RRC Group D Previous Year Paper 3 (Held On: 19 Sep 2018 Shift 1)

The logic follows here:

A sector of a circle is called the minor sector if the minor arc of the circle is a part of its boundary. It is the sector with a smaller area. The angle of a minor sector is less than 180 degrees.

In the given diagram,

5 circle is given and each circle divides into 4 sectors.

So, 5 × 4 = 20.

Hence, the "20" sectors are there in the following figure.

• Indian National Congress won the highest number of seats in the Manipur Legislative Assembly Elections held in 2017.
• Indian National Congress won 28 seats and Bharatiya Janata Party won 21 seats.
• Chief Minister of Manipur is N. Biren Singh and he belongs to Bharatiya Janata Party.

On the wrist we wear watches thus following the same pattern on the finger we wear a ring.

Hence, “ring” is the correct answer.

The pattern followed here is as follows,

Hence, “63” is the correct answer.

Shortcut Trick

Identify Radius (r) using Pythagoras triplet: r² = l² − h².

r² = 16² − (3√23)² = 256 − 207 = 49 ⇒ r = 7 cm.

Curved Surface Area (CSA) = πrl = (22/7) × 7 × 16 = 22 × 16.

CSA = 352 cm².

∴ The correct answer is 352 cm².

Alternate Method

Given:

Height (h) = 3√23 cm

Slant height (l) = 16 cm

Formula Used:

Radius (r) = √(l² − h²)

Curved Surface Area = πrl

Calculations:

⇒ r² = l² − h²

⇒ r² = 16² − (3√23)²

⇒ r² = 256 − (9 × 23)

⇒ r² = 256 − 207 = 49

⇒ r = √49 = 7 cm

⇒ CSA = π × r × l

⇒ CSA = (22/7) × 7 × 16

⇒ CSA = 22 × 16 = 352 cm²

∴ The correct answer is 352 cm².

Additional Information

Total Surface Area (TSA) of Cone

The total surface area includes the curved area and the base area: TSA = πr(l + r).

Volume of Cone

The space occupied by the cone is calculated as: Volume = (1/3)πr²h.

Relation between l, r, and h

In a right circular cone, the slant height (l), radius (r), and height (h) form a right-angled triangle: l² = r² + h².

Explanation:

• The rate of diffusion of gases do not depend upon their volume.
• Diffusion is the process of particles moving from highly concentrated region to low concentrated region.
• Rate of diffusion of gases is higher when compared to liquids and solids as gases can move freely from one region to another.
• Diffusion is only possible if the matter moves continuously as diffusion meant that moving of particles from high concentration to low concentration region.

• Corrosion is a process in which a surface of metals such as Iron, copper etc. are corroded when they are exposed to moisture/ moist air or acids.
• Corrosion can be prevented by painting, oiling, greasing, Galvanizing, Chrome Plating or making alloys.
  

• G. Satheesh Reddy was conferred with the National Design Award in December 2017.
• He is the chief of Defense Research and Development Organization as of 2019.
• He was awarded the Missile System Award 2019 by the American Institute of Aeronautics and Astronautics.

• Power is defined as the rate of doing work or the rate of transfer of energy.
• It can also be said as the amount of work done in a given amount of time.
• SI unit of power is represented by Watt (W).
• Formulae for power is given by p = W /t.
• Where W is work done and t is time.

The correct answer is 1919.

Key Points

• The Jallianwala Bagh massacre, also known as the Amritsar massacre, took place on April 13, 1919.
• On this day, around 50 troops of the British Indian Army, under the command of Colonel Reginald Dyer, fired on a crowd of Baishakhi pilgrims, who had gathered in Jallianwala Bagh, Amritsar, Punjab.
• After a public outcry, the British Government formed the Hunter Commission to probe into the Jallianwala Bagh Massacre.
• The Hunter Commission condemned the Massacre, but no action was recommended against General Dyer, who was responsible for the Massacre.
• Rabindranath Tagore returned his Knighthood in response to the massacre.
• Lord Chelmsford (1916-1921) was the Governor-General/Viceroy of India during the Jallianwala Bagh Massacre.
• Governor Michael O' Dyer was assassinated by Udham Singh in London in 1940 as revenge against the massacre.

As we know that “carrots” and “cabbages” are “vegetables” but there is no relation between “carrots” and “cabbages”. Thus the best possible venn diagram representing above relation is as follows.

Hence, “option 3” is the correct answer.

• Election Commissioner Om Prakash Rawat was appointed as the next chief election commissioner (CEC) of India. Mr Rawat is the 22nd CEC of India. He succeeded Achal Kumar Joti. The government also appointed former finance secretary Ashok Lawasa as an Election Commissioner.

Shortcut Trick

In Statement A: (1/3) × Weight = 2 kg ⇒ Weight of 1 box = 6 kg. Total weight = 6 × 6 = 36 kg.

In Statement B: Weight of (4 boxes − 2 boxes) = 12 kg ⇒ Weight of 2 boxes = 12 kg ⇒ Weight of 1 box = 6 kg.

Since both statements independently provide the weight of a single box, they are both sufficient.

∴ The correct answer is Both Statements 1 and 2 alone are sufficient.

Alternate Method

Given: Total boxes = 6, all having equal weight. Let the weight of each box be w kg.

Formula Used: Total Weight = Number of boxes × Weight of one box

From Statement A:

⇒ (1/3) × w = 2 kg

⇒ w = 2 × 3 = 6 kg

⇒ Total Weight (6 boxes) = 6 × 6 = 36 kg (Statement A is sufficient)

From Statement B:

⇒ 4w = 2w + 12 kg

⇒ 4w − 2w = 12 kg

⇒ 2w = 12 kg

⇒ w = 6 kg

⇒ Total Weight (6 boxes) = 6 × 6 = 36 kg (Statement B is sufficient)

∴ The correct answer is Both Statements 1 and 2 alone are sufficient.

Additional Information

Data Sufficiency Rules

A statement is sufficient if it leads to a unique numerical value or a definite 'Yes/No' answer for the question asked.

Linear Equations in One Variable

Equations in the form ax + b = c allow for finding the value of an unknown variable (x) using simple transposition.

Unit Consistency

Always ensure that the units (e.g., kg, grams) are consistent across the mathematical expressions to avoid calculation errors.

Shortcut Trick

In ΔABC, F and E are mid-points, so FE = BC/2 and FE || BC.

Quadrilateral FBDE is a parallelogram, so its diagonals BE and DF bisect at X, making X the mid-point of DF.

Quadrilateral DCEF is a parallelogram, so its diagonals DE and CF bisect at Y, making Y the mid-point of DE.

In ΔDEF, X and Y are mid-points of sides DF and DE respectively.

By Midpoint Theorem in ΔDEF, XY = FE/2 = (BC/2) / 2 = BC/4.

∴ The correct answer is BC/4.

Alternate Method

Given: D, E, and F are mid-points of sides BC, CA, and AB of ΔABC.

Formula Used: Midpoint Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

A B C D

• The number of moles present in one mole of copper 6.022 × 10²³ mol.
• Every compound contains same molecules in one mole.
• Mole can be defined as the amount of substance that contains as many particles as there in the 12 gm of 12C Carbon isotope.
• It is also known as Avogadro Constant and denoted by NA.
• SI unit of Mole is mol.

Using BODMAS rule,

⇒ 119 ÷ [22 - {90 ÷ (23 - 105 ÷ (7 × 3))}]

⇒ 119 ÷ [22 - {90 ÷ (23 - 105 ÷ 21)}]

⇒ 119 ÷ [22 - {90 ÷ (23 - 5)]

⇒ 119 ÷ [22 - {90 ÷ 18}]

⇒ 119 ÷ [22 - 5]

⇒ 119 ÷ 17 = 7

• The word ‘atom’ is coined by Democritus.
• He suggested that if we go on dividing matter at a certain point the atom becomes indivisible or cannot be divided further.
• He called these particles as atoms (Indivisible).

As we know in the morning, sun will be in east thus the opposite direction to the east is west.

Following figure shows the travelling path of Nina.

Clearly Nina turned towards the east direction at last.

Hence, “east” is the correct answer.

• The substances whose odour changes in acidic or basic media are called Olfactory Indicators.
• Onion, Clove, Vanilla etc. are some examples of Olfactory Indicators.
• These are the type of indicators are found naturally and used to test whether a given solution is an acid or a base.
• Some common examples are turmeric, grape juice etc.
• Synthetic indicators are different from natural indicators as the test for acids and bases is done with synthetic materials such as methyl orange and phenolphthalein.
• Any substance that indicates the presence of Acid or Base usually by changing colour is called Acid-Base indicators.
• Some common examples are red cabbage leaves, Turmeric etc.

The minimum possible Venn diagram of the given statements,

Conclusions:

1. All rocks are ores → True
2. All minerals are rocks → False (it is possible but not definite)

Hence, only conclusion 1 follows.

• Momentum is defined as the product of mass and velocity.
• Mass of the gun = 400 kg
• Its recoil velocity is 0.25 ms^-1
• We know that formula momentum (p) = mv
• Now by substituting the above values we get (p) = 400 × 0.25

 = 100 kg.m/s.

• The momentum of a gun is 100 kg.ms^-1.

Shortcut Trick

Ratio of Sooraj and Arjun currently = 3 : 1

Ratio after 8 years = 2.5 : 1 ⇒ 5 : 2

Difference in Arjun's age parts (2 − 1) = 1 unit → 8 years (Since base diff is same)

After another 8 years (total 16 years), add 1 more unit to each: Sooraj = 5 + 1 = 6, Arjun = 2 + 1 = 3 (Wait, check scaling: 3:1 vs 5:2 diff is 2 vs 3, make diff same × 3 and × 2)

Correct parts: Current (9 : 3), After 8 yrs (10 : 4). Gap 1 unit = 8 yrs. After 16 yrs: (11 : 5) ⇒ 11/5 = 2.2 times.

∴ The correct answer is 2(1/5) times.

Alternate Method

Given: Present age of Sooraj = 3 × Arjun. After 8 years, Sooraj = 2.5 × Arjun.

⇒ Let Arjun's current age be x, then Sooraj's age is 3x.

⇒ (3x + 8) = 2.5 × (x + 8)

⇒ 3x + 8 = 2.5x + 20

⇒ 0.5x = 12 ⇒ x = 24

⇒ Present ages: Arjun = 24 years, Sooraj = 72 years.

⇒ After another 8 years (Total 16 years from now):

⇒ Arjun = 24 + 16 = 40 years

⇒ Sooraj = 72 + 16 = 88 years

⇒ Ratio = 88 ÷ 40 = 2.2 = 2(1/5)

∴ The correct answer is 2(1/5) times.

Additional Information

Age Difference Property

The absolute difference between the ages of two people remains constant throughout their lives, regardless of the number of years passed.

Ratio Balancing Method

If the ratio of ages at two different times is given, multiply the ratios such that the difference between the parts of the ratio remains the same for both people.

Fraction to Ratio Conversion

A value of 2.5 times is equivalent to a ratio of 5:2, and 2.2 times is equivalent to 11:5 or 2(1/5).

The pattern followed here is as follows,

Similarly,

Hence, “FRLQV” is the correct answer.

Using BODMAS rule,

⇒ -15 - (-18 - 35 ÷ 5)

⇒ -15 - (-18 - 7)

⇒ -15 - (-25)

⇒ -15 + 25 = 10

• Alloys do not oxidize readily at high temperatures.
• Alloy is a homogenous mixture of two or more metals; or a metal and a non-metal.
• It prepared by melting a primary metal and dissolving other elements in definite proportions and cooled at room temperature.
• Alloys are usually prepared to get desired properties such as high melting point, protection against corrosion etc.
• Hence alloys do not oxidize as alloying improve properties of pure metals as alloying of iron mixed with nickel and chromium, it will become resistance to oxidization.
• But there are some alloys are prepared to get low melting points like solder which is made up of lead and tin.

Shortcut Trick

Identify the highest power of prime factors present in the numbers.

Factors: 14 = 2 × 7 | 42 = 2 × 3 × 7 | 77 = 7 × 11

LCM = 2¹ × 3¹ × 7¹ × 11¹ = 6 × 77 = 462.

∴ The correct answer is 462.

Alternate Method

Given: Numbers are 14, 42, and 77.

Formula Used: Prime Factorization Method for Least Common Multiple (LCM).

Calculations:

⇒ Prime factorization of 14 = 2 × 7

⇒ Prime factorization of 42 = 2 × 3 × 7

⇒ Prime factorization of 77 = 7 × 11

⇒ To find the LCM, take the highest power of each prime factor involved:

⇒ LCM = 2 × 3 × 7 × 11

⇒ LCM = 6 × 77

⇒ LCM = 462

∴ The correct answer is 462.

Additional Information

Relationship between LCM and HCF

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

Division Method for LCM

Write the numbers in a row and divide by the smallest prime number that divides at least two of the numbers; continue until no two numbers have a common factor.

LCM of Fractions

The LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

The minimum possible Venn diagram of the given statements,

Conclusions:

1. Some Lemons are Jump → False (“Jump” is not mentioned in the statement, so we can't say about the relation between “lemon” and “jump”)
2. Beet is a Red → False (There is no direct relation given between beet and red so it is possible but not definite)

Hence, neither conclusion 1 nor conclusion 2 follows.

• The South Asian Sports Council (SASC) was formed in the year 1983.
• South Asia Games are governed by SASC.
• The first South Asia games hosted by Kathmandu, Nepal in 1984.
• South Asian games are held once in every two years.

The pattern followed here is, every symbol in the next image is shifted to its next position and 4^th position symbol is replacing 1^st position symbol as follow,

Similarly,

Hence, “D” is the correct answer.

Shortcut Trick

Let the total monthly salary be 100%.

Expenditure = 85% → Savings = 100% − 85% = 15%.

Given 15% = ₹1200.

100% = (1200 ÷ 15) × 100 = 80 × 100 = ₹8,000.

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Percentage spent by Alok = 85%

Monthly savings = ₹1200

Formula Used:

Total Salary = Expenditure + Savings

Calculations:

⇒ Let total monthly salary be x.

⇒ Savings percentage = 100% − 85% = 15%

⇒ 15% of x = 1200

⇒ (15 ÷ 100) × x = 1200

⇒ x = (1200 × 100) ÷ 15

⇒ x = 80 × 100

⇒ x = 8000

∴ The correct answer is ₹8,000.

Additional Information

Percentage Change

To find the original value when a percentage decrease is known: Original = Final ÷ (1 − r/100).

Base Value Concept

In salary-based problems, the total income is always treated as the 100% base for all calculations.

Fractional Equivalent

15% can be written as 3/20. If 3 units = 1200, then 1 unit = 400 and 20 units (total) = 8000.

​Correct Answer Lord Canning

Key Points:

• Lord Canning (1856-1862) was the first viceroy of India.
• Viceroy is the British crown representative of the princely states of India.
• Lord Canning became first the Viceroy and governor-general of India through the government of India Act 1858.
• He was the Governor-General of India during the Indian Sepoy Mutiny in 1857.

Shortcut Trick

For a period of 3 years, the difference between CI and SI is given by the formula: D = P(R/100)² × (3 + R/100).

Substituting the values: Principal (P) = ₹4500, Rate (R) = 8%.

Difference = 4500 × (8/100)² × (3 + 8/100) ⇒ 4500 × 0.0064 × 3.08.

Difference = 28.8 × 3.08 = 88.704.

∴ The correct answer is ₹88.70.

Alternate Method

Given: Principal (P) = ₹4500, Time (T) = 3 years, Rate (R) = 8% per annum.

Formula Used: SI = (P × R × T) / 100 | CI = P[(1 + R/100)ⁿ − 1]

⇒ Simple Interest (SI) = (4500 × 8 × 3) ÷ 100

⇒ SI = 45 × 24 = ₹1080

⇒ Compound Interest (CI) = 4500 × [(1 + 8/100)³ − 1]

⇒ CI = 4500 × [(1.08)³ − 1]

⇒ CI = 4500 × [1.259712 − 1] = 4500 × 0.259712

⇒ CI = ₹1168.704

⇒ Difference = CI − SI = 1168.704 − 1080 = ₹88.704

∴ The correct answer is ₹88.70.

Additional Information

Difference for 2 years

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

Effective Rate of Interest

For 3 years at 8%, the effective CI rate is (1.08³ − 1) × 100 = 25.9712%, while the SI rate is 8 × 3 = 24%.

Successive Percentage Change

CI can be viewed as successive percentage increases: R_net = x + y + (xy/100).

Shortcut Trick

Calculate the squared lengths of the sides to identify the triangle type quickly.

Side 1² = (4−1)² + (1−1)² = 3² + 0² = 9

Side 2² = (3−1)² + (5−1)² = 2² + 4² = 20

Side 3² = (3−4)² + (5−1)² = (−1)² + 4² = 17

Since all squared lengths are different (9 ≠ 20 ≠ 17), all sides are unequal.

Also, no two squared lengths sum to the third (9 + 17 ≠ 20), so it is not right-angled.

∴ The correct answer is Scalene triangle.

Alternate Method

Given: Vertices of the triangle are A(4, 1), B(1, 1), and C(3, 5).

Formula Used: Distance between two points (x₁, y₁) and (x₂, y₂) = √((x₂−x₁)² + (y₂−y₁)²)

⇒ Length of side AB = √((4−1)² + (1−1)²) = √(3² + 0²) = 3 units

⇒ Length of side BC = √((3−1)² + (5−1)²) = √(2² + 4²) = √20 units

⇒ Length of side AC = √((3−4)² + (5−1)²) = √((−1)² + 4²) = √17 units

⇒ Comparing the sides: 3 ≠ √20 ≠ √17. Since all sides are unequal, it is a Scalene triangle.

⇒ Checking Pythagoras Theorem: 3² + (√17)² = 9 + 17 = 26. Since 26 ≠ (√20)², it is not a right-angled triangle.

∴ The correct answer is Scalene triangle.

Additional Information

Scalene Triangle

A triangle in which all three sides have different lengths and all three angles have different measures.

Isosceles Triangle

A triangle that has two sides of equal length and two equal angles opposite those sides.

Right-Angled Triangle

A triangle with one angle exactly 90°. It must satisfy the condition a² + b² = c², where c is the longest side.

Distance Formula

The distance between two points in a 2D plane is given by d = √((x₂−x₁)² + (y₂−y₁)²).

Given that it was a Thursday on 7th June 1984.

From 7th June 1983 to 7th June 1984, the number of odd days = 2 as 1984 is a leap year.

Hence, the day on 7th June 1983 was Tuesday.

• Apple introduced the iPad as a multimedia device in the year 2010.
• Apple is introduced iWatch in the year 2015 and iPhone in 2007.
• It is the first company in the world to reach the market valuation of 1 Trillion Dollars.
• CEO of the company is Tim Cook.

CONCEPT:

• Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by:

$W = \vec F \cdot \vec s$

Or, W = Fs cos θ

• Thus work done by a force is equal to the scalar or dot product of the force and the displacement of the body.

EXPLANATION:

• The product of Force and Displacement is called Work. So option 1 is correct.

• The Protozoa is not a part of the 5-Kingdom classification by Whittaker.
• R.H. Whittaker proposed a Five Kingdom Classification in the year 1969.
• The 5 Kingdoms he classified are Monera, Protista, Fungi, Plantae and Animalia.
• He defined these five kingdoms based on cell structure, thallus organization, mode of nutrition, reproduction and phylogenetic relationships.

Given expression: ((25 + 30) × 5) × 10)

After changing the symbols:

((25 - 30) ÷ 5) ÷ 10)

= ((-5) ÷ 5) ÷ 10

= -1 ÷ 10 = -0.1

Hence, “-0.1” is the correct answer.

Shortcut Trick To find the missing fraction that completes a whole (1), subtract the given fraction from 1. Required Fraction = 1 − 5/16 = 11/16 Check options for equivalent fractions: 11/16 × 2/2 = 22/32 ∴ The correct answer is 22/32.

Alternate Method Given: Initial fraction = 5/16 Target sum = 1 Formula: Missing Fraction = Target Sum − Given Fraction

Calculations: ⇒ Let the required fraction be x. ⇒ 5/16 + x = 1 ⇒ x = 1 − 5/16 ⇒ x = (16 − 5) / 16 ⇒ x = 11/16 ⇒ To match the denominators in the options, multiply the numerator and denominator by 2: ⇒ x = (11 × 2) / (16 × 2) ⇒ x = 22/32 ∴ The correct answer is 22/32.

Additional Information Equivalent Fractions Fractions that represent the same value by multiplying or dividing the numerator and denominator by the same non-zero number (e.g., 11/16 = 22/32). Proper Fractions A fraction where the numerator is less than the denominator (e.g., 5/16 is a proper fraction as 5 < 16). Reciprocal of a Fraction The reciprocal of a fraction a/b is b/a. The product of a fraction and its reciprocal is always 1.

• The first ‘Persons of Indian Origin (PIO) Parliamentarian Conference’ was held on 9 January 2018.
• It was the first PIO-Parliamentarian Conference and it was held in New Delhi.

Shortcut Trick

Let Marked Price (MP) be 100.

Cost Price (CP) = 100 − 20% of 100 = 80.

Selling Price (SP) = Marked Price = 100.

Profit = 100 − 80 = 20.

Profit% = (Profit ÷ CP) × 100 = (20 ÷ 80) × 100 = 25%.

∴ The correct answer is 25% gain.

Alternate Method

Given → Discount = 20% on MP, Selling Price (SP) = Marked Price (MP). Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100 | CP = MP × (100 − D%) ÷ 100.

⇒ Assume Marked Price = x. ⇒ Cost Price (CP) = x − 20% of x = 0.8x. ⇒ Selling Price (SP) = x (Given). ⇒ Profit = SP − CP = x − 0.8x = 0.2x. ⇒ Gain% = (0.2x ÷ 0.8x) × 100 = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25% gain.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). Formula: SP = MP × (100 − Discount%) ÷ 100.

Gain Percentage

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

• An object is placed in front of a concave mirror at a point between its focus and centre of curvature. The image formed will be Real, Inverted and enlarged.
• The position of the image will be beyond the centre.

• Weight of the object (m) = 10 kg
• Speed of the object (v) = 5 m/s
• We know that kinetic energy formulae (K.E) = ½ mv².
• Now by substituting the values in the formula we get

          K.E = ½ (10) (5)²

           = 125 J

• The kinetic energy of the object is 125 J.

The correct answer is Collenchyma

Key Points

• Simple permanent tissues in plants are made up of cells that are similar in structure and function and have lost the capacity to divide. These tissues are involved in various functions like photosynthesis, storage, and support.
• The three main types of simple permanent tissues are parenchyma, collenchyma, and sclerenchyma. Each type plays a different role in the plant structure and function.

Apical meristem: This is a type of meristematic tissue, not a simple permanent tissue.

• Meristematic tissues consist of undifferentiated cells that have the capacity to divide.
• Apical meristems are found at the tips of roots and shoots and are responsible for the lengthwise growth of the plants.
• Since these cells are capable of division and give rise to various tissues, the apical meristem does not qualify as a simple permanent tissue.

Collenchyma: This is a type of simple permanent tissue.

• Collenchyma cells are characterized by their unevenly thickened cell walls, which provide flexibility and mechanical support to growing parts of the plant like stems and leaves.
• They are living cells and are typically found beneath the epidermis.

Xylem: Xylem is a complex permanent tissue, not a simple one, involved in the transport of water and nutrients from the roots to other parts of the plant. It consists of several different types of cells, making it a complex tissue rather than a simple one.

Cambium: Cambium is not a simple permanent tissue; it is a type of meristematic tissue known as lateral meristem. It is responsible for the diameter growth in plants through the process called secondary growth. Cambium cells divide to produce new xylem and phloem cells, contributing to the thickness of stems and roots.

Therefore,among the options provided Collenchyma is the correct answer.

• Viacom 18 Media PVT. Ltd. Launched its Hindi movie channel Rishtey Cineplex in May 2016.
• It is the company first foray in Hindi films.
• Viacom 18 operates channels like MTV, Colours etc.

Concept Used:

For quadratic equation, ax² + bx + c = 0,

α + β = -b/a and αβ = c/a

Calculation:

Given equation is (5 + √2) x2 - (4 + √5) x + (8 + 2√5) = 0

On comparing this equation by ax2 + bx + c = 0, we get

a = (5 + √2), b =  - (4 + √5) and c = (8 + 2√5)

Now, αβ = (8 + 2√5)/(5 + √2) and α + β = (4 + √5)/(5 + √2)

Now, We have to find the value of 2αβ/(α + β)

⇒ 2[(8 + 2√5)/(5 + √2)] / [(4 + √5)/(5 + √2)]

⇒ 2 [(8 + 2√5) (4 - √5)] / [(4 + √5)/(4 - √5)]

⇒ 2(32 + 8√5 - 8√5 - 10)/11

⇒ 44/11 = 4

∴ The required value of 2αβ/ (α + β) is 4.

• The real name of the Indian director ‘Guru Dutt’ is Vasant Kumar Shivashankar Padukone (1925-1964).
• He was most famous for these films pyaasa and Kaagaz Ke Pool.
• He has been included in CNN top 25 actors of all time in the year 2010.

From the statement the “Of all the mobile brands, Samsung’s sales are the highest”, we can understand that there is a comparison taking place between Samsung mobile phones and all other mobile phones. Since the statement is comparing thus, we can make the conclusion that “The market share of other mobile brands is known” but there is no mention about the popularity of any other brands, thus, we cannot say that “No other mobile brand is popular”. Hence, only conclusion I follow.

• The melting point of tungsten is 3,380 °C.
• It is represented by W and has an atomic number of 74.
• It belongs to transition elements.
• Due to its high melting point, tungsten is used as filament in an incandescent bulb.

A free fall in true sense occurs only in a vacuum.

• A fall is considered as a free fall if only force acting on it was gravity.
• As the vacuum contains no matter, there is no opposite force against the free fall due to gravity.
• In air and atmosphere, there is aerodynamic drag and in the sea, there is a buoyancy force of water to oppose the movement due to gravity.

• Oxygen is not required for photosynthesis.
• Oxygen is liberated during photosynthesis.
• Photosynthesis is the process through which green plants manufacture food by converting solar energy into chemical energy. In this process, water and carbon dioxide react in the presence of sunlight to give off oxygen and glucose molecules.
• Leaves of a plant contain green colour due to the presence of chloroplasts.
• Chloroplasts contain the green substance called chlorophyll.
• Chlorophyll absorbs sunlight for photosynthesis.

Shortcut Trick

Stoppage time per hour = (Difference in speeds ÷ Speed without stoppage) × 60 minutes

Difference in speed = 80 − 60 = 20 km/hr

Stoppage time = (20 ÷ 80) × 60

Stoppage time = 1/4 × 60 = 15 minutes

∴ The correct answer is 15 min.

Alternate Method

Given:

Speed without stoppage (u) = 80 km/hr

Speed with stoppage (v) = 60 km/hr

Formula Used:

Time = Distance ÷ Speed

Stoppage time per hour = (u − v) ÷ u

Calculations:

⇒ In 1 hour, distance covered without stoppage = 80 km

⇒ In 1 hour, distance covered with stoppage = 60 km

⇒ Loss in distance due to stoppage = 80 − 60 = 20 km

⇒ Time taken to cover 20 km at original speed = 20 ÷ 80 hours

⇒ Stoppage time in minutes = (20 ÷ 80) × 60

⇒ Stoppage time = 1/4 × 60 = 15 minutes

∴ The correct answer is 15 min.

Additional Information

Average Speed Concept

Average speed is defined as the total distance traveled divided by the total time taken, including stoppage time.

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Apply the inverse proportionality rule between men and days: M₁ × D₁ = M₂ × D₂.

Ratio of days is 1024 : 256 = 4 : 1.

Ratio of men required will be the inverse: 1 : 4.

Since 1 unit = 200 men, then 4 units = 200 × 4 = 800 men.

∴ The correct answer is 800 men.

Alternate Method

Given:

Initial Men (M₁) = 200

Initial Days (D₁) = 1024

Required Days (D₂) = 256

Formula Used:

Total Work = Men × Days

M₁ × D₁ = M₂ × D₂

Calculations:

⇒ 200 × 1024 = M₂ × 256

⇒ M₂ = (200 × 1024) ÷ 256

⇒ M₂ = 200 × 4

⇒ M₂ = 800

∴ The correct answer is 800 men.

Additional Information

Chain Rule Formula

The general formula for work is (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is men, D is days, H is hours, and W is work.

Inverse Proportion

When the amount of work is constant, men and days are inversely proportional. Doubling the men halves the time required.

Work & Wages

Wages are usually distributed in the ratio of the work done or the ratio of efficiencies when the time period is same.

The pattern followed here is as follows,

Hence, “Q” is the correct answer.

• Oprah Winfrey was honoured with the Cecil B. Demille Award at the 75^th Golden Globe Awards.
• It was an award given to a person for his ‘outstanding contributions to the world of entertainment’.
• It was presented by the Hollywood Foreign Press Association.
• This award in 2019 was given to Jeff Bridges.

Shortcut Trick

Product of times ÷ Difference of times

Time taken by leak = (15 × 20) ÷ (20 − 15)

Time taken by leak = 300 ÷ 5 = 60 hours

∴ The correct answer is 60 hr.

Alternate Method

Efficiency of Tube (A) = 4 units/hr

Combined Efficiency of Tube and Leak (A + B) = 3 units/hr

⇒ Efficiency of Leak (B) = (A + B) − A = 3 − 4 = −1 unit/hr (Negative sign indicates emptying)

⇒ Time taken by Leak alone = Total Work ÷ Efficiency of Leak

⇒ Time = 60 ÷ 1 = 60 hours

∴ The correct answer is 60 hr.

Additional Information

Pipes and Cisterns Logic

Inlet pipes have positive efficiency while outlet pipes or leaks have negative efficiency.

Net Work Formula

If pipe A fills in x hours and pipe B empties in y hours, net work per hour = (1/x − 1/y).

Shortcut Trick

Compare 10 sin⁴α + 15 cos⁴α = 6 with 1 by dividing both sides by 6.

(10/6) sin⁴α + (15/6) cos⁴α = 1 ⇒ (5/3) sin⁴α + (5/2) cos⁴α = 1.

Standard Identity: sin²α + cos²α = 1. This holds when sin²α = 3/5 and cos²α = 2/5.

Value = 27 (1/sin²α)³ + 8 (1/cos²α)³ = 27 (5/3)³ + 8 (5/2)³ = 27 × (125/27) + 8 × (125/8) = 125 + 125 = 250.

∴ The correct answer is 250.

Alternate Method

Given: 10 sin⁴α + 15 cos⁴α = 6

Formula Used: sin²α + cos²α = 1; sec²α = 1/cos²α; cosec²α = 1/sin²α

⇒ 10 sin⁴α + 15 (1 − sin²α)² = 6

⇒ 10 sin⁴α + 15 (1 + sin⁴α − 2 sin²α) = 6

⇒ 25 sin⁴α − 30 sin²α + 9 = 0

⇒ (5 sin²α − 3)² = 0 ⇒ sin²α = 3/5

⇒ cos²α = 1 − 3/5 = 2/5

⇒ cosec²α = 5/3 and sec²α = 5/2

⇒ 27 cosec⁶α + 8 sec⁶α = 27 (5/3)³ + 8 (5/2)³

⇒ 27 × (125/27) + 8 × (125/8) = 125 + 125 = 250

∴ The correct answer is 250.

Additional Information

Trigonometric Identities

Fundamental relations: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

General Comparison Rule

If (a/c) sin⁴α + (b/c) cos⁴α = 1, and it mimics (sin²α/sin²α) + (cos²α/cos²α) = 1, then sin²α = c/a and cos²α = c/b.

Shortcut Trick

For a number to be divisible by 9, the sum of its digits must be divisible by 9.

Sum of given digits = x + 4 + 7 + 3 + 8 = x + 22.

The nearest multiple of 9 greater than 22 is 27.

⇒ x + 22 = 27 ⇒ x = 5.

∴ The correct answer is 5.

Alternate Method

Given: The number is x4738 and it is divisible by 9.

Property used: Divisibility rule of 9 states that the sum of all digits must be a multiple of 9.

⇒ Sum of digits = x + 4 + 7 + 3 + 8

⇒ Sum = x + 22

⇒ For (x + 22) to be divisible by 9, let (x + 22) = 9n (where n is an integer)

⇒ Since x is a single digit (0-9), the only possible value for n is 3.

⇒ x + 22 = 27

⇒ x = 27 − 22

⇒ x = 5

∴ The correct answer is 5.

Additional Information

Divisibility Rule of 3

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

Face Value vs Place Value

The face value of a digit is the digit itself, while the place value depends on its position (e.g., in x4738, the place value of x is x × 10000).

Divisibility Rule of 11

The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Here, except ‘weed’ all others are part of plants but ‘weed’ is a plant itself.

Hence, ‘weed’ is the correct answer.

• India is the largest producer, consumer, importer of Pulses.
• India mainly produces pulses like chickpea, black gram, green gram, and lentil etc.
• India is the largest producer of Jute.
• India is the second-largest producer of Sugar.
• Gujarat is the largest producer of salt in the country.

lateral mirror image of the word ‘KIT’ is as follows,

Hence, “option figure B” is the correct answer.

Calculation:

Follow BODMAS rule to solve this question, as per the order given below:

66 ÷ [67 - {43 - (17 - 117 ÷ 9 × 4)}] = ?

⇒ 66 ÷ [67 - {43 - (17 - 13 × 4)}] = ?

⇒ 66 ÷ [67 - {43 - (17 - 52)}] = ?

⇒ 66 ÷ [67 - {43 - (-35)}] = ?

⇒ 66 ÷ [67 - {43 + 35}] = ?

⇒ 66 ÷ [67 - 78] = ?

⇒ 66 ÷ -11 = ?

⇒ -6 = ?

∴ The value of ? is -6

• Hydrogen is the element that could not find a fixed place in Mendeleev’s periodic table.
• Mendeleev periodic law states that ‘the properties of elements are the periodic function of their atomic masses’.
• Hydrogen has 1 electron in its outermost orbit hence it should be placed in s- group (Alkali metals) or group 1.
• But it behaved like a halogen (group 17) which gains one electron to reach the electronic configuration of a helium atom which is a noble gas.
• Hence hydrogen did not find a fixed place in Mendeleev periodic law.

The pattern followed here is as follows,

Hence, “81N” is the correct answer.

The following figure explains the hidden image,

Hence, “A and B” is the correct answer.

• Aung-san Sukyi belongs to the country of Myanmar (Formerly Burma).
• She was awarded the Noble Peace prize in the year 1991.
• She is currently the State Counsellor of Myanmar since 2016.
• Capital of Myanmar is Naypyidaw and its currency is Burmese Kyat.

• The headquarters of the World Bank is in the United States of America (USA).
• Its headquarters is in Washington D.C. USA.
• It has a total membership of 189 countries.
• Along with the International Monetary Fund (IMF), the World Bank was established in the year 1945.
• IMF also has its headquarters in Washington D.C.

Argument I give the solid reason that “they pose a high risk to the environment” and also provide with the solution that “People can bring along their own bags to buy vegetables”. While the argument II is ambiguous and doesn’t argues on any solid base. Hence, “Only argument I is strong”.

Shortcut Trick

Property of Arithmetic Mean: If every observation in a data set is multiplied or divided by a constant non-zero value, the mean of those observations is also multiplied or divided by that same constant.

Given Original Mean of x₁, x₂, ..., x_n = 1.

Operation: Each observation is divided by k (or multiplied by 1/k).

New Mean = Original Mean ÷ k = 1 ÷ k = 1/k.

∴ The correct answer is 1/k.

Alternate Method

Given:

The Arithmetic Mean of x₁, x₂, x₃, ... x_n is 1.

New series is obtained by dividing each term by k where k > 0.

Calculations:

⇒ Sum of observations ∑x_i = x₁ + x₂ + ... + x_n

⇒ Original Mean = (∑x_i) / n = 1

⇒ ∑x_i = n

⇒ New Mean = [ (x₁/k) + (x₂/k) + ... + (x_n/k) ] / n

⇒ New Mean = [ (1/k) × (x₁ + x₂ + ... + x_n) ] / n

⇒ New Mean = [ (1/k) × ∑x_i ] / n

⇒ New Mean = [ (1/k) × n ] / n

⇒ New Mean = 1/k

∴ The correct answer is 1/k.

Additional Information

Change of Origin and Scale

The Arithmetic Mean is affected by both change of origin (adding/subtracting a constant) and change of scale (multiplying/dividing by a constant). If y_i = (x_i − a) / h, then Mean(y) = (Mean(x) − a) / h.

Sum of Deviations

The sum of deviations of a set of observations from their Arithmetic Mean is always zero, i.e., ∑(x_i − Mean) = 0.

Effect on Variance

Unlike the mean, Variance is independent of change of origin but affected by change of scale. If each term is divided by k, the new variance becomes (Original Variance) / k².

• Mechanical energy is defined as the sum of kinetic energy and potential energy in an object that is utilized to do work.
• Mechanical energy is a combination of kinetic energy and potential energy.
• Mechanical energy is the form of energy that is related to the position and motion of an object.
• Kinetic energy: The energy possessed by an object has because of its motion.

          K. E. = (½) mv²

• Potential energy: The energy stored in an object because of its specific state or position.

          P.E. = mgh

Symbol for family tree:

We can draw a family tree from the given information,

Hence, C is the “mother-in-law” of Z.

Concept:

• Work is done: The product of force and displacement is called work done
• Work was done against gravity: When an object is brought to some height going against gravity, work is said to be done against gravity.
• This work done is converted into potential energy.
• The potential energy is energy stored in a body when work is done against gravity. It is given as

P = m × g × h

• As for lifting or after lifting at height some work needs to be done, .for e.g A coolie lifting a weight in his weight, it is in the form of potential energy, so work done can also be written as,

W = P = m × g × h.

m is mass, g is the acceleration due to gravity, and h is the height obtained. 

Calculations:

• The mass of the object (m) is 1 kg.
• The height of the object (h) is 30m
• The gravity of the earth (g) is 10 m/s²
• Now Work done by the force of gravity = mgh
• Now substituting the above values, we get

= (1)(30)(10) = 300 J

• The work done by the force of gravity will be 300 J.

The pattern followed here is as follows,

Similarly,

Hence, “FGQ” is the correct answer.

the lateral mirror image of ‘LIGHT’ is shown in the following figure,

Hence, “option figure B” is the correct answer.

We can count triangle as follows,

Hence, there are “8” triangles in the given figure.

• Newlands’s law of octaves was applicable only up to calcium.
• Newland table was drawn by John Newlands in 1866 according to his Law of Octaves.
• In his theory, he purposed that when elements are arranged according to their increasing atomic weights then every eight elements have similar properties as the first element.
• After calcium, this law ceased to be valid as after calcium every eight elements do not have the same property of a first element.

Correct Answer Himalayas

Key Points:

• The Himalayas is the youngest mountain (Fold Mountain) in India.
• Due to tectonic movement, the Gondwana land collided with Eurasian plate resulting in the formation of Himalayas.
• The Himalayas acts as a source for many rivers like the Ganges, the Yamuna, The Indus, The Brahmaputra etc.
• Mount Abu is in the Aravali mountain range (it is residual Mountain range).
• Satpura mountain range (Block Mountains) is in central India.
• Anaimudi is the highest peak in the Western Ghats.

In only ‘figure C’ we observe that there are two ovals and are touching at two positions. Thus it closely resembles the question figure.

Hence, “C” is the correct answer.

• When two germ cells from two individuals combine during sexual reproduction, they form a Zygote.
• When male gametes (Sperm) feud with female gametes (Ovum) then a Zygote is formed.
• Zygote is moved down from the fallopian tubes and attached to wall of Uterus and its called embryo which further develops into Fetus.
  

Shortcut Trick

Total Work (LCM of 8, 12) = 24 units.

Efficiencies: Kuldeep = 3, Agarkar = 2.

In a 2-hour cycle (3 + 2) = 5 units are completed.

In 4 cycles (8 hours), 5 × 4 = 20 units done. Remaining = 4 units.

9^th hour: Kuldeep does 3 units. Remaining = 1 unit. 10^th hour: Agarkar takes 1/2 hour.

Total time = 9 hours 30 mins. Starting 9 a.m. + 9.5 hours = 6.30 p.m.

∴ The correct answer is 6.30 p.m.

Alternate Method

Given: Kuldeep (K) = 8 hours, Agarkar (A) = 12 hours. Start time = 9 a.m. (K starts).

Formula Used: Efficiency = Total Work ÷ Time

⇒ Work done in 1^st hour (Kuldeep) = 3 units

⇒ Work done in 2^nd hour (Agarkar) = 2 units

⇒ Total work in 2 hours = 3 + 2 = 5 units

⇒ Work done in 8 hours (4 cycles) = 5 × 4 = 20 units

⇒ Remaining work = 24 − 20 = 4 units

⇒ 9^th hour: Kuldeep completes 3 units. Remaining = 4 − 3 = 1 unit

⇒ 10^th hour: Agarkar needs time = 1 ÷ 2 = 0.5 hours (30 minutes)

⇒ Total duration = 9 hours + 30 minutes = 9 hours 30 minutes

⇒ Finish Time = 9:00 a.m. + 9 hours 30 mins = 6:30 p.m.

∴ The correct answer is 6.30 p.m.

Additional Information

Alternate Work Concept

When people work alternately, the work is calculated in cycles. If A starts, the odd hours belong to A and even hours to B.

LCM Method for Work

Total work is assumed as the Least Common Multiple of individual time periods to avoid calculations in fractions.

Time Conversion

Fraction of an hour is converted to minutes by multiplying by 60 (e.g., 1/2 hour = 30 minutes).

• Mercury (Hg) is in the form of liquid at room temperature.
• Mercury is the only metal in liquid form at room temperature.
• As mercury is sensitive to temperature changes, it is used in the devices that are used to measure temperature.
• Bromine (Br) is also in liquid form at room temperature but is a non- metal.
• Both lead (Pb) and tungsten (W) is in solid form at room temperature.

• The CEO of ICCI bank is Sandeep Bakhshi.
• Chanda Kochhar stepped down for violation of ICCI Banks code of conduct.

Initial capital with Lalitha = Rs. 20000

⇒ Percentage of money left with her for other expenses = 100 - 50 - 20 = 30%

∴ Money left = (30/100) × 20000 = Rs. 6000

• The Income Declaration Scheme was launched by the Income Tax Department of the Government of India in the year 2016.
• The Scheme provides an opportunity to the citizen who has not paid full taxes in the past to come forward and declare the undisclosed income and pay tax, surcharge and penalty totalling in all to forty-five per cent of such undisclosed income declared.
• The declaration must be made between 1^st June 2016 to 30^th September 2016.

• A constitution amendment bill must be passed by both lower house (Lok Sabha) and upper houses (Rajya Sabha) of Parliament separately.
• The article 368 (1) provides the Indian Parliament power to amend the Indian constitution.
• A constitutional amendment must be passed by both houses by a special majority ( 2/3^rd of members) of both houses.

Factors of 108900 = (2 × 2 × 3 × 3 × 5 × 5 × 11 × 11)

∴ Square root of 108900 = 2 × 3 × 5 × 11 = 330

Percentage of employees in segment 5 = 20%

Percentage of employees in segment 3 = 10%

⇒ Amount spend on segment 3 is Rs. 5000 i.e. on 10% employees

⇒ So, the expense on segment 5 i.e. on 20% employees = 2 × 5000 = Rs. 10000

∴ Expense on segment 5 = Rs. 10000

The correct answer is Hydrogen.

Key Points

• When metals react with water. It liberates hydrogen gas.
• Metals react with water to form a metal oxide and liberate hydrogen gas.
• Metal + Water → Metal oxide + Hydrogen (g)
• Metal oxides that are formed during these reactions, if soluble in water then they from metal hydroxides.
• Metal oxide + Water → Metal hydroxide
• But not all metals react with water, metals like gold, silver, lead etc. do not react with water at all.

Given:

x = y = $\frac{{\sqrt {6 - 1} }}{{\sqrt {6 + 1} }}$

Concept used:

Here we need not to put the complex value of x and y,

Only put x = y

Calculation

$\frac{{\left( {3{x^2} + 5xy + 3{y^2}} \right)}}{{\left( {3{x^2} - 5xy + 3{y^2}} \right)}}$

⇒ $;\frac{{\left( {3{x^2} + 5{x^2} + 3{x^2}} \right)}}{{\left( {3{x^2} - 5{x^2} + 3{x^2}} \right)}}$

⇒ 11x²/x²

⇒ 11

The pattern followed here is “∞” is shifting to the next quadrant in a clockwise direction and the inverted L is undergoing mirror image and water image alternatively in each quadrant in a clockwise direction

• The speed gained by the object v is 5m/s
• Time = 2s
• Initial velocity u is 0
• We know that v = u + at
• Now by substituting the values, we get

 5 = (2)(a)

a = 2.5

• The acceleration of the object is 2.5 m/s²

Assumption 1 holds as if the sales manager of an area is happy with his work in the area, it can be assumed that he/she has made some progress, or some acquisitions in his/her area. The area sales manager stated that “he is eagerly awaiting to present this year’s report to the top management”, so we can assume that “The manager has vital information that would make an impression on the top management”.

Hence, “Both assumption I and II are implicit”.

• A basic event in protein synthesis is the creation of a/an mRNA (Messenger Ribonucleic Acid) copy.
• The mRNA provides the template for the Genetic Code.
• A gene is used to build a protein using the following two step process i.e. Transcription and Translation.
• Transcription: It is the process by which DNA is copied to mRNA, which carries the information needed for protein synthesis.
• Translation: It is the process that takes the information passed from DNA as messenger RNA and turns it into a series of amino acids.

• Jhulan Goswami, an Indian woman cricketer became the highest wicket-taker in Women’s ODI in the year 2017.
• In the year 2018, she retired from T20 international Cricket.
• She was the first woman to cross 200 wickets in women’s 50 overs ODi and she is also an Ex-Indian Team Captain.
• She has a postal stamp issued in her honor in the year 2018.

Here, accept Y25, every latter is followed by the number one less than the positon value of that letter,

Ex. S = 19 – 1 = 18 ⇒ S18

Hence, “Y25” is the correct answer.

Let us check every statement individualy,

1. Nitu is the tallest → Data in this statement is inadequate since, only 1 person is mentioned here. Therefore statement 1 alone is not sufficient.
2. Tarun is taller than Manav → Data in this statement is inadequate since, only 2 persons are mentioned here. Therefore statement 2 alone is not sufficient.
3. Hema is the shortest of them all → Data in this statement is inadequate since, only 1 persons is mentioned here. Therefore statement 3 alone is not sufficient.
4. Manav is taller than Priya → Data in this statement is inadequate since, only 2 persons are mentioned here. Therefore statement 4 alone is not sufficient.

Since, no statement alone is sufficient now we can go through the options given,

From 1^st option combining all 1, 2, 3, and 4 statement together we get,

Nitu > Tarun > Manav > Priya > Hema

Hence, “Statements 1, 2, 3 and 4 together are sufficient”.