RRB Group D Previous Year Paper (Held on: 29 Aug 2022 Shift 2)

The correct answer is 3.

Key Points:

• The broad family of chemical molecules known as aromatic compounds, which includes benzene, has its origins in this substance.
• In contrast to cyclohexane, benzene only has six hydrogen atoms, which gives the perception that the ring is unsaturated and that each carbon atom is a part of one double bond.
• For benzene, two distinct configurations with alternating single and double bonds around the ring are possible.
• There are 9 single bonds and 3 double bonds between alternate carbon atoms in benzene (C₆H₆).

Additional Information:

• A double bond is formed when the two atoms share two sets of electrons.
• Electron pair sharing is constant.
• A shared pair of electrons constitutes a covalent bond.
• Because the two atoms sharing a double bond share four electrons, it takes more energy to break a double bond than a single one.

Shortcut Trick

Use the algebraic identity (a − b)(a + b) = a² − b².

Identify the base value: 10000.

9991 × 10009 = (10000 − 9) × (10000 + 9)

= 10000² − 9² = 100000000 − 81 = 99999919.

∴ The correct answer is 99,999,919.

Alternate Method

Given: 9991 × 10009

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

⇒ Let a = 10000 and b = 9

⇒ 9991 = 10000 − 9

⇒ 10009 = 10000 + 9

⇒ (10000 − 9) × (10000 + 9)

⇒ (10000)² − (9)²

⇒ 100,000,000 − 81

⇒ 99,999,919

∴ The correct answer is 99,999,919.

Additional Information

Algebraic Identities

Commonly used identities in simplification include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

BODMAS Rule

Always follow the order of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

Unit Digit Check

Multiplying the last digits 1 × 9 gives a unit digit of 9, which helps in eliminating options quickly.

The correct answer is alkene.

Key Points:

• An organic compound collection with the same functional group is referred to as a homologous series.
• A homologous series has members that are all distinct from one another by a group.
• A homologous series' members all have the same chemical characteristics.
• A homologue is a component of any homologous series.
• Butene(C₄H8) and pentene (C₃H₆) are members of the alkene homologous series and differ from one another by a group.

Additional Information:

• Alkenes are a group of unsaturated hydrocarbons (i.e., molecules with solely carbon and hydrogen) that include at least one double bond from carbon to carbon.
• Olefins is a different name for alkenes.
• Due to the double bond, alkenes are more reactive than alkanes.
• Alkenes have a double bond made of carbon and carbon.
• This double bond between carbon atoms alters the physicochemical characteristics of alkenes.
• Alkenes can be found at room temperature in solid, liquid, and gaseous states.

The logic followed here is

Thus, the next term is 32Y

Hence, the correct answer is 'option 4'.

Calculations:

30% of 199.99 + 35.023% of 550.045 = ? - 540.078

⇒ 30.01% of 199.99 + 35.023% of 550.045 = ? - 540.078

⇒ 0.3001 × 199.99 + 0.35023 × 550.045 = ? - 540.078

⇒ 60.016999 + 192.64226035 + 540.078 = ?

⇒ ? = 792.737

792.737 ~ 790

Hence, The Required value is 790.

Given:

Arun starts from his office and drives 5 km towards the east.

He then takes a right turn, drives 4 km,

turns right, and drives 5 km.

He then takes a right turn and drives 3 km and stops at a shop.

According to the given statements we have:

So, He needs to drive in the North direction to reach his office from the shop. 

Hence, the correct answer is 'option 4'.

Shortcut Trick

For a quadratic equation ax² + bx + c = 0, the positive difference between the roots is given by the formula: √D / |a|.

Here, a = 2, b = −7, and c = 5.

Discriminant (D) = b² − 4ac = (−7)² − 4 × 2 × 5 = 49 − 40 = 9.

Positive Difference = √9 / 2 = 3/2.

∴ The correct answer is 3/2.

Alternate Method

Given: The quadratic equation is 2x² − 7x + 5 = 0.

We can find the roots using the factorization method (splitting the middle term):

⇒ 2x² − 2x − 5x + 5 = 0

⇒ 2x(x − 1) − 5(x − 1) = 0

⇒ (2x − 5)(x − 1) = 0

Setting each factor to zero:

⇒ 2x − 5 = 0 ⇒ x = 5/2

⇒ x − 1 = 0 ⇒ x = 1

Let the roots be α = 5/2 and β = 1.

⇒ Positive Difference = |α − β| = |5/2 − 1|

⇒ Difference = 5/2 − 2/2 = 3/2

∴ The correct answer is 3/2.

Additional Information

Sum and Product of Roots

For ax² + bx + c = 0, the sum of roots (α + β) = −b/a and the product of roots (αβ) = c/a.

Nature of Roots

The nature depends on D = b² − 4ac: If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Root Difference Identity

The difference of roots can also be expressed as |α − β| = √[(α + β)² − 4αβ].

Shortcut Trick

Check the sum of digits for each number.

If the sum is divisible by 3, the number is divisible by 3.

Option 1: 6+8+7 = 21 (Divisible by 3)

Option 2: 7+1+3 = 11 (NOT divisible by 3)

∴ The correct answer is 713.

Alternate Method

Given: Numbers 687, 713, 927, 453.

Formula Used: Divisibility rule of 3 states that a number is divisible by 3 if the sum of its digits is a multiple of 3.

Calculations:

⇒ Case 1: 687 → 6 + 8 + 7 = 21. Since 21 ÷ 3 = 7, it is divisible.

⇒ Case 2: 713 → 7 + 1 + 3 = 11. Since 11 is not divisible by 3, 713 is not divisible.

⇒ Case 3: 927 → 9 + 2 + 7 = 18. Since 18 ÷ 3 = 6, it is divisible.

⇒ Case 4: 453 → 4 + 5 + 3 = 12. Since 12 ÷ 3 = 4, it is divisible.

∴ The correct answer is 713.

Additional Information

Divisibility by 9

Similar to 3, a number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 6

A number is divisible by 6 if it is simultaneously divisible by both 2 (even number) and 3 (sum of digits rule).

Prime Numbers

713 is not divisible by 3, but it is a composite number (23 × 31 = 713).

The correct answer is Raj Ghat.

Key Points

• Mohandas Karamchand Gandhi:-
• He is commonly known as Mahatma Gandhi, was born on October 2, and every year on that day, a celebration known as Gandhi Jayanti is held in his honour.
• Mahatma Gandhi, who is revered as the "Father of the Nation," was one of the most important figures in the Indian freedom struggle.
• In New Delhi's Raj Ghat, prayer vigils are held in front of Gandhi's statue as a mark of respect.
• The President and Prime Minister of India are present at Mahatma Gandhi's memorial to pay their respects.
• To recognise his contribution to the nation, October 2 is recognised as a national holiday.

Additional Information

• India Gate
• ​The All-India Military Memorial, formerly known as the India Gate, is a military memorial that can be found next to the Kartavya route on the eastern edge of New Delhi's "ceremonial axis," also known as the duty path.
• It serves as a memorial to the 84,000 British Indian Army personnel who lost their lives between 1914 and 1921 while serving in the Third Anglo-Afghan War, in France, Flanders, Mesopotamia, Persia, East Africa, Gallipoli, and other locations in the Near and Far East.
• Amar Jawan Jyoti
• ​After the Indo-Pakistani War of 1971, an Indian memorial known as Amar Jawan Jyoti was conceptualized, built, and dedicated on January 26, 1972.
• Up until February 2019, when the new National War Monument and its own flame were erected and lighted, it served as India's national war monument.
• Vijay Ghat
• ​Lal Bahadur Shastri was the second Prime Minister of India, and his memorial park is called Vijay Ghat, which translates to "Victory Bank." Its location next to a man-made lake gives the area a pleasant atmosphere, and the well-kept landscaped gardens, lawns, and trees around the area contribute to preserving the tranquilly of the place.

BODMAS table:

Given equation: 2 × 10 ÷ 8 + 6 - 4 = 9

Let's check all the options

1) 2, 4

Apply the changes

⇒ 4 × 10 ÷ 8 + 6 - 2 = 9

Use BODMAS rule

⇒ 4 × 1.25 + 6 - 2 = 9

⇒ 5 + 6 - 2 = 9

⇒ 11 - 2 = 9

⇒ 9 = 9, true

 

2. 6, 8

Apply the changes

⇒ 2 × 10 ÷ 6 + 8 - 4 = 9

Use BODMAS rule

⇒ 2 × 1.66 + 8 - 4 = 9

⇒ 3.33 + 8 - 4 = 9

⇒ 11.33 - 4 = 9

⇒ 7.33 = 9, false

 

3. 9,10

Apply the changes

⇒ 2 × 9 ÷ 8 + 6 - 4 = 10

Use BODMAS rule

⇒ 2 × 1.125 + 6 - 4 = 10

⇒ 2.25 + 6 - 4 = 10

⇒ 8.25 - 4 = 10

⇒ 4.25 = 10, false

 

4. 2, 8

Apply the changes

⇒ 8 × 10 ÷ 2 + 6 - 4 = 9

Use BODMAS rule

⇒ 8 × 5 + 6 - 4 = 9

⇒ 40 + 6 - 4 = 9

⇒ 46 - 4 = 9

⇒ 42 = 9, false

 

So, the numbers 2, 4 are interchanged to get the correct answer. 

Hence, the correct answer is 'option 1'.

Shortcut Trick

Total number of terms n = 7 (odd), so the median is the 4^th term.

Arranging known terms in ascending order: 9, 11, 15, 17, 19, 21.

For x to be the 4^th term, it must satisfy the condition: 15 ≤ x ≤ 17.

Possible integer values for x are 15, 16, or 17.

From the given options, only 16 satisfies this condition.

∴ The correct answer is 16.

Alternate Method

Given: Observations = {9, 11, 15, 17, x, 19, 21}; Median = x; x is an integer.

Formula Used: For n odd terms, Median = (n + 1)/2^th term.

⇒ Total terms n = 7.

⇒ Position of median = (7 + 1) / 2 = 4^th term.

⇒ Arranging the 6 known values: 9 < 11 < 15 < 17 < 19 < 21.

⇒ To make x the 4^th term, it must be placed such that there are 3 terms smaller than or equal to it and 3 terms greater than or equal to it.

⇒ This implies 15 ≤ x ≤ 17.

⇒ Since x is an integer, x ∈ {15, 16, 17}.

⇒ Evaluating options: (1) 18 (False), (2) 16 (True), (3) 13 (False), (4) 14 (False).

∴ The correct answer is 16.

Additional Information

Median for Even Number of Terms

If n is even, the median is the average of the (n/2)^th and (n/2 + 1)^th terms after sorting.

Median vs Mean

The Median is a measure of central tendency that is less affected by outliers compared to the Mean.

Empirical Relationship

For moderately skewed distributions: Mode = 3 × Median − 2 × Mean.

The correct answer is Oxygen.

Key Points:

• During autotrophic nutrition, the organism uses readily available inorganic components including water, mineral salts, and carbohydrates to make its own food in the presence of sunlight.
• All green plants, cyanobacteria-containing microorganisms, red and green algae, and other organisms all utilise an autotrophic mode of nutrition.
• Prerequisites for autotrophic nutrition include the following:
• The existence of sunlight serves as the main source of energy.
• supply of water and carbon dioxide.
• Chlorophyll is a pigment that is present in plant leaves and helps in sun energy absorption.
• The byproducts of the autotrophic mode of nutrition include oxygen and carbohydrates (glucose).

Additional Information:

• All plants have an autotrophic nutrition strategy that allows them to continue making their own nourishment.
• These are the two varieties of autotrophic nutrition:
• Photosynthesis:
• In the presence of sunshine, photosynthesis occurs when carbon dioxide and water are used to create nutrition.
• Plants, animals, microbes, and protists all use it.
• Chemosynthesis:
• A few uncommon autotrophs employ chemical processes rather than light energy to create their own sustenance.
• Living things produce organic substances, typically when there is no sunshine, by obtaining energy from chemical processes.

The correct answer is Bihar.

Key Points

• South Bihar's Ahar pynes, which are regionally endemic floodwater gathering systems, have historically been the main source of irrigation in this area.
• Ahars, reservoirs with embankments on three sides, are constructed at the termini of natural drainage systems like rivulets or man-made structures like Pynes.
• Pynes are rivers' diversion canals that are led off for irrigation and water storage in Ahars.
• When compared to North Bihar, this area receives very little rainfall, hence it is primarily to their credit that paddy agriculture has been made practicable there.
• The district of Gaya was where the system reached its pinnacle of development.

Additional Information

• Rainwater harvesting
• Technology that collects and stores rainwater for human use is known as a rainwater harvesting system, also known as a rainwater collecting system or a rainwater catchment system.
• Rainwater collection systems can be as basic as buckets or as complex as buildings with pumps, tanks, and purification systems.
• The nonpotable water can be filtered for use as drinking water and utilized to irrigate lawns, wash automobiles, wash clothes, and flush toilets.
• In affluent nations, rainwater collection is frequently used to augment the primary supply of water during times of regional water shortages.
• When a drought strikes, it supplies water, can lessen flooding in low-lying areas, and lessens the need for wells, which might allow groundwater levels to be sustained.
• By increasing the number of dried borewells and wells, rainwater collection increases the amount of water that is available during dry seasons.

Shortcut Trick

Sum of reciprocals = (Sum of numbers) ÷ (Product of numbers)

Product of numbers = LCM × HCF = 84 × 6

Sum of reciprocals = 54 ÷ (84 × 6) = 9 ÷ 84 = 3 ÷ 28

∴ The correct answer is 3/28.

Alternate Method

Given:

Sum of two numbers (x + y) = 54

LCM = 84, HCF = 6

Formula: Sum of reciprocals = (1/x) + (1/y) = (x + y) / (xy)

Step 1: Calculate the product of numbers (xy)

⇒ xy = LCM × HCF

⇒ xy = 84 × 6 = 504

Step 2: Calculate the sum of reciprocals

⇒ Sum of reciprocals = 54 / 504

⇒ Divide both by 18: 54 ÷ 18 = 3 and 504 ÷ 18 = 28

⇒ Sum of reciprocals = 3/28

∴ The correct answer is 3/28.

Additional Information

Fundamental Property of HCF and LCM

For any two numbers a and b, Product of numbers = HCF(a, b) × LCM(a, b).

HCF as a Factor

HCF is always a factor of the LCM and also a factor of the sum and difference of the numbers.

Co-prime Representation

Two numbers can be represented as Hx and Hy, where H is the HCF and x, y are co-prime numbers.

The correct answer is real and enlarged.

Key Points:

• The convex lens is a lens that converges rays of light that convey parallel to its principal axis.
• We can have diminished inverted image, small sizes inverted image, enlarged inverted image, enlarged erect image formed by convex lens.
• When an object is placed in front of the convex lens i.e., between 2F1 and F1 its image is formed beyond 2F2 and on the other side of the lens.
• The image produced is real, inverted and enlarged.

Additional Information

• Convex lens is used  in microscopes, telescopes and magnifying glasses to converge all light to a specific object.
• There are different types of convex lens as Plano-convex lens, Concavo-convex lens.
• It is also called as converging lens.

The correct answer is Nichrome.

Key Points:

• Of all the materials, nichrome has the highest resistance.
• Chromium, nickel, and iron are combined to create nichrome.
• These metals are composed of:
• Cr=15%
• Ni=60%
• Fe=25%
• Brightray is another name for Nichrome.
• Due to the extremely high resistance that opposes the flow of electric current and consequently generates a lot of heat, it exhibits the heating effect of electric current.
• Nichrome alloy therefore has the highest resistivity, 1.10× 10-⁶ Ωm.

Additional Information:

• A force that opposes the flow of current is called resistance.
• Resistivity, then, is the particular resistance of a particular conductor (material) of a particular size (length and area of cross-section).
• Additionally called electrical resistivity.
• The symbol (ρ) "rho" is used to represent it.
• The "ohm-meter," which can alternatively be written as Ωm, is the SI unit of resistivity.

Shortcut Trick

The diagonal of the square is equal to the diameter of the circumscribing circle.

Side of square (a) = 7 cm ⇒ Diagonal (d) = a√2 = 7√2 cm.

Circumference of circle = π × diameter = (22/7) × 7√2.

Circumference = 22√2 cm.

∴ The correct answer is 22√2 cm.

Alternate Method

Given: Side of square (a) = 7 cm.

Formula Used: Diameter of circumscribed circle = Diagonal of square = a√2; Circumference = πd.

⇒ Diagonal of square = √2 × 7 = 7√2 cm.

⇒ Diameter (d) of circle = 7√2 cm.

⇒ Circumference = π × d = (22/7) × 7√2.

⇒ Circumference = 22 × √2 = 22√2 cm.

∴ The correct answer is 22√2 cm.

Additional Information

Circumradius of a Square

The radius (R) of a circle circumscribing a square of side 'a' is given by R = (a√2)/2 = a/√2.

Inradius of a Square

The radius (r) of a circle inscribed inside a square of side 'a' is given by r = a/2.

Area of Circle

The area of the circumscribed circle is πR² = π(a/√2)² = πa²/2.

Calculation:

According to the question:

In 2018, 460/390 = 1.179

In 2019, 370/280 = 1.32

In 2020, 350/280 = 1/25

In 2021, 450/350 = 1.28.

So, in 2018 the value per hundred units is minimal.

Given: 

 

Code for: 3 < 5 ! 2

Let's check all the conditions given:

1. 1st and 3rd conditions are not true

2. 2nd Condition is true 

so, we have the code as Φ F K V Φ.

Thus, the code for the given set is Φ F K V Φ.

Hence, the correct answer is 'option 2'.

Given Numbers: '835647'

2 is added to each odd digit and,

3 is subtracted from each even digit.

Here,

The second number from the left is: 5

and the second number from the right is: 1

So, the sum of 5 + 1 = 6

Thus, the sum of the second digits from left and right will be 6.

Hence, the correct answer is 'option 4'.

Statements:

All lamps are lanterns.

All lanterns are torches.

All torches are candles.

Venn diagram:

Conclusions:

(I) Some candles are lamps → Follow → (All lamps are lanterns, all lanterns are torches & all torches are candles which means there is an indirect relation between some candles and lamps, so Some candles are lamps will be follow).

(II) All lanterns are lamps → Does not follow → (It can be possible not definite, so does not follow).

(III) No lantern is a lamp → Does not follow → (It is clearly given that all lamps are lanterns which means there are some lanterns which are definitely lamps thus the conclusion does not follow).

Thus, only conclusion I follow.

Hence, the correct answer is Option 3.

Given:

$\frac{{0.2 \times 0.2 \times 0.2 - 0.02 \times 0.02 \times 0.02}}{{2 \times 2 \times 2}}$

Concept used:

Simple calculation is used here

Calculation:

⇒ $\frac{{0.2 \times 0.2 \times 0.2 - 0.02 \times 0.02 \times 0.02}}{{2 \times 2 \times 2}}$

⇒ $\frac{0.008 - 0.000008}{8}$

⇒ $\frac{8(0.001-0.000001)}{8}$

⇒ 0.001 - 0.000001

⇒ 0.000999

⇒ Hence, The value of above equation is 0.000999

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

Key Points

• Given a conductor, if we connect it to a battery with some iron filings surrounding it we can see when the battery is on, the current starts flowing.
• This flowing current makes the iron fillings arrange themselves in a specific pattern which are like concentric circles indicating magnetic field lines.
• We can find the direction of the magnetic field produced by the right-hand thumb rule.
• The magnitude of this magnetic field is given by: $B={μo*I\over2πr}$.
• As, the distance between the conductor is increases the value of r also increases.

Thus, the given 2 statements are all true.

Additional Information

• Right hand thumb rule is used to find the direction of the magnetic field.
• The rule states that: "If you point the thumb in the direction of the current , the direction of fingers curl the conductor will give you the direction of the magnetic field."

Given: Five students - 1, 2, 3, 4 and 5.

1. 3 is sitting second to the right of 4 and to the immediate left of 5.

2. 3 and 4 are immediate neighbors of 1.

And, 2 will sit in the remaining place.

Now, Options:

1) 1 and 2 are the immediate neighbors of 4 - True.

2) 1 is sitting third to the left of 5 - False.

3) 2 is sitting second to the right of 1 - False.

4) 2 is sitting to the immediate left of 5 - False.

Hence, the correct answer is 'option 1'.

Given: T = S ≥ N = A ≤ U > P < Q

Conclusions:

I. S > Q ⇒ False (S ≥ N = A ≤ U > P < Q, No relation can be established).

II. A < T ⇒ False (T = S ≥ N = A, Gives T ≥ A).

So, neither conclusion I nor II is true.

Hence, the correct answer is 'option 2'.

The correct answer is Sedition.

Key Points

• The state and federal governments are not allowed to accuse anyone of sedition invoking Section 124A of the Indian Penal Code, according to the Supreme Court.
• Until the Center analyses the statute from the British era, the order will be in effect.
• It stated that until the law is reviewed, no new FIRs will be filed, investigations won't be conducted, and no further coercive actions under sedition will be performed.
• It is a cognizable, non-bailable, non-compoundable offence.
• It can be punished by imprisonment of three years or a fine or both.

Additional Information

• Inchoate
• ​Inchoate crimes are actions taken that are intended to be criminal acts or that amount to indirect participation in illegal acts.
• Although such a deed might not be a criminal in and of itself, it is done to further or advance a crime.
• Bankruptcy
• ​Through the legal process of bankruptcy, individuals or other entities that cannot pay their creditors back can seek partial or complete relief from their debts.
• Bankruptcy is typically imposed by a court order frequently requested by the debtor.
• A person who is insolvent may have more than one legal status; consequently, the term "bankruptcy" is not a synonym for insolvency.
• Homicide
• ​When someone kills another person, it is called homicide.
• A homicide merely needs to be a voluntary action or omission that results in the death of another person; therefore, it can result from careless, irresponsible, or accidental behaviour even when no malice was intended.

Shortcut Trick

Combine the first two discounts: 4 + 5 − (4 × 5)/100 = 9 − 0.2 = 8.8%

Combine with the third: 8.8 + 14 − (8.8 × 14)/100 = 22.8 − 1.232 = 21.568%

Rounding to two decimal places, we get 21.57%.

∴ The correct answer is 21.57%.

Alternate Method

Given: Successive discounts are 4%, 5%, and 14%.

Formula Used: Equivalent Discount = [1 − (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100)] × 100%

⇒ Let Marked Price (MP) = 100

⇒ After 1st discount (4%): 100 − 4% of 100 = 96

⇒ After 2nd discount (5%): 96 − 5% of 96 = 96 − 4.8 = 91.2

⇒ After 3rd discount (14%): 91.2 − 14% of 91.2 = 91.2 − 12.768 = 78.432

⇒ Total Discount = MP − Final SP = 100 − 78.432 = 21.568%

⇒ Rounded to two decimal places = 21.57%

∴ The correct answer is 21.57%.

Additional Information

Successive Discount Formula

For two successive discounts x% and y%, the single equivalent discount is (x + y − xy/100)%.

Relationship between SP and MP

The Selling Price (SP) can be calculated as SP = MP × (100 − d₁)/100 × (100 − d₂)/100...

Net Percentage Change

A successive discount is a series of percentage decreases applied to the updated value at each step.

Shortcut Trick

In direct proportion, the ratio of quantity to cost remains constant.

Ratio of notebooks (n) to their cost (1,680) = Ratio of notebooks (m) to their cost (x).

⇒ n / 1680 = m / x

∴ The correct answer is (m)/(x) = n/1680.

Alternate Method

Given:

Cost of n notebooks = ₹ 1,680

Cost of m notebooks = ₹ x

Calculations:

⇒ Unitary Method: Cost of 1 notebook = 1,680 / n

⇒ Cost of m notebooks (x) = m × (1,680 / n)

⇒ x = (m × 1,680) / n

⇒ By rearranging the terms to match the options:

⇒ x / m = 1,680 / n

⇒ Taking reciprocal on both sides:

⇒ m / x = n / 1,680

∴ The correct answer is (m)/(x) = n/1680.

Additional Information

Direct Proportion

Two quantities x and y are in direct proportion if the ratio x/y remains constant (k). If x increases, y also increases.

Inverse Proportion

Two quantities x and y are in inverse proportion if the product x × y remains constant (k). If x increases, y decreases.

Unitary Method

A technique where you first find the value of a single unit and then multiply by the required number of units.

Given: 38 students in a class standing in a straight row facing north.

Ashok is 16th from the right end and Aruna is 19th from the left end.

So, the number of students standing between Ashok and Aruna is:

= 38 - (16 + 19)

= 38 - 35

= 3 Students.

So, there are three students between Ashok and Aruna in the class.

Hence, the correct answer is 'option 3'.

Shortcut Trick

Expand the expression using the BODMAS rule: x(2x − 5) + 6(x² − 4) + 18.

Step 1: (2x² − 5x) + (6x² − 24) + 18.

Step 2: Combine like terms (2x² + 6x²) − 5x + (18 − 24) ⇒ 8x² − 5x − 6.

∴ The correct answer is 8x² − 5x − 6.

Alternate Method

Given:

The algebraic expression: x(2x − 5) + 6(x² − 4) + 18

Formula Used:

Distributive Property: a(b + c) = ab + ac

Calculations:

⇒ x × 2x − x × 5 + 6 × x² − 6 × 4 + 18

⇒ 2x² − 5x + 6x² − 24 + 18

⇒ (2x² + 6x²) − 5x + (18 − 24)

⇒ 8x² − 5x − 6

∴ The correct answer is 8x² − 5x − 6.

Additional Information

Distributive Law

The distributive law allows for the expansion of brackets by multiplying the outer term with every term inside: a(b + c) = ab + ac.

Like Terms

Terms that have the same variable raised to the same power (e.g., 2x² and 6x²) are called like terms and can be simplified together.

BODMAS Rule

Simplification always follows the BODMAS order: Brackets, Orders (Exponents), Division, Multiplication, Addition, and Subtraction.

The correct answer is real and inverted.

Given:

Power of the lens is 4.0 D, object distance is 30cm.

Formula:

$P={1\over f}$

Calculations:

As, $P={1\over f}$ we have:

$f={1\over P}={1\over 4}=0.25m$

As focal length is positive and object distance is negative.

Thus, the lens used here is convex lens.

Image formed convex lens it is always real and inverted.

Concept used:

Study the graph

Calculation:

⇒ The average of Q in 2020 and 2021 = $\frac{29.5+22.5}{2}$ = 26

⇒ The average of P in 2020 and 2021 = $\frac{35+20}{2}$ = 27.5

⇒ The average of R = $\frac{28+20}{2}$ = 24

⇒ The average of S = $\frac{30+36}{2}$ = 28

⇒ The average of T = $\frac{32+20}{2}$ = 26

⇒ Hence, The T has same average as Q

The correct answer is A yellow precipitate of lead iodide will be formed.

Key Points:

• A yellowish solid precipitates when a solution of potassium iodide is added to a solution of lead nitrate that has been taken in a test tube.
• 2KI (aq.) + Pb(NO₃)₂ (aq.) → 2KNO₃ (aq.) + PbI₂(s).
• Lead iodide is this opalescent solid.
• Lead iodide and potassium nitrate are created together.
• It's double displacement reaction.

Additional Information:

• When the reactant ions shift around to produce new products, chemical processes known as double displacement reactions take place.
• A double displacement procedure frequently results in the formation of precipitates.
• Chemical bonds between the reactants might be ionic or covalent.
• Other names for a double displacement process include double replacement, salt metathesis, and double decomposition.

Given: (Left) & X Y # F K & 3 T & * 8 W ¥ % ^ D U G $ϵ ϕ$ 5 S @ J (Right)

Numbers immediately preceded by a symbol and immediately followed by a consonant:

The pattern should be:- Symbol - Number - Consonant

Now,

(Left) & X Y # F K & 3 T & *** 8 W** ¥ % ^ D U G $ ϵ ϕ $ 5 S @ J (Right)

Thus there are 3 such numbers that are immediately preceded by a symbol and immediately followed by a consonant.

The pairs are: & 3 T,  * 8 W,  $ 5 S

Hence, the correct answer is 'option 1'.

The correct answer is Both statements are correct.

Key Points:

• The atomic masses of the elements were used by Newlands to arrange them.
• He noticed that every eighth element has the same attribute when he grouped the elements in order of their atomic masses.
• After every 8 elements, the same attributes reappear, giving the law its name, the Newlands law of octave.
• Then, known elements including hydrogen, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, sodium, magnesium, aluminium, silicon, phosphorus, sulphur, and chlorine were placed in order of increasing atomic mass.
• This indicates that lithium and sodium, the eighth element relative to lithium, have features in common and so on.
• He believed that there were only 56 elements in nature and that no new elements will ever be found.
• Later he was proved wrong.

Additional Information:

• British chemist John Alexander Reina Newlands, who researched on the periodicity of elements, was born on November 26, 1837, and died on July 29, 1898.
• The first periodic table of chemical elements organised according to their respective atomic masses was created by Newlands and published in Chemical News in February 1863.
• In 1865, Johann Wolfgang Döbereiner released his "Law of Octaves," which declared that "every given element will display analogous behaviour to the eighth element following it in the table," as a continuation of his work with triads and Jean-Baptiste Dumas' families of related components.

Shortcut Trick Identify the range: 902 = 8100 and 1002 = 10000. Since 8100 < 9604 < 10000, the square root lies between 90 and 100. The unit digit of 9604 is 4, so the square root must end in either 2 or 8. Check 982: 98 is 2 less than 100, so 982 = (100−2)2 = 10000 − 400 + 4 = 9604. ∴ The correct answer is 98.

Alternate Method Given: Number = 9604 Method: Prime Factorisation ⇒ 9604 = 2 × 4802 ⇒ 9604 = 2 × 2 × 2401 ⇒ 9604 = 2 × 2 × 7 × 343 ⇒ 9604 = 2 × 2 × 7 × 7 × 49 ⇒ 9604 = 2 × 2 × 7 × 7 × 7 × 7 ⇒ √9604 = √(22 × 72 × 72) ⇒ √9604 = 2 × 7 × 7 ⇒ √9604 = 98 ∴ The correct answer is 98.

Additional Information Perfect Square Unit Digits A perfect square ending in 4 must have a square root ending in either 2 or 8 because 22=4 and 82=64. Estimation Method For any number N, if x2 < N < (x+1)2, the square root lies between x and x+1. This narrows down the tens digit instantly. Square of numbers ending in 5 To find (n5)2, the result is always [n×(n+1)] followed by 25. Example: 952 = 9×10 and 25 = 9025.

Shortcut Trick

Remaining work in terms of man-days = 7 men × (12 − 5) days = 49 man-days.

Remaining men = 7 − 3 = 4 men.

Days required = 49 ÷ 4 = 12 1/4 days.

∴ The correct answer is 12 1/4 days.

Alternate Method

Given:

Total men (M₁) = 7, Total days (D₁) = 12

Days worked = 5, Men remaining (M₂) = 7 − 3 = 4

Formula Used:

Total Work = Men × Days

M₁ × D₁ = M₁ × d₁ + M₂ × d₂

Calculations:

⇒ Total work = 7 × 12 = 84 units

⇒ Work done in 5 days = 7 × 5 = 35 units

⇒ Remaining work = 84 − 35 = 49 units

⇒ Time taken by 4 men = 49 ÷ 4

⇒ Time = 12 1/4 days

∴ The correct answer is 12 1/4 days.

Additional Information

Chain Rule

The relationship between men, days, and work is given by (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂.

Work and Efficiency

Work is directly proportional to the number of men and time, while time is inversely proportional to the number of men for constant work.

The correct answer is a rectangular hyperbola.

Key Points

• Average fixed cost
• The fixed cost that stays the same no matter how many goods and services a company produces are called the average fixed cost (AFC).
• In a nutshell, the average fixed cost (AFC) is determined by dividing the total fixed cost by the output level and representing the fixed cost per unit.
• The average fixed cost is just for the short term because no expense is fixed for an extended period of time.
• The average fixed cost per unit of output lowers as manufacturing units rise.
• The average cost per unit also rises as the company produces fewer units.
• AFC = Total fixed cost/Output (Q)
• The typically fixed-cost AFC curve resembles a rectangle-shaped hyperbola.** It occurs as a result of the fixed cost being divided by rising output.**
• **As a result, the AFC curve slopes downward and is a rectangular hyperbola, meaning that **the area beneath the curve is constant throughout.
• Asymptotes or axes on a rectangular hyperbola are parallel to one another.
• The conjugate axis and transverse axes have lengths that are identical.

Additional Information

• Inverted V-shaped
• ​The lateral umbilical ligament sign, commonly known as the inverted "V" sign, is a symptom of pneumoperitoneum that appears as an inverted "V" shape in the pelvis on supine abdominal radiographs.
• The lateral umbilical ligaments are symbolised by free gas. The inferior epigastric vessels are located in the lateral umbilical ligaments in adults as opposed to neonates, who have umbilical arteries.
• ​Horizontal line
• ​A straight line that is parallel to the horizon or the ground is referred to as a horizontal line. There is no slope.
• It is a straight line that is drawn from right to left or left to right in the coordinate plane, parallel to the x-axis. In other words, a horizontal line is a straight line that has an intercept solely on the y-axis and not on the x-axis.

Shortcut Trick

Apply the Complementary Angle conversion: sin θ = cos (90° − θ) and cos θ = sin (90° − θ).

For sin 58° → cos (90° − 58°) = cos 32°.

For cos 82° → sin (90° − 82°) = sin 8°.

Summing both results gives cos 32° + sin 8°, where both angles are between 0° and 45°.

∴ The correct answer is cos 32° + sin 8°.

Alternate Method

Given: sin 58° + cos 82°

Formula Used:

1. sin θ = cos (90° − θ)

2. cos θ = sin (90° − θ)

Calculations:

⇒ sin 58° = sin (90° − 32°)

⇒ Using formula (1): sin (90° − 32°) = cos 32°

⇒ cos 82° = cos (90° − 8°)

⇒ Using formula (2): cos (90° − 8°) = sin 8°

⇒ Therefore, sin 58° + cos 82° = cos 32° + sin 8°

∴ The correct answer is cos 32° + sin 8°.

Additional Information

Complementary Angle Identities

For any angle θ, sin (90° − θ) = cos θ, tan (90° − θ) = cot θ, and sec (90° − θ) = cosec θ.

Trigonometric Range Conversion

To express ratios for angles > 45° into the range 0°-45°, always subtract the given angle from 90° and change the ratio to its co-function.

Logic: 2 × (First Number + Third Number) = Second Number

Given:

(14, 60, 16) 

→ 2 × (14 + 16)

⇒ 2 × 30 = 60.

(25, 80, 15) 

→ 2 × (25 + 15)

⇒ 2 × 40 = 80.

Let's check all the options as

1) (21, 120, 15) 

→ 2 × (21 + 15)

⇒ 2 × 36 = 72 $\ne$ 120

2) (20, 30, 40) 

→ 2 × (20 + 40)

⇒ 2 × 60 = 120 $\ne$ 30

3) (19, 80, 21) 

→ 2 × (19 + 21)

⇒ 2 × 40 = 80

4) (15, 45, 30) 

→ 2 × (15 + 30)

⇒ 2 × 45 = 90 $\ne$ 45

Thus, the set of numbers (19, 80, 21) follows the same pattern.

Hence, the correct answer is 'option 3'.

The correct answer is Bengaluru.

Key Points

• At the Indian Institute of Science (IISc) in Bengaluru, an Artificial Intelligence and Robotics Technology Park (ARTPARK) with seed funding of Rs 230 crore was inaugurated in March 2022.
• The Karnataka government would be responsible for the remaining Rs 230 crore, while the Center would cover Rs 170 crore.
• It would seek to develop a highly innovative ecosystem for AI and robotics in the nation.

Additional Information

• ARTPARK wants to connect the disconnected through cutting-edge technology.
• By carrying out ambitious mission-mode R&D initiatives in healthcare, education, mobility, infrastructure, agriculture, retail, and cyber-security that target solving problems specific to India**, the ARTPARK seeks to harness discoveries to have a positive social impact.**
• By 2030, it's anticipated that AI would reach $15.7 trillion.

The correct answer is Using tin foil, plastic wraps, paper towels, and plastic zip bags.

Key Points

• Decreasing and adopting a more waste-free lifestyle is one of the most crucial things we can do to help the environment.
• Waste is a problem on many different levels.
• The fact that it pollutes the environment and depletes our planet's limited resources are perhaps the two most glaring.
• Using things like tin foil, plastic wrap, paper towels, and plastic zip bags results in more waste.
• Ways to reduce waste:
• For refreshments on the go, use a reusable bottle or cup.
• Use reusable shopping bags for more than just groceries.
• Recycle and make smart purchases.
• Avoid serving food and beverages in single-use containers.
• Buy used products and donate your old ones.
• Buy in bulk and at local farmers' markets to reduce packaging.
• Reduce your consumption of paper for periodicals, receipts, and mail.

Additional Information

• 4R of Recycling
• REDUCE: This refers to utilizing environmental resources in a sustainable manner and avoiding waste. For instance, taking a bath with a bucket of water rather than a shower.
• REUSE: This indicates that we can put anything to multiple uses. Consider repurposing a polythene bag for several uses.
• RECYCLE: This refers to the processing and possible conversion of materials into other products that allow for their reuse. Paper, for instance, is recycled.
• RECOVER: This indicates that a safe and environmentally friendly substitute should be employed in its place. Using a clothes bag as opposed to a plastic bag is one illustration.

The correct answer is Insurance.

Key Points

• The ongoing costs associated with maintaining a business are known as overhead or overhead charges in the business sector. Unlike operating expenses like raw materials and labour, overheads cannot easily be linked to or recognised with any one revenue unit.
• All costs on the income statement other than direct labour, direct supplies, and direct expenses are referred to as overhead expenses.
• Accounting fees, advertising, insurance, interest, legal fees, labour costs, rent, repairs, supplies, taxes, phone bills, travel expenses, and utilities are examples of overhead costs.
• Indirect expenses and fixed costs, two accounting concepts, are frequently linked to overheads.

Additional Information

• Labour
• A labourer (or labourer) is a person employed in the construction industry who does manual labour. Workers are members of a working-class who only own their labour as a significant tangible possession.

Raw materials ​

• Materials or substances used in the initial stages of producing or manufacturing items are known as raw materials.
• On commodity exchanges around the world, raw materials are commodities that are purchased and sold. Because raw materials are production factors, businesses trade them on the factor market.
• Consumable manufacturing supplies
• ​Consumable materials include things like solder that are used up during production but do not include things like the packaging for finished goods, labels, skids, pallets, or shipping packing materials.

The logic followed in the given series is:

Logic: √(First term ÷ 4) = Second Number

Now we apply the pattern on the given series:

For, 16 ∶ 2

 ⇒ $\sqrt{16 \div 4} = \sqrt{4}$ = 2

For, 36 ∶ 3

 ⇒ $\sqrt{36 \div 4} = \sqrt{9}$ = 3

Similarly, for 64 ∶ ?

 ⇒ $\sqrt{64 \div 4} = \sqrt{16}$ = 4

Thus, the next term will be 4.

Hence, the correct answer is Option 2.

The correct answer is Continental climate.

Key Points

• There is frequently a sizable annual temperature range in continental climates (warm summers and cold winters).
• They typically occur in big landmasses at intermediate latitudes (40 to 55 north), when prevailing winds blow overland and bring some precipitation, and where seas do not act as a temperature regulator.
• Because of the substantial landmasses present there, continental climates are primarily found in the Northern Hemisphere.
• Precipitation in continental regions typically occurs in moderate amounts, mainly during the warmer months.

Additional Information

• Temperature Climate
• ​Geographically, the middle latitudes (23.5° to 66.5° N/S of Equator), which are between the tropics and the polar regions of Earth, are where moderate climates on Earth are found.
• Compared to tropical climates, where such fluctuations are frequently minimal and typically simply involve changes in precipitation, these zones typically have greater temperature ranges throughout the year and more pronounced seasonal changes.
• Extreme Climate
• ​Unexpected, uncommon, severe, or out-of-season weather as well as the weather at the extremes of the historical distribution—the range that has been experienced in the past—are examples of extreme weather or extreme climate occurrences.
• Extreme events are frequently characterized as occurring in the top ten percent of all observed occurrences based on a location's historical meteorological data.
• The three main categories of extreme weather are tropical cyclones, heat waves, and cold waves.
• Maritime Climate
• ​The humid temperate climate sub-type Cfb known as an oceanic climate also referred to as a marine climate, is typical of west coasts in higher middle latitudes of continents.
• It is characterized by generally cool summers and mild winters (for their latitude), with a relatively narrow annual temperature range and few temperature extremes.

The correct answer is -1.

Given:

Object distance u is -40cm and focal length is -20cm as it is converging.

To find:

Magnification of the image produced

Formula:

$m=-{v\over u}$

${1\over f}={1\over v}+{1\over u}$

Calculations:

As, the mirror formula

${1\over f}={1\over v}+{1\over u}$

${1\over -20}={1\over v}+{1\over -40}$

${1\over v}={1\over -20}-{1\over -40}$

${1\over v}={-2 + 1\over 40}={1\over -40}$

$v= - 40cm$

Therefore, the magnification produced is

$m=-{v\over u}=-{-40\over -40}=-1$

Thus, the magnification produced is -1.

Shortcut Trick

The net effective rate for 3% for 3 years is calculated as: 3 + 3 + 3 + (3×3 + 3×3 + 3×3)/100 + (3×3×3)/10000 = 9.2727%.

Compound Interest = Principal × Net Effective Rate

⇒ CI = 12,500 × 9.2727% = 125 × 9.2727 = 1159.0875

Rounding to the nearest rupee, we get ₹1,159.

∴ The correct answer is ₹1,159.

Alternate Method

Given:

Principal (P) = ₹12,500

Rate (R) = 3% per annum

Time (T) = 3 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Compound Interest (CI) = A − P

Calculations:

⇒ A = 12,500 × (1 + 3/100)³

⇒ A = 12,500 × (1.03)³

⇒ A = 12,500 × (1.03 × 1.03 × 1.03)

⇒ A = 12,500 × 1.092727

⇒ A = 13,659.0875

⇒ CI = A − P

⇒ CI = 13,659.0875 − 12,500

⇒ CI = 1,159.0875

⇒ CI ≈ ₹1,159 (Correct to the nearest rupee)

∴ The correct answer is ₹1,159.

Additional Information

Compound Interest Properties

In Compound Interest, the interest from the previous year is added to the principal to calculate the interest for the next period, leading to exponential growth.

Difference between CI and SI

For 2 years: CI − SI = P(R/100)². For 3 years: CI − SI = P(R/100)² × (3 + R/100).

Effective Rate of Interest

The effective rate for 3 years can be found using the successive percentage change formula: a + b + (ab/100) applied twice.

From the given information:

Dev walks 23 m towards the west from his hostel gate. He takes a left turn and walks 14 m.

Then he takes a right turn and walks 63 m. Then he takes a left turn and walks 32 m.

[He takes a left turn again and walks 86 m. Again, he takes a left turn and walks 16 m to reach a canteen.

 

So, the Distance from hostel to canteen = 14m + 32 m - 16m = 46m - 16m = 30m

Thus, the canteen is 30m south of Dev's hostel gate.

Hence, the correct answer is "Option 1".

The correct answer is 1851.

Key Points

• The "Indian Tolls Act, 1851," as it is called, was passed on July 4th of that year. Governments are now permitted to charge tolls on these routes and specific bridges thanks to the passage of the law.
• The legislation covers the areas that, as of July 4, 1851, were under the council-mandated rule of the Governor and Presidency of Fort William of the Bengal region and the Governor of Fort St. George's presidency.
• Any road or bridge that has been built or will be repaired at the government's expense may be subject to tolls at whatever rates the government deems appropriate.
• The government may also assign responsibility for managing the toll collection to whomever it deems appropriate, and any individuals working in this capacity will be subject to the same obligations as those who work in the actual toll collection.

Additional Information

• Indian Tolls Act 1901:
• The Indian Tolls (Army & Air Force) Act, 1901 is a law that was passed by the Indian Parliament and put forth by the Ministry of Defence to address the exemption of toll charges for regular armed forces, including all family members of Indian Armed Forces extending from Indian Army to Central Armed Police Forces, where applicable.
• The requirements of sections 3 and 4 were later removed from the act by the Ministry of Road Transport and Highways, and those only "on duty" would be entitled to the exemption, which does not apply to the retired individual.
• This was done in response to new legislation and policy formulation.

The correct answer is From the air spaces in between the soil particles.

Key Points:

• In addition to the leaves, the root system also contributes to plant respiration.
• The soil's tiny air pockets can provide the roots with oxygen to breathe.
• Oxygen (O₂) from the soil pores diffuses into the root hairs of root systems, where it is carried to all regions of the roots.
• During respiration, plant roots utilize photosynthates for a variety of purposes, including nutrition intake, tissue maintenance, and growth.
• The created carbon dioxide (CO₂) is subsequently released into the soil, where it diffuses into the atmosphere through soil pores.

Additional Information:

• Plant cells are constantly utilising oxygen, which is required for plant survival.
• Plant cells occasionally need to consume more oxygen from the air than they produce on their own.
• Like animals, plants also breathe.
• Breathing is not the only definition of respiration.
• All living organisms go through this procedure to release energy for utilisation in their cells.
• In plants, respiration is similar to photosynthesis done backwards; rather than storing energy by producing sugars and releasing oxygen, cells instead release energy for their own needs by dissolving carbohydrates and consuming oxygen.

Shortcut Trick

For problems involving shadows and similar triangles, use the direct formula:

Shadow Length = (Boy height × Distance from post) ÷ (Post height − Boy height)

⇒ Shadow = (1.5 × 3) ÷ (4 − 1.5)

⇒ Shadow = 4.5 ÷ 2.5 = 1.8 m

∴ The correct answer is 1.8 m.

Alternate Method

Given:

Height of the light post (H) = 4 m

Height of the boy (h) = 1.5 m

Distance of the boy from the post (d) = 3 m

By the property of Similar Triangles, the ratio of the height to the total base is constant:

⇒ (Height of Post) ÷ (Distance + Shadow) = (Height of Boy) ÷ Shadow

Let the length of the shadow be s.

⇒ 4 ÷ (3 + s) = 1.5 ÷ s

⇒ 4 × s = 1.5 × (3 + s)

⇒ 4s = 4.5 + 1.5s

⇒ 4s − 1.5s = 4.5

⇒ 2.5s = 4.5

⇒ s = 4.5 ÷ 2.5

⇒ s = 1.8 m

Comparing this result with the given options, we find that Option (2) matches the calculated value.

∴ The correct answer is 1.8 m.

Additional Information

Properties of Similar Triangles

Two triangles are similar if their corresponding angles are equal; consequently, the ratios of their corresponding sides are equal (Side-Side-Side similarity).

Angle of Elevation

In shadow problems, the angle of elevation of the light source is the same for all objects at the same time, creating similar right-angled triangles.

Shadow Inversion Rule

For a fixed object height, as the object moves closer to the light source, the shadow length increases, and as it moves away, the shadow decreases.

The correct answer is The Prohibition of Child Marriage (Amendment) Bill, 2021.

Key Points

• The National Family Health Survey 2019–21 reports that 23% of women get married before turning 18 years old.
• On December 21, 2021, the Prohibition of Child Marriage Amendment Bill was introduced.
• The Prohibition of Child Marriage Act of 2006 is amended, raising the legal age of consent for girls to marry from 18 to 21. The Hindu Marriage Act, the Special Marriage Act, and other relevant marriage laws were also altered by the bill.
• The age requirement for marriage is 21, which is older than the requirement for becoming a majority (18 years).
• Marriage between consenting adults is now recognised as a basic right by the Supreme Court.

Additional Information

• The Farm Laws Repeal Bill, 2021
• ​On November 29, 2021, Mr Narendra Singh Tomar, the Minister of Agriculture and Farmers' Welfare, introduced the Farm Laws Repeal Bill, 2021 in the Lok Sabha.
• Three farm laws passed by Parliament in September 2020 are repealed by the Bill. These include:
• (i) Farmers (Empowerment and Protection) Price Assurance and Farm Services Act.
  

(ii) the Farmers' Produce Trade and Commerce Act (Promotion and Facilitation).

• (iii) the Essential Commodities (Amendment) Act, all of which are slated to take effect in 2020.
• Amendment to the Narcotic Drugs and Psychotropic Substances Act of 2021
• ​On December 6, 2021, the Narcotic Drugs and Psychotropic Substances (Amendment) Bill, 2021, was presented to Lok Sabha.
• The Narcotic Drugs and Psychotropic Substances (Amendment) Ordinance, 2021 is intended to be replaced by this one.
• The Narcotic Drugs and Psychotropic Substances Act, of 1985 is amended by the bill to fix a drafting mistake.
• The Surrogacy (Regulation) Bill, 2021
• If a medical condition dictates it, a couple, defined as a woman and man who are legally married, or a woman who is a widow or a divorcee between the ages of 35 and 45, may choose to utilise a surrogate.

Given: Nine people, 1 to 9, are sitting in a straight row, facing south.

1. 8 sits in the middle of the row and his immediate left and right neighbors are 5 and 1, respectively.

2) 3 sits between 7 and 4. 1 and 7 are immediate neighbors.

3. 9 sits at one of the extreme ends and his immediate right neighbor is 2.

4. Only five people are there between 2 and 3.

Thus the final arrangement is:

Thus, if 7 and 6 exchange their positions then 2 will be the immediate left neighbor of 7.

Hence, the correct answer is 'option 4'.

The logic followed here used is:

Thus, the next number is 192.

Hence, the correct answer is 'option 1'.

The correct answer is "The direction of the force depends on the direction of the magnetic field in which the conductor is placed".

Key Points

• A push or a pull of an object is called the force.
• Force can make a body move at rest or accelerate the object's speed.
• Force can change the direction of a moving body.
• So, the direction of the force depends on the direction of the magnetic field in which a conductor is placed.

Additional Information

• Force is of two types:
• Contact force
• Non-contact force
• Contact force is a force that acts on a body either directly or through a medium.
• Examples: Muscular force, Mechanical force, Frictional force.
• Non-contact force is a force that makes contact without direct contact.
• Examples: Gravitational force, Electrostatic force, Magnetic force.

Given terms: (Left) E # R & H & @ J & M N # B & V & & D # P @ W % & Q & A % & # E & (Right)

Now, the letters immediately preceded and immediately followed by the symbol '&'.

Here, there are three pairs: & H &, & V &, & Q &.

Hence, the correct answer is "Option 4".

The correct answer is P and S.

Key Points

Valency is defined as the combining capacity of an atom. The number of bonds that an atom can form as part of a compound is expressed by the valency of the element. Here, the electronic configuration determines the valency of a particular atom. Thus, the electronic configuration of the given atoms is:

P (Atomic number 2) -> 2 (Helium, Noble gas, Valency = 0) Q (Atomic number 6) -> 2, 4 (Valency = 4) R (Atomic number 13) -> 2, 8, 3 (Valency = 3) S (Atomic number 18) -> 2, 8, 8 (Argon, Noble gas, Valency = 0)

Therefore, the atoms P and S have the same valency i.e., 0, as both are noble gases with completely filled outermost shells.

Additional Information

Valency also indicates the number of atoms with which a particular atom can form a covalent bond with the other atom. This concept is very important as it determines how strong the bond can be. It also helps to find how atoms join together to form molecules.

The correct answer Both the statements are true.

Key Points:

• Plaster of Paris's characteristics:
• When wetted with water or exposed to a mixture and left to dry, it solidifies into a hard mass.
• The substance is a fine white powder.
• Applications:
• In order to assure proper healing, it is used in hospitals to fix broken bones.
• Due to its setting property, it is used to make toys, decorative items, inexpensive ornaments, cosmetics, blackboard chalk, and statue casts.
• It serves as a fire-retardant substance.
• It is used in chemistry labs to close air gaps in equipment when an airtight arrangement is necessary.

Additional Information:

• Calcium sulphate hemihydrate is what makes plaster of Paris (calcium sulphate half-hydrate).
• CaSO₄.12H₂O is the plaster of Paris's chemical formula.
• Gypsum (CaSO4.2H2O) is heated to a temperature of 100 °C to prepare it.
• Gypsum loses three-fourths of its water of crystallization when heated to a temperature of 100°C (373K), creating Plaster of Paris.

The logic followed here is:

Thus, the next term is 197.

Hence, the correct answer is 'option 2'.

The correct answer is Lynda Kom.

Key Points

• The third SAFF U-18 Women's Football Championship has been crowned as India's victory.
• The JRD Tata Sports Complex in Jamshedpur hosted the 2022 edition of the international football tournament for women's under-18 national teams.
• Lynda Kom, who scored a total of five goals, was the most valuable player and top goal scorer in the competition.

Additional Information

• Purnima Kumari
• ​One of the six girls from the state, Purnima Kumari (17), who will represent India in the U-17 FIFA World Cup in Bhubaneswar, has overcome several challenges, including extreme poverty, to pursue her love.
• Her family members reside in a mud home in Simdega district's Jambahar village, which is part of the Thethaitangar block. While Purnima's mother Chaiti Devi passed away in 2006 from probable meningitis when she was just one and a half years old, Purnima's father, Jitu Manjhi (70), has been bedridden since 2018.
• Ritu Rani
• ​Ritu Rani, an international football player for both the India women's team and Gokulam Kerala, was born on May 25, 1997. She plays as a defender.
• Ritu presently plays for Gokulam Kerala in India after having previously played for FC Alakhpura.
• In 2017, Ritu was selected to play for the national squad in a series of exhibition games in Malaysia. During the 2019 Cotif Women's Tournament, she earned a senior-level cap for India.

The correct answer is Sanjeev Sanyal.

Key Points

• Sanjeev Sanyal
• Sanjeev Sanyal has been appointed as a full-time member of the Economic Advisory Council to the Prime Minister of India in February 2022.
• An economist and popular historian from India is named Sanjeev Sanyal. He has assisted in the creation of six versions of the Economic Survey of India since its inception in 2017,
• He is a member of the Economic Advisory Council to the Prime Minister of India. Several works on Indian history that Sanyal has published have received mixed reviews.
• Sanyal champions the application of the Complex Adaptive Systems paradigm to economic concerns and hails the 1991 liberalisation reforms as the beginning of the Indian Renaissance
• Sanyal asserts that Ashoka did not become a Buddhist because of sorrow for the Kalinga War but rather as a result of political pressure from the Jains.
• Sanyal emphasises the urgent necessity for a post-socialist understanding of history and places the blame for Ashoka's elevation to the status of "great king" squarely on the Nehruvian ambition.
• Sanyal's work on urban challenges earned him an Eisenhower Fellowship in 2007. He received the World Economic Forum's Young Global Leader award in 2010.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by (100 − Discount%) : (100 + Profit%).

CP : MP = (100 − 5) : (100 + 90) = 95 : 190.

Simplifying the ratio, CP : MP = 1 : 2.

Given CP = 1 unit = Rs. 210.

Therefore, MP = 2 units = 2 × 210 = Rs. 420.

∴ The correct answer is Rs. 420.

Alternate Method

Given → Cost Price (CP) = Rs. 210, Gain% = 90%, Discount% = 5%. Formulas: SP = CP × (100 + Gain%) ÷ 100 | MP = (SP × 100) ÷ (100 − Discount%).

⇒ Calculate Selling Price (SP): SP = 210 × (100 + 90) ÷ 100. ⇒ SP = 210 × 190 ÷ 100 = 21 × 19 = Rs. 399. ⇒ Calculate Marked Price (MP): MP = (399 × 100) ÷ (100 − 5). ⇒ MP = (399 × 100) ÷ 95 = 39900 ÷ 95 = Rs. 420.

∴ The correct answer is Rs. 420.

Additional Information

Marked Price & Discount

Marked Price (MP) is the price printed on the label. Discount is always calculated on the MP to arrive at the Selling Price (SP).

Profit and CP-MP Relation

Profit is always calculated on the Cost Price (CP). The formula linking CP, MP, Discount%, and Profit% is: CP ÷ MP = (100 − D%) ÷ (100 + P%).

Calculation:

$\frac{3}{7} + \frac{2}{7} + \frac{1}{{14}} + \frac{2}{7} - 3$

$\frac{6+ 4 + 1 + 4 - 42}{14}$

⇒ $\frac{-27}{14}$

⇒ Hence, Option 1 is correct

The correct answer is Tropical Deciduous Forests. 

Key Points

• Tropical Deciduous Forests
• ​In India, Tropical Deciduous Forests has dominating species i.e., teak, sal and shisha.
• In regions with significant yearly rainfall followed by a definite dry season, tropical deciduous forests develop.
• These forest formations are dense and lush in the wet summers, but they become a bleak scene in the dry winters when most of the trees lose their leaves.
• Tropical deciduous forests grow in warm, year-round conditions that occasionally get several hundred centimetres of rain.
• They have long dry seasons that can extend for several months.
• Tropical deciduous forests are often found in two bands, one between 10° and 20°N latitude and the other between 10° and 20°S latitude.

Additional Information

• Tropical Thorn Forests and Scrubs
• The tropical Thorn forests and Scrubs are a type of forest or area that receives too little or inadequate rainfall, with an average annual total of less than 70 cm. Typically, they can be found in India's semi-arid states of Rajasthan, Gujarat, Chhattisgarh, Madhya Pradesh, Uttar Pradesh, Haryana, and the dry Deccan Plateau regions.
• Mangrove Forests
• ​Mangrove forests are fertile wetlands that grow in coastal intertidal zones.
• They are also known as mangrove swamps, mangrove thickets, or mangals. Due to mangroves' inability to survive subfreezing temperatures, mangrove forests are primarily found in tropical and subtropical latitudes.
• Tropical Evergreen Forests
• ​A forest with evergreen trees is known as an evergreen forest.
• Conifers and holly in frigid regions, eucalyptus, Live oak, acacias, magnolias, and banksia in more moderate zones, and rainforest trees in tropical zones are just a few examples of the diverse range of trees that may be found in these ecosystems.

The correct answer is Only ii.

Key Points:

• Washing soda is a frequent name for sodium carbonate decahydrate.
• It resembles a white crystalline solid in appearance.
• It has a fundamental nature.
• Uses:
• It's used in laboratories as a reagent.
• It is used to eliminate stains.
• It is used to remove the lingering hardness of the water.
• It is also used to make paper and soap in addition to glass.
• It is used in both the refinement of oil and textiles.

Additional Information:

• In soda-acid fire extinguishers, sodium bicarbonate and sulfuric acid are both used.
• It is the best fire extinguisher to use at home.
• Sulfuric acid is included in a separate bottle along with sodium bicarbonate in water solution in the fire extinguisher.
• Sulphuric acid combines with sodium bicarbonate solution when fire extinguisher's knob is turned, resulting in production of a small amount of carbon dioxide gas.

The correct answer is birds.

Key Points:

• Ammonia, urea, uric acid, carbon dioxide, water, and ions are all accumulated by animals either by metabolic processes or through other methods, such as excessive intake.
• Ammonotelism is the process of excreting ammonia.
• The liver of the animal converts ammonia produced by metabolism into urea, which is then released into the blood and filtered and eliminated by the kidneys.
• To maintain the desired osmolarity, some of these animals may retain a little quantity of urea in their kidney matrix.
• Animals that excrete nitrogenous wastes as uric acid in the form of pellets or paste while losing the least amount of water are referred to as uricotelic.
• These include reptiles, birds, land snails, and insects.

Additional Information:

• Uric acid is a typical bodily waste substance.
• It grows as purine-containing compounds break down.
• Purines are a substance that the human body naturally contains.
• A number of foods, such as liver, seafood, and alcohol, also contain them.
• They may potentially arise within the body when DNA is damaged.

Shortcut Trick

Apply Value Substitution: Let θ = 30°.

cos⁴ 30° − sin⁴ 30° = (√3/2)⁴ − (1/2)⁴ = 9/16 − 1/16 = 8/16 = 1/2. ∴ k = 1/2.

Expression (1 + k)/(1 − k) = (1 + 1/2)/(1 − 1/2) = (3/2)/(1/2) = 3.

Check options: cot² 30° = (√3)² = 3. This matches.

∴ The correct answer is cot² θ.

Alternate Method

Given: cos⁴θ − sin⁴θ = k

Formula Used: a² − b² = (a − b)(a + b) and cos²θ − sin²θ = cos 2θ

⇒ (cos²θ − sin²θ)(cos²θ + sin²θ) = k

⇒ cos 2θ × 1 = k ⇒ k = cos 2θ

⇒ (1 + k)/(1 − k) = (1 + cos 2θ)/(1 − cos 2θ)

⇒ (1 + 2 cos²θ − 1) / (1 − (1 − 2 sin²θ))

⇒ 2 cos²θ / 2 sin²θ = cot²θ

∴ The correct answer is cot² θ.

Additional Information

Double Angle Formulas

cos 2θ can be written as cos²θ − sin²θ, 2 cos²θ − 1, or 1 − 2 sin²θ.

Pythagorean Identity

The fundamental identity is sin²θ + cos²θ = 1.

Trigonometric Ratios

cot θ = cos θ / sin θ and tan θ = sin θ / cos θ.

The correct answer is 0.50 A.

Key Points

• Parallel combination
• Three resistors connected in parallel to a battery of voltage V are depicted in the figure below.
• In this type of connection, the resistors are typically connected on parallel wires that originate from a common point.
• The voltage that flows through each resistor is the same in this instance. The equivalent resistance of the three resistances is depicted in the figure on the right.
• The equation for the relationship between voltage and current is, V=IR
• The voltages across individual resistors will be, 
  

I₁ = V/R1, I₂ = V/R₂, I₃ = V/R_3​​

​

Additional Information

• Calculation
• ​Two resistors, A=10 Ω and B=15 Ω, are connected in parallel
  

we know, 1/Rt= 1/R1+ 1/R2

1/R_t= 1/10+ 1/15

1/R_t= 3+2/30= 5/30= 1/6

R_t= 6Ω

The combination is connected to a 3 V battery,

As we know, V= IR

3= I× 6

I= 1/2= 0.5A

The correct answer is 10.

Key Points

• Indian Premier League
• As per the new format, IPL 2022 was played among 10 teams in total.
• The 2022 Indian Premier League, often referred to as IPL 15 or, for sponsorship purposes, Tata IPL 2022, was the league's fifteenth season (IPL).
• The competition took place between 26 March 2022 and 29 May 2022. Mumbai and Pune, both in the state of Maharashtra, hosted the games during the competition's group stage.
• The entire tournament schedule was published on March 6, 2022. Yeh Ab Normal Hai was the slogan.

Additional Information

• Additionally, the BCCI declared that two of the six towns it shortlisted—Ahmedabad, Cuttack, Dharamshala, Guwahati, Indore, and Lucknow—would serve as the locations for the franchises.
• On January 11, 2022, Vivo resigned as the tournament's title sponsor. Vivo secured a contract to serve as the title sponsor through 2023 after withdrawing as a sponsor in 2020.
• For the remaining year of Vivo's deal, The Tata Group was designated as the title sponsor.

Statement:

Floods caused widespread damage to crops in Odisha this year.

Arguments:

I. There has been a bumper production of food grains in Odisha this year - False (Flood causes damage, so this argument is totally vague according to the statement).

II. The number of crop insurance claims has seen a significant increase in Odisha this year - True (Flood causes damage to the crop which in turn affect directly on the number of crop insurance claims so this argument strengthens the statement).

Thus, argument I weakens, while argument II strengthens the statement.

Hence, the correct answer is Option 1.

According to the given statement:

Step 1) K is kept on one of the positions above L. Only one box is kept between K and L.

We place K at top then we place L leaving one position.

Step 2) Only two boxes are kept between M and H. Only one box in kept between L and N.

We place M and H such that only two boxes are kept between them. Then we place N such that only one box in kept between L and N.

Step 3) J is kept immediately above M. H is kept immediately below L. 

We place J above M and H below L.

From the arrangement we can see that, there are three boxes are kept between N and K.

Hence, the correct answer is Option 4.

Given:

The shaded part shows the medallists who are also Indians.

So, the medallists who are also Indians are 36 + 19 = 55.

Thus, there are 55 such medallists who are also Indians.

Hence, the correct answer is 'option 2'.

The correct answer is two.

Key Points:

• Two organisms that have different variations at the same genetic locus are combined to form a monohybrid cross.
• In a monohybrid cross, two or more mutations at a single gene locus control the features being studied.
• After that, each parent is chosen to have the desired characteristic in homozygosity, or true breeding (locus).
• The monohybrid ratio, also known as the distribution of second-generation (F2) offspring, is often used to determine if a cross qualifies as a monohybrid cross.

Additional Information:

• Austrian monk Gregor Mendel (1822–1884) developed the basic principles of heredity theory.
• In his monastery garden from 1858 to 1866, he crossed garden peas (Pisum sativum) and studied the progeny.
• The garden pea was chosen as the experimental organism because it was widely available, bred accurately for qualitative features, and allowed for controlled pollination.
• Mendel looked into seven different traits in pea plants, including:
• seed texture (round vs wrinkled).
• seed color (yellow vs green).
• flower color (white vs purple).
• growth habit (tall vs dwarf).
• pod shape (pinched or inflated).
• pod color (green vs yellow).
• flower position (axial or terminal).

The alphabets and their positions:

The logic followed in the given codes is:

First term is increased by 3.

Second term is decreased by 3.

The number is multiplied by its root value.

Now, FM 25 is related to IJ 125

For, NO 36 is related to QL 216

Similarly, for MP16:

Hence, the correct answer is Option 2.

According to the given statements:

X has duty on a day immediately before U. S and T have duties on one of the days before X. Only W has duty on the day between S and T. V has duty on Tuesday.

1) X has duty on a day immediately before U. 

2. V has duty on Tuesday.

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3. S and T have duties on one of the days before X. 

4) Only W has duty on the day between S and T. 

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And, R will done his duties on remaining day.

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From the arrangement we can see that, R has duty on Monday. 

Hence, the correct answer is "Option 1".