The correct answer is the 8th five-year plan

Key Points

• The economic reforms were initiated by the Narasimha Rao government during the 8th five-year plan.
• The 8th five-year plan spanned from 1992 to 1997.
• These reforms aimed at liberalizing the economy, promoting private sector participation, and integrating India into the global economy.
• Key measures included deregulation of industries, reduction in import tariffs, and opening up to foreign direct investment (FDI).
• The reforms marked a significant shift from the previous socialist policies to a more market-oriented approach.

Additional Information

• The economic liberalization in India was a response to a severe balance of payments crisis that the country faced in 1991.
• The reforms were spearheaded by the then Finance Minister Dr. Manmohan Singh under the leadership of Prime Minister P. V. Narasimha Rao.
• The New Economic Policy of 1991 included measures such as devaluation of the rupee, disinvestment in public sector enterprises, and tax reforms.
• The economic reforms led to a significant increase in India's GDP growth rate and transformed India into one of the fastest-growing economies in the world.
• The success of these reforms paved the way for further liberalization and economic policies in subsequent years.

The correct answer is acid; base

Key Points

• During a neutralization reaction, the H+ ion comes from an acid and the OH- ion comes from a base.
• When these ions combine, they form a water molecule (H₂O).
• This reaction typically results in the formation of a salt and water as products.
• Neutralization reactions are fundamental in understanding the behavior of acids and bases in chemical reactions.

Additional Information

• Acids are substances that release hydrogen ions (H⁺) in a solution.
• Bases are substances that release hydroxide ions (OH^-) in a solution.
• The pH scale is used to measure the acidity or basicity of a solution, with acids having a pH less than 7 and bases having a pH greater than 7.
• Neutralization reactions are important in various real-life applications, including antacid medications, agriculture, and environmental science.

Shortcut Trick

The product is a sequence of trigonometric sines starting from sin 90° down to sin 0°.

In any product of terms, if any one term is zero, the entire product becomes zero.

Since the last term is sin 0° = 0, the product of all terms is 0.

∴ The correct answer is 0.

Alternate Method

Given:

Expression = sin 90° × sin 89° × sin 88° × sin 87° × ... × sin 0°

Formula Used:

The value of sin 0° = 0.

Calculations:

⇒ Let P = sin 90° × sin 89° × sin 88° × ... × sin 1° × sin 0°

⇒ We know that the value of sin 0° is 0.

⇒ P = (sin 90° × sin 89° × ... × sin 1°) × 0

⇒ P = 0

∴ The correct answer is 0.

Additional Information

Standard Sine Values

Important values include sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, and sin 90° = 1.

Zero Product Property

If a series of numbers are multiplied together and at least one factor is zero, the result is always zero.

Similar Product Cases

In a product like cos 0° × cos 1° × ... × cos 100°, the result is 0 because cos 90° = 0.

Given:

Conditions:

Now, consider the group of numbers and symbols: '5 < = 2 @ 6'

Step-by-step solution:

1. Code the elements using the given table:

• 5: C
• <: E
• =: G
• 2: P
• @: T
• 6: F

So initially, we have: 'C E G P T F'

2. Apply the conditions:

Check Condition (i): The first element is not a symbol, so this condition does not apply.

Check Condition (ii): The first element is an odd number (5) and the last element is an even number (2), so their codes should be interchanged. Therefore, 'P' and 'D' are interchanged.

After applying Condition (ii), we have: 'F E G P T C'

Check Condition (iii): The second element (6) and the third element (=) are not both perfect squares, so this condition does not apply.

Final coded group: 'F E G P T C'

Hence, the correct answer is "Option 1".

Shortcut Trick

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

Given Area = 4√3

(√3/4) × a² = 4√3

a² = 16 ⇒ a = 4

∴ The correct answer is 4 unit.

Alternate Method

Given:

Area of the equilateral triangle = 4√3 sq. unit

Formula Used:

Area of equilateral triangle = $\frac{\sqrt{3}}{4} a^{2}$

Calculations:

⇒ Area = (√3 / 4) × side²

⇒ 4√3 = (√3 / 4) × side²

⇒ 4 = (1 / 4) × side²

⇒ side² = 4 × 4

⇒ side² = 16

⇒ side = √16

⇒ side = 4 unit

∴ The correct answer is 4 unit.

Additional Information

Height of Equilateral Triangle

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

Perimeter of Equilateral Triangle

Since all three sides are equal, the perimeter (P) is simply 3 × a.

Inradius and Circumradius

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

Shortcut Trick

Recognize that the given equation 16x² − 8x + 1 = 0 is a perfect square: (4x − 1)² = 0.

Solving for x: 4x − 1 = 0 ⇒ 4x = 1 ⇒ x = 1/4.

Substitute x = 1/4 into the required expression: 16(1/4)² + 1/(4(1/4)²).

Value = 16(1/16) + 1/(4 × 1/16) ⇒ 1 + 1/(1/4) ⇒ 1 + 4 = 5.

∴ The correct answer is 5.

Alternate Method

Given:

Quadratic Equation: 16x² − 8x + 1 = 0

Target Expression: 16x² + 1/(4x²)

Formula Used:

Factorization of Quadratic Equation ax² + bx + c = 0 and direct substitution.

⇒ 16x² − 4x − 4x + 1 = 0

⇒ 4x(4x − 1) − 1(4x − 1) = 0

⇒ (4x − 1)(4x − 1) = 0

⇒ 4x − 1 = 0

⇒ x = 1/4

⇒ Now, substitute x = 1/4 in 16x² + 1/(4x²):

⇒ 16(1/4)² + 1 / (4 × (1/4)²)

⇒ 16 × (1/16) + 1 / (4 × 1/16)

⇒ 1 + 1 / (1/4)

⇒ 1 + 4 = 5

∴ The correct answer is 5.

Additional Information

Perfect Square Trinomial

An expression of the form a² − 2ab + b² can be simplified as (a − b)². In this case, (4x)² − 2(4x)(1) + 1² fits the pattern.

Nature of Roots

For a quadratic equation ax² + bx + c = 0, if the discriminant D = b² − 4ac = 0, the roots are real and equal. Here, D = (−8)² − 4(16)(1) = 64 − 64 = 0.

Reciprocal Identities

If 4x + 1/(4x) = k, then 16x² + 1/(16x²) = k² − 2. Dividing the given equation by 4x gives 4x − 2 + 1/(4x) = 0, or 4x + 1/(4x) = 2.

The correct answer is option 1

Key Points

• The sign of the magnification produced by a concave mirror is positive when the image is virtual and negative when the image is real.
• In a concave mirror, when the object is placed between the focal point and the mirror, a virtual, erect, and magnified image is formed, resulting in a positive magnification.
• When the object is placed beyond the focal point, a real, inverted, and reduced or enlarged image is formed, resulting in a negative magnification.
• This property is a consequence of the mirror equation and the nature of image formation by concave mirrors.

Additional Information

• Magnification (m) is given by the ratio of the height of the image (h_i) to the height of the object (h_o): m=hihom=hihom=hihom=hihom=hihom=hiho .
• For mirrors, magnification can also be expressed in terms of object distance (u) and image distance (v): m=−vum=−vum=−vum=−vum=−vum=−vu .
• A positive magnification indicates that the image is erect and virtual.
• A negative magnification indicates that the image is inverted and real.
• Concave mirrors are used in various applications such as telescopes, shaving mirrors, and headlights due to their ability to form real and magnified images.

The correct answer is 2

Key Points

• Element A (9) corresponds to Fluorine, which is a halogen located in Group 17 of the periodic table.
• Element B (11) corresponds to Sodium, which is an alkali metal located in Group 1 of the periodic table.
• Element C (19) corresponds to Potassium, which is also an alkali metal located in Group 1 of the periodic table.
• Element D (37) corresponds to Rubidium, another alkali metal located in Group 1 of the periodic table.
• Among these elements, Element A (Fluorine) is the odd one out as it is the only element that is not an alkali metal.

Additional Information

• Alkali metals are located in Group 1 of the periodic table and include elements like Sodium (Na), Potassium (K), and Rubidium (Rb).
• Halogens are located in Group 17 of the periodic table and include elements like Fluorine (F).
• Elements in the same group typically share similar chemical properties.
• The periodic table is arranged so that elements with similar properties fall into the same vertical columns, known as groups.

The correct answer is Western Ghats

Key Points

• The Western Ghats receive the maximum rainfall from the South-west Monsoon winds in India.
• This mountain range runs parallel to the western coast of the Indian peninsula and significantly influences the monsoon patterns.
• The Western Ghats are known for their rich biodiversity and are recognized as one of the world's eight "hottest hotspots" of biological diversity.
• Regions such as Maharashtra, Goa, Karnataka, Kerala, and Tamil Nadu benefit from the heavy rainfall brought by the South-west Monsoon.

Additional Information

• The South-west Monsoon typically arrives in India around early June and lasts until September, bringing the majority of the country's annual rainfall.
• The monsoon is crucial for agriculture in India, as it directly impacts the water supply for irrigation and reservoirs.
• Areas like Cherrapunji and Mawsynram in Meghalaya, although not part of the Western Ghats, are also known for receiving extremely high rainfall during the monsoon season.
• The Western Ghats not only contribute to rainfall distribution but also play a significant role in the climate and weather patterns of the Indian subcontinent.

Shortcut Trick

For a continued proportion a : b :: b : c, the third proportional c = b² ÷ a.

Here, a = 18 and b = 30.

x = (30 × 30) ÷ 18

x = 900 ÷ 18 = 50

∴ The correct answer is 50.

Alternate Method

Given:

First term (a) = 18

Mean term (b) = 30

Third term (c) = x

Formula Used:

If a, b, c are in continued proportion, then a/b = b/c ⇒ b² = a × c

Calculations:

⇒ 18 : 30 :: 30 : x

⇒ 18 / 30 = 30 / x

⇒ 18 × x = 30 × 30

⇒ 18x = 900

⇒ x = 900 ÷ 18

⇒ x = 50

∴ The correct answer is 50.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional and is calculated as d = (b × c) ÷ a.

Continued Proportion

Three quantities a, b, c are in continued proportion if a : b = b : c.

Shortcut Trick

Ratio of efficiency A : B : C = 1 : 2 : 4

Total efficiency of (A + B + C) = 1 + 2 + 4 = 7 units/hr

Total capacity of tank = Total efficiency × Total time = 7 × 4 = 28 units

Time taken by Pipe A = Total capacity ÷ Efficiency of A = 28 ÷ 1 = 28 hours

∴ The correct answer is 28 hr.

Alternate Method

Given:

Total time taken by A, B, and C together = 4 hours

Efficiency relation: C = 2B and B = 2A

Calculations:

⇒ Let the efficiency of Pipe A be 1 unit/hr.

⇒ Efficiency of Pipe B = 2 × 1 = 2 units/hr

⇒ Efficiency of Pipe C = 2 × 2 = 4 units/hr

⇒ Total efficiency of (A + B + C) = 1 + 2 + 4 = 7 units/hr

⇒ Total capacity of the tank = Efficiency × Time = 7 × 4 = 28 units

⇒ Time taken by Pipe A alone = 28 ÷ 1 = 28 hours

∴ The correct answer is 28 hr.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. Work = Efficiency × Time.

Pipes and Cisterns Logic

If an inlet pipe fills in x hours and an outlet pipe empties in y hours, the net work done in one hour is (1/x − 1/y).

The correct answer is Dr. Jitendra Singh

Key Points

• "Dare2eraD TB" by the Department of Biotechnology, Ministry of Science & Technology, was launched on the occasion of World TB Day.
• The initiative was launched by Dr. Jitendra Singh.
• World TB Day is observed on March 24 each year to raise public awareness about the devastating health, social, and economic consequences of tuberculosis.
• The program aims to eliminate tuberculosis (TB) in India by the year 2025.

Additional Information

• Tuberculosis is a potentially serious infectious disease that mainly affects the lungs. The bacteria that cause TB are spread from one person to another through tiny droplets released into the air via coughs and sneezes.
• India has the highest burden of both TB and multidrug-resistant TB. The government has implemented the National Strategic Plan for TB Elimination 2017-2025 to tackle this issue.
• The Revised National TB Control Programme (RNTCP) is being strengthened and integrated with the health system to ensure comprehensive coverage and effective management of TB cases.

Shortcut Trick

LCM of 3, 4, 5, and 6 is 60.

Divide 2488 by 60 → 2488 ÷ 60 gives remainder 28.

Least number to be added = Divisor − Remainder = 60 − 28 = 32.

∴ The correct answer is 32.

Alternate Method

Given: Number = 2488, Divisors = 3, 4, 5, 6.

Formula: Least number added = LCM(divisors) − (Number % LCM).

⇒ LCM of (3, 4, 5, 6):

⇒ 3 = 3¹, 4 = 2², 5 = 5¹, 6 = 2 × 3.

⇒ LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.

⇒ Dividing 2488 by 60:

⇒ 2488 = 60 × 41 + 28.

⇒ Remainder = 28.

⇒ Least number to be added = 60 − 28 = 32.

∴ The correct answer is 32.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers. It is found by taking the product of the highest powers of all prime factors.

Divisibility Rules

A number is divisible by 60 if it is divisible by 3, 4, and 5 simultaneously. To find the next multiple, add (Divisor − Remainder).

Subtraction Case

If the question asks for the least number to be subtracted, the answer is simply the Remainder itself.

The correct answer is 3 Both a and b.

Key PointsLaw of Demand in Economics:

• The Law of Demand is a fundamental principle in economics which states that, all else being equal, as the price of a good increases, the quantity demanded of that good decreases, and vice versa. This is reflected in option a.
• Demand and Marginal Utility: Demand is derived from the law of diminishing marginal utility, which is based on the fact that consumers prioritize satisfying their most urgent needs first. This is captured in option b.
• While the shape and magnitude of demand can shift in response to various factors, including price, this is a broader concept that encompasses changes in demand rather than the fundamental law itself. Therefore, option c is not specifically about the Law of Demand.
• Hence, the correct answer is both a and b.

The correct answer is angle of deviation.

Key Points

• The angle of deviation is the angle between the incident ray and the emergent ray.
• In a prism, the ray of light bends twice, once when it enters the prism and once when it exits.
• The angle of deviation depends on the angle of incidence, the refractive index of the prism material, and the angle of the prism.
• The angle of deviation is minimum when the angle of incidence is such that the light ray passes symmetrically through the prism.

Additional Information

• Snell's Law
• It describes how light bends when it passes from one medium to another.
• It is given by the formula: n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
• Refractive Index
• The refractive index of a medium is a measure of how much it can bend light.
• It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.
• Prism Formula
• The relationship between the angle of incidence, angle of refraction, and the angle of the prism can be described using the prism formula: A = r1 + r2, where A is the angle of the prism and r1 and r2 are the angles of refraction at the two surfaces of the prism.

Given: (left) 347, 486, 627, 113, 721, 418, 779 (right)

If 2 is added to the digit in the hundred's place of each number given above, the modified numbers will be:

• 347 → 547
• 486 → 686
• 627 → 827
• 113 → 313
• 721 → 921
• 418 → 618
• 779 → 979

Now, we need to check if the modified digit in the hundred's place is exactly divisible by the digit in the ten's place:

• 547: 5 ÷ 4 = not exactly divisible
• 686: 6 ÷ 8 = not exactly divisible
• 827: 8 ÷ 2 = exactly divisible
• 313: 3 ÷ 1 = exactly divisible
• 921: 9 ÷ 2 = not exactly divisible
• 618: 6 ÷ 1 = exactly divisible
• 979: 9 ÷ 7 = not exactly divisible

So, the modified hundred's place digit is exactly divisible by the ten's place digit in 3 numbers.

The correct answer is "Option 4".

The correct answer is option 3

Key Points

• Thermal decomposition reaction is a type of chemical reaction where a single compound breaks down into two or more simpler substances when heated.
• In the given options, ZnCO3 → ZnO + CO2 (option 3) is an example of a thermal decomposition reaction.
• When zinc carbonate (ZnCO3) is heated, it decomposes into zinc oxide (ZnO) and carbon dioxide (CO2).
• Other options like the decomposition of water (H2O) and sodium chloride (NaCl) involve different types of reactions such as electrolysis.

Additional Information

• Thermal decomposition reactions require energy in the form of heat to break chemical bonds in the compound undergoing decomposition.
• Common examples of thermal decomposition reactions include the breakdown of calcium carbonate (CaCO3) into calcium oxide (CaO) and carbon dioxide (CO2), and the decomposition of potassium chlorate (KClO3) into potassium chloride (KCl) and oxygen (O2).
• These reactions are important in various industrial processes, such as the production of lime from limestone and the preparation of oxygen in laboratories.

Shortcut Trick

To find the greatest number that leaves the same remainder, find the HCF of the differences between the numbers.

Difference 1: 9806 − 8954 = 852

Difference 2: 11297 − 9806 = 1491

Difference 3: 11297 − 8954 = 2343

HCF(852, 1491, 2343) = 213 because 852 = 4 × 213 and 1491 = 7 × 213.

∴ The correct answer is 213.

Alternate Method

Given: Numbers are 8954, 9806, and 11297.

Formula Used: Required number = HCF(|x − y|, |y − z|, |z − x|)

⇒ Step 1: Calculate the differences between the numbers.

⇒ 9806 − 8954 = 852

⇒ 11297 − 9806 = 1491

⇒ Step 2: Find the HCF of 852 and 1491.

⇒ Using division method: 1491 = 852 × 1 + 639

⇒ 852 = 639 × 1 + 213

⇒ 639 = 213 × 3 + 0

⇒ The Last Divisor is 213.

∴ The correct answer is 213.

Additional Information

HCF with same remainder

The largest number that divides x, y, and z leaving the same remainder is HCF(|x − y|, |y − z|, |z − x|).

HCF with different remainders

The largest number that divides x, y, and z leaving remainders a, b, and c is HCF(x − a, y − b, z − c).

LCM concept

The smallest number which when divided by x, y, and z leaves the same remainder r is [LCM(x, y, z) + r].

Given: Six persons, L, M, N, O, P and Q, have cooking classes in different months of the same year, viz. February, March, June, August, September and December.

1. P has the class immediately before Q.

2. Only M has the class before O.

3. L has the class immediately after N and before Q.

Check all the options:

Option (1): Q has the class in February → False

Option (2): M has the class in March → False

Option (3): P has the class in September → True

Option (4): L has the class in June → False

So, P's class is in September.

Hence, the correct answer is "Option 3".

According to the given information,

1) W is to the immediate right of Y. 

2) W and Z are not at the opposite corners

Here, we can see that W sits opposite to X.

Hence, the correct answer is "W".

Calculation:

We have,

x2 + 5x - 12 - 3(x2 - 2x + 9)

⇒ x2 + 5x - 12 - 3x2 + 6x - 27

⇒ -2x2 + 11x - 39

∴ Option 3 is the correct answer.

The correct answer is Article 343(1)

Key Points

• Article 343(1) of the Indian Constitution specifies that "The official language of the Union shall be Hindi in Devanagari script."
• The Constitution initially provided for the continued use of English for all official purposes of the Union for a period of 15 years from its commencement, after which Hindi was to become the sole official language.
• However, due to the linguistic diversity of India, the Official Languages Act, 1963 was passed, allowing for the continued use of English alongside Hindi for official purposes.
• This provision highlights the importance of Hindi as the official language, while also recognizing the practical need for English in official communication.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Official Languages Act, 1963 plays a crucial role in the continued use of English for official purposes, reflecting the linguistic diversity of the nation.

The logic followed here is:

Hence, the correct answer is "318".

The correct answer is to freeze the production of CFCs at 1986 level

Key Points

• The main aim of the agreement made by UNEP in 1987 was to freeze the production of CFCs at the 1986 level.
• This agreement is known as the Montreal Protocol on Substances that Deplete the Ozone Layer.
• The protocol was designed to protect the ozone layer by phasing out the production of numerous substances responsible for ozone depletion, primarily chlorofluorocarbons (CFCs).
• The Montreal Protocol is considered one of the most successful environmental agreements to date.

Additional Information

• The United Nations Environment Programme (UNEP) facilitated the Montreal Protocol, which was agreed upon on September 16, 1987, and entered into force on January 1, 1989.
• As of today, the protocol has undergone several amendments and adjustments to include more substances and to accelerate the phase-out schedules.
• The Montreal Protocol has significantly contributed to the recovery of the ozone layer and is a model for international cooperation on environmental issues.
• Due to its success, September 16 is celebrated as International Day for the Preservation of the Ozone Layer.

The correct answer is 4 Only.

Key Points

• Sodium hydroxide (NaOH) is indeed prepared by the chlor-alkali process. This process involves the electrolysis of brine (sodium chloride solution), which produces chlorine gas, hydrogen gas, and sodium hydroxide. Hence, Statement I is correct.
• Sodium hydroxide is also used in the production of artificial textile fibers such as rayon. Rayon is made from cellulose, which is treated with sodium hydroxide to produce a solution that can be spun into fibers. Hence, Statement II is also correct.
• Given that both statements are correct, the correct answer is option 4.

The correct answer is ASIGMA

Key Points

• ASIGMA is the in-house messaging application released by the Indian Army for the military sector.
• The app stands for Army Secure IndiGeneous Messaging Application (ASIGMA), designed to provide a secure communication platform within the army.
• This app replaces other commercial messaging applications to ensure enhanced security and confidentiality of military communications.
• ASIGMA is developed as part of the Army's ongoing efforts to modernize communication systems and enhance operational efficiency.

Additional Information

• The Indian Army has been focusing on indigenization and self-reliance in its technology and communication systems.
• ASIGMA is part of the broader initiative to reduce dependency on foreign applications and improve the security of sensitive communications.
• The app is expected to be regularly updated with new features and security enhancements to keep pace with evolving threats.
• In addition to ASIGMA, the Indian Army has been working on other indigenous projects to enhance its technological capabilities and operational readiness.

The correct answer is 2 Only.

Key PointsHomologous Series:

• A homologous series is a series of compounds in which the same functional group substitutes for hydrogen in a carbon chain. Hence, Statement I is correct.
• As the molecular mass increases in any homologous series, a gradation in physical properties is observed. This means properties such as boiling point, melting point, and solubility change progressively with increasing molecular mass. Hence, Statement II is correct.
• For example, in the homologous series of alkanes (methane, ethane, propane, etc.), the boiling point increases with increasing molecular mass.
• This gradation in physical properties is due to the increasing van der Waals forces as the molecular size increases.

Based on the above points, both Statement I and Statement II are correct. Therefore, the correct answer is 2 Only.

Shortcut Trick

For an algebraic expression of the form x + 1/x = k, the value of x² + 1/x² is always k² − 2.

Given the value k = 4.

Applying the shortcut formula: 4² − 2 = 16 − 2 = 14.

∴ The correct answer is 14.

Alternate Method

Given:

The linear equation is x + 1/x = 4.

Formula Used:

Using the standard algebraic identity: (a + b)² = a² + b² + 2ab

Calculations:

⇒ (x + 1/x)² = 4² (Squaring both sides of the equation)

⇒ x² + (1/x)² + 2 × x × (1/x) = 16

⇒ x² + 1/x² + 2 = 16

⇒ x² + 1/x² = 16 − 2

⇒ x² + 1/x² = 14

∴ The correct answer is 14.

Additional Information

Negative Sign Identity

If the given expression is x − 1/x = k, then the value of x² + 1/x² is k² + 2.

Cubic Identity Relation

If x + 1/x = k, then the value of x³ + 1/x³ is calculated as k³ − 3k.

Higher Power (Quartic) Relation

If x + 1/x = k, then x⁴ + 1/x⁴ = (k² − 2)² − 2.

Square Root Relation

If x² + 1/x² = k, then x + 1/x = √(k + 2).

Calculation:

We have,

23k - 5 = 4096

⇒ 23k - 5 = 2¹²

Now,

3k - 5 = 12

⇒ 3k = 12 + 5

⇒ k = 17/3

∴ Option 2 is the correct answer.

Given Equation: 64 + 32 - 8 × 11 ÷ 3 = ?

BODMAS Rule:

Decoding the given information:

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 64 - 32 ÷ 8 + 11 × 3 

⇒ 64 - 4 + 11 × 3

⇒ 64 - 4 + 33

⇒ 97 - 4

⇒ 93

Hence, the correct option is "Option 2".

Calculation:

Vishal's sale in May = 125

Total sale in May = (125 + 140 + 188 + 125) = 578

Percentage contribution of Vishal's May sale in the total sale of May = (125/578) × 100

⇒ 21.6%

∴ Option 4 is the correct answer.

The correct answer is Electric generator

Key Points

• Electric generator is based on the principle of electromagnetic induction.
• Electromagnetic induction is the process of generating electric current with a changing magnetic field.
• When a conductor moves through a magnetic field, an electromotive force (EMF) is induced in the conductor.
• This principle was discovered by Michael Faraday in 1831 and forms the working basis of generators.
• Generators convert mechanical energy into electrical energy using this principle, making them essential in power generation.

Additional Information

• Electric motors work on the principle of electromagnetic induction but in reverse, converting electrical energy into mechanical energy.
• Electric fans use electric motors to convert electrical energy into mechanical energy to create airflow.
• Electric bulbs convert electrical energy into light energy through the heating of a filament.
• While electric motors and electric fans also involve electromagnetic principles, they are not primarily based on the principle of electromagnetic induction for generating electricity.

The correct answer is a solution in water

Key Points

• The term (aq) stands for aqueous, which means the substance is dissolved in water.
• In a chemical equation, indicating a substance as (aq) specifies that it is in an aqueous solution.
• This is different from other states of matter such as solid (s), liquid (l), and gas (g).
• An aqueous solution means that the substance is mixed with water, forming a homogeneous mixture.

Additional Information

• Water is often called the "universal solvent" because it can dissolve more substances than any other liquid.
• In chemical reactions, the state of the substances involved is crucial for predicting the outcome and understanding the reaction mechanism.
• The use of (aq) helps chemists and students to quickly identify that the substance is in a solution form, which can affect the reaction rate and equilibrium.
• Common examples of aqueous solutions include saltwater (NaCl in water) and sugar water (C₁₂H₂₂O₁₁ in water).

→ The number of women who are speakers but not professor = 62 

→ The number of professors who are speakers and not women = 49

Hence, the correct answer is "62 and 49, respectively".

Shortcut Trick

Combined efficiency of (Madhu + Shiney + Rosy) × 2 = Total Efficiency.

Total Work = LCM(20, 12, 15) = 60 units.

Efficiencies: (M+S) = 3, (S+R) = 5, (R+M) = 4.

Sum of efficiencies = 3 + 5 + 4 = 12 (this is twice the combined efficiency).

Efficiency of (M+S+R) = 12 ÷ 2 = 6 units/day.

Time taken = 60 ÷ 6 = 10 days.

∴ The correct answer is 10 days.

Alternate Method

Given:

Time taken by Madhu and Shiney = 20 days

Time taken by Shiney and Rosy = 12 days

Time taken by Rosy and Madhu = 15 days

Calculations:

⇒ Adding the efficiencies: 2 × (Madhu + Shiney + Rosy) = 3 + 5 + 4

⇒ 2 × (Madhu + Shiney + Rosy) = 12

⇒ Efficiency of (Madhu + Shiney + Rosy) = 12 ÷ 2 = 6

⇒ Time taken together = Total Work ÷ Combined Efficiency

⇒ Time taken = 60 ÷ 6 = 10 days

∴ The correct answer is 10 days.

Additional Information

Combined Work Formula

When pairs work together, the individual efficiency of one person (e.g., Madhu) can be found by: [Total Efficiency (M+S+R)] − [Efficiency of (S+R)].

Work and Time Relationship

Time taken is inversely proportional to Efficiency. Time = Total Work ÷ Efficiency.

LCM Method for Work

Using the Least Common Multiple (LCM) of the given time periods as the 'Total Work' simplifies calculations into whole numbers instead of fractions.

Concept:

Let’s analyze each statement:

(A) Resistance is not independent of temperature. In fact, resistance of most conductors increases with temperature due to increased collision of electrons. So this statement is  Incorrect.

(B) Resistance is not directly affected by voltage. According to Ohm’s law, $V = IR$, resistance is a property of the material and does not increase just because voltage increases. So this statement is  Incorrect.

(C) The S.I. unit of resistance is ohm (Ω), which is absolutely Correct.

Shortcut Trick

Use the direct algebraic identity: a³ + b³ + c³ − 3abc = (a + b + c) × [(a + b + c)² − 3(ab + bc + ca)]

Substitute the given values: Sum (S) = 6 and Sum of products (P) = −2

Value = 6 × [6² − 3 × (−2)]

Value = 6 × [36 + 6] = 6 × 42 = 252

∴ The correct answer is 252.

Alternate Method

Given:

a + b + c = 6

ab + bc + ca = −2

Formula Used:

1. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

2. a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca))

Calculations:

First, find the value of a² + b² + c²:

⇒ (6)² = a² + b² + c² + 2(−2)

⇒ 36 = a² + b² + c² − 4

⇒ a² + b² + c² = 36 + 4 = 40

Now, substitute this into the cubic identity:

⇒ a³ + b³ + c³ − 3abc = 6 × (40 − (−2))

⇒ a³ + b³ + c³ − 3abc = 6 × (40 + 2)

⇒ a³ + b³ + c³ − 3abc = 6 × 42

⇒ a³ + b³ + c³ − 3abc = 252

Therefore, the value is 252, which corresponds to Option (4).

∴ The correct answer is 252.

Additional Information

Conditional Algebraic Identity

If a + b + c = 0, then the expression a³ + b³ + c³ − 3abc becomes zero, which implies a³ + b³ + c³ = 3abc.

Square of a Trinomial

The expansion of (a + b + c)² is always a² + b² + c² + 2ab + 2bc + 2ca. This is used to find the sum of squares.

Alternative Form of Cubic Identity

a³ + b³ + c³ − 3abc = 1/2 × (a + b + c) × [(a − b)² + (b − c)² + (c − a)²]. This form is useful when differences between variables are given.

The correct answer is metals

Key Points

• Elements with 2 electrons in their outermost shell are generally metals.
• These elements are often found in the second group of the periodic table and are known as the alkaline earth metals.
• The common examples include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).
• Alkaline earth metals are characterized by their shiny appearance and high reactivity.

Additional Information

• Alkaline earth metals have an oxidation state of +2, which is why they readily lose two electrons to form cations.
• These metals are less reactive than alkali metals (group 1) but are still highly reactive, particularly with water and oxygen.
• Due to their reactivity, they are not found in their free elemental state in nature but are commonly found in various minerals.
• Their reactivity increases as you move down the group in the periodic table.
• These metals also have relatively low densities and low melting points compared to other metals.

Shortcut Trick Identify two numbers that multiply to the constant term −26 and add to the middle coefficient 11. The numbers are 13 and −2 (since 13 × −2 = −26 and 13 − 2 = 11). The roots are the values with signs reversed: −13 and 2. ∴ The correct answer is -13 and 2.

Alternate Method Given: x2 + 11x − 26 = 0 Formula Used: Factorisation by splitting the middle term. ⇒ x2 + 13x − 2x − 26 = 0 ⇒ x(x + 13) − 2(x + 13) = 0 ⇒ (x + 13)(x − 2) = 0 ⇒ x + 13 = 0 or x − 2 = 0 ⇒ x = −13 or x = 2 ∴ The correct answer is -13 and 2.

Additional Information Standard Quadratic Equation A quadratic equation is of the form ax2 + bx + c = 0. The roots can also be found using the formula x = [−b ± √(b2 − 4ac)] / 2a. Nature of Roots The value D = b2 − 4ac is called the discriminant. If D > 0, the roots are real and distinct; if D = 0, the roots are real and equal. Relation between Roots and Coefficients For the equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Shortcut Trick

Net percentage change formula = a + b + (a × b)/100

Here, a = −40% (decrease) and b = +50% (increase).

Net change = −40 + 50 + [(−40 × 50)/100] = 10 − 20 = −10%.

Negative sign indicates a loss.

∴ The correct answer is 10%.

Alternate Method

Given: Initial salary decrease = 40%, Subsequent salary increase = 50%.

⇒ Let the initial salary of Rajiv be 100.

⇒ After 40% decrease, salary = 100 − 40 = 60.

⇒ After 50% increase on 60, increase = 60 × (50/100) = 30.

⇒ Final salary = 60 + 30 = 90.

⇒ Percentage loss = [(Initial − Final)/Initial] × 100

⇒ Percentage loss = [(100 − 90)/100] × 100 = 10%.

∴ The correct answer is 10%.

Additional Information

Successive Percentage Change

When a value is changed by x% and then y% successively, the net change is given by [x + y + (xy/100)]%.

Multiplying Factor Method

Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100). Use plus for increase and minus for decrease.

Percentage Loss

Loss % = (Amount of Decrease ÷ Original Value) × 100.

Given: # 9 1 @ 4 * 7 ^ 5 3 # 9 1 < 5 4 @ 3 $ # 2 * 6 ! 4 2 & 9 < 3 6

• Numbers that are immediately preceded by a symbol and immediately followed by an even number:

9 1 @ 4 * 7 ^ 5 3 # 9 1 < 5 4 @ 3 $ # 2 * 6 ! 4 2 & 9 < 3 6

Here: < 5 4, ! 4 2, < 3 6

Clearly, there are 'three' numbers immediately preceded by a symbol and immediately followed by an even number.

Hence, the correct answer is "Three".

The correct answer is Pankaj Advani

Key Points

• Pankaj Advani has won his eighth title at the 19th Asian 100 UP Billiards Championship, 2022.
• Pankaj Advani is a renowned Indian billiards and snooker player who has won multiple world titles across different formats of both games.
• He is one of the most successful cueists in the history of the sport, with numerous national and international titles to his name.
• Advani's consistent performance has made him a prominent figure in the world of billiards and snooker.
• He has been honored with several awards, including the Padma Bhushan, Padma Shri, and the Rajiv Gandhi Khel Ratna Award.

Additional Information

• The Asian Billiards Championship is an annual event where top billiards players from across Asia compete for the title.
• The championship is governed by the Asian Confederation of Billiard Sports (ACBS), which is responsible for promoting cue sports in Asia.
• Billiards is a cue sport that requires precision, strategy, and skill, and has a rich history and tradition in many countries, including India.
• Pankaj Advani's achievements have significantly contributed to the popularity and development of cue sports in India.

Shortcut Trick

Assume an Assumed Mean (Base) = 20.

Find deviations of each number from 20: −15, −5, +3, +6, and +9.

Sum of deviations = (−15 − 5 + 3 + 6 + 9) = −20 + 18 = −2.

Average deviation = −2 ÷ 5 = −0.4.

Actual Arithmetic Mean = 20 − 0.4 = 19.6.

∴ The correct answer is 19.6.

Alternate Method

Given: The set of observations = 5, 15, 23, 26, 29.

Formula Used: Arithmetic Mean = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Sum of observations = 5 + 15 + 23 + 26 + 29

⇒ Sum = 98

⇒ Total number of observations (n) = 5

⇒ Arithmetic Mean = 98 ÷ 5

⇒ Arithmetic Mean = 19.6

∴ The correct answer is 19.6.

Additional Information

Properties of Arithmetic Mean

The sum of the deviations of all items from their arithmetic mean is always zero. If every observation is increased by a constant k, the new mean also increases by k.

Combined Mean Formula

If two groups have sizes n₁, n₂ and means x₁, x₂, the Combined Mean = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Weighted Average

When values have different importance, Weighted Mean = Σw_ix_i ÷ Σw_i, where w represents the weight of each observation.

The correct answer is Water enters the guard cells and they swell

Key Points

• Water enters the guard cells and they swell causing the stomata to open.
• Guard cells are specialized cells located in the epidermis of leaves, stems, and other organs that are used to control gas exchange.
• When water enters the guard cells, they become turgid and the stomatal pore opens.
• This mechanism allows for the uptake of carbon dioxide and the release of oxygen and water vapor during photosynthesis and respiration.
• Conversely, when guard cells lose water, they become flaccid and the stomatal pore closes, reducing water loss through transpiration.

Additional Information

• Guard cells are the only epidermal cells that contain chloroplasts, which are essential for photosynthesis.
• The opening and closing of stomata are influenced by factors such as light, carbon dioxide concentration, and internal water balance.
• Stomatal movement is a critical process in plant physiology, impacting water use efficiency and photosynthetic capacity.
• Regulation of stomatal aperture is crucial for the plant's adaptation to environmental conditions.
• The process is also linked to the plant's internal circadian rhythms, which help optimize gas exchange and water use during different times of the day.

The correct answer is short term

Key Points

• Microfinance in India is a form of financial service which provides small loans and other financial services to poor and low-income households.
• These services are primarily aimed at providing short-term financial assistance, helping individuals to manage immediate needs and stabilize their economic conditions.
• Microfinance institutions (MFIs) offer a range of products including small loans, savings accounts, insurance, and remittance services.
• Loans provided by MFIs are typically of small amounts and have shorter repayment periods compared to traditional bank loans.
• The goal of microfinance is to promote financial inclusion and empower economically disadvantaged individuals by providing them with the necessary financial tools.

Additional Information

• Microfinance has played a significant role in poverty alleviation by providing the poor with access to financial resources that were previously unavailable to them.
• The concept of microfinance gained global recognition through the work of Dr. Muhammad Yunus and the Grameen Bank in Bangladesh, which was awarded the Nobel Peace Prize in 2006.
• In India, microfinance has been supported by various policies and regulatory frameworks to ensure its sustainable growth and positive impact on society.
• Microfinance institutions must adhere to guidelines set by regulatory bodies such as the Reserve Bank of India (RBI) to ensure transparency and protect the interests of borrowers.

Shortcut Trick A Quadratic Equation is identified when the highest power (degree) of the variable is exactly 2 after full simplification. Quickly check the highest terms: In A, x2 cancels out on both sides. In B and C, cubic terms (y3 and k3) are generated. In D, the p3 terms cancel out, leaving a p2 term. ∴ The correct answer is Only D.

Alternate Method We need to simplify each equation to find the degree of the variable. For Equation A: ⇒ x(x − 4) = 2x + x2 − 7 ⇒ x2 − 4x = 2x + x2 − 7 ⇒ −4x = 2x − 7 (Subtracting x2 from both sides) ⇒ 6x − 7 = 0 (Linear equation, degree 1) For Equation B: ⇒ 5(2y + 3) − 6y = 5y(y2 − 8y) ⇒ 10y + 15 − 6y = 5y3 − 40y2 ⇒ 5y3 − 40y2 − 4y − 15 = 0 (Cubic equation, degree 3) For Equation C: ⇒ k(k + 1) − k(k − 2) × 2k = 0 ⇒ (k2 + k) − (k2 − 2k) × 2k = 0 ⇒ k2 + k − 2k3 + 4k2 = 0 ⇒ −2k3 + 5k2 + k = 0 (Cubic equation, degree 3) For Equation D: ⇒ p(p2 + 7) = p2 + p3 − 18 ⇒ p3 + 7p = p2 + p3 − 18 ⇒ 7p = p2 − 18 (Subtracting p3 from both sides) ⇒ p2 − 7p − 18 = 0 (Highest power is 2) ∴ The correct answer is Only D.

Additional Information Standard Form A quadratic equation in the variable x is an equation of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Degree of Equation The degree is the highest exponent of the variable in the polynomial. For quadratic, degree = 2; for cubic, degree = 3; for linear, degree = 1. Discriminant (D) The value D = b2 − 4ac determines the nature of roots. If D > 0 (real and distinct), D = 0 (real and equal), D < 0 (imaginary).

The logic followed here is:

Total number of students in the class = 17

A's rank from the top = 9th

B's rank from the bottom = 11th

To find B's rank from the top, we subtract B's rank from the bottom from the total number of students and add 1:

B's rank from the top = 17 - 11 + 1 = 7th

C's rank is better than A's but worse than B's. Hence, C's rank from the top must be between A's and B's ranks.

So, C's rank from the top = 8th

Hence, the correct answer is "Option 2".

The correct answer is Onam

Key Points

• Onam is the main harvest festival celebrated in South India, particularly in the state of Kerala.
• It marks the homecoming of the mythical King Mahabali and is celebrated with much fervor and enthusiasm.
• The festival includes various cultural events, traditional games, music, dance, and the famous boat races.
• Onam is traditionally observed with elaborate feasts, known as Onam Sadhya, which consist of a variety of dishes served on a banana leaf.

Additional Information

• Uttarayan, also known as Makar Sankranti, is a festival celebrated in Gujarat and other parts of India, marking the transition of the sun into the zodiac sign of Capricorn.
• Bihu is the main harvest festival celebrated in Assam, consisting of three different Bihu festivals in a year: Rongali Bihu, Kongali Bihu, and Bhogali Bihu.
• Maghi is a harvest festival celebrated in Punjab, marking the start of the month of Magh in the Hindu calendar.
• Onam is unique to Kerala and is not just a harvest festival but also a celebration of the cultural heritage of the region.

Shortcut Trick

Total distance = 12,800 − 12,000 = 800 km

Average speed in km/hr = 800 ÷ 4 = 200 km/hr

To convert km/hr to m/sec, multiply by 5/18: 200 × (5/18) = 1000/18 = 500/9 m/sec

∴ The correct answer is 500/9 m/sec.

Alternate Method

Given: Initial reading = 12,000 km, Final reading = 12,800 km, Total time = 4 hours.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Total Distance = Final Reading − Initial Reading

⇒ Total Distance = 12,800 km − 12,000 km = 800 km

⇒ Average Speed (km/hr) = 800 ÷ 4 = 200 km/hr

⇒ Conversion factor: 1 km/hr = 5/18 m/sec

⇒ Average Speed (m/sec) = 200 × (5 ÷ 18)

⇒ Average Speed (m/sec) = 1000 ÷ 18 = 500/9 m/sec

∴ The correct answer is 500/9 m/sec.

Additional Information

Speed Conversion Rules

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

Average Speed Formula

Average speed is defined as the total distance traveled divided by the total time taken (Total Distance ÷ Total Time).

Odometer

An odometer or odograph is an instrument used for measuring the distance traveled by a vehicle.

FEELING: VVUOTMR

HEAVILY: ZVSEBOR

Similarly,

FORTUNE: ?

Hence, the correct answer is "ILUGVMF".

Given,

Statement:

Onion prices have skyrocketed due to shortage of onions and largescale hoarding by a few traders.

Conclusions:

I. The government must crackdown on the hoarders and impose stringent penalties on hoarders - True (Because, the statement indicates that hoarding by a few traders is one of the reasons for the skyrocketing prices of onions, which suggests that action against hoarders could address the issue).

II. People must stop eating onions and switch to potatoes instead - False (Because, the statement does not provide any basis to conclude that people should change their eating habits).

So, Only conclusion I follows.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "1971".

According to the given information,

1) T is 40 m to the east of Q. P is 30 m to the south of Q.

2) R is 40 m to the west of Q. Q is 35 m to the south of S. 

Here, we can see that R is in west direction with reference to T.

Hence, the correct answer is "West".

The correct answer is violet

Key Points

• Violet light has the maximum refractive index among the components of white light.
• The refractive index of a medium depends on the wavelength of the light passing through it.
• Shorter wavelengths of light, such as violet, are refracted more than longer wavelengths like red when passing through a medium.
• This phenomenon is why violet light bends more and has a higher refractive index compared to other colors in the visible spectrum.

Additional Information

• The refractive index is a measure of how much the speed of light is reduced inside a medium compared to its speed in a vacuum.
• The refractive index is given by the formula n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium.
• Light of different wavelengths travels at different speeds in a medium, leading to dispersion and the separation of white light into its constituent colors.
• This principle is utilized in prisms and lenses to create various optical effects.

Given: Six boxes A, B, C, D, E, and F are kept one over the other, but not necessarily in the same order.

1. Only one box is kept between B and D.

2. Only two boxes are kept between B and E.

3. E is kept just above A.

Condition 1:

Condition 2:

4. F is kept just above B.

Condition 1:

Condition 2:

5. Box A is not kept in the bottom-most position.

So, Condtion 2 is not fulfill this statement condition.

From statement 1, Only one box is kept between B and D.

Only C is remaining,

So, 'E' box is kept at the top.

Hence, the correct answer is "Option 1".

The correct answer is It reduces

Key Points

• It reduces is the correct option regarding th20e effect of addition of water on the concentration of hydroxide ions.
• When water is added to lemon juice, the solution becomes more diluted.
• This dilution decreases the concentration of all ions present, including hydroxide ions.
• The sourness of lemon juice is due to the presence of citric acid, and adding water reduces the concentration of citric acid as well, making it less sour.

Additional Information

• The concentration of hydroxide ions is inversely proportional to the dilution of the acidic solution.
• Adding water to any acidic or basic solution will decrease the concentration of the ions responsible for its pH.
• In the case of lemon juice, which is acidic, adding water will lower the concentration of hydrogen ions (H⁺) and hydroxide ions (OH⁻).

The logic followed here is:

Logic: The letters are coded with the opposite letters as per the positional value table.

KDRB: PWIY

UNCG: FMXT

Now, let's check each option,

1) FTZN: UGVW

2) DHEL: WSVO

 ⇒ Follows the logic.

3) VQCX: EPXZ

4) TNDK: GMRP

Here, we can see that Option 2 follows the logic.

Hence, the correct answer is "DHEL: WSVO".

Calculation:

Money spends on ration is 36%.

Money spends on Rent is 20%.

Difference = 36% - 20% = 16%

According to the question.

16% of 85,200 = Rs. 13,632

∴ Option 3 is the correct answer.

The correct answer is Gandak

Key Points

• Gandak is not a tributary of the Brahmaputra River.
• Gandak is a major river in Nepal and India, which is a tributary of the Ganges River, not the Brahmaputra.
• The main tributaries of the Brahmaputra River include Subansiri, Lohit, and Manas among others.
• The Brahmaputra River flows through Tibet, India, and Bangladesh, playing a crucial role in the river systems of these regions.

Additional Information

• The Brahmaputra River originates from the Angsi Glacier in the Himalayas in Tibet and flows through India and Bangladesh before emptying into the Bay of Bengal.
• It is known as the Yarlung Tsangpo in Tibet and the Jamuna in Bangladesh.
• The river is known for its strong currents and seasonal flooding, which play a significant role in the agriculture and ecology of the regions it flows through.
• The Brahmaputra River basin supports diverse ecosystems and is home to numerous species of flora and fauna.

Given word: 'QUALITY'

After arranged in alphabetical order:

After arranged in alphabetical order,

The letters that remain in their original positions are:

Last alphabet from the left end is: Y

Hence, the correct answer is "Option 3".

Shortcut Trick

Profit% for a dishonest dealer selling at cost price is calculated as:

Profit% = (Error ÷ True Value − Error) × 100

Profit% = (False Weight Given ÷ Actual Weight Sold) is also expressed as (Weight Gap ÷ Weight Actually Given) × 100.

Here, for every 40 kg (True Value), he gives only 35 kg.

Profit% = (5 ÷ 35) × 100 = (1 ÷ 7) × 100 = 14.28%.

∴ The correct answer is 14.28%.

Alternate Method

Given: Total weight promised = 40 kg, Weight actually given = 35 kg, Selling Price (SP) = Cost Price (CP) per unit.

Formulas: Profit% = (Profit ÷ CP) × 100 | Total CP = Weight given × CP per kg | Total SP = Weight promised × CP per kg.

⇒ Let the CP of 1 kg sugar be 1 unit.

⇒ The shopkeeper delivers 35 kg, so his Total CP = 35 units.

⇒ He charges the customer for 40 kg at CP, so his Total SP = 40 units.

⇒ Profit = SP − CP = 40 − 35 = 5 units.

⇒ Profit% = (5 ÷ 35) × 100 = 14.2857...

∴ The correct answer is 14.28%.

Additional Information

Dishonest Dealer Concept

When a dealer claims to sell at CP but uses false weights, the profit is always calculated on the actual quantity delivered to the customer.

Effective Profit with Markup

If a dealer marks up the price by x% and also uses y% less weight, the overall profit is compounded using the ratio method.

The logic followed here is:

Logic: 1st number × (1st number ÷ 2) = 2nd number.

Now,

For, 4 : 8

⇒ 4 × (4 ÷ 2) = 4 × 2 = 8.

For, 8 : 32

⇒ 8 × (8 ÷ 2) = 8 × 4 = 32.

Similarly, for 12 ∶ ?

⇒ (12 × (12 ÷ 2) = 12 × 6 = 72.

Hence, the correct answer is "Option 1".

The correct answer is Temperature

Key Points

• Temperature determines the sex of fertilised eggs in a few reptiles.
• This phenomenon is known as temperature-dependent sex determination (TSD).
• In some reptiles, such as certain species of turtles, crocodilians, and lizards, the ambient temperature during a critical period of embryonic development determines whether the offspring will be male or female.
• This is different from the genetic sex determination seen in many other animals, where sex is determined by specific chromosomes (allosomes).
• For example, in many turtle species, higher incubation temperatures produce females, while lower temperatures produce males.

Additional Information

• Temperature-dependent sex determination (TSD) is a type of environmental sex determination, where the environment plays a crucial role in determining the sex of the offspring.
• This mechanism allows for the adjustment of sex ratios in response to environmental conditions, potentially providing an evolutionary advantage.
• Research into TSD can help in the conservation of endangered reptile species, as understanding the temperature ranges that produce both sexes can inform breeding programs.
• In contrast, in genetic sex determination systems, such as those in humans, sex is determined at fertilization by the combination of sex chromosomes (XX for females and XY for males).

Given: Six girls Natasha, Yuvika, Aditi, Tanya, Shahnaz, and Daljeet are comparing their heights.

No two girls are of the same height.

1. Aditi is taller than only Natasha and one other girl.

__ > __ > __ > Aditi > __ > Natasha

2. Shahnaz is shorter than Daljeet, who is shorter than Yuvika.

Yuvika > Daljeet > Shahnaz

Combining the information:

From the first statement, since Aditi is taller than Natasha and one other girl, Aditi must be the fourth tallest.

From the second statement, the order among Yuvika, Daljeet, and Shahnaz is clear.

Thus, the height order is:

Yuvika > Daljeet > Shahnaz > Aditi > __ > Natasha

Since Aditi is the fourth tallest and there are only one girl left, Tanya must be the one taller than Natasha but shorter than Aditi.

So the final order is:

Yuvika > Daljeet > Shahnaz > Aditi > Tanya > Natasha

Therefore, the third tallest girl is Shahnaz.

Hence, the correct answer is "Option 3".

Shortcut Trick

Total Area to be painted = Lateral Surface Area + Area of Ceiling.

Total Area = 2H(L + B) + (L × B)

Total Area = 2 × 21 × (15 + 17) + (15 × 17) = 42 × 32 + 255 = 1344 + 255 = 1599 m².

Total Cost = 1599 × 40 = Rs. 63,960.

∴ The correct answer is Rs. 63,960.

Alternate Method

Given:

Length (L) = 15 m

Breadth (B) = 17 m

Height (H) = 21 m

Rate = Rs. 40/m²

Formula Used:

Area of four walls = 2 × Height × (Length + Breadth)

Area of ceiling = Length × Breadth

Calculations:

⇒ Area of 4 walls = 2 × 21 × (15 + 17)

⇒ Area of 4 walls = 42 × 32 = 1344 m²

⇒ Area of ceiling = 15 × 17 = 255 m²

⇒ Total Area to be painted = 1344 + 255 = 1599 m²

⇒ Total Cost = 1599 × 40

⇒ Total Cost = Rs. 63,960

∴ The correct answer is Rs. 63,960.

Additional Information

Total Surface Area of Cuboid

The total surface area includes all six faces: 2(LB + BH + HL).

Volume of Cuboid

The capacity or space occupied by the room: V = L × B × H.

Diagonal of Cuboid

The longest rod that can be placed in the room: D = √(L² + B² + H²).

The logic followed here is:

Logic: (1st number × 12) = 2nd number.

Now,

For, 15 : 180

⇒ 15 × 12 = 180.

For, 17 : 204

⇒ 17 × 12 = 204.

Similarly, for 21 ∶ ?

⇒ 21 × 12 = 252.

Hence, the correct answer is "Option 1".

The correct answer is 900

Key Points

• The power consumption of the electric heater per day is 1000 W * 5 hours = 5000 Wh or 5 kWh.
• There are 30 days in the month of September.
• Total energy consumption for the month = 5 kWh/day * 30 days = 150 kWh.
• The cost per unit (kWh) is Rs. 6.00.
• Total cost = 150 kWh * Rs. 6.00/kWh = Rs. 900.

Additional Information

• Electric heaters are typically used for heating spaces and can consume a significant amount of electricity.
• It's important to consider the cost of running high-power devices for extended periods to manage electricity bills effectively.
• Using energy-efficient devices or limiting usage can help reduce electricity consumption and costs.
• Regular maintenance of electrical appliances can also improve their efficiency and reduce energy consumption.

Given Statements:

I. Some lions are cats.

II. All cats are animals.

III. Some animals are not lions.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some animals are lions - True (Because, Some lions are cats and all cats are animals, so some lions are animals).

II. All lions are animals - False (Because, It may be possible but not defined).

III. No animal is a lion - False (Because, Some lions are cats and all cats are animals, so some animals are lions).

So, Only conclusion I follows.

Hence, the correct answer is "Option 2".

Given:

$4\frac{7}{9}\times7\frac{8}{9}\times81+2\frac{3}{4}$

⇒ $\frac{43}{9}\times\frac{71}{9}\times81+2\frac{3}{4}$

⇒ ${43}\times{71}+\frac{11}{4}$

⇒ 3053 + 2.75

⇒ 3055.75

∴ Option 4 is the correct answer.

Shortcut Trick

Ratio of adjacent sides = 3 ∶ 2

Sum of ratio parts = 3 + 2 = 5

Perimeter = 2 × (Sum of adjacent sides) ⇒ 65 = 2 × (5 units)

10 units = 65 cm ⇒ 1 unit = 6.5 cm

Shorter side (2 units) = 2 × 6.5 = 13 cm

∴ The correct answer is 13 cm.

Alternate Method

Given: Ratio of adjacent sides = 3 ∶ 2, Perimeter = 65 cm

Formula: Perimeter of Parallelogram = 2(a + b), where a and b are adjacent sides.

⇒ Let the adjacent sides be 3x and 2x.

⇒ Perimeter = 2(3x + 2x)

⇒ 65 = 2(5x)

⇒ 65 = 10x

⇒ x = 65 ÷ 10 = 6.5

⇒ Length of shorter side = 2x = 2 × 6.5

⇒ Shorter side = 13 cm

∴ The correct answer is 13 cm.

Additional Information

Parallelogram Properties

Opposite sides are equal and parallel. Opposite angles are also equal.

Area of Parallelogram

Area = Base × Height. If adjacent sides a, b and angle θ are given, Area = ab sinθ.

Diagonal Property

The diagonals of a parallelogram bisect each other. Sum of squares of diagonals = 2(a² + b²).

The correct answer is 1) 4.7

Key Points

• Bharti Airtel has signed an agreement to buy 4.7% of Vodafone's stake in Indus Towers.
• This acquisition will strengthen Airtel's position in the telecom infrastructure sector.
• Indus Towers is one of the largest telecom tower companies in India, providing shared telecom infrastructure to telecom operators.
• The move is seen as part of Bharti Airtel's strategy to consolidate its holdings and enhance its operational capabilities.

Additional Information

• Indus Towers was formed as a joint venture between Bharti Infratel, Vodafone India, and Aditya Birla Telecom.
• The company provides passive infrastructure services to all telecom operators in India.
• With this acquisition, Bharti Airtel aims to optimize its network and enhance service quality for its customers.
• The telecom sector in India is witnessing significant consolidation and strategic partnerships to improve competitiveness and service delivery.

Given Statement: X < Z = T > V > P < Y = O

Now,

Conclusions:

Option 1: T > Y → False (T > V > P < Y It gives T > V > P < Y, but no direct relation between T and Y)

Option 2: O > P → True (P < Y = O It gives O > P)

Option 3: T < X → False (X < Z = T It gives X < T)

Option 4: V > Y → False (V > P < Y It gives V > P < Y, but no direct relation between V and Y)

Hence, the correct answer is "Option 2".

Shortcut Trick

Given Cost Price (CP) = 4,500 and Gain% = 5%.

Using multiplier method: Selling Price (SP) = CP × (100 + Gain%) ÷ 100.

SP = 4,500 × (105 ÷ 100) = 4,500 × 1.05.

SP = 4,725.

∴ The correct answer is Rs. 4,725.

Alternate Method

Given: CP = Rs. 4,500, Gain% = 5%.

Formulas: Profit = (Gain% × CP) ÷ 100 | SP = CP + Profit.

⇒ Profit = (5 × 4,500) ÷ 100 = 5 × 45 = 225.

⇒ Selling Price (SP) = 4,500 + 225 = 4,725.

∴ The correct answer is Rs. 4,725.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price (SP) is greater than Cost Price (CP). Profit = SP − CP.

Profit Percentage

It is always calculated on the Cost Price unless stated otherwise. Profit% = (Profit ÷ CP) × 100.

The correct answer is Rule of Law

Key Points

• The principle of Rule of Law asserts that the laws apply equally to all individuals, regardless of their status.
• This principle ensures that no one is above the law, and everyone is subject to the same legal standards.
• It is a fundamental aspect of democratic governance and is essential for maintaining justice and equality in society.
• The Rule of Law promotes transparency, accountability, and fairness within the legal and judicial systems.
• It is a cornerstone of modern legal systems and is crucial for the protection of human rights and the prevention of arbitrary use of power.

Additional Information

• The concept of the Rule of Law dates back to ancient civilizations and has been a central theme in legal and political philosophy.
• It is often contrasted with the "Rule of Man," where decisions are made based on the whims of individuals rather than established laws.
• Modern interpretations of the Rule of Law include principles such as legal certainty, procedural transparency, and the protection of fundamental rights.
• International organizations, such as the United Nations, advocate for the Rule of Law as a means to achieve sustainable development and peace.
• Many countries have enshrined the Rule of Law in their constitutions and legal frameworks to ensure governance based on justice and equality.

The correct answer is 250

Key Points

• 250 is the maximum strength of the Rajya Sabha as per Article 80 of the Constitution of India.
• The Rajya Sabha, also known as the Council of States, is the upper house of India's bicameral Parliament.
• Out of the total 250 members, 238 members are elected by the legislatures of the states and union territories using a single transferable vote system, while the President of India nominates 12 members for their contributions to art, literature, science, and social services.
• The Rajya Sabha is a permanent body and is not subject to dissolution, but one-third of its members retire every two years.
• The Vice President of India is the ex-officio Chairman of the Rajya Sabha.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Parliament of India consists of two houses: the Rajya Sabha (Council of States) and the Lok Sabha (House of the People).
• The Rajya Sabha plays a crucial role in the legislative process, including the review and passage of bills, and serves as a forum for representing the states of India.

According to the given arrangement,

1) I was second to the left of K.

2) I was to the immediate left of G.

3) There were exactly two girls between J and G.

4) K was to the immediate left of H.

Here, we can see that 'I' is sitting to the immediate right of L.

Hence, the correct answer is "I".

Given Statements:

All gifts are letters.

All letters are chats.

All words are gifts.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some chats are words - True (Because, all words are gifts, and all gifts are letters, and all letters are chats, so some chats are words).

II. All gifts are chats - True (Because, all gifts are letters, and all letters are chats, so all gifts are chats).

III. Some words are not letters - False (Because, all words are gifts, and all gifts are letters, so some words are not letters cannot be true).

So, Only conclusions I and II follow.

Hence, the correct answer is "Option 4".

The correct answer is Platelets

Key Points

• Platelets are the blood components primarily responsible for the formation of clots.
• They are small, disc-shaped cell fragments that circulate in the bloodstream and are essential for normal blood clotting.
• When a blood vessel is injured, platelets adhere to the site of injury, aggregate together, and form a plug to help stop the bleeding.
• This process is known as hemostasis, which is crucial for preventing excessive blood loss.

Additional Information

• In addition to platelets, plasma proteins like fibrinogen also play a significant role in the clotting process by forming a mesh that traps blood cells.
• White blood cells are part of the immune system and help fight infections but are not involved in clot formation.
• Red blood cells carry oxygen throughout the body but do not contribute to clotting.
• Maintaining a proper balance of platelets is vital; too few can lead to excessive bleeding, while too many can cause abnormal clotting, leading to conditions such as thrombosis.

Given:

12.999 - 3.998 + 14.002 × 3.998 + 27.008 ÷ 3.001 + 35.999 ÷ 5.998 = ?

Concept used:

Calculation:

⇒ 12.999 - 3.998 + 14.002 × 3.998 + 27.008 ÷ 3.001 + 35.999 ÷ 5.998 = ?

⇒ 13 - 4 + 14 × 4 + 27 ÷ 3 + 36 ÷ 6

⇒ 9 + 56 + 9 + 6

⇒ 80

∴ Option 2 is the correct answer.

The logic followed here is:

Hence, the correct answer is "32Q".

Shortcut Trick

In Compound Interest, if time intervals are equal (0 to 3 years and 3 to 6 years), the amounts are in Geometric Progression (G.P.).

Common ratio (k) = Amount₂ ÷ Amount₁ = 20,070 ÷ 13,380 = 1.5

Principal (P) = Amount₁ ÷ k

P = 13,380 ÷ 1.5 = 8,920

∴ The correct answer is ₹8,920.

Alternate Method

Given:

Amount after 3 years (A₁) = ₹13,380

Amount after 6 years (A₂) = ₹20,070

Formula Used:

A = P(1 + r/100)ⁿ

Calculations:

⇒ 13,380 = P(1 + r/100)³ --- (i)

⇒ 20,070 = P(1 + r/100)⁶ --- (ii)

Divide equation (ii) by (i):

⇒ (1 + r/100)³ = 20,070 ÷ 13,380

⇒ (1 + r/100)³ = 2,007 ÷ 1,338 = 3/2

Substitute the value of (1 + r/100)³ in equation (i):

⇒ 13,380 = P × (3/2)

⇒ P = (13,380 × 2) ÷ 3

⇒ P = 4,460 × 2

⇒ P = 8,920

∴ The correct answer is ₹8,920.

Additional Information

Constant Growth Property

In Compound Interest, the amount increases by a constant factor over equal intervals of time. If A₁ is the amount after t years and A₂ is the amount after 2t years, then P = (A₁)² ÷ A₂.

CI vs SI Difference (2 Years)

The difference (D) between Compound Interest and Simple Interest for 2 years at rate r% is given by D = P(r/100)².

Effective Rate of Interest

When interest is compounded half-yearly, the effective annual rate is [ (1 + r/200)² − 1 ] × 100%.

The correct answer is 6 Ω.

Key Points

• For resistors in series, equivalent resistance adds directly: R_eq = R₁ + R₂.
• Substituting the values: R_eq = 2 Ω + 4 Ω = 6 Ω.
• In a series circuit, the same current flows through each resistor, so adding resistance increases total opposition to current.
• The result 6 Ω corresponds to Option 3, which is larger than each individual resistance, as expected for series connections.

Additional Information

• Resistance (R)
• Measures how strongly a component opposes electric current.
• Unit is the ohm denoted by the Greek letter Ω.
• Depends on material resistivity, length, and cross-sectional area of the conductor.
• Measured using an ohmmeter or via V and I using Ohm’s law.
• Series Connection
• Components are connected end to end, forming a single path for current.
• Current is the same through all elements; voltages divide across them.
• Total or equivalent resistance is the sum of individual resistances.
• Characteristic check: R_eq is always greater than any individual series resistor.
• Equivalent Resistance
• A single resistance that can replace a combination with the same V–I behavior at its terminals.
• For series: R_eq = R₁ + R₂ + R₃ + …
• Contrast with parallel: 1/R_eq = 1/R₁ + 1/R₂ + …, where R_eq is less than the smallest branch.
• Useful for simplifying networks before applying circuit laws.
• Ohm’s Law and Voltage Drops
• Ohm’s law: V = I R, relates voltage, current, and resistance.
• In series, with current I, each drop is V_k = I R_k; the source voltage equals the sum of drops.
• Example check: if a 12 V source drives 2 Ω and 4 Ω in series, R_eq = 6 Ω, so I = 12/6 = 2 A; drops are 4 V and 8 V.
• This verifies both the arithmetic and the distribution of voltages in series circuits.
• Power Considerations
• Power dissipated: P = I²R = V²/R = V I.
• In series, the higher resistance dissipates more power for the same current.
• For the example above at 2 A: P_2Ω = 8 W, P_4Ω = 16 W, total 24 W equals source power.
• Ensures component ratings are not exceeded during operation.

The correct answer is Bauxite

Key Points

• The districts of Koraput, Rayagada, Kalahandi, and Balangir in Odisha are famous for bauxite mining.
• Bauxite is the principal ore of aluminum and is used in the production of various aluminum products.
• These districts have rich bauxite deposits, which are extensively mined and contribute significantly to Odisha's economy.
• The mining activities in these regions have also led to the development of related industries and employment opportunities.

Additional Information

• Odisha is one of the leading states in India in terms of bauxite production.
• Bauxite mining in Odisha is regulated by various state and central government agencies to ensure sustainable mining practices.
• The mined bauxite is processed in nearby aluminum plants to produce alumina and aluminum.
• Efforts are being made to balance the economic benefits of bauxite mining with environmental conservation and the well-being of local communities.

The correct answer is Vacuoles

Key Points

• Vacuoles are membrane-bound organelles found in plant cells.
• They are primarily used to store waste material, nutrients, and other substances that the cell might need to survive.
• In addition to storage, vacuoles also help maintain the cell's turgor pressure, which is essential for maintaining the plant's structure and rigidity.
• Vacuoles can occupy a significant portion of the cell's volume, especially in mature plant cells.

Additional Information

• Plastids are involved in photosynthesis and storage of starches, lipids, and proteins.
• Lysosomes contain digestive enzymes to break down waste materials and cellular debris.
• Nucleus houses the cell's genetic material and controls cellular activities.
• While vacuoles are prominent in plant cells, animal cells may have small, temporary vacuoles.

Shortcut Trick

For two triangles to be similar, they must have the same shape but can have different sizes.

The core mathematical conditions for similarity are:

1. Corresponding angles must be equal (Condition d).
2. Corresponding sides must be in the same ratio or proportional (Condition b).

Condition a refers to isosceles properties, and while c (AA criterion) is sufficient to prove similarity, b and d constitute the primary definition.

∴ The correct answer is both b and d.

Alternate Method

Given: Properties of similar triangles.

Formula Used: Two triangles are similar if they satisfy the AAA (Angle-Angle-Angle) or SSS (Side-Side-Side) similarity criteria.

⇒ In the diagram, ΔABC and ΔEDF are similar because their corresponding angles are equal (both have a 90° angle and same base angles).

⇒ Their corresponding sides are proportional: EF/BC = 6/3 = 2 and FD/CA = 8/4 = 2.