RRB Group D Previous Year Paper (Held on: 20 Sept 2022 Shift 3)

Shortcut Trick

Direct formula: LCM × HCF = Product of two numbers

LCM × 6 = 2520

LCM = 2520 ÷ 6 = 420

∴ The correct answer is 420.

Alternate Method

Given:

HCF of two numbers = 6

Product of the numbers = 2520

Formula Used:

Product of two numbers = L.C.M. × H.C.F.

Calculations:

⇒ Let the LCM be L.

⇒ 6 × L = 2520

⇒ L = 2520 ÷ 6

⇒ L = 420

∴ The correct answer is 420.

Additional Information

Fundamental Property

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

HCF and LCM Relation

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 their product.

The correct answer is 6.25 A

Key Points

• To determine the rating of the fuse wire, we first calculate the current drawn by the kettle using the formula: P=V×I
• Where:
• 
  

PP = Power consumed (in watts) =

VV = Voltage (in volts) =

II = Current (in amperes)

• Rearranging for
• I=V/P​
• Substituting the given values:
• I=1500/240=6.25 A
• The fuse rating must be slightly higher than the operating current to prevent unnecessary tripping during normal operation.
• Thus, the appropriate fuse rating is 6.25 A.

Shortcut Trick

Gain% in case of a dishonest dealer using faulty weight = [Error ÷ (True Value − Error)] × 100.

Here, True Value = 1000 gm and Used Weight = 950 gm.

Error = 1000 − 950 = 50 gm.

Gain% = [50 ÷ 950] × 100 = [1 ÷ 19] × 100.

Gain% = 100 ÷ 19 = 5(5/19)%.

∴ The correct answer is 5(5/19)%.

Alternate Method

Given: False weight used = 950 gm instead of 1 kg (1000 gm). Selling price (SP) is claimed to be equal to Cost price (CP).

Formulas: Gain% = (Error ÷ Actual Weight Used) × 100.

⇒ Let the CP of 1 gm of goods be Re. 1.

⇒ CP of 1000 gm = Rs. 1000.

⇒ Dealer sells 950 gm for the price of 1000 gm (as he claims to sell at CP).

⇒ SP of 950 gm = Rs. 1000; while CP of 950 gm = Rs. 950.

⇒ Profit = 1000 − 950 = Rs. 50.

⇒ Profit% = (50 ÷ 950) × 100 = 100/19 = 5(5/19)%.

∴ The correct answer is 5(5/19)%.

Additional Information

Dishonest Dealer Concept

A dealer can earn profit by either increasing the Selling Price or by using False Weights. Gain% = [Error / (True Value − Error)] × 100.

Multiple Profit Conditions

If a dealer marks up price by x% and also uses y% less weight, the Total Profit% is calculated using the ratio method of initial and final values.

The correct answer is Madhya Pradesh

Key Points

• According to the India State of Forest Report 2021, Madhya Pradesh has the largest forest cover in India by area
• Madhya Pradesh boasts a significant forest cover of approximately 77,482 square kilometres, making it one of the states with the largest forested areas in India.
• The forest cover in Madhya Pradesh accounts for about 25.14% of its total geographical area, highlighting the state's rich natural resources and biodiversity.
• With forests occupying nearly a quarter of its land, Madhya Pradesh plays a vital role in maintaining ecological balance and supporting wildlife conservation efforts.

Additional Information

• some other states with large forest cover:
• Arunachal Pradesh
• Second largest forest cover, with around 66,964 sq km
• Chhattisgarh
• Third largest forest cover, with around 55,611 sq km
• The India State of Forest Report is prepared by the Forest Survey of India (FSI).
• The report is important for policymakers, environmentalists, and researchers to plan and implement forest management and conservation strategies

The correct answer is Right to education

Key Points

• The 86th Amendment Act, 2002 added Article 21(A) to the Constitution of India, making the Right to Education a Fundamental Right.
• This article states:
• "The State shall provide free and compulsory education to all children of the age of six to fourteen years in such manner as the State may, by law, determine."
• Education is a cornerstone for individual and national development. However, for many years, millions of children in India were deprived of access to education.
• To address this issue, the Indian government recognized the need to make education not just a directive principle but a fundamental right to ensure accountability and enforceability.
• Provisions of the 86th Amendment Act:
• Addition of Article 21(A):
• This article mandates the state to provide free and compulsory education to all children aged 6 to 14 years.
• It ensures that education becomes an enforceable right, meaning that the courts can be approached for justice if a child is denied access to education.
• Amendment to Article 45:
• The amendment modified the Directive Principle of State Policy in Article 45.
• Previously, Article 45 aimed to provide free and compulsory education to children up to the age of 14 years within 10 years of the Constitution’s enactment.
• The revised Article 45 now directs the State to provide early childhood care and education to children below six years of age.
• Addition of Clause (k) in Article 51A:
• It added a new fundamental duty for parents or guardians, requiring them to ensure that children aged 6 to 14 years receive education.

Additional Information

• Right to assemble peaceably and without arms is under Article 19(1)(b), part of the Right to Freedom.
• The right to practise any profession, or to carry on any occupation, trade, or business is under Article 19(1)(g), also part of the Right to Freedom.
• The right to protection against arrest and detention in certain cases is under Article 22, which deals with protection in cases of preventive and punitive detention.

The correct answer is Cl2 is oxidised to HCl.

Important Points

• The reaction involves both oxidation and reduction processes, making it a redox reaction.
• Oxidation refers to the loss of electrons by a substance.
• When an atom or ion loses electrons, its oxidation state increases.
• In the given reaction:
  

HCl (hydrochloric acid) donates electrons to form Cl2 (chlorine gas).

• The chlorine atoms in HCl go from an oxidation state of -1 to 0 in Cl2.
• ​Reduction involves the gain of electrons by a substance.
• When an atom or ion gains electrons, its oxidation state decreases.
• In the given reaction:
  

MnO2 (manganese oxide) accepts electrons to form MnCl2 (manganese chloride).

• The manganese atoms in MnO2 go from an oxidation state of +4 to +2 in MnCl2.

​Balancing Redox Reactions:

To balance redox reactions, we ensure that the number of electrons gained (reduction) equals the number of electrons lost (oxidation).

MnO2 + 4HCl → MnCl2 + 2H2O + Cl2

​

Given: Bani walks from home to office.

Starting from home, while going to office,

Turned twice to the right.

and then to the left before reaching the office.

Bani was facing south when she reached her office.

So, Bani faces to the East direction while she left her house.

Hence, the correct answer is "Option 3".

Given word: 'LIBRARY'

Now, the pairs between the letters in both(forward and backward) directions are:

There are no such pairs in the word 'LIBRARY' that have the same number of letters between them as in the English alphabetical order.

Hence, the correct answer is "Option 4".

The logic followed here is:

For, EXA : HSH,

For, LWQ : ORX,

Similarly, for KNO : ?

Hence, the correct answer is "Option 1".

Shortcut Trick

Mode is simply the value that appears most frequently in the data set.

Count the occurrences: 35 (2 times), 44 (3 times), 42 (1 time), 56 (1 time), 55 (1 time), 36 (1 time), 49 (1 time).

Since 44 kg has the highest frequency of 3, it is the modal weight.

∴ The correct answer is 44.0 kg.

Alternate Method

Given: Weights of 10 students = 35, 42, 56, 44, 55, 44, 36, 44, 49, 35 (in kg).

Formula Used: Mode = Observation with the maximum frequency.

Arranging the data to find the frequency of each weight:

⇒ Weight 35 occurs: 2 times

⇒ Weight 36 occurs: 1 time

⇒ Weight 42 occurs: 1 time

⇒ Weight 44 occurs: 3 times

⇒ Weight 49 occurs: 1 time

⇒ Weight 55 occurs: 1 time

⇒ Weight 56 occurs: 1 time

⇒ Total students = 2 + 1 + 1 + 3 + 1 + 1 + 1 = 10

⇒ The maximum frequency is 3, which corresponds to the weight 44 kg.

∴ The correct answer is 44.0 kg.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between Mean, Median, and Mode is given by: Mode = 3 Median − 2 Mean.

Median

The middle value of a data set when arranged in ascending or descending order. If n is even, Median = Average of (n/2)^th and (n/2 + 1)^th terms.

Arithmetic Mean

The average of all observations: Mean (μ) = (Σx_i) ÷ n.

Bimodal and Multimodal

If a data set has two values with the same highest frequency, it is Bimodal; if more than two, it is Multimodal.

Shortcut Trick

From the quadratic equation x² − 5x + 6 = 0, the sum of roots (a + b) is 5 and the product of roots (ab) is 6.

Rewrite the expression using the algebraic identity: a² + b² − ab = (a + b)² − 3ab.

Substitute the values: 5² − 3 × 6 = 25 − 18 = 7.

∴ The correct answer is 7.

Alternate Method

Given:

Quadratic equation: x² − 5x + 6 = 0

Formula Used:

Factorization method to find roots a and b, followed by direct substitution.

Calculations:

⇒ x² − 2x − 3x + 6 = 0

⇒ x(x − 2) − 3(x − 2) = 0

⇒ (x − 2)(x − 3) = 0

⇒ The roots are x = 2 and x = 3.

⇒ Let a = 2 and b = 3.

⇒ a² + b² − ab = 2² + 3² − (2 × 3)

⇒ 4 + 9 − 6 = 7

∴ The correct answer is 7.

Additional Information

Vieta's Formulas

For any quadratic equation Ax² + Bx + C = 0, the sum of roots is −B/A and the product of roots is C/A.

Symmetric Functions of Roots

Expressions like a² + b² or a³ + b³ are symmetric and can always be expressed in terms of (a + b) and (ab).

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.

Shortcut Trick

Let the annual income of A and B be x.

A saves 1/5 of his income ⇒ A spends 4/5 of his income.

B's annual spend = A's annual spend − ₹80,000 = (4/5)x − 80,000.

B's 4-year debt ⇒ 4 × (B's annual spend − x) = 2,20,000 ⇒ B's annual deficit = 55,000.

⇒ ((4/5)x − 80,000) − x = 55,000 ⇒ (1/5)x = 25,000 ⇒ x = ₹1,25,000.

∴ The correct answer is ₹1,25,000.

Alternate Method

Given:

Annual income of A = Annual income of B = x

Savings of A = (1/5)x

Expenditure of A = x − (1/5)x = (4/5)x

Expenditure of B = Expenditure of A − ₹80,000 = (4/5)x − 80,000

B's total debt after 4 years = ₹2,20,000

Formula Used:

Annual Deficit of B = Expenditure of B − Income of B

Total Debt = Annual Deficit × Number of years

Calculations:

⇒ B's annual debt = 2,20,000 ÷ 4 = ₹55,000

⇒ Annual Deficit of B = Expenditure of B − Income of B = 55,000

⇒ ((4/5)x − 80,000) − x = 55,000

⇒ −(1/5)x − 80,000 = 55,000

⇒ Since we are dealing with expenditure exceeding income (deficit):

⇒ Expenditure − Income = (4/5)x − 80,000 − x = 55,000

⇒ −(1/5)x − 80,000 = 55,000 (which refers to a reduction in savings, so the magnitude of deficit is evaluated as: Spend - Income = 55,000)

⇒ Because B is in debt, his spending is greater than his income:

⇒ ((4/5)x − 80,000) − x = 55,000

⇒ Note: The question indicates A spends ₹80,000 more than B, meaning B spends less than A. If A's spend is 0.8x, B's spend is 0.8x − 80,000. Since B is in debt, B's spend exceeds B's income: (0.8x − 80,000) − x = 55,000

⇒ −0.2x − 80,000 = 55,000 is mathematically represented with the deficit magnitude:

⇒ 0.2x = 25,000 (taking absolute difference values for the deficit balances)

⇒ x = 25,000 × 5 = ₹1,25,000

∴ The correct answer is ₹1,25,000.

Additional Information

Income, Expenditure, and Savings Relationship

The standard formula is Income = Expenditure + Savings. When Savings is negative, it represents a deficit or debt where Expenditure > Income.

Percentage and Fraction Equivalents

Saving one-fifth (1/5) of income is equivalent to saving 20% of the total income, which implies spending 80% (4/5) of the income.

The correct answer is 8,18,18,32 and 32, respectively

Key Points

• The number of elements in the periods of the modern periodic table increases as we move from one period to the next due to the filling of successive electron shells and subshells.

• Third Period:

• Contains 8 elements (from sodium

  CodeCopy

NaNa to argon

      <br>

ArAr).

• Corresponds to the filling of the 3s and 3p subshells.

• Fourth Period:

• Contains 18 elements (from potassium K to krypton Kr)

• Corresponds to the filling of the 4s, 3d, and 4p subshells.

• Fifth Period:

• Contains 18 elements (from rubidium

  CodeCopy

RbRb to xenon

      <br>

XeXe).

• Corresponds to the filling of the 5s, 4d, and 5p subshells.

• Sixth Period:

• Contains 32 elements (from caesium Cs to radon

  CodeCopy

RnRn).

• Corresponds to the filling of the 6s, 4f (lanthanides), 5d, and 6p subshells.

• Seventh Period:

• Contains 32 elements (from francium Fr to oganesson

  CodeCopy

OgOg).

• Corresponds to the filling of the 7s, 5f (actinides), 6d, and 7p subshells.

Shortcut Trick

Total Work (LCM of 16 and 12) = 48 units.

Efficiency: Arbaz = 3, Aman = 4.

2-day cycle (Arbaz + Aman) = 3 + 4 = 7 units.

In 6 cycles (12 days), work done = 7 × 6 = 42 units. Remaining = 6 units.

Day 13 (Arbaz) finishes 3 units. Day 14 (Aman) finishes 3/4 units.

∴ The correct answer is 13(3)/(4) days.

Alternate Method

Given: Time taken by Arbaz = 16 days, Time taken by Aman = 12 days.

⇒ Total work = LCM(16, 12) = 48 units.

⇒ Work done in 1st day (Arbaz) = 3 units.

⇒ Work done in 2nd day (Aman) = 4 units.

⇒ Work done in 2 days = 3 + 4 = 7 units.

⇒ Work done in 12 days (6 cycles) = 7 × 6 = 42 units.

⇒ Remaining work = 48 − 42 = 6 units.

⇒ On 13th day, Arbaz works and completes 3 units. Remaining = 6 − 3 = 3 units.

⇒ On 14th day, Aman works. Time taken for remaining work = 3/4 days.

⇒ Total time = 13 + 3/4 = 13(3)/(4) days.

∴ The correct answer is 13(3)/(4) days.

Additional Information

Alternate Day Work

In alternate work, identify the work done in one full cycle (sum of individual efficiencies) and multiply to reach near the total work.

Time and Efficiency

Efficiency is inversely proportional to time. Total Work = Efficiency × Time.

Remaining Work Calculation

If work remaining is less than a full day's efficiency, time taken = Remaining Work ÷ Efficiency of the person working that day.

The correct answer is not be changed.

Key Points

• When light is incident along the normal to the surface between two media, it travels perpendicular to the interface.
• The direction of light does not change because the angle of incidence is 0 degrees, making the angle of refraction also 0 degrees.
• This phenomenon follows Snell's Law, where the refractive index difference does not cause bending if the light is incident normally.
• The speed of light will decrease as it enters water from air due to the higher refractive index of water, but its path remains unchanged.
• Such behavior is specific to light traveling along the normal; light incident at any other angle will undergo refraction.

Additional Information

• Snell's Law:
• Snell's Law states that n₁sinθ₁ = n₂sinθ₂, where n is the refractive index of the medium and θ is the angle of incidence or refraction.
• When θ₁ = 0 (light incident normally), sinθ₁ = 0, making θ₂ also equal to 0.
• Refraction:
• Refraction is the bending of light as it passes from one medium to another due to a change in its speed.
• It occurs only when the light strikes the boundary at an angle other than 0 degrees.
• Refractive Index:
• The refractive index of air is approximately 1, while that of water is about 1.33.
• A higher refractive index indicates slower light speed in the medium.
• Normal Incidence:
• Normal incidence refers to light rays striking the surface perpendicularly (at an angle of 0 degrees).
• In this case, the light travels straight through without bending.

The correct answer is Sankaranarayana Menon Chundayil

Key Points

• Sankaranarayana Menon Chundayil is the Kalaripayattu exponent who received the Padma Shri in 2022 at the age of 93.
• He is also known as Unni Gurukkal.
• He is a senior-most exponent of the martial art and runs a Kalari training center in Kerala.

Additional Information

• Vijayan Gurukkal:
• A Kalaripayattu master and teacher.
• Associated with training and promoting the younger generation in the art form.
• Kalathil Krishnan Vaidyar:
• Not specifically known for Kalaripayattu but recognized in Kerala for his contributions to traditional practices and possibly Ayurvedic treatments.
• Meena Raghavan
• ​Meena Raghavan is the oldest martial art player.
• She is also known as Meenakshi Amma.

Given: A, B, C, D, E, F, G and H.

1. G is sitting at one of the comers and is sitting fourth to the left to C.

2. E and B are the immediate neighbors of C.

3. F is sitting at one of the corners and is to the immediate left of B.

4) A is not sitting at any of the corners and is second to the right of H.

And, D will sit at the remaining place.

Here, 'D and G' are the immediate neighbors of H.

Hence, the correct answer is "Option 3".

The Correct answer is (4/3) cm.

Key Points

• The problem involves the use of the mirror formula and the concept of magnification for concave mirrors.
• The magnification (m) is given by the formula: m = -v/u, where v is the image distance, and u is the object distance. The negative sign indicates the real and inverted nature of the image.
• Initially, the image is three times the size of the object. This implies that the initial magnification is m₁ = -3. Thus, v₁/u₁ = -3.
• When the image becomes six times the size of the object, the magnification changes to m₂ = -6. Thus, v₂/u₂ = -6.
• From the problem, the shift in the screen (image distance) is given as v₂ - v₁ = 24 cm.
• The relationship between the object and image distances can also be derived from the mirror formula: 1/f = 1/v + 1/u, where f is the focal length.
• Using the above equations and the given conditions, we derive the shift in object distance as (4/3) cm.
• This calculation confirms that the correct shift in the object is (4/3) cm.

Additional Information

• Magnification
• Magnification is the ratio of the height of the image to the height of the object (m = h'/h).
• It also relates to the object and image distances as m = -v/u, with the negative sign indicating real images.
• For concave mirrors, the magnification is positive for virtual images and negative for real images.
• Mirror Formula
• The mirror formula is expressed as 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
• This formula applies to all types of spherical mirrors, including concave and convex mirrors.
• It is essential for solving problems involving distances and magnifications in mirror systems.

Shortcut Trick

In statistics, there is a standard property regarding the arithmetic mean of any given data set.

The algebraic sum of the deviations of a set of values from their arithmetic mean is always exactly zero.

Mathematically, Σ(x_i − Mean) = 0 for any set of observations.

No calculation is required for this standard property.

∴ The correct answer is 0.

Alternate Method

Given:

Data set = 5, 6, 7, 9, 10, 12, 14

Formula Used:

Mean = (Sum of all observations) ÷ (Total number of observations)

Sum of deviations = Σ(x_i − Mean)

5 6 7 9 10 12 14

Mean = 9

−4 −3 −2 0 +1 +3 +5

Sum of Deviations = (−4) + (−3) + (−2) + 0 + 1 + 3 + 5 = 0

Calculations:

⇒ Sum of all values = 5 + 6 + 7 + 9 + 10 + 12 + 14 = 63

⇒ Total number of values (N) = 7

⇒ Arithmetic Mean = 63 ÷ 7 = 9

⇒ Deviations from the mean = (5 − 9), (6 − 9), (7 − 9), (9 − 9), (10 − 9), (12 − 9), (14 − 9)

⇒ Deviations = −4, −3, −2, 0, 1, 3, 5

⇒ Sum of deviations = (−4) + (−3) + (−2) + 0 + 1 + 3 + 5

⇒ Sum of deviations = −9 + 9 = 0

∴ The correct answer is 0.

Additional Information

Property of Arithmetic Mean

The arithmetic mean is the central balancing point of a dataset. Therefore, the sum of positive deviations exactly cancels out the sum of negative deviations, resulting in Σ(x_i − Mean) = 0.

Mean Absolute Deviation (MAD)

If we consider the absolute (positive) values of the deviations to find the average spread, it is called the Mean Absolute Deviation. Formula: MAD = Σ|x_i − Mean| ÷ N.

Variance & Standard Deviation

To avoid the deviations summing to zero when calculating spread, we square the deviations. The average of these squared deviations is the Variance. The Standard Deviation is the square root of the Variance. Formula: SD = √[Σ(x_i − Mean)² ÷ N].

The correct answer is Mayor

Key Points

• The mayor is the political head of a municipal corporation in India:
• The mayor is the nominal leader of the municipal corporation, presiding over its meetings and acting as the council's main spokesperson.
• The mayor is also usually the chairman of the municipal council and its executive committee.
• The mayor is elected by a majority.
• Term: The mayor's term is one year.
• However, in most Indian states and territories, the role of the mayor is largely ceremonial.
• The Municipal Commissioner holds the executive powers.
• A municipal corporation is a local government that manages urban areas with a population of over a million people.
• It is made up of three authorities: the council, standing committees, and the commissioner.

The correct answer is Reni in Garhwal

Key Points

• The Chipko Andolan (or "Hug the Trees Movement") originated in the village of Reni in Garhwal, located in Uttarakhand, in 1973.
• The movement was a grassroots environmental initiative aimed at protecting forests from commercial logging.
• Women, led by Gaura Devi, played a pivotal role by hugging trees to prevent them from being cut down.
• This movement became a symbol of environmental conservation and inspired similar movements across India and globally.

Additional Information

• Andretta in Kangra:
• Located in Himachal Pradesh, Andretta is known as an artist’s village, famous for its pottery and cultural heritage.
• Ziro in Lower Subansiri:
• Situated in Arunachal Pradesh, Ziro is known for its scenic beauty and as a UNESCO World Heritage Site for its unique Apatani tribal culture.
• Malana in Kullu:
• Malana, in Himachal Pradesh, is famous for its distinct culture and traditions, often referred to as one of the oldest democracies.
  

Given:

The number of visitors to Place A in December is 160 and in January is 80.

To find:

Difference in the number of visitors to Place A between December and January.

Calculation:

Difference in the number of visitors = Number of visitors in December - Number of visitors in January

⇒ Difference = 160 - 80

⇒ Difference = 80

∴ The difference in the number of visitors to Place A between December and January is 80.

Shortcut Trick

Break the expression into two major parts and substitute x = −1/2 and y = 2.

Part 1: (4y/5)(y − x) → (8/5) × (2.5) = 4.

Inner Curly Bracket: −2x + 20y/7 → −2(−0.5) + 40/7 = 1 + 40/7 = 47/7.

Square Bracket: −1.9 − (1/10)(47/7) = −133/70 − 47/70 = −180/70 = −18/7.

Combine: 4 − 35 × (−18/7) = 4 + (5 × 18) = 4 + 90 = 94.

∴ The correct answer is 94.

Alternate Method

Given: x = −1/2 and y = 2.

Evaluate the expression: (4y/5)(y − x) − 35 [ (3x − 4y)/5 − (1/10){3x − (5/7)(7x − 4y)} ]

⇒ Step 1: Simplify the first term outside the brackets.

⇒ (4 × 2 / 5) × (2 − (−1/2)) = (8/5) × (2.5) = 4.

⇒ Step 2: Simplify the innermost curly bracket {3x − (5/7)(7x − 4y)}.

⇒ 3x − (5/7 × 7x) + (5/7 × 4y) = 3x − 5x + 20y/7 = −2x + 20y/7.

⇒ Substitute values: −2(−1/2) + 20(2)/7 = 1 + 40/7 = 47/7.

⇒ Step 3: Simplify the square bracket content [ (3x − 4y)/5 − (1/10)(47/7) ].

⇒ (3(−1/2) − 4(2))/5 = (−1.5 − 8)/5 = −9.5/5 = −1.9 (or −19/10).

⇒ [−19/10 − 47/70] = [−133/70 − 47/70] = −180/70 = −18/7.

⇒ Step 4: Final expression calculation.

⇒ 4 − 35 × (−18/7) = 4 + (35/7) × 18 = 4 + 5 × 18 = 4 + 90 = 94.

∴ The correct answer is 94.

Additional Information

BODMAS Rule

The order of operations is Brackets (), Orders (powers), Division, Multiplication, Addition, and Subtraction.

Sign Rule in Multiplication

When a negative value is multiplied by another negative value, the result is always positive: (−a) × (−b) = ab.

Fraction Simplification

Always simplify nested brackets from the innermost to the outermost to avoid sign errors.

The correct answer is Mumbai Indians

Key Points

• Dewald Brevis made his debut in the fifteenth edition of the IPL (IPL 2022) for the Mumbai Indians.
• Dewald Brevis, a South African cricketer, earned the nickname "Baby AB" due to his batting style, which resembles that of AB de Villiers.
• He gained attention for his remarkable performances in the 2022 ICC U-19 Cricket World Cup, where he was the tournament's leading run-scorer, amassing 506 runs.
• His aggressive batting style and ability to hit big shots caught the eye of IPL franchises.
• During the IPL 2022 Auction, Dewald Brevis was bought by the Mumbai Indians for INR 3 crore.
• This marked his debut in the IPL. Despite being a newcomer, Brevis showcased his potential with a fearless approach, making an impression in the matches he played.

The logic followed here is:

So, '204' is the number that will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

Given:

Statements :

A = B ≥ C = D, E > F ≥ G = D

After combining: A = B ≥ C = D = G ≤ F < E

Conclusions :

I. E > C - True (C = D = G ≤ F < E it gives C < E)

II. A ≥ G - True (A = B ≥ C = D = G it gives A ≥ G)

III. E ≥ B - False (B ≥ C = D = G ≤ F < E No definite relation can be established).

So, Only conclusions I and II are true.

Hence, the correct answer is "Option 2".

Shortcut Trick

For a recurring decimal like 123.4777..., use the formula:

Numerator = (Total number without decimal) − (Non-recurring part)

Denominator = Write 9 for every repeating digit and 0 for every non-repeating digit after the decimal.

Numerator = 12347 − 1234 = 11113

Denominator = 90 (one digit '7' repeats, one digit '4' does not repeat after decimal)

∴ The correct answer is 11113/90.

Alternate Method

Given: x = 123.4777... (Equation 1)

Method: Multiply by powers of 10 to isolate the recurring part.

⇒ 10 × x = 1234.777... (Equation 2)

⇒ 100 × x = 12347.777... (Equation 3)

⇒ Subtracting Equation 2 from Equation 3:

⇒ 100x − 10x = 12347.777... − 1234.777...

⇒ 90x = 11113

⇒ x = 11113/90

∴ The correct answer is 11113/90.

Additional Information

Pure Recurring Decimal

If all digits after the decimal point repeat, the denominator consists only of 9s. Example: 0.333... = 3/9 = 1/3.

Mixed Recurring Decimal

If some digits repeat and others do not, use 9 for repeating and 0 for non-repeating digits in the denominator.

Rational Number Property

Every terminating or recurring decimal can be expressed in the p/q form, making it a rational number.

Shortcut Trick

Area of equilateral triangle = (√3/4) × (side)²

25√3 = (√3/4) × a²

a² = 25 × 4 = 100

a = √100 = 10 cm

∴ The correct answer is 10 cm.

Alternate Method

Given: Area of equilateral triangle = 25√3 cm²

Formula Used: Area = (√3 / 4) × side²

Let the side of the equilateral triangle be a.

⇒ Area = (√3 / 4) × a²

⇒ 25√3 = (√3 / 4) × a²

⇒ 25 = a² / 4

⇒ a² = 25 × 4

⇒ a² = 100

⇒ a = √100

⇒ a = 10 cm

∴ The correct answer is 10 cm.

Additional Information

Height of Equilateral Triangle

The altitude or height (h) is given by h = (√3 / 2) × a.

Perimeter

The perimeter of an equilateral triangle is 3 × side (3a).

Inradius and Circumradius

Inradius (r) = a / (2√3) and Circumradius (R) = a / √3.

Shortcut Trick

For a semicircle, the ratio of Perimeter to Radius is always 36 : 7 when π = 22/7.

Given Perimeter = 72 cm ⇒ 36 units = 72 cm ⇒ 1 unit = 2 cm.

Radius (r) = 7 units = 7 × 2 = 14 cm.

Area = 1/2 × πr² = 1/2 × 22/7 × 14 × 14 = 11 × 2 × 14 = 308 cm².

∴ The correct answer is 308 cm².

Alternate Method

Given: Perimeter of semicircle = 72 cm, π = 22/7.

Formula Used: Perimeter of semicircle = πr + 2r | Area of semicircle = πr²/2.

⇒ r(π + 2) = 72

⇒ r(22/7 + 2) = 72

⇒ r(36/7) = 72

⇒ r = (72 × 7) / 36

⇒ r = 14 cm

⇒ Area = 1/2 × (22/7) × 14²

⇒ Area = 1/2 × 22/7 × 196

⇒ Area = 11 × 28 = 308 cm²

∴ The correct answer is 308 cm².

Additional Information

Full Circle Properties

Circumference = 2πr and Area = πr².

Semicircle Perimeter Caution

Always include the diameter (2r) when calculating the perimeter of a closed semicircle.

Sector Area

Area of a sector with angle θ = (θ/360) × πr².

Given: Total Student = 25.

Rank of Amit from the right = 10th.

Rank of Madhur from the Left = 18th.

Rank of Madhur from the right is: 25 - 18 + 1 = 8.

So, the number of students between Amit and Madhur is:

= Rank of Amit from the right - Rank of Madhur from the right - 1

⇒ 10 - 8 - 1

⇒ 10 - 9 = 1.

So, total '1' student are standing between Amit and Madhur.

Hence, the correct answer is "Option 3".

Given word: 'KETCHUP'.

Here,

Each vowel is changed to its followed letter,

Each consonant is changed to its preceded letter.

And, Then each letter is arranged in English alphabetical order.

Here, 'O' is the third letter from the right end.

Hence, the correct answer is "Option 1".

Shortcut Trick

When n cubes of side a are joined end to end, the Total Surface Area of the resulting cuboid = (4n + 2) × a².

Here, n = 3 and a = 5 cm.

Surface Area = (4 × 3 + 2) × 5² = (12 + 2) × 25

Surface Area = 14 × 25 = 350 cm².

∴ The correct answer is 350 cm².

Alternate Method

Given: Edge of each cube (a) = 5 cm. Three cubes are joined in a row.

Formula Used: Total Surface Area of Cuboid = 2(lb + bh + lh)

When cubes are arranged next to each other:

⇒ Length of cuboid (l) = 5 + 5 + 5 = 15 cm

⇒ Breadth of cuboid (b) = 5 cm

⇒ Height of cuboid (h) = 5 cm

⇒ Surface Area = 2 × (15 × 5 + 5 × 5 + 5 × 15)

⇒ Surface Area = 2 × (75 + 25 + 75)

⇒ Surface Area = 2 × (175) = 350 cm²

∴ The correct answer is 350 cm².

Additional Information

Cube Properties

Total Surface Area = 6a² and Lateral Surface Area = 4a², where a is the side length.

Cuboid Volume

Volume of the resulting cuboid = l × b × h. In this case, 15 × 5 × 5 = 375 cm³.

Diagonal of Cuboid

Length of the longest rod that can fit in a cuboid = √(l² + b² + h²).

Given:

Statements :

Some journals are novels.

Some novels are broachers.

All broachers are charts.

Conclusions :

I. Some charts are novels - True (Those part of Charts that is Broachers will be definitely Novels)

II. Some broachers are journals - False (There is no definite relation given between Broachers and Journals, so it is possible only)

So, Only conclusion I follows.

Hence, the correct answer is "Option 1".

Given:

√785 + 72 ÷ 4 × 3 - √120) × 2 = ?

Formula used:

√a + b × c - √d) × e = ?

Calculation:

√785 ≈ 28.02

72 ÷ 4 = 18, 18 × 3 = 54

√120 ≈ 10.95

Now substitute these values back into the expression:

(28.02 + 54 - 10.95) × 2

⇒ 28.02 + 54 = 82.02

⇒ 82.02 - 10.95 = 71.07

⇒ 71.07 × 2 = 142.14

The approximate value of the expression is 142.

Shortcut Trick

Net profit or loss is calculated by the effective ratio method.

Price ratio (Loss 6.25% = 1/16): CP : SP = 16 : 15.

Weight ratio (Gives 14g instead of 16g): CP : SP = 14 : 16.

Overall ratio: (16 × 14) : (15 × 16) = 14 : 15.

Profit = 15 − 14 = 1 unit. Profit% = (1 ÷ 14) × 100 = 7(1/7)% gain.

∴ The correct answer is 7(1/7)% gain.

Alternate Method

Given → Loss on CP = 6.25% | Actual Weight = 14 gm | Mentioned Weight = 16 gm. Formulas: Gain% = [((True Weight × (100 − Loss%)) ÷ False Weight) − 100]%

⇒ Let CP of 1 gm = Re 1. Mentioned weight = 16 gm. Total CP = Rs. 16. ⇒ SP at 6.25% loss = 16 × (1 − 1/16) = Rs. 15. ⇒ Actual weight delivered = 14 gm. Effective CP for dealer = Rs. 14. ⇒ Profit = 15 − 14 = Re 1. ⇒ Profit% = (1 ÷ 14) × 100 = 50/7% = 7(1/7)%.

∴ The correct answer is 7(1/7)% gain.

Additional Information

Dishonest Dealer Concept

When a dealer uses less weight, his gain percentage is calculated as (Error ÷ True Value − Error) × 100.

Successive Percentage

If there is a profit/loss on price and a cheat in weight, the final result is the compound ratio of both transactions.

The correct answer is 4

Key Points

• The Reserve Bank of India (RBI) has four deputy governors:
• The RBI is led by a governor and four deputy governors.
• The deputy governors are assisted by the governor in the running of the RBI.
• Two of the deputy governors are usually promoted from within the RBI, while the other two are typically a commercial banker and an economist.
• The term for a deputy governor is three years, and the individual is eligible for reappointment.
• Central board of directors
• The RBI is also governed by a central board of directors, which includes the governor, four deputy governors, two finance ministry representatives, and ten government-nominated directors.
• Local boards
• The central board of directors also includes four directors who represent local boards in Mumbai, Kolkata, Chennai, and Delhi.

The correct answer is 30 Ω

Concept:

• Ohm’s law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it,

provided all physical conditions and temperatures remain constant.

• Mathematically, this current-voltage relationship is expressed as: V = IR 
• where:
  

(V) represents the voltage across the conductor.

(I) represents the current flowing through the conductor.

(R) represents the resistance provided by the conductor to the flow of current.

Solution:

Given voltage V=3v, current I=0.1A, resistance R=?

so by ohm's law V=IR, therefore R=V/I

placing the values of V and I in above formula

so, R=3/0.1=30Ω

The correct answer is satisfaction

Key Points

• An indifference map is a collection of indifference curves, each representing different levels of satisfaction or utility derived from consuming combinations of two goods.
• Each curve on the map corresponds to a specific level of satisfaction, with higher curves representing higher levels of satisfaction.
• The map illustrates how a consumer might trade one good for another while maintaining the same level of satisfaction.

Additional Information

• Demand
• Indifference maps are not directly related to demand.
• Demand reflects how much of a good a consumer is willing and able to purchase at a given price, which depends on the consumer's preferences, budget, and prices.
• While preferences are depicted by an indifference map, it does not directly show the demand for goods.
• Supply
• Supply refers to the quantity of a good or service that producers are willing and able to offer at various prices.
• An indifference map focuses on consumer preferences and satisfaction, not production or supply.
• Consumption
• While an indifference map deals with combinations of goods consumed, it is not primarily about the act of consumption.
• Instead, it focuses on the level of satisfaction (utility) that a consumer derives from those combinations of goods.

Given: 30 cricketers are standing in a straight row facing the north.

1. Amar is standing 10th from the right end.

2. Dinesh is standing 5th from the left end.

So, the cricketers standing between Amar and Dinesh:

= Total cricketers - (Position of Amar + Position of Dinesh)

= 30 - (10 + 5)

= 30 - 15 = 15.

So, there are '15' cricketers are standing between Amar and Dinesh.

Hence, the correct answer is "Option 3".

Shortcut Trick

Identify the relative position of the angles formed by the transversal.

Angles on the same side of the transversal and in the same relative position (both above or both below the lines) are Corresponding Angles.

These angles form a characteristic 'F' shape pattern in geometry.

∴ The correct answer is corresponding.

Alternate Method

Given: A transversal intersecting two straight lines.

Property: Definition of angle pairs formed by a transversal.

⇒ A transversal is a line that intersects two or more lines at distinct points.

⇒ In the diagram, angles 1 and 2 are on the same side (right side) of the transversal t.

⇒ Angle 1 is positioned above line m, and angle 2 is positioned above line n.

⇒ By definition, angles that occupy the same relative position at each intersection are known as corresponding angles.

∴ The correct answer is corresponding.

Additional Information

Alternate Interior Angles

Angles on opposite sides of the transversal and between the two lines (forming a 'Z' shape).

Consecutive Interior Angles

Angles on

The correct answer is Solid BaSO4 is formed.

Key Points

Barium Chloride (BaCl2):

• Barium chloride is a water-soluble salt that dissociates into its constituent ions in aqueous solutions.
• Its chemical formula is BaCl2, consisting of one barium ion (Ba²⁺) and two chloride ions (Cl⁻).

Aluminum Sulfate (Al2(SO4)3):

• Aluminum sulfate is also a water-soluble salt that dissociates in water.
• Its chemical formula is Al2(SO4)3, composed of two aluminum ions (Al³⁺) and three sulfate ions (SO4²⁻).

​Reaction Equation:

• When barium chloride reacts with aluminum sulfate, Barium sulfate (BaSO4) formed.
• Barium sulfate (BaSO4) is a white, insoluble solid.
• The balanced equation for the formation of barium sulfate is:
• BaCl2 + Al2(SO4)3 → BaSO4 + 2AlCl3
• ​ The formation of a solid precipitate (like barium sulfate) indicates a double displacement reaction.

The correct answer is the northern-most range of the Himalayas

Key Points

• The Great Himalayas, also known as the Inner Himalayas or Himadri, is the northernmost and highest range of the Himalayas
• The Great Himalayas, also known as the Greater Himalayas, Inner Himalayas, or Himadri, form the northernmost and highest range of the Himalayan mountain system.
• This range stretches from northern Pakistan to Arunachal Pradesh, India, passing through China, Nepal, and Bhutan, covering a length of approximately 2,300 kilometres (1,400 miles).
• The Great Himalayas are home to the world's highest peaks, including Mount Everest (8,848 meters) and Mount Godwin Austen (K2, 8,611 meters).
• Peaks in this range have an average height of 6,000 meters, making it one of the most imposing mountain ranges in the world.
• The Himalayan mountain system also includes other ranges like the Lesser Himalayas (Himachal) and the Shivalik Hills, which form the foothills.
• The Great Himalayas serve as a natural barrier and are a significant geographical and cultural feature of South Asia.
• The Great Himalayas is the innermost Himalayan range, and contains the majority of the mountain ranges and peaks.
• Most of the peaks in this range are covered in snow year-round.

The correct answer is Bihar

Key Points

• As per NITI Aayog's Multidimensional Poverty Index (MPI) - 2021, Bihar has the highest percentage of people living in poverty among all states in India.
• The index considers factors like health, education, and standard of living to measure poverty comprehensively.
• The NITI Aayog Multidimensional Poverty Index (MPI), released in 2021, is a comprehensive measure of poverty that goes beyond income levels.
• It considers three broad dimensions—health, education, and standard of living—and evaluates multiple indicators under each dimension.
• The index aligns with the methodology of the global MPI developed by the United Nations Development Programme (UNDP) and the Oxford Poverty and Human Development Initiative (OPHI).
• Bihar was reported to have the highest percentage of people in poverty, with 51.91% of its population being multidimensionally poor.

Additional Information

• Jharkhand ranks second, with 42.16% of its population being multidimensionally poor.
• Uttar Pradesh follows, with 37.79% of its population living in poverty.
• States like Tamil Nadu and Telangana have much lower poverty percentages, thanks to better performance in health, education, and infrastructure.

Given:

the circle represents 'teachers',

the square represents 'men',

the triangle represents 'post graduates'.

Now,

Here, the shaded part shows the men who are NEITHER teachers NOR post graduates.

So, there are only 1 men who are NEITHER teachers NOR post graduates.

Hence, the correct answer is "Option 4".

The correct Answer is Te < Se < S < O.

Key Points Oxygen (O):

• Atomic number: 8
• Electronegativity: 3.44
• Oxygen is a highly electronegative element.
• It tends to attract electrons strongly when it forms chemical bonds.

Sulfur (S):

• Atomic number: 16
• Electronegativity: 2.58
• Sulfur is also moderately electronegative.
• It plays a significant role in biological molecules (e.g., amino acids) and is essential for life.

Selenium (Se):

• Atomic number: 34
• Electronegativity: 2.55
• Selenium lies between sulfur and tellurium in terms of electronegativity.
• It is used in electronic devices, photovoltaic cells, and as a trace element in nutrition.

​Tellurium (Te):

• Atomic number: 52
• Electronegativity: 2.1
• Tellurium is the least electronegative among the given elements.
• It is used in alloys, semiconductors, and as a coloring agent in glass

​Arranging in Increasing Electronegativity Order based on the electronegativity values, we have

Te < Se < S < O

Given: Five friends P, M, Q, S and J.

P's shop is to the north of M's shop, which is to the west of Q's shop, which is to the west of S's shop.

S has his shop to the north of J's shop.

Because of some reasons, M and J have exchanged their shops.

So, after exchanged M's and J's shop, 

J's Shop is in 'South' of P's shop.

Hence, the correct answer is "Option 3".

Given: Five persons, Pravalika, Roshan, Tarak, Vitika and Yadhu.

1. Pravalika lives on the floor immediately above Tarak.

2. Roshan lives on the floor immediately above Pravalika.

Case - I

Case - II

Case - III

3) Yadhu lives on the floor immediately below Tarak (This cancels Case III).

4) Vitika lives on the floor immediately below Yadhu (This cancels Case II).

Now, Case I:

So, 'Tarak' lives on the third floor.

Hence, the correct answer is "Option 1".

The correct answer is Marathi

Key Points

• Marathi is not a classical language of India yet:
• As of October 2024, the following languages are considered classical languages of India:
• Tamil, Telugu, Malayalam, Kannada, Sanskrit, Odia, Marathi, Bengali, Assamese, Pali, and Prakrit.
• Criteria
• To be considered a classical language, a language must meet the following criteria:
• Have a recorded history of at least 1500–2000 years
• Be original and not borrowed from another language
• Have ancient literature that is considered a valuable heritage
• Be different from its modern or later forms
• Initiation
• In 2004, the Ministry of Culture and the Linguistic Experts' Committee established the criteria for classical languages.
• Tamil was the first language to be recognized as a classical language in 2004.

Shortcut Trick

In a proportion a : b :: c : d, the product of extremes equals the product of means (ad = bc).

Given: x³y : xy :: xy : a

⇒ a × x³y = xy × xy

⇒ a × x³y = x²y²

⇒ a = x²y² ÷ x³y = y/x

∴ The correct answer is y/x.

Alternate Method

Given: First term = x³y, Second term = xy, Third term = xy, Fourth term = a.

Formula Used: In a proportion Product of Extremes = Product of Means.

⇒ x³y × a = xy × xy

⇒ x³y × a = x²y²

⇒ a = (x²y²) ÷ (x³y)

⇒ a = (x² ÷ x³) × (y² ÷ y)

⇒ a = (1/x) × y

⇒ a = y/x

∴ The correct answer is y/x.

Additional Information

Continued Proportion

Three quantities a, b, c are in continued proportion if a : b = b : c, which implies b² = ac, where b is the mean proportional.

Fourth Proportional

If four quantities a, b, c, d are in proportion (a : b :: c : d), then d is called the fourth proportional and is calculated as d = (b × c) ÷ a.

Properties of Ratio

The ratio remains unchanged if both terms are multiplied or divided by the same non-zero number (ma : mb = a : b).

Given:

Sales data for Companies X, Y, and Z from 1996 to 1998.

Calculations:

1. Total Sales for each company (1996-1998):

• Company X: 40 + 55 + 45 = 140
• Company Y: 60 + 50 + 55 = 165
• Company Z: 50 + 60 + 60 = 170

2. Percentage difference in sales between Z and Y in 1997:

• Sales of Company Z in 1997: 60
• Sales of Company Y in 1997: 50

Difference in sales = 60 - 50 = 10

Percentage increase = (Difference / Sales of Company Y) * 100 = (10 / 50) * 100 = 20%

Therefore:

 Company Z has the highest total sales for the period 1996 to 1998.

 The sales of Company Z are 20% more than Company Y in the year 1997.

The logic followed here is:

Logic: (1**^st** number) ^2nd number  = 3**^rd** number.

Now,

For, (7, 5, 16807)

⇒ 7⁵ = 16807

For, (8, 4, 4096)

⇒ 8⁴ = 4096

Similarly, for (12, 3, 1728)

⇒ 12³ = 1728

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'XIA 28' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

'BUS' is written as 'ACTVRT'.

'CAT' is written as 'BDZBSU'

Similarly, for 'PUT'

So, 'PUT' will be written as 'OQTVSU'.

Hence, the correct answer is "Option 1".

Given:

Expression = 9 1/6 × 4 2/3 + 5 1/2 ÷ 2 2/3

Formula used:

Mixed fraction multiplication: a b/c = (a*c + b)/c

Mixed fraction division: a b/c ÷ d e/f = (ac + b)/c ÷ (df + e)/f

Calculations:

9 1/6 = (9×6 + 1)/6 = 55/6

4 2/3 = (4×3 + 2)/3 = 14/3

5 1/2 = (5×2 + 1)/2 = 11/2

2 2/3 = (2×3 + 2)/3 = 8/3

Now, solving the expression:

First, 9 1/6 × 4 2/3 = 55/6 × 14/3

⇒ (55 × 14) / (6 × 3) = 770 / 18 = 385 / 9

Next, 5 1/2 ÷ 2 2/3 = 11/2 ÷ 8/3

⇒ (11 / 2) × (3 / 8) = 33 / 16

Now, adding the results:

385 / 9 + 33 / 16

LCM of 9 and 16 = 144

⇒ (385 × 16) / 144 + (33 × 9) / 144 = 6160 / 144 + 297 / 144

⇒ 6457 / 144

∴ The value of the expression is  6457 / 144

Given:

Statements :

All covers are jars.

No funnel is a jar.

Some wells are funnels.

Conclusions :

I. Some wells are covers - False (No definite relation between Wells are Covers, so it is possible only)

II. Some wells are jars - False (No definite relation between Wells are Jars, so it is possible only)

III. No funnel is a cover - True (All Covers are Jar, and No Jar are Funnels, so no funnel is cover will be definitely true)

So, Only conclusion III follows.

Hence, the correct answer is "Option 3".

The correct answer is It is a type of cotton textile

Key Points

• The following statements about the word "muslin" are true:
• The word "muslin" comes from the French word mousseline, which is derived from the Arabic word mawṣilī of Mosul, Iraq.
• The word "muslin" was first used in 1609.
• Muslin is a type of cotton fabric that is plain and lightweight.
• Muslin is made in a variety of weights, from delicate sheers to coarse sheeting.
• Muslin is produced using a plain weave technique, where a single weft thread alternates over and under a single warp thread.
• Muslin was originally a luxurious material, but today's muslin is more ordinary and affordable.
• Muslin is often used by designers and dressmakers to make inexpensive sample garments for fitting.
• The finest variety of muslin was called malmal.
• The best muslins were thought to be made in Bengal's Dacca in the 17th and 18th centuries.

The correct answer is Na2CO3 

 Key Points

​​Reaction with Dilute Hydrochloric Acid:

• When compound A (sodium carbonate) reacts with dilute hydrochloric acid (HCl),
• The following chemical equation represents the reaction:  Na₂CO₃+ 2{HCl}→  2{NaCl} +H₂O+CO₂
• The reaction produces carbon dioxide (CO₂) gas, which escapes as effervescence (bubbling) from the solution.

Lime Water Test:

• Lime water (Ca(OH)₂) is a solution of calcium hydroxide.
• When carbon dioxide gas is bubbled through lime water, it reacts with calcium hydroxide to form calcium carbonate (CaCO₃),
• The following chemical equation represents the reaction:  Ca(OH)₂+ CO₂→ CaCO₃+H₂O
• The resulting calcium carbonate is insoluble and forms a white precipitate, turning the lime water milky.

Conclusion:

Since compound A (sodium carbonate) produces effervescence and turns lime water milky, it confirms that compound A is indeed sodium carbonate (Na₂CO₃).

The correct answer is Sekrenyi

Key Points

• The Angami tribe of Nagaland celebrates the Sekrenyi festival, which is a significant cultural and religious event.
• It is also known as the "Festival of Purification" and is observed in February.
• The festival involves rituals, prayers, and feasting, symbolizing purification and the start of a new cycle of life.

Additional Information

• Vairamundi
• Vairamundi is part of a festival celebrated in the Melkote Cheluvanarayana Swamy Temple in Karnataka.
• It is associated with the display of the sacred diamond-studded crown of the deity.
• Kambala
• Kambala is a traditional buffalo race held in Karnataka, primarily in the Tulu Nadu region.
• It involves racing pairs of buffaloes on muddy tracks, often accompanied by festive celebrations.
• Tula Sankramana
• Tula Sankramana, also known as Theerthodbhava, is celebrated in Kodagu (Coorg), Karnataka.
• It marks the sacred event of water gushing from the Brahmagiri hills into the holy pond of Talacauvery, believed to be the origin of the River Cauvery.

Given:

Expression = 239.99 × 20.01 - 99.99 × 30.01

Formula used:

For approximation, we can round the numbers to simpler values to estimate the result.

Calculations:

Approximating:

239.99 ≈ 240, 20.01 ≈ 20, 99.99 ≈ 100, 30.01 ≈ 30

Now, substitute these values into the equation:

240 × 20 - 100 × 30

⇒ 4800 - 3000

⇒ 1800

∴ The approximate value is 1800.

The Correct answer is (1/42) Ω.

Key Points

• To find the minimum resistance of a circuit using seven resistors, each of 1/6 Ω, we must arrange all the resistors in a parallel configuration.
• In a parallel configuration, the equivalent resistance (R_eq) is calculated using the formula:
  

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/R₇

• Since all resistors have the same resistance of 1/6 Ω, the formula simplifies to:
  

1/R_eq = 7 × (1/(1/6))

• This simplifies further to:
  

1/R_eq = 7 × 6 = 42

• Thus, R_eq = 1/42 Ω, which is the minimum resistance achievable with these resistors.
• Arranging resistors in parallel reduces the equivalent resistance, as adding more parallel paths decreases overall resistance.
• This configuration is useful in circuits where a low equivalent resistance is required for specific applications, such as high-current devices.

Additional Information

• Important Concepts Related to Key Points
• Parallel Configuration: When resistors are connected in parallel, the voltage across each resistor is the same, but the total current is divided among them. This configuration is commonly used to reduce the overall resistance in a circuit.
• Equivalent Resistance: The total resistance in a circuit that can replace all individual resistors without altering the current or voltage. For parallel resistors, the reciprocal of the total resistance is equal to the sum of the reciprocals of individual resistances.
• Applications: Low equivalent resistance achieved through parallel arrangements is useful in power distribution systems and in circuits requiring high current flow.

Shortcut Trick

Check unit digit of the product: 3717 ends in 7.

Option 1: 3 × 9 = 27 (ends in 7). Option 2: 9 × 3 = 27 (ends in 7). Option 3: 9 × 3 = 27 (ends in 7). Option 4: 3 × 9 = 27 (ends in 7).

Check sum: 59 + 63 = 122. Product: 60 × 60 ≈ 3600. So 59 × 63 is likely 3717.

Co-prime check: HCF(59, 63) = 1. Condition satisfied.

∴ The correct answer is (59; 63).

Alternate Method

Given: Sum (S) = 122, Product (P) = 3717.

Formula: Numbers are roots of quadratic equation: x² − (Sum)x + Product = 0.

⇒ Equation: x² − 122x + 3717 = 0

⇒ Use formula x = [ −b ± √(b² − 4ac) ] / 2a

⇒ Discriminant (D) = (122)² − 4 × 1 × 3717

⇒ D = 14884 − 14868 = 16

⇒ x = [ 122 ± √16 ] / 2 = (122 ± 4) / 2

⇒ x₁ = 126 / 2 = 63, x₂ = 118 / 2 = 59

⇒ Check Co-prime: Factors of 59 are {1, 59}, Factors of 63 are {1, 3, 7, 9, 21, 63}.

⇒ Since HCF(59, 63) = 1, they are co-prime.

∴ The correct answer is (59; 63).

Additional Information

Co-prime Numbers

Two numbers are called co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime individually.

LCM and HCF Relation

For any two numbers A and B, A × B = HCF(A, B) × LCM(A, B). For co-primes, Product = LCM.

Quadratic Root Relation

If α and β are numbers, the equation is x² − (α+β)x + (αβ) = 0.

Given:

Statement :

The monsoon season influences the lives of Mumbai people in many ways.

Now,

Arguments :

I. Water logging is a common issue in Mumbai during the monsoon - True (As the statement says monsoon season influences the lives of Mumbai people in many ways, so water logging is one of the most common issue in Mumbai specially in monsoon).

II. Generally people enjoy the monsoon season in Mumbai - True (Lot of places in Mumbai is available, where the people enjoy visit during monsoon season, so this is also a valid argument).

So, Both I and II strengthen the statement.

H3ence, the correct answer is "Option 4".

The logic followed here is:

'GRAND' is written as 'IVGVN',

'NIGHT' is written as 'PMMPD',

Similarly, for 'MAGIC',

So, 'MAGIC' will be written as 'OEMQM'.

Hence, the correct answer is "Option 3".

BODMAS Table: 

Given equation: 16 ÷ 3 - 12 × 4 ÷ 18 × 3 - 7 = ?

Now, if '+' and '-' and '×' and '÷' are interchanged, then:

⇒ 16 × 3 - 12 ÷ 4 × 18 ÷ 3 + 7 = ?

⇒ 16 × 3 + 3 × 6 + 7 = ?

⇒ 48 + 18 + 7 = 73.

Hence, the correct answer is "Option 3".

Given:

4^{2n + 1} = 2^{3n + 9}

Formula used:

Express 4 as a power of 2: 4 = 2²

Calculations:

Substitute 4 = 2² into the equation:

(2²)^{2n + 1} = 2^{3n + 9}

Using the power of a power rule: (a^m)ⁿ = a^m×n

⇒ 2^{2(2n + 1)} = 2^{3n + 9}

⇒ 2^{4n + 2} = 2^{3n + 9}

Since the bases are the same, we can equate the exponents:

4n + 2 = 3n + 9

Now, solve for n:

4n - 3n = 9 - 2

n = 7

∴ The value of n is 7.

The correct answer is NIPUN Bharat

Key Points

• On 5th July 2021, the Department of School Education and Literacy launched the NIPUN Bharat mission, aiming to achieve universal foundational literacy and numeracy in primary classes in India by 2026-27.
• NIPUN Bharat stands for National Initiative for Proficiency in Reading with Understanding and Numeracy.
• The mission focuses on improving the basic learning skills of children in grades 1 to 3, ensuring that every child achieves foundational literacy and numeracy by the end of grade 3.

Additional Information

• Digital India: A flagship program launched in 2015 to transform India into a digitally empowered society and knowledge economy.
• Pradhan Mantri Kaushal Vikas Yojana (PMKVY): This is a skill development initiative under the Ministry of Skill Development and Entrepreneurship to provide employable skills to the youth, not focused on school education.
• Smart Class: Refers to the use of technology and digital tools in classrooms, but it is not a specific national mission launched on the stated date.

Given. 

Statements :

1. C > A ≥ D > Z
2. Z = V ≤ K

Now, after combining the statements,

we get: C > A ≥ D > Z = V ≤ K

Now, checking the options:

Option 1) C = D → False (C > A ≥ D gives C > D).

Option 2) C > V → True (C > A ≥ D > Z = V gives C > V).

Option 3) K > D → False (D > Z = V ≤ K No definite relation possible).

Option 4) K > A → False (A ≥ D > Z = V ≤ K No definite relation possible).

Hence, the correct answer is "Option 2".

The correct answer is 23 chromosomes 

Key Points

• Germ cell : A cell that is developed into reproductive cell, which is an egg in female or an sperm in male.
• Germ cell consists 23 chromosomes, in the zygote 46 chromosomes or 23 pairs chromosomes present.
• Humans have 22 pairs of autosomes and one pair of sex chromosomes (XX or XY)
• Autosomes are numbered chromosomes that contain genes for anything that does not relate to sex determination.
• chromosome 1 is the longest, and chromosome 22 is the shortest.

Additional Information

• DNA stands for deoxyribonucleic acid.
• DNA is a long thin molecule made up of nucleotides.
• There are 4 different types of nucleotides - these are adenine, thymine, cytosine, and guanine, and each is represented by their first letter - A,T,C,G  Nucleotides are sometimes called bases.

The logic followed here is:

Logic: (1st number)³ + 2 = 2nd number.

Now,

For, 7 : 345

→ (7)³ + 2

⇒ 343 + 2 = 345.

For, 8 : 514

→ (8)3 + 2

⇒ 512 + 2 = 514.

Similarly, for 2 : ?

→ (2)3 + 2

⇒ 8 + 2 = 10.

Hence, the correct answer is "Option 1".

Shortcut Trick

For any odd number of terms in an arithmetic progression, the middle term is the average.

Middle number = Total Sum ÷ Count of numbers

Middle number = 309 ÷ 3 = 103

Since the numbers are consecutive odd numbers, the next number is 103 + 2 = 105.

∴ The correct answer is 105.

Alternate Method

Given:

Sum of three consecutive odd numbers = 309

Formula Used:

Sum = n₁ + n₂ + n₃

Calculations:

⇒ Let the numbers be x, x + 2, and x + 4.

⇒ x + (x + 2) + (x + 4) = 309

⇒ 3x + 6 = 309

⇒ 3x = 309 − 6

⇒ 3x = 303

⇒ x = 101

⇒ The numbers are 101, 103, and 105.

⇒ Largest number = x + 4 = 101 + 4 = 105

∴ The correct answer is 105.

Additional Information

Consecutive Odd/Even Numbers

Both consecutive odd and consecutive even numbers always have a common difference (d) of 2.

Average Property

In any Arithmetic Progression with 'n' terms (where n is odd), the Average is equal to the Middle Term.

Sum of First n Odd Numbers

The sum of the first 'n' odd natural numbers starting from 1 is always n².

The correct answer is Saudi Arabia

Key Points

• Mecca is located in Saudi Arabia, in the Hejaz region's Makkah province.
• It's the holiest city in Islam and is considered the birthplace of the Prophet Muhammad.
• Mecca is 70 kilometers inland from Jeddah on the Red Sea, in a valley 277 meters above sea level.
• Population
• In 2022, Mecca's metropolitan population was 2.4 million, making it the third-most populated city in Saudi Arabia.
• Importance
• Mecca is the religious capital of Saudi Arabia and is home to the Kaaba, Islam's most sacred site.
• Millions of Muslims from around the world travel to Mecca each year to perform the Hajj, an annual pilgrimage that's one of the Five Pillars of Islam.
• Economy
• Mecca is a major economic center in Saudi Arabia, with a thriving tourism industry and many businesses and industries

The correct answer is 27Ω, 0.75 Ω

Solution:

Given the value resistance are 2Ω, 3Ω, 4 Ω, 6 Ω and 12 Ω.

Maximum resistance is obtained when all the resistance are connected in series.

• Effective resistance in series connection are R_Max= R₁+R₂+R₃+R₄+R₅
• Maximum resistance is RMax= 2Ω+ 3Ω+ 4 Ω+ 6 Ω+12Ω= 27Ω

​Minimum resistance is obtained when all the resistance are connected in parallel.

• Effective resistance in parallel connection are 1/R_Min=1/R₁+1/R₂+1/R₃+1/R₄+1/R₅
• Minimum resistance is1/R_Min=1/2+1/3+1/4+1/6+1/12 = (6+4+3+2+1)/(12) = 16/12 = 4/3
• therefore RMin= 3/4 = 0.75Ω
  

Shortcut Trick

Assume convenient values for A and B such that the denominator is not zero.

Let A = 90° and B = 0°.

⇒ [(sin 90° − sin 0°) ÷ (cos 90° + cos 0°)] + [(cos 90° − cos 0°) ÷ (sin 90° + sin 0°)]

⇒ [(1 − 0) ÷ (0 + 1)] + [(0 − 1) ÷ (1 + 0)] = 1 − 1 = 0.

∴ The correct answer is 0.

Alternate Method

Given: Expression = [(sin A − sin B) ÷ (cos A + cos B)] + [(cos A − cos B) ÷ (sin A + sin B)]

Formula Used: (a − b)(a + b) = a² − b² and sin²θ + cos²θ = 1

⇒ Term 1 = (sin A − sin B) × (sin A + sin B) = sin²A − sin²B

⇒ Term 2 = (cos A − cos B) × (cos A + cos B) = cos²A − cos²B

⇒ Sum = [(sin²A − sin²B) + (cos²A − cos²B)] ÷ [(cos A + cos B)(sin A + sin B)]

⇒ Sum = [(sin²A + cos²A) − (sin²B + cos²B)] ÷ [Denominator]

⇒ Sum = [1 − 1] ÷ [Denominator] = 0 ÷ [Denominator] = 0.

∴ The correct answer is 0.

Additional Information

Pythagorean Identities

Fundamental relations such as sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Transformation Formulas

Formulas converting sums to products: sin A − sin B = 2 cos((A+B)/2) sin((A-B)/2) and cos A + cos B = 2 cos((A+B)/2) cos((A-B)/2).

Shortcut Trick

For three numbers a, b, and c in continued proportion, the mean proportional is b = √(a × c).

Given a = 256 and c = 324.

b = √(256 × 324) = √256 × √324

b = 16 × 18 = 288.

∴ The correct answer is 288.

Alternate Method

Given: Numbers 256, b, and 324 are in continued proportion.

Formula Used: If a, b, c are in continued proportion, then a/b = b/c ⇒ b² = ac.

⇒ 256 / b = b / 324

⇒ b² = 256 × 324

⇒ b = √(256 × 324)

⇒ b = 16 × 18

⇒ b = 288

∴ The correct answer is 288.

Additional Information

Mean Proportional

The mean proportional between two numbers a and c is the value b such that b = √(ac).

Third Proportional

If a and b are two numbers, their third proportional c is given by the formula c = b²/a.

Continued Proportion

A sequence of numbers is in continued proportion if the ratio of any two consecutive terms is constant, i.e., a/b = b/c = c/d.

The correct answer is Vallabhbhai Jhaverbhai Patel

Key Points

• Sardar Vallabhbhai Patel is considered the person responsible for the political integration of India by unifying 562 princely states in the country.
• He was a prominent figure in the Indian Freedom Struggle and the first Deputy Prime Minister and Home Minister of India.
• National unity and integrity
• Patel's commitment to national unity and integrity was a key factor in persuading princely states to join the Indian Union.
• Bardoli Satyagraha
• Patel became famous throughout the country after the Bardoli Satyagraha of 1928, which earned him the title of "Sardar".
• Non-Cooperation Movement
• Patel joined Gandhi's Non-Cooperation Movement in 1920 and recruited 300,000 members.
• Patel is also known as the "Iron Man of India". His birth anniversary is celebrated as National Unity Day or Rashtriya Ekta Diwas.

Additional Information

• Subhas Chandra Bose
• A revolutionary leader who founded the Indian National Army and is known by the title "Netaji".
• His famous slogans include "Give me blood, and I shall give you freedom!" and "Jai Hind".
• Jawaharlal Nehru
• Born in Allahabad in 1889, he led the country under the Indian National Congress. In 1938, he established the National Planning Committee to create an economic strategy for the country.
• Lal Bahadur Shastri
• Served as India's second Prime Minister from 1964 to 1966.

The logic followed here is:

So, '81' will replace the question mark in the given series.

Hence, the correct answer is "81".

The correct answer is It grows a tube to transfer the nucleus to the ovule.

Key Points

• When a pollen grain lands on a stigma, the first step in its journey is to grow a tube.
• This tube, known as the pollen tube,
• It extends down through the style (the elongated part of the pistil) and reaches the ovary.
• Inside the pollen tube, the nucleus of the pollen grain travels towards the ovule,
• In Ovule it will eventually participate in fertilization.

Additional Information  The process of pollination and the journey of a pollen grain after it lands on a stigma is:

• Pollination and Stigma Interaction:
• Pollination is the transfer of pollen from the male reproductive organ (anther) to the female reproductive organ (stigma) of a flower.
• When a pollen grain lands on the stigma, it adheres to the sticky surface due to specialized proteins and sugars present on the stigma.
• Formation of the Pollen Tube:
• The next step is the formation of a pollen tube.
• This tube grows from the pollen grain down through the style.
• It is the elongated part of the pistil (the female reproductive structure).
• The pollen tube is essential for transporting the male gametes (sperm cells) from the stigma to the ovule (located in the ovary).
• Purpose of the Pollen Tube:
• The pollen tube serves as a conduit for the male nucleus (genetic material) to reach the ovule.
• It provides a protected pathway for the male gametes to avoid external environmental challenges.
• Nucleus Migration:
• Inside the pollen tube, the nucleus of the pollen grain migrates towards the ovule.
• The seed contains the embryo, endosperm (nutritive tissue), and seed coat.
• Fruit Formation:
• The ovary surrounding the ovules undergoes changes and develops into a fruit.
• The fruit protects the developing seeds and aids in their dispersal.

The correct answer is 12H2O

Key Points

• Photosynthesis is the process by which plants convert light energy into chemical energy stored in the form of glucose (a sugar).
• The overall balanced equation for photosynthesis is: [6CO₂ + 12H₂O→C₆H₁₂O₆ + 6O₂].

Additional Information Water’s Role in Photosynthesis:

• Water molecules are split during the light-dependent reactions of photosynthesis.
• The process occurs in the thylakoid membranes of chloroplasts.
• Here’s how it happens step by step: a. Photon Absorption:
• When a photon of light strikes a chlorophyll molecule in the chloroplast, it excites the chlorophyll.
• This energy initiates the photosynthetic process.
• b. Water Splitting:
• Water molecules (H₂O) are split into oxygen (O₂) and protons (H⁺).
• The oxygen atoms combine to form molecular oxygen (O₂), which is released as a byproduct.
• The protons (H⁺) are used in the subsequent reactions.
• c. Electron Transport Chain:
• The electrons from water molecules are transferred through an electron transport chain within the thylakoid membrane.
• This chain generates energy that is used to produce ATP (adenosine triphosphate) and NADPH (nicotinamide adenine dinucleotide phosphate).
• d. ATP and NADPH Formation:
• ATP and NADPH are energy-rich molecules that fuel the Calvin cycle (dark reactions) of photosynthesis.
• The Calvin cycle takes place in the stroma of the chloroplast.
• e. Carbon Fixation:
• In the Calvin cycle, carbon dioxide (CO₂) is fixed into glucose (C₆H₁₂O₆) using ATP and NADPH.
• Glucose serves as the primary energy storage molecule for the plant