RRB Group D Previous Year Paper (Held on: 16 Sept 2022 Shift 3)

According to english alphabet series 

The pattern followed here is : 

Hence, "Option 1" is the correct answer.

The correct answer is parallel to principal axis.

Key Points:

• There are numerous uses for concave mirrors.
• They create upright, magnified images, making them helpful for shaving and doing makeup.
• They are also employed in telescopes because they focus light to produce noticeably larger images, as well as spotlights and headlights since they project parallel light beams.
• As a result, when the incident ray is parallel to the primary axis, the image of a star can be obtained at F of a concave mirror.

Additional Information:

• A concave mirror is a sort of spherical mirror in which the reflecting surface is the inner curved surface of the sphere; hence, the reflecting surface seems to be farther away from the incident light source in this type of mirror.
• They are also known as converging mirrors because of how they are made, which causes the incident light to be reflected inward.
• They are used to focus light.
• At every location along the curved surface of the mirror, both rules of reflection hold true.
• By connecting the mirror's curvature's centre to the point of incidence, the normal is drawn along the radius.
• Because the normal to the reflecting surface varies at each point on the mirror, the beams' convergence occurs after reflection.

Concept Used:

The recurring decimal is the digit after the point (0.) Which gets repeated periodically till infinity

Calculation:

According to question

$\frac{23}{11}$ can be written as:

= $\frac{(22 + 1)}{11}$

= 2 + $\frac{1}{11}$

= 2 + 0.09090909...........

= 2.09090909.......

= $2.\overline{09}$  (When digits start repeating we put the bar over the number which gets repeated periodically)

Thus, the required value is  $2.\overline{09}$.

Hence, the correct answer is option 1).

From the given information:

Step 1: E travelled in the month immediately before B, who travelled in the month of October.

Here we place B with October as given and then place E before B with September.

Step 2: C travelled between the trips of E and F.

Now according to the condition we place C between E and F which means C travelled before E in August & F travelled before C in July.

Step 3: Exactly four people travelled after D’s trip.

Here we place D at fifth position because four people travelled after him which means D travelled in June.

Step 4: G travelled in the month immediately before A’s trip.

Lastly we have to place A and G where G travelled before A so we place A with May and G with April.

From the arrangement, we can see that F travelled in July.

Hence the correct answer is option 4)

The correct answer is a basic salt.

Key Points:

• We know that sodium hydrogen carbonate is a basic salt because it is made when a strong base, such as NaOH, and a weak acid, such as H2CO3, neutralise one another.
• Strong heating of sodium hydrogen carbonate results in the production of sodium carbonate, water, and carbon dioxide.
• It involves the subsequent reactions:
• NaHCO_{3 +} heat → Na₂CO₃+H₂O+CO₂
• By crystallising NaHCO3, Na₂CO3.10H₂O is produced (washing soda).
• Washing soda is sodium carbonate, which is formed upon crystallisation as Na₂CO3.10H2O.

Additional Information:

• Washing soda is a salt of carbonic acid, a substance that also yields a variety of other salts referred to as carbonates.
• In order to help other cleaning agents remove filth from garments and suspend it in the wash water, sodium carbonate softens water.
• The washing soda bonds to the minerals, making the water harder and enabling the detergent to adequately penetrate the fibres to clean the clothing.

Shortcut Trick

Substitute standard values: cos 45° = 1/√2, sec 30° = 2/√3, and cosec 30° = 2.

Expression = (1/√2) ÷ (2/√3 + 2) = (1/√2) ÷ [(2 + 2√3)/√3].

Invert and multiply: (1/√2) × [√3 / (2(1 + √3))].

Result = √3 / [2√2(1 + √3)].

∴ The correct answer is √3 / (2√2(1 + √3)).

Alternate Method

Given: cos 45° / (sec 30° + cosec 30°)

Trigonometric Values Used:

⇒ cos 45° = 1/√2

⇒ sec 30° = 1/cos 30° = 2/√3

⇒ cosec 30° = 1/sin 30° = 2

Calculations:

⇒ Numerator = 1/√2

⇒ Denominator = 2/√3 + 2 = (2 + 2√3)/√3

⇒ Expression = (1/√2) / [(2(1 + √3))/√3]

⇒ Expression = (1/√2) × (√3 / (2(1 + √3)))

⇒ Expression = √3 / (2√2(1 + √3))

∴ The correct answer is √3 / (2√2(1 + √3)).

Additional Information

Standard Trigonometric Ratios

For an angle θ = 30°, sin θ = 1/2, cos θ = √3/2, and tan θ = 1/√3.

Reciprocal Identities

sec θ = 1/cos θ and cosec θ = 1/sin θ.

Rationalization

To simplify fractions with radicals in the denominator, multiply the numerator and denominator by the conjugate (e.g., √3 − 1).

The correct answer is Chandrayaan-2.

Key Points

• Chandrayaan-2 is the second lunar mission of India after the success of Chandrayaan-1. This mission was conducted for topographical research and mineralogical studies to have a better understanding of the Moon's origin and evolution.
• Chandrayaan-2 Mission was launched from the Satish Dhawan Space on July 22, 2019, by GSLV Mk III-M1. The main aim of Chandrayaan-2 was to trace the location and abundance of lunar water on the Moon's surface.
• Highlights of Chandrayaan-2
• Chandrayaan-2 fostered the findings of Chandrayaan-1 as reported by the ISRO.
• The mission targeted the "south polar region " of the moon which was completely unexplored.
• The mission focused on the extensive mapping of the lunar surface for studying variations in its composition and tracing the Moon's origin and evolution.
• Chandrayaan-2 has been considered a challenging mission as the South Polar Region of the Moon was unexplored by any space agency before.
• Components of Chandrayaan-2: Launch Vehicle 
• S200 solid rocket booster
• L110 liquid state
• C25 Upper stage
• The Chandrayaan-2 mission consisted of three main modules:

1. Lunar Orbiter
2. Vikram Lander
3. A Lunar rover named Pragyan, all these parts were developed in India.

• Significance of Chandrayaan-2
• In all the space Missions, no country has ever attempted to land a spacecraft in the polar regions of the moon. This gave India the lead in space exploration on an International level.
• Due to the moon's axis, few regions on the south pole always remain dark, especially the craters and have higher chances of containing water.
• The 2nd de-orbiting maneuver for the Chandrayaan-2 spacecraft was performed successfully on September 04, 2019, beginning at 0342 hrs IST as planned, using the onboard propulsion system. the duration of the maneuver was 9 seconds.
• On October 14, 2019, Chandrayaan-2 detected the presence of Argon-40 in the lunar exosphere.
• On July 30th, 2020 Chandrayaan-2 imaged the Sarabhai crater located on the northeast quadrant of the moon.

Additional Information

• India's 1st lunar Mission Chandrayaan-1 was launched on 22nd October 2008 from Satish Dhawan Space Center at Sriharikota, Andhra Pradesh.
• Objectives of Chandrayaan-1:
• To perform high-resolution remote sensing of the moon's surface.
• To provide a 3-dimensional atlas of the Moon.
• To conduct chemical and mineralogical studies for mapping the entire lunar surface.
• Chandrayaan-3 is a planned 3rd lunar exploration mission by the Indian Space Research Organization.

Given:

$(6-3)\div[(9-6)\div{(6-4)\div\left(2+\frac{8}{13}\right)}]$

Formula used:

BODMAS rule

Calculations:

$(6-3)\div[(9-6)\div{(6-4)\div\left(2+\frac{8}{13}\right)}]$

⇒ $3 \div [3 \div {2 \div \frac{26+8}{13}}]$

⇒ $3 \div [3 \div {2 \div \frac{34}{13}}]$

⇒ $3 \div [3 \div {2 \times \frac{13}{34}}]$

⇒ $3 \div [3 \div \frac{13}{17}]$

⇒ $3 \div [3 \times \frac{17}{13}]$

⇒ $3 \div \frac{51}{13}$

⇒ $3 \times \frac{13}{51}$

⇒ $\frac{13}{17}$

∴ The correct answer is option (3).

Shortcut Trick

Area of a square with side s is given by s².

Apply identity (a − b)² = a² − 2ab + b².

Here a = 5x and b = 8.

Area = (5x)² − 2 × 5x × 8 + 8² = 25x² − 80x + 64.

∴ The correct answer is 25x² − 80x + 64 cm².

Alternate Method

Given:

Side of the square (s) = (5x − 8) cm

Formula Used:

Area of square = side × side = s²

Algebraic Identity: (a − b)² = a² − 2ab + b²

Calculations:

⇒ Area = (5x − 8)²

⇒ Area = (5x)² − 2(5x)(8) + (8)²

⇒ Area = 25x² − 80x + 64

∴ The correct answer is 25x² − 80x + 64 cm².

Additional Information

Perimeter of a Square

The total boundary length of a square is 4 × side. For this case, Perimeter = 4(5x − 8) = 20x − 32 cm.

Diagonal of a Square

The distance between opposite vertices is s√2. Area can also be expressed as (Diagonal)² ÷ 2.

Square Identity

Recall that (a + b)² = a² + 2ab + b² and (a − b)(a + b) = a² − b² for various polynomial side lengths.

The logic followed here is :

Given series: (Left) K B # A @ S * B Q @ R V N % & S (Right)

The element that is third from the right end is %

(Left) K B # A @ S * B Q @ R V N % & S (Right)

The element that is sixth from the left end of the given series is S

(Left) K B # A @ S * B Q @ R V N % & S (Right)

(Left) K B # A @ S * B Q @ R V N % & S (Right)

Thus, there are a total of 5 letters that are B, Q, R, V, N 

Hence, the correct answer is  "Option 2".

Shortcut Trick

For the quadratic equation x² + x − 2 = 0, find two numbers whose sum is −1 (−b/a) and product is −2 (c/a).

The numbers 1 and −2 satisfy these conditions: 1 + (−2) = −1 and 1 × (−2) = −2.

Therefore, the roots of the equation are 1 and −2.

∴ The correct answer is (1, −2).

Alternate Method

Given:

The quadratic equation is x² + x − 2 = 0.

Formula Used:

We use the factorization method (splitting the middle term) where we split the coefficient of x into two numbers whose sum is 1 and product is −2.

Calculations:

⇒ x² + 2x − x − 2 = 0

⇒ x(x + 2) − 1(x + 2) = 0

⇒ (x + 2)(x − 1) = 0

Now, set each factor equal to zero:

⇒ x + 2 = 0 → x = −2

⇒ x − 1 = 0 → x = 1

The roots are 1 and −2.

∴ The correct answer is (1, −2).

Additional Information

Nature of Roots

For ax² + bx + c = 0, the discriminant D = b² − 4ac determines the nature: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Sum and Product of Roots

For a quadratic equation, the Sum of roots (α + β) = −b/a and the Product of roots (αβ) = c/a.

Quadratic Formula

The roots can also be found using x = [−b ± √(b² − 4ac)] / 2a.

The correct answer is the PC Mahalanobis model.

Key Points

• The Second Five-Year Plan is based on the so-called Mahalanobis model. This was the USSR model Indianized by PC Mahalanobis, the founder of the Indian Statistical Institute and close aid of Nehru.
• This Model is known to have set the statistical foundation for state-directed investment and created the intellectual underpinnings of the License Raj through an elaborate input-output model.
• This Model suggested that heavy industries should be emphasized, which can lead the Indian economy to a long-term higher growth path.
• India's Second Five-Year Plan and Industrial policy Resolution 1956, which paved the way for the Development of the Public Sector and License Raj were based upon this model.
• The Second Five-Year plan, based on a Socialistic pattern, targeted an increase of 25% in National Income by Rapid Industrialization; however, achieved a target of only 20%. Further, per capita income grew by 8% only.
• During this plan Domestic Production of Industrial products was encouraged, particularly in the development of the Public Sector.
• During this Plan Period the Industry policy resolution was amended and the primary responsibility for development was left to the Public Sector.
• The Private Sector was more or less confined to the Consumer Industries only.

Additional Information

• The Harrod Domar Model is a Keynesian Model of Economic Growth in development economics, developed by F. Harrod in 1939 and Evsey Domar in 1946. This Model focused on understanding economic instability by analyzing the Dynamic nature of Capital and Investment.
• Manmohan Plan abolished licensing in all industries except a few of the 18 MRTP companies, which were free from the ceiling limit of assets. It reduced import barriers to globalizing the economy, by granting greater autonomy and making management more professional.
• Features of the Manmohan plan were,

1. Devaluation of the rupee was carried out against major Currencies by around 9 percent on 1 July 1991.
2. India's Gold holdings were pledged with the Bank of England in four tranches from 4-18 July 1991 raising around $ 400 million through this route.

• The Planning Commission of India was an Institution of the Government of India. It is a Non-Constitutional body, whose main task was to make Five-Year Plan. On 13th August 2014, the Planning Commission was abolished and replaced by the NITI Aayog, effective from Jan 1st, 2015.
• The fifth Five-Year Plan (1974-79) was also called the 'Investment Model of Planning Commission'.
• The 2 main Objectives of this Plan were

1. Poverty Eradication.
2. Attainment of Self-reliance.

Shortcut Trick

Total additional interest percentage = Increase in Rate × Time

⇒ 2% × 4 years = 8%

Given that this 8% is equal to Rs. 640.

⇒ 100% (Principal) = (640 ÷ 8) × 100 = 80 × 100 = 8000

∴ The correct answer is ₹8000.

Alternate Method

Given:

Time (T) = 4 years

Increase in Rate (R_diff) = 2%

Increase in Simple Interest (SI_diff) = Rs. 640

Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) ÷ 100

Increase in Interest (SI_diff) = (Principal × R_diff × Time) ÷ 100

Calculations:

⇒ 640 = (Principal × 2 × 4) ÷ 100

⇒ 640 = (Principal × 8) ÷ 100

⇒ Principal × 8 = 640 × 100

⇒ Principal = 64000 ÷ 8

⇒ Principal = 8000

∴ The correct answer is ₹8000.

Additional Information

Compound Interest Formula

The amount (A) in compound interest is calculated as A = P(1 + r/100)ⁿ, where P is principal, r is rate, and n is time.

Difference between CI and SI

For a period of 2 years, the difference between CI and SI is given by P(r/100)².

Effective Rate of Interest

In simple interest, the effective rate for T years at R% is simply (R × T)%. For compound interest, it follows the successive percentage change rule.

The correct answer is Article 154.

Key Points

• The Indian Constitution's Article 154 addresses the State's administrative authority.
• It stipulates that the governor shall have the executive authority of the state and shall exercise such authority directly or through persons who report to him in line with this Constitution.
• Discussions of Draft Article 130 (Article 154) took place on 30 May 1949 and 16 October 1949. It gave a State's government control over its executive branch.
• By Article 154, the governor has the authority to act directly as the state's executive head or through representatives who answer to him.
• Nothing in this article shall be construed as preventing parliament or the state Legislature from establishing positions for any authority under the Governor through legislative action or from transferring to the Governor any duties granted to any other authority by any law currently in force.
• The governor will have the authority to act in the state's executive capacity, provided that they do so by the law and the Constitution.

Additional Information

• Article 124 deals with the Establishment and constitution of the supreme court. It states that there shall be a Supreme court of India constituting of a Chief Justice of India and, until Parliament by law prescribes a larger number, of not more than seven other judges.
• Article 144 of the Indian constitution advises civil and Judicial authorities to act in aid of the Supreme Court. It says that all authorities, civil and judicial, in the territory of India shall act in aid of the Supreme court.
• Article 134 with the Appellate Jurisdiction of the Supreme court in Criminal cases.
• Article 134 A deals with the Certificate for appeal to the supreme court in civil cases.

The correct answer is Cs > Rb > K > Na > Li.

Key Points:

• Lithium:
• Atomic number- 3
• Symbol- Li
• Electronic configuration: 2, 1
• Sodium-
• Atomic number- 11
• Symbol- Na
• Electronic configuration: 2, 8, 1
• Potassium-
• Atomic number- 19
• Symbol- K
• Electronic configuration: 2, 8, 8, 1
• Rubidium-
• Atomic number- 37
• Symbol- Rb
• It's Electronic configuration: 2, 8, 18, 8, 1
• Caesium-
• Atomic number- 55
• Symbol- Cs
• Electronic configuration: 2, 8, 18, 18, 8, 1
• This demonstrates that, among the specified elements in a group, lithium has the smallest atomic radius and cesium has the biggest atomic radius.

Additional Information:

• The atomic radius of an element essentially serves as a gauge for atom size.
• It is commonly stated as the sum of the distances between an atom's nucleus and its outermost orbital of electrons.
• Calculating an atom's atomic radius requires the use of spectroscopic methods such as X-rays or others.
• The atomic radii of elements are shown in a regular way on the periodic table.

Given statement : J < P = C, T < Q < M = J < A 

Let us check the conclusion for the given options:

Option 1) A > P → False 

A > J < P : we cannot conclude the relation between A and P.

Option 2) C = A → False 

J < P = C so J < C and J < A : no direct relationship found between C and A.

Option 3) P > A → False

J < P and J < A : no direct relationship found between P and A.

Option 4) T < A → True

T < Q < M = J < A,

T < M = J < A if both are equal then we can use any one of them

T < M/J < A so T is smaller than A.

Hence, the correct answer is Option 4**.**

The least possible venn diagram of given statement is,

Conclusions:

(I) Some monkeys are cats. → **True (**As there is a definite relation between Monkeys and Cats as shown above)

(II) All monkeys are rats. → False (As all rats are dogs but not all monkeys are rats)

Hence, the correct answer is "Option 2".

Explanation:

Step 1:

• C travelled in 2018.
• Only three people travelled between D and A.
• A travelled after D

Step 2:

• Only one person travelled between F and E.
• F travelled before E.

Thus, E travelled in 2014.

Hence, the correct answer is "Option 4"**.**​

The least possible Venn diagram of the given statement is,

Conclusions:

I. Some towels are conditioners.→ False (It is given that No conditioner is a towel)

Il. No shampoo is a towel.→ False (There is no definite relation between shampoo and towels as shown above)

III. Some brushes are shampoos. → True (As all shampoos are brushes so some brushes are shampoos)

Hence, the correct answer is  "Option 1".

Shortcut Trick

1. Angle Bisectors: In a parallelogram, adjacent angles sum to 180°. Their bisectors meet at 90°, forming a rectangle. (True)
2. Trapezium: A trapezium requires at least one pair of parallel sides. A parallelogram has two, so it is always a trapezium. (True)
3. Rhombus: Diagonals of a rhombus are perpendicular bisectors but are not equal unless it is a square. (False)

∴ The correct answer is Only (a) and (b).

Alternate Method

Given: Properties of a parallelogram, trapezium, and rhombus.

Formula/Property Used:

1. Sum of adjacent angles of a parallelogram = 180°.
2. Definition of Trapezium: A quadrilateral with at least one pair of parallel sides.
3. Rhombus diagonals bisect each other at 90° but are unequal in length.

Calculations:

⇒ Statement (a): In parallelogram ABCD, ∠A + ∠B = 180°. Let bisectors of ∠A and ∠B meet at P. In ΔAPB, ∠PAB + ∠PBA = 1/2(∠A + ∠B) = 1/2 × 180° = 90°. ∴ ∠APB = 180° − 90° = 90°. Similarly, all angles of the inner quadrilateral are 90°, making it a rectangle. (True)

⇒ Statement (b): A trapezium is defined as a quadrilateral with at least one pair of parallel sides. Since a parallelogram has two pairs of parallel sides, it satisfies the condition. (True)

⇒ Statement (c): For a rhombus, diagonals bisect each other at 90°, but they are equal only if the rhombus is a square. Thus, they are not always equal. (False)

∴ The correct answer is Only (a) and (b).

Additional Information

Properties of a Rhombus

All sides are equal, opposite angles are equal, and diagonals are perpendicular bisectors of each other.

Rectangle and Square

A rectangle is a parallelogram with four right angles. A square is a special rhombus where all angles are 90° and diagonals are equal.

Trapezium Classification

Under the inclusive definition, parallelograms, rhombuses, rectangles, and squares are all special types of trapeziums.

Shortcut Trick

Map distance 1 unit represents 400000 units actual distance.

Actual distance = 5 cm × 400000 = 2000000 cm.

To convert cm to km, divide by 100000 (since 1 km = 10⁵ cm).

Actual distance = 2000000 ÷ 100000 = 20 km.

∴ The correct answer is 20 km.

Alternate Method

Given:

Distance on map = 5 cm

Scale = 1 : 400000

Formula Used:

Actual Distance = Map Distance × Scale Factor

Calculations:

⇒ Actual distance in cm = 5 × 400000

⇒ Actual distance in cm = 20,00,000 cm

⇒ Convert cm to meters: 20,00,000 ÷ 100 = 20,000 m

⇒ Convert meters to km: 20,000 ÷ 1000 = 20 km

∴ The correct answer is 20 km.

Additional Information

Representative Fraction (RF)

It is the ratio of map distance to actual distance, expressed as 1/n where both quantities are in the same units.

Unit Conversion Rule

1 km = 1,000 meters = 1,00,000 centimeters. Use this to shift decimals during map calculations.

Linear Scale

A line divided into equal parts used on maps to measure distances directly in ground units.

The correct answer is Marathi.

Key Points

• The third most spoken language of India is Marathi which has 8.30 crore speakers according to the 2011 Census data.
• It is spoken by 6.86% of the total population.
• The census of India 2011 was organized in 2 stages trials House listing and Housing Census and Population Enumeration. The population of India has been augmented by more than 181 million during the decade 2001-2011.
• As per the 2011 census population report of India is pegged at 1.21 billion, a surge of more than 181 million in the last 10 years.
• The 15th Census of India and the 7th Census of Independent India-2011 were started on 1st April 2010 with the president being the first citizen to be enumerated, followed by the Vice President of India.
• The Slogan of the census 2011 was 'our Census, Our future'. C. Chandramouli was the Census Commissioner of India in 2011.
• Census of India 2011 was conducted in 2 stages:
• House listing and Housing Census: (April to September 2010)
• Population Enumeration (9th to 28 February 2011).
• The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
• Uttar Pradesh is the most populous state in India its population is more than the population of Brazil.

Additional Information

• The second most spoken language in India by the number of speakers is Bengali which has 9.72 crore speakers. The Bengali-speaking population is 8.03% of the total population.
• According to the 2011 Census data Gujarati is the 6th most spoken language and it has 5.54 crore speakers. Also, it is estimated that 4.58% of the total population speaks this language. It is the official language of Gujarat. Also, the official language of Daman, Diu, Dadra, and Nagar Haveli is in India.
• According to the 2011 Census Tamil is the 5th most spoken language in India. it is spoken by 6.90 crore speakers, which is 5.70% of the total population. It is widely spoken in the areas of Tamil Nadu, Puducherry, and Andaman & Nicobar Islands.

Shortcut Trick

Average of squares ≈ 74 ÷ 2 = 37.

The perfect square nearest to 37 is 36, which is 6².

Since the numbers are consecutive odd natural numbers, they must be 6 − 1 = 5 and 6 + 1 = 7.

Check: 5² + 7² = 25 + 49 = 74. (Satisfied)

Sum = 5 + 7 = 12.

∴ The correct answer is 12.

Alternate Method

Given: Sum of squares of two consecutive odd natural numbers = 74.

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

⇒ Let the two consecutive odd numbers be x and x + 2.

⇒ x² + (x + 2)² = 74

⇒ x² + x² + 4x + 4 = 74

⇒ 2x² + 4x − 70 = 0

⇒ x² + 2x − 35 = 0

⇒ x² + 7x − 5x − 35 = 0

⇒ x(x + 7) − 5(x + 7) = 0

⇒ (x − 5)(x + 7) = 0

⇒ x = 5 (since it is a natural number, ignore x = −7).

⇒ The numbers are 5 and 5 + 2 = 7.

⇒ Sum = 5 + 7 = 12.

∴ The correct answer is 12.

Additional Information

Consecutive Odd/Even Numbers

The difference between any two consecutive odd or consecutive even numbers is always 2.

Sum of First n Odd Numbers

The sum of the first n odd natural numbers is given by the formula n².

Quadratic Roots Nature

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product is c/a.

The correct answer is 19 December.

Key Points

• The day marks the occasion when the Indian armed forces freed Goa in 1961 from 450 years of Portuguese rule.
• The Portuguese colonized several parts of India in 1510 but by end of the 19th century Portuguese colonies in India were limited to Goa, Daman, Diu, Dadra, Nagar Haveli, and Anjediva Island(a part of Goa).
• As India gained independence on 15th August 1947, it requested the Portuguese to cede their territories but they refused.
• Following a myriad of unsuccessful negotiations and diplomatic efforts with the Portuguese, the former Prime minister of India, Jawaharlal Nehru, decided that military intervention was their only option.
• The 36-hour military operation, conducted on December 18, 1961, was code-named 'Operation Vijay' meaning 'Operation Victory', and involved attacks by the Indian Navy, Airforce, and Army.
• The Goa liberation movement started with small-scale revolts but reached its peak between 1940 to 1960.​
• During the historic moment, Indian troops reclaimed the Goan territory with little resistance, and General Manuel Antonio Vassalo e Silva signed the certificate of surrender.
• 451 years of Portuguese rule in the region officially came to end and the territory was taken back by India on December 19, 1961.
• The action incited mixed responses internationally at the time. Though many praised the move and backed India, others, including Portugal, criticized the Indian forces "invasion" of Goa.
• Now Goa Liberation Day is marked by an abundance of events and festivities in Goa.
• A torchlight procession is ignited from 3 different locations in the state, eventually all meeting at the Azad Maidan.
• This is where Tribute is made to those who lost their lives in the takeover of Goa.

The correct answer is The solution turns milky.

Key Points:

• Calcium oxide is known as quicklime or pure lime.
• As a result of its chemical characteristics and simplicity of production, it is a significant industrial chemical.
• Calcium hydroxide and water can be combined to create limewater, which can then be purified to remove any extra undissolved solids.
• Lime water is calcium hydroxide, and when carbon dioxide gas is pumped through it for a brief period of time, calcium carbonate forms and causes the limewater to turn milky.
• Following is the reaction:
• CO₂ + Ca(OH)₂ ⇒ CaCO₃ + H₂O

Additional Information:</sub>

• Milkiness of lime water:
• When too much carbon dioxide is added to lime water, the developed milkiness disappears.
• The reason for this is calcium bicarbonate, which is colourless and water soluble, develops.
• Following is the reaction:
• CaCO3 + H2O + CO2 ⇒ Ca(HCO3)2.

The correct answer is horses.

Key Points

• CSIR-Centre for Cellular and Molecular Biology (CCMB), VINS Bioproducts, and the University of Hyderabad (UOH) has collaborated to create the drug 'Vincov-19'.
• To create this drug, the SARS-CoV-2 virus is inactivated and injected into horses.
• The antibodies that are generated through the blood serum are synthesized and then purified and turned into a drug. this drug is then injected into humans to neutralize the COVID virus.
• CSIR-Centre for Cellular and Molecular Biology (CCMB), is an Indian fundamental life science research institute based in Hyderabad.
• UNESCO'S Global Molecular and Cell Biology Network have designated CCMB as a "center of excellence." It is a leading research institute that conducts high-quality basic research and training in areas of modern biology, as well as promoting centralized national facilities for new techniques in interdisciplinary fields of biology.
• On April 1, 1977, it was established as a semi-autonomous center.
• Phase 2 clinical trials of 'Vinco-19' were conducted across multiple centers in the country involving over 200 patients and were completed in September. These trials also included testing the antidote against the Omicron variant to ensure maximum coverage against the virus and its known mutation.
• One group of patients was given VINCOV-19, along with Standard Care (SoC), and another group was given Standard of Care only. VINCOV-19 showed an excellent safety profile in the phase 2 trials. There were good and early improvements in the clinical condition of the patients administered VINCOV-19.
• VINCOV-19 contains Equine polyclonal antibodies (EpAbs) against the COVID-19 virus and comprises highly purified F(ab)2 antibody fragments that have a high neutralizing capacity against the SARS-CoV-2 virus.
• Since neutralizing antibodies could block the internalization of SARS-CoV-2 to lung cells, it was postulated that their passive administration should render maximal clinical benefits if they are applied at the early stages of the disease.
• UoH Vice-Chancellor B.J. Rao congratulated the team members for their efforts in completing phase 2 trials for VINCOV-19 and the academia and industry collaboration.

The correct answer is CH₄O.

Key Points:

• We examine possible intermolecular forces that may be in play and prevent the molecules from breaking apart.
• The one with the lowest boiling point will have the weakest IMF.
• All the others have dispersion plus either dipole-dipole (C4H10O, C3H8O, C2H6O) or hydrogen bonding, whereas CH₄O simply possesses dispersion forces.
• Therefore, the lowest boiling point will be for CH₄O.

Additional Information:

• Methanol has the chemical structure CH₄O.
• It falls under the category of alcohol because of the hydroxyl group.
• Alcohols are designated by the suffix "-al" in the IUPAC nomenclature.
• It consists of four hydrogen atoms, one oxygen atom, and one carbon atom.
• As a result, the geometric centers of methanol are carbon and oxygen.

The given statements are: 

• ‘now you can come’ is written as ‘wp ae nz rf’,
• “you are kind’ is written as ‘ae dz tq’
• ‘kind is virtue’ is written as ‘tq sf be’.

The logic followed here is: 

Thus, 'Kind, You'  is coded as 'tq, ae'

Hence, "Option 4" is the correct answer.

Shortcut Trick

Convert percentage to fraction: 36(2/3)% = 11/30.

Let Total Income = 30 units, then Expenditure = 11 units.

Savings = 30 − 11 = 19 units.

Given: 19 units = ₹5,700 ⇒ 1 unit = ₹300.

Monthly Expenses = 11 units = 11 × 300 = ₹3,300.

∴ The correct answer is ₹3,300.

Alternate Method

Given:

Expenditure Percentage = 36(2/3)% = 110/3%

Monthly Savings = ₹5,700

Calculations:

⇒ Savings Percentage = 100% − 36(2/3)% = 63(1/3)%

⇒ 63(1/3)% = 190/3%

⇒ According to the question, (190/3)% of Total Income = 5,700

⇒ Total Income = (5,700 × 3 × 100) / 190

⇒ Total Income = 30 × 3 × 100 = ₹9,000

⇒ Monthly Expenses = Total Income − Savings

⇒ Monthly Expenses = 9,000 − 5,700 = ₹3,300

∴ The correct answer is ₹3,300.

Additional Information

Percentage to Fraction Conversion

Common fractions like 33(1/3)% = 1/3 and 66(2/3)% = 2/3 help in faster calculations during exams.

Income, Expenditure and Savings Relation

Income = Expenditure + Savings. Always ensure the sum of percentages equals 100%.

Base Change in Percentages

If A is x% more than B, then B is [x / (100+x)] × 100 % less than A.

As we can clearly see that:

The people who are researchers, scientists, and professors are 8.

And the people who are Researchers and Scientists but Not Professors are 6.

Hence, "Option 4" is the correct answer.

The correct answer is 0.67A.

Given:

Three resistors of 5 Ω are connected in series and $V=10V$

Formula:

Ohm's law: $V=IR$

Calculations:

As the three resistors are connected in series, their equivalent resistance is:

$Rs=5+5+5=15Ω$

Now by applying Ohm's law we get:

$V=IR$

$I={V \over R}={10 \over 15}=0.67A$

Thus, the current flowing is 0.67A.

The correct answer is Bharat Sanchar Nigam Limited (BSNL).

Key Points

• On July 27, the Union Cabinet authorized a 1.64 lakh crore package for the rehabilitation of the state-owned telecom provider Bharat Sanchar Nigam Limited (BSNL), in yet another attempt to bring it back to life.
• The package will include the administrative allotment of 4G spectrum worth 44,993 crores, which contains a cash component worth 43,964 crores and a non-cash component worth 1.2 lakh crores spread over four years. The ambitious Bharat Net project's implementation vehicle, Bharat Broadband Network Ltd (BBNL), would also be amalgamated into BSNL.
• Bharat Sanchar Nigam Limited, also known as BSNL, is an Indian central public sector organization with its headquarters in New Delhi. The owner is the Department of Telecommunications within the Ministry of Communications of the Government of India. The Indian government formally incorporated it on October 1st, 2000.

Additional Information

• Air India
• ​With an 18.6% market share, Air India dominates the Indian international aviation industry.
• More than 60 foreign locations on four continents are served by Air India. As the 27th member of Star Alliance, the airline joined on July 11, 2014. The airline was started by J. R. D.
• Container Corporation of India Limited (CONCOR)
• ​The Container Corporation of India Ltd. (CONCOR) was established in March 1988 in accordance with the Companies Act, and it started operating in November 1989 after assuming control of the Indian Railways' previous network of seven ICDs.
• CONCOR is dedicated to offering its clients responsive, affordable, effective, and dependable logistics solutions. It aspires to be the top option for its clients. Customer satisfaction, performance, and results are the top priorities at CONCOR, which is committed to giving its clients value for their money.
• Oil and Natural Gas Corporation Limited
• ​The Ministry of Petroleum and Natural Gas, Government of India, is the owner of the Oil and Natural Gas Corporation (ONGC), a central public sector organization. Its main office is in New Delhi. The Indian government formed ONGC on August 14, 1956.
• It is the largest government-owned oil and gas explorer and producer in the nation and produces over 84% of India's natural gas and about 70% of its crude oil, which corresponds to around 57% of the nation's total consumption.
• The Indian government granted ONGC the Maharatna designation in November 2010.

Logic : First number × 2 + 2 = Second number

3 : 8 → 3 × 2 + 2 ⇒ 6 + 2 = 8 

and,

7 : 16  → 7 × 2 + 2 ⇒ 14 + 2 = 16 

Similarly,

4 : 10 → 4 × 2 + 2 ⇒ 8 + 2 = 10

and,

8 : ? → 8 × 2 + 2 ⇒ 16 + 2 = 18

Thus, ? can be replaced with 18

Hence, "Option 4" is the correct answer.

From the given information:

Step 1: Jayant started from a point ‘A’ and walked 15 meters towards South. He turned left and walked 20 meters.

Step 2: He then. turned right and walked 15 meters. He again turned right and walked 20 meters and reached a point ‘B’.

Distance from Point A to B = 15m + 15m = 30m

From the diagram, we can see that point B is 30 meters south from point point A.

Hence the correct answer is option 2).

The correct answer is perpendicular to the focal plane.

Key Points:

• The mirror surface will always be struck perpendicularly by a ray passing through the centre of curvature.
• As a result, both the angle of incidence and the angle of reflection are zero.
• As a result, the light ray will essentially go in the same direction.
• If you can extend the path to the centre of curvature, this also applies to convex mirrors.

Additional Information:

• Different kinds of images can be created by shifting the object's position in the concave mirror.
• When an object is positioned, various images are created:
• Towards infinity.
• Past the point of curvature.
• In the centre of the curve.
• Between the major focus and the centre of curvature.
• The primary emphasis.
• Between the pole and main focus.

From the given information:

Step 1: Chitra starts driving from the resort and drives 15 km towards west and then turns left and drives 115 km.

Step 2: Then she turns right and drives 25 km. After that, she again tums right and drives 90 km.

Step 3: She finally turns right and drives 40 km to reach her home.

Distance from resort to home = 115 - 90 = 25 km

From the diagram, we can see that resort is 25 km away from her home.

Hence, the correct answer is option 1).

Given statement: C ≥ V < B ≥ N > Z > L

Now we consider the given options:

Option 1) C ≥ V < L → False

We have C ≥ V but  V < L is incorrect because there is no direct relation between V and L.

Option 2) B > Z > L → True

We have B ≥ N > Z > L 

Option 3) C > B ≥ N → False

We have B ≥ N but C > B is incorrect because we can not conclude the relation between C and B.

Option 4) B > L > V → False

We have B > L but L > V is incorrect.

Hence, the correct answer is option 2).

Shortcut Trick

In a proportion, the product of means equals the product of extremes.

Middle terms (means) are y and 7; Outer terms (extremes) are 14 and 8.

y = (14 × 8) ÷ 7

y = 2 × 8 = 16

∴ The correct answer is 16.

Alternate Method

Given: 14 : y :: 7 : 8

Formula Used: a : b :: c : d ⇒ a/b = c/d

⇒ 14/y = 7/8

⇒ 7 × y = 14 × 8

⇒ y = (14 × 8) ÷ 7

⇒ y = 112 ÷ 7

⇒ y = 16

∴ The correct answer is 16.

Additional Information

Fourth Proportional

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

Mean Proportional

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

Continued Proportion

Three numbers a, b, c are in continued proportion if a:b = b:c, which implies b² = ac.

From the given information:

Step 1: K and N live on the topmost and bottommost floors, respectively. 

 We place K on top and N on bottom.

Step 2: M lives on the floor immediately above N.

Now we place M above N.

Step 3: J lives on the floor immediately above L.

Now we have to place J and L such that J is above L. 

From the arrangement, we can see that M lives on second floor.

Hence, the correct answer is option 3).

The correct answer is the direction of both, the magnetic field and the current.

Key Points:

• A conductor is said to generate an electric current when it moves through a magnetic field in accordance with Faraday's law of electromagnetic induction.
• The direction of the induced current is determined using Fleming's right-hand rule.
• A force perpendicular to the field's direction and the direction of the current flow is experienced by a current-carrying conductor when it is exposed to an external magnetic field.
• To determine the force operating on a current-carrying conductor in a magnetic field, Fleming's left-hand rule is utilized.
• The thumb should point in the direction of force acting on the conductor.
• When the thumb, index finger, and middle finger are all placed mutually perpendicular to one another, with the middle finger pointing in the direction of current flow and the index finger pointing in the direction of the magnetic field.

Additional Information:

• ​We can see that the right-hand rule applies to generators and the left-hand rule applies to motors.
• There are two visual mnemonics called Fleming's left-hand rule and Fleming's right-hand rule (mnemonics are learning techniques or memory aids, such as an abbreviation, rhyme or mental image that helps to remember something).
• In reality, these laws are only ever applied as a handy ruse to ascertain the resultant's direction—current or thrust.
• The Lorentz Force determines the magnitude of force along this direction according to these rules.

Shortcut Trick

Volume of a sphere is proportional to the cube of its radius (V ∝ r³).

If the radius is scaled by a factor of 1/2, the volume scales by (1/2)³.

(1/2)³ = 1/8.

∴ The correct answer is 1/8 times.

Alternate Method

Given: Original radius = r, New radius = r/2.

Formula Used: Volume of sphere = (4/3)πr³

⇒ Original Volume (V₁) = (4/3)πr³

⇒ New Volume (V₂) = (4/3)π(r/2)³

⇒ V₂ = (4/3)π(r³/8)

⇒ V₂ = (1/8) × [(4/3)πr³]

⇒ V₂ = (1/8) × V₁

∴ The correct answer is 1/8 times.

Additional Information

Surface Area Change

Surface area of a sphere is 4πr². If the radius is halved, the area becomes (1/2)² = 1/4 of the original.

Hemisphere Volume

The volume of a hemisphere is exactly half of a sphere: V = (2/3)πr³.

Ratio of Volumes

If the ratio of radii of two spheres is a:b, then the ratio of their volumes is a³:b³.

The correct answer is Juned Khan.

Key Points

• When they took first place in the ninth Indian Open Race-Walking Competition, Juned Khan of Haryana and Ramandeep Kaur of Punjab respectively rewrote the men's and women's 35km race walking National Records.
• Juned Khan, who did so in 2:40:16.00, set the previous national record.
• After 20 kilometres in the men's race, Juned Khan, 22, separated himself from Ram Baboo and Chandan Singh, lowering the national record by five minutes.

Additional Information

• Ram Baboo
• ​On the final day of sports activities at the National Games in this city on Tuesday, Uttar Pradesh athlete Ram Baboo set a new national record for the 35km race walk with a time of 2 hours, 36 minutes, and 34 seconds.
• The 23-year-old Ram Baboo easily defeated Haryana's Juned Khan, who finished in 2:40:51.00 here and held the national record of 2:40:16.00 set in the National Race Walking championships in Ranchi this year, in a race that was established last year and made its National Games debut this week.
• Chandan Singh
• ​Chandan Singh, an Indian racewalker who competes in the 20-kilometer and 20-kilometer walk races, was born on June 8, 1987.
• Akshdeep Singh
• ​Akshdeep Singh, a trainee at SAI Bengaluru, took home the gold medal in the men's 20-kilometre racewalk in the Khelo India University Games in 2021.
• Before heavy rain stopped the athletic competition at the 2nd Khelo India University Games at the Sree Kanteerava Stadium, Akshdeep Singh of Punjabi University won the gold medal in the men's 20km race walk and Aparna Roy of Kerala won the women's 100m hurdles.

We arrange the given number in ascending order from left to right and then compare it with the given order:

We can see that the position value of only '2' remains unchanged.

Hence the correct answer is option 1).

The correct answer is round and yellow seeds.

Key Points:

• Following the principles of Mendelian genetics, specifically the concept of dominant and recessive traits, let's define the traits given:
• Round seeds (R) are dominant over wrinkled seeds (r).
• Yellow seeds (Y) are dominant over green seeds (y).
• A round, green-seeded plant would have the genotype RRyy.
• A wrinkled, yellow-seeded plant would have the genotype rrYy
• For simplicity, we'll assume the round, green seeded plant is (Rryy).
• When these two plants are crossed (Rryy x rrYy), the resulting F1 generation will inherit one allele from each parent for each trait.
• Possible combinations:
• The round seed trait (R) is dominant, so any offspring with at least one R allele will have round seeds.
• The yellow seed trait (Y) is also dominant, so any offspring with at least one Y allele will have yellow seeds.
• The potential combinations for the F1 generation are:
• RrYy (round, yellow)
• Rryy (round, green)
• rrYy (wrinkled, yellow)
• rryy (wrinkled, green)
• However, the dominant traits (round and yellow) will be most likely observed in the F1 generation since the cross involves dominant alleles.
• Given this cross, the F1 generation will most likely exhibit the dominant traits.

Additional Information:

• Allogamy, or cross-fertilization, is the union of gametes (sex cells) from male and female individuals of the same species.
• All animal species with separate male and female individuals as well as dioecious plants (those with male and female organs on separate individuals) require cross-fertilization.
• Many species of hermaphrodites, or organisms that generate both sperm and eggs in the same individual, have highly evolved mechanisms that assure cross-fertilization.
• In addition, many hermaphrodite species that are able to cross-fertilize are also able to self-fertilize.

The correct answer is option 4) RA = 36 Ω and RB = 20 Ω

Given:

12 resistors each of resistance RA and R_B and it is having $Ia=10A,Ib=18A$

whose voltage is $V=30V$

Formula used:

Ohm's law: $V=IR$

Calculations:

As per the given statement in each circuit, the resistors are in such a way that the net resistance of each circuit is the minimum the resistors must be arranged in parallel. So their net resistance would be:

${1 \over R'a}=12*{1 \over Ra}$

${1 \over R'b}=12*{1 \over Rb}$

Thus using Ohm's law we get for circuit A:

$V=IR$

$30=Ia*R'a$

$30=10*{Ra\over12}$

$Ra={12*30 \over 10}={360 \over 10}=36Ω$

Similarly for circuit B we have:

$V=IR$

$30=Ib*R'b$

$30=18*{Rb\over12}$

$Rb={12*30 \over 18}={360 \over 18}=20Ω$

Therefore we have the resistances values as RA = 36 Ω and RB = 20 Ω.

The correct answer is Ammonium cyanate.

Key Points

• Ammonium cyanate is transformed into urea during the Wöhler synthesis.
• Friedrich Wöhler first wrote about this **chemistry-**related process in 1828.
• It is regularly credited with serving as the foundation for contemporary organic chemistry.

Additional Information

• Friedrich Wohler produced urea for the first time.
• Potassium cyanate and ammonium sulfate are dissolved in water in an equimolecular ratio.
• Ammonium Cyanate, which has the same chemical makeup as urea, was produced as a result of this reaction.
• A gas with no smell or color is called carbon monoxide (CO).
• It can result in rapid disease and death and is created whenever fossil fuel is burned.
• The CDC collaborates with local, state, national, and other partners to track CO-related disease and death monitoring data in the United States and to increase public awareness of CO poisoning.
• Ammonia is a poisonous gas or liquid that, when concentrated, corrodes bodily tissues on contact.
• It is possible to die from ammonia exposure at large enough doses.
• Ethanenitrile, CH3CN, the smallest organic nitrile, was once known as methyl cyanide or acetonitrile and is occasionally still referred to as than nitrile.

Shortcut Trick Expand both sides of the equation: (x3 − x2 + x − 1) = (x3 + 3x2 − 3x − 9). Cancel the common x3 term from both sides: −x2 + x − 1 = 3x2 − 3x − 9. Rearrange the terms to the right side to keep the x2 coefficient positive: 4x2 − 4x − 8 = 0. ∴ The correct answer is 4x2 − 4x − 8 = 0.

Alternate Method Given: (x2 + 1)(x − 1) = (x2 − 3)(x + 3) Formula Used: Standard representation of a quadratic equation is ax2 + bx + c = 0. ⇒ x2(x − 1) + 1(x − 1) = x2(x + 3) − 3(x + 3) ⇒ x3 − x2 + x − 1 = x3 + 3x2 − 3x − 9 ⇒ −x2 + x − 1 = 3x2 − 3x − 9 (since x3 cancels out) ⇒ 3x2 + x2 − 3x − x − 9 + 1 = 0 ⇒ 4x2 − 4x − 8 = 0 ∴ The correct answer is 4x2 − 4x − 8 = 0.

Additional Information Standard Form of Quadratic Equation A quadratic equation is always expressed as ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Discriminant and Roots The nature of roots is determined by D = b2 − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal. Simplification Rule While 4x2 − 4x − 8 = 0 is the standard representation, it can be further simplified to x2 − x − 2 = 0 by dividing the entire equation by 4.

Shortcut Trick

Check options for sum of digits = 15: 7+8 = 15 (Only option 3 and 4 fit, but 9+8=17).

Check the difference rule: If digits are x and y, then 10y + x − (10x + y) = 9(y − x).

Given 9(y − x) = 9 ⇒ y − x = 1.

Digits of 78: 8 − 7 = 1. Condition satisfied.

∴ The correct answer is 78.

Alternate Method

Given: Sum of digits = 15. Interchanged number − Original number = 9.

Formula Used: Original Number = 10x + y | Interchanged Number = 10y + x

⇒ Let the ten's digit be x and unit's digit be y.

⇒ x + y = 15 ---(i)

⇒ (10y + x) − (10x + y) = 9

⇒ 9y − 9x = 9 ⇒ y − x = 1 ---(ii)

⇒ Adding (i) and (ii): 2y = 16 ⇒ y = 8

⇒ Substituting y in (i): x + 8 = 15 ⇒ x = 7

⇒ Number = 10(7) + 8 = 78

∴ The correct answer is 78.

Additional Information

Difference of Reversed Numbers

The difference between a two-digit number and its reversed counterpart is always a multiple of 9, specifically 9 × |x − y|.

Sum of Reversed Numbers

The sum of a two-digit number and the number formed by reversing its digits is always a multiple of 11, specifically 11 × (x + y).

Digit Value vs Place Value

For a digit 'd' in the tens place, its face value is d, but its place value is 10 × d.

The correct answer is a plant was tall regardless of whether it had one gene (allele) or two genes (alleles) for tallness.

Key Points:

• The hybrid offspring generated will only acquire the dominant characteristic in the phenotype, in accordance with Mendel's first law of inheritance or law of dominance.
• Recessive traits are those that are suppressed, whereas dominant traits are those that control a trait.
• Tallness is the dominant characteristic.
• Because tallness is the dominating characteristic, a cross between a tall plant (TT) and a short pea plant (tt) produced only tall plants.

Additional Information:

• Mendel researched the inheritance of peas' height, flower colour, seed colour, and seed shape, among other seven other traits.
• For example, he initially established pea lines with tall vs. short height as two different versions of a feature.
• He bred these lines to each other and watched to see how the traits were passed down.
• He had grown these lines for generations until they were purebred, or always produced offspring that were identical to the parent.
• Mendel counted the precise number of plants that displayed each feature in addition to noting how the plants appeared in each generation.
• Surprisingly, he discovered fairly similar inheritance patterns for all seven traits he examined.

The correct answer is Meghalaya.

Key Points

• The Cathedral of Mary Help of Christians is a Roman Catholic church situated in Shillong's Laitumkhrah neighborhood, 3.5 kilometers from the bus terminal.
• It is also referred to as the Cathedral Catholic Church. It is Shillong's main house of worship and one of the city's most well-known tourist attractions.
• In Shillong, Meghalaya, India, there is a church called the Cathedral of Mary Help of Christians.
• It serves as the Metropolitan Archbishop of Shillong's residence and is the cathedral church of the Shillong Roman Catholic Archdiocese.
• It covers the East Khasi Hills and Ri-Bhoi districts, which contain 35 "Parishes" or church districts.
• The main venue of worship for the more than 342,169 Catholics in the Shillong Archdiocese is the Cathedral, which was constructed more than 50 years ago.

Additional Information

• The Cathedral of Mary Help of Christians
• ​The Cathedral Church of Mary Help of Christians was constructed by the Germans in 1913 and is dedicated to mother Mary. The first church was destroyed by a fire accident in 1936, and this led to the creation of the current shrine, according to history.
• After the Catholic Church had been present in Northeast India for 100 years, it was given the title of a shrine in 1980.
• The main place of worship for the about 300,000 Catholic residents of Ri Bhoi and the East Khasi Hills district of Meghalaya is this church, which is part of the Shillong Roman Catholic Archdiocese.
• The church was built in the Gothic style and is perched on an emerald-colored hill. The church is surprisingly huge and is most likely the biggest in Meghalaya.
• The interiors feature stained glass windows, terracotta cross stands, and a bronze cavalry monument.
• Hubert D'Rosario, Shillong's first archbishop, is buried there. Inside the chapel, there is a variety of artwork depicting passages and scenes from the Bible as well as the biographies of many saints. It also contains an underground chapel grotto dedicated to Our Lady of Lourdes that was cut out of a mound.

The correct answer is the Colloidal solution.

Key Points

• Light scatters in a variety of directions through a colloidal solution.
• As a result of the Tyndall effect.
• The Tyndall effect is a phenomenon that occurs when particles in a colloidal solution scatter light.
• The light frequency and particle density both affect how much scattering occurs.

Additional Information

• The colloidal particles in the solution prevent a light beam from passing completely through a colloid when it does so.
• The light is scattered when it strikes the colloidal particles.
• The Tyndall Effect is a light scattering phenomenon that only occurs in colloidal dispersion and does not exist in a true solution.
• This result is used to distinguish between a true solution and a colloid in a mixture.

The correct answer is the Equilibrium price.

Key Points

• The only price at which consumer and producer plans align is the equilibrium price, which is attained when the quantities sought by consumers and supplied by producers, respectively, are equal. This pervasive quantity is called the equilibrium quantity.
• Any other price throws the market out of balance since there is an imbalance between the quantity asked and the quantity delivered.
• Equilibrium simply means balance. If a market's equilibrium price and quantity are present, it has no incentive to change.
• However, when a market is out of balance, economic pressures begin to accumulate and push it in the direction of the equilibrium price and quantity.

Additional Information

• Product price
• ​The amount that customers must pay for a good or service is known as the price. Price, then, is an offer to sell something for a specific sum of money. Here, the word "offer" means that the price is liable to alter if it turns out that there aren't enough buyers willing to pay the product's original price.
• Total price
• ​Total Price refers to the total amount due from the debtor under a conditional sale or hire-purchase agreement, including any payments due upon exercising a purchase option, but omitting any payments due as a fine or as compensation for a breach of the agreement.
• Surplus price
• ​A consumer surplus occurs when consumers pay less than they would be willing to for a commodity or service. The difference between the price a producer is ready to pay for a good and the price they actually receive in the transaction is known as a producer surplus.

The correct option is 1 pair.

Key Points

• A total of 46 chromosomes make up a human, including one pair of XX or XY chromosomes and 22 pairs of numbered chromosomes autosomes.
• Sex chromosomes, the 23rd pair, are different in males and females.
• In contrast to males, who have one X and one Y chromosome, females have two copies of the X chromosome.
• By size, the 22 autosomes are numbered. The sex chromosomes are X and Y, the other two chromosomes.

Additional Information

• During these cell divisions, DNA can be precisely copied thanks to chromosomes.
• Our cells' nuclei contain chromosomes, which allow DNA to be precisely copied during cell division.
• This makes sure that everything inside of us operates effectively and smoothly.

Shortcut Trick

By definition, coprime numbers are numbers that have no common factors other than 1.

Therefore, their Highest Common Factor (HCF) must always be 1.

∴ The correct answer is 1.

Alternate Method

Given: A set of coprime numbers.

Formula / Definition Used:

⇒ Two or more numbers are said to be coprime if their only common positive divisor is 1.

⇒ For any two coprime numbers 'a' and 'b':

⇒ Factors of 'a' ∩ Factors of 'b' = {1}

⇒ HCF(a, b) = 1

Example:

⇒ Let us consider the coprime numbers 8 and 15.

⇒ Factors of 8 = 1, 2, 4, 8

⇒ Factors of 15 = 1, 3, 5, 15

⇒ Common factors = 1

⇒ Highest Common Factor (HCF) = 1

∴ The correct answer is 1.

Additional Information

LCM of Coprime Numbers

The Least Common Multiple (LCM) of any set of coprime numbers is always equal to their product. For example, LCM of coprime numbers 'a' and 'b' = a × b.

Consecutive Numbers are Coprime

Any two consecutive integers are always coprime to each other (e.g., 14 and 15, 99 and 100). Thus, HCF of consecutive numbers is always 1.

Prime Numbers and Coprimes

All prime numbers are coprime to each other, but coprime numbers do not necessarily have to be prime numbers themselves (e.g., 8 and 9 are composite but coprime).

The correct answer is option 2)3 Ω

Given:

$R1=5Ω,R2=10Ω,R3=30Ω$ are three resistors connected in parallel

Formula:

For resistances in parallel:

${1 \over Rp}={1 \over R1}+{1 \over R2}+{1 \over R3}$

Calculations:

${1 \over Rp}={1 \over R1}+{1 \over R2}+{1 \over R3}$

${1 \over Rp}={1 \over 5}+{1 \over 10}+{1 \over 30}$

${1 \over Rp}={6+3+1 \over 30}={10 \over 30}$

$Rp={30 \over 10}=3Ω$

Therefore the total resistance in the circuit is 3 Ω

The correct answer is PItcher.

Key Points

• A plant that consumes other living things is the pitcher plant.
• For food, carnivorous plants capture and eat insects like bees.
• Some of the names of insectivorous plants are pitcher plant, cobra lily, and venus flytrap.
• They are frequently known as carnivorous plants.

Additional Information

• Facts about insectivorous plants.
• In areas with low-nutrient soil, insectivorous plants can be found.
• It is deficient in nitrogen, crucial for plant growth in places like acidic bogs and rock outcrops.
• By breaking down the insects, this nitrogen is produced.
• Insectivorous plants catch insects because they need to eat insects to meet their nutritional needs because their soil is typically shallow and deficient in nutrients.
• Lichens are an entirely unique kind of organism that are neither plants nor animals.
• When it comes to lichen, most people mistakenly believe they are a form of moss.
• In reality, lichens are a hybrid of algae and a fungus.
• While the algae nourish the fungus, it also gives the algae a structure to live in.
• The family Cuscutaceae includes plants in the genus Cuscuta.
• Plant parasites include the Cuscuta genus.
• Since they are chlorophyll-deficient, they cannot manufacture their food through photosynthesis.
• Cuscuta relies on nutrients from other plants to flourish, which weakens the host plant.
• Some fungi create reproductive structures called mushrooms.
• Mushrooms resemble a plant's fruit in some ways, but instead of producing actual seeds, the mushroom instead generates millions of tiny spores called gills or pores.

Shortcut Trick

Area of a triangle = 1/2 × base × height

4 = 1/2 × 3 × height

8 = 3 × height

height = 8/3 = 2(2/3) cm

∴ The correct answer is 2(2/3) cm.

Alternate Method

Given:

Base (b) = 3 cm

Area (A) = 4 cm²

Formula Used:

Area = (1/2) × Base × Height

Calculations:

⇒ 4 = (1/2) × 3 × Height

⇒ 4 × 2 = 3 × Height

⇒ 8 = 3 × Height

⇒ Height = 8/3

⇒ Height = 2(2/3) cm

∴ The correct answer is 2(2/3) cm.

Additional Information

Heron's Formula

When all three sides (a, b, c) are known: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.

Right-Angled Triangle

In a right-angled triangle, the base and perpendicular act as the base and height respectively.

Equilateral Triangle Area

The area of an equilateral triangle with side 'a' is given by (√3/4) × a².

The correct answer is CaO.

Key Points

• Calcium oxide, also known as lime or CaO.
• Dissolves in water, it produces the compound calcium hydroxide, which is most commonly used in the production of cement.
• With the generation of a great deal of heat.
• Paste, mortar, and concrete are examples of cement-based materials, all of which have a high initial pH of 12.0 to 13.8.

Additional Information

• Gypsum, also known as the cement's "retarding agent," is a crucial ingredient that is primarily used to control the cement's setting time.
• Cement clinker can instantly condense when combined with water and release heat without the need for gypsum.
• The natural elements limestone, shale, and clay, to mention a few, are used to create cement, a fine powder-like substance.
• In a kiln, the component ingredients are heated to generate the little lumps known as "clinker," which are then crushed down while gypsum is added to create the more well-known cement powder.

The correct answer is electromagnetic induction.

Key Points

• A current can be made to flow as a result of a shifting magnetic field through a process called electromagnetic induction.
• Magnetic force, we examined the force that moving charges encounter in a magnetic field.
• By changing the magnetic field across a wire loop, electromagnetic induction creates an induced emf.
• Magnetic flux shifts when a magnet and a coil move in relation to one another, and the coil produces an electromotive force.
• This electromotive force is responsible for producing the induced current.

Additional Information

• According to Faraday's Law of Electromagnetic Induction, whenever there is a change in the magnetic field associated with the changes in the electric circuits, an emf is induced.
• The creation of an electromotive force across a conductor of electricity in a magnetic field that is changing is known as electromagnetic induction.
• Transformers and electric generators are two significant devices that rely on electromagnetic induction.
• In creating and controlling the electric current that is essential to our daily lives, both devices perform crucial roles.
• To convert kinetic energy to electrical energy, electric generators use electromagnetic induction.

The pattern followed in the given series is:

The difference between the terms is the increasing natural number.

Hence the correct answer is option 3)

Given word: SQUARE

In the given word 1st condition will be applied which says, 'If there is more than 1 vowel in the word, the vowels will be coded as 4.'

Now the code for the word SQUARE becomes:

Hence, the correct answer is option 1).

The correct answer is Dr Atma Ram Pandurang.

Key Points

• The Prarthana Samaj movement also referred to as the "Prayer Society," was a religious and social reform movement in Bombay, India, modelled after earlier reform movements.
• When Keshub Chandra Sen visited Maharashtra in 1863, Dadoba Pandurang and his brother Atmaram Pandurang established the Prarthana Samaj. It was done with the intention of converting people to monotheistic belief and worship. When Mahadev Govind Ranade joined, it became more well-known.
• The intellectuals who favoured changes to the Hindu social order were the key reformers. Its dissemination in southern India was aided by Telugu reformer and writer Kandukuri Veeresalingam.

Additional Information

• Prarthana Samaj
• ​​The movement was started by Atmaram Panduranga, and after reformer and scholar Mahadev Govind Ranade joined it, it acquired speed and popularity.
• The Samaj was distinct from the Bengali Brahmo Samaj in that it was less extreme and approached reformist programmes with caution. It also garnered better feedback from the general population as a result.
• The group's members all identified as Hindus and did so throughout. They want internal religious reform. They weren't opposed to religion per se; rather, they were against the societal ills that were common at the time, such as child marriage, widow repression, dowry, sati, untouchability, etc.
• They also promoted monotheism and condemned the worship of idols.
• Meetings of the society were held behind closed doors out of concern for a reaction from the orthodoxy. In actuality, neither the orthodox segments of society nor Brahminical power was ever specifically assailed by the Prarthana Samaj.
• The Brahmo Samaj and the Arya Samaj of Dayananda Saraswati had a significant impact on the Samaj, although it persisted as a separate organisation.
• Along with Ranade, the Sanskrit scholar Sir Ramakrishna Gopal Bhandarkar and the political figure Sir Narayan Chandavarkar were significant Samaj members.

The correct answer is Odisha.

Key Points

• The imaginary line at 23.50 degrees north of the equator is known as the Tropic of Cancer.
• The Tropic of Cancer crosses eight Indian states: Gujarat, Rajasthan, Madhya Pradesh, Chattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.
• The State of Odisha is not a part of it.

Additional Information

• Tropic of Cancer
• ​The Tropic of Cancer, commonly referred to as the Northern Tropic, is the northernmost circle of latitude on Earth where the Sun can be directly overhead.
• This happens in June when the Northern Hemisphere is tilted most strongly toward the Sun.
• Additionally, it sinks to 90 degrees below the horizon at solar midnight on the December Solstice.
• The circle is presently 23.43631° north of the Equator, according to a formula that is updated regularly.
• The tilt of the earth's axis with respect to the plane of its orbit is 23 degrees and 27 minutes.
• This tilt is also known as the earth's declination.
• At noon on June 21, the sun is at 23.5° north and is parallel to the earth's surface.
• This is why a globe has a designation for the Tropic of Cancer.

Concept used:

BODMAS,

B = Bracket

O = of

D = Division

M = Multiplication

A = Addition

S = Substraction

Preference will be given on the basis of the Letter coming first in the word Bodmas.

Calculation:

27.92 × 4 + 3.96 × 5 - 18 ÷ 2 + 1

Taking appro×imation: 28 × 4 + 4 × 5 - 18 ÷ 2 + 1

= 112 + 20 - 9 + 1 = 124

Hence, The Required value is 124.

Given:

Calculation:

According to the question,

Total weight of the ingredients = 2(3,50,000) = 7,00,000 g

Weight of almonds = 50% of total

Weight of flour = 10% of total

Difference between them

= (50 - 10)%

= 40% of 7,00,000

= 2,80,000 g

Hence, The Required value of weight is 2,80,000 g.

The logic followed here is:

The difference of difference between the terms is 6.

The pattern followed in the given series is:

Hence, the correct answer is option 3).

The logic followed in the given series is:

(First term)³ - 1 = Second term

Now we apply the logic to the given series:

9 : 728 :: 4 : 63 :: 7 : ?

(9)³ - 1 = 728

729 - 1 = 728

728 = 728 

and,

9 : 728 :: 4 : 63 :: 7 : ?

(4)3 - 1 = 63

64 - 1 = 63 

63 = 63 

Similarly,

9 : 728 :: 4 : 63 :: 7 : ?

(7)3 - 1 = ?

343 - 1 = ?

342 = Answer

Hence, the correct answer is option 2).

Shortcut Trick

Selling at a 20% loss means the selling price is 80% of the cost price (CP).

80% of CP = Rs. 840

To obtain a 25% gain, the required selling price must be 125% of CP.

Required SP = (840 ÷ 80) × 125

Required SP = 10.5 × 125 = Rs. 1,312.50

∴ The correct answer is Rs. 1,312.50.

Alternate Method

Given: First selling price (SP₁) = Rs. 840, Loss = 20%, Target Gain = 25%.

Formula Used:

1. CP = [SP × 100] / [100 − Loss%]
2. New SP = [CP × (100 + Gain%)] / 100

Calculations:

⇒ CP = (840 × 100) / (100 − 20)

⇒ CP = 84000 / 80

⇒ CP = Rs. 1050

⇒ New Selling Price = 1050 × (100 + 25) / 100

⇒ New Selling Price = 1050 × 125 / 100

⇒ New Selling Price = 1050 × 1.25

⇒ New Selling Price = Rs. 1,312.50

∴ The correct answer is Rs. 1,312.50.

Additional Information

Cost Price (CP)

The price at which an article is purchased. It is the base for calculating Profit or Loss percentage.

Profit and Loss Formulas

Profit = SP − CP (when SP > CP). Loss = CP − SP (when CP > SP).

Direct Relation Shortcut

SP₁ / (100 ± Gain₁/Loss₁) = SP₂ / (100 ± Gain₂/Loss₂). This allows finding the new price directly without calculating CP.

Calculations:

$\rm\left(\frac{25}{9}\right)^{x+1}\left(\frac{81}{625}\right)^{x-1}=\frac{9}{25} \$

⇒$(\frac{25}{9})^{(x + 1)}(\frac{9²}{25²})^{(x-1)}$= $\frac{ 9}{25}$

⇒$(\frac{25^{(x+1)}}{9^{(x+1)}})(\frac{9^{2(x-1)}}{25^{2(x-1)}})$ = $\frac{ 9}{25}$

⇒ $\frac{9^{2(x-1)-(x+1)}}{25^{2(x-1)-(x+1)}}$ = $\frac{ 9^1}{25^1}$