The correct answer for this is 2000 km.

Key Points

• Kavach
• To increase the safety of moving trains, Indian Railways created the Automatic Train Protection (ATP) system known as Kavach.
• KAVACH is an indigenous train protection system that was created by the Research Design and Standards Organization (RDSO) in collaboration with three Indian manufacturers.
• By preventing Signal Passing at Danger (SPAD) and excessive velocity, KAVACH will assist Loco Pilot. Additionally, it will make it possible for the trains to run in adverse conditions like a thick fog. ​
• In the event that the Loco Pilot fails, it automatically applies the brakes to manage the train's speed.

Additional Information

• This technology's development has cost a total of Rs. 16.88 crores thus far. Kavach is responsible for over 1,098 kilometres of the South Central Railway's network route.
• Indian Railway tested Kavach on the absolute block portion of the South-Central Railway's Lingamapalli-Vikarabad-Wadi, Vikarabad-Bidar (250 KM) segment. Three vendors received approval for developmental orders on Indian Railways following the satisfactory conclusion of trials.
• The South-Central Railway's Manmad - Mudkhed - Dhone - Guntakal & Bidar - Parbhani segment is now working on a Kavach project spanning 1199 kilometres after a successful trial.
• Currently, the sections of New Delhi-Howrah and New Delhi-Mumbai are scheduled for the Kavach rollout, with completion dates of March 2024.

Shortcut Trick

Weight of the new man = Weight of the replaced person + (Total persons × Increase in average)

⇒ Weight = 72 + (6 × 2)

⇒ Weight = 72 + 12 = 84 kg

∴ The correct answer is 84 kg.

Alternate Method

Given:

Total number of persons = 6

Weight of the person leaving = 72 kg

Average weight increase = 2 kg

Formula Used:

Total Increase in Weight = Number of persons × Increase in average

Weight of New Person = Weight of replaced person + Total Increase

Calculations:

⇒ Total weight of the group increases because the new man is heavier than the person who left.

⇒ Net increase in total weight = 6 × 2 = 12 kg

⇒ Weight of the new man = 72 kg + 12 kg

⇒ Weight of the new man = 84 kg

∴ The correct answer is 84 kg.

Additional Information

General Replacement Rule

When one item is replaced, the new value is calculated as: New = Old ± (Total Count × Change in Average). Use '+' for increase and '−' for decrease.

Average Concept

The average is the central value of a set of data, calculated as (Sum of all observations) ÷ (Total number of observations).

Net Deviation

The sum of deviations of all values in a data set from their arithmetic mean is always zero. This principle is often used to solve complex average problems quickly.

Shortcut Trick

Selling Price (SP) of 10 pens = Rs. 7

SP of 1 pen = 7 ÷ 10 = Rs. 0.70

Profit = 40%

Multiplier: SP = CP × (100 + P%) ÷ 100

0.70 = CP × (140 ÷ 100) ⇒ CP = 0.70 × (100 ÷ 140) = 0.70 ÷ 1.4 = Rs. 0.50

∴ The correct answer is Rs. 0.50.

Alternate Method

Given: Number of pens = 10, Total SP = Rs. 7, Profit% = 40%.

Formulas: CP = [SP ÷ (100 + Profit%)] × 100

⇒ Selling Price of one pen = 7 ÷ 10 = Rs. 0.70

⇒ Let the Cost Price (CP) of one pen be x.

⇒ x + 40% of x = 0.70

⇒ 1.4x = 0.70

⇒ x = 0.70 ÷ 1.4 = 0.5

∴ The correct answer is Rs. 0.50.

Additional Information

Cost Price and Selling Price

The price at which an article is purchased is called its Cost Price (CP) and the price at which it is sold is its Selling Price (SP).

Profit Percentage

Profit% is always calculated on the Cost Price unless specified otherwise. Formula: Profit% = (Profit ÷ CP) × 100.

The correct answer is 1872.

Key Points

• Chemist and inventor Dmitri Ivanovich Mendeleev was from Russia. His most famous works are the Periodic Law and a modified periodic chart of elements. The first periodic table was created by Mendeleev, and printed in 1869.
• In order to represent similarities and patterns in the behaviour of elements, Mendeleev created the periodic table, which is an arrangement of elements in an increasing atomic mass order in tablet form.
• In the periodic table, the elements were arranged into 7 Horizontal rows in ascending order of atomic known as periods and 8 vertices column known as groups.
• When two elements are highly similar to one another, the new element is positioned immediately below the older element that shares the same characteristic to begin a new period. Lithium, potassium, rubidium, and other first-group elements are some examples.
• One period below the other creates a "column" (group). Thus, the horizontal rows and vertical columns, or the periods and groups, respectively, make up Mendeleev's periodic table.
• If two elements are similar but not by much, they are separated by being placed below but somewhat distant from one other. Each column will contain two sub-columns (A and B), allowing for more similarity between entries inside each sub-column.
• Transitional elements are categorised into group VIII, while normal elements are divided into groups I through VII.
• Group VIII consists of three parts, while Groups I through VII is split into two subgroups.
• The first series and the second series are separated into the fourth through seventh grades.

Additional Information

Difference between the Modern periodic table and Mendeleev's periodic table -

Statement:

1. Some pants are coats.
2. All coats are red.
3. All red are shirts.

Venn Diagram:

Conclusions:

I. All pants are shirts. → False (Some pants are coats and all coats are shirts but we do NOT have a direct relation between pants and shirts so we can't conclude that all pants are shirts)

Il. All coats are shirts. → True (Since we have All coats are red and All red are shirts, so we can say that All coats are shirts)

IIl. Some red are coats. → True (Since All coats are red so we can say that Some red are coats)

IV. Some shirts are pants. → True (Since we have All coats are shirts and some pants are coats so we can say that Some shirts are pants)

According to the diagram, conclusions II, III, and IV follow.

Hence, the correct answer is option 1).

The correct answer is Rishabhanatha.

Key Points 

• Tirthankara of Jainism
• In Jainism, a Tirthankara is a saviour and divine guide on the dharma (righteous path).
• The word "Tirthankara" refers to the creator of a "samsara," or fordable route through the sea of limitless births and deaths.
• According to Jains, a Tirthankara is a person who, by himself, has conquered "samsara," the cycle of rebirth and death, and created a way for others to follow.
• The Tirthankara attains "Kevala Jnana" after realising his or her actual nature as spirit or self.
• Rishabhanatha is the first Tirthankara ("ford-maker") of Jainism and the creator of the Ikshvaku dynasty born to king Nabhi Raja and Queen Marudevi at Ayodhya
• Abhadeva, Rishabhadeva, and Abha are other names for Rishabhanatha.
• According to Jain tales, he lived millions of years ago.

Additional Information

Given series:

(Left) A D 4 F @ T 5 H $ B R @ V T 6 # 7 H 6 D 8 $ % & G $ 3 C F (Right)

When all the symbols are dropped from the series,

Ninth to the left of fifth from the right → This means 14^th position to left from the right end.

(Left) A D 4 F T 5 H B R V T 6 7 H 6 D 8 G 3 C F (Right)

The letter 'B' is ninth to the left of fifth from the right.

Hence, the correct answer is option 4).

The correct answer is C3H7OH.

Key Points

Alcohols

• C_nH_2n+1OH is the general molecular formula of the homologous sequence of alcohols.
• Given carbon with one, two, and four atoms which are in homologous series, so left out is 3 atoms of carbon.
• The Formula containing 3 molecules of Carbon is C₃H_2*3+1OH which is C₃H₆₊₁OH, yielding C₃H₇OH.​
• So the answer is C3H7OH.

Additional Information

• An organic molecule known as alcohol has a saturated carbon atom linked to at least one hydroxyl (OH) functional group.
• The principal alcohol is ethanol (also known as ethyl alcohol), which is used as a narcotic.
• Ethanol is the main alcohol found in alcoholic beverages.

Shortcut Trick

Ratio of the two numbers = 1 : 3/2 = 2 : 3.

Let the common ratio factor be k. Then the numbers are 2k and 3k.

Product of numbers = HCF × LCM ⇒ (2k) × (3k) = 44 × 264.

6k² = 44 × 264 ⇒ k² = 44 × 44 = 1936.

k = √1936 = 44.

Smaller number = 2k = 2 × 44 = 88.

∴ The correct answer is 88.

Alternate Method

Given:

HCF of two numbers = 44

LCM of two numbers = 264

One number (N₁) = 3/2 × Other number (N₂)

Formula Used:

Product of two numbers = HCF × LCM

Calculations:

⇒ Let the smaller number be x. Then the larger number is (3/2)x.

⇒ x × (3/2)x = 44 × 264

⇒ (3/2)x² = 11616

⇒ x² = (11616 × 2) ÷ 3

⇒ x² = 3872 × 2 = 7744

⇒ x = √7744

⇒ x = 88

The numbers are 88 and (3/2) × 88 = 132.

∴ The correct answer is 88.

Additional Information

Fundamental Relation

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

HCF and Co-primes

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

LCM in terms of HCF

The Least Common Multiple (LCM) is always divisible by the Highest Common Factor (HCF). LCM = HCF × x × y.

The correct answer is the squamous epithelium.

Key Points       Squamous epithelium

• Squamous epithelial cells are flat, spherical, and have a tiny nucleus in the middle.
• These are also known as Alveolar cells, which line the walls of the alveoli.
• The diffusion of gases in the lungs is best accomplished by this single layer of squamous cells.
• The presence of tightly packed cells with a single nucleus positioned on the basement membrane defines the cells.

 

 

              Squamous epithelium

Additional Information 

• Simple columnar to cuboidal epithelium lines the bronchioles.
• Thin squamous epithelium lines the alveoli, allowing for gas exchange.

Given:

<br>

We substitute the values in the given equation and solve it using BODMAS rule:

Substituting the symbols, as per the above table,

⇒ 76 - 5 × 6 ÷ 3 + 4 

⇒ 76 - 5 × 2 + 4

⇒ 76 - 10 + 4

⇒ 80 - 10

⇒ 70

Hence, the correct answer is option 3.

Shortcut Trick

Sum of ratio parts = 7 + 5 + 4 = 16 units

16 units = 48 m → 1 unit = 3 m

Sides are a = 21 m, b = 15 m, c = 12 m

Semi-perimeter (s) = 24 m

Area = √(24 × 3 × 9 × 12) = √(24 × 324 × 3) = 36√6 m²

∴ The correct answer is 36√6 m².

Alternate Method

Given: Ratio of sides = 7 : 5 : 4 and Perimeter = 48 m

Formula Used: Heron's Formula Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2

⇒ Let the sides be 7x, 5x, and 4x

⇒ 7x + 5x + 4x = 48

⇒ 16x = 48 ⇒ x = 3

⇒ Sides are a = 21 m, b = 15 m, c = 12 m

⇒ Semi-perimeter s = 48 / 2 = 24 m

⇒ Area = √[24 × (24−21) × (24−15) × (24−12)]

⇒ Area = √[24 × 3 × 9 × 12]

⇒ Area = √[2 × 12 × 3 × 9 × 12] = 12 × 3 √[2 × 3] = 36√6 m²

∴ The correct answer is 36√6 m².

Additional Information

Heron's Formula

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

Equilateral Triangle Area

For a triangle with all sides equal to 'a', Area = (√3 / 4) × a².

Right-Angled Triangle Area

When base 'b' and height 'h' are perpendicular, Area = 1/2 × b × h.

The correct answer is parallel to the principal axis of the concave mirror.

Key Points Concave mirror

• The reflective surface of a concave mirror is curled inward and away from the light source.
• Light is reflected inward to a single focal point via concave mirrors.
• A concave mirror, also known as a converging mirror, has an inwardly depressed reflecting surface.

Additional Information 

    In the case of concave mirrors, rays parallel to the principal axis converge and meet at the focus.

Shortcut Trick

Apply the identity (a − b)(a + c) or (x + a)(x + b) where x = 100.

95 × 103 = (100 − 5) × (100 + 3)

⇒ 100² + (3 − 5) × 100 + (−5 × 3)

⇒ 10000 − 200 − 15 = 9785

∴ The correct answer is 9785.

Alternate Method

Given: 95 × 103

Formula Used: Algebraic identity (x + a)(x + b) = x² + (a + b)x + ab

⇒ Let x = 100, a = −5, and b = 3.

⇒ 95 × 103 = (100 − 5)(100 + 3)

⇒ (100)² + (−5 + 3)(100) + (−5 × 3)

⇒ 10000 + (−2)(100) − 15

⇒ 10000 − 200 − 15

⇒ 9800 − 15

⇒ 9785

∴ The correct answer is 9785.

Additional Information

BODMAS Rule

Always follow the order of Brackets, Orders, Division, Multiplication, Addition, and Subtraction for complex calculations.

Square of Numbers near 100

For (100 ± x)², the result is 100 ± 2x | x². For example, 103² = 10609.

Distributive Property

The property a(b + c) = ab + ac helps in breaking down large multiplications into simpler parts.

Given word: 'ACQUIRED'

Conditions:

i. If the first letter of the word is a vowel and last letter is a consonant, then both these letters will be coded as ‘*'.

ii. If the second letter of the word is a vowel and the fifth letter is a consonant, then both these letters will be coded as ‘&’.

Here, the first letter 'A' is a vowel and the last letter 'D' is a consonant therefore the first condition follows.

So the code for the word is,

A ⇒ *, C ⇒ >, Q ⇒ %, U ⇒ ^, I ⇒ =, R ⇒ $, E ⇒ +, D ⇒ *

Thus, the code for the word 'ACQUIRED' is >%^=$+.

Hence, the correct answer is option 2).

Given series:

_ _b a d c _ _ d _ b a d c b _

Checking the options:

1. dcbaac →  d c b a d c b a d a b a d c b c → doesn't follow any pattern. 2. cdabca →  c d b a d c a b d c b a d c b a  → doesn't follow any pattern. 3. dcbaca →  d c b a d c b a d c b a d c b a → this follows the pattern and a repeating sequence is developed. 4. dbcaca → d b b a d c c a d c b a d c b a → doesn't follow the pattern.

Hence, the correct answer is option 3.

The given letter clusters are,

AIN, ONK, AST, EJO

When each letter is changed to the next letter in the English alphabetical order, the words formed are

BJO, POL, BTU, FKP

From the above words, only one word doesn't have a vowel.

Hence, the correct answer is option 4).

Given,

U, V, W, X, Y, and Z live on different floors of the same building.

Step 1: The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6.

Step 2: a) Z lives on the floor immediately above Y

b) W lives immediately above Z and immediately below V.

Step 3): Only one person lives between U and V.

According to the arrangement, Z lives on the second floor.

Hence, the correct answer is option 1).

​​​The correct answer is Both statements are false

Key Points

• Properties of metals
• ​​​The metals high up in the reactivity series are very reactive.​
• ​​Reactivity series refer to the metal series in which metals are arranged according to their reactivity from highest to lowest. It is also known as activity series which is used to predict whether a metal can displace another metal in a displacement reaction or not. This is a series in descending order of the reactivity of metals.
• ​​The metals at the top of the reactivity series are powerful reducing agents so they are easily oxidized. These metals corrode very easily.
• Metals that are placed higher on the reactivity series have the ability to displace metals that are placed lower from their salt solutions.
• Higher-ranking metals require greater amounts of energy for their isolation from ores and other compounds.

Additional Information 

• Metallic  behaviour
• ​The metals high up in the reactivity series can not be obtained from their compounds by heating with carbon since these metals have more affinity for oxygen than carbon
• ​The oxides of very reactive metals cannot be reduced with carbon cause these metals have more affinity (more attraction) for oxygen than carbon. So carbon is unable to remove oxygen from these metal oxides and hence cannot convert them into free metals.
• The highly reactive metals are extracted by the electrolytic reduction of their molten chloride.​​​​​ ​During electrolysis, the electric current passes through an ionic substance in a molten or dissolved state causing the electrodes to react chemically and the materials to decompose.

Shortcut Trick

For any polygon with n sides, the sum of all interior angles is given by (n − 2) × 180°.

A heptagon has 7 sides (n = 7).

Sum = (7 − 2) × 180°

Sum = 5 × 180° = 900°

∴ The correct answer is 900°.

Alternate Method

Given:

Geometric Shape = Heptagon

Number of sides (n) = 7

Formula Used:

Sum of interior angles of a polygon = (n − 2) × 180°

Calculations:

⇒ A heptagon is a polygon with 7 vertices and 7 sides.

⇒ By applying the interior angle sum theorem:

⇒ Sum = (n − 2) × 180°

⇒ Sum = (7 − 2) × 180°

⇒ Sum = 5 × 180°

⇒ Sum = 900°

∴ The correct answer is 900°.

Additional Information

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles is always equal to 360°.

Individual Interior Angle (Regular Polygon)

For a regular polygon, each interior angle is calculated as [(n − 2) × 180°] ÷ n. For a regular heptagon, this is 900° ÷ 7 ≈ 128.57°.

Number of Diagonals

The number of diagonals in a polygon with n sides is given by [n × (n − 3)] ÷ 2. For a heptagon, it is [7 × 4] ÷ 2 = 14 diagonals.

Shortcut Trick

Compare the two sets: 2 plates + 3 spoons = Rs. 86 and 4 plates + 1 spoon = Rs. 112.

Double the first set: 4 plates + 6 spoons = Rs. 172.

Subtract the second set from this: (4P + 6S) − (4P + 1S) ⇒ 5 spoons = 172 − 112 = Rs. 60.

Cost of 1 spoon = 60 ÷ 5 = Rs. 12.

Cost of 1 plate from the second set ⇒ (112 − 12) ÷ 4 = Rs. 25.

Difference between plate and spoon = 25 − 12 = Rs. 13.

∴ The correct answer is Rs. 13.

Alternate Method

Given:

Cost of 2 plates (P) and 3 spoons (S) = Rs. 86

Cost of 4 plates (P) and 1 spoon (S) = Rs. 112

Formula Used:

Elimination method for linear equations in two variables.

Calculations:

Let the cost of one plate be P and one spoon be S.

⇒ 2P + 3S = 86 → (i)

⇒ 4P + S = 112 → (ii)

Multiplying equation (i) by 2:

⇒ 2 × (2P + 3S) = 2 × 86

⇒ 4P + 6S = 172 → (iii)

Subtracting equation (ii) from equation (iii):

⇒ (4P + 6S) − (4P + S) = 172 − 112

⇒ 5S = 60

⇒ S = 60 ÷ 5 = Rs. 12

Substituting S = 12 in equation (ii):

⇒ 4P + 12 = 112

⇒ 4P = 112 − 12

⇒ 4P = 100

⇒ P = 100 ÷ 4 = Rs. 25

The difference between the cost of a plate and a spoon is:

⇒ Difference = P − S = 25 − 12 = Rs. 13

∴ The correct answer is Rs. 13.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by = c represent straight lines. They can be solved using substitution, elimination, or cross-multiplication.

Elimination Method

A process where you multiply equations by constants to align coefficients of one variable, allowing its removal by addition or subtraction.

Cost-Price Logic

Total Price = (Quantity₁ × Price₁) + (Quantity₂ × Price₂). This is the base for solving such purchase-based word problems.

According to the given Venn diagram,

No. of persons who are only Entrepreneurs = 12

No. of persons who are only Engineers = 20

No. of persons who are only Under 35 years = 10

No. of persons who are Engineer, Entrepreneurs, and under 35 years of age = 8

No. of persons who are Engineers and Entrepreneurs and not under 35 years of age = 7

No. of persons who are Entrepreneurs and under 35 years of age but not Engineer = 5

No. of persons who are under 35 years of age and Engineers but not an Entrepreneurs = 6

Hence, the correct answer is option 3).

​​​The correct answer is Because it reduces the oxygen-carrying capacity of the blood. 

Explanation:

• The haemoglobin in our blood takes oxygen to different parts of our body from the Lungs.
• The oxygen affinity of haemoglobin is less than that of  CO affinity towards haemoglobin.
• When we inhale air polluted with carbon monoxide (CO), carbon monoxide (CO) will combine with haemoglobin, forming carboxyhemoglobin in the blood and Stopping oxygen transport.
• The binding of carbon monoxide to haemoglobin, forming carboxyhemoglobin, reduces the amount of oxygen available to the heart muscle and other tissues for synthesizing ATP.
• It is a pollutant for humans since it reacts with Haemoglobin. It is harmful when breathed since it displaces oxygen in the blood and deprives the heart, brain and other important organs.

The correct answer is the United States of America.

Key Points

• The American Constitution served as a model for the idea of judicial review.
• The Indian Constitution specifies the Supreme Court's judicial review authority in Articles 32 and 136 and the High Court's judicial review authority in Articles 226 and 227.
• Judicial review states that the court has the authority to examine rules and laws, determine whether they are constitutional, and also to invalidate them if they are found to be unconstitutional.

Additional Information 

• The Weimar Constitution of Germany, which addressed the suspension of fundamental rights during a national emergency, served as the model for these clauses.
• The provisions relating to the Centre's residuary powers and the Centre's appointment of the Governors in the states were taken from Canada.
• The Russian Constitution, which the Soviet Union is today, is where the principles of fairness (social, economic, and political) in the Indian Preamble originated.

Given:

A certain number of people are sitting in a row, facing North.

Step 1): P is an immediate neighbour of both V and T.

OR  

Step 2): (a) R is an immediate neighbour of both T and Q.

(b) V is at the extreme right end.

(c) There are only two people on the left of Q.

According to the arrangement, seven persons are seated in a row.

Hence, the correct answer is option 2).

Shortcut Trick

Apply M₁D₁ = M₂D₂ directly.

16 × 5 = M₂ × 20

80 = M₂ × 20

M₂ = 80 ÷ 20 = 4

∴ The correct answer is 4 men.

Alternate Method

Given:

Number of men in first case (M₁) = 16

Number of days in first case (D₁) = 5

Number of days in second case (D₂) = 20

Formula Used:

Total Work = Men × Days

M₁D₁ = M₂D₂

Calculations:

⇒ Total Work = 16 × 5 = 80 man-days

⇒ Required Men (M₂) = Total Work ÷ D₂

⇒ M₂ = 80 ÷ 20

⇒ M₂ = 4 men

∴ The correct answer is 4 men.

Additional Information

General Work Formula

For varying efficiency and hours, use (M₁D₁H₁E₁)/W₁ = (M₂D₂H₂E₂)/W₂.

Inverse Proportion

The number of men is inversely proportional to the time taken to complete a constant piece of work.

Work and Wages

Wages are generally distributed in the ratio of the work done by each person.

The correct answer is Nethra Kumanan.

Key Points

• Nethra Kumanan
• ​Nethra Kumanan, who was born on August 21, 1997, learned to sail in 2009 at a summer camp run by the Tamil Nadu Sailing Association. At the time, she was twelve.
• India was formerly represented by Nethra Kumanan at the 2014, and 2018 Asian Games, and the 2020 Sailing World Cup.
• Nethra Kumanan won a bronze medal in the 2020 Sailing World Cup in Miami, USA, becoming the first Indian woman to do so in sailing

 Additional Information

• Tokyo Olympics 2021
• Due to the COVID-19 pandemic, the 2020 Summer Olympics, which were originally scheduled to take place from 24 July to 9 August 2021, were moved up a year to 2021.
• On July 23, 2021, at Tokyo's Olympic Stadium, Emperor Naruhito gave the opening address for the Tokyo Olympics.
• The theme of the Tokyo Summer Olympics in 2020 is "Moving Forward: Unified by Emotion."

Shortcut Trick

When the Cost Price of x articles equals the Selling Price of y articles:

Profit/Loss % = [(No. of CP articles − No. of SP articles) / No. of SP articles] × 100

Given: x = 42, y = 36

Profit % = [(42 − 36) / 36] × 100 = 6/36 × 100 = 1/6 × 100

Profit % = 16 2/3%

∴ The correct answer is 16 2/3% gain.

Alternate Method

Given:

CP of 42 articles = SP of 36 articles

⇒ Let CP of 1 article = ₹1

⇒ CP of 42 articles = ₹42

⇒ Since CP of 42 = SP of 36, then SP of 36 articles = ₹42

⇒ CP of 36 articles = ₹36

⇒ Profit = SP of 36 − CP of 36

⇒ Profit = ₹42 − ₹36 = ₹6

⇒ Gain % = (Profit / CP) × 100

⇒ Gain % = (6 / 36) × 100 = 1/6 × 100

⇒ Gain % = 16 2/3%

∴ The correct answer is 16 2/3% gain.

Additional Information

Profit and Loss Percentages

Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100. Profit or loss is always calculated on the Cost Price unless specified otherwise.

Article Quantity Relationship

If CP of x = SP of y, the Profit % = (x − y)/y × 100. If the result is negative, it represents a Loss %.

Fraction to Percentage Conversion

Common fractions: 1/6 = 16.66% or 16 2/3%, 1/7 = 14.28% or 14 2/7%, 1/8 = 12.5%.

Given: 75#2

The code for 75#2

Here, the first element is an odd number, and the last, is an even number so the second conclusion follows.

In the given cluster, 

7 - The odd number

2 - The even number

Therefore, condition (ii) is satisfied so, the first and last elements are to be coded as $.

Thus, the code for 75#2 is $FK$.

Hence, the correct answer is option 2).

The correct answer is PESA Act 1996.

Key Points

• PESA Act 1996 ​
• Tribal communities that reside in Scheduled Areas have the legal right to rule themselves according to their own forms of self-government, which is recognized under the PESA Act.
• The Scheduled Area is not automatically covered by the legislation, hence the PESA Act was passed on the advice of the Bhuria Committee Report, which was submitted in 1995.
• The PESA Act was passed in December 1996 to allow Tribal Self Rule in the scheduled territories by extending the rules created by the 73rd constitutional amendment to those areas.

Additional Information

• Part IX of the constitution related to panchayats consists of articles 243 to 243-O.
• Article 243A: Gram Sabha
• At the village level, a Gram Sabha may exercise the authority and carry out the duties that a state's legislature may by law designate.
• Article 243B: Constitution of Panchayats
• In conformity with the guidelines in this Part, Panchayats at the village, intermediate, and district levels shall be established in each State
• Article 243C: Composition of Panchayats
• ​The Legislature of a State may, by law, establish rules regarding the makeup of Panchayats, provided that, to the greatest extent possible, there shall be uniformity throughout the State in the ratio between the population of a Panchayat's territorial area at any level and the number of seats in such Panchayat to be filled by election.

Shortcut Trick

Ratio of parts = 5 : 3

Total ratio units = 5 + 3 = 8 units

8 units = ₹1,368 → 1 unit = 1368 ÷ 8 = ₹171

Greater part (5 units) = 5 × 171 = ₹855

∴ The correct answer is ₹855.00.

Alternate Method

Given: Total amount = ₹1,368, Ratio = 5 : 3.

Formula: Value of a part = (Ratio of that part ÷ Sum of ratios) × Total Value

⇒ Sum of ratio parts = 5 + 3 = 8

⇒ Greater part corresponds to the ratio 5.

⇒ Value of greater part = (5 ÷ 8) × 1368

⇒ Value of greater part = 5 × 171

⇒ Value of greater part = ₹855

∴ The correct answer is ₹855.00.

Additional Information

Ratio and Proportion

A ratio compares two quantities. If a total S is divided in ratio a:b, the parts are [a/(a+b)]×S and [b/(a+b)]×S.

Direct Proportion

When the total amount increases, the value of each individual part in the ratio increases proportionally.

Difference between parts

The difference between parts can be found directly using: Difference = [(a−b)/(a+b)]×Total.

Shortcut Trick

For any two consecutive natural numbers n and (n + 1), the number of non-square numbers between their squares is always 2n.

Here, n = 87 and n + 1 = 88.

Number of non-square numbers = 2 × 87 = 174.

∴ The correct answer is 174.

Alternate Method

Given: Two consecutive squares 87² and 88².

Formula: Number of integers between a and b (where a) is (b − a) − 1.

⇒ 87² = 7569

⇒ 88² = 7744

⇒ Number of non-square numbers = (7744 − 7569) − 1

⇒ Number of non-square numbers = 175 − 1 = 174.

∴ The correct answer is 174.

Additional Information

Consecutive Squares Property

There are 2n non-perfect square numbers between the square of n and (n + 1).

Difference of Squares

The difference between (n + 1)² and n² is always 2n + 1.

Sum of First n Odd Numbers

The square of any natural number n is equal to the sum of the first n odd natural numbers.

Shortcut Trick

Effective rate of compound interest for 2 years at 10% = 10% + 10% + (10 × 10) ÷ 100% = 21%

Total amount payable after 2 years = Principal × (100% + 21%)

⇒ Total Amount = 121% of 12500

⇒ Total Amount = 1.21 × 12500 = 15125

∴ The correct answer is Rs. 15,125.

Alternate Method

Given:

Principal (P) = Rs. 12,500

Rate of Interest (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P × (1 + R ÷ 100)ⁿ

Principal ₹12,500

+10%

After 1st Year ₹13,750

+10%

Final Amount ₹15,125

Calculations:

⇒ A = 12500 × (1 + 10 ÷ 100)²

⇒ A = 12500 × (1 + 1 ÷ 10)²

⇒ A = 12500 × (11 ÷ 10)²

⇒ A = 12500 × (121 ÷ 100)

⇒ A = 125 × 121

⇒ A = 15125

∴ The correct answer is Rs. 15,125.

Additional Information

Compound Interest Formula

A = P(1 + R ÷ 100)ⁿ, where A is the total amount, P is the principal, R is the rate of interest, and n is the time period in years.

Effective Rate for 2 Years

The effective compound interest rate for 2 years at R% per annum is calculated directly using the successive percentage formula: [2R + (R² ÷ 100)]%.

Difference Between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest on a certain sum is calculated as P(R ÷ 100)².

Given:

${\sqrt {1296} \over \sqrt{121}} \times { 15 \over (216)^{1/3} } \times {11 \over{ \sqrt{225}}}$

Calculation:

As, we know that 

⇒(36)² = 1296 , 11² = 121 , 6³ = 216 , 15² = 225 

⇒ $\sqrt{36 \times 36}\over \sqrt{11 \times 11}$ × $15\over \sqrt[3]{6^3}$ × $11\over \sqrt{15 \times 15}$ 

⇒ $\frac{36 \times 15 \times 11}{{11} \times 6 \times 15}$

⇒ $\frac{36}{6}$ = 6

Hence, the correct answer is option 3.

The correct answer is oic acid.

Key Points

• Carboxylic acids have carbon particles and are called propanoic corrosive, from propane, the name for a three-carbon chain, with - oic corrosive, the postfix for this class of mixtures, added.
• The postfix of this carbon chain is then supplanted, as carboxylic acids generally end in "- oic corrosive." A model is CH2O2, in which the longest nonstop carbon chain is methane.
• The sub-atomic equation of propanoic corrosive is C3H6O2. This corrosive contains three carbon particles, six hydrogens, and two oxygens. The carbon particles are reinforced directly.
• Propionic corrosive, otherwise called propionate or methane carboxylic corrosive, is an individual from the class of mixtures known as carboxylic acids.

Additional Information

• This compound has a place with the class of natural mixtures known as carboxylic acids.
• Propane is a three-carbon alkane gas (C3H8). It is put away under tension inside a tank as a dismal, unscented fluid.
• As strain is delivered, the fluid propane disintegrates and transforms into gas that is utilized in the ignition.
• A prop is a recognizable term in the theater or film domain. Props are those items that an entertainer might deal with or control to satisfy the qualities or activities of a person.

The correct answer is 32.

Key Points

• The seventh time frame contains 32 components, tied for the most with period 6, starting with francium and finishing with oganesson, the heaviest component presently found.
• The all-out number of electrons that can be obliged in the seventh period is 2 ( in 7s) + 14(in 5f) + 10(in 6d )+ 6(in 7p) = 32. The most extreme number of components present in it is 32.
• A period 7 component is one of the substance components in the seventh column (or time) of the occasional table of the compound components.
• Generally speaking, period 7 components fill their 7s shells first, then, at that point, their 5f, 6d, and 7p shells in a specific order, however, there are exemptions, like uranium.

Additional Information

• Francium has the substance image Fr and nuclear number 87.
• Radium (Ra, nuclear number 88), is a practically unadulterated white basic earth metal, however, it promptly oxidizes, responding with nitrogen (as opposed to oxygen) on openness to air, becoming dark in variety.
• The actinide or actinoid (IUPAC classification) series envelops the 15 metallic substance components with nuclear numbers from 89 to 103, actinium through lawrencium.
• Transactinide components are likewise transuranic components, that is to say, have a nuclear number more noteworthy than that of uranium (92), an actinide.

The correct answer is 9W.

Calculations:

Given:

$P=36W,V=12V$

Formula:

 

$P={V^2\over R}$

$R={V^2\over P}$

$R={12^2\over 36}={144\over 36}=4$ ohm

Now at 6V supply,

$P={V^2\over R}$

$P={6^2\over 4}={36\over 4}=9W$

Therefore the power consumed is 9W.

Given:

Step 1): Five persons are sitting in a straight row facing north.

Step 2): (a) Ram is sitting at the extreme left end

(b) Sita is sitting at the extreme right end of the row.

(c) Kamal sits exactly in the middle of the row.

Step 3: (a) Ravi is sitting exactly third to the left of Sita.

(b) Ritu is sitting exactly third to the right of Ram.

According to the arrangement, Ritu is the immediate neighbour of Sita.

Hence, the correct answer is option 4).

The correct option is Neena Gupta. 

Key Points

• Professor Neena Gupta, a mathematician at the Indian Statistical Institute in Kolkata, received the Ramanujan Prize for Young Mathematicians on February 22, 2022, in a virtual ceremony.
• The world's largest mathematical problem is said to be the Zariski Cancellation Issue, a fundamental algebraic geometry problem.
• Other awards received by Professor Neena Gupta:-​
• The 2015 Ramanujan Prize from the Ramanujan Institute for Advanced Study in Mathematics.
• 2014 Young Scientists Award of the Indian National Science Academy for her work on the Zariski cancellation problem
• The inaugural Professor A. K. Agarwal Award from the Indian Mathematical Society in 2015.
• The 2017 B. M. Birla Science Prize in Mathematics.

Additional Information

• It is given in the honor of Srinivasa Ramanujan, a pure mathematics genius who largely learned the subject on his own and made outstanding contributions to the study of elliptic functions, continuous fractions, infinite series, and number theory.
• ​Sponsored and funded by 
• DST ( The Department of Science and Technology ) of the Government of India.
• IMU ( International Mathematical Union ).
• ICTP ( International Centre for Theoretical Physics )
• Eminent mathematicians were chosen for the Committee after discussions between the ICTP, the IMU, and the DST. The award's name was changed to the "DST-ICTP-IMU Ramanujan Prize in 2021.
• List of Ramanujan Prize winners (2005-2021)

Shortcut Trick

Savings percentage = (Savings ÷ Salary) × 100

Savings % = (88,000 ÷ 2,00,000) × 100

Savings % = 88 ÷ 2 = 44%

∴ The correct answer is 44.00%.

Alternate Method

Given:

Total Salary = ₹2,00,000

Total Savings = ₹88,000

Formula: Percentage = (Part value ÷ Total value) × 100

⇒ Savings % = (88,000 ÷ 2,00,000) × 100

⇒ Savings % = 88,000 / 2,000

⇒ Savings % = 88 / 2

⇒ Savings % = 44%

∴ The correct answer is 44.00%.

Additional Information

Income-Expenditure Relation

Income = Expenditure + Savings. This fundamental equation is used to find any missing component when two are known.

Expenditure Percentage

Expenditure % = (Expenditure ÷ Total Income) × 100 or simply (100% − Savings %).

Percentage Change

Percentage Increase/Decrease = (Difference ÷ Original Value) × 100.

The correct answer is option 3)Rs. 215/-

Given:

The power of the refrigerator is 350W operated for 8 hours/day, the TV set is rated as 150 W for 5 hours/day and for electric heater is rated as 1500 W for 30 minutes/day. The energy cost per unit is Rs. 5.00.

Formula:

Electrical energy, $E=P*t$  where P is the power and T is the time taken.

Calculations:

Refrigerator:

$t=8*10=80hours$

$P=350W={350\over1000}=0.35kW$

So, $E=0.35*80=28kWh$

TV:

$t=5*10=50hours$

$P=150W={150\over1000}=0.15kW$

$E=0.15*50=7.5kWh$

Electric heater:

$t=30min={1\over 2}*10=5hours$

$P=1500W={1500\over1000}=1.5kW$

$E=1.5*5=7.5kWh$

Total energy consumed is: $E=28+7.5+7.5=43kWh$

Thus, the cost is $Cost=43*5=Rs. 215$

Therefore the total expenditure of that house for 10 days for the TV set, refrigerator and electric heater will be Rs. 215/-

Given:

Step 1): Six friends C, D, E, F, G, and H are sitting in a row facing north.

Step 2): (a) F is 2nd to the left of E

(b) E is 2nd to the left of G.

OR, 

Step 3): (a) D is 2nd to the right of H

(b) H is an immediate neighbour of E and G.

According to the arrangement, C is sitting between E & F.

Hence, the correct answer is option 2).

The correct answer is option 1)1 ∶ 4

Calculations:

Given:

Two wires are made up of the same material, but the ratio of their cross-sectional areas is 1 ∶ 10 and the ratio of their lengths is 2 ∶ 5 and have same voltage of 10V.

Formula:

Ohm's law: $V=IR$

Resistance: $R=p{l\over A}$

As we know that $R=p{l\over A}$ we have for the wires:

${R1\over R2}={l1\over A1}*{A2\over l2}$

${R1\over R2}={l1\over l2}*{A2\over A1}$

${R1\over R2}={2\over 5}*{10\over 1}={4\over 1}$

Thus R1:R2 is obtained as 4:1.

But according to Ohm's law, we have current I is inversely proportional to resistance R.

Therefore, ${I1\over I2}={R2\over R1}={1\over 4}$

Thus, the ratio of current in the wires of the same material is 1:4.

The logic follows here is:

The first letter cluster is related to the second letter cluster in the following way:

and,

Similarly,

Thus, the letter cluster with the same logic is TJQ : WGT.

Hence, the correct answer is option 3).

The logic followed here is:

2^nd number - 1^st number = 3^rd number

(OR)

2nd number - 3rd number = 1st number

(OR)

1st number + 2nd number = 3rd number 

Given:

(76, 171, 95) → 171 - 76 = 95

and,

(28, 63, 35) → 63 - 28 = 35

By checking the options,

1) (44, 88, 55) → 88 - 44 ≠ 55

2) (60, 105, 70) → 105 - 60 ≠ 70

3) (24, 48, 30) → 48 - 24 ≠ 30

4) (52, 117, 65) →117 - 52 = 65

Hence, the correct answer is option 4.

Given,

Akshay starts from the restaurant and travels 2 km southwards and then turns right and travels 4 km. He then turns left and travels 10 km, then he turns left and travel 4 km to reach his home.

The direction & distance diagram is shown below:

According to the diagram, the shortest distance between the restaurant to home is 12 km and is to the North of his home.

Hence, the correct answer is option 1).

The correct answer is $\rm P = {V^2 \over R}$

Key Points

• Electric power is the rate at which work is done or energy is transformed into an electrical circuit.
• It is a Scalar quantity.
• The formula for electric power is given by, $P=VI$
• But, we know according to ohms law we have: $V=IR$
• So we have $I={V\over R}$
• Substituting, I in the power equation we have: $P={V*V\over R}={V^2\over R}$
• Therefore, $P={V^2 \over R}$.

The correct option is Kerala. 

Key Points

• One of India's leading institutes for Sanskrit instruction, study, and invention is the Sree Sankaracharya University of Sanskrit (SSUS). In 1993, the University was established in Kalady, Kerala.
• Student percentage -
• Over 90% of the university's students and research scholars come from economically and socially underprivileged communities and families,
• More than 70% of the students are female.
• Nine regional centres - 
• Kalady, Thiruvananthapuram, Thrissur, Panmana, Thuravoor, Ettumanoor, Tirur, Koyilandy, and Payyannur are the principal campuses.
• Location of the university - 
• In order to serve students from disadvantaged backgrounds, the bulk of these campuses are located in rural areas of the State.

Additional Information

• Surabhi Lakshmi, a Malayalam actress, has won a National Film Award.
• Dileesh Pothan is a well-known director, actor, and producer in Malayalam cinema.
• Malayalam film music is composed by Arun Muraleedharan. Grace Antony, a cinema actress.
• Politician V. P. Sanu now serves as the Students' Federation of India's National President.
• Renu Soundar is a Malayalam television and film actress.
• Hima Shankar, an artist, works in both theatre and movies.
• Sneha Sreekumar, an Indian actress and dancer, appears in theatrical productions as well as Malayalam films and TV programmes.

The correct answer is Lymph.

Key Points

• Lymph is like the plasma of blood yet dull and contains less protein.
• Lymph conveys processed and consumed fats from the digestive system since fats are insoluble in the fluid mechanism of blood.
• The lymph contains lesser proteins since they have been separated by the kidneys and eliminated from the plasma.
• The quantity of proteins that got away from the vessels to tissue is exceptionally less.

Additional Information

• For sure, when contrasted and plasma, lymph is advanced with proteins of cells beginning to set free from the parenchyma.
• A sort of platelet that is made in the bone marrow and tracked down in the blood. Red platelets contain a protein called hemoglobin, which conveys oxygen from the lungs to all pieces of the body.
• The ordinary number of WBCs in the blood is 4,500 to 11,000 WBCs for each microliter (4.5 to 11.0 × 109/L). Typical worth reaches might fluctuate somewhat among various labs
• Their essential capability is to forestall and quit dying. On the off chance that a vein is harmed, the body conveys messages to platelets which make them travel to the harmed region.

Shortcut Trick From the quadratic equation x2 − 11x + 18 = 0: Sum of roots (α + β) = −(−11)/1 = 11 Product of roots (αβ) = 18/1 = 18 Using the algebraic identity: α2 + β2 = (α + β)2 − 2αβ ⇒ α2 + β2 = (11)2 − 2 × 18 = 121 − 36 = 85 ∴ The correct answer is 85.

Alternate Method Given: Quadratic equation: x2 − 11x + 18 = 0 α and β are the roots of the equation. Calculations: Factorizing the given equation by splitting the middle term: ⇒ x2 − 9x − 2x + 18 = 0 ⇒ x(x − 9) − 2(x − 9) = 0 ⇒ (x − 9)(x − 2) = 0 ⇒ The roots are x = 9 and x = 2. Let α = 9 and β = 2. We need to find the value of α2 + β2: ⇒ α2 + β2 = (9)2 + (2)2 ⇒ α2 + β2 = 81 + 4 ⇒ α2 + β2 = 85 ∴ The correct answer is 85.

Additional Information Nature of Roots The discriminant D = b2 − 4ac determines the nature of the roots. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are complex or imaginary. Sum and Product of Roots For a quadratic equation ax2 + bx + c = 0, the sum of the roots is given by −b/a and the product of the roots is c/a. Algebraic Identities Other useful identities for root manipulation: α3 + β3 = (α + β)3 − 3αβ(α + β) and (α − β)2 = (α + β)2 − 4αβ.

Given three-digit numbers series:

(Left) 653 831 933 476 715 (Right)

If 2 is added to the third digit of every number, the new number formed is shown below:

655 833 935 478 717

In the new number series 655, 833, and 717, are the numbers where the third digit can be exactly divided by the second digit of that number.

Hence, the correct answer is option 2).

Given:

88 × 22 - 15 ÷ 40 + 19 = ? 

We substitute the values in the given equation and solve it using the BODMAS rule:

By decoding the equation,

Substituting the operators, we get,

⇒ 88 ÷ 22 × 15 + 40 - 19

⇒ 4 × 15 + 40 - 19

⇒ 60 + 40 - 19

⇒ 100 - 19

⇒ 81

Hence, the correct answer is option 3).

Shortcut Trick

Put θ = 45° as it is defined for all terms in the expression.

sec² 45° + (cosec² 45° − 1) − (1 + tan² 45°) − cot² 45°

⇒ (√2)² + ((√2)² − 1) − (1 + 1²) − 1²

⇒ 2 + (2 − 1) − (1 + 1) − 1 ⇒ 2 + 1 − 2 − 1 = 0

∴ The correct answer is 0.

Alternate Method

Given: sec² θ + (cosec² θ − 1) − (1 + tan² θ) − cot² θ

Step 1: Simplify the terms inside the parentheses using standard identities.

⇒ cosec² θ − 1 = cot² θ

⇒ 1 + tan² θ = sec² θ

Step 2: Substitute these simplified forms back into the main expression.

⇒ sec² θ + (cot² θ) − (sec² θ) − cot² θ

Step 3: Cancel out the positive and negative terms.

⇒ (sec² θ − sec² θ) + (cot² θ − cot² θ)

⇒ 0 + 0 = 0

∴ The correct answer is 0.

Additional Information

Fundamental Identities

There are three main Pythagorean identities: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

The primary reciprocal functions are cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ.

Value Substitution Method

For identities that hold for all angles, choosing an easy angle (like 0, 45, or 90 degrees) where functions are defined is a fast way to eliminate options.

Shortcut Trick

Effective rate for 2 years at 10% compounded annually = 10 + 10 + (10 × 10)/100 = 21%

Total Amount = 100% (Principal) + 21% (Interest) = 121%

Amount = 121% of 10,000 = 1.21 × 10,000

Amount = ₹12,100

∴ The correct answer is ₹12,100.

Alternate Method

Given:

Principal (P) = ₹10,000

Rate (R) = 10% per annum

Time (T) = 2 years

Formula Used:

Amount (A) = P × (1 + R/100)^T

Calculations:

⇒ A = 10,000 × (1 + 10/100)²

⇒ A = 10,000 × (1 + 0.1)²

⇒ A = 10,000 × (1.1)²

⇒ A = 10,000 × 1.21

⇒ A = 12,100

∴ The correct answer is ₹12,100.

Additional Information

Compound Interest (CI) Formula

CI = Amount − Principal = P[(1 + R/100)^T − 1].

CI vs SI Difference (2 Years)

The difference between CI and SI for 2 years is given by: D = P(R/100)².

Effective Rate of Interest

For a rate R compounded annually for n years, the effective rate is [(1 + R/100)ⁿ − 1] × 100.

Given:

Seven businessmen, G, H, I, J, K, L and M, travelled in the same month on different dates 4th, 8th, 11th, 14th, 17th, 22nd and 28th.

Step 1): (a) K travelled on the 11th

(b) Only two people travelled between K and M.

(c) L travelled the last.

Step 2): (a) Exactly one person travelled between G and K, and K travelled after G.

(b) K travelled just after I but before J.

According to the arrangement, M travels on the 22nd of the same month.

Hence, the correct answer is option 4).

The correct answer is Jammu & Kashmir

Key Points

• Around 80% of all apples produced in the nation are produced in Jammu and Kashmir. With annual earnings of over Rs. 1500 crores, apple agriculture and its value chain are one of the foundations of rural economies.
• Apple producing districts in Kashmir -
• Srinagar, Ganderbal, Budgam, Baramulla, Kupwara, Anantnag, and Shopian districts produce the majority of the country's apples, However smaller amounts are also reported in Udhampur, Doda, Poonch, Ramban, and Reasi.
• Apple production -
• Kashmir produces about 11 MT/hectare, compared to over 40 MT/hectare in countries like Italy, Chile, France, etc.
• Area under cultivation -
• A 250 hectare area has been covered with high density plantation.

Additional Information

• Agricultural exports from Jammu and Kashmir include-
• apples, barley, cherries, corn, millet, oranges, rice, peaches, pears, saffron, sorghum, vegetables, and wheat.
• Production of apple in India -

Given,

Radhika moves 30 metres in West direction.

Then she turns to her right and moves 10 metres.

Then she turns to her left and moves 30 metres.

According to the statements,  the direction and distance diagram is shown below;

According to the direction and distance diagram, Radhika is in the North-West direction from the starting point.

Hence, the correct answer is option 4).

The correct answer is 39.8%.

Key Points

• Worker Population Ratio (WPR): It expanded from 38.2% in the earlier year to 39.8%.
• The Laborer Populace Proportion (WPR) has expanded to 52.6 percent in 2020-21 from 46.8 percent in 2017-18, said Association serve Jitendra
• Singh on Thursday in a composed answer to an inquiry in Rajya Sabha.
• India Laborer Populace Proportion information accounted for 34.70 % in 2018.
• The provincial regions recorded a joblessness pace of 3.3% and metropolitan regions recorded a joblessness pace of 6.7%.

Additional Information

• The joblessness rate in the nation expanded strongly to 6.1%, according to the Occasional Workforce Overview 2017-18 information, from 2.2%, in light of the Public Example Study, 68th cycle, 2011-12.
• The specialist populace proportion is characterized as the quantity of utilized individuals per thousand individuals. WPR = number of utilized individuals duplicated by 1000/complete populace The Laborer Populace Proportion is a pointer used to survey the country's business circumstance.
• The Workforce, as per Current Week by week Status (CWS), is the number of people either utilized or jobless on a normal in seven days going before the date of the study.
• The movement rate is 28.9%. The movement rate among ladies was 48% and 47.8% in provincial and metropolitan regions, separately.

Shortcut Trick

Let LCM be L and HCF be H.

L + H = 1050 and L − H = 630.

L = (1050 + 630) ÷ 2 = 840.

H = (1050 − 630) ÷ 2 = 210.

Product of numbers = L × H = 840 × 210 = 176400.

∴ The correct answer is 176400.

Alternate Method

Given:

Sum of LCM and HCF = 1050

Difference between LCM and HCF = 630

Formula Used:

Product of two numbers = LCM × HCF

Calculations:

⇒ Let LCM = L and HCF = H

⇒ L + H = 1050 ---(i)

⇒ L − H = 630 ---(ii)

⇒ Adding (i) and (ii): 2L = 1680

⇒ L = 840

⇒ Substituting L in (i): 840 + H = 1050

⇒ H = 1050 − 840 = 210

⇒ Product of two numbers = 840 × 210

⇒ Product of two numbers = 176400

∴ The correct answer is 176400.

Additional Information

Fundamental Property of HCF and LCM

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

HCF as a Factor

The HCF of two or more numbers is always a factor of their LCM.

Co-prime Numbers

If the HCF of two numbers is 1, they are called co-prime numbers, and their LCM is equal to their product.

The correct answer is the centre of curvature .

Key Points

• If a hollow sphere is cut into parts and the outer surface of the cut part is painted, then it becomes a mirror with its inner surface as the reflecting surface. This type of mirror is known as concave mirror.
• In this mirror light converges at a point when it strikes and reflects back from the reflecting surface of the concave mirror. Hence it is also known as a converging mirror.
• When the concave mirror is placed very close to the object a magnified, erect and virtual image is obtained.
• However, if the distance between the object and the mirror increases, the size of the image is formed inverted at the same point of the object where it is located and hence we obtain a real and inverted image.
• Thus, when an object is kept at the centre of curvature of a concave mirror, the image will be formed at the centre of curvature itself.

​

Shortcut Trick

Ratio of ages of A and B is 7 : 1.

Total ratio parts = 7 + 1 = 8 units.

8 units = 48 years ⇒ 1 unit = 6 years.

A age = 7 × 6 = 42 years; B age = 1 × 6 = 6 years.

∴ The correct answer is 42 and 6 years.

Alternate Method

Given:

A's age = 7 × B's age

Sum of ages = 48 years

Calculations:

⇒ Let B's age be x.

⇒ Then A's age = 7x.

⇒ According to the question, 7x + x = 48

⇒ 8x = 48

⇒ x = 48 ÷ 8

⇒ x = 6 years (B's age)

⇒ A's age = 7 × 6 = 42 years

∴ The correct answer is 42 and 6 years.

Additional Information

Ratio and Proportion in Ages

If the ratio of ages of two persons is a : b and the sum of their ages is S, then their ages are [a/(a+b)] × S and [b/(a+b)] × S.

Age Difference Property

The difference between the ages of two persons remains constant throughout their lives, regardless of how many years pass.

Percentage Change in Ages

Percentage increase in age over 'n' years = (n / Original Age) × 100.

Given Statements:

I ≥ R > U ≤ T > Q ≥ O

Conclusions:

1. I > U → True (As, I ≥ R > U)
2. O > T → False ( As, T > Q ≥ O) It doesn't follow
3. R > T → False ( As, R > U ≤ T) It doesn't follow
4. U < Q → False (As, U ≤ T > Q) It doesn't follow.

Hence, the correct answer is option 1).

The correct answer is a forest.

Key Points

• In India throughout the 1970s, rural inhabitants, particularly women, engaged in a peaceful social and biological movement known as Chipko development, sometimes known as Chipko Andolan, with the goal of defending trees and forests slated for government-sponsored logging.
• Dhoom Singh Negi, Bachni Devi, Gaura Devi, and Sudesh Devi were a few of the main individuals that were crucial to the Chipko movement.
• The initiative was aided by the Gandhian lobbyist Sunderlal Bahuguna, whose appeal to Indira Gandhi, the Indian State leader at the time, led to the ban on tree cutting.
• The five Fs of the Chipko movement are necessities for a self-sufficient community and include food, grub, fuel, fibre, and manure.

Additional Information

• Sunderlal Bahuguna started the Chipko movement in the Garhwal forest.
• The campaign aimed to put an end to the practise of cutting down trees for commercial gain.
• Locals peacefully embraced trees to stop them from being cut down during the protest.
• The decision by the administration to provide wooded land to a company that sells video games was what started the Chipko movement.
• When the public authorities announced the sale of 2,500 trees in January 1974, disregarding the Alaknanda watercourse, that was the turning point.

The correct answer is Bandhan Financial Services Pvt Ltd.

Key Points

• Bandhan Monetary Administration, the primary microfinance organization in the country to win a bank permit, is likewise one of the most youthful elements to be permitted to enter the financial space.
• Ghosh's Bandhan Monetary Administration was the main microfinance organization in the country to win a financial permit from the Hold Bank of India (RBI) in April 2014.
• In 1974, SEWA (Independently employed Ladies' Affiliation) Bank, a helpful bank, was laid out in Ahmedabad; as one of the primary cutting-edge microfinance organizations in the country.
• The methodology of microfinance was regulated by Yunus in 1976, with the groundwork of Grameen Bank in Bangladesh.

Additional Information

• Madura is a main NBFC-MFI giving unstable microfinance credits to ladies' self-improvement gatherings in the country and semi-metropolitan regions.
• Annapurna Money is appraised 4.2 out of 5, in view of 694 audits by representatives on AmbitionBox.
• Annapurna Money is known for Employer stability which is evaluated at the top and given a rating of 4.2. Be that as it may, Balance between serious and fun activities is appraised the least at 3.8 and can be gotten to the next level.
• BSS Microfinance Restricted is a microfinance organization that at present goes about as a 'Business Reporter' of Kotak Mahindra Bank Restricted however at first was doing tasks as a Trust which was set up in 1999.

According to the given information,

The given word is ARGUMENT.

When the alphabet are arranged in alphabetical order.

As we see that the position of A and G remain unchanged in the newly formed word.

Hence, the correct answer is option 3).

The correct answer is Drass.

Key Points

• Throughout the colder time of the year 1995, when the warm perusing diminished to - 60 degrees Celsius, the most minimal temperature decrease was seen in Dras.
• At 34.4°E, Dras town is found. In India, Dras is the coldest spot, encountering a Mediterranean mainland environment impacted by elevation.
• Arranged at a height of 3350 m, Drass is the coldest spot in India and second to the coldest occupied locale on The planet.
• The typical temperature throughout the colder time of the year season goes down to - 23 ºC.

Additional Information

• A forlorn town in the scandalous Kargil locale of Jammu and Kashmir, Dras is prominently known as 'the doorway to Ladakh'.
• Oymyakon is the coldest forever occupied put on The planet and is tracked down in the Icy Circle's Northern Pole of Cold.
• Jammu is the colder time of year capital of the Indian association region of Jammu and Kashmir.
• The town is renowned for lovely strolling encounters on slopes encompassed by pine and oak timberlands.
• Mount Abu, relatively close to Jodhpur and Udaipur, is home to numerous strict landmarks, the most popular being the Dilwara sanctuary, Brahmakumari Ashram, Master Shikhar, and the sanctums of Jainism.

The correct answer is Gujarat.

Key Points

• The Swaminarayan Sampraday was spread out by Bhagwan Swaminarayan some time back in Gujarat and later formalized by His third significant substitution Brahmaswarup Shastriji Maharaj in the unobtrusive local area of Bochasan, Gujarat.
• The Swaminarayan Gadi (Maninagar) was established during the 1940s by Muktajivandas Master after he left the Ahmedabad bishopric with the conviction that Gopalanand Master, a Paramhansa from Swaminarayan's time, was the profound replacement to Swaminarayan.
• The ongoing profound pioneer is Jitendrapriyadasji Master.
• These six sanctuaries were underlying the presence of Bhagwan Shree Swaminarayan around quite a while back.

Additional Information

• The main sanctuary Swaminarayan developed was in Ahmedabad in 1822, with the land for development given by the English Royal Government.
• Umaid Bhawan Castle: It is the biggest Illustrious Royal residence in Rajasthan. It is likewise quite possibly the biggest confidential home on the planet.
• The Kalka-Shimla Rail route is a mountain rail route that is a UNESCO World Legacy Site. Shimla is likewise a renowned skiing fascination in India.
• Aside from these, Bandhavgarh Public Park, Kanha Public Park, Bhimbetka Caverns, Omkareshwar, Chitrakuta, and Amarkantak are some other renowned traveler objections in Madhya Pradesh

The correct answer is pop sound.

Key Points

• Hydrogen gas is developed generally when a metal responds with a corrosive.
• At the point when zinc responds with weakened sulphuric corrosive, zinc sulfate, a salt, is shaped with the arrival of hydrogen gas.
• When a consuming matchstick is brought close to the test tube containing hydrogen gas,
• it puts off the consuming matchstick and produces a pop strong.
• Hydrogen gas is delivered when zinc is responded with sulphuric corrosive.

          Zn+H 2SO4(aq)→ZnSO4(aq)+H2​

Additional Information

• A gas fire seeming yellow or orange in a variety of acting with pops of yellow or orange shows an ill-advised proportion of oxygen for burning.
• These green flares are delivered by the discharge of energized copper particles when copper sulfate is added to the copying liquor.
• Red or yellow flares mean there could be an issue, like fragmented ignition.
• This tone is brought about by extremely fine ash particles created by the fire, which consumes almost a portion of the temperature it should.
• Pop sound means the presence of any ignitable gas, which would promptly burst into flames when it is acquired contact with adequate intensity or fire.

Given:

5n+2 = 3125

Calculation:

⇒ 5n+2 = 3125

Express 3125 in the form of factors of 5,

⇒ 5n+2 = 5⁵

Equating the powers,

⇒ n + 2 = 5

⇒ n = 5 – 2 = 3

Therefore, the required value of n is 3.

Hence, the correct answer is option 2).

Given:

Amongst six friends P, Q, R, S, T, and U, each has a different height.

_ > _ > _ > _ > _ > _

Step 1) R is taller than only two other friends.

_ > _ > _ > R > _ > _

Step 2) T is shorter than only one friend.

_ > T > _ > R > _ > _

Step 3) Q is shorter than R but taller than P.

_ > T > _ > R > Q > P

Step 4) S is shorter than U.

 U > T > S > R > Q > P 

According to the arrangement, T is the second tallest among all the friends.

Hence, the correct answer is option 1).

the correct answer is United Nations Environment Programme.

Key Points

• Coordination of environmental responses across the United Nations system is the responsibility of the United Nations Environment Programme (UNEP).
• Maurice Strong, its first director, created it following the United Nations Conference on the Human Environment in Stockholm in June 1972.
• Its goal is to give leadership, produce science, and develop solutions to a wide variety of issues, including climate change, the management of marine and terrestrial ecosystems, and green economic growth.
• The group also creates worldwide environmental treaties, disseminates environmental knowledge, and aids national governments in achieving environmental goals.

Additional Information

World Organization and Headquarters

Given,

Statements:

1. All statements are books.
2. Some books are copies.
3. No copy is a thesaurus.

The Venn Diagram:

Conclusions:

I. Some thesauruses are copies. → False (No copy is a thesaurus)

Il. No statement is a thesaurus. → False (No definite relation between statement and thesaurus)

Ill. Some books are statements. → True (All statements are books.)

Hence, the correct answer is option 1).