODMAS order: Brackets, Orders (powers), Division, Multiplication, Addition, and Subtraction.

Factoring

The process of finding the Highest Common Factor (HCF) and rewriting the expression as a product, which is the reverse of distribution.

Shortcut Trick

In parallel lines AB || CD || EF, the transversal BE creates equal angles.

Given ∠BGD = 62°, then ∠ABG = 62° (Alternate Interior Angles).

Since AB || EF, ∠BEF = ∠ABG = 62° (Alternate Interior Angles).

Given EA ⊥ AB and AB || EF, it implies ∠AEF = 90°.

Therefore, w = ∠AEF − ∠BEF = 90° − 62° = 28°.

∴ The correct answer is 28 °.

Alternate Method

Given: AB || CD, CD || EF, EA ⊥ AB, and ∠BGD = 62°.

Formula Used: Sum of interior angles on the same side of a transversal is 180°; alternate interior angles are equal; corresponding angles are equal.

⇒ AB || CD and CD || EF ∴ AB || EF (Lines parallel to the same line are parallel to each other).

⇒ EA ⊥ AB (Given) ⇒ ∠EAB = 90°.

⇒ Since AB || EF and EA is a transversal: ∠EAB + ∠AEF = 180° (Co-interior angles).

⇒ 90° + ∠AEF = 180° ⇒ ∠AEF = 90°.

⇒ Since CD || EF, ∠BGD and ∠GEF are Alternate Interior Angles or Corresponding Angles depending on position.

⇒ In the transversal BE, ∠GEF = ∠BGD = 62° (Alternate interior angles).

⇒ Now, ∠AEF = ∠AEG + ∠GEF.

⇒ 90° = w + 62°.

⇒ w = 90° − 62° = 28°.

∴ The correct answer is 28 °ree;.

Additional Information

Alternate Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles on opposite sides of the transversal and between the parallel lines are equal.

Transitivity of Parallel Lines

If line L1 is parallel to L2 and L2 is parallel to L3, then L1 is parallel to L3.

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.

The logic follows here is as,

Hence, '685' is the correct answer.

The correct answer is Railways.

Key Points

• Finance Minister Nirmala Sitharaman announced, while presenting the India’s budget 2022, the innovative idea of ‘one station, one product’ for the country’s extensive railway network, one of the longest in the world.
• The idea is to better promote supply chain of local product using the railways and making each railway station a promotional hub and showcase destination for a local product.
• This will help develop more efficient logistics for farmers and agri-enterprises and present unique regional products to a wide audience, i.e. railway travellers, passing through the stations.
• One station, one product takes forward the ‘one district, one product’ programme of the government which has successfully started promoting unique products from every district of India.

Additional Information

• Budget 2023-24 (ODOP)
• One District District One Product Product (ODOP) is a theme introduced by the government of India that aims to reap the benefit of scale in terms of procurement of inputs, availing common services, and marketing of products.
• ODOP for the scheme provides the framework for value chain development and alignment of support infrastructure.
• Districts as Export Hubs is the first such initiative of the Government of India which aims to target export promotion, manufacturing, and employment generation at the grass-root level and has made States and Districts accountable for the export growth from the districts in the country.

The correct answer is IIT Hyderabad.

Key Points

• Swarajability, India's first AI-based job portal for persons with disabilities, has been launched to widen their opportunities with tech applications.
• The platform aids people with disabilities like visual, hearing impairment, and locomotive disorders in seeking employment.
• IIT-Hyderabad provided expertise for the Artificial Intelligence component.
• The project is funded by Kotak Mahindra Bank.

Important Points 

• It is developed in both web and mobile app versions for maximum reach.
• Visual Quest India is the developer and Youth4Jobs offered its experience in skilling, disability, and job linkages.
• It is a one-stop-shop for organisations that want to hire persons with disabilities.
• Also, it supports NGOs, educational institutions, and governments in their efforts to promote diversity and inclusion.

Explanation:

Given: 

Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. 

solution:

(1) P's exam is on Tuesday.

(2) R's exam is on Sunday. 

(3) S's exam is immediately before R.

(4) Q's exam is immediately before S.

(5) Only two people have exams between S and V. 

(6) Only three people have exams between U and Q

(7) Now, T has exam on Thursday.

Hence, 'U' has exam on Monday.

Given :

In year 2018

• The value of India's cotton export in year 2018 = 410 crores
• The Quantity of India's cotton export in year 2018 = 348 thousand ton

 In year 2019

• The value of India's cotton export in year 2019 = 320 crores
• The Quantity of India's cotton export in year 2019 = 270 thousand ton

 In year 2020

• The value of India's cotton export in year 2020 = 350 crores
• The Quantity of India's cotton export in year 2020 = 280 thousand ton

 In year 2021

• The value of India's cotton export in year 2021 = 450 crores
• The Quantity of India's cotton export in year 2021 = 350 thousand ton

Calculation:

1. The value per thousand tons of year 2018 =(410/348)  = 1.178 crores per thousand ton
2. The value per thousand tons of year 2019 =(320/270)  = 1.185 crores per thousand ton
3. The value per thousand tons of year 2020 = (350/280) = 1.250 crores per thousand ton
4. The value per thousand tons of year 2021 = (450/350) = 1.280 crores per thousand ton

 

Hence, The value per thousand tons the minimum in year 2018.

Given:

For institute B,

• The  number of students called for an interview in year 2018 is 120
• The  number of students called for an interview in year 2019 is 92
• The  number of students called for an interview in year 2020 is 100

For institute C,

• The number of students called for an interview in year 2018 is 108
• The number of students called for an interview in year 2019 is 100
• The number of students called for an interview in year 2020 is 80

Calculation :

 The average number of students called for an interview from institute B in the period 2018 to 2020 = $120+92+100 \over 3$ = 104

 The average number of students called for an interview from institute C in the period 2018 to 2020 = $108+100 +80 \over 3$ = 96

Now,

The ratio of the average number of students called for an interview from institute C in the period 2018 to 2020 to the average number of students called for an interview from institute B in the same period is 96:104  = 12 : 13.

That is , The Required ratio is 12:13.

The correct answer is Virat Kohli.

Key Points

• The flamboyant and fearless, top-order Indian batsman Virat Kohli gets 1st place in terms of scoring the most runs in IPL, with 6411 runs in 216 Matches (208 innings).
• Making his IPL debut for Royal Challengers Bangalore in 2008, Kohli has played all IPL games for RCB so far and averaged 36.43 in the event.
• The modern-day great also holds the record of amassing the most runs in a single IPL season, 973 runs in 16 matches in 2016.
• Unfortunately, despite being one of the best, Virat Kohli is yet to win an IPL trophy.

Additional Information

• WPL 2023 Highlights:
• ​Recently WPL 2023 was organized by BCCI the final match of the tournament was played at Brabourne Stadium in Mumbai.
• Mumbai Indians defeated Delhi Capitals and won the first tournament title.
• Orange Cap Award (For Most Runs) – Meg Lanning (Delhi Capitals)
• Purple Cap Award (for most wickets) – Hayley Mathews (Mumbai Indians)
• The mascot of the WPL:  a tiger.
• Sponsored: The Tata Group
• WPL had organized for the first time in the year 2023.
• Men’s IPL started in the year 2008.
• The Women’s Premier League was hosted at DY Patil Stadium and closed at Barabourne Stadium in Mumbai.
• A total of 5 teams have been included in the Women’s Premier League.
• Gujarat Giant – Adani
• Mumbai Indians – Relines
• Royal Challenger Bangalore – Diageo
• Delhi Capital – JSW
• UP Warrior – Capri Global

Given Statements:  C = U < F ≤ H > G = I > R

Conclusions:

I. H > R → True (as H > G = I > R → as H is greater than G,I and I is greater than R.)

II. H > C → True (as in  C = U < F ≤ H → as C is equal to U and less than F . F is less than H. hence, H is greater than C. )

Hence, 'Both conclusions I and II are true'.

The correct answer is The President of India.

Key Points

• The Chief Justice of India (CJI) is appointed by the President of India under clause (2) of Article 124 of the Constitution.
• The chief justice is appointed by the president after consultation with such judges of the Supreme Court and high courts as he deems necessary.
• The other judges are appointed by the president after consultation with the chief justice and such other judges of the Supreme Court and the high courts as he deems necessary.
• Consultation with the chief justice is obligatory in the case of the appointment of a judge other than the Chief justice.

Additional Information

• The basic procedure to be followed for the appointment of CJI is:
• Appointment to the office of the Chief Justice of India should be of the senior-most Judge of the Supreme Court considered fit to hold the office.
• The Union Minister of Law, Justice and Company Affairs would, at the appropriate time, seek the recommendation of the outgoing Chief Justice of India for the appointment of the next Chief Justice of India.
• Whenever there is any doubt about the fitness of the senior-most Judge to hold the office of the Chief Justice of India, consultation with other Judges as envisaged in Article 124 (2) of the Constitution would be made for the appointment of the next Chief Justice of India.
• After receipt of the recommendation of the Chief Justice of India, the Union Minister of Law, Justice and Company Affairs will put up the recommendation to the Prime Minister who will advise the President on the matter of appointment.

The correct answer is mental.

 Key Points

• The Ministry of Women and Child Development (MoWCD) and NIMHANS Bengaluru launched a Project’ in March 2022 with the goal of improving women’s mental health in India.
• The increasing ability of OSC (One-Stop Center) officials in terms of tools and procedures for One-Stop Centers, particularly those who have experienced violence and distress, with compassion and care.
• One-Stop Center performed admirably during the COVID time.
• There are already over 700 One-Stop Centers operating across the country.
• People who work in these one-stop shops will be taught how to appropriately operate the Self Defense Shaheed Women helpline and counsel.
• The advanced training programme will be delivered in all of the regional languages that they want to be able to com website dedicated to this, which contains a wealth of information on training.

Additional Information

• Ministry of Women and Child Development:
• ​The Department of Women and Child Development was set up in the year 1985 as a part of the Ministry of Human Resource Development to give the much-needed impetus to the holistic development of women and children.
• With effect from 30 January 2006, the Department has been upgraded to a Ministry.
• The Ministry of Women and Child Development, a branch of the Government of India, is an apex body for the formulation and administration of the rules and regulations and laws relating to women and child development in India.
• The current minister for the Ministry of Women and Child Development is Smriti Irani having held the portfolio since 31 May 2019.

The correct answer is '$\bf \bar{C}+\bar{I}+c Y : :$'.

Key Points 

• In an economy without a government, the ex-ante aggregate demand for final goods is the sum total of the ex-ante consumption expenditure and ex-ante investment expenditure on such goods, viz. AD = C + I.
• Aggregate demand for final goods can be written as

AD = $\bar{C}+\bar{I}+c Y$

• If the final goods market is in equilibrium this can be written as

Y = $\bar{C}+\bar{I}+c Y$

• where Y is the ex-ante, or planned, output of final goods.
• This equation can be further simplified by adding up the two autonomous terms, C and I, making it

Y = A + c.Y

• Where A = C + I is the total autonomous expenditure in the economy.
• In reality, these two components of autonomous expenditure behave in different ways.
• C, representing the subsistence consumption level of an economy, remains more or less stable over time.
• However, I have been observed to undergo periodic fluctuations.

• The shaded part represents people eat potatoes and eggs for dinner but NOT chickens.

 

• The number representing people eat potatoes and eggs for dinner but NOT chickens = 21.Hence, ‘21’ is the correct answer.

Given Statements: B > Y ≤ Z = A < X > O

Conclusions:

I. B > X → False (as B > Y ≤ Z = A < X → clear relation between B and X cannot be determined).

II.  Y < O → False (as in Y ≤ Z = A < X > O → clear relation between Y and O cannot be determined).

III.  Y < X → True (as in Y ≤ Z = A < X  → Because X is greater than A. A is equal to Z. Z is greater than Y. Hence X is greater than Y).

IV. A > O → False (as in A < X > O → clear relation between A and O cannot be determined).

Here, Only the conclusion III follows.

Hence, 'Option 1' is the correct answer.

The correct answer is H2 + Br2 → 2HBr.

Key-points:

• The balanced chemical reaction for the reaction between hydrogen and bromine to form hydrogen bromide can be represented as follows:
• H2 + Br2 → 2HBr
• Explanation:
• The reaction you provided involves the combination of hydrogen gas (H2) and bromine gas (Br2) to produce hydrogen bromide gas (HBr).
• In the reaction, two molecules of hydrogen gas (H2) react with one molecule of bromine gas (Br2) to produce two molecules of hydrogen bromide gas (HBr).
• Let's break down the reaction step by step:
• Hydrogen gas (H2): Hydrogen gas is a diatomic molecule, meaning it consists of two hydrogen atoms bonded together.
• Bromine gas (Br2): Bromine gas is also a diatomic molecule, comprising two bromine atoms bonded together.
• Balanced Equation:
• To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.
• In this case, we have two hydrogen atoms on the left side (2H) and two hydrogen atoms on the right side (2H), as well as two bromine atoms on the left side (Br2) and two bromine atoms on the right side (2HBr).
• Thus, the equation is balanced.

The correct answer is Both (a) and (b).

Key-points

• Magnetic field: The region around a magnet in which its force can be experienced.
• Solenoid:  A long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it.
• Explanation:

Magnetic field due to a long solenoid carrying current I:

• The magnetic field around a solenoid is similar to that around a bar magnet.
• The magnetic field lines move from south to north inside the solenoid and north to south outside the solenoid. Thus, forming closed loops.
• Inside the solenoid, the magnetic field lines move parallel to each other. Thus, it is uniform inside the solenoid.
• The magnetic field is strongest inside the solenoid.
• 

​

Shortcut Trick

When the distance traveled is the same for both journeys, use the harmonic mean formula.

Average Speed = (2 × x × y) ÷ (x + y)

Average Speed = (2 × 30 × 60) ÷ (30 + 60)

Average Speed = 3600 ÷ 90 = 40 km/h.

∴ The correct answer is 40 km/h.

Alternate Method

Given:

Distance (one way) = 90 km

Forward Speed (v₁) = 30 km/h

Return Speed (v₂) = 60 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Calculations:

⇒ Time taken for forward journey (t₁) = 90 ÷ 30 = 3 hours

⇒ Time taken for return journey (t₂) = 90 ÷ 60 = 1.5 hours

⇒ Total Distance = 90 + 90 = 180 km

⇒ Total Time = 3 + 1.5 = 4.5 hours

⇒ Average Speed = 180 ÷ 4.5 = 40 km/h

∴ The correct answer is 40 km/h.

Additional Information

Average Speed (Equal Distances)

If an object covers equal distances at speeds u and v, the average speed is (2uv) ÷ (u + v). This is independent of the actual distance.

Average Speed (Equal Time)

If an object travels for equal time intervals at speeds u and v, the average speed is the arithmetic mean: (u + v) ÷ 2.

Relative Speed

For objects moving in the same direction, relative speed is |u − v|. For objects moving in opposite directions, it is (u + v).

Drawing figure as per given information,

• P is 400 m to the west of K.
• M is 200 m to the east of L.
• O is 300 m to the north of K.
• N is 150 m to the south of L.
• L is 250 m to the south of K.

Straight distance between O and N = 300 + 250 + 150 = 700

Hence, '700 m' is the correct answer.

Given:

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

Solution:

(1) Z sits at one of the extreme ends of the row.

(2) Only one person sits to the right of S.

 

 

(3)  Only one person sits between Q and S.

(4) Only two people sit between D and Z. This is possible only in Case 1.

 

(5) P sits to the immediate left of Q.

(6) P sits second to the right of L.

(7) K sits to the immediate right of D.

(8) L sits second to the right of D.

So here, 12 is the total number of persons seated.

Hence, '12' is the correct answer.

The logic follows here is as,

                       

Similarly,

Hence, 'option 4' is the correct answer.

The correct answer is A - iii, B - iv, C - i, D - ii.

Key-points

• Based on the descriptions given, the epithelial tissues can be matched to their corresponding locations in the body as follows:
• Pseudostratified Columnar Epithelium  - Respiratory Tract
• Stratified Squamous Epithelium - Skin
• Simple Squamous Epithelium - Lining of Blood Vessels
• Simple Cuboidal Epithelium - Ducts of Salivary Glands

Additional Information

• Pseudostratified Columnar Epithelium (Respiratory Tract):
• This is a single-layered tissue with nuclei at different levels, making it appear stratified.
• It lines the trachea and bronchi, where it secretes and moves mucus using its cilia.
• Stratified Squamous Epithelium (Skin):
• This multi-layered tissue is found in areas exposed to friction like the skin.
• The cells on the surface are flat, while those underneath can be cuboidal or columnar.
• This tissue protects underlying tissues from injury, infection, and dehydration.
• Simple Squamous Epithelium (Lining of Blood Vessels):
• This is a single layer of flat cells that allows rapid diffusion or transport of substances.
• Found in the lining of blood vessels, it reduces friction for the flowing blood.
• Simple Cuboidal Epithelium (Ducts of Salivary Glands):
• Consisting of a single layer of cube-shaped cells, this tissue is involved in secretion, absorption, and excretion.
• Found in glands and their ducts like salivary glands, it helps in transporting saliva to the mouth.

Given : 

$\frac{5^3 \times 27 \times 10^3}{5^6 \times 3^2 \times 4}$

Concept Used 

Indices law

Calculation :

$\frac{5^3 \times 27 \times 10^3}{5^6 \times 3^2 \times 4}$

⇒$\frac{5^3 \times 3^3 \times (5\times2)^3}{5^6 \times 3^2 \times 2 ^2}$

⇒$\frac{5^{(3-6) }\times 3^{(3-20)} \times 5^3 \times 2 ^3}{ 2 ^2}$

⇒${5^{(-3) }\times 3^{(1)} \times 5^3 \times 2 ^{(3-2)}}$

⇒${5^{(-3 +3) }\times 3^{(1)}\times 2 ^{1}}$

⇒6 

The required value of $\frac{5^3 \times 27 \times 10^3}{5^6 \times 3^2 \times 4}$ is 6.

Shortcut Trick

Subtract the coefficients of the variable: 7 − 5 = 2 units.

Add the constants (since one is reduced and one is added): 14 + 6 = 20.

Equate the differences: 2 units = 20.

Therefore, 1 unit = 20 ÷ 2 = 10.

∴ The correct answer is 10.

Alternate Method

Given:

Let the unknown number be x.

Seven times the number = 7x

Reduced by 14 = 7x − 14

Sum of five times the number and 6 = 5x + 6

Calculations:

⇒ 7x − 14 = 5x + 6

⇒ 7x − 5x = 6 + 14

⇒ 2x = 20

⇒ x = 20 ÷ 2

⇒ x = 10

∴ The correct answer is 10.

Additional Information

Linear Equations in One Variable

An equation of the form ax + b = cx + d where x is the variable and its highest power is 1.

Transposition Rule

When a term is moved from one side of the equation to the other, its sign changes (+ becomes −, and − becomes +).

Verification of Roots

Substitute the value back into both sides: LHS = 7(10) − 14 = 56 | RHS = 5(10) + 6 = 56. Since LHS = RHS, the solution is correct.

Given: 

28 March 2017 was a Tuesday.

Concept used:

Divide the number of days into seven to determine the odd days. After division, we are left with the remainder which are specified as odd days for the particular number.

2017 is not a leap year so days in February will be 28 days.

Consider, 

Monday= 1, Tuesday = 2, Wednesday = 3, Thursday = 4, Friday = 5, Saturday = 6, Sunday = 7 or 0

Calculation:

Number of odd days after 12 February 2017 to 28 February 2017 = 28 - 12 = 16 = 2 odd days

Number of odd days from 1st march till 28th march, 2017 = 28 = 0 odd days

Total number of odd days from 12 February 2017 till 28th March 2017 = 2 + 0 = 2

odd days = 2 odd days

So, the day on 12 February 2017 = Tuesday - 2 = 0 means Sunday.

Hence, 'Sunday' is the correct answer.

Given : 

W # 2 ∞ D @ 4 Y 3 D Ω R 7 & S F @ 6 ^ < X 2 2

The logic follows here is as,

• Letter $\Large \rightarrow$ Symbol $\large\rightarrow$ Number

here, there are 3 symbols each of which is immediately preceded by a letter and immediately followed by a number.

Hence, 'option 3' is the correct answer.

Shortcut Trick

For a rate of 10% and time of 2 years, the effective Compound Interest rate is 10 + 10 + (10 × 10)/100 = 21%.

Total Amount percentage = 100% + 21% = 121%.

Total amount paid = 121% of ₹9,000

⇒ 1.21 × 9000 = ₹10,890.

∴ The correct answer is ₹10,890.

Alternate Method

Given:

Principal (P) = ₹9,000

Rate of Interest (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 9000 × (1 + 10/100)²

⇒ A = 9000 × (110/100) × (110/100)

⇒ A = 9000 × (11/10) × (11/10)

⇒ A = 9000 × 121 / 100

⇒ A = 90 × 121

⇒ A = 10890

∴ The correct answer is ₹10,890.

Additional Information

Compound Interest (CI)

CI = Amount − Principal. It is the interest calculated on the initial principal and also on the accumulated interest of previous periods.

SI and CI Difference for 2 Years

The difference between Simple Interest and Compound Interest for 2 years is given by: D = P × (R/100)².

Half-Yearly Compounding

When interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n) in the formula A = P(1 + R/200)²ⁿ.

The correct answer is '17°C to 24°C'.

Key Points

• Climatic conditions: 
• Mean annual rainfall is 75 cm to 125 cm.
• The average annual temperature is 17°-24°C.
• Humidity is 80 per cent.
• Distribution:
• Eastern Himalayas to the east of 88°E longitude at altitudes varying from 1000 to 2000 m.

Additional Information

• Characteristics Forests of evergreen species.
• Commonly found species are evergreen oaks, chestnuts, ash, beech, sales and pines.
• Climbers and epiphytes [a plant that grows non-parasitically on a tree or other plant] are common.
• These forests are not so distinct in the southern parts of the country.
• They occur only in the Nilgiri and Palni hills at 1070-1525 metres above sea level.
• It is a “stunted rainforest” and is not so luxuriant as the true tropical evergreen.
• The higher parts of the Western Ghats such as Mahabaleshwar, the summits of the Satpura and the Maikal Range, the highlands of Bastar and Mt. Abu in the Aravali Range carry sub-types of these

The correct answer is NaCl + H2O + CO2 + NH3  → NH4Cl + NaHCO3.

Key-points

• The Chemical Reaction:
• NaCl + H2O + CO2 + NH3 → NH4Cl + NaHCO3
• In this reaction, the ammonia (NH3) combines with the water (H2O) and the carbon dioxide (CO2) to form ammonium bicarbonate (NH4HCO3).
• This ammonium bicarbonate then reacts with the sodium chloride (NaCl) in a double displacement reaction, forming ammonium chloride (NH4Cl) and sodium bicarbonate (NaHCO3).
• This reaction occurs in a solution and can be influenced by conditions such as temperature, pressure, and pH. Under certain conditions, this reaction could be used to capture and neutralize CO2, a greenhouse gas, potentially contributing to climate change mitigation strategies.

​Additional information

• Reactants:
• Sodium chloride (NaCl) - Sodium chloride is a salt composed of sodium ions (Na+) and chloride ions (Cl-). It's a common compound, which, among many other uses, is well-known as table salt.
• Water (H2O) - Water is a simple inorganic compound that is a crucial life-sustaining molecule. It's a solvent for many ionic compounds like salts.
• Carbon dioxide (CO2) - Carbon dioxide is a linear molecule with a central carbon atom double bonded to two oxygen atoms. It's a waste product in organisms during respiration, but it's also used in various industrial processes.
• Ammonia (NH3) - Ammonia is a compound of nitrogen and hydrogen. It's a colorless gas with a pungent smell. It's used in several industries, including agriculture (as a fertilizer), pharmaceuticals, and cleaning supplies.
• ​Products:
• Ammonium chloride (NH4Cl) - Ammonium chloride is a product of ammonia (NH3) and hydrochloric acid (HCl). It's used in various applications such as a nutrient in yeast fermentation and as an ingredient in cough medicine.
• Sodium bicarbonate (NaHCO3) - Sodium bicarbonate, also known as baking soda, is a white crystalline powder. It's used in baking as a leavening agent, in medicine to soothe heartburn and acid indigestion, and in cleaning products.

The correct answer is We should not place waste in plastic bags and discard them. 

Key Points

• The major impact of plastic bags on the environment is that it takes many years for them to decompose.
• In addition, toxic substances are released into the soil when plastic bags perish under sunlight and, if plastic bags are burned, they release a toxic substance into the air causing ambient air pollution.
• Waste from plastic bags poses a serious environmental danger to human and animal health. Thus, we should not place waste in plastic bags and discard them.
• If plastic bags are not properly disposed of, they can impact the environment by causing littering and stormwater drain blockages.
• Animals may also get tangled and drown in plastic bags.
• Animals often confuse the bags for food and consume them, therefore blocking their digestive processes.

Hence statement 2 is correct. 

• Plastic bags when used to keep food release toxic chemicals into them, which directly harm us and our digestive system.
• Burning of plastic bags releases a lot of greenhouse gases which harms the environment as well as our health.
• By law, shopkeepers are restricted from using plastic bags, instead, they are bags by law.

Hence the statement 1, 3, and 4 are incorrect.

The correct answer is '-3D' .

Key-points:

• Converging lens has positive focal length f₁ = 50 cm
• Diverging lens has negative focal length f₂ = -20 cm
• The focus of the combination of two lenses is given by
  

${1\over f}={1\over f_1}+{1\over f_2}$

${1\over f}={1\over 50}+{1\over-20}$

${f}={100\over-3}$

• The power of any lens is given by $P={100\over f}$
• P = -3 D

The correct answer is 'I2R t' .

Key-points:

• Generally

​                 Energy produced = Power$\times$ Time 

• Heat energy = Electrical Power $\times$ time

                                = P $\times$ t

                                = VI $\times$ t

                             H = VIt

• By Ohm's law ( V = IR )we can write

                            H = IR$\times$It

                            H =  I2R t

 

Additional information:

• Ohm's Law
• ​Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperatures remain constant.
• V = IR

The correct answer is Ministry of Civil Aviation.

Key Points

• The Minister of Civil Aviation Shri Jyotiraditya M. Scindia launched National Air Sport Policy 2022 (NASP 2022).
• NASP 2022 lays out the vision of making India one of the top sports nations by 2030, by providing a safe, affordable, accessible, enjoyable and sustainable air sports ecosystem in India.
• The NASP 2022, is a step toward providing safe and affordable sustainable air sports.
• It has been drafted based on the inputs received from policymakers, air sports practitioners and the public at large and will ensure the establishment of good quality infrastructure, equipment, instructors and services.
• The main ministry in India for developing national policies and initiatives for the growth and regulation of civil aviation is the Ministry of Civil Aviation.
• It develops and puts into action plans for the country's civil aviation industry's orderly expansion.
• Its duties also include controlling airport infrastructure, managing air traffic, and transporting people and things by air.

Additional Information

• Ministry of Defence:
• India's defence, in its entirety, is the responsibility of the Indian government.
• The President has full authority over the armed forces.
• The Cabinet is in charge of overseeing national defence.
• This is done through the Ministry of Defence, which gives the Armed Forces the resources and the policy framework they need to carry out their duties in the context of national defence.
• The Ministry of Defence is led by the Defence Minister.
• The current Defence Minister of India is Rajnath Singh.
• ​Ministry of Culture:
• ​India's unique culture serves as a metaphor for the nation's diversity.
• The Ministry of Culture's mandate centres on tasks like protecting and promoting all forms of art and culture, both tangible and ethereal, as well as preserving and conserving our cultural legacy.
• The Ministry's job is to establish and maintain strategies for ensuring that people's aesthetic and creative sensitivities are alive and well.
• The current Minister of Culture is G. Kishan Reddy.
• Ministry of Youth Affairs and Sports:
• ​Throughout the year, the Minister of State (Independent Charge) for Youth Affairs & Sports provided overall leadership to the Ministry of Youth Affairs & Sports.
• The Department of Youth Affairs and the Department of Sports in India are both under the control of the Ministry of Youth Affairs and Sports, a division of the Indian government.
• The current Minister of Youth Affairs and Sports is Anurag Thakur, who is succeeded by Nisith Pramanik as his deputy.

The correct answer is 'Self-combining capacity to form a long chain of atoms' .

Key-points:

• Catenation:
• ​Catenation refers to the property of self–linking of atoms of an element.
• It depends upon bond energy, size, and bond length between the atoms of the same element.
• Thus, the element capable of forming stronger and shorter self – linking bonds will have the best catenation property.​

​

**Additional information:**​

• Property of occurring as different allotropes
• The property of some metals and alloys that exhibit different crystalline lattices at different temperatures is called allotropy.
• ​Self-degeneration property
• ​Degeneracy is thus a relational property that requires comparing the behavior of two or more components.
• ​Property of carbon to give combustive nature to its compounds
• ​When carbon burns in the presence of oxygen, it produces heat and light.
• This process of burning carbon and its compounds to release energy is known as combustion.

The correct answer is Used to generate electricity in thermal plants and are cost effective.

Key Points

• Fossil Fuel:
• There are three major types of fossil fuels, they are coal, petroleum and natural gas.
• Coal is a hard substance which is black in colour and composed of carbon, hydrogen, nitrogen, oxygen and sulphur.

Additional Information

• Advantages of Fossil Fuel
• Fossil fuels have the ability to create a huge amount of electricity at a single location.
• Moreover, they are found easily and also cost-effective.
• Further, we can easily transport oil and gas through pipelines.
• Over time, they have become safer. Besides, most of our infrastructure is designed to operate through the use of fossil fuels.
• Finally, even though it is a finite resource, it is available in abundance.
• Disadvantages of Fossil Fuel
• They emit carbon dioxide, a major greenhouse gas, on burning, which is also a major source of pollution and contributes to global warming.
• When we burn coal and oil, it releases sulfur dioxide that can cause breathing problems and acid rain.
• Most importantly, we cannot replace them.
• Further, when we burn them, they make the environment more acidic due release of nitrogen and sulphur.
• Being nonrenewable energy resources, their limited supply means we will run out eventually.
• Moreover, harvesting them results in fatal diseases like coal miners suffer from Black Lung Disease sometimes and natural gas drillers are exposed to chemicals which is also dangerous health-wise.

Given:

3 - 6 ÷ 9 + 6 × 2 = 6 

Calculation:

By option Method:

Option I: After interchanging - and ×

⇒ 3 × 6 ÷ 9 + 6 - 2 = 6 

⇒ 2 + 6 - 2 = 6

⇒ 6 = 6

This is correct the equation.

Option II: After interchanging  ÷ and  +

⇒ 3 - 6 + 9 ÷ 6 × 2 = 6 

⇒ 3 - 6 + 3  = 6

⇒ 0 ≠ 6

This is not correct the equation.

Option III: After interchanging  + and × 

⇒ 3 - 6 ÷ 9 × 6 + 2 = 6 

⇒ 3 - 4 + 2 = 6

⇒ 1 ≠ 6

This is not correct the equation.

Option IV: After interchanging  ÷ and × 

⇒ 3 - 6 x 9 + 6 ÷ 2 = 6 

⇒ 3 - 0.66 + 3 = 6

⇒ 5.33 ≠ 6

This is not correct the equation.

∴ Interchanges (- , x) would make the given equation correct.

• The shaded part represents the people prefer salads but NOT stew.

 

• The number representing the people prefer salads but NOT stew = 29 + 12 = 41

Hence, ‘41’ is the correct answer.

Shortcut Trick

Sum of digits of the number = (Sum of number and its reverse) ÷ 11 = 99 ÷ 11 = 9.

Difference between the digits is given as 5.

Larger digit = (Sum + Difference) ÷ 2 = (9 + 5) ÷ 2 = 7.

Smaller digit = (Sum − Difference) ÷ 2 = (9 − 5) ÷ 2 = 2.

Possible two-digit numbers are 72 or 27.

∴ The correct answer is 27.

Alternate Method

Given: Sum of number and its reverse = 99, Difference between digits = 5.

Formula Used: Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.

⇒ (10x + y) + (10y + x) = 99

⇒ 11x + 11y = 99

⇒ 11(x + y) = 99

⇒ x + y = 9 ... (Eq. 1)

⇒ Case 1: x − y = 5 ... (Eq. 2)

⇒ Adding (Eq. 1) and (Eq. 2): 2x = 14 ⇒ x = 7, y = 2. Number = 72.

⇒ Case 2: y − x = 5 ... (Eq. 3)

⇒ Adding (Eq. 1) and (Eq. 3): 2y = 14 ⇒ y = 7, x = 2. Number = 27.

∴ The correct answer is 27.

Additional Information

Sum of Reversed Digits Rule

The sum of a 2-digit number and the number formed by reversing its digits is always 11 × (sum of its digits).

Difference of Reversed Digits Rule

The difference between a 2-digit number and the number formed by reversing its digits is always 9 × (difference of its digits).

Linear Equations for Digits

When the sum (S) and difference (D) of two values are known, the values are (S+D)÷2 and (S−D)÷2.

The correct answer is 'Electric fuse' .

 Key Points

• A fuse consists of a piece of wire made of a metal or an alloy of an appropriate melting point, for example, aluminum, copper, iron, lead etc.
• If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases.
• This melts the fuse wire and breaks the circuit.

​ 

Additional Information

• Loudspeaker
• Every amplifier (speaker) has an electrical current.
• When the current is changing, it produces a magnetic field.
• To make the cone (or panel) of the speaker move, magnets are used to create an opposing magnetic field which creates vibrations.
• These vibrations are the sound we hear.
• Ammeter and Voltmeter
• ​When an electric current passes through the coil, the electromagnetic field created around it reacts against the permanent magnetic field producing a deflecting torque that causes it to move.
• A pointer or needle attached to the coil indicates the amount of deflection.​

Shortcut Trick

Since 8 men + 6 women and 6 men + 8 women take the same 5 days, their total efficiency is equal.

Total persons in Case 1 = 8 + 6 = 14 persons | Total persons in Case 2 = 6 + 8 = 14 persons.

Since 14 persons take 5 days, then 7 men + 7 women (which is also 14 persons) will take the same time.

∴ The correct answer is 5 days.

Alternate Method

Given: Case 1 = (8M + 6W) × 5 | Case 2 = (6M + 8W) × 5

Formula Used: Total Work = Efficiency × Time

⇒ (8M + 6W) × 5 = (6M + 8W) × 5

⇒ 8M + 6W = 6M + 8W

⇒ 2M = 2W → 1 Man = 1 Woman

⇒ Total Work = (8M + 6M) × 5 = 14M × 5 = 70M units

⇒ Efficiency of (7M + 7W) = 7M + 7M = 14M units/day

⇒ Time required = 70M ÷ 14M = 5 days

∴ The correct answer is 5 days.

Additional Information

Man-Day Formula

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

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If efficiency doubles, time is halved.

Work & Wages

Wages are always distributed in the ratio of the work done by individuals, which is usually the ratio of their efficiencies.

Shortcut Trick

Convert the equation into standard form x² − 15x + 14 = 0.

Identify Sum of roots (−b/a) = 15 and Product of roots (c/a) = 14.

Check which option satisfies both conditions: 1 + 14 = 15 and 1 × 14 = 14.

Only the values 1 and 14 satisfy these conditions simultaneously.

∴ The correct answer is 1 and 14.

Alternate Method

Given: (x − 5)² = 5x + 11

Formula Used: (a − b)² = a² − 2ab + b²

⇒ (x − 5)² = 5x + 11

⇒ x² − 10x + 25 = 5x + 11

⇒ x² − 10x − 5x + 25 − 11 = 0

⇒ x² − 15x + 14 = 0

⇒ x² − 14x − x + 14 = 0

⇒ x(x − 14) − 1(x − 14) = 0

⇒ (x − 1)(x − 14) = 0

⇒ x = 1 or x = 14

∴ The correct answer is 1 and 14.

Additional Information

Quadratic Formula

For a quadratic equation ax² + bx + c = 0, the roots are given by x = [−b ± √(b² − 4ac)] / 2a.

Nature of Roots

The discriminant D = b² − 4ac determines the nature: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Relation between Roots and Coefficients

If α and β are the roots, then sum (α + β) = −b/a and product (αβ) = c/a.

Shortcut Trick

Multiply the ratio terms directly by their respective percentage change factors.

New First Number = 5 × 140% = 7.0

New Second Number = 8 × 85% = 6.8

New Ratio = 7.0 : 6.8 → 70 : 68 = 35 : 34.

∴ The correct answer is 35 : 34.

Alternate Method

Given:

Initial Ratio of two numbers = 5 : 8

Percentage Increase in first number = 40%

Percentage Decrease in second number = 15%

Formula Used:

New Value = Original Value × (100 ± Change%)/100

Calculations:

Let the two numbers be 50x and 80x respectively.

⇒ First number after 40% increase = 50x × (140/100) = 70x

⇒ Second number after 15% decrease = 80x × (85/100) = 68x

⇒ New Ratio = 70x : 68x

⇒ New Ratio = 70 : 68

⇒ Dividing both terms by 2:

⇒ New Ratio = 35 : 34

∴ The correct answer is 35 : 34.

Additional Information

Concept of Multiplier

For an increase of x%, multiply the base value by (1 + x/100). For a decrease of x%, multiply by (1 − x/100).

Simplifying Ratios

A ratio a : b remains unchanged if both terms are multiplied or divided by the same non-zero constant k.

Successive Percentage Change

If a value changes by a% and then by b%, the net change is [a + b + (a × b)/100]%.

The correct answer is 'Pepsin'.

Key Points

• Gastric juice contains three substances: hydrochloric acid, enzyme pepsin, and mucus.
• Hydrochloric acid in the stomach is used to make the medium acidic to facilitate the action of the enzyme pepsin and to kill germs if any.
• Enzyme pepsin digests proteins and converts them into peptones.

​

Additional Information

• Trypsin
• Trypsin is an enzyme that is essential for your body to digest protein, a critical component for building and repairing tissue including bones, muscles, cartilage, skin, and blood.
• When combined with chymotrypsin, trypsin can help in injury recovery.
• ​Lipase
• ​Lipase is an enzyme the body uses to break down fats in food so they can be absorbed in the intestines.
• Lipase is produced in the pancreas, mouth, and stomach.
• ​Amylase
• ​Amylase is responsible for the breaking of the bonds in starches, polysaccharides, and complex carbohydrates into easier-to-absorb simple sugars.
• Salivary amylase is the first step in the chemical digestion of food.

The correct answer is 'Ministry of AYUSH'.

Key Points

• Prime Minister Shri Narendra Modi laid the foundation stone of the WHO Global Centre for Traditional Medicine (GCTM) in Jamnagar, Gujarat.
• A groundbreaking ceremony was attended by the Prime Minister of Mauritius Shri Pravind Kumar Jugnauth and Dr Tedros Ghebreyesus, Director-General, of the World Health Organization (WHO).
• The Ministry of Ayush and the World Health Organization (WHO) is establishing the world’s first and only Global Centre for Traditional Medicine (WHO GCTM) in Jamnagar, Gujarat.
• Speaking on this occasion the Prime Minister said, “The WHO Global Centre for Traditional Medicine is recognition of India's contribution and potential in this field.
• India’s traditional medicine system is not limited only to treatment.
• India takes this partnership as a huge responsibility for serving the entire humanity.”

 Additional Information

• Ministry of Women and Child Development:
• The Department of Women and Child Development, Government of India, came into existence as a separate Ministry with effect from 30th January 2006, earlier since 1985 it was a Department under the Ministry of Human Resources Development.
• The Ministry was constituted with the prime intention of addressing gaps in State action for women and children to promote inter-Ministerial and inter-sectoral convergence to create gender-equitable and child-centred legislation, policies and programmes.
• Ministry of Health and Family Welfare:
• On August 7, 2014, vide extraordinary Gazette notification on Thursday, August 7, 2014, the Department of AIDS Control has been merged with the Department of Health & Family Welfare and is now known as National AIDS Control Organization (NACO).
• As per the amendment in the allocation of business rules vide the Cabinet secretariat’s Notification on December 8, 2014, the Department of AYUSH has been made Ministry of Ayurveda, Yoga and Naturopathy, Unani, Siddha and Homeopathy (AYUSH) with focused attention on the development of education and research in Ayurveda, Yoga & naturopathy, Unani, Siddha and Homoeopathy systems.
• Now Ministry of Health and Family Welfare comprises the following two departments, each of which is headed by a Secretary to the Government of India.
• Ministry of Cooperation:
• The Union Ministry of Cooperation is a ministry under the Government of India which was formed in July 2021.
• The ministry provides a separate administrative, legal and policy framework for strengthening the cooperative movement in the country.
• The ministry's creation was announced on 6 July 2021 along with its vision statement of "Sahkar se Samriddhi".
• Before the creation of this ministry, the objectives of this ministry were looked after by the Ministry of Agriculture.

The correct answer is "either a concave lens or a concave mirror".

Key Points

• In contrast to convex mirrors and convex lenses, concave mirrors and concave lenses produce larger pictures.
• A hollow spherical can be made into a mirror by cutting it into pieces, painting the exterior of each piece, and then polishing the interior to reflect light.
• A convex lens, which is thicker in the center and gets thinner as we move toward the edges, condenses a straight beam of light.
• Images are magnified using a concave mirror and convex lens.

Additional Information

• A concave lens is a lens that bends a direct light beam away from the source into a cropped, upright virtual image.
• Both actual and virtual images can be created using it. At least one internal surface of concave lenses is curved.
• Since it is rounded at the center and bulges outward at the borders, a concave lens is also known as a diverging lens because it causes the light to diverge.
• Since they make distant objects appear smaller than they actually are, they are used to cure myopia.

The correct answer is Three-tier.

Key Points

• Balwant Rai Mehta Committee was appointed to examine the working of the community development program and the national extension service.
• Balwant Rai Mehta Committee was appointed in 1957.
• Balwant Rai Mehta was the chairman of this committee.
• The Balwant Rai Mehta Committee recommended establishing a three-tier Panchayati Raj structure.
• The Balwant Rai Mehta committee suggested that the structure of the Panchayati Raj should consist of the village, the block, and the district level.
• Gram Panchayat at the village level.
• Panchayat Samiti at the block level.
• Zila Parishad at the district level.
• The National Development Council approved the committee's recommendations in 1958.

Additional Information

• Other committees related to Panchayati raj:
• Ashok Mehta Committee:
• In December 1977, the Janata Government appointed a committee on Panchayati raj institutions under the chairmanship of Ashok Mehta.
• It submitted its report in August 1978 and made 132 recommendations to revive and strengthen the declining Panchayati raj system in the country.
• Due to the collapse of the Janata Government before the completion of its term, no action could be taken on the recommendations of the Ashok Mehta committee at the central level.
• However, the three states of Karnataka, West Bengal and Andhra Pradesh took steps to revitalise the Panchayati raj, keeping in view some of the recommendations of the Ashok Mehta Committee.
• L. M. Singhvi Committee-
• In 1986, the Rajiv Gandhi government appointed a committee to prepare a concept paper on ‘Revitalisation of Panchayati Raj Institutions for Democracy and Development’ under the chairmanship of L M Singhvi.
• G. V. K. Rao Committee:
• The Committee to review the existing Administrative Arrangements for Rural Development and Poverty Alleviation Programmes under the chairmanship of G.V.K. Rao was appointed by the Planning Commission in 1985.

The correct answer is "Roti, pulses, vegetables".

Key Points

• A healthy diet is one that enhances or maintains general health.
• The body receives the key nutrients it needs from a balanced diet, including proper amounts of hydration, macronutrients like protein, micronutrients like vitamins, and fibre.
• Fruits, vegetables, whole grains, and little to no processed food or beverages with added sugar can all be found in a healthy diet.
• A combination of plant-based and animal-based foods can satisfy dietary needs, though vegans must obtain their vitamin B12 from sources other than plants.

Additional Information

• By consuming roughly the same number of calories that your body requires, you can maintain a healthy weight.
• Limit your fat intake to no more than 30% of your total daily calories, and choose unsaturated fats over saturated fats. Avoid trans fats.
• Consume 400 grams or more of fruits and vegetables every day (not counting potatoes, sweet potatoes, cassava and other starchy roots). Nuts, whole grains, and legumes (such as lentils and beans) are also components of a balanced diet.

Given:

621, 443, 227, 316, 625, 118, 231

By applying operation of,

5 is added to the digit in ten's place of each number and 1 is subtracted from the digit in unit's place of each number. We got,

Here, 6 digit will be repeated the greatest number of times ( Five times ) in the transformed number series thus formed.

Hence, '6' is the correct answer.

Statement:

Use of re-usable cloth bags for shopping will help in reducing pollution caused by indiscriminate use of plastic bags.

Arguments:

I. The government has banned the use of single-use plastic from 1 July 2022. → strengthen the statement

• Banning of single-use plastic help in reducing pollution. As It control proliferation of plastic bags. So the Argument l  is supporting the statement. Hence it is True and strengthen the statement.

II. Cloth bags are eco-friendly since they are re-usable and can be made from scrap fabric that would otherwise go to landfills. → strengthen the statement

• As reusable Cloth bags which biodegrade in very less time  that can break down naturally and there disposition also very easy as ether go for landfill or fire burning. So the Argument ll  is supporting the statement. Hence it is True and strengthen the statement.

Hence, Both arguments I and II strengthen the statement.

The correct answer is Mumbai.

Key Points

• Mahindra & Mahindra Financial Services Limited (MMFSL) is an Indian rural non-banking financial company headquartered in Mumbai.
• It is amongst the top tractor financers in India, with 1000+ offices across the country.
• Mahindra Finance started on 1 January 1991, as Maxi Motors Financial Services Limited.
• They received the certificate of commencement of business on 19 February 1991.
• On 3 November 1992, Mahindra Finance changed its name to Mahindra & Mahindra Financial Services Limited.
• Mahindra Finance is registered with the Reserve Bank of India as an asset finance, deposit-taking NBFC.

Additional Information

• The National Institute for the Visually Handicapped(NIVH) is situated at Dehradun, Uttarakhand.
• This organization works under the administrative control of the Department of Empowerment of Persons with Disabilities (Divyangjan), Ministry of Social Justice and Empowerment, Government of India.
• NIVH is engaged in training visually challenged persons and is also engaged in the production of Braille literature, Aids, and Appliances for the visually handicapped.
• National Institute for Orthopaedically Handicapped, Kolkata.
• ​Providing services to the Orthopaedically Handicapped population under the training of Physiotherapists, Occupational Therapists, Orthotists & Prosthetists, Employment & Placement Officers, and Vocational Counsellor, etc.
• Conduct and funded research in all aspects related to the rehabilitation of the Orthopaedically handicapped.
• The National Institute of Mentally Handicapped is located in Hyderabad.
• The Institute was established in 1978.
• The objective of the institute is "Human Resource Development to develop manpower for providing services to the Orthopaedically Handicapped population".
• The Ali Yavar Jung National Institute for Hearing Handicapped, in Mumbai, has its regional centres in New Delhi, Kolkata, Hyderabad and Bhubaneswar.
• These centres will be able to give details about the programmes available in the country. The Rehabilitation Council of India in New Delhi also can be contacted to get the details.
• The Welfare departments in the states and the Rehabilitation Centres run by the states can be contacted to find out about the facilities available in a particular area.

Shortcut Trick

Sum of ratio parts = 4 + 3 + 5 = 12 units.

Total sum of angles in a triangle = 180°.

1 unit = 180° ÷ 12 = 15°.

Angles = (4 × 15°), (3 × 15°), (5 × 15°) = 60°, 45°, 75°.

∴ The correct answer is 60°, 45°, 75°.

Alternate Method

Given: The angles of triangle ABC are in the ratio 4 : 3 : 5.

Formula Used: Sum of all interior angles of a triangle = 180°.

Let the three angles be 4x, 3x, and 5x.

⇒ 4x + 3x + 5x = 180°

⇒ 12x = 180°

⇒ x = 180° ÷ 12

⇒ x = 15°

⇒ First angle = 4 × 15° = 60°

⇒ Second angle = 3 × 15° = 45°

⇒ Third angle = 5 × 15° = 75°

∴ The correct answer is 60°, 45°, 75°.

Additional Information

Angle Sum Property

The sum of all interior angles of any triangle is always 180&

The correct answer is "Translocation".

Key Points

• Translocation is the transport of substances within the plant from leaves to other tissues.
• While photosynthesis allows plants to manufacture carbohydrates (sugars) in their leaves, other organic and inorganic substances are also needed by nonphotosynthetic plant components.
• Because of this, nutrients are moved from sources (areas with a surplus of carbohydrates, typically mature leaves) to sinks (regions where the carbohydrate is needed).

Additional Information

• Roots, flowers, fruits, stems, and emerging leaves are a few significant sinks.
• As sources later, when they are roughly halfway developed, leaves are particularly fascinating because they are sinks while they are young.

Given:

 

 

Given code - LEMON

Here, the Rule number 3 is applied in the given code. i.e. If both the second and the fourth elements are vowels, the fourth element is to be coded as the code for the third element and vice-versa.

Hence, code for LEMON is “63879”.

Shortcut Trick

A quadratic equation with roots α and β is formed as: x² − (Sum of Roots)x + (Product of Roots) = 0.

Sum of roots = 3 + (−2) = 1.

Product of roots = 3 × (−2) = −6.

Plugging in the values: x² − (1)x + (−6) = 0 ⇒ x² − x − 6 = 0.

∴ The correct answer is x² − x − 6 = 0.

Alternate Method

Given: The roots of the required quadratic equation are 3 and −2.

Method: If x = 3 and x = −2 are the roots, then (x − 3) and (x + 2) must be the linear factors of the quadratic expression.

⇒ (x − 3)(x + 2) = 0

⇒ x(x + 2) − 3(x + 2) = 0

⇒ x² + 2x − 3x − 6 = 0

⇒ x² − x − 6 = 0

∴ The correct answer is x² − x − 6 = 0.

Additional Information

Standard Quadratic Form

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Relationship between Coefficients and Roots

For the equation ax² + bx + c = 0, Sum of roots = −b/a and Product of roots = c/a.

Discriminant and Nature of Roots

The term D = b² − 4ac determines the nature of roots: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Given: 

L E A P K X O Z A E Y W U D O A D S L Y R K E V U L

The logic follows here is as,

• Vowel $\rightarrow$ Consonant $\rightarrow$ Vowel

=> Y repeated = 2 times

=> D repeated = 2 times

=> K repeated = 2 times

=> L repeated = 3 times

Here, consonants are immediately preceded and immediately followed by a vowel, and consonant is repeated the most number of times in the series are 3, L respectively.

Hence, 'Option 4' is the correct answer.

The logic follows here is as,

Addition of digits of first number = second number

Hence, '12' is the correct answer.

The correct answer is 'D > B > E  > C > A'.

Key Points

• A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column (Figure ).
• Each box represents an element and contains its atomic number, symbol, average atomic mass, and (sometimes) name.
• The elements are arranged in seven horizontal rows, called periods or series, and 18 vertical columns, called groups.

Now here,

 

So  the order is,

Tellurium > Antimony > Bromine > Oxygen > Nitrogen.

The correct answer is 'Assam'.

Key Points

• Powa Mecca Hajo Assam :
• The Muslim place of pilgrimage in Hajo is Powa Mecca Mosque.
• The name of the mosque means one-quarter of Mecca, which is the holiest city for Muslims situated in Arab.
• It is said that by offering prayers in this mosque, devotees gain one-fourth of the good grace that they would have gotten in the real Mecca.
• On the top of Garurachal Hill, the Powa Mecca mosque stands.
• This is the tomb of the pioneer of the Muslim religion in this area, Pir Ghiyasuddin Auliya.
• In 1657 AD, Sujauddin Muhammad Shah built this mosque. At that time Shah Jahan was the ruling Mughal emperor of India.
• The mosque is situated on the hill over the banks of the Brahmaputra River and is only 24 kms away from Guwahati.

Additional Information

• Important Hills Station:
• ​Leh Ladakh – Land of the High Passes.
• Nainital, Uttarakhand – The Hill Station of Lakes.
• Manali, Himachal Pradesh – Valley of the Gods.
• Mussoorie, Uttarakhand – The Queen of the Hill Stations.
• Gulmarg, Jammu and Kashmir – Popular Hill Station and Skiing Destination.
• Darjeeling, West Bengal - Land of the Celestial Thunderbolt.

The correct answer '$(\ {2\over3} : and :1 ), : :$'.

Key Points

• According to Ohm's Law, the potential drop (V) across a resistor is given by V = IR, where I is the current passing through the resistor and R is its resistance.
• For resistor A:
• V1 = I1 * R1 = I1 * 8 Ω
• For resistor B:
• V2 = I2 * R2 = I2 * 12 Ω
• Currents through resistors:
• In a series circuit, the current passing through each resistor is the same. Therefore, I1 = I2 = I.
• Battery voltage:
• The total voltage provided by the battery is equal to the sum of the potential drops across the resistors in a series circuit.
• V_total = V1 + V2
• 6 V = V1 + V2
• Now, we can use these equations to find the ratios (V1/V2) and (I1/I2):
• (V1/V2) = (I1 * 8 Ω) / (I2 * 12 Ω)
• (I1/I2) = I1 / I2 (since I1 = I2 = I)
• Let's substitute I2 with I1 in the first equation:
• (V1/V2) = (I1 * 8 Ω) / (I1 * 12 Ω)
• (V1/V2) = 8 Ω / 12 Ω
• (V1/V2) = 2/3
• (I1/I2) = I1 / I2 = 1 (since I1 = I2 = I)
• Therefore, (V1/V2) = 2/3 and (I1/I2) = 1.

The correct answer is 'Montane forests'.

Key Points

• Montane forests:
• Montane forests are found on mountain slopes. Montane Forest is a type of mountain ecosystem.
• It is influenced by the colder climate at moderate elevations.
• Dense forests are common in these areas.
• Rainfall and a temperate climate cause natural vegetation to change in the Mountain Forest.
• The forests found in the mountains are known as montane forests.
• Wet temperate forests are found between 1000 and 2000 metres in elevation.
• Temperate forests and grasslands give way to Alpine vegetation at high altitudes, generally more than 3,600 metres above sea level.
• Tibetan antelope, yak, spotted deer, wild sheep, snow leopard, squirrels, Kashmir stag, jackrabbit, Shaggy horned wild ibex, bear and rare red panda, sheep and goats with thick hair are common animals found in this forest.

Additional Information

• Mangrove Forests:
• ​A Mangrove is a small tree or shrub that grows along coastlines, taking root in salty sediments, often underwater.
• The word ‘mangrove’ may refer to the habitat as a whole or to the trees and shrubs in the mangrove swamp.
• Mangroves are flowering trees, belonging to the families Rhizophoraceae, Acanthaceae, Lythraceae, Combretaceae, and Arecaceae.
• The major mangroves in India are found at:
• Sundarban Groves.
• Mahanadi Mangroves.
• Krishna Godavari Mangroves.
• Cauvery Deltaic Mangroves.
• Krishan-Godavari Mangrove.
• Andaman- Nicobar Mangrove.
• Tropical Deciduous Forests:
• Tropical Deciduous Forests are one of the five types of natural vegetation found in India.
• Being a tropical country (a country that lies in the zone between the Tropic of Cancer and the Tropic of Capricorn), the tropical deciduous forest is the most widespread forest in India, around 65.6% of the total forest is covered in tropical deciduous forests.
• On the basis of the availability of precipitation, the tropical deciduous forests in India are classified into two types:
• moist deciduous forests
• dry deciduous forests.
• The trees and shrubs of the tropical deciduous forest in India shed their leaves during the dry season (mostly in autumn) in order to conserve water.
• In India, the tropical deciduous forests are found: Madhya Pradesh, Uttar Pradesh, Odisha, Chhattisgarh, Jharkhand, and, Some parts of Maharashtra.
• Thorn Forests:
• ​The trees are low (6 to 10 metres maximum) and widely scatteredly distributed. Acacias and Euphorbias are very prominent flora.
• Rajasthan, southwestern Punjab, western Haryana, Kachchh and neighbouring parts of Saurashtra.
• Here they degenerate into desert type in the Thar desert.
• Such forests also rised on the leeside of the Western Ghats and expand in large areas of Maharashtra, Karnataka, Telangana, Andhra Pradesh and Tamil Nadu.
• The important flora species are neem, babul, cactii, etc.

Given:

 6x+4 = 67

Concept used:

 If x^a = x^b

 Then a=b

Calculations:

 6x+4 = 67

 x+4 = 7

 x = 7 - 4

 x = 3

Thus the correct option is '3' .

The correct answer is William carey.

Key Points

• Serampore Mission (1800-1845):
• It was India's first Christian missionary organization.
• William Carey and his two associates established this mission on 10 January 1800.
• The Mission started preaching the message of Jesus from two places in the Hughli district.
• The first Catholic Church in this district was established at Bandel in 1599. About two hundred years later a Protestant Church was built in Serampore (1800).
• William Carey established this Church and the mission on 17 August 1761.
• It was through his initiative that the Baptist Missionary Society was formed. On 24 April 1800, the Serampore Mission Church was inaugurated.
• Carey became the Chief Priest of the Church, while Marshman and Ward were made Assistant Priests.
• This Mission was self-supportive.
• The cost of the missionary activities was borne by Joshua Marshman, William Ward, and William Carey from their own earnings; Marshman from the schools, Ward from the Press, and Carey from his teaching job at Fort William College.

Shortcut Trick

Internal radius r = External radius − Thickness = 9 − 2 = 7 cm.

Capacity = (4/3) × (22/7) × 7³ = (4/3) × 22 × 49.

Capacity = 4312 ÷ 3 = 1437.33 cm³.

∴ The correct answer is 1437.33 cm³.

Alternate Method

Given:

External radius (R) = 9 cm

Thickness (t) = 2 cm

Formula Used:

Internal radius (r) = R − t

Volume of Sphere = (4/3)πr³

Calculations:

⇒ Internal radius (r) = 9 − 2 = 7 cm

⇒ Capacity = (4/3) × (22/7) × 7 × 7 × 7

⇒ Capacity = (4/3) × 22 × 1 × 49

⇒ Capacity = (88 × 49) ÷ 3

⇒ Capacity = 4312 ÷ 3

⇒ Capacity ≈ 1437.333...

∴ The correct answer is 1437.33 cm³.

Additional Information

Volume of a Hollow Sphere

The material volume of a hollow sphere is given by V = (4/3)π(R³ − r³), where R is external and r is internal radius.

Surface Area of a Sphere

The total surface area of a solid sphere is 4πr².

Volume of a Hemisphere

The capacity of a hemispherical bowl is exactly half of a sphere: V = (2/3)πr³.

Shortcut Trick

Total Marked Price = 20 × 750 = ₹15,000.

Successive Discounts: First 20% then flat ₹500.

Price after 20% discount = 15,000 × (80 ÷ 100) = ₹12,000.

Final Total SP = 12,000 − 500 = ₹11,500.

Final SP per shirt = 11,500 ÷ 20 = ₹575.

∴ The correct answer is ₹575.

Alternate Method

Given → Quantity = 20, Marked Price (MP) per unit = ₹750, Percentage Discount = 20%, Cash Discount = ₹500. Formulas: Total MP = MP per unit × Quantity | SP = MP × (100 − D%) ÷ 100 | Final SP = SP after % discount − Flat Discount.

⇒ Total MP = 20 × 750 = ₹15,000. ⇒ SP after 20% discount = 15,000 − (20% of 15,000) = 15,000 − 3,000 = ₹12,000. ⇒ Final Total SP after ₹500 cash discount = 12,000 − 500 = ₹11,500. ⇒ Final SP per shirt = 11,500 ÷ 20 = ₹575.

∴ The correct answer is ₹575.

Additional Information

Marked Price & Selling Price

Marked price is the price printed on the label. Discount is always calculated on the Marked Price unless stated otherwise. SP = MP − Discount.

Successive Discounts

When multiple discounts are applied, the second discount is applied to the value obtained after the first discount. In this case, a percentage discount was followed by a flat cash discount.