RRC Group D Previous Year Paper 15 (Held On: 29 Oct 2018 Shift 2)

The correct answer is option 4 i.e 10.8

Silver: 

Formula: Ag

Atomic number: 47

• Relative density: It is defined as the ratio of the density of a substance to the density of water.
• It is also known as specific gravity.
• Relative density = Density of substance / Density of water
• Relative density= 10.8 × 10³ /10³
• Hence Relative Density = 10.8

Shortcut Trick

Total Income is always 100%.

If Savings = 20%, then Expenditure = 100% − 20% = 80%.

Amount spent = 80% of 14,500 = 0.8 × 14,500 = 11,600.

∴ The correct answer is Rs. 11,600.

Alternate Method

Given: Monthly Income = Rs. 14,500, Savings % = 20%.

Formula: Expenditure = Total Income − Savings

⇒ Savings = 20% of 14,500

⇒ Savings = (20 ÷ 100) × 14,500 = 2,900

⇒ Expenditure = 14,500 − 2,900

⇒ Expenditure = 11,600

∴ The correct answer is Rs. 11,600.

Additional Information

Income-Expenditure Relation

Income = Expenditure + Savings. This is the fundamental equation for all personal finance math problems.

Percentage Expenditure

Expenditure % = (Expenditure ÷ Income) × 100. If savings percent is given as s%, expenditure percent is always (100 − s)%.

Ratio Method

If savings is 20% (1/5), then for every 5 parts of income, 1 part is saved and 4 parts are spent (Ratio 4:1).

Bloggers and writers deal with similar type of work of writing the blogs, articles, novels, etc.

Similarly,

Illustrator and artist deal with similar type of work of drawing the pictures for magazines, books and advertising.

Hence, ‘Artist’ is the correct answer.

Shortcut Trick

Ratio of Area to (product of ratio parts) → 1,350 ÷ (3 × 2) = 225.

Square root of this constant (k²) gives the unit value → √225 = 15.

Perimeter = 2 × (3 + 2) × 15 = 150 m.

Total Cost = 150 × 30 = ₹4,500.

∴ The correct answer is ₹4,500.

Alternate Method

Given: Ratio of Length (L) and Breadth (B) = 3 : 2, Area = 1,350 m², Rate = ₹30/m.

Formula Used: Area = L × B | Perimeter = 2(L + B) | Cost = Perimeter × Rate

⇒ Let Length = 3x and Breadth = 2x.

⇒ Area = 3x × 2x = 6x².

⇒ 6x² = 1,350

⇒ x² = 225

⇒ x = 15 m.

⇒ Length = 3 × 15 = 45 m, Breadth = 2 × 15 = 30 m.

⇒ Perimeter = 2(45 + 30) = 2(75) = 150 m.

⇒ Total Cost = 150 × 30 = ₹4,500.

∴ The correct answer is ₹4,500.

Additional Information

Rectangular Field Properties

Area is the region inside the boundary (L × B), while Perimeter is the length of the boundary 2(L + B).

Fencing Concept

Fencing is always done along the Perimeter. If fencing is required for multiple rounds (n), the cost is Perimeter × n × Rate.

Diagonal of Rectangle

The distance between opposite corners is given by √(L² + B²).

⇒ $\frac{1}{{ - 6}},;\frac{2}{{ - 12}},\frac{3}{{ - 18}},\frac{4}{{ - 24}},; \ldots \ldots \ldots$

⇒ 1/(-6)

Similarly,

⇒ 2/(-12) = 1/(-6)

⇒ 3/(-18) = 1/(-6)

⇒ 4/(-24) = 1/(-6)

From option (4), follow the same pattern

$\Rightarrow ;\frac{5}{{ - 30}},\frac{6}{{ - 36}},\frac{7}{{ - 42}},\frac{8}{{ - 48}}$

⇒ 5/(-30) = 1/(-6)

⇒ 6/(-36) = 1/(-6)

⇒ 7/(-42) = 1/(-6)

⇒ 8/(-48) = 1/(-6)

So correct option is (4).

Option 1 is correct:

The correct answer is option 1 i.e Kerala

• Kerala is the first state of India to receive rainfall by the southwest monsoon.
• Rainfall received from the southwest monsoons is seasonal, which occurs between June and September.

Kerala: 

• Capital: Thiruvananthapuram
• **Governor:**Shri Rajendra Vishwanath Arlekar
• CM: Pinarayi Vijayan

As we know,

1 km = 1000 m

1 m = 100 cm

1 cm = 10 mm

⇒ 0.5035 km = 0.5035 × 1000 = 503.5 m

⇒ 332.9 cm = 332.9 × (1/100) = 3.329 m

⇒ 1771 mm = 1772 × (1/1000) = 1.771 m

⇒ Sum of 503.5 + 3.329 + 1.771 = 508.6 m

According to the first 2 diagrams, the shaded circle is added into the empty circle.

Similarly,

In the next two figures, the shaded circle will be inserted into the empty triangle.

Hence, figure B is the correct answer.

⇒ 3.8/1.25

Multiply by 8/8

⇒ (3.8/1.25) × (8/8)

⇒ 30.4/10

⇒ 3.04

Relation between first and second figures:

The figure is moving in 90 degree anticlockwise direction.

Similar relation will be applicable for the next two figures.

Hence, figure 3 is the correct answer.

Statement:

Child labour is punishable

Conclusion:

I: Poverty of parents and their inability to send their children to school is the reason behind child labour: it not completely true because inability of education is not the reason behind the child labour. According to the right to free and compulsory Education Act is an Act of the parliament to provide free and compulsory education for children between the age of 6 to 14. Hence, conclusion one does not satisfy completely.

II. Government has issued a ban on child labour: According to Child Labour (Prohibition and Regulation) Act 1986. Article 24 of Indian constitution clearly assumes that No child below the fourteen years shall be employed to work in any factory or mine or employed in any hazardous employment.

Hence, only conclusion II follows.

Argument

1. Yes, safety of the country is top priority: the first priority of every country is safety. If country is secured than only development is possible.

Hence, argument 1 is strong.

Option 1 is correct:

• Goods and Services Tax (GST) is an indirect tax levied on the supply of commodities and services.
• The GST was launched at midnight on 1 July 2017 by the President of India, Pranab Mukherjee, and the Prime Minister of India Narendra Modi.
• There are two types of GST – Central GST (CGST) and State GST (SGST).
• GST is established under the 101^st amendment of the constitution.
• The Goods and Services Tax (GST) was first implemented in France.
• GST in India was made on the recommendation of the Vijay Kelkar Committee.
• GST has been implemented under 279 of the India constitution.

The correct answer is option 1 i.e 48 J

Work: It is defined as the force required to move an object from its place in a direction.

• W = QV

Where W = work

            Q = charge

            V = Potential difference

• W = 4 C × 12 V
• W = 48 J

The correct answer is option 1 i.e (NH4)₃PO4

• The Chemical formula of Ammonium phosphate: (NH₄)₃PO4
• It is the salt of Ammonia and Phosphoric acid
• Other names of this salt are Triammonium phosphate, Diazanium hydrogen phosphate.
• All other options are wrong

• The carpels(female) and stamens(male) are surrounded by petals.
• Carpel- One of the leaflike, seed-bearing structures that constitute the innermost whorl of a flower.
  

One or more carpels make up the pistil.

Fertilization of an egg within a carpel by a pollen grain from another flower results in seed development within the carpel.

Carpels, present in the centre of a flower, form the female reproductive part. It is surrounded by male reproductive structures called stamens.

• The petals are protected by sepals, which are green.
• The carpels are the female reproductive part of the flower. It is divided into three parts namely- ovary, style and stigma.
• The ovary contains ovules and the style acts as a passage for the pollen tubes carrying the male gametes.
• The stigma is the terminal part of the carpel which is receptive and it receives the pollen grains and provides nutrition for the growth and development of pollen tube which carries male gametes through style and reaches the ovules to fertilise an egg.

Option 2 is correct:

• Complex permanent tissue: The complex tissues are made of more than one type of cells and these work together as a unit.
• Xylem and phloem constitute the complex tissues in plants.
• Xylem is one of the important tissues of the vascular system of plants. The main activity of this tissue is to transport minerals and water from roots and carry them to other parts of the plants. It has two separate chambers tracheids and vessels for transporting minerals and water.
• Phloem is also important as the xylem tissues for the vascular system of plants. The main activity of this tissue is to transport nutrients and food from leaves to other growing parts of plants.

Difference between Phloem and Xylem:-

Option 3 is correct:

• The human male reproductive system consist of the following organs:

The correct answer is option 1 i.e Cochlea

EAR:

• The ears perform two sensory functions one is hearing and other is maintenance of body balance.
• The ear can be divided into three major sections 1) the outer ear 2) the middle ear and 3) the inner ear.
• The fluid the filled inner ear is called the labyrinth, and the coiled portion of the labyrinth is called cochlea.
• The vibrations produced in the eardrum are transmitted through the ear ossicles and oval window to the fluid-filled inner ear.
• The inner ear also contains a complex system located above the cochlea called the vestibular apparatus.
• It is influenced by gravity and movements and helps us in maintaining the balance of the body and posture.

Shortcut Trick

Use the constant distance formula: Distance = [S₁ × S₂ / (S₂ − S₁)] × Time Difference

Let original speed be S. Then, 1200 = [S × (S + 120) / 120] × 0.5

⇒ S(S + 120) = 1200 × 120 / 0.5 = 288000

⇒ S = 480 km/hr (since 480 × 600 = 288000). Original time = 1200 ÷ 480 = 2.5 hours.

∴ The correct answer is 2 hr 30 min.

Alternate Method

Given: Distance = 1200 km, Speed increase = 120 km/hr, Time reduction = 30 min = 0.5 hr.

Formula: Time = Distance ÷ Speed

⇒ Let original speed = x km/hr

⇒ (1200 / x) − (1200 / (x + 120)) = 0.5

⇒ 1200 [ (x + 120 − x) / (x(x + 120)) ] = 0.5

⇒ 1200 × 120 = 0.5 × (x² + 120x)

⇒ 288000 = x² + 120x ⇒ x² + 120x − 288000 = 0

⇒ (x + 600)(x − 480) = 0 ⇒ x = 480 km/hr

⇒ Duration = 1200 ÷ 480 = 2.5 hours = 2 hr 30 min

∴ The correct answer is 2 hr 30 min.

Additional Information

Constant Distance Relation

When distance is constant, speed is inversely proportional to time (S ∝ 1/T). The product of speed and time remains the same.

Tailwind and Headwind

Tailwind increases the effective speed of the aircraft (V_air + V_wind), while headwind decreases it (V_air − V_wind).

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances at speeds a and b, Average Speed = 2ab / (a + b).

No. of hours between 2 am and 2 pm in a day = 12 hours

No. of hours between 2 pm and 9 pm in a day = 7 hours.

Therefore, total no. of hours between 2 am and 9 pm of the same day = 12 + 7 = 19 hours.

Angle rotated by a minute hand in 1 hour = 360°

Therefore, total rotation in 19 hours = 19 × 360° = 6840°

Hence, the correct answer is 6840°.

$\left( {\frac{3}{{11}} \times \frac{{33}}{6}} \right) - \left( {\frac{9}{4} \times \frac{{12}}{3}} \right) + \left( {\frac{5}{{11}} \times \frac{{22}}{{10}}} \right)$

⇒ 3/2 – 9 + 1

⇒ (3 – 18 + 2)/2

⇒ (-13)/2

Shortcut Trick

Successive Ratios: 4% = 1/25 (25 → 26) and 8% = 2/25 (25 → 27)

Overall Ratio = (25 × 25) : (26 × 27) = 625 : 702

Interest Units = 702 − 625 = 77 units

Given 625 units = ₹18,750 ⇒ 1 unit = 30

Total Interest = 77 × 30 = ₹2,310

∴ The correct answer is ₹2,310.

Alternate Method

Given: Principal (P) = ₹18,750, Rate 1 (R₁) = 4%, Rate 2 (R₂) = 8%, Time = 2 years.

Formula: Amount (A) = P × (1 + R₁/100) × (1 + R₂/100)

⇒ Amount (A) = 18,750 × (104/100) × (108/100)

⇒ A = 18,750 × (26/25) × (27/25)

⇒ A = (18,750 ÷ 625) × 26 × 27

⇒ A = 30 × 702 = ₹21,060

⇒ Compound Interest (CI) = A − P

⇒ CI = 21,060 − 18,750 = ₹2,310

∴ The correct answer is ₹2,310.

Additional Information

Effective Rate for Variable Interest

If rates are R₁ and R₂, the net effective rate is R₁ + R₂ + (R₁ × R₂)/100. For 4% and 8%, Net Rate = 4 + 8 + (4 × 8)/100 = 12.32%.

Compound Interest Formula

For different rates every year: A = P(1 + R₁/100)(1 + R₂/100)...(1 + R_n/100). The total earning is always (A − P).

Successive Percentage Change

Compound interest is an application of successive percentage increase where the interest of the previous year is added to the principal for the next year.

Option 4 is correct:

• Halogen: The Group 17 elements are known as the halogens.
• They are reactive non-metals and are always found in compounds with other elements.
• Chlorine, bromine, and iodine are all halogens.
• The halogens become darker as you go down the group.

Hence, the correct answer is figure 1.

The correct answer is option 1 i.e 784 J

• The energy possessed by an object of mass at height will be Potential energy.
• The energy possessed by a body on account of its position, shape and size is called Potential energy.

• Potential Energy = mgh
• Potential Energy = 10 kg × 9.8 ms^-2 × 8 m
• Potential Energy = 784 J

Shortcut Trick

Identify the highest power of prime factors: 150 = 2 × 3 × 5², 144 = 2⁴ × 3², 96 = 2⁵ × 3.

LCM = 2⁵ × 3² × 5²

⇒ 32 × 9 × 25 = 800 × 9 = 7200.

∴ The correct answer is 7200.

Alternate Method

Given: Numbers are 96, 144, and 150.

Formula Used: LCM (Least Common Multiple) by Prime Factorization method.

⇒ Prime factorization of 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3¹

⇒ Prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3 = 2⁴ × 3²

⇒ Prime factorization of 150 = 2 × 3 × 5 × 5 = 2¹ × 3¹ × 5²

⇒ LCM = Highest power of all primes present = 2⁵ × 3² × 5²

⇒ LCM = 32 × 9 × 25 = 7200

∴ The correct answer is 7200.

Additional Information

Relation between LCM and HCF

For two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

LCM of Fractions

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

Least Common Multiple (LCM)

It is the smallest positive integer that is perfectly divisible by each of the given numbers.

Option 3 is correct:

• Best Child Artist at 64th National Film Awards 2017:

• Established in 1954.
• Directorate of film festivals comes under the Ministry of Information and Broadcasting
• The award is given for the best work in the film industry
• Two types of awards are awarded – Golden lotus award and Silver lotus award.
• Featured and Non- featured films certified by CBFC are eligible for this award.

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

$\Rightarrow \left( {\frac{3}{2} \times \frac{1}{6}} \right) + \left( {\frac{5}{3} \times \frac{7}{2}} \right) - \left( {\frac{{13}}{4} \times \frac{4}{3}} \right)$

⇒ 1/4 + 35/6 – 13/3

⇒ (3 + 70 – 52)/12

⇒ 21/12

Alligator and tortoise both are Reptiles

Hence, figure 3 is the correct answer.

*NOTE: This is a question from of official paper of RRC Group D, but we have made some improvements in this as the question asked was erroneous.

Let the present ages of two persons be x and y.

The sum of the present age of two person is seven times that of the difference between their ages.

x + y = 7 (x - y)

x + y = 7x - 7y

6x = 8y

x/y = 8/6

x/y = 4/3

x = 4

y = 3

let x and y be 4k and 3k (k is constant term)

After 5 years, the sum of their ages will become nine times that of the difference

4k + 5 + 3k + 5 = 9 {(4k + 5) - (3k + 5)}

7k + 10 = 36k + 45 - 27k - 45

2k = 10

K = 5

X = 4k = 4 × 5 = 20

Y = 3k = 3 × 5 = 15

Hence, elder person is 20 years old.

Hence, the correct answer is option 4.

the correct answer is option 2 i.e Buoyant Force

Buoyant Force:

• It is the force that causes objects to float.
• It is the upward force applied by the fluid on the object or the body when an object is put in or submerged in the fluid.
• It is also known as the buoyant force.
• Buoyancy is the phenomenon due to Buoyant Force.
• The unit of the buoyant force is the Newton (N).
• The buoyant force depends upon the density of the fluid.
• Buoyancy is defined as an upward force exerted by any fluid when an object is immersed in it.
• The pressure is more on the bottom of the object than the top of the object as the pressure increases with depth.
• These forces acting on the body are called the Buoyant force.
• Upward pressure exerted by the fluid depends upon the density of a fluid.
• The formulae for Buoyant force (f)=ρgv.
• Where ρ is the density of the fluid, g is the gravity, and v is the volume of fluid displaced.

Shortcut Trick

Volume of a cuboid is directly proportional to its dimensions: V ∝ l × b × h.

Change in length = 2 times, Change in height = 2 times, Change in breadth = 1 time.

New Volume = 2 × 1 × 2 = 4 times the original volume.

New Volume = 4V.

∴ The correct answer is 4V.

Alternate Method

Given:

Original length = l, Original breadth = b, Original height = h.

Original Volume (V) = l × b × h

New Dimensions:

⇒ New length (l') = 2l

⇒ New height (h') = 2h

⇒ New breadth (b') = b (remains same)

Calculations:

⇒ New Volume (V') = l' × b' × h'

⇒ V' = (2l) × b × (2h)

⇒ V' = 4 × (l × b × h)

⇒ V' = 4V

∴ The correct answer is 4V.

Additional Information

Total Surface Area of Cuboid

The total area of all six faces is given by 2(lb + bh + hl).

Diagonal of a Cuboid

The length of the longest rod that can be placed in a cuboid is √(l² + b² + h²).

Lateral Surface Area

The area of the four walls of a room is given by 2h(l + b).

The correct answer is option 1 i.e Chandrashekar Kambar

• Jnanpith recipient and Kannada literature Chandrashekhar Kambar (81) was elected as 44^th President of the Sahitya Akademi.
• The Sahitya Akademi was started by the GOI on 12 March 1954.
• Apart from 22 languages which are in listed in the constitution of India the Sahitya Akademi has recognized English and Rajasthani as languages in which the program can be implemented
• The Sahitya Akademi award amount is now Rs.100,000.
• The first Awards were given in 1955.

Option 1 is correct: Telangana Rashtra Samithi (TRS)

• The Telangana state was inaugurated formally on June 2^nd 2014.
• In the General Elections held in April 2014, Telangana Rashtra Samithi emerged victorious by winning 63 of the 119 seats and formed the government. Sri K Chandrashekar Rao was sworn in as the First Chief Minister of Telangana.
• The State Bird - Palapitta (Indian Roller or Blue Jay).
• The State Animal - Jinka (Deer).
• The State Tree - Jammi Chettu (Prosopis Cineraria).
• The State Flower - Tangedu (Tanner’s Cassia).

Shortcut Trick

Total 8 trolleys are present in the supermarket.

From Statement 1: 8 cans (2 per trolley) occupy 8 ÷ 2 = 4 trolleys.

From Statement 2: Remaining 8 − 4 = 4 trolleys contain 4 cans each = 16 cans.

Total cans = 8 (Statement 1) + 16 (Statement 2) = 24 cans.

Since both statements are required to find the total, they are together sufficient.

∴ The correct answer is Statement 1 and 2 together are sufficient.

Alternate Method

Given:

Total trolleys in supermarket = 8

Statement 1: 8 cans fit as 2 cans per trolley.

Statement 2: Remaining trolleys have 4 cans each.

⇒ Number of trolleys used for first type = 8 ÷ 2 = 4 trolleys

⇒ Remaining number of trolleys = 8 − 4 = 4 trolleys

⇒ Cans in remaining trolleys = 4 × 4 = 16 cans

⇒ Total cans loaded = 8 + 16 = 24 cans

Both statements are required to reach a unique numerical value for the total number of cans.

∴ The correct answer is Statement 1 and 2 together are sufficient.

Additional Information

Data Sufficiency Basics

In data sufficiency, you must determine if the provided information is necessary and enough to find a unique answer, even without calculating the final value.

Logical Distribution

Total Quantity = (Items per group₁ × Groups₁) + (Items per group₂ × Groups₂). Missing any one variable makes the total indeterminate.

Complementary Information

When a statement mentions the rest or remaining, it implies a dependency on the previous partition defined by other statements or the question stem.

Shortcut Trick

Mass of Solute (Salt) = 42 g

Mass of Solvent (Water) = 320 g

Total Mass of Solution = 42 + 320 = 362 g

Concentration % = (42 ÷ 362) × 100 ≈ 11.6%

∴ The correct answer is 11.6%.

Alternate Method

Given:

Mass of solute (salt) = 42 g

Mass of solvent (water) = 320 g

Formula Used:

Mass by mass percentage = [Mass of solute ÷ Mass of solution] × 100

Calculations:

⇒ Total mass of solution = Mass of salt + Mass of water

⇒ Total mass of solution = 42 g + 320 g = 362 g

⇒ Concentration % = (42 ÷ 362) × 100

⇒ Concentration % = 4200 ÷ 362

⇒ Concentration % ≈ 11.602%

∴ The correct answer is 11.6%.

Additional Information

Mass by Volume Percentage

It is defined as the mass of solute dissolved in 100 mL of solution. Formula: (Mass of solute ÷ Volume of solution) × 100.

Saturated Solution

A solution in which no more solute can be dissolved at a specific temperature is called a saturated solution.

Solubility

The maximum amount of solute that can be dissolved in 100 g of solvent at a given temperature is its solubility.

Option 2 is correct:

• Alkynes - The simplest alkyne—a hydrocarbon with carbon-to-carbon triple bond—has the molecular formula C₂H_2n-2 and is known by its common name—acetylene. Acetylene is used in oxyacetylene torches for cutting and welding metals.
• Eg.Propyne

Application:

C3H4 follows the general formula for a compound with n = 3

Hence C3H4 belongs to the alkyne family.

• Alkenes are unsaturated hydrocarbons that contain one or more double bonds. The general formula for Alkenes is CnH2n. Example: Ethylene (C2H4).
• Alkanes are saturated hydrocarbons that contain a single bond.
• The General Formula for Alkanes is CnH2n+2.
• Example: Ethane (C2H6)

Option 1 is correct:​ 5 Moles.

• One mole of Carbon dioxide contains One part Carbon, Two parts Oxygen.
• The Molar mass of carbon is 12 g and oxygen is 16 g.
• So 1 mole of CO₂ weighs :
• (16*2)g = 32g for Oxygen, 12 g for carbon.
• The molar mass of CO₂ is 32 + 12 = 44 g.
• The number of moles of CO₂ in 220 g of CO₂ is 220/44 = 5 moles.

Shortcut Trick

Total percentage is always 100%.

White balls = 45% → Black balls = 100% − 45% = 55%.

Number of black balls = 55% of 120 = 0.55 × 120 = 66.

∴ The correct answer is 66.

Alternate Method

Given:

Total number of balls = 120

Percentage of white balls = 45%

Calculations:

⇒ Number of white balls = 45% of 120

⇒ White balls = (45 ÷ 100) × 120 = 0.45 × 120 = 54

⇒ Number of black balls = Total balls − White balls

⇒ Black balls = 120 − 54 = 66

∴ The correct answer is 66.

Additional Information

Percentage Basics

To find the percentage of a quantity, use the formula: (Value ÷ Total) × 100.

Complementary Percentage

If a whole is divided into two parts A and B, then Percentage of B = 100% − Percentage of A.

Ratio Conversion

The ratio of white to black balls here is 45:55, which simplifies to 9:11.

Shortcut Trick

Let Total Work be LCM(32, 24, 8) = 96 units.

Efficiency of Prasid = 96 ÷ 32 = 3 units/day.

Efficiency of Deep = 96 ÷ 24 = 4 units/day.

Combined efficiency of Prasid + Deep + Niloy = 96 ÷ 8 = 12 units/day.

Efficiency of Niloy = 12 − (3 + 4) = 5 units/day.

Time taken by Niloy alone = 96 ÷ 5 days.

∴ The correct answer is 96/5 days.

Alternate Method

Given: Time taken by Prasid = 32 days, Deep = 24 days, and All together = 8 days.

Formula Used: 1/T_total = 1/T₁ + 1/T₂ + 1/T₃

⇒ Efficiency of Niloy = (Efficiency of All) − (Efficiency of Prasid + Efficiency of Deep)

⇒ Efficiency of Niloy = 12 − (3 + 4) = 5 units/day.

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

⇒ Time taken = 96 ÷ 5 days.

∴ The correct answer is 96/5 days.

Additional Information

Total Work Concept

Total work is usually assumed as the Least Common Multiple (LCM) of the individual days to make efficiency calculations into whole numbers.

Work and Wages

In problems involving wages, money is always distributed in the ratio of the efficiencies of the workers, provided they work for the same duration.

Inverse Relationship

Time taken to complete a work is inversely proportional to the efficiency of the person. Time = Work ÷ Efficiency.

Hence, total number of squares in the given figure are 24.

The correct answer is option 4 i.e Half potential energy and half kinetic energy.

• Kinetic Energy: The energy required to change the state of a body from rest to motion is called
• Kinetic Energy = 1/2 mv².
• Potential energy: It is the energy possessed by a body due to its change in position or shape.
• Potential Energy: Mgh
• Law of conservation of energy: According to the law, energy can only be transformed from one form to another, energy can neither be created nor destroyed. It can only be transformed from one form to another.
• The total energy before and after the transformation remains constant.
• potential energy + kinetic energy = constant
• Mgh + 1/2mv² = constant

Option 1 is correct i.e Auxins.

• Auxins, Gibberellins, and Cytokinins are grouped into plant growth promoters while abscisic acid and ethylene are grouped into plant growth inhibitors.
• Auxins are the main hormones responsible for cell elongation in phototropism and gravitropism by promoting cell growth.
• Insulin- Insulin is a hormone made in the pancreas, a gland located behind your stomach. It allows your body to use glucose for energy.

The correct answer is option 1 i.e 3 to 12

• The d-block of the periodic table contains the elements of the groups 3-12.
• The d-block element is known as a transition element.
• There total of 4 blocks in the modern periodic table. They are as follows: s block, p block, d block, f block.
• There are 18 groups and 7 periods in the modern periodic table.
• Total elements are 118 out of which 92 are metals, 7 are metalloids, and 19 are non-metal.

Except figure D, in all figures the stars are arranged in the consecutive manner.

Whereas in figure D, stars are arranged opposite to each other.

Hence, figure D is odd one out.

Shortcut Trick

Speed ratio (Usual : New) = 100 : (100 − 12) = 100 : 88 = 25 : 22.

Since distance is constant, Time ratio is inverse of Speed ratio = 22 : 25.

Difference in time ratio parts = 25 − 22 = 3 units → 18 minutes.

1 unit = 6 minutes ⇒ Usual time (22 units) = 132 minutes = 132/60 hours = 2.2 hours.

Distance = Usual Speed × Usual Time = 75 × 2.2 = 165 km.

∴ The correct answer is 165 km.

Alternate Method

Given: Usual Speed (S₁) = 75 km/hr, Speed decrease = 12%, Time difference (Δt) = 18 minutes = 18/60 hours.

Formula: Distance (D) = [S₁ × S₂ / (S₁ − S₂)] × Δt

⇒ New Speed (S₂) = 75 × (88/100) = 66 km/hr.

⇒ Speed difference (S₁ − S₂) = 75 − 66 = 9 km/hr.

⇒ D = [75 × 66 / 9] × (18 / 60)

⇒ D = [550/1] × (3 / 10)

⇒ D = 165 km.

∴ The correct answer is 165 km.

Additional Information

Inverse Proportionality Rule

When distance is constant, Speed (S) is inversely proportional to Time (T). If speed ratio is a:b, then time ratio is b:a.

Average Speed Formula

For two equal distances covered at speeds x and y, Average Speed = 2xy / (x + y).

Relative Speed

In the same direction, relative speed = S₁ − S₂. In the opposite direction, relative speed = S₁ + S₂.

Yes, a dress code will bring unity and eliminate discrimination. There will be no discrimination if all will wear the similar dress.

Total number of sold books over the years (January to December) = 2000 + 1500 + 2500 + 3000 + 2000 + 1000 + 1500 + 2000 + 5000 + 2000 + 150 + 6000 = 28650

Required average = 28650/12 = 2387.5

In March, April, September and December he sold the more books than average sold books.

Except Kotak Mahindra, all other are technical institutes.

Whereas ‘Kotak Mahindra’ is a bank.

Hence, ‘Kotak Mahindra’ is odd one out.

The circular figure inside the rectangular figure is rotating in a clock wise manner,

Hence, the correct answer is figure B.

According to the given information,

Avant and the girl in the photograph are cousins.

Hence, the correct answer is ‘Cousins’.

Option 4 is correct: Literature

• Bharatiya Jnanpith is one of the premier literary organizations of India, which is nurturing literature and culture through its literary endeavours, which include Awards, Publication, Fellowship and Research for the last several decades.
• This was instituted in 1961 and is given only to Indian writers who write in Indian languages and English.
• Amitab Ghosh is honoured with the 54th Jnanpith Award for his contribution to English Literature and also became the 1st English language writer in the list as all previous winners of the prestigious award have been writers in Indian languages.
• Eminent Malayalam poet Akkitham Achuthan Namboothiri has been chosen for the 55th Jnanpith Award

Some important fact about Jnanpith Award,

• The winner is given a cash prize of Rs. 11 lakh and a bronze replica of Goddess Saraswati, the Hindu goddess of learning.
• The first recipient of the award was Malayalam writer G Sankara Kurup in 1965 for his novel ‘Odakkuzhal’ (The Bamboo Flute).
• The first woman writer to be awarded this award was Ashapoorna Devi, a Bengali writer, in 1976.

The correct answer is option 1 i.e Big investment in island nations

Key Points

• A quiet Maritime strategic diplomacy has emerged as the key theme of this year's Union Budget 2018-19, for a big investment in all island nations in the strategic Indian Ocean region.
• The beneficiaries island nation of the Budget is Seychelles, Mauritius, Sri Lanka, and the Maldives.

The pattern followed here is,

O + 2 = Q; Q + 2 = S; S + 2 = U; U + 2 = W;

V - 1 = U; U - 1 = T; T - 1 = S; S - 1 = R

Hence, ‘WR’ is the correct answer.

CONCEPT:

• Work done (W): When a force is applied on a body and there is a displacement of the body in the direction of force then the work is said to be done by the force.
• The SI unit of work is Joule.
• 1 Joule (J) = 1 Nm

Work (W) = Force (F) × Displacement (S)

• Power (P): The rate of work done is called power.
• The SI unit of power is the watt (W).

Power (P) = work done (W) / time (t)   (P = W / t = J / s)

EXPLANATION:

Since 1 KW = 1000 W

1 hr = 3600s

1 K Wh = 1000 W × 3600s (w = j / s)

1 Kwh = 3.6 × 10⁶ J

The correct answer is option 3.

The correct answer is option 2 i.e MS Dhoni

• M.S. Dhoni inaugurated his first global cricket academy in UAE.
• The academy was jointly launched by the Dubai-based Pacific Sports Club and Aarka Sports Club.
• The coaches required in this academy will be from India.

UAE:

• Capital: Abu Dhabi
• Currency: United Arab Emirates dirham

1. Yes, the money can be used for the development of poor people. This argument is false.

Argument 2 is strong because Sports help athletes gain international exposure and plays a significant role in exposing talent.

Shortcut Trick

The required numbers are of the form LCM(35, 49) × k + 30, where k is a non-negative integer.

LCM of 35 and 49 is 245.

For k = 0, the number is 30 (not a multiple, but leaves remainder 30 when divided by 35 and 49).

For k = 1, the number is 245 + 30 = 275.

For k = 2, the number is 490 + 30 = 520 (greater than 500).

Therefore, the natural numbers less than 500 are 30 and 275, but since 30 < 35 and 30 < 49, it trivially leaves remainder 30.

Among the standard positive integers satisfying the divisor condition, 30 and 275 are the only two valid values.

∴ The correct answer is 2.

Alternate Method

Let the required natural number be N.

According to the question, when N is divided by 35 and 49, the remainder is 30 in each case.

⇒ N = LCM(35, 49) × k + 30

To find the LCM of 35 and 49:

⇒ 35 = 5 × 7

⇒ 49 = 7²

⇒ LCM(35, 49) = 5 × 7² = 5 × 49 = 245

Now, the general form of the number is:

⇒ N = 245 × k + 30, where k = 0, 1, 2, ...

We need to find the number of such natural numbers less than 500:

⇒ For k = 0: N = 245 × 0 + 30 = 30 (Since 30 is a positive integer, it is a natural number)

⇒ For k = 1: N = 245 × 1 + 30 = 275

⇒ For k = 2: N = 245 × 2 + 30 = 520 (which is greater than 500)

Thus, there are exactly 2 such natural numbers: 30 and 275.

∴ The correct answer is 2.

Additional Information

Remainder Theorem & LCM

The smallest number which when divided by x, y, and z leaves a remainder r in each case is given by LCM(x, y, z) + r.

Natural Numbers definition

Natural numbers are positive integers starting from 1, 2, 3, ... etc. Since 30 is positive, it qualifies as a valid natural number under this condition.

Except figure D, all other figures are showing water images for letters T, Z, and M.

Hence, figure D is odd one out.

The correct answer is option 2 i.e Momentum

• Momentum: It is defined as the quantity of motion of the body.
• It is measured by mass × velocity.
• Momentum depends on both speed and direction
• Momentum is a vector quantity as mass is scaler and velocity is vector
• Momentum = Mass X Velocity (p = mv).
• SI unit Kg-m.s-1

According to the given information,

Varun’s opponents Samarth will sit opposite to him.

Hence, the correct answer is North-East.

• Sangama literature is one of the main sources used for documenting the early history of the ancient Tamil country.
• The ancient Sangam poems mention numerous kings and princes, the existence of some of whom have been confirmed through archaeological evidence.
• The Sangam landscape is the name given to a poetic device that was characteristic of love poetry in classical Tamil Sangam literature. The core of the device was the categorisation of poems into different tiṇais.
• Each tiṇai was closely associated with a particular landscape, and imagery associated with that landscape—its flowers, trees, wildlife, people, climate and geography—was woven into the poem in such a way as to convey a mood
• In Tolkappiyam, there is a reference to the five-fold division of lands - Kurinji (hilly tracks), Mullai (pastoral), Marudam (agriculture).
• Silappadikaram and Manimekalai are epics of Tamil poetry.
• Silappadikaram is the story of Kovalan, Kannagi his wife, and Madhavi.
• Manimekalai is a Tamil Buddhist poem which gives information about the daughter of Kovalan and Madhavi.

The correct answer is option 2 i.e Hyderabad

• Wings India 2018 was hosted by Hyderabad.
• It was the four-day biennial event.
• It was jointly organized by Ministry of Civil Aviation, Airport Authority of India and FICCI
• The theme of the event was "India-Global Aviation Hub".

According to the given information,

Given: 62 - 2 ÷ 8 + 15 × 4 + 6

After changing symbols according

62 ÷ 2 + 8 × 15 - 4 × 6

Now, solving the equation according to BODMAS rule,

= 31 + 8 × 15 - 4 × 6

= 31 + 120 - 24

= 151 - 24

= 127

Hence, the correct answer is 127.

All figures except figure 3 are folded in 90 degree angle.

Hence, the correct answer is option 3.

Total sale of all types of toys = 387200

The sales revenue earned on soft toys is = 25% of 387200 = 387200 × (25/100) = 9,68,00

Shortcut Trick

Given ∠A = 60°, find sin(A/2) and cosec A separately.

sin(60°/2) = sin 30° = 1/2

cosec 60° = 1/sin 60° = 1/(√3/2) = 2/√3

Sum = 1/2 + 2/√3 = (√3 + 4)/(2√3)

∴ The correct answer is (√3 + 4)/2√3.

Alternate Method

A (60°) B C (90°) Expression: sin(A/2) + cosec A

Given: ∠C = 90°, ∠A = 60°

Formula Used: sin 30° = 1/2; cosec 60° = 2/√3

⇒ Required value = sin(60°/2) + cosec 60°

⇒ Required value = sin 30° + cosec 60°

⇒ Required value = (1/2) + (2/√3)

⇒ Taking LCM of 2 and √3 = 2√3

⇒ Result = (√3 + 2 × 2) / (2√3)

⇒ Result = (√3 + 4) / 2√3

∴ The correct answer is (√3 + 4)/2√3.

Additional Information

Trigonometric Ratios of Specific Angles

Standard values: sin 30° = 1/2, sin 60° = √3/2, cos 30° = √3/2, cos 60° = 1/2.

Reciprocal Relations

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

Sum of Angles in a Triangle

In any triangle, ∠A + ∠B + ∠C = 180°.

Given: Total customer = 50 

Number of customer who like any of two brands

= B1 + B2 + C

= 25 + 20 + 5

= 50

Hence, all likes any of the two brands or both the brands.

So, number of customer who liked none of two brands

= Total customer - Number of customer who like any of two brands

= 50 - 50 = 0

Hence, the correct answer is "0".

The correct answer is option 4 i.e 6.25

The new reverse Repo rate announced by the Reserve Bank of India (RBI) as of 1st August 2018 was **6.25 %.**​

• The rate mentioned in the table are as per Dec 2019.

Shortcut Trick

For any expression of the form a cosec²θ + b sin²θ, the minimum value is given by 2√(ab).

Here, a = 4 and b = 9.

⇒ Minimum value = 2 × √(4 × 9)

⇒ Minimum value = 2 × √36 = 2 × 6 = 12.

∴ The correct answer is 12.

Alternate Method

Expression: 4 cosec² 2A + 9 sin² 2A

a = 4 b = 9 Using AM ≥ GM for positive terms

Given: Expression 4 cosec² 2A + 9 sin² 2A, where 0° < A ≤ 90°.

Formula Used: Minimum value of a tan²θ + b cot²θ or a sin²θ + b cosec²θ is 2√ab.

⇒ Let f(A) = 4 cosec² 2A + 9 sin² 2A

⇒ By Arithmetic Mean ≥ Geometric Mean (AM ≥ GM):

⇒ [4 cosec² 2A + 9 sin² 2A] / 2 ≥ √[4 cosec² 2A × 9 sin² 2A]

⇒ 4 cosec² 2A + 9 sin² 2A ≥ 2 × √[36 × (sin² 2A / sin² 2A)]

⇒ 4 cosec² 2A + 9 sin² 2A ≥ 2 × √36

⇒ 4 cosec² 2A + 9 sin² 2A ≥ 2 × 6 = 12

∴ The correct answer is 12.

Additional Information

Trigonometric Minimum Values

For a sin²θ + b cosec²θ, the minimum value is 2√ab if b ≤ a, otherwise it is a + b (if considering a specific range where sinθ cannot reach the extreme value).

Standard Form Results

The minimum value of a sec²θ + b cosec²θ is (√a + √b)². The minimum value of a cos²θ + b sec²θ is 2√ab.

AM-GM Inequality

For any set of positive numbers, the Arithmetic Mean is always greater than or equal to the Geometric Mean (Equality holds when all numbers are equal).

The correct answer is option 1 i.e Badminton

• Kidambi Srikanth is an Indian badminton player.
• He was ranked no. 1 player in men's singles in the world in April 2018
• He was conferred with Padma Shri award in 2018
• He was also conferred with Arjuna award in 2015.

Shortcut Trick

Assume all 100 questions were correct: 100 × 4 = 400 marks.

Actual marks obtained = 340 marks.

Total marks lost due to incorrect answers = 400 − 340 = 60.

Marks lost for every wrong answer (penalty + missing correct marks) = 1 + 4 = 5 marks.

Number of wrongly answered questions = 60 ÷ 5 = 12.

∴ The correct answer is 12.

Alternate Method

Given: Total questions = 100, Total score = 340, Correct = +4, Wrong = −1.

Average marks per question = 340 ÷ 100 = 3.4 marks.

⇒ Ratio of Correct to Wrong answers = 4.4 : 0.6

⇒ Ratio = 44 : 6 = 22 : 3

⇒ Total parts = 22 + 3 = 25 units

⇒ 25 units = 100 questions

⇒ 1 unit = 100 ÷ 25 = 4

⇒ Number of wrongly answered questions = 3 units × 4 = 12.

∴ The correct answer is 12.

Additional Information

Equation Method

Let c be correct and w be wrong. c + w = Total, and (c × marks per correct) − (w × penalty) = Net Score.

Alligation in Scoring

The rule of alligation can be used when the average score per question is known to find the ratio of correct to incorrect responses.

Accuracy Rate

Accuracy % = (Number of correct answers ÷ Total attempted questions) × 100. In this case, (88/100) × 100 = 88%.

The dotted figure is coincided in the complete figure and in the next step the dotted figure become complete figure.

Hence, figure B will be the next figure in the given set of figures.

Formula Used:

In a quadratic equation ax² + bx + c = 0

If α and β are the roots of the equation then

α + β (Sum of roots) = -b/a, α . β (Product of the roots) = c/a

Calculation:

Let the roots of the equation (l – m)x² – (6l – 6m)x + 1 = 0 be α and 2α.

if we compare the above equation by ax2 + bx + c = 0

we get a = (l – m), b = –(6l – 6m) and c = 1

Now, Sum of roots = -b/a,

Sum of roots (α + 2α) = – { – (6l – 6m)}/(l – m) = 6

⇒ α = 6/3 = 2      ----(1)

Given, l ∶ α = 5 ∶ 8

⇒ l = 5/4

Now, the Product of the roots = c/a

Product of the roots α × 2α = 1/(l – m)

⇒ 5/4 – m = 1/8

∴ m = 9/8

Note: For this question, the discrepancy is found in the question/answer. So, This question is ignored for all candidates in the exam.

Shortcut Trick To find the least number to be subtracted, find the remainder when 9999 is divided by 16. 9999 ÷ 16 ⇒ 16 × 600 = 9600; Remainder = 399. 16 × 24 = 384; Remainder = 399 − 384 = 15. The remainder is the number to be subtracted. ∴ The correct answer is 15.

Alternate Method Given: Number = 9999, Divisor = 16. Formula Used: Dividend = (Divisor × Quotient) + Remainder

Perform long division of 9999 by 16: ⇒ 99 ÷ 16 → Quotient = 6, Remainder = 3 (since 16 × 6 = 96) ⇒ Bring down 9: 39 ÷ 16 → Quotient = 2, Remainder = 7 (since 16 × 2 = 32) ⇒ Bring down 9: 79 ÷ 16 → Quotient = 4, Remainder = 15 (since 16 × 4 = 64) ⇒ Total Quotient = 624 and Remainder = 15. ⇒ Required number to subtract = Remainder = 15. ∴ The correct answer is 15.

Additional Information Divisibility by 16 A number is divisible by 16 if the number formed by its last four digits is divisible by 16. Least Number to be Added To make a number perfectly divisible by adding, the value to be added is (Divisor − Remainder). Division Algorithm For any integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.

The logic followed here is:

Peacock, Ostrich and Hen are more or less flightless birds whereas Eagle can fly even at a high altitude. 

Hence, ‘Eagle’ is odd one out.

The correct answer is option 2 i.e Meghalaya

• Shillong is the capital of Meghalaya.
• The State of Meghalaya is situated in the northeast of India.
• The emergence of Meghalaya as an Autonomous State on 2nd April 1970 and as a full-fledged State on 21st January 1972.

Shortcut Trick

Convert 4 years 9 months into years: 4 + 9/12 = 4.75 years.

Total interest percentage = Rate × Time = 8% × 4.75 = 38%.

Total amount percentage = Principal (100%) + Interest (38%) = 138%.

Given 138% = Rs. 1,035 ⇒ 100% = (1,035 ÷ 138) × 100 = 7.5 × 100 = Rs. 750.

∴ The correct answer is Rs. 750.

Alternate Method

Given: Amount (A) = Rs. 1,035 | Rate (R) = 8% p.a. | Time (T) = 4 years 9 months

Formula Used: Amount (A) = Principal (P) + Simple Interest (SI) = P × (1 + (R × T) ÷ 100)

⇒ Convert Time to years: T = 4 + 9/12 = 4 + 3/4 = 19/4 years = 4.75 years

⇒ 1,035 = P × (1 + (8 × 19/4) ÷ 100)

⇒ 1,035 = P × (1 + (2 × 19) ÷ 100)

⇒ 1,035 = P × (1 + 38 ÷ 100)

⇒ 1,035 = P × (1.38)

⇒ P = 1,035 ÷ 1.38

⇒ P = Rs. 750

∴ The correct answer is Rs. 750.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is the Principal, R is the Rate per annum, and T is Time in years.

Effective Interest Rate

The total interest earned on the Principal can be represented as (R × T)%, which helps in solving Amount-based questions directly.

Time Conversion

Always ensure Time is in years; if given in months, divide by 12; if in days, divide by 365.

The correct answer is option 1 i.e P

Key Points

• Atomic radii- The distance from the centre of the nucleus to the outermost shell containing electrons called the atomic radius.
• While moving left to right across a period in the periodic table, the atomic number increases.
• Due to this the effective nuclear charge also increases.
• This is because the nucleus pull is high for the electrons,
• From right to left in the periodic table the atomic radius increase.
• As Ar is the 18 group element, Cl is the 17 group element, S is the 16 group element, and P is the 15 group element so P has the largest- size ions among these elements.

The correct answer is option 3 i.e Mass × Velocity

• Momentum: It is defined as the quantity of motion of the body.
• It is measured by mass × velocity.
• Momentum depends on both speed and direction
• Momentum is a vector quantity as mass is scaler and velocity is vector
• Momentum = Mass X Velocity (p=mv).
• SI unit Kg-m.s^-1

The correct answer is option 1 i.e Only A is true

• Sound is produced by vibrating objects.
• Medium: It is the matter or substance through which sound is transmitted.
• It can be solid, liquid or gas
• Speed of sound in a different medium at 25º C

The correct answer is option 2 i.e Lok Janshakti Party

• The Lok Jan Shakti Party (LJP) is a premier Indian political organization formed on 28th October 2000 and led by the Honourable Shri Ram Vilas Paswan.
• The party was formed after the separation from the Janata Dal (United).
• The party has considerable amongst Dalits in Bihar.

Lok Janshakti Party: 

• Leader: Ram Vilas Paswan
• Founder: Ram Vilas Paswan
• Founded: November 2000

The correct answer is option 1 i.e Metal oxide + acid ⇨ salt + water

Key Points

• Metal oxides are basic in nature.
• When an acid reacts with a metal oxide they both neutralize each other.
• The new compounds formed are salt and water.

           Acid + Metal Oxide ⇨ Salt + Water

• Example: Calcium is metal and calcium oxide is a metallic oxide which is basic in nature.
• When an acid (hydrochloric acid) reacts with calcium oxide, a neutralization reaction takes place and calcium chloride along with water is formed.

          2HCl + CaO ⇨ CaCl2 + H2O

Shortcut Trick

The expression follows the algebraic identity pattern: (a³ − b³) / (a² + ab + b²) = (a − b).

Identify a = 0.22 and b = 0.11.

Verify denominators: a² = 0.0484, ab = 0.0242, and b² = 0.0121.

Final Value = a − b = 0.22 − 0.11 = 0.11.

∴ The correct answer is 0.11.

Alternate Method

Given:

Expression = ((0.22)³ − (0.11)³) / (0.0484 + 0.0242 + 0.0121)

Formula Used:

The difference of cubes identity is: a³ − b³ = (a − b)(a² + ab + b²)

Calculation:

⇒ Let a = 0.22 and b = 0.11.

⇒ Calculate a² = (0.22) × (0.22) = 0.0484.

⇒ Calculate b² = (0.11) × (0.11) = 0.0121.

⇒ Calculate ab = (0.22) × (0.11) = 0.0242.

⇒ We can see the denominator is (0.0484 + 0.0242 + 0.0121) = (a² + ab + b²).

⇒ Substituting these into the expression: [(a − b)(a² + ab + b²)] / (a² + ab + b²).

⇒ Expression = a − b.

⇒ Expression = 0.22 − 0.11 = 0.11.

∴ The correct answer is 0.11.

Additional Information

Sum of Cubes Identity

The formula for the sum of two cubes is a³ + b³ = (a + b)(a² − ab + b²).

Difference of Squares

One of the most used identities in simplification is a² − b² = (a − b)(a + b).

BODMAS Rule

Always follow the order: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction for multi-step calculations.

Shortcut Trick

By the Factor Theorem, if (x − 1) is a factor, then the sum of coefficients 4 + k + 5 = 0 ⇒ k = −9.

The expression becomes 4x² − 9x + 5.

Let the factors be (x − 1) and (ax + b). Comparing the constant term: (−1) × b = 5 ⇒ b = −5.

Comparing the leading coefficient: (1) × a = 4 ⇒ a = 4.

The other factor is 4x − 5.

∴ The correct answer is 4x − 5.

Alternate Method

Given: The polynomial f(x) = 4x² + kx + 5 is divisible by (x − 1).

Formula: According to the Remainder Theorem, if f(x) is divisible by (x − a), then f(a) = 0.

⇒ f(1) = 4(1)² + k(1) + 5 = 0

⇒ 4 + k + 5 = 0

⇒ 9 + k = 0

⇒ k = −9

Now, substitute the value of k back into the original expression:

⇒ f(x) = 4x² − 9x + 5

Factorize the quadratic expression by splitting the middle term:

⇒ f(x) = 4x² − 4x − 5x + 5

⇒ f(x) = 4x(x − 1) − 5(x − 1)

⇒ f(x) = (x − 1)(4x − 5)

The factors of the expression are (x − 1) and (4x − 5).

∴ The correct answer is 4x − 5.

Additional Information

Factor Theorem

A polynomial f(x) has a factor (x − a) if and only if f(a) = 0. This is used to find unknown coefficients.

Remainder Theorem

When a polynomial f(x) is divided by (ax − b), the remainder is given by f(b/a).

Relationship between Roots and Coefficients

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

Splitting the Middle Term

To factorize ax² + bx + c, find two numbers that multiply to (a × c) and add to b.

The correct answer is option 1 i.e Bhartruhari Mahtab

Outstanding Parliamentarian Award:

• This award was instituted by Indian Parliamentary Group (IPG) and was given annually since 1995.
• This award is given to the most Outstanding Parliamentarians selected by the Award Committee.
• The President of India, Shri Ram Nath Kovind, presented the Outstanding Parliamentarian Award for the years 2013-2017, on August 1, 2018, in New Delhi.​

Outstanding Parliamentarian Award 2013-2017