RRC Group D Previous Year Paper 30 (Held On: 28 Sept 2018 Shift 2)

Simplify using BODMAS: Bracket – Of – Division – Multiplication – Addition – Subtraction

{20 – (25 – 33)} ÷ {- 5 × 4 – (- 6)} + 56 ÷ (- 27 + 13)

⇒ {20 – (–8)} ÷ {- 5 × 4 + 6)} + 56 ÷ (- 14)

⇒ {20 + 8} ÷ {- 20 + 6} + 56 ÷ (-14)

⇒ {28} ÷ {- 14} + 56 ÷ (-14)

⇒ −2 – 4

⇒ −6

The Correct Answer is West Bengal.

The first argument claims that the benefit of issuing penalty would be the reduced number of accidents caused by mobile phone usage while driving.

Thus, it is able to strongly support the given statement.

Therefore, argument I is strong.

Having a habit of using mobile phones everywhere does not justify the need to use it while driving. Therefore, this argument is not strong enough to reject the idea of penalising such offenders.

Therefore, argument II is not strong.

Hence, only argument I is strong.

The logic followed here is:

Tyre is a part of Car.

Similarly,

Legs are a part of Chair.

Hence, ‘legs’ is the correct answer.

The logic followed here is:

In each figure the complete central image turns 90 degrees in clockwise direction. 

Hence, the option figure D will complete the series.

The statement does not imply that Mr. X fails to get thoughts at other periods of time besides morning.

Hence, neither conclusion I nor conclusion II follows.

The Correct Answer is Option 1 i.e Sodium.

According to the problem,

$\sqrt {45} + \sqrt {20} = 11.180$

$\Rightarrow \sqrt {9 \times 5} + \sqrt {4 \times 5} = 11.180$

$\Rightarrow 3\sqrt 5 + 2\sqrt 5 = 11.180$

$\Rightarrow 5\sqrt 5 = 11.180$

$\Rightarrow \sqrt 5 = 11.180/5 = 2.236$     ...i)

∴ The value of $\sqrt {180} + 4\sqrt 5$ = $\sqrt {9 \times 5 \times 4} + 4\sqrt 5$

$\Rightarrow 6\sqrt 5 + 4\sqrt 5$

⇒ 10√5

⇒ 10 × 2.236 [value of $\sqrt 5$ = 2.236 we get from (1)]

⇒ 22.36

The Correct Answer is Option 1 i.e 200 N.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

CALCULATION:

Given that:

Mass, m = 25 kg and 

Acceleration, a = 8 ms^-2

Force (F) = 25 × 8

Force = 200 N

Shortcut Trick

Identify the Highest Common Factor (HCF) of 60 and 54, which is 6.

Express both numbers as multiples of 6: 60 = 6 × 10 and 54 = 6 × 9.

The LCM is the product of the common factor and the remaining unique factors: 6 × 10 × 9.

∴ The correct answer is 6 × 10 × 9.

Alternate Method

Given: Numbers 60 and 54.

Formula Used: LCM × HCF = Product of two numbers.

Calculations:

⇒ Prime factorization of 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

⇒ Prime factorization of 54 = 2 × 3 × 3 × 3 = 2 × 3³

⇒ LCM = 2² × 3³ × 5 = 4 × 27 × 5 = 540

⇒ Now check the options provided:

⇒ Option 1: 6 × 5 × 9 = 270

⇒ Option 2: 6 × 10 × 3 = 180

⇒ Option 3: 6 × 10 × 9 = 540

⇒ Since 540 matches Option 3, the expression is 6 × 10 × 9.

∴ The correct answer is 6 × 10 × 9.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by both 'a' and 'b'.

HCF (Highest Common Factor)

The greatest common divisor of two or more integers, which are not all zero.

Relationship Formula

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

Total number of screws manufactured in the unit over the given 6 months,

⇒ (200 + 300 + 250 + 250 + 250 + 250) thousand = 1500 thousand

∴ Average number of screws manufactured in the unit over the given 6 months,

⇒ 1500 thousand/6 = 250 thousand

The Correct Answer is Option 4 i.e Fertilizers.

Important Points 

• Grey Revolution
• Grey Revolution is associated with increased fertilizer production, which basically means it is related to the main effects of India's green revolution.
• But only zeroing down to fertilizer won't be an appropriate thing.
• Because the grey revolution includes everything that would take place due to the excessive green revolution.
• It is actually a glimpse of what can happen if the new agricultural equipment turns things wrong.
• White Revolution
• White Revolution in India also known as Operation Flood.
• Operation Flood started in the year 1970 and was aimed to create a nationwide milk grid.
• It was a rural development program initiated by NDDB – National Dairy Development Board of India.
• White revolution period intended to make India a self-dependent nation in milk production.
• Today, India is the world's largest producer of milk.
• Dr. Verghese Kurien is known as the father of the White Revolution in India.
• Blue Revolution
• The Blue Revolution in India was launched during the 7th Five Year Plan(1985-1990) during the sponsorship of the Fish Farmers Development Agency(FFDA) by the Central Government of India.
• The main objective is to develop, manage, and promote fisheries to double the farmers’ income.
• Dr. Arun Krishnsan and Dr. Hiralal Chaudhari, are known as the fathers of the Blue Revolution.
• Green Revolution
• Green Revolution is associated with agricultural production.
• It is the period when agriculture of the country was converted into an industrial system due to the adoption of modern methods and techniques like the use of high-yielding variety seeds, tractors, irrigation facilities, pesticides, and fertilizers.
• The term green revolution was first used by William Gaud and Norman Borlaug is the Father of the Green Revolution.
• In the year 1965, the government of India launched the Green Revolution with help of M.S. Swaminathan, now known as the father of the Green revolution( India).

Any number in the form of a/b is called fraction.

Let, x = $0.\overline6$ = 0.6666     ---- (1)

Multiplying above equation by 10, we get

10x = 6.6666      ---- (2)

Subtracting equation (1) from equation (2), we get

10x - x = 6.6666 - 0.6666

⇒ 9x = 6

⇒ x = 6/9

∴ x = 2/3

The Correct Answer is Option 2 i.e Three Atoms.

• The chemical formula of ethane is C₂H₆.
• In Ethane, each carbon atom is bonded to three hydrogen atoms.
• In the structural formula, each dash (-) represents a single covalent bond, in which two atoms share one pair of valence electrons.

Some suffix says

Ane - Single bond

Ene - Double bond

Yne - Triple bond

Additional Information

Hydrocarbons

• Compounds made of carbon and hydrogen atoms only are called hydrocarbons.
• Saturated hydrocarbons:
• The hydrocarbons in which carbon atoms are singly bonded are called saturated hydrocarbons.
• Saturated hydrocarbons are also called alkanes or paraffin.
• The general formula of alkane– CnH2n+2.
• Unsaturated hydrocarbons:
• The hydrocarbons in which carbon atoms are either doubly or triply bonded are called unsaturated hydrocarbons.
• Doubly bonded (carbon atoms) hydrocarbons are called alkenes.
• The general formula of alkene is CnH2n.
• Triply-bonded carbon:
• Hydrocarbons containing at least one carbon-carbon triple bond between two carbon atoms are called alkynes.
• The general formula of alkynes is CnH2n-2.

Hence, the minimum 18 lines are required to make the given figure.

The Correct Answer is Option 4 i.e Li3N.

• The formula of Lithium Nitride is Li3N**.**
• Lithium nitride is the only stable alkali metal nitride.
• It has high melting point of about 813 ^oC.
• Other anions: Lithium oxide
• Solubility in water: reacts

The correct answer is Option 4, i.e Mauryan.

• The Arthashastra is an Indian treatise on politics, economics, military strategy, the function of the state, and social organization attributed to the philosopher Kautilya.
• The Arthashastra is thought to have been written by Kautilya as a kind of handbook for Chandragupta instructing him in how to reign over a kingdom and encouraging direct action in addressing political concerns without regard for ethical considerations.
• Hence, the correct answer is Mauryan Administration.

The Correct Answer is Option 3 i.e Zero.

• When two equal force are acting on a body and opposite in direction, the net force acting on the body becomes zero.
• A two forces of equal size, acting on body, in opposite direction is known as Balanced Force.
• Force can be defined as the pull or push applied on an object.

The Correct Answer is Option 2 i.e Cytokinins.

CONCEPT:

The systematic diagram of reflection through the spherical mirror is given by:

• Pole: The center of the reflecting surface of a spherical mirror is called the pole.
• Centre of curvature (C): The reflecting surface of the spherical mirror forms a part of the sphere. The center of this sphere is called the center of curvature of the mirror.
• Focus (F): Rays which are coming parallel to the principal axis falling on spherical mirror intersect or meet at the point on the principal axis is called as the principal focus.
• Focal length (f): The distance between pole and principal focus is called the principal focal length.​

EXPLANATION:

• The distance between focal and pole is termed as focal length, outside the mirror.
• The center of curvature is not a part of the mirror and lies outside its reflecting surface.
• Pole lies on the reflecting surface of the mirror.

The Correct Answer is Option 4 i.e Water

• White phosphorous is stored in water.
• White phosphorous is insoluble in water so it is stored underwater to prevent oxidation.
• Also white phosphorous is highly reactive, flammable and igniting naturally in the air unless it is stored underwater.

Shortcut Trick

Using the Alligation Method to find the ratio of the two groups:

Group 1 (8 smallest): 17 | Group 2 (Remaining): 22 | Overall Mean: 20

Ratio of (Group 1) : (Group 2) = (22 − 20) : (20 − 17) = 2 : 3

According to the question, 2 units = 8 numbers ⇒ 1 unit = 4 numbers.

Therefore, Total numbers (2 + 3 = 5 units) = 5 × 4 = 20.

∴ The correct answer is 20.

Alternate Method

Given:

Mean of 8 smallest numbers = 17

Mean of the remaining numbers = 22

Mean of the entire group = 20

Let the total numbers in the group be n.

⇒ Total Sum of numbers = n × 20

⇒ Sum of 8 smallest numbers = 8 × 17 = 136

⇒ Count of remaining numbers = (n − 8)

⇒ Sum of remaining numbers = (n − 8) × 22

⇒ Total Sum = Sum of smallest + Sum of remaining

⇒ 20n = 136 + 22(n − 8)

⇒ 20n = 136 + 22n − 176

⇒ 20n = 22n − 40

⇒ 22n − 20n = 40

⇒ 2n = 40

⇒ n = 20

∴ The correct answer is 20.

Additional Information

Weighted Average

Used to find the overall mean when two or more groups with different averages are combined. Formula: A_total = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Alligation Rule

The ratio of the quantities is the inverse of the differences between their individual values and the mean value: n₁/n₂ = (A₂ − A_m) / (A_m − A₁).

Property of Mean

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero.

The rectangles are XUON, UVTO, XVTN, PRVU, OTHI, PRHI, PDSU, RYWT, REGH, CFED, PEGI, LQVM, ABSM, KQHJ, PRTO, UVHI, RDVS.

Hence, 17 is the correct answer.

Shortcut Trick

Gold cost is directly calculated as 20% of the raw material investment.

Gold cost = 20% × ₹3,00,000

Gold cost = 0.2 × 3,00,000 = ₹60,000

∴ The correct answer is ₹60,000.

Alternate Method

Given:

Selling Price (SP) = ₹10,00,000

Raw Material Cost = ₹3,00,000

Labour Charge = ₹2,00,000

Gold Cost % = 20% of Raw Material

Calculations:

⇒ Amount spent on gold = 20% of Raw Material Cost

⇒ Amount = (20 ÷ 100) × 3,00,000

⇒ Amount = 0.20 × 3,00,000

⇒ Amount = ₹60,000

∴ The correct answer is ₹60,000.

Additional Information

Total Cost Price (CP)

Total CP = Raw Material Cost + Labour Charges + Other Overheads. In this case, CP = 3,00,000 + 2,00,000 = ₹5,00,000.

Profit Calculation

Profit = Selling Price − Total Cost Price. Here, Profit = 10,00,000 − 5,00,000 = ₹5,00,000.

Percentage Component

To find a specific component value: Value = (Component % ÷ 100) × Base Value.

11 + 9 = 20;

20 + 7 = 27;

27 + 9 = 36;

36 + 7 = 43;

43 + 9 = 52;

52 + 7 = 59;

59 + 9 = 68;

68 + 7 = 75;

Hence, 52 and 59 are the missing term in the given series.

Shortcut Trick

To find the number of sides (n) of a polygon, divide the sum of interior angles by 180° and add 2.

n = (1260 ÷ 180) + 2

n = 7 + 2 = 9

∴ The correct answer is 9.

Alternate Method

Given:

Sum of interior angles of the polygon = 1260°

Formula Used:

The sum of all interior angles of a polygon with n sides is given by: (n − 2) × 180°

Calculations:

⇒ (n − 2) × 180° = 1260°

⇒ n − 2 = 1260 ÷ 180

⇒ n − 2 = 7

⇒ n = 7 + 2

⇒ n = 9

The polygon is a nonagon.

∴ The correct answer is 9.

Additional Information

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon is always 360°.

Number of Diagonals

The number of diagonals in a polygon with n sides is given by the formula: n(n − 3) ÷ 2.

Regular Polygon Interior Angle

Each interior angle of a regular polygon is [(n − 2) × 180°] ÷ n.

The correct answer is Option 1, i.e Information and Broadcasting Ministry.

• Smriti Irani held the porfolio of Information and Broadcasting Ministry till May 2018.
• The Ministry of Information and Broadcasting (Ministry of I&B) is responsible for the formulation and administration of rules, regulations and laws in the areas of information, broadcasting, the press and the Cinema of India.
• The Ministry is responsible for the administration of Prasar Bharati.
• The Central Board of Film Certification is the other important statutory body under this ministry being responsible for the regulation of motion pictures broadcast in India.

Shortcut Trick

Let Total Work = 1 unit. Given 1/x + 1/y = 1/1.2 ⇒ (x + y)/xy = 5/6.

Condition 2: 0.5x + 0.5y = 2.5 ⇒ x + y = 5.

Substituting x + y = 5 in first eq: 5/xy = 5/6 ⇒ xy = 6.

We need two numbers whose sum is 5 and product is 6. The numbers are 2 and 3.

Since B is more efficient, B takes less time. ∴ Time for B = 2 days.

∴ The correct answer is 2.0 days.

Alternate Method

Given: A and B together take 1.2 days.

⇒ 1/x + 1/y = 1/1.2 = 5/6 ... (Eq 1)

⇒ 0.5x + 0.5y = 2.5 ⇒ x + y = 5 ... (Eq 2)

⇒ From (Eq 2), y = 5 − x. Put this in (Eq 1):

⇒ 1/x + 1/(5 − x) = 5/6

⇒ (5 − x + x) / (x(5 − x)) = 5/6

⇒ 5 / (5x − x²) = 5/6

⇒ 5x − x² = 6 ⇒ x² − 5x + 6 = 0

⇒ (x − 2)(x − 3) = 0 ⇒ x = 2 or x = 3

⇒ Since B is more efficient than A, B must take the lesser number of days.

⇒ B = 2.0 days and A = 3.0 days.

∴ The correct answer is 2.0 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken. If Efficiency ratio is a:b, then Time ratio is b:a.

Combined Work Formula

If two people take x and y days respectively, together they take (xy) ÷ (x + y) days.

Work-Rate Concept

Total Work = Time × Efficiency. For a constant work, Efficiency₁ × Time₁ = Efficiency₂ × Time₂.

Shortcut Trick

The Marked Price (MP) is 4600 and the Selling Price (SP) is 2990.

Ratio of MP to SP = 4600 : 2990 = 460 : 299.

Divide both by 23: 20 : 13.

Discount units = 20 − 13 = 7 units.

Discount % (P) = (7 ÷ 20) × 100 = 35%.

∴ The correct answer is 35.

Alternate Method

Given: Marked Price (MP) = Rs. 4600, Selling Price (SP) = Rs. 2990.

Formulas: Discount = MP − SP | Discount % = (Discount ÷ MP) × 100

⇒ Discount = 4600 − 2990 = 1610

⇒ P% = (1610 ÷ 4600) × 100

⇒ P = 161 ÷ 4.6 = 35

∴ The correct answer is 35.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on the product. Discount is always calculated on the Marked Price unless otherwise specified.

Selling Price Calculation

Selling Price = Marked Price × (100 − Discount%) ÷ 100. This is useful for finding the final price after a single or successive discount.

The Correct Answer is Option 1 i.e Parenchyma.

The Correct Answer is Option 4 i.e S. S. Rajamouli.

• The Director of the blockbuster movie "Baahubali" is S. S. Rajamouli.
• It was written by K. V. Vijayendra Prasad.
• Screen Play was done by K. V. Vijayendra Prasad and S. S. Rajamouli.
• It was produced by Shoba Yarlagadda and Prasad Devineni.
• It was released on 10^th July 2015.
• Baahubali was one of the highest grossing movie in India and 3^rd highest grossing Indian film across the world.

Shortcut Trick

Option Elimination Method: Check the last symbol to reach 10.

Using Option (4): -, ×, +

((10 − 10) × 25) + 10 ⇒ (0 × 25) + 10 ⇒ 0 + 10 = 10.

∴ The correct answer is -, ×, +.

Alternate Method

Given Expression: ((10 ? 10) ? 25) ? 10 = 10

Formula Used: VBODMAS rule (Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction).

Checking Option (4) symbols: −, ×, +

⇒ ((10 − 10) × 25) + 10

⇒ (0 × 25) + 10 (Solving the innermost bracket first)

⇒ 0 + 10 (Solving the multiplication)

⇒ 10

LHS = RHS. The equation is satisfied.

Checking Option (1): ((10 − 10) × 25) ÷ 10 ⇒ 0 ÷ 10 = 0 (Incorrect)

Checking Option (2): ((10 × 10) × 25) + 10 ⇒ 2500 + 10 = 2510 (Incorrect)

Checking Option (3): ((10 + 10) ÷ 25) ÷ 10 ⇒ (20 ÷ 25) ÷ 10 = 0.08 (Incorrect)

∴ The correct answer is -, ×, +.

Additional Information

VBODMAS Rule

Operations must be performed in the order: Bracket, Of, Division, Multiplication, Addition, and Subtraction.

Mathematical Equality

The goal is to make the Left Hand Side (LHS) equal to the Right Hand Side (RHS) by substituting operators.

Zero Property

Any number multiplied by 0 results in 0 (a × 0 = 0), which is a key shortcut in simplification problems.

Glass and Metal are not the only material used to make a vessel. Clay, plastic and other materials are also used to make vessels. 

Hence, the figure given above is the correct diagram that represents the given relationship.

The Correct Answer is Option 3 i.e Pankaj Advani.

• Pankaj Advani was honoured with the prestigious 2018 Padma Bhushan award in the field of Sports-Billiards / Snooker.
• Padma Bhushan is an 4^th highest civilian award which is awarded by Government of India.

Shortcut Trick

Identify the common element: Zinc. In first ratio, Zinc = 16. In second, Zinc = 24.

Balance Zinc by finding LCM(16, 24) = 48.

Multiply first ratio by 3 and second ratio by 2.

Copper : Zinc : Nickel = (21 × 3) : (16 × 3) : (7 × 2) = 63 : 48 : 14.

∴ The correct answer is 63 : 48 : 14.

Alternate Method

Given:

Ratio of Copper to Zinc = 21 : 16

Ratio of Nickel to Zinc = 7 : 24

Formula Used:

To combine two ratios with a common term, the value of the common term must be equal in both ratios.

⇒ Let the common value of Zinc be the LCM of 16 and 24.

⇒ LCM(16, 24) = 48

⇒ Scaling Copper : Zinc → (21 × 3) : (16 × 3) = 63 : 48

⇒ Scaling Nickel : Zinc → (7 × 2) : (24 × 2) = 14 : 48

⇒ Combined Ratio of Copper : Zinc : Nickel = 63 : 48 : 14

∴ The correct answer is 63 : 48 : 14.

Additional Information

German Silver

It is an alloy of Copper, Zinc, and Nickel. Despite its name, it contains no Silver unless plated.

Compound Ratio

If ratios are a : b and c : d, the compound ratio is (a × c) : (b × d).

Ratio Scaling Property

The ratio a : b remains unchanged if both terms are multiplied or divided by the same non-zero constant k, i.e., a : b = ak : bk.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 160 m

Total Time = 1 minute = 60 seconds

Average Speed = 160 ÷ 60 = 8 ÷ 3 = 2.67 ms⁻¹

∴ The correct answer is 2.67 ms⁻¹.

Alternate Method

Given:

Length of the pool = 80 m

Total distance covered (D) = 160 m

Total time taken (T) = 1 minute

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Time in seconds = 1 × 60 = 60 s

⇒ Average Speed = 160 m ÷ 60 s

⇒ Average Speed = 16 ÷ 6

⇒ Average Speed = 2.666... ms⁻¹

⇒ Average Speed ≈ 2.67 ms⁻¹

∴ The correct answer is 2.67 ms⁻¹.

Additional Information

Average Velocity

It is defined as Total Displacement divided by Total Time. In this case, since Ram returns to the starting point, displacement is 0, so average velocity is 0 ms⁻¹.

Unit Conversion

To convert kmph to ms⁻¹, multiply by 5/18. To convert ms⁻¹ to kmph, multiply by 18/5.

Average Speed for Equal Distances

If an object covers two equal distances at speeds v₁ and v₂, then Average Speed = 2v₁v₂ ÷ (v₁ + v₂).

The Correct Answer is Option 4 i.e 2 Diopter.

The Focal length of a lens is 50 centimetre then its power is 2 Diopter.

Formula for Power of Lens:

P = 1 / f

where P is a power of lens measured in Diopters (D)

f is a focal length which is given in centimeter (m).

50 cm = 50*10^-2 m

Calculation:

P = 1 / f

P = 1 / (50*10^-2)

P=10²/50

P = 2

Power, P = 2  Diopter.

The Correct Answer is Option 4 i.e Hyderabad.

• The host city for the 8th annual Global Entrepreneurship Summit (GES – 2017) was Hyderabad.

The Correct Answer is Option 2 i.e 6 × 1024 kg.

The Mass of the Earth is 5.972 x 10²⁴ kg and it gets converted to 6 x 10²⁴ kg because of decimal point greater than 5.

The logic followed here is that each alphabet is coded as second number of its positional value.

F (06) → 6;

L (12) → 2;

U (21) → 1;

T (20) → 0;

E (05) → 5;

Similarly,

H (08) → 8;

A (01) → 1;

R (18) → 8;

M (13) → 3;

O (15) → 5;

N (14) → 4;

I (09) → 9;

C (03) → 3;

A (013 → 1;

Hence, ‘HARMONICA’ is coded as ’818354931’

The Correct Answer is Option 1 i.e 2000 J

Formula of Kinetic Energy:

Kinetic Energy = 1 / 2 × m × v²

Calculation:

Mass, m = 10 kg

Speed, v = 20 m/s

Kinetic Energy = 1 /2 × 10 × (20)²

K.E = 1 / 2 × 10 × 400

K.E = 5 × 400

Kinetic Energy = 2000 J

The correct answer is Option 2, i.e Transition Elements.

Important Points 

• There are elements which differ in the capacity to combine with other elements.
• This depends on the nature of the reaction.
• The property of such kind of elements is called variable valency.
• For example, the iron in ferrous oxide exhibits a valency of +2, whereas in ferric oxide, it has a valency of +3.
• The transition elements are those elements having a partially filled d or f subshell in any common oxidation state.
• The term "transition elements" most commonly refers to the d-block transition elements.
• Variable valency is thus exhibited by the Transition elements due to partially filled subshells.

The correct answer is Option 3, i.e 6.

• In 2017, India had emerged as the sixth largest economy, while France was pushed to the seventh place in the global GDP league table.
• India became the fifth-largest economy in 2019, overtaking the United Kingdom and France.
• India ranks third when GDP is compared in terms of purchasing power parity at $11.33 trillion.

The Correct Answer is Option 3 i.e Bharatiya Janta Party.

• The Chief Minister of Goa as of March 2018. Manohar Parrikar, belongs to Bharatiya Janata Party.
• Here is the list of Chief Ministers of Goa with respective party and year of their administration.

Shortcut Trick

Apply the Tangent-Secant Theorem: DE² = BD × AD.

Given DE = 9 cm and AB = 24 cm, let BD = x.

Then AD = x + 24. The equation becomes: 9² = x × (x + 24).

81 = x² + 24x ⇒ x² + 24x − 81 = 0.

Identify factors of 81 that differ by 24: 27 and 3. Thus, x = 3.

∴ The correct answer is 3 cm.

Alternate Method

Given:

Length of chord AB = 24 cm

Length of tangent DE = 9 cm

Formula Used:

According to the Tangent-Secant Theorem, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part.

DE² = BD × DA

Calculations:

⇒ Let the length of BD be x cm.

⇒ Then, the length of DA = BD + AB = x + 24 cm.

⇒ Using the theorem: DE² = BD × DA

⇒ 9² = x × (x + 24)

⇒ 81 = x² + 24x

⇒ x² + 24x − 81 = 0

⇒ x² + 27x − 3x − 81 = 0

⇒ x(x + 27) − 3(x + 27) = 0

⇒ (x + 27)(x − 3) = 0

⇒ x = 3 or x = −27

⇒ Since length cannot be negative, x = 3 cm.

∴ The correct answer is 3 cm.

Additional Information

Tangent-Secant Theorem

For an external point D, the square of the tangent DE is equal to the product of the external secant segment BD and the total secant segment DA (DE² = BD × DA).

Intersecting Chords Theorem

If two chords AB and CD intersect at a point P inside a circle, then PA × PB = PC × PD.

Tangent-Radius Property

The radius of a circle is always perpendicular to the tangent at the point of contact (OE ⊥ DE).

The Correct Answer is Option 2 i.e Angiosperms.

• Wood vessels are the chief water-conducting elements of angiosperms.
• In contrast to the tracheids the final walls of the single vessels are perforated or, much more so, completely resolved.

Y → 25;

E → 5;

L → 12;

L → 12;

Similarly,

L → 12;

E → 5;

N → 14;

T → 20

Hence, ‘LENT’ will be coded as ‘1251420’.

Shortcut Trick

Total interest percentage = Rate × Time

Total Interest % = 8% × 5 = 40%

Simple Interest = 40% of Rs. 3,125

SI = 0.4 × 3,125 = 1,250

∴ The correct answer is Rs. 1,250.

Alternate Method

Given:

Principal (P) = Rs. 3,125

Rate of interest (R) = 8% per annum

Time period (T) = 5 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI = (3125 × 8 × 5) ÷ 100

⇒ SI = (3125 × 40) ÷ 100

⇒ SI = 125000 ÷ 100

⇒ SI = 1,250

∴ The correct answer is Rs. 1,250.

Additional Information

Amount in Simple Interest

The total amount (A) is the sum of the principal and the interest earned: A = P + SI = P × (1 + RT/100).

Constant Interest Property

In Simple Interest, the interest earned remains the same every year because it is always calculated on the original Principal.

Rate and Time Calculation

To find the Rate (R), use R = (SI × 100) ÷ (P × T). To find Time (T), use T = (SI × 100) ÷ (P × R).

Shortcut Trick

A number is divisible by 12 if it is divisible by both 3 and 4.

Check divisibility by 4: Last two digits must be divisible by 4. All options end in 08, so all are divisible by 4.

Check divisibility by 3: Sum of digits must be divisible by 3.

For 83508: 8 + 3 + 5 + 0 + 8 = 24. Since 24 is divisible by 3, the number is divisible by 12.

∴ The correct answer is 83508.

Alternate Method

Given: Numbers 73508, 63508, 83508, 93508.

Rule: Number must satisfy divisibility of co-prime factors of 12, which are 3 and 4.

⇒ Divisibility by 4: Last two digits are 08. 08 ÷ 4 = 2 (Valid for all).

⇒ Divisibility by 3 (Sum of digits):

⇒ Option 1: 7 + 3 + 5 + 0 + 8 = 23 (Not divisible by 3)

⇒ Option 2: 6 + 3 + 5 + 0 + 8 = 22 (Not divisible by 3)

⇒ Option 3: 8 + 3 + 5 + 0 + 8 = 24 (Divisible by 3 because 24 ÷ 3 = 8)

⇒ Option 4: 9 + 3 + 5 + 0 + 8 = 25 (Not divisible by 3)

∴ The correct answer is 83508.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 4

A number is divisible by 4 if the last two digits form a number that is divisible by 4.

Composite Divisibility

To check divisibility by a composite number N, check divisibility by its co-prime factors (e.g., for 15 check 3 and 5).

The Correct Answer is Option 2 i.e Dia Mirza.

• Dia Mirza was appointed as the UN Environment’s Goodwill Ambassador for India in November 2017.
• On 29^th November 2017, Former Miss Asia Pacific, Actor, Producer, Entrepreneur and Environmentalist, Dia Mirza was appointed as UN Environment's Goodwill Ambassador for India.
• Dia has supported her efforts in the field of social change, conservation and environment.
• As a Goodwill Ambassador, Dia will work with the United Nations to expand areas including clean air, clean seas, wildlife protection and climate change.

The Correct Answer is Option 4 i.e Regeneration.

The Correct Answer is Option 1 i.e Sri Sri Ravi Shankar.

Sri Sri Ravi Shankar is the proponent and propagandist of the “Art of Living”.

The Correct Answer is Option 2 i.e Goa.

• The 48th International Film Festival of India held at Goa in 2017.

Hence, answer figure D is combined to form the given shape.

The correct answer is Option 4, i.e Kanchanmala Pande.

• Kanchanmala Pande, who hails from Amravati, won a gold medal at 2017 and thus became the first Indian to win gold at World Para Swimming Championship.
• Curtis Lovejoy was inducted into the Atlanta Sports Hall of Fame in the United States of America.
• Tucker Dupree is an American swimmer who has won three medals at the 2012 Paralympic Games and one at the 2016 Paralympic Games.
• Jessica Long has held multiple world records and has won multiple gold medals over four Summer Paralympics.

Shortcut Trick

Let Total Capacity of the cistern be the LCM of 5 and 6.25 (i.e., 25/4), which is 25 units.

Efficiency of Pipe A = 25 ÷ 5 = 5 units/hour.

Efficiency of Pipe B = 25 ÷ 6.25 = 4 units/hour.

Since Pipe A worked for the entire 3.4 hours, work done by A = 5 × 3.4 = 17 units.

Remaining work done by B = 25 − 17 = 8 units ⇒ Time for which B was open = 8 ÷ 4 = 2 hours.

∴ The correct answer is 2 hours.

Alternate Method

Given:

Time taken by Pipe A = 5 hours

Time taken by Pipe B = 6.25 hours = 25/4 hours

Total time to fill the cistern = 3.4 hours

Formula Used:

Work done = Efficiency × Time

Calculations:

⇒ Let Pipe B be open for t hours.

⇒ Work done by Pipe A in 3.4 hours + Work done by Pipe B in t hours = Total Work

⇒ (5 × 3.4) + (4 × t) = 25

⇒ 17 + 4t = 25

⇒ 4t = 8

⇒ t = 2 hours

∴ The correct answer is 2 hours.

Additional Information

Pipes and Cisterns Efficiency Rule

The efficiency of an inlet pipe is positive, whereas the efficiency of an outlet or leak pipe is negative. Total work is the LCM of individual times.

Alternate Operation of Pipes

If two pipes operate alternately hour by hour, the combined cycle work is computed as the sum of their individual efficiencies per cycle of 2 hours.

The Correct Answer is Option 4 i.e Narendra Modi.

• A 112 ft tall Shiva statue (Adiyogi) was unveiled on 24th February 2017 in Tamil Nadu by Narendra Modi.
• It is funded by Isha Foundation and founded by popular yoga guru Jaggi Vasudev.
• The Main reason behind the statue for 112 feet tall because there are 112 chakras in the human system in which we work to explore 112 dimension of Life.

The correct answer is Option 4, i.e Wetlands.

• The mangrove forests or wetlands are called by various names like tidal forests, coastal woodlands, walking forests in the sea, roots of the sea or oceanic rainforests.
• Wetlands occur where water meets land.
• They include mangroves, peatlands and marshes, rivers and lakes, deltas, floodplains and flooded forests, rice-fields, and even coral reefs.
• Wetlands exist in every country and in every climatic zone, from the polar regions to the tropics, and from high altitudes to dry regions.

Shortcut Trick

Ratio of Chairs : Tables = 9 : 7

Difference in ratio units = 9 − 7 = 2 units

Given, 2 units = 42 chairs

⇒ 1 unit = 21

Number of Chairs = 9 units = 9 × 21 = 189

∴ The correct answer is 189 chairs.

Alternate Method

Given:

Ratio of chairs to tables = 9 : 7

Difference between chairs and tables = 42

Calculations:

Let the number of chairs be 9x and tables be 7x.

⇒ 9x − 7x = 42

⇒ 2x = 42

⇒ x = 42 ÷ 2

⇒ x = 21

⇒ Number of chairs = 9x = 9 × 21

⇒ Number of chairs = 189

∴ The correct answer is 189 chairs.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b = c : d, then ad = bc (Product of extremes = Product of means).

Unitary Method in Ratios

To find the total or specific parts, first find the value of one 'unit' by dividing the given numerical difference or sum by the corresponding ratio difference or sum.

The correct answer is Option 4, i.e 60 ms-1 

• Time to reach Maximum height = 12/2 = 6 s
• v = 0 (at the maximum height)
• a = 10 m s^-2
• Using, v = u + at, we get
• 0 = u - 10 × 6 s
• or, u = 60 ms^-1

The Correct Answer is Option 4 i.e Double salt.

Shortcut Trick

Efficiency of Sunny + Paula = 1/12

Efficiency of Paula = 1/18

Efficiency of Sunny = 1/12 − 1/18 = (3 − 2)/36 = 1/36

Efficiency of Sunny + Jane = 1/36 + 1/45 = (5 + 4)/180 = 9/180 = 1/20

∴ The correct answer is 20 hours.

Alternate Method

Given: Time taken by (Sunny + Paula) = 12 hours, Paula = 18 hours, Jane = 45 hours.

Formula Used: Total Work = LCM of individual times; Efficiency = Total Work ÷ Time.

⇒ Efficiency of Sunny = (Sunny + Paula) − Paula = 15 − 10 = 5

⇒ Combined Efficiency of Sunny and Jane = 5 + 4 = 9

⇒ Time taken by (Sunny + Jane) = Total Work ÷ Combined Efficiency = 180 ÷ 9 = 20 hours

∴ The correct answer is 20 hours.

Additional Information

Total Work Concept

Work is always considered as 1 unit or the LCM of the time taken by individuals to simplify calculations.

Efficiency Relation

Efficiency is inversely proportional to Time. If A is twice as efficient as B, A will take half the time of B.

Combined Work Formula

For two people A and B, the time taken together is (T_A × T_B) ÷ (T_A + T_B).

The Correct Answer is Option 2 i.e Sanjay Leela Bhansali.

• Sanjay Leela Bhansali is the Director of the movie ‘Padmavaat’ released in 2018.

The Correct Answer is Option 2 i.e Prakash Javadekar.

Prakash Javadekar is the Union Minister of Human Resource Development, Government of India, as of 1 March 2018.

The Correct Answer is Option 2 i.e Divya Deskmukh.

Hence, answer figure A is the pattern that the given transparent sheet will resemble when it is folded at the dotted line.

Hence, answer figure C is the correct horizontal mirror image of LICK.

Shortcut Trick

Let radius of cone be r_c and altitude be h. Given r_c = h/3 ⇒ h = 3r_c.

Equating volumes: (1/3)πr_c²(3r_c) = (2/3)πr_h³.

πr_c³ = (2/3)πr_h³ ⇒ r_c³/r_h³ = 2/3.

Taking cube root: r_c : r_h = ³√2 : ³√3.

∴ The correct answer is ³√2 : ³√3.

Alternate Method

Given:

Radius of cone (r_c) = (1/3) × Altitude (h)

Volume of Cone = Volume of Hemisphere

Formula Used:

Volume of Cone = (1/3)πr²h

Volume of Hemisphere = (2/3)πR³

⇒ Let altitude of cone be h. Then base radius r_c = h/3 ⇒ h = 3r_c.

⇒ Volume of cone = (1/3) × π × r_c² × (3r_c) = πr_c³

⇒ Volume of hemisphere = (2/3) × π × r_h³

⇒ πr_c³ = (2/3) × π × r_h³

⇒ r_c³ / r_h³ = 2 / 3

⇒ r_c / r_h = (2/3)^1/3 = ³√2 / ³√3

∴ The correct answer is ³√2 : ³√3.

Additional Information

Right Circular Cone

Slant height l = √(r² + h²). Total Surface Area = πr(l + r).

Sphere and Hemisphere

Volume of Sphere = (4/3)πr³. Curved Surface Area of Hemisphere = 2πr².

Ratio of Volumes

If two solids have equal volumes, their dimensions are inversely proportional to the cube root of the constant coefficients in their volume formulas.

Since the meteorologist emphasizes that a shortage in rainfall would result in crop failure, it can assumed that rainfall is a necessity to avoid the failure.

Therefore, assumption I is implicit.

However, nothing is mentioned or suggested about the relation between irrigation and rainfall.

Therefore, assumption II is not implicit.

Hence, only assumption I is implicit.

In each figure the arrow is on one of the sides of the polygon whereas in figure C arrow is on one of the corners of the polygon.

Hence, figure C is the odd one among the given figures.

Shortcut Trick

Work done by A + B in 8 hours = 8/24 = 1/3 of the tank.

Remaining work = 1 − 1/3 = 2/3 of the tank.

Time taken by A alone to finish 2/3 work = 28 − 8 = 20 hours.

Time for A alone to fill the full tank = 20 × (3/2) = 30 hours.

∴ The correct answer is 30 hr.

Alternate Method

Given: Total work = 24 units (LCM of 24). Combined efficiency = 1 unit/hr.

Calculations:

⇒ Work done by A and B in 8 hours = 8 × 1 = 8 units.

⇒ Remaining work = 24 − 8 = 16 units.

⇒ Total time taken = 28 hours. Time A worked alone = 28 − 8 = 20 hours.

⇒ Efficiency of A = Remaining work ÷ Time = 16 ÷ 20 = 0.8 units/hr.

⇒ Time for A alone to fill tank = Total work ÷ Efficiency of A = 24 ÷ 0.8

⇒ Time = 240 ÷ 8 = 30 hours.

∴ The correct answer is 30 hr.

Additional Information

Efficiency Concept

Efficiency is inversely proportional to the time taken to complete a work. If A is twice as fast as B, A takes half the time B takes.

Pipes and Cisterns

Inlet pipes have positive efficiency, while outlet (leakage) pipes have negative efficiency. Total work = Time × Net Efficiency.

Bird sanctuaries provide natural habitats to the birds who take shelter here.

Therefore, it is safe to assume that the birds are migratory and stay in the sanctuary during a particular period of the year

Therefore, assumption I is implicit.

However, since the statement does not talk about water bodies at all, assumption II is not implicit.

Hence, only assumption I is implicit.

Preparing the family tree using the following symbols:

Hence, Vandana is cousin of Amit.

Shortcut Trick

Father’s age at Monika’s birth = 38 years.

Mother’s age at sister’s birth (4 years later) = 36 years.

Mother’s age at Monika’s birth = 36 − 4 = 32 years.

Age difference = 38 − 32 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given:

Father’s age when Monika was born = 38 years.

Sister is 4 years younger than Monika.

Mother’s age when Sister was born = 36 years.

Calculations:

⇒ Let Monika’s birth year be Year 0.

⇒ Father’s age in Year 0 = 38 years.

⇒ Sister’s birth year = Year 4 (since she is 4 years younger).

⇒ Mother’s age in Year 4 = 36 years.

⇒ Mother’s age in Year 0 = 36 − 4 = 32 years.

⇒ Difference between parents’ ages = 38 − 32 = 6 years.

∴ The correct answer is 6 years.

Additional Information

Constant Age Difference

The difference between the ages of any two individuals always remains constant regardless of the number of years passed.

Relative Age Calculation

To find the age of a person at a different point in time, add or subtract the number of years lapsed from their known age at a specific event.

Siblings Age Logic

If Person A is n years younger than Person B, then Person A is born n years after Person B.

The correct answer is option 1, i.e. Darwin's theory of evolution.

Key Points

Darwin's theory of evolution tells us how life evolved from simple to more complex form.

• Evolution is a process of change happening over generations.
• Darwin published his theory of evolution with evidence in his book 'On the Origin of Species' in 1859.
• The book introduced the scientific theory of evolution over the course of generations through the process of Natural Selection.

Shortcut Trick

Convert crate dimensions to cm: 180 cm × 150 cm × 120 cm.

Max Cubes = (L/side) × (W/side) × (H/side)

Max Cubes = (180/6) × (150/6) × (120/6)

Max Cubes = 30 × 25 × 20 = 15,000

∴ The correct answer is 15,000 cubes.

Alternate Method

Given:

Length of wooden crate (L) = 1.8 m = 180 cm

Width of wooden crate (W) = 1.5 m = 150 cm

Height of wooden crate (H) = 1.2 m = 120 cm

Side of iron cube (a) = 6 cm

Formula Used:

Number of cubes = Volume of crate ÷ Volume of one cube

Volume of cuboid = L × W × H

Volume of cube = a³

Calculations:

⇒ Volume of crate = 180 × 150 × 120 = 3,240,000 cm³

⇒ Volume of one iron cube = 6 × 6 × 6 = 216 cm³

⇒ Number of cubes = 3,240,000 ÷ 216

⇒ Number of cubes = 15,000

∴ The correct answer is 15,000 cubes.

Additional Information

Volume of Cuboid

The total space occupied by a cuboid is given by Length × Breadth × Height.

Fitting Rule

When fitting objects, the number of objects is only equal to (Total Volume / Object Volume) if the dimensions are perfectly divisible by the object side.

Unit Conversion

Always ensure all measurements are in the same unit before calculation (1 m = 100 cm).

Hence, 82L is the next term in the given series.

The correct answer is option 2, i.e. 20 m/s.

A boy standing at the top of the tower drops a stone from the height 20 m.

Velocity at which it will hit the ground is calculated as,

Given:

Height of the tower h = 20 m

g = 10 m/s²

Initial Velocity u = 0 (drops)

Final Velocity v =?

Using Equation of motion,

v² - u² = 2gh

v2 = u2 + 2gh

v2 = (0)² + 2 ×10 × 20 

v2 = 400

v = 20 m/s

The stone touches the ground at the velocity of 20 m/s when drops from the height of 20 m.

The Correct Answer is Option 3 i.e Maruti Suzuki.

• The Government of India has tied up with Maruti Suzuki to support Skill India in the automobile industry.
• Ministry of Skill Development and Maruti Suzuki enters into an agreement to support Skill India in Automobile industry.
• This agreement objective is to provide a unique opportunity to the youth to acquire skills related to automobile and manufacturing industry through the "Learn and Earn" approach.
• On 18^th December 2017, the flexi MoU was signed by Shri Vijay Kumar Dev, Director General, DGT (Ministry of Development and Entrepreneurship) and Shri Mukesh Kumar Gupta, Vice President (Maruti Suzuki India Limited).

The correct answer is Option 2, i.e Contraction Effect.

• Contraction is a method in Chemistry. It is related to Lanthanoid.
• Lanthanoid contraction: The gradual decrease in atomic and ionic radii of lanthanoids with the increase in atomic number is called lanthanoid contraction. It has a definite effect on the properties of lanthanoids.
• Chemical Effect, Heating Effect, Magnetic Effect are all produced by current.

The correct answer is Ne or Neon.

• The element which has two shells both of which are completely filled with electrons is Neon with electronic configuration (2,8).
• Helium (He) only has 2 electrons and therefore it has a configuration of 1s².
• Argon (Ar) electron configuration will be 1s22s22p63s23p6.
• Electron configuration of Krypton (Kr) : 1s22s22p63s23p63d104s24p6.

Shortcut Trick

Using Alligation Method: Average speed = 220 ÷ 4.5 = 440/9 km/h.

Speed 1 (Train): 60 | Speed 2 (Bus): 40 | Mean: 440/9

Ratio of Time (Bus : Train) = (60 − 440/9) : (440/9 − 40) = 100/9 : 80/9 = 5 : 4.

Bus Time = (5 ÷ 9) × 4.5 hours = 2.5 hours.

∴ The correct answer is 2 hr 30 min.

Alternate Method

Given: Total distance = 220 km, Total time = 4.5 hours, Train speed = 60 km/h, Bus speed = 40 km/h.

Let Time traveled by bus be 't' hours.

Then, Time traveled by train = (4.5 − t) hours.

⇒ Total Distance = (Speed_train × Time_train) + (Speed_bus × Time_bus)

⇒ 220 = 60 × (4.5 − t) + 40 × t

⇒ 220 = 270 − 60t + 40t

⇒ 220 = 270 − 20t

⇒ 20t = 270 − 220

⇒ 20t = 50

⇒ t = 50 ÷ 20 = 2.5 hours

⇒ 2.5 hours = 2 hours + 0.5 × 60 minutes = 2 hours 30 minutes.

∴ The correct answer is 2 hr 30 min.

Additional Information

Average Speed

Average Speed is the Total Distance divided by the Total Time taken for the journey.

Alligation Rule for Speed

When alligation is applied to Speeds, the resulting ratio is always the Ratio of Time spent on each part.

Relative Speed

If two objects move in the opposite direction, relative speed is the sum (S₁ + S₂). If in the same direction, it is the difference (S₁ − S₂).

The Correct Answer is Option 2 i.e 6 and 7.

The question figure has a triangle which is at the left of two opposite facing arrows.

The triangle does not touch the arrows and the arrows are outside the rectangle.

Hence, the pattern given in answer figure A is the pattern that most closely resembles the question figure.

Circle, Square and Rectangle are figures where as Volume is the quantity that represents the measure of space within a three dimensional figure.

Hence, Volume does not belong to the group.

Drawing the diagram as per the directions given.

If the home entrance is east facing this means when someone enters he/she must be west facing. 

Now she went to the shop which is adjacent means while entering she must be facing west.

Now she takes a right turn means the final direction will be in the North. 

Hence, Meenu is facing North direction.

Shortcut Trick Pick small natural numbers n > 1. If n = 2, n2 = 4. Since 4 = (3 × 1) + 1, it exceeds a multiple of 3 by 1. If n = 3, n2 = 9. Since 9 = (3 × 3), it is a multiple of 3. If n = 4, n2 = 16. Since 16 = (3 × 5) + 1, it exceeds a multiple of 3 by 1. ∴ The correct answer is 1. Alternate Method Given: A natural number n > 1. Concept: Any natural number can be represented in the form 3k, 3k+1, or 3k+2.

⇒ Case 1: If n = 3k ⇒ n2 = (3k)2 = 9k2 = 3(3k2), which is a multiple of 3. ⇒ Case 2: If n = 3k + 1 ⇒ n2 = (3k + 1)2 = 9k2 + 6k + 1 = 3(3k2 + 2k) + 1, which exceeds a multiple of 3 by 1. ⇒ Case 3: If n = 3k + 2 (or 3k − 1) ⇒ n2 = (3k + 2)2 = 9k2 + 12k + 4 = 9k2 + 12k + 3 + 1 = 3(3k2 + 4k + 1) + 1, which exceeds a multiple of 3 by 1. ∴ The correct answer is 1. Additional Information Square of a Number (mod 4) The square of any integer is either a multiple of 4 or exceeds a multiple of 4 by 1 (n2 ≡ 0, 1 mod 4). Euclid Division Lemma For any positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Perfect Square Properties A perfect square never ends in the digits 2, 3, 7, or 8.

Simplify using BODMAS: Bracket – Of – Division – Multiplication – Addition – Subtraction

3 + [32 ÷ 8 × 52 ÷ (4 + 9)]

⇒ 3 + [32 ÷ 8 × 52 ÷ 13]

⇒ 3 + [4 × 4]

⇒ 3 + 16

⇒ 19