RRC Group D Previous Year Paper 19 (Held On: 10 Dec 2018 Shift 2)

• Mumbai team was the winner of Vijay Hazare trophy 2018-19.
• It was the 3^rd title of the Mumbai team, in which the Mumbai team beat the Delhi team.
• Vijay Hazare Trophy is also known as Ranji one day trophy which was started in 2002-03 as a limited over cricket domestic cricket competition, in which the state team is involving from the Ranji trophy plates.
• The name of this trophy is after the name of the famous International Indian cricketer Vijay Hazare.
• In 2019, Karnataka won the Vijay Hazare trophy by defeating Tamil Nadu.

Shifting agriculture has many benefits.

It helps to ensure weed control, pest control, sustainability etc. It is also effective in reducing the rate of environmental degradation.

Thus, the argument that this agricultural practice is unworthy is incorrect.

Therefore, argument 1 is not strong.

In shifting agriculture, an area of land is cleared off its vegetation by burning them and cultivated for a period of time and then abandoned. Thus, that abandoned land then gets ample time to restore its fertility naturally. 

This method saves a wide range of resources and provides nutrients because a small area is usually cleared and the burned vegetation offers many nutrients eventually saving the costs involved in improving the fertility of the land.

Therefore, this method is considered less expensive compared to modern methods of farming.

The economic nature of shift farming is reason enough for it to be preferred over the conventional methods.

Thus, argument 2 is strong.

Hence, only argument 2 is strong.

The statement only talks about specific types of frequencies.

• Though music is a type of frequency, we cannot be certain that this is the type mentioned in the statement.
• Therefore, the conclusion that the human brain responds to music is possible but not definite.
• Thus, conclusion I does not follow.

The statement says that specific type of frequencies aid in the healing of problems related to the human brain.

• As the brain is an internal organ of the human body, it is safe to conclude that these frequencies are used to heal diseases (at least related to the brain) in human body.

Therefore, conclusion II follows.

Hence, only conclusion II follows.

The pattern followed is,

Hence, UF21 is the correct answer.

Shortcut Trick

Volume of Hemisphere = Volume of Cone ⇒ (2/3)πr³ = (1/3)πr²h ⇒ h = 2r.

Slant height (l) of cone = √(r² + h²) = √(r² + (2r)²) = r√5.

Ratio of CSAs = (2πr²) : (πrl) = 2r² : (r × r√5) = 2 : √5.

∴ The correct answer is 2/√5.

Alternate Method

Given: Radius of Hemisphere = r, Base radius of Cone = r.

Formula Used: Volume of Hemisphere = (2/3)πr³; Volume of Cone = (1/3)πr²h; CSA of Hemisphere = 2πr²; CSA of Cone = πrl.

⇒ Volume of Hemisphere = Volume of Cone

⇒ (2/3)πr³ = (1/3)πr²h

⇒ 2r = h

⇒ Slant height of cone (l) = √(r² + h²) = √(r² + 4r²) = r√5

⇒ Ratio = (CSA of Hemisphere) / (CSA of Cone)

⇒ Ratio = (2πr²) / (πrl) = (2πr²) / (πr × r√5)

⇒ Ratio = 2/√5

∴ The correct answer is 2/√5.

Additional Information

Total Surface Area (TSA)

TSA of Hemisphere = 3πr² and TSA of Right Circular Cone = πr(l + r).

Melting and Recasting Rule

When one solid is melted and recast into another, the Volume remains constant, regardless of the change in shape.

Slant Height Property

In a cone, the relationship between radius (r), height (h), and slant height (l) is given by the Pythagorean theorem: l² = r² + h².

Shortcut Trick

The overall average of 4 numbers is 26.5.

The average of the first 2 numbers (a and b) is 20, which is 6.5 below the overall average.

To maintain the balance, the average of the remaining 2 numbers (c and d) must be 6.5 above the overall average.

Required Average = 26.5 + 6.5 = 33.

∴ The correct answer is 33.

Alternate Method

Given:

Number of observations (n) = 4

Overall average of (a, b, c, d) = 26.5

Average of (a, b) = 20

Formula Used:

Sum of observations = Average × Total number of observations

⇒ Total sum (a + b + c + d) = 26.5 × 4

⇒ Total sum = 106

⇒ Sum of (a + b) = 20 × 2

⇒ Sum of (a + b) = 40

⇒ Sum of (c + d) = Total sum − Sum of (a + b)

⇒ Sum of (c + d) = 106 − 40 = 66

⇒ Average of (c and d) = 66 ÷ 2

⇒ Average of (c and d) = 33

∴ The correct answer is 33.

Additional Information

Basic Average Formula

The average is calculated as the Sum of all observations ÷ Total number of observations.

Sum of Observations

If the average and number of items are known, the Total Sum is found by Average × Number of items.

Weighted Average

When combining two groups, the combined average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the count and x is the group average.

• 2018 Assembly elections took place in Meghalaya, which was held on 27^th February 2018.
• In this election three largest parties, Indian National Congress (INC) won 21 seats, National People’s Party(NPP) won 19 seats and the United Democratic Party (UDP) won 6 seats.
• The Chief Minister of Meghalaya is Conrad Sangma belongs to the National people’s party.

Meghalaya:

Capital: Shillong

 State Animal: Cloud Leopard

 State Bird: Hill Myna

 State Tree: White Teak

 State Flower: Lady Slipper

Least possible venn diagram is,

1. All leopards are jaguars → False
2. Some panthers are cheetahs → True

Hence, only conclusion 2 follows.

The pattern followed here is,

Number are given in descending order.

24 – 23, 22 – 21, 20 – 19.

According to alphabetical series,

24 → X

23 → W

22 → V

21 → U

20 → T

19 → S

Hence, “20TS19” is the correct answer.

• The Defence Acquisition Council (DAC) which is the ministry of defence's highest decision-making body approved the proposal for the Indian Navy.
• In this proposal, DAC approved the procurement of 111 utility helicopters for the Indian Navy at a cost of over 21000 crores.
• The utility helicopters will be used in attack missions as well as for search and rescue and surveillance operations.
• This is the first project under the MoD's prestigious Strategic Partnership model that aims at providing significant fillip to the government's 'Make in India' programme.

The correct answer is Nucleotides.

Key Points

• The Genetic information is carried by the long chains of molecules that are called the Nucleotides
• Nucleotides are molecules, which is consisting of nucleoside and phosphate groups.
• A nucleotide consists of three components: a phosphate group, a sugar (deoxyribose in DNA and ribose in RNA), and a nitrogenous base (adenine, guanine, cytosine, thymine in DNA; adenine, guanine, cytosine, uracil in RNA).
• Nucleotides link together through their phosphate and sugar groups to form the long chains of DNA or RNA, which are the molecules that carry genetic information.
• Nucleotides are the basic unit of building a structure of DNA and RNA.

• Astronauts in space communicate with each other by the radio links because sound waves can’t travel in space.
• A sound is a mechanical wave, which requires a medium to travel.
• In this, the motion of the particle of the medium vibrates parallel to the motion of the wave, which characterizes the sound as the longitudinal wave.

The mirror image will be,

Hence, option c is the correct answer.

• Rajagopalan Vasudevan is also called as the ‘Plastic Man of India’ who has found a way to reuse plastic waste and make durable rods.
• Rajagopalan Vasudevan is an Indian scientist who basically works for waste management system.
• He is currently working as a professor at Thiagarajar college of engineering.
• He developed an innovative method to reuse of plastics waste to better, durable and cost-effective roads, has recently been awarded for this work of India's fourth-highest civilian honor Padma Shri in 2018.

According to given information,

At point F, the man is facing towards the South direction.

Hence, South is the correct answer.

The correct answer is m°.

As per the question, it is given that mass of the object is =m,

The body is moving under the constant force.

$a = \frac{F}{m}$

We know that,

⇒ v² = u² + 2as

⇒ v² = 2as

$\Rightarrow {\rm{v}} = \sqrt {2{\rm{as}}}$

$\Rightarrow {\rm{v}} = \sqrt {2{\rm{;}}\left( {\frac{F}{m}} \right)s}$

 Now, the kinetic energy of the object

$KE = \frac{{m{v^2}}}{2}$

$\Rightarrow KE = \frac{m}{2}\left( {\frac{{2Fs}}{m}} \right) = Fs$

Hence, it is independent of mass.

• The royal city at Fatehpur Sikri was built by the Mughal emperor Akbar during the second half of the 16^th century.
• It was celebrated as the city of Victory of the Mughal empire, which was the capital city for more than 10 years from 1571 to 1585.
• It was turned as a Fatehabad (the city of Victory) where the legend sons of Akbar were born.
• It’s also known for the complex of monuments and temples all in uniform architectural style.

The use of the word ‘definitely’ indicates the employer’s need for a good computer programmer.

Therefore, conclusion 2 follows.

The author of the statement certainly needs a good computer programmer.

But we cannot conclude that this is the case in general for any employer.

Nor do we know if there are as many jobs as the number of good computer programmer.

Therefore, conclusion 1 does not follow.

Hence, only conclusion 2 follows.

Option 1: × & +

5 × 6 + 3 – 4 ÷ 2 = 30 + 3 – 2 = 31 ≠ - 1

Option 2: - & ÷

5 + 6 × 3 ÷ 4 – 2 = 5 + 4.5 – 2 = 7.5 ≠ - 1

Option 3: ÷ & ×

5 + 6 ÷ 3 – 4 × 2 = 5 + 2 – 8 = 7 – 8 = -1

Option 4: + & -

5 – 6 × 3 + 4 ÷ 2 = 5 – 18 + 2 = - 11 ≠ -1

Hence, “ ÷ & × ” is the correct answer.

Alight and Descend are synonyms,

Similarly,

House and Home are synonyms.

Hence, Home is the correct answer.

• Non-Metals are generally more electronegative due to their Smaller atomic radii.
• Non-metals having high pull forces on their electron because they are closer to having a full valance shell, which makes them stable.
• The much number of valance electrons have more electronegative.

Statement 1: The shape of 6 tins is such that in one trolley, only 2 can fit.

No relation with trolly is given so not sufficient to answer the question.

Statement 2: The tins contain processed sauce.

Data given in this statement is not relevant to question.

Hence, “The statements are not sufficient ”.

• Amir Khan played the lead role in the movie ‘Dangal’ released in 2016.
• The director of the movie ‘Dangal’ is Nitesh Tiwari, which was released on 23 December 2016.
• In this movie, a character Mahaveer Singh Phogat, a farmer wrestler decides to full fill his dream of winning the gold medal for his country by training his daughter for the commonwealth games.

Shortcut Trick

∠CBE = 180° − 80° = 100° (Opposite angles of cyclic quadrilateral BCDE).

In isosceles ▵BCE, ∠BCE = (180° − 100°) ÷ 2 = 40°.

By Alternate Segment Theorem, ∠BEA = ∠BCE = 40°.

∴ The correct answer is 40°.

Alternate Method

Given: ∠CDE = 80°, m(BC) = m(BE), AF is a tangent at E.

Formula Used: Sum of opposite angles of a cyclic quadrilateral is 180°; Alternate Segment Theorem.

⇒ BC

• The property of the metals wherein they can be beaten into thin sheets is called the Malleability.
• Malleability is the ability of the material to deform under the pressure.
• Malleability occurs in metal because of the metallic bonds that keep the metal in place. Metallic bonds are characterized as the sea of the electron, and electrons easily can move from atom to another, which allows the atom to slide on each other by applying the force.
• Expansion- It is the action of becoming larger.
• Ductility- It is the physical property of the material which is associated with the ability to be hammered thin or stretched wire without breaking.
• Conduction- It is the property of the material to allow the flow of charges in the metals.

CONCEPT:

• Pressure (P): The force per unit area is called pressure.
• The SI unit of pressure is the pascal (Pa).

Pressure (P) = Force (F)/ Area (A)

• Force (F): The interaction that changes the state of rest or state of motion of a body is called force.
• The SI unit of force is Newton (N).

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

• Density (ρ): The mass per unit volume is called density.
• The SI unit of Density is Kilogram per cubic meter (kg/m³).

Density (ρ) = Mass (m)/Volume (V).

EXPLANATION:

Mass/Volume = Density.

So option 3 is correct.

• Adipose tissue is found beneath the skin, around the kidneys, and between the internal organs.
• Ligament- It connects one bone to another bone to form joints.
• Areolar- It is the loose connective tissue that consists of a meshwork of collagen elastic tissue and reticular fibers with many connective tissue cells in between meshwork of fibers.
• Tendons-It connects bones to muscles. It is the tough band of fibrous connective tissue that connects muscle to bone and is capable of withstanding tension.

• The comptroller and Auditor General of India is also known as the Guardian of Public Purse.
• All the govt. official payment goes through the approval of the comptroller and Auditor General of India.
• This authority was given to general under article 148 constitution of India.

The least possible venn diagram:

I) All crayons are nibs → True

II) All nibs are crayons → False (Possible but not definite)

Hence, only conclusion I follows.

Shortcut Trick

एक पूर्ण वर्ग (Perfect Square) संख्या के गुणनखंडों की संख्या हमेशा विषम (Odd) होती है।

अन्य सभी संख्याएं (जो पूर्ण वर्ग नहीं हैं) के गुणनखंडों की संख्या सम (Even) होती है।

विकल्पों में 1600 = 40², 52900 = 230² और 36100 = 190² सभी पूर्ण वर्ग हैं।

30000 एक पूर्ण वर्ग नहीं है, इसलिए इसके गुणनखंडों की संख्या सम होगी।

∴ The correct answer is 30000.

Alternate Method

माना संख्या N = p₁^a × p₂^b × p₃^c ... (जहाँ p अभाज्य संख्याएं हैं)

कुल गुणनखंड = (a + 1)(b + 1)(c + 1) ...

⇒ 1600 = 16 × 100 = 2⁴ × 2² × 5² = 2⁶ × 5² → गुणनखंड = 7 × 3 = 21 (विषम)

⇒ 52900 = 23² × 10² = 23² × 2² × 5² → गुणनखंड = 3 × 3 × 3 = 27 (विषम)

⇒ 30000 = 3 × 10⁴ = 3¹ × 2⁴ × 5⁴ → गुणनखंड = 2 × 5 × 5 = 50 (सम)

⇒ 36100 = 19² × 10² = 19² × 2² × 5² → गुणनखंड = 3 × 3 × 3 = 27 (विषम)

∴ The correct answer is 30000.

Additional Information

Perfect Square Property

एक संख्या पूर्ण वर्ग होती है यदि और केवल यदि उसके गुणनखंडों की कुल संख्या विषम हो।

Number of Factors Formula

यदि N = p^aq^br^c, तो गुणनखंडों की संख्या = (a+1)(b+1)(c+1) होती है।

Prime Factors

सम गुणनखंडों के लिए, कम से कम एक अभाज्य घात विषम होनी चाहिए (जैसे 3¹)।

• The SI unit of thrust is Newton.
• When any object is put into the water then the object will replace the water the same as its volume and the cause of which there is a force acting upwards, to balance this weight is called the thrust force.

CONCEPT:

• Electrostatic field: Filed of lines starts from the positive charge and end at the negative charge.

• It is formed only by a charged particle, not by electric current.

• Magnetic field: Magnetic field line starts from the North pole and ends at the south pole, it always makes a closed loop.

• It is formed by electric currents and magnets.

• Magnetic field lines: The imaginary lines which represent the direction of the magnetic field are called magnetic field lines.

• The tangent at any point on the field lines gives the direction of the magnetic field vector at that point.

• Magnetic lines of force always emerge or start from the North Pole and terminate on the South Pole.

• Electromagnetic field: It is a field that is getting produced by the accelerated charged particle.

• Static field: It is a kind of field, which is getting produced by the state charge.

EXPLANATION:

• From the above discussion, we can say that the magnetic field lines are produced by a current-carrying wire. So option 2 is correct.

• In the case of electric current, the electrons flow in the wire but there are equal and opposite charges, that is the same number of protons are there in that wire which doesn't flow.

• That's why the overall current-carrying wire is neutral and it can't produce an electric field.

• A charge at rest produces an electric field only.

• A charge moving with a constant velocity produces both electric field as well as the magnetic field.

• A charge moving with some acceleration produces electromagnetic waves/fields.

Shortcut Trick

Ratio of Selling Price to Cost Price percentage: 125% corresponds to Rs. 6250.

Unitary method: Rs. 1 = 125 ÷ 6250 %.

For Rs. 6000: (125 ÷ 6250) × 6000 = 120%.

Profit percentage = 120% − 100% = 20%.

∴ The correct answer is 20%.

Alternate Method

Given → SP₁ = Rs. 6250, Profit% = 25%, SP₂ = Rs. 6000. Formulas: CP = [SP × 100] ÷ [100 + P%] | Profit% = [(SP − CP) ÷ CP] × 100

⇒ First, find the Cost Price (CP): CP = (6250 × 100) ÷ (100 + 25) ⇒ CP = (6250 × 100) ÷ 125 = 50 × 100 = Rs. 5000. ⇒ Now, if New SP = Rs. 6000, then New Profit = 6000 − 5000 = Rs. 1000. ⇒ New Profit% = (1000 ÷ 5000) × 100 = 1/5 × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Cost Price & Selling Price Relation

When there is a profit, Selling Price is always greater than Cost Price. The formula is SP = CP + Profit.

Profit Percentage Calculation

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

• Cartilage- In the cartilage tissue, the cells are widely spaced. This tissue helps in soothing the bone surfaces at the joints.
• Tendons-It connects bones to muscles. It is the tough band of fibrous connective tissue that connects muscle to bone and is capable of withstanding tension.
• Bone- Bone is rigid organs in the body that provide the shape and strength to the body.
• Ligament- It connects one bone to another bone to form joints

• All India Anna Dravida Munnetra Kazhagam (AIADMK) party is a regional political party of Tamil Nadu and the union territory of Puducherry.
• The founder of the AIADMK party is MG Ramachandran on 17 October 1972.
• From the 1989 to 5 December 2016 J. Jayalalitha led this party who serves six times a CM of Tamil Nadu, the party has won seven times in the majority.
• J. Jayalalitha was known as the Mother of AIADMK.

• We know that Pressure= Force Thrust/ Area
• Thrust Force= Pressure × Area
• Thrust is a kind of pull force, which is applied by the medium on the object.
• Inertia- It is a kind of resistive force of any object to change its state.
• Momentum- When any massive object moving with a certain velocity, then the momentum of that object will be multiplication of the mass and velocity.
• Volume-It is the quantity of three-dimensional space enclosed by a closed surface.

The inside figure is rotated by 45° in an anticlockwise direction and an alphabet/ symbol is added from the extreme end in each step.

In step number f, one symbol is towards the end of c.

Complete series will be,

Hence, figure given in option 1 will complete the series.

Shortcut Trick

Volume of hollow sphere = Volume of cylinder

4/3 × π × (R³ − r³) = π × R_c² × h

4/3 × (12³ − 8³) = 16² × h

4/3 × (1728 − 512) = 256 × h ⇒ 4/3 × 1216 = 256 × h

h = 1216 / (3 × 64) = 19 / 3 = 6.33 cm

∴ The correct answer is 6.33 cm.

Alternate Method

Given:

External diameter (D) = 24 cm ⇒ External radius (R) = 12 cm

Internal diameter (d) = 16 cm ⇒ Internal radius (r) = 8 cm

Cylinder diameter = 32 cm ⇒ Cylinder radius (R_c) = 16 cm

Formula Used:

Volume of hollow sphere = 4/3 × π × (R³ − r³)

Volume of cylinder = π × r² × h

Calculations:

⇒ Volume of metal in sphere = 4/3 × π × (12³ − 8³)

⇒ Volume of metal = 4/3 × π × (1728 − 512) = 4/3 × π × 1216 cm³

⇒ Let height of cylinder be h.

⇒ Volume of cylinder = π × 16² × h = 256 × π × h

⇒ Equating volumes: 256 × π × h = 4/3 × π × 1216

⇒ 256 × h = 4864 / 3

⇒ h = 4864 / (3 × 256) = 1216 / (3 × 64)

⇒ h = 19 / 3 ≈ 6.333... cm

∴ The correct answer is 6.33 cm.

Additional Information

Volume Invariance

When a solid is melted and recast into another shape, the total volume remains constant, provided there is no wastage.

Cylinder Properties

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(r + h).

Sphere Properties

Surface Area of a sphere = 4πr². For a hollow sphere, the material surface area is 4π(R² + r²).

By combining given pieces,

Hence, option 1 is the correct answer.

• Dr. Bhimrao Ambedkar University is a non zero profit public higher education institution located in the urban setting of the large city of Agra, Uttar Pradesh.
• It is founded in 1927 and officially accredited by University Grants Commission, India.
• Initially in this institute had only four faculties Arts, Sciences, Commerce and Law.
• It is also known as the Agra university, which was established by the great efforts of the educationalist Rev Canon, AW Davis, Munshi Narayan Prashad Asthana, etc which was later renamed as Dr. B. R. Ambedkar University in 1996.

• Ratnagiri mines are found in Maharastra.
• It is the part of the Konkan division and a port town in the Maharastra.
• This district was founded by the British.
• Minerals like Bauxite, Ilmenite found in these mines.
• It was also a birthplace of great Indian freedom fighter Lokmanya Bal Gangadhar Tilak.

• 18 groups are there in the modern periodic table.
• In each group, have the same number of a valance electron.
• Mendeleev was the first scientist who arranges the known elements as per the order of their atomic weight.
• The concept of the modern periodic table was given by the chemist Mosely, in which he arranged the elements based on their atomic number.

Shortcut Trick

If a root is given as a fraction a/b, the corresponding linear factor is (bx − a).

For the root 5/3, the factor is (3x − 5).

For the root −3/10, the factor is (10x − (−3)) = (10x + 3).

The quadratic equation is the product of these factors: (10x + 3) (3x − 5) = 0.

∴ The correct answer is (10x + 3) (3x − 5) = 0.

Alternate Method

Given:

Roots of the quadratic equation are x = 5/3 and x = −3/10.

Formula Used:

If α and β are the roots, the equation is represented as (x − α)(x − β) = 0.

Calculations:

⇒ First root (α) = 5/3 → (x − 5/3) = 0

⇒ 3x − 5 = 0

⇒ Second root (β) = −3/10 → (x + 3/10) = 0

⇒ 10x + 3 = 0

⇒ Combining the linear factors to form the equation:

⇒ (10x + 3) × (3x − 5) = 0

∴ The correct answer is (10x + 3) (3x − 5) = 0.

Additional Information

Standard Form of Quadratic Equation

The general form is ax² + bx + c = 0, where a ≠ 0.

Sum and Product of Roots

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

Nature of Roots

The value of the discriminant (D = b² − 4ac) determines if roots are real and distinct (D > 0), real and equal (D = 0), or imaginary (D < 0).

According to given information:

Hence, North- West is the correct answer.

Let,

Age of Heera = x

Arijit’s age = 1.5x + 3

According to given conditions,

$\frac{2}{3};$ of Deepika’ s age = x – 10

Deepika’s Age = $\frac{3}{2}x - 15;$

According to given conditions,

$\frac{{15x;}}{2} - 75; = ;4.5x; + ;9$

$15x - 150; = ;9;x; + ;18$

$6x; = ;18; + ;150$

x = 28

Age of Heera = 28

Age of Arijit = 45

Age of Deepika = 27

Total = 28 + 45 + 27 = 100

Hence, 100 is the correct answer.

Birds live in Nest.

Similarly,

Lion lives is Den.

Hence, Den is the correct answer.

Drawing family tree diagram:

Hence, Preethi is the Aunt of Kajol.

Shortcut Trick

Rate is 30% per annum, so for 4 months, Rate = 30% ÷ 3 = 10%.

Time is 1 year, so number of periods (n) = 3 (since 12 ÷ 4 = 3).

Using the ratio method for 10% (10 → 11): (10)³ → (11)³ ⇒ 1000 → 1331.

Given 1000 units = ₹10000 ⇒ 1 unit = ₹10.

∴ The correct answer is ₹13310.

Alternate Method

Given:

Principal (P) = ₹10000

Annual Rate (R) = 30%

Time (T) = 1 year

Compounding Period = 4 months

Formula Used:

Amount (A) = P(1 + r/100)ⁿ

Where r = rate per conversion period and n = total number of conversion periods.

Calculations:

⇒ Conversion periods in a year = 12 months ÷ 4 months = 3 periods.

⇒ Rate per period (r) = 30% ÷ 3 = 10%.

⇒ Total periods (n) = 1 × 3 = 3.

⇒ A = 10000 × (1 + 10/100)³

⇒ A = 10000 × (11/10)³

⇒ A = 10000 × (1331 / 1000)

⇒ A = 10 × 1331 = 13310

∴ The correct answer is ₹13310.

Additional Information

Effective Annual Rate (EAR)

The actual interest rate earned or paid after compounding. Formula: EAR = [1 + (R/n)]ⁿ − 1, where n is the number of compounding periods per year.

Compounding Frequencies

For half-yearly compounding, divide rate by 2 and multiply time by 2. For quarterly compounding, divide rate by 4 and multiply time by 4.

Difference between CI and SI

For the first period (e.g., first 4 months here), Simple Interest and Compound Interest are identical. The difference arises from the second period onwards due to interest on interest.

Shortcut Trick

A number is divisible by 4 if its last two digits are divisible by 4.

Check options: (1) 00 → Yes, (2) 66 → No (66/4 = 16.5), (3) 84 → Yes, (4) 08 → Yes.

The number 76166 is the only one not divisible by 4.

∴ The correct answer is 76166.

Alternate Method

Given: Numbers (1) 89700, (2) 76166, (3) 43584, (4) 74708.

Rule Used: Divisibility test of 4 states that a number is divisible by 4 if the number formed by the tens and units digits is divisible by 4 or if both digits are zero.

⇒ For 89700: Last two digits = 00. Since 00 is divisible by 4, 89700 is divisible.

⇒ For 76166: Last two digits = 66. 66 ÷ 4 = 16 remainder 2. So, 76166 is NOT divisible.

⇒ For 43584: Last two digits = 84. 84 ÷ 4 = 21. So, 43584 is divisible.

⇒ For 74708: Last two digits = 08. 08 ÷ 4 = 2. So, 74708 is divisible.

∴ The correct answer is 76166.

Additional Information

Divisibility by 2

A number is divisible by 2 if its unit digit is even (0, 2, 4, 6, or 8).

Divisibility by 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Divisibility by 3

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

Calculation:

• As per the question, the mass of the moving body = m and velocity=4 km/hour
• Mass of the second object = 3m
• The velocity of the second object after the collision will be
• Here, masses are getting coalesced, which means here collision is inelastic,
• Hence, applying the conservation of momentum,

⇒  P_i = P_f

⇒ Mu = ( m₁+m₂) V

⇒ 4m = (m+3m)v

⇒ V= $\frac{4}{4}$= 1 $\frac{km}{hr}$

Shortcut Trick

A rational square root exists only for perfect square numbers.

A perfect square never ends with the unit digits 2, 3, 7, or 8.

Option 1 ends in 8, Option 2 ends in 2, Option 3 ends in 3 → All irrational.

Only Option 4 ends in 4, which can be a perfect square.

∴ The correct answer is 43264.

Alternate Method

Given: Four numbers to check for rational square roots.

Concept: The square root of a natural number is rational if and only if the number is a perfect square.

⇒ Step 1: Check unit digits of all options.

⇒ 16848 ends in 8 (Not a perfect square).

⇒ 41872 ends in 2 (Not a perfect square).

⇒ 49883 ends in 3 (Not a perfect square).

⇒ 43264 ends in 4 (Potential perfect square).

⇒ Step 2: Verify 43264 using long division or estimation.

⇒ 200² = 40000 and 210² = 44100.

⇒ Since 43264 ends in 4, the root could be 208.

⇒ 208 × 208 = 43264.

∴ The correct answer is 43264.

Additional Information

Properties of Perfect Squares

The digital root (sum of digits) of a perfect square is always 1, 4, 7, or 9. For 43264: 4+3+2+6+4 = 19 → 1+9 = 10 → 1+0 = 1.

Last Two Digits Rule

The last two digits of a perfect square must be the same as the last two digits of the squares of numbers from 1 to 24.

Rational vs Irrational Roots

If √n is not an integer for a natural number n, then √n is always an irrational number.

Number of triangles in the figure are as fillows,

Hence, 14 is the correct answer.

• The eighth nuclear power station is located at Rawatbhata in Rajasthan.
• Rawatbhata is tehsil, city and Nagar Palika of Chittorgarh district in Rajasthan, India.
• Rawatbhata also has one of the biggest dams in Rajasthan, called Rana Pratap Sagar Dam, which is on the Chambal river.

Shortcut Trick

Apply divisibility rules for prime numbers like 3, 7, or 13.

For 273, the sum of digits is 2 + 7 + 3 = 12.

Since 12 is divisible by 3, the number 273 is also divisible by 3.

Any number with more than two factors is a composite number.

∴ The correct answer is 273.

Alternate Method

Given: Numbers 263, 293, 283, 273.

To identify a composite number, we check for factors other than 1 and the number itself.

⇒ 263: Not divisible by 2, 3, 5, 7, 11, 13, 17. (√263 ≈ 16.2). It is Prime.

⇒ 283: Not divisible by 2, 3, 5, 7, 11, 13, 17. (√283 ≈ 16.8). It is Prime.

⇒ 293: Not divisible by 2, 3, 5, 7, 11, 13, 17. (√293 ≈ 17.1). It is Prime.

⇒ 273: Sum of digits = 2 + 7 + 3 = 12 (Divisible by 3).

⇒ 273 = 3 × 91 = 3 × 7 × 13.

∴ The correct answer is 273.

Additional Information

Composite Numbers

Numbers that have more than two factors (1 and themselves) are called composite numbers.

Prime Testing Rule

To check if N is prime, test divisibility by all primes up to √N.

Divisibility by 3

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

The pattern followed is,

48 – 1 = 47

47 + 3 = 50

50 – 1 = 49

49 + 3 = 52

Hence, 52 is the correct answer.

• Prasoon Joshi was appointed as the new Chairman of the Central Board of Film Certification(CBFC), in February 2018.
• The Union Information and Broadcasting Ministry has appointed Prasoon Joshi. He replaced the Pahlaj Nihalani and shall have the tenure of three years.
• The central board of film certification film rating system is also known as the Censor board.
• It is a statutory censorship and classification body under the ministry of information and broadcasting, Govt of India.
• It is established with regulation and public exhibition of films under the provisions of the Cinematography act 1952.

By counting number of sectors,

Sectors with internal angle 45° = 8

Sectors with internal angle 90° = 8

Sectors with internal angle 135° = 8

Sectors with internal angle 180° = 8

Sectors with internal angle 225° = 8

Sectors with internal angle 270° = 8

Sectors with internal angle 315° = 8

Total = 7 × 8 = 56

Hence, 56 is the correct answer.

• The Oxides of non-metals are usually acidic in nature.
• Non-metal react with oxygen in the presence of air and produce non-metal oxides.
• Non-metal oxides are usually gases at room temperature.
• Non-metal oxides are easily dissolved in the water and form an acidic solution.

• Myrmecophily describes pollination by the agency of ants.
• Ants are the busy insect and great lover of nectar, who used to crawl over the flower and carry the nectar without effectively cross-pollinating the flower.
• In the exchange of food and shelter, ants add myrmecophyte in pollination.
• The domatia adopted to ants may be called as the myrmecodomatia.
• Emasculation: Removal of stamens or anthers or killing the pollen of a flower without the female reproductive organ.

• BarkhaDutt is known for her role as a Journalist.
• She is an Indian television journalist working with the Tiranga TV.
• BarkhaDutt is born on 18 December 1971 in Delhi. She was previously working with NDTV for the last 21 years.
• She left NDTV in 2017. She emerged as a prominent figure after the reporting on the frontline of the Kargil war between India and Pakistan in 1999.

• The process of releasing an egg from the ovary is called the Ovulation.
• The process of Ovulation occurs in women when the ovarian follicles rupture and release the secondary oocyte ovarian cells.
• Reproduction-It is defined as the biological process by which new individual organisms are produced from their "parents".
• Fertilization- It is the process of fusion of haploid gametes, egg, and sperm to form the diploid zygote.
• Gestation- It is defined as the time between conception and birth.

span style='display: flex;gap: 6px;align-items: center;'> Shortcut Trick Sum of 4 numbers = 90 × 4 = 360. To maximize range, minimize the smallest number. Maximize other two distinct numbers: 119 and 118 (less than 120). Smallest number = 360 − (120 + 119 + 118) = 3. ∴ The correct answer is 117.

Alternate Method Given: Arithmetic mean = 90, Number of observations (n) = 4, Greatest number = 120. Formula: Sum = Mean × n | Range = Maximum − Minimum.

⇒ Total Sum of four numbers = 90 × 4 = 360 ⇒ Let the four distinct numbers be x1 < x2 < x3 < x4 ⇒ Given x4 = 120 ⇒ x1 + x2 + x3 + 120 = 360 ⇒ x1 + x2 + x3 = 240 ⇒ To maximize Range (x4 − x1), we must minimize x1 ⇒ To minimize x1, we maximize x2 and x3 such that x1 < x2 < x3 < 120 ⇒ Max possible integer values are x3 = 119 and x2 = 118 ⇒ x1 = 240 − (119 + 118) = 240 − 237 = 3 ⇒ Maximum Range = 120 − 3 = 117 ∴ The correct answer is 117.

Calculation:

105 × 2 ÷ (3 × 5) - 6

⇒ 105 × 2 ÷ (15) - 6

⇒ 105 × 2/15 - 6

⇒ 7 × 2 - 6

⇒ 14 - 6

⇒ 8  

Shortcut Trick ⇒ 105 × 2 / (3 × 5) - 6

⇒ (210 / 15) - 6

⇒ 14 - 6 = 8

Let,

Present age of Mohan = x

Mohan’s age 10 years ago = x – 10

Mohan’s mothers age, 10 years ago = 4x – 40

Mohan’s age after 10 year = x + 10

Mohan’s mothers age, after 10 years = 2x + 20

Mohan’s mother’s present age = 4x – 40 + 10 = 2x + 20 – 10

4x – 40 + 10 = 2x + 20 – 10

2x = 10 + 30

x = 40 ÷ 2 = 20

Hence, 20 is the correct answer.

Shortcut Trick

Rise in water level = Volume of immersed object ÷ Base Area of vessel

Volume of cube = 9 × 9 × 9 = 729 cm³

Base area of vessel = 12 × 15 = 180 cm²

Rise = 729 ÷ 180 = 4.05 cm

∴ The correct answer is 4.05 cm.

Alternate Method

Given:

Edge of the cube (a) = 9 cm

Dimensions of the rectangular vessel base = 12 cm × 15 cm

Formula Used:

Volume of cube = a³

Volume of water displaced = Base Area × Rise in height

Calculations:

⇒ Volume of the cube = 9 × 9 × 9 = 729 cm³

⇒ Let the rise in water level be h cm.

⇒ Volume of water displaced = 12 × 15 × h

⇒ 180 × h = 729

⇒ h = 729 ÷ 180

⇒ h = 4.05 cm

∴ The correct answer is 4.05 cm.

Additional Information

Archimedes Principle in Mensuration

When a solid is completely immersed in a liquid, the volume of liquid displaced is exactly equal to the volume of the solid.

Volume of Cuboid

The volume of a rectangular vessel (cuboid) is given by Length × Breadth × Height.

Base Area Relationship

For any uniform cross-section vessel, Rise in level = Volume added ÷ Area of base.

8^th, 12^th,13^th,15^th letters from left are, O T M E

Meaningful word will be, TOME.

M is at 3^rd place.

Hence, M is the correct answer.

Shortcut Trick

The first 25 whole numbers are 0, 1, 2, 3, ..., 24.

This is an Arithmetic Progression (AP) with first term (a) = 0 and last term (l) = 24.

For any AP, the Median is equal to the Arithmetic Mean of the first and last terms.

Median = (First term + Last term) ÷ 2

Median = (0 + 24) ÷ 2 = 12.

∴ The correct answer is 12.

Alternate Method

Given: First 25 whole numbers.

Formula Used:

Median (when n is odd) = ((n + 1) ÷ 2)^th term.

⇒ First 25 whole numbers = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}

⇒ Total terms (n) = 25 (which is odd)

⇒ Median = ((25 + 1) ÷ 2)^th term

⇒ Median = (26 ÷ 2)^th term = 13^th term

⇒ Since the sequence starts from 0, the k^th term = k − 1

⇒ 13^th term = 13 − 1 = 12

∴ The correct answer is 12.

Additional Information

Whole Numbers

Whole numbers include all natural numbers (1, 2, 3...) along with zero (0). The first n whole numbers always range from 0 to (n − 1).

Median for Even n

If n is even, the median is the average of the (n/2)^th and (n/2 + 1)^th observations.

Mean of First n Whole Numbers

The arithmetic mean of the first n whole numbers is given by the formula: (n − 1) ÷ 2.

• The lens is a transparent device which has two curved surfaces, It is usually made of glasses or plastics.
• In the lense, a ray of light is getting refract.
• It has two focal lengths, on both sides of the lens.
• Mirror- It can be a curved surface or plane, and here a ray of light is getting reflected back in the same medium.
• The mirror can have a maximum one focal length.

Shortcut Trick

Difference in percentage = 80% − 75% = 5%

This 5% difference is caused by 2 students.

∴ 5% → 2 students

Total students (100%) = 2 × 20 = 40 students.

∴ The correct answer is 40.

Alternate Method

Given: Initial pass percentage = 75%, New pass percentage = 80%, Difference in count = 2 students.

Let the total number of students in the class be x.

⇒ 75% of x + 2 = 80% of x

⇒ 0.75x + 2 = 0.80x

⇒ 0.80x − 0.75x = 2

⇒ 0.05x = 2

⇒ x = 2 ÷ 0.05

⇒ x = 200 ÷ 5 = 40

∴ The correct answer is 40.

Additional Information

Percentage Change

To find the total value when a percentage change is given: Total = (Change in Value ÷ Change in Percentage) × 100.

Base Value Concept

Always ensure the percentages refer to the same base value (total students) before subtracting or adding them directly.

• The Mission Olympic Cell (MOC) of the Union Ministry of Sports and youth affairs included the Men’s Hockey team of India in the Target Olympic Podium Scheme(TOPS).
• The decision has been taken after reviewing the improved performance as they had finished the runners up in the champion trophy in the Netherlands.
• Under the TOPS, 18 team member will be given 50,000 Rs. each monthly allowance.
• TOPS was launched within the ministry of sports within the ambit of the National sports of Development Fund.

• The pH will decrease if its Hydrogen ion concentration is increased.
• If we are increasing the concentration of the Hydrogen ion, then the pH value of the solution is getting decrease because the system is getting more acidic.
• When we are mixing the acid with the water, then the H-Plus ion is getting dissociate from the acid and starts to bonding with water and they form the hydronium ions.

Shortcut Trick:

• The least reactive element of the periodic table is Noble gases.
• It is not reacting with the other elements in the normal state, for this reason, they are also called the inert gases.
• The octave of the noble gases are completely filled, so they don’t have a tendency to loss of an electron, or gain of electron or share of the electron, so the noble gases are nonreactive in nature under the normal condition.

CONCEPT:

Newton’s First law:

• A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.
• If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
• Newton’s first law defines inertia and is rightly called the law of inertia.

Newton’s Second Law:

• The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.
• If a body of mass m moves with velocity $\vec v$ then its linear momentum can be given by $\vec p = m\vec v$ and if force $\vec F$ is applied on a body, then

$\therefore \vec F = m\vec a$

Where F = Force, m = mass  and a = acceleration

Newton’s Third Law:

• To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
• When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first.
• Forces in nature always occur in pairs. A single isolated force is not possible.

EXPLANATION:

• From above it is clear that Newton’s second law of motion explains about change in momentum. Therefore option 4 is correct

Shortcut Trick

Difference Method: The HCF must be a factor of the difference between the numbers.

Difference = 176 − 132 = 44

Check if 44 divides both numbers: 132 ÷ 44 = 3 and 176 ÷ 44 = 4.

Since 44 divides both, it is the Highest Common Factor.

∴ The correct answer is 44.

Alternate Method

Given: Numbers are 132 and 176.

Method: Prime Factorization

⇒ Prime factorization of 132 = 2 × 2 × 3 × 11

⇒ Prime factorization of 176 = 2 × 2 × 2 × 2 × 11

⇒ Common factors = 2 × 2 × 11

⇒ HCF = 4 × 11 = 44

∴ The correct answer is 44.

Additional Information

HCF and LCM Relation

The product of two numbers is equal to the product of their HCF and LCM. Formula: n₁ × n₂ = HCF × LCM.

Successive Division Method

Divide the larger number by the smaller number, then divide the previous divisor by the remainder until the remainder is 0. The last divisor is the HCF.

HCF of Fractions

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

Shortcut Trick

Actual Travel Time = Total Distance ÷ Average Speed = 420 ÷ 60 = 7 hours.

Total Break Time = Total Journey Time − Travel Time = 8 − 7 = 1 hour = 60 minutes.

Break Ratio (Shorter : Longer) = 1 : 3 → Total units = 4.

Long break = (3 ÷ 4) × 60 minutes = 45 minutes.

∴ The correct answer is 45 minutes.

Alternate Method

Given: Total distance = 420 km, Total time allowed = 8 hours, Average speed = 60 km/h.

Formula: Time = Distance ÷ Speed

⇒ Time spent driving = 420 ÷ 60 = 7 hours

⇒ Total rest time = Total journey time − Driving time = 8 − 7 = 1 hour

⇒ Convert to minutes: 1 hour = 60 minutes

⇒ Let long break be 3x and shorter break be x

⇒ x + 3x = 60 ⇒ 4x = 60 ⇒ x = 15 minutes

⇒ Long break = 3 × 15 = 45 minutes

∴ The correct answer is 45 minutes.

Additional Information

Average Speed with Stoppages

Average speed including stoppages is always less than the speed excluding stoppages. Stoppage time per hour = (Speed_excl − Speed_incl) ÷ Speed_excl.

Time, Speed, and Distance Relation

Distance = Speed × Time. To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Ratio Division

To divide a quantity Q in ratio a:b, the parts are [a/(a+b)] × Q and [b/(a+b)] × Q.

The correct answer is 2000 J – 5000 J

Concept:

• Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.

The expression for kinetic energy is given by:

$KE = \frac{1}{2}m{v^2}$

Where m = mass of the body and v = velocity of the body

Calculation:

As per the given question,

• We know that the average weight of the man is between 50 - 65 kg,
• Hence the average weight of the athlete = 60 kg
• Distance covered by man = 100 m
• Time is taken by the athlete to cover 100 m = 10 sec
• Let the initial speed of the athlete = 0 m/ sec

Speed = 100/10 = 10 m/s

Now we can calculate the kinetic energy,

Now, applying the conservation of energy =

K.E = 1/2 mv²

K.E = 1/2 × 60 × 10² = 3000 J

Hence option 4 (2000 J – 5000 J) is the correct answer.

Shortcut Trick

For half-yearly compounding, the rate becomes 5% (10% ÷ 2) and the time becomes 2 periods (1 year × 2).

Using the fraction method: 5% = 1/20. So, the Principal to Amount ratio for one period is 20 : 21.

For 2 periods, the ratio is 20² : 21² ⇒ 400 : 441.

Given Maturity Amount (441 units) = Rs. 44,100 ⇒ 1 unit = Rs. 100.

Sum invested (400 units) = 400 × 100 = Rs. 40,000.

∴ The correct answer is Rs. 40000.

Alternate Method

Given:

Maturity Amount (A) = Rs. 44,100

Rate of Interest (R) = 10% per annum

Time Period (T) = 1 year

Compounding: Half-yearly

Formula Used:

A = P(1 + r/100)ⁿ

Where r = half-yearly rate (R/2) and n = number of half-years (2T).

Calculations:

⇒ Effective Rate (r) = 10% ÷ 2 = 5%

⇒ Total periods (n) = 1 × 2 = 2 half-years

⇒ 44100 = P(1 + 5/100)²

⇒ 44100 = P(1 + 1/20)²

⇒ 44100 = P(21/20)²

⇒ 44100 = P × (441 / 400)

⇒ P = (44100 × 400) / 441

⇒ P = 100 × 400

⇒ P = 40,000

∴ The correct answer is Rs. 40000.

Additional Information

Effective Rate for Half-Yearly Compounding

When interest is compounded half-yearly, the effective annual rate is always slightly higher than the nominal rate, calculated as R_eff = (1 + r/200)² − 1.

Compound Interest Formula Variations

For quarterly compounding, the rate is divided by 4 and the time is multiplied by 4 in the formula A = P(1 + R/400)^4T.

Comparison with Simple Interest

For the first year with annual compounding, SI and CI are equal. However, for half-yearly compounding, CI is greater than SI even in the first year.

Betwa, Chambal and Yamuna are rivers which flow inside india.

But Jhelum has some part in Pakistan too.

Hence, Jhelum is the correct answer.

• The NHAI(National Highways Authority of India) has created a National Highways Investment Promotion Cell (NHIPC) for attracting domestic and foreign investment for highways projects.
• The main focus of the government to attract global investors in road infrastructure projects.
• The govt is ambitious to make a 35000 km road with an investment of 535000 crore rs under the project of Bharatmala.

The statement does not mention anything about the taste or the temperature of the tea in the cup.

Hence, neither conclusion I nor conclusion II follows.

Family tree diagram,

Hence, daughter is the correct answer.

Professor, Student, Player.

A professor can also be student to someone else and can also be a player.

A student can be a professor and a player.

Hence, option 3 is the correct answer.

• SheshAnandMadhukar is a Magahi writer who was honored with the Sahitya Academy BhasaSamman Award in January 2018.
• Madhukar conferred this award by Sahitya Academy President ViswanathPrashad Tiwari.
• Madhukar started his career from BSK college as a professor of Hindi literature. His contribution to the research and development of the Magahi language is very significant.
• He has written a few famous books like- Magahi KavitaKeBimb, Eklavya, andBhagwanBirsa.

Pattern followed here is,

Similarly,

Hence, KCOLC is the correct answer.

VI, IX, VII are roman number.

7 is not a roman number.

Hence, 7 is the correct answer.

Shortcut Trick

Total Work (LCM of 36, 90, 60) = 180 units.

Efficiency of Sarthak = 180 ÷ 36 = 5 units/day.

Efficiency of Vivan = 180 ÷ 90 = 2 units/day.

Efficiency of Ali (Outlet) = −(180 ÷ 60) = −3 units/day.

Combined Efficiency = 5 + 2 − 3 = 4 units/day.

Time taken = 180 ÷ 4 = 45 days.

∴ The correct answer is 45 days.

Alternate Method

Given:

Time taken by Sarthak (Positive work) = 36 days

Time taken by Vivan (Positive work) = 90 days

Time taken by Ali (Negative work/Emptying) = 60 days

Formula Used:

Total Efficiency = Efficiency_Sarthak + Efficiency_Vivan − Efficiency_Ali

Time = Total Work ÷ Total Efficiency

Calculations:

⇒ Total Work = LCM(36, 90, 60) = 180 units

⇒ Net efficiency of all three = 5 + 2 − 3

⇒ Net efficiency = 4 units/day

⇒ Time required to fill the pit = 180 ÷ 4

⇒ Time = 45 days

∴ The correct answer is 45 days.

Additional Information

Pipes and Cisterns Logic

Filling a sandpit is analogous to inlet pipes, while removing sand is analogous to an outlet pipe. Work done by an outlet pipe is always taken as negative.

LCM Method for Time and Work

To find Total Work, calculate the Least Common Multiple of individual time periods. Efficiency is then calculated as Total Work ÷ Individual Time.

Net Work Done

If A and B are filling and C is emptying, 1/Total Time = 1/A + 1/B − 1/C.

• Godavari, Krishna, Kaveri, and Vaigai are flowing in the direction of the East.
• Godavari river- Godavari river is India's second-largest river after the Ganga, it originates from the Triambakeshwar, Maharastra and ends at the way of Bengal.
• Krishna river- The river Krishna is the 3^rd longest river India after the Brahmaputra, Ganga and Godavari. The source of this river is Mahabaleshwar, Maharastra and ends at the Bay of Bengal, it is also called the Krishnaveni.
• **Kaveri-**This the third-longest river in south India after the Godavari and Krishna, this river originates from Tala Kaveri and ends at the Bay of Bengal.

Shortcut Trick

Let a rational number be 2 and an irrational number be √3.

Sum = 2 + √3

Since the sum contains a non-terminating and non-repeating decimal part, the result is always irrational.

∴ The correct answer is Irrational number.

Alternate Method

Given: A rational number (r) and an irrational number (i).

Property: The sum of any rational number and any irrational number is always an irrational number.

⇒ Let r = p/q (where p, q are integers and q ≠ 0)

⇒ Let s = r + i

⇒ If we assume s is rational, then i = s − r

⇒ Since the difference of two rational numbers is always rational, this would mean i is rational.

⇒ This contradicts the fact that i is irrational.

⇒ ∴ The sum must be irrational.

∴ The correct answer is Irrational number.

Additional Information

Product of Rational and Irrational

The product of a non-zero rational number and an irrational number is always irrational.

Sum of two Irrational Numbers

The sum of two irrational numbers may be rational or irrational (e.g., √2 + (−√2) = 0, which is rational).

Definition of Rational Numbers

Numbers that can be expressed in p/q form where p and q are integers and q ≠ 0.

Shortcut Trick

To find the value of z, we need the value of the variable a from Statement 1.

Statement 2 provides the value of x = 8, which allows us to calculate a = x² = 64.

By combining both, z² = 36 + 64 = 100, which gives z = ± 10.

Neither statement alone can provide the value of z as they contain interdependent unknowns.

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

Alternate Method

Given:

Statement 1: z² = 36 + a

Statement 2: a = x² and x = 8

Calculations:

From Statement 1 alone:

⇒ z² − a = 36

⇒ There are two variables and only one equation, so z cannot be determined.

From Statement 2 alone:

⇒ x = 8

⇒ a = 8² = 64

⇒ This provides the value of a but no information about z.

Combining Statement 1 and Statement 2:

⇒ Substitute a = 64 into the equation from Statement 1.

⇒ z² = 36 + 64

⇒ z² = 100

⇒ z = √100 = ± 10

⇒ Since the value of z can be determined using both statements together, they are sufficient.

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

Additional Information

Data Sufficiency Rules

A question is sufficient if a unique value or a consistent set of values can be derived. If multiple statements are needed to solve for variables, they are mutually dependent.

Algebraic Equations

To solve for n unknown variables, at least n independent equations are required. Here, z, a, and x are three variables requiring three relationships (provided by the two statements).

Square Roots

When solving x² = k, the roots are always ±√k. In data sufficiency, finding a specific range or set of roots is often considered a sufficient result.

• When the pH of the mouth is less than 5.5, then tooth decay starts. Because the bacteria present in the mouth produce acids by the degradation of sugar and food particles remaining in the mouth after eating. The acid produced in the mouth attack the enamel results in creating tooth decay.
• Tooth enamel made of calcium phosphate is the hardest substance in the body.
• Using toothpaste, which are generally basic, helps neutralize the excess acid and prevent tooth decay.

Shortcut Trick

Total Work (LCM of 70, 52.5, 42) = 210 units.

Efficiencies: (A+B) = 3, (B+C) = 4, (C+A) = 5.

2(A+B+C) = 3 + 4 + 5 = 12 ⇒ A+B+C = 6.

Individual efficiencies: C = 6−3 = 3, A = 6−4 = 2, B = 6−5 = 1.

Days: A = 210÷2 = 105, B = 210÷1 = 210, C = 210÷3 = 70.

∴ The correct answer is 105, 210 and 70 days.

Alternate Method

Given: (A+B) = 70 days, (B+C) = 52.5 (or 105/2) days, (C+A) = 42 days.

Formula Used: Efficiency = Total Work ÷ Time

⇒ Summing efficiencies: 2(A + B + C) = 3 + 4 + 5 = 12

⇒ A + B + C = 6

⇒ Efficiency of A = (A+B+C) − (B+C) = 6 − 4 = 2

⇒ Efficiency of B = (A+B+C) − (A+C) = 6 − 5 = 1

⇒ Efficiency of C = (A+B+C) − (A+B) = 6 − 3 = 3

⇒ Time taken by A = 210 ÷ 2 = 105 days

⇒ Time taken by B = 210 ÷ 1 = 210 days

⇒ Time taken by C = 210 ÷ 3 = 70 days

∴ The correct answer is 105, 210 and 70 days.

Additional Information

Combined Work Principle

When individuals work in pairs, summing their combined efficiencies gives twice the total efficiency: 2(A+B+C) = E_(A+B) + E_(B+C) + E_(C+A).

LCM Method for Fractions

To find the LCM of fractions like 105/2 and 70, take (LCM of Numerators) ÷ (HCF of Denominators).

Work and Wages

Wages are always distributed in the ratio of the efficiencies of the workers if they work for the same amount of time.

CONCEPT:

• Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
• These equations are only valid when the acceleration of the body is constant and they move on a straight line.

There are three equations of motion:

V = u + at

V2 = u2 + 2 a S

${\text{S}} = {\text{ut}} + \frac{1}{2}{\text{a}}{{\text{t}}^2}$

Where, V = final velocity, u = initial velocity, s = distance travelled by the body under motion, a = acceleration of body under motion, and t = time taken by the body under motion.

EXPLANATION:​

• From the above explanation, it is clear that the equation given in option 1 is not the equation of motion. So option 1 is correct.

• The Jungle Book is the children’s movie features the famous song “The Bare Necessities”.
• This song is written by Gilkyson from the animated Disney film the Jungle book.
• This song was sung by Phil Harris as Baloo and Bruce Reitherman as the Mowgli.
• The movie Jungle featured by the Doctor Dolittle and composed by Terry Gilkyson.