RRB Group D Previous Year Paper (Held on: 22 Aug 2022 Shift 1)

The correct answer is the Use of jute bags.

Key Points

• At the Household level, the practice of waste segregation should be enforced and promoted.
• Education on waste disposal and management should be highly promoted at the school level.
• Sustainable alternatives like paper bags and cloth bags are evidence of the presence of alternatives from historical times.
• Strictness of laws is required for Waste disposal and management.
• At the commercial level, the use of plastic bags should be minimized and replaced with sustainable alternatives.

Additional Information 

• Single-use plastics ban should be imposed with Greater strictness.
• The concept of 3R's Reduce, Reuse, Recycle is well efficient in Managing Non-biodegradable waste.
• There is a clear need for proper disposal of waste like Batteries, glass, and Heavy metals.
• Example of the City of Indore which gradually imbibed the culture the waste disposal and management and become the cleanest city in India.
• Use of International platforms like COP26 and United Nations for integrated approach on progress towards Sustainable Development Goals(SDG's).

Given:

Petrol = 35%

Water = 12%

100% = Rs. 1,12,000

Solution:

100% = Rs. 1,12,000

1% = Rs. 1,120

Total(Water + Petrol)

= 35% + 12% = 47%

Total expenditure

= 47% of 1,12,000

= 47 x 1120 = Rs.52,640

Hence, the correct option is 3.

Shortcut Trick

Group terms with common coefficients: 2(sec²A − tan²A) + 4(cosec²A − cot²A).

Apply identities: sec²A − tan²A = 1 and cosec²A − cot²A = 1.

Calculation: 2(1) + 4(1) = 2 + 4 = 6.

∴ The correct answer is 6.

Alternate Method

Given: Expression = 2sec²A + 4cosec²A − 2tan²A − 4cot²A

Formula Used: 1 + tan²A = sec²A ⇒ sec²A − tan²A = 1; 1 + cot²A = cosec²A ⇒ cosec²A − cot²A = 1

⇒ Rearranging the expression: (2sec²A − 2tan²A) + (4cosec²A − 4cot²A)

⇒ Factorizing: 2(sec²A − tan²A) + 4(cosec²A − cot²A)

⇒ Substituting the identity values: 2 × 1 + 4 × 1

⇒ 2 + 4 = 6

∴ The correct answer is 6.

Additional Information

Trigonometric Identities

Primary identities include sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, and cosec²θ − cot²θ = 1.

Reciprocal Relations

sec θ = 1/cos θ, cosec θ = 1/sin θ, tan θ = sin θ/cos θ, and cot θ = cos θ/sin θ.

The correct answer is current flowing through the conductor.

Key Points:

• Consider a conductor with a cross sectional area of A and a length l.
• Let the material's resistivity be ρ.
• The conductor's resistance is therefore expressed as
• $x = {ρl\ \over A}$.
• Temperature affects a conductor's resistance.
• The resistivity of the conductor increases as the conductor's temperature rises, and drops as the conductor's temperature falls.
• Since a conductor's resistance and resistivity are directly inversely correlated, resistance rises with rising temperature and falls with falling temperature.
• Thus, among the alternatives, a conductor's resistance is determined by its length, thickness (i.e., cross sectional area), and temperature.
• It does not depend on the conductor's current level.

Additional Information:

• A conductor is any material that enables the movement of an electrical current.
• How well a conductor can transport current in an electrical circuit depends on its resistance.
• Resistance is the capacity to obstruct the flow of an electric current.
• Current flows through a conductor as a result of the electrical force known as voltage, however the more resistance a conductor has, the less current will flow for any given magnitude of applied voltage.
• The resistance of a conductor is primarily affected by three variables:
• The length of the conductor.
• The cross-sectional area of the conductor.
• The building material of the conductor.

The correct answer is Barchans.

Key Points

• Barchans
• The horns of the crescent on barchans, which are convex facing the wind and indicate the lateral advance of sand.
• A landform known as Barchan, often spelt Barkhan, is both erosional and depositional in nature.
• The name "barchan" refers to the characteristics of wide-open, inland desert areas like Turkistan.
• Where the plains have little sand cover, Barchan dunes are likely to occur.
• Both the white sand dunes at the National Monument in New Mexico and the Grand Erg Oriental in the Sahara Desert are iconic examples of barchans.

Additional Information

• Alluvial fan-
• It is a fan-shaped mound of alluvium that forms as a river's flow slows down.
• Moraine-
• It is material left behind by a moving glacier. This material is usually soil and rock.

The correct answer is 2000.

Given:

$V=5V$

$I=2.5mA={2.5\over1000}=0.0025A$

To find: Resistance (R)

Formula used:

Ohm's law: $V=IR$

Calculations:

$V=IR$

$5=0.0025*R$

$R={5\over 0.0025}=2000Ω$

Thus, the resistance is 2000Ω.

According to the given information:

The given code is : 7 6 & 5 8 % 6 2

Here, the first condition follows:

"If the first element is an odd number and the last element is an even number, the codes for these two (the first and the last elements) are to be interchanged"

Therefore, 7 will be coded as A(2) & 2 will be coded as S(7). 

Hence, the correct answer is "Option 2".

Given: Seven boxes, P, Q, R, S, T, U and V.

1. V is the topmost box.

2) Only three boxes are between V and U.

3. V is kept just above Q, which is just above S.

4) 4) R is kept just below T.

And, P will placed on the remaining place.

So, from the given arrangement P is placed Immediately below S.

Hence, the correct answer is "Option 4".

From the given information:

Mahesh started from a point facing towards the west, turned left and walked for X m, then turned right and walked for 22 m

Turn left and walked for 11 m, then turn left again and walked for 22 m.

The value of X = 21 - 11 = 10m.

Hence, the correct answer is "Option 3".

The correct answer is hydrogen.

Key Points:

• Alcohol with the chemical formula C₂H₅OH is ethanol.
• Alcohols react with sodium metals to produce hydrogen gas and sodium alkoxide, which are both released.
• In the process of forming sodium ethoxide from ethanol and sodium metal, hydrogen gas is produced.
• 2 C2H5OH + 2 Na → 2 C2H5ONa + H₂
• As a result, hydrogen is the gas that results from the reaction of ethanol and sodium.

Additional Information:

• To determine whether ethanol is present in a mixture of organic molecules, the reaction of ethanol and salt is utilised as a confirmatory test.
• In this test, a supposedly alcoholic organic molecule is given a tiny bit of salt.
• It is confirmed that the unknown sample is ethanol if the addition of sodium metal to the liquid results in effervescence or rapidly rising bubbles that show the evolution of hydrogen gas.
• If the liquid does not bubble when sodium metal is added, the sample is not alcohol.
• This test is only a preliminary one; other tests are needed to definitively determine whether ethanol is present.

The correct answer is m = -1.

Key Points

• When an object is placed at a distance of 2f from a convex lens, the image is formed at a distance of 2f on the other side of the lens.
• The image formed is real, inverted, and of the same size as the object.
• Magnification (m) = Height of Image / Height of Object = -1 (negative sign indicates inversion).
• This scenario is a standard case in lens formulas and ray diagrams of convex lenses.
• Thus, magnification 'm' = -1 for object placed at 2f in convex lens.

Additional Information

• Convex Lens (Converging Lens)
• A convex lens is thicker at the center and converges parallel rays of light to a point called the focus.
• It forms real and inverted images for object distances greater than focal length (f), and virtual, erect images when the object is within f.
• Magnification (m)
• Magnification = v/u or Height of Image / Height of Object.
• Positive magnification indicates an erect image, negative indicates an inverted image.
• Lens Formula
• 1/f = 1/v - 1/u where f = focal length, v = image distance, u = object distance.
• All distances are measured from the optical center of the lens.
• Applications of Convex Lens
• Used in magnifying glasses, microscopes, cameras, and human eye correction.

Concept Used:

Calculation:

As, $\sqrt{360}$ = 18.97 and $\sqrt{170}$ = 13.03

Here, we have 

( $\sqrt{360}$ + 12 ÷ 6 × 3 $\sqrt{170}$ )÷ 2

(18.97 + 12 ÷ 6 ×3 - 13.03) ÷ 2  

(18.97 + 2 × 3 - 13.03 ) ÷ 2

( 18.97 + 6 - 13.03 ) ÷ 2 

( 24.97 - 13.03) ÷ 2

⇒ 11.94 ÷ 2 = 5.97 ≈ 6

Hence, the required approximate value is 6 .

From the given information:

Starting from a point X, Shekhar walks 70 m towards the north. Then, he takes a left turn and walks 150 m.

Now, takes a left turn and walks 70 m.

And Finally, he takes a left turn and walks 90 m to reach point Y.

So, Distance from Y to X = 150 -90 =  60m.

Here, Point X is 60 m towards the east of Y.

Hence, the correct answer is "Option 3".

Shortcut Trick

Term 1 percentage = 100% (Full marks)

Term 2 percentage = 75/90 × 100 = 83.33%

Weighted % = (100 × 0.40) + (83.33 × 0.60)

Final Score = 40 + 50 = 90%

∴ The correct answer is 90%.

Alternate Method

Given:

Term 1 score = 80/80 (Full marks)

Term 2 score = 75/90

Weightage of Term 1 = 40% and Term 2 = 60%

Calculations:

⇒ Percentage score in Term 1 = (80 ÷ 80) × 100 = 100%

⇒ Percentage score in Term 2 = (75 ÷ 90) × 100 = 83.33%

⇒ Contribution of Term 1 = 100 × (40 ÷ 100) = 40%

⇒ Contribution of Term 2 = 83.33 × (60 ÷ 100) = 50%

⇒ Final score = Contribution 1 + Contribution 2

⇒ Final score = 40 + 50 = 90%

∴ The correct answer is 90%.

Additional Information

Weighted Average Formula

The final score is calculated using the formula: Weighted Average = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂), where w is the weight and x is the value.

Percentage Calculation

Percentage = (Obtained Marks ÷ Maximum Marks) × 100. This standardizes scores across different totals.

Rounding Off Decimals

When calculating to the nearest integer, if the decimal part is 0.5 or greater, round up; otherwise, round down.

We apply the options on the given equation and solve it using BODMAS rule:

Given equation: 28 - 28 ÷ 14 + 7 × 2 = 16

Checking the options, after interchanging the symbols:

Option 1) × and -

28 × 28 ÷ 14 + 7 - 2 = 16

28 × 2 + 7 - 2 = 16

56 + 7 - 2 = 16

63 - 2 = 16

61 ≠ 16

Option 2) + and ÷

28 - 28 + 14 ÷ 7 × 2 = 16

28 - 28 + 2 × 2 = 16

28 - 28 + 4 = 16

32 - 28 = 16

4 ≠ 16

Option 3) × and ÷

28 - 28 × 14 + 7 ÷ 2 = 16

28 - 28 × 14 + 3.5 = 16

28 - 392 + 3.5 = 16

31.5 - 392 = 16

-360.5 ≠ 16

Option 4) + and -

28 + 28 ÷ 14 - 7 × 2 = 16

28 + 2 - 7 × 2 = 16

28 + 2 - 14 = 16

30 - 14 = 16

16 = 16

Hence the correct answer is option 4)

Shortcut Trick

Given Selling Price (SP₁) = ₹1,148 at 30% loss, so 70% of CP = 1,148.

To gain 5% profit, we need to find 105% of CP.

Ratio of SPs = 70 : 105 = 2 : 3.

Since 2 units = ₹1,148, then 1 unit = ₹574.

New Selling Price (SP₂) = 3 units = 3 × 574 = ₹1,722.

∴ The correct answer is ₹1,722.

Alternate Method

Given → SP₁ = ₹1,148, Loss% = 30%, Target Gain% = 5%. Formulas: CP = [SP × 100] ÷ [100 − Loss%] | New SP = [CP × (100 + Gain%)] ÷ 100.

⇒ Cost Price (CP) = (1148 × 100) ÷ (100 − 30) = (1148 × 100) ÷ 70. ⇒ CP = 16.4 × 100 = ₹1,640. ⇒ New Selling Price = [1640 × (100 + 5)] ÷ 100 = (1640 × 105) ÷ 100. ⇒ New SP = 16.4 × 105 = ₹1,722.

∴ The correct answer is ₹1,722.

Additional Information

Relation between SP and CP

When there is a profit, SP = CP × (100 + Gain%) / 100. When there is a loss, SP = CP × (100 − Loss%) / 100.

Direct Calculation

Required SP = [Initial SP ÷ (100 − Loss%)] × (100 + Gain%). This skips the explicit Cost Price calculation step.

The correct answer is the Indian Statistical Institute.

Key Points

• On December 17, 1931, he opened the Indian Statistical Institute in Calcutta.
• The institution was designated as "an institute of national importance" and a "deemed university" in 1959.
• Mahalanobis made contributions to the field of statistics with his work and discoveries. The Mahalanobis Distance, abbreviated D2, is what most people remember him for.
• He also served on India's planning commission when the country gained independence. He became well-known for his work on India's second five-year plan.
• The Indian government decided to declare June 29th, the anniversary of his birth, as "National Statistical Day" in 2006.

Additional Information 

• He also created the Profiloscope, a device used to measure the dimensions of the skull. He also made contributions to the field of physical anthropology.
• His contribution to large-scale sample surveys was the most significant. Pilot surveys were conceived by Mahalanobis.
• He developed a random sampling method that is thought to be the most precise in the entire globe. His research also enhanced agricultural yield estimates.
• He was particularly well-known for his Mahalanobis Plan, which was represented in the second draught of the five-year plan and called for significant investment in the establishment of fundamental heavy industries.

According to the English alphabets and their positional values:

The pattern followed here is:

For, PARTS : RDVYY

For, CLOSE : EOSXK

Now we consider the options:

Option 1) RHINO : TKMSU

Option 2) TIME: PQOFU

Option 3) MANGO : ODRTS

Option 4) CLASS : EODVV

Hence, the correct answer is option 1).

The correct answer is Stamens and pistils.

Key Points:

• The reproductive components of a flower, which also contain germ cells, are the stamens and the pistil.
• A flower can be either unisexual (watermelon, papaya) or bisexual (hibiscus, mustard) depending on whether it has stamens or pistils.
• The male reproductive component, the stamen, creates pollen grains with a yellowish hue.
• The female reproductive component of a flower is the pistil, which is located in the center.
• There are three pieces to it.
• The stigma is located at the end of the style and may be sticky.
• The ovary is located at the bottom, where it is enlarged.
• Ovules are found in the ovary, and each ovule contains an egg cell.
• The female gamete is found in the ovule and the male germ-cell is created by the pollen grain mate.

Additional Information:

• Sepals: 
• A sepal is a part of the flower of an angiosperm (flowering plants).
• The often green sepals support the petals while they are in bloom and protect the flower while it is still in the bud stage.
• Anther:
• The portion of a flower that sheds pollen at the top of a stamen is called an anther.
• Petals:
• Flowers' reproductive organs are enclosed by petals, which are modified leaves.
• To lure pollinators, they are frequently brightly coloured or shaped differently.
• Style: 
• ​The pistil stalk is referred to as the "style."
• When pollen reaches the stigma, it starts to form a pollen tube that will eventually go through the style and reach the ovary.
• Because only suitable pollen can form a pollen tube, the style protects against pollen contamination.

Given, Six students P, Q, R, S, T and U.

1) P and S sit at the ends of the row.

2) T sits immediate neighbor of P, while U sits immediate neighbor of S.

3) Only one person sits between Q and S.

And, R will sit at the remaining place.

Here, U sits immediately next to Q.

Hence, the correct answer is "Option 4".

The correct answer is Advocate-General.

Key Points

• As the chief legal representative of the State's government, the Advocate General carries out the responsibilities listed below:
• To provide legal advice to the state government on subjects that the governor refers to him for.
• To carry out any additional legal obligations that the state governor delegates to you.
• To perform the duties assigned to him or her by the Constitution or another piece of legislation.
• The Advocate General is permitted to represent the State in any court of law while carrying out his official responsibilities.
• The Advocate General is entitled to speak and participate in both Houses of the State legislature's sessions.
• Additionally, he or she has the ability to participate in committee meetings without being able to vote in any committee of the State legislature.
• Solicitor General
• ​In common law nations, a solicitor general or solicitor-general is typically a legal officer who serves as the principal advocate for a regional or national government in court proceedings.
• Attorney General
• ​The Attorney General of India acts as the chief court representative as well as the government's senior legal advisor.
• According to Article 76(1) of the Constitution, they are chosen by the Indian President at the request of the Union Cabinet and serve at the President's leisure.
• Comptroller and Auditor General
• ​According to Article 148 of the Indian Constitution, the Comptroller and Auditor General of India is the country's top auditing body.
• They have the authority to examine all monies received and spent by the Indian and state governments, as well as any autonomous organizations and businesses that get significant government funding.

The correct answer is 2 × 108m / sec.

Given:

Refractive index $n=1.5$

To find: Speed of light in the medium

Formula used:

The refractive index is defined as:

$n={Speed-of-light-in-vaccum \over Speed-of-light -in-medium}$

Calculations:

Here we have,

$n={Speed-of-light-in-vaccum \over Speed-of-light -in-medium}$

$1.5={3*10^8 \over Speed-of-light -in-medium}$

Speed of light in the medium is \(={310^8\over 1.5}=210^8m/sec\)

So, the speed of light in the medium is 2 × 108m / sec.

The correct answer is AFC Women's Asian Cup.

Key Points

• In 2022, Mumbai and Pune will host the AFC Women's Asian Cup.
• All of the matches of the AFC Women's Asian Cup 2022 were played in the D.Y. Patil Stadium in Navi Mumbai, the Mumbai Football Arena in Andheri, and the Shiv Chhatrapati Sports Complex in Balewadi, Pune.
• It is planned to hold the competition from January 20 to February 6, 2022.

Additional Information

• FIFA Women's World Cup:-
• ​The FIFA Women's World Cup is an international association football championship where the senior women's national teams of the FIFA (Fédération Internationale de Football Association), the sport's global governing body, participate.
• Asian Champions Trophy:-
• ​The Asian Hockey Federation hosts the Men's Asian Champions Trophy every year (since 2011). In a round-robin style, it comprises the best six field hockey squads from Asia from that season. The two most successful teams in the history of this competition are India and Pakistan.
• Asian Track & Para-Cycling Championships:-
• ​The Asian Cycling Championship (Road & Track) includes the Asian Track Cycling Championships (ATCC), which is only for Asian cyclists who have been chosen by their national governing bodies and other Asian Cycling Confederation member countries.
• Track cycling has an annual continental championship. Cycling contests for the road and the track are now held separately as of 2017.

The correct answer is 

i. A - Mitosis, B - Meiosis

ii. Meiosis takes place in reproductive cells for the formation of gametes

Key Points

• Meiosis is a type of cell division that results in the formation of four daughter cells each with half the number of chromosomes as the parent cell.
• Mitosis is the type of cell division that results in the formation of two daughter cells each with the same number and kind of chromosomes as the parent cell.
• Mitosis is the process where the division of cells occurs by asexual reproduction.
• The meiosis mode of reproduction is through sexual reproduction and takes place in reproductive cells to form gametes.
• So from the question, it is clear that  A - Mitosis, B - Meiosis, and Meiosis takes place in all the cells of the body.

​So, option 2) is the correct answer.

Additional Information

• Mitosis and meiosis take place in the cell nuclei where both involve cell division.
• Both processes occur in the M-phase of the cell cycle.
• In both cycles, the stages are common- prophase, metaphase, anaphase and telophase.
• Synthesis of DNA occurs in both processes.

Given: T % N 9 + M $ 3 U = L 8 Y @ G & 3 E > W.

The Letters are immediately followed by a symbol and immediately preceded by a number.

So, the sequence will be Number, Letter, Symbol.

Here, 3 pairs are immediately followed by a symbol and immediately preceded by a number.

3U=, 8Y@, 3E>

Hence, the correct answer is "Option 3".

According to the English alphabets and their positional values:

The pattern followed in the given codes is:

 Each alphabet is increased to the positional value of its place value.

 The alphabets are arranged backwards to form the code.

For, 'ACADEMY' is written as 'FSJHDEB'

For, 'BARRIER' is written as 'YKNVUCC'

Similarly, for 'ATTEMPT'

So, 'ATTEMPT' is written as 'AVRIWVB'

Hence the correct answer is option 4).

Shortcut Trick

Effective Rate of Interest for 2 years = 7% × 2 = 14%

Total Simple Interest = 14% of ₹2,00,000

⇒ Simple Interest = 14 × 2000 = ₹28,000

∴ The correct answer is ₹28,000.

Alternate Method

Given:

Principal (P) = ₹2,00,000

Rate of Interest (R) = 7% per annum

Time period (T) = 2 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI = (2,00,000 × 7 × 2) ÷ 100

⇒ SI = 2,000 × 7 × 2

⇒ SI = 2,000 × 14

⇒ SI = ₹28,000

∴ The correct answer is ₹28,000.

Additional Information

Total Amount (A)

The total sum of money payable after the time period is the sum of Principal and Interest: A = P + SI.

Constant Interest

In Simple Interest, the interest amount remains the same for every year because it is always calculated on the original Principal.

Compound Interest (CI)

Unlike SI, Compound Interest is calculated on the principal plus the accumulated interest of previous periods. Formula: A = P(1 + R/100)^T.

Statements:

1. Some pamphlets are copies.
   
2. All copies are readers.
   
3. All readers are scrolls.

Venn diagram:

Conclusions:

I. All pamphlets are scrolls→ Does not follow → Since some pamphlets are copies when means only some pamphlets can be scrolls and the same can be seen in the Venn diagram thus the conclusion does not follow.

II. All copies are scrolls→ Follow → We have 'all copies are readers' & 'all readers are scrolls' then it is correct to conclude that all copies are scrolls therefore the conclusion follows. 

III. Some readers are copies→ Follow → From the statements, 'all copies are readers' which means there have to be some part of readers who are copies and it is clearly visible in the Venn diagram therefore the conclusion follows.

IV. Some scrolls are pamphlets→ Follow → Here 'all copies are readers' & 'all readers are scrolls' which implies all copies are scrolls, also 'some copies are pamphlets' similarly some scrolls are pamphlets therefore the conclusion follows.

So only conclusions II, III & IV follows.

Hence the correct answer is option 1)

Given:

Statements:

1. All tigers are lions.
2. No cat is a lion.
3. Some jaguars are cats.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some jaguars are lions - Does not follow (As, there is no direct relation given between Jaguars and Lions, so it can be possible not definite).

II. No jaguar is tiger - Does not follow (As, there is no direct relation given between Jaguars and Lions, so it can be possible not definite).

So, None follows.

Hence, the correct answer is "Option 1".

Shortcut Trick Sum = 335 + 265 = 600 (Divisor) Difference = 335 − 265 = 70 Quotient = 3 × 70 = 210 Number = (600 × 210) + 35 = 126000 + 35 = 126035 ∴ The correct answer is 126035. Alternate Method Given: Divisor (D) = Sum of 335 and 265 Quotient (Q) = 3 × (Difference of 335 and 265) Remainder (R) = 35 Formula Used: Number (Dividend) = (Divisor × Quotient) + Remainder

Calculations: ⇒ Divisor = 335 + 265 = 600 ⇒ Difference = 335 − 265 = 70 ⇒ Quotient = 3 × 70 = 210 ⇒ Number = (600 × 210) + 35 ⇒ Number = 126000 + 35 ⇒ Number = 126035 ∴ The correct answer is 126035. Additional Information Division Algorithm For any whole numbers a and b (b ≠ 0), there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Remainder Property The remainder must always be smaller than the divisor and can never be a negative value in standard arithmetic division. Verification Rule To verify a division result, always check if (Dividend − Remainder) is exactly divisible by both the Divisor and the Quotient.

The correct answer is Yeast.

Key Points

• Yeast plays a vital role in the production of all alcoholic beverages.
• In food manufacture, yeast is used to cause fermentation and leavening.
• These fungi feed on sugars, producing alcohol(ethanol) and carbon-di-oxide; in beer and wine.
• The alcohol producers use yeast to ferment the mixture and make it alcoholic.

Additional Information

• Yeasts are eukaryotic, single-celled microorganisms classified as members of the fungus kingdom.
• They also grow in normal temperatures as well as in the laboratory on solid growth media and liquid broths.
• They reproduce both asexually and sexually.

µ_AV_B = µ_AV_A

V_A = 2 * 108m/sec, V_B = 2.25 * 108 m/sec

According to Snell's law

µ_AV_A = µ_BV_B

µ is the refractive index w.r.t air and V is the velocity in that medium

The refractive index of medium A with respect to medium B is equal to = µAB

µAB = µA  / µ_B = VB/VA = 2.25 * 10⁸ / 2 * 10⁸ = 1.125

µAB  = 1.125

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

Calculation:

Here, we have 62 + 72 +$\sqrt16$ 

⇒ 36 + 49 + 4  = 85 + 4 

⇒ 89 

Hence, the required value is 89 .

The correct answer is Jharkhand.

Key Points

• A large portion of Jharkhand, as well as adjacent regions of Bihar, Odisha, West Bengal, and Chhattisgarh, are included in the Chhota Nagpur Plateau, an eastern Indian plateau.
• To the North and East of the plateau are the Indo-Gangetic Plains, and to the South is the Mahanadi River Basin.
• Precambrian rocks make up the Plateau. The plateau was created by continental uplift brought on by forces that originated deep inside the earth.
• The Rajmahal Hills, which make up the Chhota Nagpur Plateau's northern edge, is primarily made of basalt and are covered in basaltic lava flows.

Additional Information 

• The Sanjay National Park in Chhattisgarh and the Palamau Tiger Reserve in Jharkhand are nearby.
• A tropical and subtropical dry broadleaf forests ecoregion surrounds the plateau and is found in the Chhota Nagpur.
• Sal Trees are another prominent feature of the area. These trees are a good source of both food and lumber.
• The greatest concentration of mineral resources in India is located in the Chhota Nagpur region. Resources including bauxite, iron ore, and others are abundant in the area.

Shortcut Trick

Total Time required = Total Distance ÷ Average Speed = 800 ÷ 60 = 40/3 hours.

Time spent on first part = 300 ÷ 50 = 6 hours.

Remaining Time = 40/3 − 6 = 22/3 hours.

Required Speed = Remaining Distance ÷ Remaining Time = 500 ÷ (22/3) = 1500/22 = 750/11 km/h.

∴ The correct answer is 750/11 km/h.

Alternate Method

Given:

Total Distance (D) = 800 km, Target Average Speed (V_avg) = 60 km/h.

Part 1: d₁ = 300 km, s₁ = 50 km/h.

Part 2: d₂ = 800 − 300 = 500 km, s₂ = V km/h.

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Time (T) = 800 ÷ 60 = 40/3 hours

⇒ Time for first part (t₁) = 300 ÷ 50 = 6 hours

⇒ Time for remaining part (t₂) = T − t₁ = 40/3 − 6

⇒ t₂ = (40 − 18) ÷ 3 = 22/3 hours

⇒ Speed for remaining part (s₂) = d₂ ÷ t₂

⇒ s₂ = 500 ÷ (22/3) = (500 × 3) ÷ 22

⇒ s₂ = 1500 ÷ 22 = 750/11 km/h

∴ The correct answer is 750/11 km/h.

Additional Information

Average Speed Formula

Average Speed is defined as total distance divided by total time: V_avg = (d₁ + d₂) / (t₁ + t₂).

Special Case: Equal Distances

If a journey is divided into two equal distances with speeds x and y, the Average Speed = 2xy / (x + y).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Shortcut Trick

Relative Speed (km/h) = (Distance ÷ Time) × (18/5)

Relative Speed = (210 ÷ 12) × (18 ÷ 5) = 17.5 × 3.6 = 63 km/h

Since they move in opposite directions, Relative Speed = Speed of Train + Speed of Man

Speed of Train = 63 − 4.5 = 58.5 km/h

∴ The correct answer is 58.5 km/h.

Alternate Method

Given: Length of train (L) = 210 m, Speed of man (V_m) = 4.5 km/h, Time (t) = 12 s

Formula Used: Speed = Distance ÷ Time; Relative Speed (Opposite) = V₁ + V₂

⇒ Let the speed of the train be V km/h.

⇒ Relative speed = (V + 4.5) km/h

⇒ Convert speed to m/s: Relative speed = (V + 4.5) × (5/18) m/s

⇒ Distance = Speed × Time

⇒ 210 = (V + 4.5) × (5/18) × 12

⇒ 210 = (V + 4.5) × (60/18)

⇒ 210 = (V + 4.5) × (10/3)

⇒ 21 × 3 = V + 4.5

⇒ 63 = V + 4.5

⇒ V = 63 − 4.5 = 58.5 km/h

∴ The correct answer is 58.5 km/h.

Additional Information

Relative Speed Rules

When two objects move in opposite directions, relative speed is the sum of their speeds (V₁ + V₂). In the same direction, it is the difference (V₁ − V₂).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Train Crossing a Man

When a train crosses a stationary or moving person, the distance covered is equal to the length of the train.

The correct answer is Oman.

 Key Points

• At the World Race Walking Team Championships 2022, which were conducted over the weekend in Muscat, Oman, three athletes from India Tokyo Olympian Bhawna Jat, Ravina, and Munita Prajapati joined forces to win India a bronze medal in the team classification of the women's 20km race walk.
• In the women's 20km race in Muscat, Ravina finished 14th, which was the best result for an Indian.

Additional Information

• The World Athletics Race Walking Team Championships have been held for 61 years, and this is India's first medal in that time.
• With a third-place result behind China and Greece and a bronze medal, the Indian team of Bhawna Jat, Ravina, and Munita Prajapati. Fourth place in the standings went to Lithuania.
• It was the first medal Indian women have ever won at a major race walking competition. In the 2012 men's 20km, the Indian trio of KT Irfan, Surinder Singh, and Babubhai Kesharabhai Panucha took home the bronze medal.

The correct answer is Federalism.

Key Points

• Federalism- 
• It Is a system of government in which powers have been divided between the center and the state.
• There are two types of federation:-Holding together federation, Coming together federation.
• The Constitution establishes a dual polity consisting of the Union at the Centre and the states at the periphery.
• Powers and functions of each tier of government are specified and guaranteed by the constitution i.e. Division of Power.
• India has a bi-cameral legislature and it is an essential feature of federalism.

 Additional Information

• The Supreme Court has been given the power to settle disputes between central and state governments.
• Federalism was introduced into modern India by the government of India Act of 1919.
• Secularism:-
• It is the principle of separation of the state from religious institutions.
• Parliamentary system-
• It is a form of government where executives hold the power with the majority support of the legislature.

Given statement:

T = S ≥ N = A ≤ U > P < Q

Conclusion:

I. S > Q → False (S ≥ N = A ≤ U > P < Q → No definite relation can be possible between S and Q).

II. A ≤ T → True → (T = S ≥ N = A gives T ≥ A).

So, only conclusion II is correct.

Hence, the correct answer is option 1).

The correct answer is Fe2O3 and AI.

Key Points:

• In the aforementioned reaction, ferric oxide reacts with aluminium to produce aluminium oxide and iron, which is;
• 2Al + Fe2O3 → Al2O3 + 2Fe.
• Here, aluminium (Al) is the oxidised substance, and iron (Fe) is the reduced substance .
• We can quickly determine which substance is oxidising and which is decreasing because of the difference in the oxidation numbers of iron and aluminium.
• Aluminum (Al) undergoes oxidation reactions that increase its oxidation number from zero to three while also introducing oxygen into the mix.
• Fe2O3 acts as an oxidising agent.
• Due to the removal of oxygen from Fe2O3 and the addition of Al, Fe2O3 is reduced to Fe.
• Aluminum (Al) thus serves as the reducing agent.

Additional Information:

• The addition of oxygen or any other electronegative element, or the removal of an electropositive element, is a process known as oxidation.
• Oxidizing agent:
• In a redox reaction, an oxidising agent is a chemical that absorbs or gains electrons or has a tendency to add oxygen atoms.
• Hydrogen or any other electropositive element is introduced while oxygen or any other electronegative element is subtracted during the reduction reaction.
• Reducing agent:
• A reducing agent is a type of chemical that has the ability to eliminate oxygen from elements or take hydrogen.

The correct answer is Kerala.

Key Points

• It is a joint venture of the Digital University of Kerala, the Centre for Materials for Electronics Technology (C-MET) and Tata Steel Limited. It will be set up in Thrissur Kerala.
• Graphene is a one-atom-thick layer of carbon atoms arranged in a hexagonal arrangement.
• An Innovation Center is a cross-functional plan that creates a safe haven for new ideas.
• Earlier in 2020, researchers from the City University of Hong Kong produced a laser-induced form of graphene masks that inactivate the coronavirus species.

 Additional Information

• The state government would provide the basic infrastructure for the project. The Centre would help attract investors to develop graphene products.
• The project would give a major boost to scientific research as well as the state’s industrial sector.
• This result in Kerala’s human resources capital being effectively exploited, which will help Kerala to emerge as a knowledge-based economy.

Shortcut Trick

Find the missing angles: In Δ ABC, ∠C = 180° − (40° + 55°) = 85°. In Δ DEF, ∠F = 180° − (55° + 85°) = 40°.

Match vertices with equal angles: A (40°) ↔ F (40°), B (55°) ↔ D (55°), and C (85°) ↔ E (85°).

Check the given side: AB = FD. Since A ↔ F and B ↔ D, side AB corresponds to side FD.

By ASA congruence rule, the triangles are congruent in the order of their corresponding vertices.

∴ The correct answer is Δ ABC ≅ Δ FDE.

Alternate Method

Given: In Δ ABC, ∠A = 40°, ∠B = 55°. In Δ DEF, ∠D = 55°, ∠E = 85°, and AB = FD.

Formula Used: Angle Sum Property (Sum of angles = 180°) and ASA (Angle-Side-Angle) Congruence Rule.

A B C F D E

We have to find the number of people who like Hazelnut but do not like Cashew so we highlight the region with Hazelnut.

The shaded part shows the person who likes Hazelnut but does not like Cashew.

Total = 120 + 19 = 139.

Hence, the correct answer is "Option 3".

The pattern followed in the given series is:

Logic: First term × (Second term ÷ 4) = Third term

Now we apply the pattern on the given sets:

(24, 12, 72)

24 × (12 ÷ 4) = 72

24 × 3 = 72

72 = 72

(15, 16, 60)

15 × (16 ÷ 4) = 60

15 × 4 = 60

60 = 60

Now we apply the pattern on the given options:

Option 1) (20, 24, 120)

20 × (24 ÷ 4) = 120

20 × 6 = 120

120 = 120

Option 2) (30, 40, 156)

30 × (40 ÷ 4) = 156

30 × 10 = 156

300 ≠ 156

Option 3) (17, 20, 65)

17 × (20 ÷ 4) = 65

17 × 5 = 65

85 ≠ 65

Option 4) (18, 12, 56)

18 × (12 ÷ 4) = 56

18 × 3 = 56

54 ≠ 56

Hence, the correct answer is "Option 1".

Shortcut Trick

Total distance = Sum of lengths = 120 + 140 = 260 m.

Relative speed = Total distance ÷ Time = 260 ÷ 10 = 26 m/s.

Since both trains have the same speed and move in opposite directions, Relative Speed = 2 × Speed.

Speed of each train = 26 ÷ 2 = 13 m/s.

∴ The correct answer is 13 m/s.

Alternate Method

Given: Length of train 1 (L₁) = 120 m, Length of train 2 (L₂) = 140 m, Time (t) = 10 s, Speed (v₁ = v₂ = v).

Formula Used: Relative Speed = (L₁ + L₂) ÷ Time

⇒ Total distance = 120 + 140 = 260 m

⇒ Relative speed in opposite direction = v + v = 2v

⇒ 2v = 260 ÷ 10

⇒ 2v = 26 m/s

⇒ v = 13 m/s

∴ The correct answer is 13 m/s.

Additional Information

Relative Speed (Opposite Direction)

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Relative Speed (Same Direction)

When two objects move in the same direction, their relative speed is the difference of their individual speeds: S_rel = |S₁ − S₂|.

Speed Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Given Ratio = 5 : 7 and HCF = 17.

Numbers are always multiples of their HCF.

First number = 5 × 17 = 85.

Second number = 7 × 17 = 119.

∴ The correct answer is 85, 119.

Alternate Method

Given:

Ratio of two numbers = 5 : 7

Highest Common Factor (HCF) = 17

Formula Used:

If ratio is a : b and HCF is h, then numbers are (a × h) and (b × h).

Calculations:

⇒ Let the numbers be 5x and 7x.

⇒ The HCF of 5x and 7x is x.

⇒ Since HCF is given as 17, x = 17.

⇒ First number = 5x = 5 × 17 = 85.

⇒ Second number = 7x = 7 × 17 = 119.

∴ The correct answer is 85, 119.

Additional Information

LCM and HCF Relationship

Product of two numbers = HCF × LCM. This is valid for any two positive integers.

LCM of Numbers in Ratio

If ratio of two numbers is a : b and their HCF is h, then their LCM = a × b × h.

Co-prime Numbers

If the HCF of two numbers is 1, they are called co-prime numbers (e.g., 5 and 7).

Calculations:

⇒ $\left(a+\frac{1}{b}\right)^r\left(a-\frac{1}{b}\right)^s\div\left(b+\frac{1}{a}\right)^r\left(b-\frac{1}{a}\right)^s$

⇒ $\left(\frac{ab+1}{b}\right)^r\left(\frac{ab-1}{b}\right)^s\div\left(\frac{ab+1}{a}\right)^r\left(\frac{ab-1}{a}\right)^s$

⇒ $\frac{\left(\frac{(ab+1)^r}{b^r}\right)\left(\frac{(ab-1)^s}{b^s}\right)}{\left(\frac{(ab+1)^r}{a^r}\right)^r\left(\frac{(ab-1)^s}{a^s}\right)}$

⇒ $\frac{a^r \times a^s}{b^r \times b^s)}$

⇒ $\frac{a^{r+s}}{b^{r+s}}$

⇒ ${(\frac{a}{b})}^{r+s}$

Hence, The correct option is 3.

The correct answer is 25Ω.

Key Points

• Resistance
• ​The property of materials that makes it possible for electric current to flow is known as resistance.
• The flow of current is certainly impeded by resistance.
• The Greek uppercase letter omega is the unit of resistance, and the resistance varies depending on the voltage across a particular resistor and the current passing through it.
• A measure of the resistance to current flow in a specific electrical circuit is referred to as resistance.
• Resistance in parallel: 1/R_tot= 1/R₁+1/R₂
• Resistance in series: R_tot= R₁+R₂

Additional Information

• Calculations
• Since the wire is in form of circle it has the upper and lower part of resistance to be 50Ω each.
  

So as the other two 50Ω are connected in parallel, the equivalent resistance is, 

​1/Rtot= 1/50+1/50= 2/50= 1/25

Rtot= 25Ω

• ​Thus, the equivalent resistance between two diametrically opposite points of the circle is 25Ω.

The correct answer is 16.

Key Points

• Group 16 elements
• The elements in Group 16 of the periodic table make up the oxygen family, which is also known as the chalcogens. It is considered to be one of the main groups of elements.
• Oxygen, sulfur, selenium, tellurium, or polonium increase metallic properties first. Polonium is primarily made of metal. M. Curie discovered it and gave it the name Poland in honor of her home country.
• As the group's atomic weight rises, so does its electronegativity, ionization energy (or IP), and electron affinity.
• The melting point and atomic radius increase.
• Due to its small size, oxygen has distinct chemical properties from sulfur. There are more differences between O and S than there are between the other members.

Additional Information

• Acidic oxide
• ​An oxide that, upon addition to water, either produces an acidic solution or serves as an acceptor of hydroxide ions, effectively acting as a Lewis acid, is known as an acidic oxide.
• Typically, acidic oxides have a low pKa and can be organic or inorganic.​
• When dissolved, carbon dioxide, a common acidic oxide, results in the formation of carbonic acid and the formation of an acidic solution.

Now, Each letter is changed to the next letter in the English alphabetical order, then:

Here, 2 such clusters formed with no vowels: MBZN & KPFL.

Hence, the correct answer is "Option 1".

The pattern followed in the given series is:

Logic: First term × First term + 1 = Second term.

Now we apply the pattern on the given series:

For, 12 : 145

12 × 12 + 1 = 145

144 + 1 = 145

145 = 145

For, 9 : 82

9 × 9 + 1 = 82 

81 + 1 = 82

82 = 82

Similarly, 11 : ?

11 × 11 + 1 = ?

121 + 1 = 122.

Hence, the correct answer is "Option 4".

According to the English alphabets and their positional values:

The pattern followed in the given series is:

   The difference between numbers are the square of natural numbers.

   The first alphabet is increased to +3,+6,+9,+12 positional value.

   The last alphabet is decreased by -3,-6,-9,-12 positional value.

Hence, the correct answer is "Option 1".

Given: Six students P, Q, R, S, T and U.

1. P is taller than only two students.

_ > _ > _ > P > _ > _  

2. T is taller than only one student but shorter than exactly four students.

_ > _ > _ > P > T > _  

3. S is taller than only four students but is not the tallest.
   

_ > S > _ > P > T > _ 

4) Q is not taller than any student.

5. R is not the tallest.

_ > S > R/Q > P > T > Q/R

And, U will place o the remaining position,

U > S > R > P > T > Q

Here, U is the tallest.

Hence, the correct answer is "Option 3".

Shortcut Trick

Present Ratio (Father : Daughter) = 3 : 1 (Difference = 2 units)

Future Ratio (after 10 years) = 2 : 1 (Difference = 1 unit)

Equate difference by multiplying future ratio by 2 → 4 : 2

Change in units = 4 − 3 = 1 unit, which represents 10 years.

Daughter’s present age = 1 unit × 10 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given: Present ratio is 3:1 and ratio after 10 years is 2:1.

⇒ Let Daughter’s present age = x years.

⇒ Father’s present age = 3x years.

⇒ According to the question: (3x + 10) = 2 × (x + 10)

⇒ 3x + 10 = 2x + 20

⇒ 3x − 2x = 20 − 10

⇒ x = 10

∴ The correct answer is 10 years.

Additional Information

Ratio Difference Method

When the same number of years is added to two people, the difference between their ages remains constant. Adjusting ratios to keep this difference equal simplifies the calculation.

Algebraic Verification

If present age is 3x and x, then (3x + n) / (x + n) = m / k, where n is the number of years and m:k is the future ratio.

Linear Equations in Ages

Most age problems can be solved by setting up a linear equation based on the relationship given for different points in time.

Solve it using BODMAS rule:

Given equation: 7 × 7 ÷ 8 - 12 × 6 + 17 - 14 - 100 = ?

After interchanging '+' and '-' and '÷' and '×'

7 ÷ 7 × 8 + 12 ÷ 6 - 17 + 14 + 100 = ?

⇒ 1 × 8 + 2 - 17 + 14 + 100 = ?

⇒ 8 + 2 - 17 + 14 + 100 = ?

⇒ 124 - 17 = 107.

Hence, the correct answer is "Option 3".

The correct answer is "Telangana".

Key Points

• The Department of Women and Child Development, Telangana provided logistical support, finance, and assistance for the establishment of BHAROSA as a Society for Protection of Women and Children in Hyderabad in May 2016.
• BHAROSA offers rapid access to expert services to everyone who knocks on its doors.
• In addition to psychological counselling, a variety of police, medical, legal, and prosecution services are offered in an integrated manner.
• Relief and rehabilitation are the results of this multifaceted help, if necessary.
• Thus, as per information received till July 2022, Telangana has set up 'Bharosa Kendras', which provide one-stop services for women and children, who are victims of sexual assault and violence.

Additional Information

• Over the years, there has been an increase in sexual offences in the nation.
• Although the government adopted the Prevention of Children from Sexual Offences Act, 2012 (POCSO) in response to the need for a specific law to address crimes against children, its execution required significant support on the ground.
• Up to 3,000 POCSO incidents are reported and looked into annually, and four child sexual assault victims are denied justice every day because police close their investigations due to a lack of information or insufficient proof.

The correct answer is 1 July 2017.

Key Points

• The GST Bill, 2014 was passed in May 2015. It was enacted as Constitution Act, 2016, with effect from, 16th September, 2016. The GST was launched on 1st July 2017.
• It is a tax levied when a consumer buys a good or service. It is meant to be a single, comprehensive tax that will subsume all the other smaller indirect taxes on consumption like service tax, etc.
• It subsumed 17 large taxes and 13 cesses. It is a single tax on the supply of goods and services, right from the manufacturer to the end consumer.
• It is a step towards 'One Nation, One Tax'.

 Additional Information

• It is Simple and Easy to administer because multiple indirect taxes at the central and state levels are being replaced by a single tax “GST”.
• It makes Better control on leakage because of better tax compliance, reduction of rent-seeking, transparency in taxation due to IT use.
• It has Higher revenue efficiency since the cost of the collection will decrease along with an increase in the ease of compliance, it will lead to higher tax revenue.
• The single and transparent tax will provide a lowering of inflation. and provide Relief in overall tax burden.
• It has Tax democracy that is luxury items will be taxed more and basic goods will be tax-free.

The correct answer is Mahatma Gandhi National Rural Employment Guarantee Act.

Key Points

• A rural wage employment scheme called MGNREGA was launched in India in 2005.
• The Ministry of Rural Development (MRD), which oversees the full implementation of this programme with state governments, keeps an eye on it.
• By creating chances for wage employment, it helps the impoverished in rural areas improve the security of their means of subsistence.
• Additionally, it strives to build a rural asset base that would improve productive job opportunities and increase and sustain a rural household's income.

 Additional Information

• Adult members of rural households now have the legal right to employment due to the Act. At least one-third of the recipients must be women.
• It promotes the empowerment of disadvantaged groups. The largest social security programme in the world is MGNREGA.
• It functions as a plan to fight poverty. It was a tool that many utilised to escape poverty.
• Also, it contributes to the creation of jobs and financial inclusion of individuals.
• It also gave the rural economy a boost.

Given:

Table below

Calculations:

Total Number of students

= Total male + Total female

= 656 + 647

= 1303

Females in commerce

= 190

Percentage required

= 190 × 100/1303

= 14.58%

Hence, The Required value is 14.58%.

The Correct answer is Alkaline.

Key Points

• Metal oxides have a simple chemical structure.
• An oxygen atom is connected to another atom in a chemical known as an oxide.
• These compounds can be created by partnering oxygen atoms with metals, which donate their electrons in their valence shells in the process.
• Since they react with weak acids to produce salt and water, metal oxides are basic in nature.
• Ionic metal oxides typically react with substances that produce water and contain hydroxide ions. A basic solution is created as a result of the reaction with water.

 Additional Information

• They are basic because salt and water are created when metal oxides and acids react. They are basic because they neutralise the acids.
• Acidic oxides can be produced by metalloids or nonmetals. With water, they react, producing an acidic solution.
• The oxides known as amphoteric oxides exhibit both acidic and basic behaviour. Amphoteric oxides are neutralizers of both acids and bases with characteristics of both acidic and basic oxides.

The correct answer is leucoplastids.

Key Points

• Leucoplastids
• ​Leucoplasts are organelles found in plant cells and belong to the plastid family. In contrast to other plastids like chloroplast, they lack pigmentation.
• They are referred to as amyloplasts, elaioplasts, or proteinoplasts (also known as aleuroplasts), depending on whether they are specialized for the bulk storage of protein, lipid, or starch.
• Leucoplasts serve a wide range of essential biosynthetic functions and do not serve a major storage function in many cell types.

Additional Information

• Plastids
• ​The plastid is a membrane-bound organelle that is found in the cells of some eukaryotic organisms, including plants, algae, and bacteria.
• Cyanobacteria that live inside cells are known as intracellular endosymbiotics.
• Leucoplasts are non-pigmented plastids that can occasionally differentiate, chromoplasts are used for pigment synthesis and storage, and chloroplasts are used for photosynthesis.

Shortcut Trick

Ratio of Kohli to Rohit = 7 : 8

Difference in ratio parts = 8 − 7 = 1 unit

Given age difference = 3 years ⇒ 1 unit = 3 years

Age of Kohli = 7 units = 7 × 3 = 21 years

∴ The correct answer is 21 years.

Alternate Method

Given: Ratio of ages = 7 : 8 and Age difference = 3 years.

⇒ Let the age of Kohli be 7x and the age of Rohit be 8x.

⇒ According to the question: 8x − 7x = 3

⇒ x = 3

⇒ Age of Kohli = 7x = 7 × 3 = 21 years

⇒ Age of Rohit = 8x = 8 × 3 = 24 years

∴ The correct answer is 21 years.

Additional Information

Ratio and Proportion Basics

If two quantities are in the ratio a : b, they can be represented as ax and bx where x is a common multiplier.

Constant Age Difference

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

Finding Values from Ratio

Value of a part = (Total Value ÷ Sum of Ratio parts) × Specific Ratio part.

Shortcut Trick Recognize the equation as a perfect square trinomial. x2 − 14x + 49 = (x − 7)2 = 0 Since the equation is in the form (x − k)2 = 0, both roots are equal to k. Therefore, the roots are x = 7 and x = 7, which are real and equal. ∴ The correct answer is real and equal roots.

Alternate Method Given: Quadratic equation x2 − 14x + 49 = 0 Formula: For a quadratic equation ax2 + bx + c = 0, the nature of roots is determined by the Discriminant (D) where D = b2 − 4ac. ⇒ Comparing x2 − 14x + 49 = 0 with ax2 + bx + c = 0, we get: ⇒ a = 1, b = −14, c = 49 ⇒ D = (−14)2 − 4 × 1 × 49 ⇒ D = 196 − 196 ⇒ D = 0 ⇒ When the Discriminant is zero, the roots are always real and equal. ∴ The correct answer is real and equal roots.

Additional Information Nature of Roots Cases

1. If D > 0, the roots are real and distinct. 2. If D = 0, the roots are real and equal. 3. If D < 0, the roots are non-real or imaginary. Discriminant Formula The discriminant D = b2 − 4ac is used to find the nature of roots without solving the entire quadratic equation. Quadratic Formula Roots are calculated as x = (−b ± √D) ÷ 2a. If D = 0, then x = −b ÷ 2a.

The correct answer is El Nino.

Key Points

• El Niño
• Trade winds deteriorate during El Nino. The west coast of the Americas receives a push of warm water from the east.
• El Nio is Spanish for Little Boy, sometimes known as the Christ Child. In the 1600s, South American fishermen were aware of stretches of exceptionally warm Pacific Ocean water. El Nio de Navidad was the full term they used because it usually peaks in December.
• El Nio has a big impact on our weather. The Pacific jet stream shifts south of its neutral location due to the warmer waters.
• The northern U.S. and Canada are seeing drier and warmer weather than typical as a result of this shift. However, these times are wetter than typical and have more flooding in the Southeast and Gulf Coast regions of the United States.
• El Nino has a significant impact on marine species off the Pacific coast as well. Under typical circumstances, upwelling delivers cold, nutrient-rich water from the depths to the top. Upwelling weakens or ceases entirely during El Nino.
• There are fewer phytoplankton off the coast when the nutrients from the deep are absent. This has an impact on fish that consume phytoplankton, which has an impact on everything that consumes fish.
• Tropical animals like yellowtail and albacore tuna may enter regions that are usually too cold as a result of the warmer waters.

Additional Information

• La Niña
• La Nia is Spanish for "Little Girl." La Nina is also frequently referred to as El Viejo, the opposite of El Nino, or just "a cold event." El Nino's influence is reversed by La Nina.
• Trade winds are even stronger than usual during La Nina occurrences, bringing more warm water into Asia. Upwelling increases off the west coast of the Americas, sending cold, nutrient-rich water to the surface.
• The Pacific's chilly waters force the jet stream northward. Drought in the southern United States and severe rainfall and flooding in the Pacific Northwest and Canada are typically the results of this.
• Wintertime temperatures are often warmer in the South and cooler in the North during a La Nina year.
• Over the eastern Pacific, La Nina causes the jet stream to weaken and migrate northward. The South experiences warmer and drier winters than usual during La Nina events. Canada and the North generally have a cooler, wetter climate.
• The waters off the Pacific coast are cooler and richer in nutrients during La Nina. Because of the ecology, areas like the California coast are home to more marine life and cold-water species like squid and salmon.
• El Nino and  La Nina episodes normally last nine to twelve months, but can occasionally last for years.In general, El Nino and La Nina events happen every two to seven years, but they don't always happen at the same time.
• El Nino seems to happen more frequently than La Nina.

Shortcut Trick

For a quadratic equation with rational coefficients, irrational roots always occur in conjugate pairs.

If one root is 1 + √3, the other root must be 1 − √3.

Sum of roots = (1 + √3) + (1 − √3) = 2

Product of roots = (1 + √3) × (1 − √3) = 1 − 3 = −2

Equation: x² − (Sum)x + (Product) = 0 ⇒ x² − 2x − 2 = 0.

∴ The correct answer is x² − 2x − 2 = 0.

Alternate Method

Given: One root of the quadratic equation (α) = 1 + √3

Formula: If the coefficients of the quadratic equation ax² + bx + c = 0 are rational, then irrational roots occur in conjugate pairs.

⇒ If α = 1 + √3, then the second root (β) = 1 − √3.

⇒ Sum of roots (α + β) = (1 + √3) + (1 − √3)

⇒ Sum of roots = 2

⇒ Product of roots (αβ) = (1 + √3) × (1 − √3)

⇒ Product of roots = (1)² − (√3)² = 1 − 3 = −2

⇒ The quadratic equation is given by: x² − (α + β)x + αβ = 0

⇒ x² − (2)x + (−2) = 0

⇒ x² − 2x − 2 = 0

∴ The correct answer is x² − 2x − 2 = 0.

Additional Information

Conjugate Root Theorem

For equations with rational coefficients, if p + √q is a root, then p − √q is the second root.

Sum and Product of Roots

For ax² + bx + c = 0, sum = −b/a and product = c/a.

Discriminant and Nature of Roots

Nature is determined by D = b² − 4ac. If D is not a perfect square, roots are irrational and occur in pairs.

Formation of Quadratic Equation

If roots are known, the equation is x² − (Sum of roots)x + (Product of roots) = 0.

The correct answer is Devendra Nath Tagore.

Key Points

• Debendranath Tagore
• Maharishi Debendranath Tagore was a social reformer and scholar. In 1842, he became a member of the Brahmo Samaj, which Raja Rammohan Roy had established in 1828.
• Prior to that, he served as the leader of the 1839-founded Tattvabodhini Sabha.
• He was born in Calcutta in May 1817.
• Along with Raja Rammohan Roy, his father, Dwarkanath Tagore, was a very successful merchant and philanthropist in Calcutta.
• Rabindranath Tagore, a well-known Bengali poet, artist, writer, and essayist, was his son.
• The monthly theological newspaper Tattvabodhini Patrika was launched by the Debendranath Tagore-founded Tattvabodhini Sabha.
• Both Tattvabodhini Sabha and Tattvabodhini Patrika promoted the theories of Raja Rammohan Roy and concentrated on the methodical study of India's past with a reasonable viewpoint.

Additional Information

• A Tatwabodhini Pathshala or Theological School was established by Debendranath in 1844 to teach Vedanta and prepare young men to instruct in the Brahmo religion.
• Soon after Keshab Chandra Sen joined the Samaj in 1858, he appointed him the acharya.
• Keshab Chandra Sen and his adherents established the Brahmo Samaj of India in 1866 following his removal as acharya in 1865.
• Debendranath Tagore's Samaj later became known as the Adi Brahmo Samaj.
• He wrote and published the theistic treatise of religion and ethics known as the Brahma Dharma Grantha.

Shortcut Trick

Put x = 1 in the given expression: 3(1)(1 − 6) + 1² + 6(1) − 9 + 24 − 1³

⇒ 3(−5) + 1 + 6 − 9 + 24 − 1 = −15 + 21 = 6.

Now, check Option 2: 15 − 12(1) + 4(1)² − (1)³ = 15 − 12 + 4 − 1 = 6.

Since the values match, Option 2 is the correct simplification.

∴ The correct answer is 15 − 12x + 4x² − x³.

Alternate Method

Given Expression: 3x(x − 6) + x² + 6x − 9 + 24 − x³

Method: Expand terms using the Distributive Law and combine Like Terms.

⇒ 3x² − 18x + x² + 6x − 9 + 24 − x³

⇒ −x³ + (3x² + x²) + (−18x + 6x) + (24 − 9)

⇒ −x³ + 4x² − 12x + 15

⇒ 15 − 12x + 4x² − x³

∴ The correct answer is 15 − 12x + 4x² − x³.

Additional Information

BODMAS Rule

It stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction, defining the sequence of operations.

Distributive Property

The rule a × (b + c) = (a × b) + (a × c) is used to expand products of polynomials.

Degree of Polynomial

The degree is the highest power of the variable in the polynomial; for −x³ + 4x² − 12x + 15, the degree is 3.

The pattern followed here is:

The difference between the numbers is prime number.

Hence, the correct answer is "Option 3".

The correct answer is At C.

Key Points

• Concave mirror image formation at C
• ​The object emits two rays, one of which passes through the mirror's focus and the other parallel to the principal axis.
• After reflection at point C, these rays form an image that is real and inverted and has the same size as the object.
• So, at C the image formed is real, inverted, and the same size.

Additional Information

• Other Concave mirror image formation
• ​When the Object is at Infinity: We take into account two rays from the object that are parallel to the principal axis under this circumstance. After reflection, these rays converge to form an image in front of the mirror at F, the primary focus of the mirror. As a result, an extremely reduced, point-sized, real, and inverted image is created.
• The Object is Placed Between C and F: One of the two rays under consideration here is parallel to the principal axis, and the other is passing through the concave mirror's principal focus. The image is real and inverted, it is larger than the object's size, and it is formed beyond C.
• The Object is Placed Between F and P: One ray is going parallel to the principal axis, and the other is going through the mirror's center of curvature. The resulting image is virtual, straight, and larger than the object.

Calculations:

Let $1.\overline{24}$ be x.

Then, 100x = $124.\overline{24}$

⇒ 100x - x = $124.\overline{24}$ -  $1.\overline{24}$ 

⇒ 99x = 123

⇒ x = 123/99 = 41/33

Hence, The Required value is 41/33.

The correct answer is 29.

Key Points

• The 73rd Constitution Amendment Act of 1992 added the 11th Schedule to the Indian Constitution. 29 subjects are on this programme.
• This schedule includes crucial subjects including the authority of Panchayats, rural development, eradicating poverty, markets, roads, and clean water, among others.

Additional Information

• The following operational elements, which fall under the jurisdiction of the Panchayats, are listed in the eleventh schedule of the Indian Constitution:
• Agriculture, especially the expansion of agriculture
• Soil conservation, land reform implementation, land consolidation, and land enhancement.
• 3. Poultry, dairying, and animal husbandry
• It is expected that the subjects covered under the eleventh schedule of the Indian constitution are made to ensure the development of the rural India.

The pattern followed here is:

Here, '275' will complete the series.

Hence, the correct answer is "Option 3".

The correct answer is Only statement II is correct.

Key Points

• Role of HCL in Stomach
• The stomach's pH typically falls between 1.5 and 3.
• This is because the stomach releases hydrochloric acid.
• In order to prevent microbial diseases, this acidic condition is necessary for microbial digestion.
  

Numerous microbes are killed in this acidic environment as well.

• Additionally, it assists in the digestion of food particles.
• It has a crucial function in activating pepsin.
  

Pepsin is a gastric juice that the stomach uses to break down proteins.

• The stomach's hydrochloric acid is also necessary for vitamin B12 absorption.
• Additionally, RBCs and nerve tissues cannot function without vitamin B12.

Additional Information

• HCL in Stomach
• Hydrochloric acid is the acronym for HCl.
• Different gastric juices are released by the gastric glands during digestion.
• Hydrochloric acid is also secreted by gastric glands in addition to these juices.
• Hydrochloric acid is secreted during digestion as a result of parietal cells being activated.

Shortcut Trick

Identify sides a = 5, b = 7, c = 10.

Calculate semi-perimeter s = (5 + 7 + 10) ÷ 2 = 11.

Apply Heron's Formula: Area = √[s(s−a)(s−b)(s−c)].

Area = √[11 × (11−5) × (11−7) × (11−10)] = √[11 × 6 × 4 × 1] = √264.

Factor out perfect square: √(4 × 66) = 2√66.

∴ The correct answer is 2√66 cm².

Alternate Method

Given: Sides of the triangle a = 5 cm, b = 7 cm, and c = 10 cm.

Formula Used: Heron's Formula for area of triangle = √[s(s − a)(s − b)(s − c)], where s is the semi-perimeter.

⇒ Semi-perimeter (s) = (a + b + c) ÷ 2

⇒ s = (5 + 7 + 10) ÷ 2 = 22 ÷ 2 = 11 cm

⇒ Area = √[11 × (11 − 5) × (11 − 7) × (11 − 10)]

⇒ Area = √[11 × 6 × 4 × 1]

⇒ Area = √[264]

⇒ Area = √[4 × 66] = 2√66 cm²

∴ The correct answer is 2√66 cm².

Additional Information

Heron's Formula

Used for finding the area of any triangle when the lengths of all three sides are known: Area = √[s(s−a)(s−b)(s−c)].

Semi-perimeter (s)

It is half the perimeter of the triangle, calculated as s = (a + b + c) / 2.

Right-Angled Triangle Area

For a right triangle, Area = 1/2 × Base × Height. Heron's formula will give the same result if applied.

Shortcut Trick

Let Cost Price (CP) be 100.

Marked Price (MP) = 100 × 1.20 = 120.

Successive discount of 5% and 5% = 5 + 5 − (5 × 5) ÷ 100 = 9.75%.

Selling Price (SP) = 120 × (100 − 9.75) ÷ 100 = 120 × 0.9025 = 108.3.

Profit above CP = 108.3 − 100 = 8.3%.

∴ The correct answer is 8.3%.

Alternate Method

Given → Markup % = 20%, Successive Discounts = 5% and 5%.

Formulas: SP = CP × (100 + Increase%) ÷ 100 × (100 − D₁%) ÷ 100 × (100 − D₂%) ÷ 100

⇒ Let Cost Price = 100 units.

⇒ Marked Price = 100 + 20% of 100 = 120 units.

⇒ Price after 1^st discount = 120 − (5% of 120) = 120 − 6 = 114 units.

⇒ Selling Price (after 2^nd discount) = 114 − (5% of 114) = 114 − 5.7 = 108.3 units.

⇒ Percentage above CP = [(108.3 − 100) ÷ 100] × 100 = 8.3%.

∴ The correct answer is 8.3%.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the total discount is calculated on the reducing balance. Formula for two discounts: a + b − (ab ÷ 100).

Effective Percentage Change

The net change can be calculated using the fractional multiplier method: Initial × (1 + r₁) × (1 − r₂) × (1 − r₃).