RRC Group D Previous Year Paper 48 (Held On: 11 Dec 2018 Shift 2)

Shortcut Trick

A fraction in its simplest form is a terminating decimal if the prime factors of its denominator are only 2 and/or 5.

Check denominators: 24 = 2³×3, 32 = 2⁵, 96 = 2⁵×3, 48 = 2⁴×3.

Only 1/32 has a denominator with no prime factors other than 2.

∴ The correct answer is 1/32.

Alternate Method

Given: Fractions (1) 1/24, (2) 1/32, (3) 1/96, (4) 1/48.

Concept: For a fraction p/q to be a terminating decimal, q must be of the form 2ⁿ × 5^m, where n and m are non-negative integers.

⇒ Option 1: 1/24 → 24 = 2³ × 3 (Contains 3, so non-terminating)

⇒ Option 2: 1/32 → 32 = 2⁵ × 5⁰ (Contains only 2, so terminating)

⇒ Option 3: 1/96 → 96 = 2⁵ × 3 (Contains 3, so non-terminating)

⇒ Option 4: 1/48 → 48 = 2⁴ × 3 (Contains 3, so non-terminating)

∴ The correct answer is 1/32.

Additional Information

Non-terminating Repeating Decimals

If the prime factorization of the denominator contains factors other than 2 or 5, the decimal expansion is non-terminating repeating (recurring).

Simplified Form Requirement

Always ensure the fraction is in its simplest form (p and q are co-prime) before checking the factors of the denominator.

Decimal Value of 1/32

1/32 = 1/2⁵ = (1 × 5⁵) / (2⁵ × 5⁵) = 3125 / 100000 = 0.03125.

Shortcut Trick

Given: LCM = 3 × HCF and LCM × HCF = 867

⇒ (3 × HCF) × HCF = 867 ⇒ 3 × HCF² = 867

⇒ HCF² = 289 ⇒ HCF = 17

⇒ LCM = 3 × 17 = 51

Since the numbers are factors of LCM and multiples of HCF, and HCF is 17 while LCM is 51, the numbers are 17 and 51.

∴ The correct answer is 17, 51.

Alternate Method

Given:

⇒ Let HCF be h and LCM be L.

⇒ L = 3h

⇒ L × h = 867

Formula Used:

⇒ Product of two numbers = HCF × LCM

Calculations:

⇒ Substituting L = 3h in the product equation:

⇒ 3h × h = 867

⇒ 3h² = 867

⇒ h² = 867 ÷ 3 = 289

⇒ h = √289 = 17

⇒ L = 3 × 17 = 51

⇒ Since LCM is a multiple of both numbers and HCF is a factor, and the product of numbers equals L × h,

⇒ The numbers must be 17 and 51 as 17 × 51 = 867 and HCF(17, 51) = 17.

∴ The correct answer is 17, 51.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, a × b = HCF(a, b) × LCM(a, b). Also, HCF is always a factor of LCM.

Co-prime Numbers

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

HCF of Fractions

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

The correct answer is Virtual.

Key Points

• When the object is placed between the principal focus (F) and the pole of a concave mirror, an enlarged, virtual and erect image is formed behind the mirror.

• The position of the image is behind the mirror.

• The image will be Enlarged, Virtual, Erect.

Given,

8 December 2007 was a Saturday, then what was the day on 12 August 2008.

Here we see the number of odd days from 8 December 2007 to 12th August 2008 are,

Total number of days,

8 ^th December 2007 to 31^th December = 23 days

January 2008 = 31 days

February 2008 = 29 days

March 2008 = 31 days

April 2008 = 30 days

May 2008 = 31 days

June 2008 = 30 days

July 2008 = 31 days

August 2008 = 12 days

∴ Total number of days = 23 + 31 + 29 + 31 + 30 + 31 + 30 + 31 + 12 = 248

∴ Number of odd days = 248 ÷ 7 = 3 odd days

Saturday + 3 odd days = Tuesday 

<br>

∴ The 12^th August 2008 was Tuesday

Hence, the correct answer is Tuesday.

Shortcut Trick

The expression x² − y² is a standard algebraic identity equivalent to (x + y)(x − y).

To find its value, we directly need the sum (x + y) and the difference (x − y) of the variables.

Statement 1 provides the sum (2) and Statement 2 provides the difference (6).

Value = 2 × 6 = 12, which requires information from both statements.

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

Alternate Method

Given:

Statement 1: x + y = 2

Statement 2: x − y = 6

Formula Used:

a² − b² = (a + b)(a − b)

Calculations:

⇒ We need to determine the value of the expression x² − y².

⇒ From the algebraic identity, x² − y² = (x + y) × (x − y).

⇒ If we use only Statement 1, we know (x + y) = 2, but the value of (x − y) remains unknown.

⇒ If we use only Statement 2, we know (x − y) = 6, but the value of (x + y) remains unknown.

⇒ By combining both statements, we can substitute the values into the identity: x² − y² = 2 × 6 = 12.

⇒ Since a specific numerical value is obtained only when both statements are used, they are together sufficient.

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

Additional Information

Difference of Two Squares

The identity a² − b² = (a + b)(a − b) is a fundamental tool in algebra for simplifying expressions and solving quadratic equations.

Linear Equations in Two Variables

When given x + y = A and x − y = B, the individual values can be found using x = (A + B) ÷ 2 and y = (A − B) ÷ 2.

Data Sufficiency Strategy

In Data Sufficiency, always check if the required expression can be formed directly from the given statements before attempting to find individual variable values.

Given,

Hand, Nose, Heart, Eyes

Here we see all the body parts are external except the heart.

The heart is internal body part therefore it is odd or mismatch from others.

Hence, the correct answer is the heart.

The correct answer is The fraction of molecules increases with the most possible speed.

Key Points

• On increasing the temperature, the motion of the gas molecules becomes rapid and hence the value of the most probable velocity also increases.
• As a result, the entire distribution curve becomes flatter, and peak shifts to regions of higher velocities
• As the temperature of the gas increases, the particles gain kinetic energy, and their speed increases.
• The most probable speed is directly proportional to the square root of temperature.
• The area under the distribution curve remains the same as under the lower temperature.
• The total area under the curve is independent of the temperature.
• The area under the distribution curve represents the total number of molecules.

The correct answer is Malabar.

Key Points

• The Malabar coast in Kerala is a beautiful backwater lined with coconut trees.
• Backwaters in Kerala are a network of 1500 km of canals both artificial and natural, with 38 rivers and 5 big lakes extending from one end of Kerala.
• Malabar Coast, a name long applied to the southern part of India's western coast, is approximately from the state of Goa southward, which is bordered on the east by the Western Ghats range.

Important Points

The correct answer is Bharat Watwani.

Key Points

• Bharat Watwani and Sonam Wangchuk were won the Ramon Magsaysay Award 2018.
• Bharat Vaswani was recognized for his tremendous courage and healing compassion in embracing India's mentally-afflicted destitute.
• Sonam Wangchuck's initiative to harness science and culture creatively for economic progress improved the lives of the Ladakhi youth.

Important Points

• The Ramon Magsaysay Award, Asia’s premier prize, and highest honor celebrate the greatness of spirit and transformative leadership in Asia.
• The Award is presented to them in formal ceremonies in Manila, the Philippines on August 31st, the birth anniversary of the much-esteemed Philippine President whose ideals inspired the Award’s creation in 1957.

Additional Information

• In 2019, Ravish Kumar an Indian Journalist, author, and media personality got this prestigious award.
• Human rights activist, Vinoba Bhave was the 1st Magsaysay Award winner in 1958.
• In the year 2000, Aruna Roy got this award in the field of Community Leadership.
• In the year 2001, Rajendra Singh got this award in the field of Community Leadership.
• In the year 2008, Prakash Amte got this award in the field of Community Leadership.

Calculation:

4.5 + 0.45 + 0.045 + 0.0045 = ?

⇒ 4.9995

∴ The required value is 4.9995

Calculation:

(11/13) + (13/11) = ?

⇒ LCM of 13 and 11 = 143

So, [(11 × 11) + (13 × 13)]/143 = ?

⇒ [121 + 169)/143 = ?

⇒ 290/143 = ?

∴ The value of ? is 290/143

The correct answer is Lucknow.

Key Points

• The largest school in terms of pupils is the City Montessori School in Lucknow, Uttar Pradesh, India, which had 55,547 pupils as of 16 January 2019 across 18 campuses in the city.

Additional Information

• The school was founded by Dr. Jagdish Gandhi and his wife Dr. Bharti Gandhi.
• The pair launched their first campus in 1959 in rented premises with only five students.
• City Montessori School is celebrating its Diamond Jubilee in 2019.
• The school was the recipient of the 2002 UNESCO Prize for Peace Education – the only school ever to have received this award.

Given,

The farmer left a cow to walk west. The cow started grazing. After some time, the cow started moving to its right and reached a position that was 90 degrees from its starting position.

∴ 

 

Here we see cow is facing North direction.

Hence, the correct answer is North.

Shortcut Trick

Initial Ratio of Cu : Zn : Ni = 4 : 3 : 2 (Sum = 9 units).

9 units = 54 kg ⇒ 1 unit = 6 kg.

Since only zinc is added, multiply final ratio 2 : 5 : 1 by 2 to equate Cu and Ni units.

New equivalent ratio = 4 : 10 : 2.

Increase in Zinc = 10 − 3 = 7 units ⇒ 7 × 6 kg = 42 kg.

∴ The correct answer is 42 kg.

Alternate Method

Given:

Total weight of initial mixture = 54 kg

Initial ratio of Cu : Zn : Ni = 4 : 3 : 2

Initial (54 kg) Cu: 24 kg Zn: 18 kg Ni: 12 kg

• x kg Zinc

Final (2:5:1) Cu: 24 kg Zn: 18 + x kg Ni: 12 kg

Cu and Ni amounts remain constant

Calculations:

⇒ Sum of initial ratio parts = 4 + 3 + 2 = 9 parts

⇒ Initial Copper = (4 ÷ 9) × 54 = 24 kg

⇒ Initial Zinc = (3 ÷ 9) × 54 = 18 kg

⇒ Initial Nickel = (2 ÷ 9) × 54 = 12 kg

⇒ Let the amount of zinc added be x kg.

⇒ New amount of Zinc = (18 + x) kg

⇒ Given the new ratio of Copper : Zinc : Nickel is 2 : 5 : 1

⇒ Taking proportion of Copper and Zinc: 24 ÷ (18 + x) = 2 ÷ 5

⇒ 2 × (18 + x) = 24 × 5

⇒ 36 + 2x = 120

⇒ 2x = 120 − 36

⇒ 2x = 84

⇒ x = 42 kg

∴ The correct answer is 42 kg.

Additional Information

Ratio Equalization Method

When a pure quantity is added to a mixture, the quantities of other components remain unchanged. Multiplying the new ratio to match the unchanged components gives the direct increase in units.

Proportion Rule

If A : B : C = x : y : z, then A ÷ x = B ÷ y = C ÷ z. This property is used to directly equate two components and solve for the unknown value.

Mixtures & Replacement

When a portion of a mixture is removed, the remaining mixture still retains the same ratio as the original mixture before any pure component is added.

Shortcut Trick

Net efficiency = Efficiency of Pipe M − Efficiency of Pipe N

Total Capacity (LCM of 45, 90) = 90 units

Efficiency M = 90 ÷ 45 = 2; Efficiency N = 90 ÷ 90 = 1

Time to fill half tank (45 units) = 45 ÷ (2 − 1) = 45 hours

∴ The correct answer is 45 hr.

Alternate Method

Given: Tank is half empty (which means it is also half full).

⇒ Work to be done = Total Capacity ÷ 2

⇒ Work = 90 ÷ 2 = 45 units

⇒ Combined Efficiency of (M + N) = 2 − 1 = 1 unit/hr

⇒ Time taken = Work ÷ Combined Efficiency

⇒ Time taken = 45 ÷ 1 = 45 hours

∴ The correct answer is 45 hr.

Additional Information

Inlet and Outlet Pipes

Efficiency of an Inlet pipe is always positive, while the efficiency of an Outlet pipe (leak) is considered negative.

Time and Work Relation

Time taken = Total Work ÷ Net Efficiency. If net efficiency is positive, the tank fills; if negative, the tank empties.

Given,

Four couples go to a party. All the women are wearing different colour sarees. All men are wearing different coloured shirts. The colour of a shirt and a saree can be the same. Consider all the statements given below and answer the questions.

Statement:

1. Rama is married to Ramesh who is wearing a red shirt.
2. Purva, who is not Anup's wife, is wearing a blue sari.
3. Anup and Shreya are wearing green clothes.
4. Sandesh's wife Mrunmayi has not worn a yellow sari.
5. Vijay is wearing a yellow shirt.

Here we see Anup is Shreya's husband.

Hence, the correct answer is Anup.

The correct answer is Sublimation.

Key Points

• Sublimation is the conversion between the solid and the gaseous phases of matter, with no intermediate liquid stage.
• Example: Snow and ice changing into water vapor in the air without first melting into water.

Important Points

Additional Information

• The opposite of sublimation is "deposition", where water vapor changes directly into the ice—such as snowflakes and frost.

The correct answer is C₄H₁₀.

Key Points

• Compounds with different physical properties were found to have the same elemental composition and molecular weight. Such compounds were called isomers.
• The below table shows the number of constitutional isomers for each of the acyclic alkanes C_nH_2n+2, where n=1-10.
• The molecular formula of isobutane C4H10.

Additional Information

• If the number of carbon atoms increases, the number of possible constitutional isomers increases rapidly.

Given:

16³ ÷ 8³ ÷ 2² = ?

Concept used:

x^a ÷ x^b = x^{(a - b)}

x^a × x^b = x^{(a + b)}

Calculation:

⇒ (2⁴)³ ÷ (2³)³ ÷ 2² = ?

⇒ 2¹² ÷ 2⁹ ÷ 2² = ?

⇒ 2³ ÷ 2² = ?

⇒ 2¹ = ?

∴ The value of ? is 2¹

The correct answer is the f - Block element.

Key Points

• There are thirty total elements in the lanthanides and actinides. They are often called the "inner transition metals".
• Lanthanides:
• The lanthanides are the elements with atomic numbers from 57 to 71.
• These 15 metals (along with scandium and yttrium) are often called the rare earth elements.
• They are all silvery-white metals that are often found in the same ores.
• They are called the lanthanides because they exhibit similar chemical properties to lanthanum, the first element in the group.
• Actinides:
• Actinides are the 15 elements with atomic numbers from 89 to 103.
• They are named after the first element in the series, actinium.
• The actinides group includes mostly man-made elements with only a few exceptions such as uranium and thorium.
• The actinides are most known for the elements uranium and plutonium which are used in nuclear reactors and nuclear bombs.

Additional Information

• The actinide americium is used in smoke detectors.
• Both actinides and lanthanides are highly reactive with elements from the halogen group.
• All of the lanthanides have at least one stable isotope except for promethium.
• None of the actinides have a stable isotope. They are all radioactive.

The correct answer is Hydra.

Key Points

• Organisms such as hydra use regenerative cells for reproduction in the process of budding.

• Budding, in biology, a form of asexual reproduction in which a new individual develops from some generative anatomical point of the parent organism.

• Hydra and Yeast both use Budding for reproduction.

• But Hydra uses its regenerated cells, it will regeneration upon being cut into pieces, but the yeast will not survive and will simply die.

Additional Information

• Yeast is single-celled microorganisms that are classified, along with moulds and mushrooms, as members of the Kingdom Fungi.
• It is called Saccharomyces cerevisiae, which needs food, warmth, and moisture to thrive.
• It converts its food—sugar and starch—through fermentation, into carbon dioxide and alcohol. It's the carbon dioxide that makes baked goods rise.
• Planarian flatworms are well known for their amazing regenerative capacity that live in freshwater.
• It depends on the presence of stem cells called neoblasts.
• Amoebae are eukaryotes protozoans of the rhizopodan order Amoebida.
• It is found on decaying bottom vegetation of freshwater streams and ponds.
• Amoeba can be both fungi, animals, and algae.

Given,

4 W X Z 8 Q P O J 6 G T M V E U H 5 3 B

 

∴ 

Here we see B is the 5th term to the right of 15th term from the left.

Hence, the correct answer is B.

The opposite faces of the cube are,

As Two opposite faces are never seen together or adjacent to each other:

In Option Figure 1 :- Dark circle and cross are opposite faces but here they are seen together which is wrong.

In Option Figure 2 :- Dark circle and cross are opposite faces but here they are seen together which is wrong.

In Option Figures 4 none of the opposite faces are seen together nor they are adjacent to each other.

Thus option figure 4 can be formed by folding the dice.

∴ The correct representation is 

Hence, the correct answer is option 4).

Important Points

• The reflection of an object into the water is its water image.
• It appears by inverting an object vertically i.e. upside down.
• The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Given, 91238769AZ

In the water image, the left and right part of the figure remains the same and the top and bottom part of the figure changes.

∴ 

Hence the correct answer is 

.

The correct answer is 519 meters.

**Speed of Sound = 346 ms^-1     (**A)

Time is taken to echo the be heard = 3 second

• Let’s consider the distance between the boy and rock = d

Now, In order to echo to be heard the sound had to 1^st travel to the rock and then come back.

• This means the sound has to cover distance= 2d

According to the question, Time is taken to travel 2d distance = 3 s

So, Time to travel distance d = 3/2 sec    (B)

Now**, Distance = Speed** × Time

                          = 346 ms^-1 $×3/2$s [From (A) and (B)]

                          = 519 m

So, the distance between the boy and the rock(d) = 519 m

The correct answer is Both 1 and 2 follow.

Key Points

• The consociational theory challenges the two paradigmatic notions that democracy should be equated with majority rule and that democracy is not a viable form of government in deeply divided societies.
• The essence of democracy is majority rule, the making of binding decisions by a vote of more than one-half of all persons who participate in an election.
• Articles of the Indian Constitution can be amended by a simple majority in the Parliament (Second Schedule, Article 100(3), 105, 11, 124, 135, 81, 137).
• It is not less than two-thirds of the members of each House present and voting and a majority of the total membership of each House.

The correct answer is minutes before 11 o'clock.

At 10 o'clock the hour hand is at 10 and the minute hand is at 12.

∴ The minute and hour hand of a clock overlap somewhere between 10 and 11.

That is minutes before 11 o'clock.

Hence the correct answer is minutes before 11 o'clock.

The correct answer is Thalamus.

Key Points

• A flower is the sexual reproductive organ in plants it consists of four basic parts:
• Sepal - is the outer part of the flower (often green and leaf-like) that encloses a developing bud. It is a defensive organ that encloses and protects the developing reproductive structures.
• Petal - is the part of a flower that is often conspicuously coloured.
• Stamen - is the pollen-producing part of a flower, usually with a slender filament supporting the anther.
• Pistil - is the female reproductive part that consists of stigma, style and ovary.
• Thalamus -
• It is also known as the receptacle.
• It is usually the slightly swollen part of the pedicel or stalk of the flower.
• It is the basis on which all the floral parts are present.

Additional Information

• Placenta - In a flower, placenta is the connection between the ovules in an ovary. While, in human reproduction placenta is a structure that develops in the uterus to provide nutrients to the developing fetus.
• Fallopian Tube - is a part of human reproductive system which connects the ovary to the uterus.

The correct answer is Momentum and force.

Important Points

• Option (a), Speed = Distance / time = ms^-1
  

Velocity = Displacement / time = ms^-1

Thus both have the same unit.

• Option (b), Gravity (g) = ms^-2
  

Acceleration due to gravity = ms^-2

Thus, both have the same unit.

• Optiion (c), Momentum = Mass * Velocity = Kg * ms^-1 = Kgms^-1
  

Force =  Mass * Acceleration = Kg * ms^-2 = Kgms^-2

Thus the unit of Momentum and force is not the same.

• Option (d), Distance = m(meter)
  

Displacement = m(meter)

Thus both have the same unit.

The correct answer is 0,1.

Key Points

• Formula for speed after impact
• v_a  =[ m_au_a + m_bu_b + m_b C_R(u_b - u_a)]/(m_a + m_b)              {1}
• v_b  =[ m_au_a + m_bu_b + m_a C_R(u_a – u_b)]/(m_a + m_b)            {2}
• Where,
• v_a  = Velocity of a after impact
• v_b = Velocity of b after impact
• u_a = Velocity of a before impact
• u_b  = Velocity of b before impact
• C_R = Coefficient of restitution
• M_a =  mass of object a
• M_b  = Mass of object b
• Let us consider,
• Object a = ball and object b = gate
• Now given in question:
• u_{a =}  2m/s
• u_b = 0 m/s
• Let, M_{b =} x the m_b  = 2x
• C_R = 0.5
• Now putting the values in equation {1}
• v_a = [2x + 2x * 0 + 2x * 0.5(0 - 2)]/ x + 2x
• = [2x  – x * 2]/3x
• = [2x – 2x]/3x
• = 0/3x m/s
• = 0 m/s
• v_b  =  [2x + 2x * 0 + x * 0.5(2 - 0)]/ (x + 2x)
• = [2x + 0 + x]/3x
• = 3x/3x
• = 1 m/s
• So, after impact speed of
• Ball = v_a  = 0 m/s
• Gate = v_b = 1 m/s
• Thus the answer is 0, 1.

The correct answer is Saraswati.

Key Points

• The Saraswati River is one of the rivers mentioned in the Rig Veda and later Vedic and post-Vedic texts.
• Saraswati is the name of a river originating in the Aravalli mountain range in Rajasthan, passing through Sidhpur and Patan before submerging in the Rann of Kutch desert.

Important Points

• Sapta Sindhu is the seven rivers that are considered the most sacred ones in India: Indus, Jhelum, Chenab, Ravi, Sutlej, Beas.
• Chenab River, a river of the Indian subcontinent in northwestern India and northeastern and eastern Pakistan.
• The Chenab is formed by the confluence of two streams, Chandra and Bhaga.
• The Yamuna rises on the slopes of the Bandarpunch massif in the Great Himalayas near Yamnotri (Jamnotri) in western Uttarakhand.
• It is the second-largest tributary river of the Ganga and the longest tributary in India.
• Jhelum River, a river of northwestern India and northern and eastern Pakistan.
• the source of this river is Pir Panjal Range and falls into the Chenab River.

Shortcut Trick

Assume Aditya's sum is 1 unit.

Ravi's sum → 16 × 1 = 16 units.

Suraj's sum → 4 × 16 = 64 units.

Ratio of Aditya to Suraj → 1 : 64.

∴ The correct answer is 1 : 64.

Alternate Method

Given:

Suraj (S) = 4 × Ravi (R)

Ravi (R) = 16 × Aditya (A)

Calculations:

⇒ Let Aditya's sum (A) = x

⇒ Ravi's sum (R) = 16x

⇒ Suraj's sum (S) = 4 × (16x) = 64x

⇒ Ratio required = Aditya : Suraj

⇒ Ratio = x : 64x

⇒ Ratio = 1 : 64

∴ The correct answer is 1 : 64.

Additional Information

Compound Ratio

If A:B = a:b and B:C = c:d, then A:C is calculated by multiplying the ratios (a/b × c/d).

Ratio Normalization

To combine ratios like A:B and B:C, make the common term (B) equal in both ratios by multiplying with suitable constants.

Given,

Question: Who among P, N, K and J get the highest payment?

Statement:

1. P earns more than K and J.

P > K, P > J.

2. N earns more than K.

N > K.

From both statement, the order of payment from highest to lowest is,

P > N > K > J ; P > N > J > K 

or

N > P > K > J ; N > P > J > K

Here we see we don't know who gets the highest payment.

∴ Both statements are not correct.

Hence, the correct answer is Statements 1 and 2 both are not correct.

The correct answer is 250 J.

• Given, mass (m) = 20 kg, velocity (v) = 5 ms^-1.
  

Kinetic energy = (½)mv²

So, the kinetic energy of the object is (½)∗20∗52 = 250 J**.**

Key Points

• It is the energy of an object's mass in motion.
• When an objects' mass doubles, its kinetic energy also doubles.
• When an objects' speed doubles, its kinetic energy quadruples.
• When a pendulum goes uphill (top point), it loses kinetic energy.

Shortcut Trick

By the Factor Theorem, if (x − 8) divides the polynomial, then substituting x = 8 must result in zero.

3(8)² + 8a − 12 = 0

192 + 8a − 12 = 0

180 + 8a = 0 ⇒ a = −180 ÷ 8

a = −22.5

∴ The correct answer is −22.5.

Alternate Method

Given:

Polynomial f(x) = 3x² + ax − 12

Divisor = x − 8

Formula Used:

According to the Remainder Theorem, if a polynomial f(x) is divided by (x − k), the remainder is f(k). If it is completely divisible, the remainder is 0.

Calculations:

⇒ x − 8 = 0

⇒ x = 8

⇒ f(8) = 3(8)² + a(8) − 12 = 0

⇒ 3(64) + 8a − 12 = 0

⇒ 192 + 8a − 12 = 0

⇒ 180 + 8a = 0

⇒ 8a = −180

⇒ a = −180 ÷ 8

⇒ a = −22.5

∴ The correct answer is −22.5.

Additional Information

Remainder Theorem

When a polynomial p(x) is divided by a linear divisor (ax − b), the remainder is always p(b/a).

Factor Theorem

A polynomial p(x) has a factor (x − k) if and only if p(k) = 0, which is a specific case of the remainder theorem.

Synthetic Division

A shorthand method of polynomial division, especially when the divisor is a linear factor like (x − k).

Quadratic Identity

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

Shortcut Trick

Identify the alternating pattern: −4, +8, −4, +8.

The sequence follows a repeating logic of subtracting 4 and adding 8.

Last term is 152, so the next operation is +8.

152 + 8 = 160.

∴ The correct answer is 160.

Alternate Method

Given Series: 152, 148, 156, 152, ?

152

−4 →

148

+8 →

156

−4 →

152

+8 →

160

The series follows an arithmetic operation pattern where 4 is subtracted and 8 is added alternately.

⇒ 152 − 4 = 148

⇒ 148 + 8 = 156

⇒ 156 − 4 = 152

⇒ 152 + 8 = 160

∴ The correct answer is 160.

Additional Information

Mixed Series

A series where two or more different operations (like addition and subtraction) are applied alternately to find the next term.

Alternate Series Pattern

Sometimes a series consists of two independent sequences at alternate positions (1st, 3rd, 5th terms and 2nd, 4th, 6th terms).

Common Differences

Always calculate the gap between consecutive terms first to identify if the pattern involves constant or changing increments.

Given,

In the mirror image, the top and bottom part of the figure remains unchanged and left and right part of the figure changes.

∴ 

Hence, the correct answer is A.

Additional InformationIn a mirror image Left changes to right and the right changes to left vice-versa.

When placement of mirror not given, By default we will assume it in Vertical direction.

The Letter adjacent to the mirror after the mirror image will adjacent to it just with the left change to right and right change to left vice-versa.

The starting letter of the word will be at last after the mirror image drawn with left changes to right and right changes to left.

Shortcut Trick

Let Total Work be LCM of 7, 8.75 (35/4), and 10.5 (21/2) = 105 units.

Efficiency of (A + B) = 105 ÷ 7 = 15; Efficiency of A = 105 ÷ 10.5 = 10.

⇒ Efficiency of B = 15 − 10 = 5.

Efficiency of (B + C) = 105 ÷ 8.75 = 12 ⇒ Efficiency of C = 12 − 5 = 7.

Time for Double Work by C = (105 × 2) ÷ 7 = 30 days.

∴ The correct answer is 30 days.

Alternate Method

Given: Time taken by (A + B) = 7 days, (B + C) = 8.75 days, and A = 10.5 days.

Formula Used: Total Work = Efficiency × Time; Efficiency = Work ÷ Time.

⇒ Efficiency of B = Efficiency(A + B) − Efficiency(A)

⇒ Efficiency of B = 15 − 10 = 5 units/day.

⇒ Efficiency of C = Efficiency(B + C) − Efficiency(B)

⇒ Efficiency of C = 12 − 5 = 7 units/day.

⇒ Double Work = 105 × 2 = 210 units.

⇒ Time taken by C = 210 ÷ 7 = 30 days.

∴ The correct answer is 30 days.

Additional Information

Combined Efficiency

When multiple people work together, their individual efficiencies (work done per unit time) are added to find the total work rate.

Work-Efficiency Relation

Time taken to complete a specific piece of work is inversely proportional to efficiency: Time = Work ÷ Efficiency.

LCM Method for Work

Using the LCM of time periods as the total work unit simplifies calculations by converting fractions into whole number efficiencies.

Given,

Gun, Sword, Write, Spade

Here we see all are tools except Write.

Write is a process in which one can communicate.

Hence the correct answer is Write.

The correct answer is Period.

Key Points

• All elements can be classified into one of three classes: metals, metalloids, or nonmetals.
• Elements in each class share certain basic properties. From left to right across each period of the periodic table, elements change from metals to metalloids to nonmetals.

Important Points

• Ionization energy increases on going from left to right and from down to top.
• Electron affinity increases on going from left to right and from down to top.
• The atomic radius increases from right to left and top to bottom
• The atomic radius decreases moving from left to right in the Modern Periodic Table.
• No of valance electron increases as we go left to right in a period.

Additional Information

• A group is a vertical column of the periodic table, based on the organization of the outer shell electrons.
• There are a total of 18 groups.
• Elements with similar chemical properties appear at regular intervals, within the vertical columns.
• A period is a horizontal row of the periodic table.
• There are seven periods in the periodic table, with each one beginning at the far left.
• A new period begins when a new principal energy level begins filling with electrons.
• Period 1 has only two elements (hydrogen and helium).
• Periods 2 and 3 have 8 elements.
• Periods 4 and 5 have 18 elements.
• Periods 6 and 7 have 32 elements.
• Group can be used to characterize an element:
• Group 1: alkali metals, or lithium family
• Group 2: alkaline earth metals, or beryllium family
• Group 3: the scandium family
• Group 15: the pnictogens, or nitrogen family
• Group 16: the chalcogens, or oxygen family
• Group 17: the halogens, or fluorine family
• Group 18: the helium/neon family. These included the Nobel gases for the first six periods

The correct answer is the USA.

Key Points

• The first edition (2018) of the 2+2 dialogue between India-US held in New Delhi.
• In the inaugural meeting, Minister of External Affairs (MEA) Sushma Swaraj and Defence Minister Nirmala Sitharaman hosted US Secretary of State Michael R. Pompeo and US Secretary of Defence James Mattis.

Additional Information

• The third India-Australia Secretary-level 2+2 dialogue was held on 9 December 2019 in New Delhi.
• The Indian side was led by Defense Secretary Ajay Kumar and Foreign Secretary Vijay Gokhale, while its counterpart delegation was led by Australia’s Defense Secretary Greg Moriarty and Foreign Secretary Frances Adamson.

Hint

• The 2+2 dialogue is the second-highest level of engagement between both countries after summit-level engagement between the Prime Minister and the US President.
• 2+2 dialogue is aimed to enhance strategic coordination between both countries and maintaining peace and stability in the Indo-Pacific region.

The shortest distance between point B and point F is - 

After final arrangement:

∴ By Pythagoras theorem,

BF² = BX² + XF²

∴ BF2 = 8² + 8²

∴ BF2 = 64 + 64 = 128 = 8${\sqrt{2} }$

∴ The shortest distance between B and F is 8${\sqrt{2} }$.

Hence, the correct answer is 8√2.

The logic followed here is:

• Odometer used to measure the Distance.

Similarly,

• Ammeter used to measure the current.

Hence, the correct answer is Current.

Given,

Dhawan plans to buy a flat at Shyamla Society.

Shyamala Society has placed the following conditions for allotment of flats in its society:

Applicant:

(I). State domicile certificate must be submitted.

(II). Must have done a job of at least 5 years.

(III). If needed, he will be ready to pay the entire amount in 5 years.

(IV). Should not be the owner or co-owner (if spouse) of the residential facility in that city

(V). Should not be below 35 years of age as on 31 December 2016.

 

Information about Dhawan,

Dhawan is an industrialist and from another state who established his factory in 2000 and has a state residence certificate. He is ready to pay the full amount in 4 years if necessary. He does not have a house in that city but his wife has a flat. His date of birth is 11 November 1970.

Here we see Dhawan's wife has a flat in that city.

Therefore, the Shyamala Society will not allot flat to Dhawan as his wife has a flat in the same city.

Hence, the correct answer is Do not allot flat.

The correct answer is 1206 AD and 1526 AD.

Key Points

• Delhi Sultanate, five short-lived dynasties, based in Delhi, from 1206 to 1526 AD, when it fell to the Mughal Empire.
• During this period of over three hundred years, five dynasties ruled in Delhi.

1. The Slave dynasty (1206-90)
2. Khilji dynasty (1290-1320)
3. Tughlaq dynasty (1320-1413)
4. Sayyid dynasty (1414-51)
5. Lodhi Dynasty (1451-1526)

Additional Information

• Qutub-ud-din Aibak, a slave of Muhammad Ghori, who became the ruler after the death of his master, founded the Slave Dynasty.
• He was a great builder who built the majestic 238 feet high stone tower known as Qutub Minar in Delhi.
• The next important king of the Slave dynasty was Shams-ud-din Iltutmush, who himself was a slave of Qutub-ud-din Aibak.
• Razia Begum, the capable daughter of Iltutmush, was the first and the only Muslim lady who ever adorned the throne of Delhi.
• Balban consolidated the administrative set up of the empire and completed the work started by Iltutmush.
• Jalal-ud-din Khilji on the throne and this marked the beginning of the Khilji dynasty.
• Ala-ud-din Khilji, a nephew of Jalal-ud-din Khilji hatched a conspiracy and got Sultan Jalal-ud-din killed and proclaimed himself as the Sultan in 1296.
• Ghyasuddin Tughlaq, who was the Governor of Punjab during the reign of Ala-ud-din Khilji, ascended the throne in 1320 A.D. and founded the Tughlaq dynasty.
• Muhammad-Bin-Tughlaq succeeded his father and extended the kingdom beyond India, into Central Asia.
• He first shifted his capital from Delhi to Devagiri in Deccan.
• He died in 1351 A.D. and his cousin, Feroz Tughlaq succeeded him.
• Sayyid dynasty was founded by Khizar Khan.
• Bahlūl Lodī was the founder of the Lodhi dynasty.
• Ibrahim Khan Lodhi was the last ruler of the Lodi dynasty when he was defeated and killed at the Battle of Panipat by Babur's invading army, giving way to the emergence of the Mughal Empire in India.

Concept:

1. We have to check the conclusions are 100% match with the statement. If the conclusion is 100% match with the given statement then the conclusion is true. If there is a 1% chance of not following the statement then the conclusion is considered to be false.

2. The possibility case can be considered to be "false" in "definite case".

3. In Possibility case, either "can" or "possible" word must be present.

Explanation

Given,

Statement: All tonics are poisonous substances. All poisonous substances are poison.

Conclusions:

1. All poison are tonics.
2. Some poison are tonics.
   

<br>

The least possible Venn diagram for the given statements is as follows,

Conclusions:

1. All poison are tonics → False (It is possible but not definite)
2. Some poison are tonics → True (From Venn diagram we see some poison are tonics)
   

<br>

Hence, the correct answer is Only 2 follows.

 

Additional Information

The correct answer is Gujarat.

Key Points

• The Kakrapar Atomic Power Station (KAPS) is located near Surat in the state of Gujarat.
• KAPS currently operates two PHWRs, the first of which (Unit-1) began commercial operations on 6 May 1993.

Important Points

• Nuclear power plants in India:

• Kudankulam Nuclear Power Plant is the largest atomic energy station in India.
• Its capacity is 2,000MW.
• Tarapur Atomic Power Station is the first nuclear power plant in India.
• This plant is situated in Boisar, Maharastra in Oct-1969.
• India's and Asia's first nuclear reactor was the Apsara research reactor at Mumbai.

Given,

Hockey : Field :: Badminton : ?

Here we see the game Hockey is played on the rectangular ground which we called field.

Similarly, the game Badminton is played on court.

Hence, the correct answer is Court.

Additional Information

Shortcut Trick

Total ratio units of Mohan and Sohan = 5 + 4 = 9 units.

Given total present age = 36 years.

Value of 1 unit = 36 ÷ 9 = 4 years.

Sohan present age (4 units) = 4 × 4 = 16 years.

∴ The correct answer is 16 years.

Alternate Method

Given:

Ratio of ages of Mohan and Sohan = 5 : 4

Sum of their ages = 36 years

Formula Used:

Age of Person = (Individual Ratio ÷ Sum of Ratios) × Total Age

Calculations:

⇒ Let age of Mohan be 5x and Sohan be 4x.

⇒ 5x + 4x = 36

⇒ 9x = 36

⇒ x = 36 ÷ 9 = 4

⇒ Present age of Sohan = 4x = 4 × 4 = 16 years.

∴ The correct answer is 16 years.

Additional Information

Ratio & Proportion Basics

If a quantity is divided in ratio a:b, then parts are [a/(a+b)] × Total and [b/(a+b)] × Total.

Age Difference Property

The difference between the ages of two persons remains constant regardless of the number of years passed or before.

The correct answer is Chhatrapati Shivaji Maharaj International Airport.

• Chhatrapati Shivaji Maharaj International airport sets a record with 980 flights in 24 hours.
• On January 20, 2018, this airport created a new world record for single-runway operations by handling 980 arrivals and take-offs in 24 hours.

Important Points

• List of some airports in India:

• India has a total of 34 operational International Airports.

The correct answer is Sitaram Yechury.

• The Communist Party of India (Marxist) (CPIM) is a communist national political party in India.
• The CPI(M) was formed in Calcutta in 1964.
• General Secretary: Sitaram Yechury
• Lok Sabha leader: P.R. Natarajan
• Rajya Sabha leader: Elamaram Kareem
• the party was often referred to by different names such as 'Left Communist Party' or 'Communist Party of India (Left)'.
• Kerala is the communist state in India.

Important Points

• Ram Madhav is the National General Secretary of the Bharatiya Janata Party.
• His written book is 'Uneasy Neighbours: India and China After 50 Years of the War'.
• Yogi Adityanath is Chief Minister of Uttar Pradesh.
• Viplav dev is Chief Minister of Tripura.

Shortcut Trick

Apply the M₁D₁ = M₂D₂ rule for Inversely Proportional work.

63 × 126 = 98 × D₂

D₂ = (63 × 126) ÷ 98 = 9 × 9 = 81

∴ The correct answer is 81 days.

Alternate Method

Given:

Initial people (M₁) = 63

Initial days (D₁) = 126

New people (M₂) = 98

Formula Used:

Total Work = Men × Days (M₁ × D₁ = M₂ × D₂)

Calculations:

⇒ Total Work = 63 × 126

⇒ 63 × 126 = 98 × D₂

⇒ D₂ = (63 × 126) ÷ 98

⇒ D₂ = (9 × 7 × 126) ÷ (14 × 7)

⇒ D₂ = (9 × 126) ÷ 14

⇒ D₂ = 9 × 9

⇒ D₂ = 81

∴ The correct answer is 81 days.

Additional Information

Chain Rule Formula

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

Inverse Proportion

In Time and Work, the number of people is inversely proportional to the time taken to complete the constant work.

Work and Efficiency

Efficiency = Total Work ÷ Time. If people increase, total efficiency increases, reducing the total time.

The correct answer is Calculation not possible.

• Given,
• Initial speed (u) = 5 ms^-1
• Final speed (v) = 36 ms^-1
• Now, the equation of motion
• v = u + at
• v = final speed,
• u = initial speed,
• a = acceleration and
• t = time
• = a = (v – u)/t
• So in order to find acceleration, we need initial speed, final speed and time. But in question time is not given. So acceleration cannot be calculated.

The correct answer is Padma Bhushan.

Key Points

• Former Indian cricket team captain MS Dhoni has been given the country's third-highest civilian honor.
• MS Dhoni received the prestigious Padma Bhushan from President Ramnath Kovind.
• Dhoni is the only captain in world cricket to win all three ICC trophies - 2007 World T20, 2011 World Cup, and 2013 Champions Trophy.
• Dhoni is the co-owner of the Chennai FC Indian Super League team.
• He has the record of the highest ODI score by a wicketkeeper, which is 183.
• Apart from CSK, the Pune team has bought Dhoni for IPL.

Important Points

• People who received the Padma Bhushan award in 2018:

• Padma Vibhushan Winners 2018:

Given,

 

The number of lines used to draw the above figure is,

Horizontal lines = 6

Slant lines = 12

Vertical lines = 13

∴ Total lines = 31

Hence the correct answer is 31.

Given,

In the mirror image, the top and bottom part of the figure remains unchanged and the left and right part of the figure interchanges.

∴ 

Hence, the correct answer is 3.

Given,

Pointing to a woman, Khan said, "She is the daughter of my brother's son's wife."

The family tree is as follows,

Here we see the woman is the granddaughter of Khan.

Hence, the correct answer is the Granddaughter.

The correct answer is Maharashtra.

• Shiv Sena, is a right-wing Marathi regional political party in India founded in 1966 by cartoonist Bal Thackeray.
• Uddhav Thackeray is the youngest child of Bal Thackeray.
• Eknath Shinde is the current CM of Maharashtra.

Additional Information

• Saamana is a Marathi newspaper launched in 1988 by Bal Thackeray who was also the editor of the newspaper.
• Its student wing is called Bharatiya Vidyarthi Sena.
• Its women wing is called Shiv Sena Mahila Aghadi.

Shortcut Trick

The least value of a quadratic function x² + px + q occurs at its vertex and is given by q − (p/2)².

In the given function f(x) = x² − 4bx + 9, we have p = −4b and q = 9.

Applying the trick: 9 − (−4b/2)² = −27

⇒ 9 − 4b² = −27 ⇒ 4b² = 36 ⇒ b² = 9 ⇒ b = ±3

∴ The correct answer is 3 or -3.

Alternate Method

Given: Quadratic function f(x) = x² − 4bx + 9 and its minimum value is −27.

Formula: For a quadratic equation ax² + bx + c (where a > 0), the minimum value is given by (4ac − b²) / 4a.

⇒ Here, a = 1, the coefficient of x is −4b, and c = 9.

⇒ Minimum value = [4 × 1 × 9 − (−4b)²] / (4 × 1) = −27

⇒ (36 − 16b²) / 4 = −27

⇒ 9 − 4b² = −27

⇒ −4b² = −27 − 9

⇒ −4b² = −36

⇒ b² = 9

⇒ b = √9 = ±3

∴ The correct answer is 3 or -3.

Additional Information

Vertex of a Parabola

The vertex of the quadratic function f(x) = ax² + bx + c is located at x = −b/2a. If a > 0, the function has a minimum; if a < 0, it has a maximum.

Discriminant and Extremum

The extremum value (least or greatest) can also be expressed as −D/4a, where D is the discriminant (b² − 4ac).

Perfect Square Method

A quadratic can be written in the form a(x − h)² + k, where (h, k) is the vertex and k represents the minimum or maximum value.

The correct answer is Lalji Singh.

• Lalji Singh, widely regarded as the father of DNA fingerprinting in India.
• He is a former director of Hyderabad-based Centre for Cellular and Molecular Biology (CCMB).
• DNA fingerprinting was invented in 1984 by Professor Sir Alec Jeffreys after he realized you could detect variations in human DNA, in the form of these minisatellites.

Important Points

• Watson and Crick Propose the Double Helix structure of DNA with the two strands connected by hydrogen bonds.
• DNA is a long molecule that contains our unique genetic code.
• It holds the instructions for making all the proteins in our bodies and the function of living things.
• In the cell nucleus, the DNA (deoxyribonucleic acid) molecule is packaged into thread-like structures called chromosomes.
• A chromosome (microscopic structure) is made up of DNA tightly coiled many times around proteins called histones that support its structure.
• A chromosome has two arms - a p arm (short arm) and a q arm (long arm), joined in the location of the centromere.
• The information in DNA (double helix structure) is stored as a code made up of four chemical bases: adenine (A), guanine (G), cytosine (C), and thymine (T).
• DNA has two base pairs, A-T and G-C, attached to a sugar-phosphate backbone.

Additional Information

• Gregor Mendel is known as the Father of modern genetics.
• Mendel's laws of inheritance include the law of dominance, the law of segregation, and the law of independent assortment.
• Hargovind Khorana got the Nobel Prize in Physiology or Medicine in 1968 for his interpretation of the genetic code and its function in protein synthesis.

Given, L12O, N14M, P16K, _____.

The pattern followed here is,

Here we see the letters follow a particular pattern and the positional value of the first letter is written at the centre.

Hence, the correct answer is R18I.

The correct answer is ϵ = W/Q.

• Electromotive force (EMF) is equal to the terminal potential difference when no current flows.
• EMF and terminal potential difference (V) are both measured in volts, however, they are not the same thing.
• EMF (ϵ) is the amount of energy (E) provided by the battery to each coulomb of charge (Q) passing through.
• The potential is kept high on the positive terminal and low on the negative terminal to maintain the potential difference between the two terminals.
• The emf is equal to the work done (dW) on the charge per unit charge (ϵ=dW/dq) when there is no current flowing.
  

Since the unit for work is the joule and the unit for a charge is the coulomb, the unit for emf is the volt (1V = 1J/C).

The correct answer is Baking soda.

• Baking soda does not contain water of crystallization.
• The water of crystallization means having a fixed number of molecules present in one formula of a unit of salt. 
• e.g ​Blue vitriol (CuSO4.5H20)
• The chemical formula of baking soda is NaHCO₃.
• Its formula does not show any association with water molecules.
• Baking soda is commercially manufactured on a large scale by the ammonia-soda Solvay process, named after Ernest Solvay, a Belgian industrial chemist.
• Nahcolite is naturally occurring sodium bicarbonate, and is extracted by "solution mining".

Important Points

• The other three options contain water of crystallization.
• Blue vitriol (CuSO₄.5H₂0)
• Washing soda (Na₂CO₃ .1OH₂O)
• Gypsum (CaSO₄.2H₂0)
• Baking soda is white amorphous powder whereas blue vitriol, and washing soda are salts.

CONCEPT:

Here we need to look at the graph and find the value in y-axis corresponding to the year asked represented on the x-axis.

SOLUTION:

From the given bar graph we can say that,

Year on x-axis corresponds with value 20 on y-axis.

∴ No. of units sold in 2006 is 20 lakhs.

Shortcut Trick

Area of Triangle = 1/2 × Base × Height

Area of Parallelogram = Base × Height

Given: Area_T = Area_P and Base_T = (5/7) × Base_P

1/2 × (5/7)B_P × H_T = B_P × H_P ⇒ H_T / H_P = (2 × 7) / 5 = 14/5

∴ The correct answer is 14 : 5.

Alternate Method

Given:

Base of triangle (b₁) = 5/7 × Base of parallelogram (b₂)

Area of triangle (A₁) = Area of parallelogram (A₂)

Formula Used:

Area of triangle = 1/2 × base × height

Area of parallelogram = base × height

Calculations:

⇒ Let base of parallelogram (b₂) = 7 units

⇒ Base of triangle (b₁) = 5/7 × 7 = 5 units

⇒ Area_Triangle = 1/2 × b₁ × h₁

⇒ Area_{Parallelogram} = b₂ × h₂

⇒ 1/2 × 5 × h₁ = 7 × h₂

⇒ 5 × h₁ = 14 × h₂

⇒ h₁ / h₂ = 14 / 5

∴ The correct answer is 14 : 5.

Additional Information

Area of Geometric Shapes

Area of a Rhombus = 1/2 × d₁ × d₂ where d₁, d₂ are diagonals. Area of a Trapezium = 1/2 × (sum of parallel sides) × height.

Properties of Parallelogram

Opposite sides are equal and parallel. Diagonals bisect each other but are not necessarily equal unless it is a Rectangle.

Heron's Formula

Area of triangle = √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter (a+b+c)/2.

The pattern followed here is:

Parallelograms in Equilateral Triangles:

Formula:

Number of Parallelograms $=\frac{n(n-1)(n+1)(n+2)}{8}$

Given figure:

Used formula:

Here n = 4;

Parallelograms = [4(4 - 1) (4 +1) (4 + 2)] / 8

= (4 × 3 × 5 × 6] / 8

= 360 / 8 = 45

Hence, the correct answer is "45".

Alternate Method

The number of parallelograms is,

The parallelograms consist of two triangles are,

ABFC, BDIF, CFJE, DGLI, FIMJ, EJNH, GKLI, ILMJ, JMNH, DGIF, FIJE, BDFC, GLMI, IMNJ, JNOH, DMNF, FJEC, BFEC = 18

The parallelograms consist of four triangles are,

GJMK, IHNL, DEJG, GJNL, IHOM, DEHI, DFLK, BCIG, FEML, FEON, BCHJ, DFNM, ACID, AEJB, BFLG, BJMD, CHNF, CEMI = 18

The parallelograms consist of six triangles are,

ACLG, BAHN, BCON, BCLK, GHNK, GHOL = 6

The parallelograms consist of eight triangles are,

DEMK, DEOM, AEMD = 3

∴ The total number of parallelogram = 18 + 18 + 6 + 3 = 45

Hence, the correct answer is 45.

Shortcut Trick

Ratio of packets received in January and February = 4 : 8 = 1 : 2

Using Weighted Average method: Average = [(n₁ × A₁) + (n₂ × A₂)] ÷ (n₁ + n₂)

Average = (1 × 300 + 2 × 400) ÷ (1 + 2)

Average = (300 + 800) ÷ 3 = 1100 ÷ 3 = 366.67 g

∴ The correct answer is 366.67 g.

Alternate Method

Given:

Number of packets in January = 4 | Average weight = 300 g

Number of packets in February = 8 | Average weight = 400 g

Formula Used:

Total Average = (Total weight of all packets) ÷ (Total number of packets)

Calculations:

⇒ Total weight in January = 4 × 300 = 1200 g

⇒ Total weight in February = 8 × 400 = 3200 g

⇒ Total weight for both months = 1200 + 3200 = 4400 g

⇒ Total number of packets = 4 + 8 = 12

⇒ Combined average weight = 4400 ÷ 12

⇒ Combined average weight = 1100 ÷ 3 ≈ 366.666...

⇒ Combined average weight = 366.67 g

∴ The correct answer is 366.67 g.

Additional Information

Weighted Average Formula

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method

Assume a temporary average (A), then Net Average = A + (Sum of Deviations ÷ Total Number). This simplifies large calculations.

Alligation Method

The ratio of the quantities is inversely proportional to the difference between their averages and the mixture average: n₁/n₂ = (A₂ − A_m) / (A_m − A₁).

The correct answer is 2005.

Important Points

• 2005 was a momentous year for the right to information (RTI) in India because it saw the enactment of a national right to information law.
• The Central Act was passed by the Indian Parliament on 12 May 2005.
• The Right to Information Act, which gives legal rights to people to seek information from the government and curb corruption.
• The law promises accountability and transparency to climb up several notches, especially as it provides for hefty fines and disciplinary action against erring officials.

Additional Information

• On October 12, 2005, a person called Shahid Raza Burney submitted India’s first-ever Right To Information application to a police station in Pune and thus we entered the RTI age.
• The application fee for one single RTI is 10 rupees.

The given number is:

213 × 35 × 53 × 76

For each term, the perfect cubes can be obtained as:

For 2¹³ = 2⁰, 2³, 2⁶, 2⁹, 2¹²; i.e. 5 terms

For 3⁵ = 3⁰, 3³; i.e. 2 terms

For 5³ = 5⁰, 5³; i.e. 2 terms

For 7⁶ = 7⁰, 7³, 7⁶; i.e. 3 terms

So, we have the multiples of the number 213 × 35 × 53 × 76 as perfect cubes = 5 × 2 × 2 × 3 = 60 

∴ The number of multiples of the number 213 × 35 × 53 × 76 are perfect cubes or complete cubes, are 60

The correct answer is It is a disease caused by the absence of genes responsible for the factors that cause blood clotting.

• Haemophilia is a group of bleeding disorders. Blood clotting factors are needed to stop bleeding.
• The most common types are:
• Hemophilia A (classic haemophilia)—caused by too little or no factor VIII (most common)
• Hemophilia B (Christmas disease)—happens in males, caused by too little or no factor IX
• Causes of this disease is a faulty gene on a certain DNA strand.
• Females carry 2 copies of the strand. If one is faulty, the other one takes over. The faulty gene can pass to their children. If so, the female child will carry the gene. If it passes to the male, they will get the disease because they carry one copy of the strand.

Additional Information

• Haemoglobin disorders (also known as hemoglobinopathies) are rare blood conditions that affect a person’s haemoglobin which is the protein in the blood that carries oxygen.
• Sickle Cell Disease includes a group of related disorders that affect a person's red blood cells.
• With sickle cell disease, a person's red blood cells can become hard, sticky, and sickle-shaped.

The least possible overlapping venn diagram is shown below:

Option1) All monkeys have two legs → True ( As seen from the figure all monkeys are men and all men have two legs, thus all monkeys have two legs is definitely correct)

Option 2) Some monkeys are not cats → False ( We can draw a big circle of cat which will include all monkeys, then the statement Some monkeys are not cats becomes incorrect)

Option 3) Some men are cat →  False ( as seen from the figure men and cat have no connection so it is incorrect)

Option 4) All men have four legs → False (as there is no mention of 4 legs in the statement so we can't assume anything on own, thus it is also incorrect ) 

Therefore, the option "All monkeys have two legs" is definitely correct.

Hence, the correct answer is All monkeys have two legs.

NOTE:

There is a discrepancy in the original paper and the board itself considered it invalid. so we modify this question a little bit according to the standard of the previous question.

Given,

Statement:

"Please note that the company will only provide accommodation to outside candidates if selected."

Assumptions:

I. The company plans to select only external candidates 

→ Not implicit as the company is not planning to select only external candidates or we don't know by the statements that the company is selecting internal or external candidates.

II. The second company plans to select only local candidates.

→ Not implicit as the company is not planning to select only local candidates or we don't have anything about the second company in the statement.

Therefore, neither assumption I nor II is implicit.

Hence the correct answer is, neither assumption I nor II is implicit.

The correct answer is Mass per unit volume.

• Density is an important physical property for characterizing a material or chemical system.
• Mathematically, density is calculated as a substance's mass per the volume it occupies.
• The formula for density is d = M/V, where d is density, M is mass, and V is volume.
• Density is commonly expressed in units of grams per cubic centimetre (g/cm³).

Key Points

• Water achieves its maximum density at 4ºC (39.2ºF).
• The natural density of milk is 1.200 times greater than normal water at 4ºC, i.e. the standard density of water 1 gm/cc.

The correct answer is Singapore.

• India and Singapore signed the Second Protocol amending the Comprehensive Economic Cooperation Agreement (CECA) in New Delhi.
• The Protocol was signed by Deputy Chief Negotiators, Shri Rajneesh, Joint Secretary, Ministry of Commerce and Industry, Government of India, and Mr Francis Chong, Senior Director, Ministry of Trade and Industry, Government of Singapore.
• CECA will boost bilateral trade between India and Singapore.

Hint

• Singapore is the second-largest trading partner of India within ASEAN.
• Singapore’s trade with India constitutes about 21.8% of the total trade with ASEAN.

The correct answer is 25%.

Given Data:

• Mass of sugar = 50 grams
• Maas of water = 150 grams
• Mass of total solution = 200 grams
• The concentration of the solution in terms of mass by mass percent of the solution is as given below:
• $Mass= {Mass of solute \over Mass of solution}*100$
• $= {50 \over200}*100$
• 25%

The correct answer is Kamal Hassan.

• Kamal Hassan had won the Henri Langlois Award for his contribution to cinema in France as a child artist in his debut movie Kalathoor Kannamma in 1959.
• In 2016, He was awarded the Knight Of the Order of Arts and Letters for his huge contribution to cinema.

Important Points

• Bollywood artists who were honoured by foreign countries for their contribution to cinema:

The correct answer is Telangana.

• The Singareni coal reserves stretch across 350 Km of the Pranahita located in Godavari Valley of Telangana.
• Singareni Collieries Company Limited (SCCL) is currently operating 18 opencast and 27 underground mines in 4 districts of Telangana.
• The present Company was incorporated on 23rd December 1920.

Important Points

• Important mines in Odisha:
• Iron ore in Joda, Keonjhar, Jajpur.
• Manganese in Keonjhar, Rayagada, Sundergarh.
• Bauxite in Balangir, Koraput, Kalahandi, Sambalpur.
• Coal in Jharsuguda, Talcher.
• The principal mineral-bearing belts in Maharashtra are the Vidarbha area in the east and the Konkan area in the west.
• Important mineral occurrences are:
• Bauxite in Kolhapur, Raigad, Ratnagiri, Satara, Sindhudurg, Thane districts.
• China clay in Amravati, Bhandara, Chandrapur, Nagpur, Sindhudurg, Thane districts.
• Chromite in Bhandara, Chandrapur, Nagpur, Sindhudurg districts.
• Coal in Nagpur, Chandrapur, Yavatmal districts.
• Dolomite in Chandrapur, Nagpur, Yavatmal districts.
• Gold in Bhandara, Nagpur districts.
• Important mines in Chhattisgarh:
• Iron ore in Bailadila, Raoghat, Hahaladdi/Kodapakha, Metabodeli, Dalli Rajhara.
• Bauxite in Mainpat, Kandraja block, Jamirapat, Pendrapat.
• Coal in Sohagpur, Jhilimili, Chirimiri, Bisrampur, Lakhanpur, Panch Bhahni, Korba, Mand Raigarh.

Shortcut Trick

Identify the LCM of 6, 9, 12, 13, and 15.

LCM (6, 9, 12, 13, 15) = 2340.

Find the largest 4-digit multiple of 2340.

2340 × 4 = 9360 (which is < 10000).

∴ The correct answer is 9360.

Alternate Method

Given: Divisors are 6, 9, 12, 13, and 15. We need the largest 4-digit number divisible by all.

Step 1: Find the LCM of the numbers.

⇒ Prime factorization:

⇒ 6 = 2 × 3

⇒ 9 = 3²

⇒ 12 = 2² × 3

⇒ 13 = 13¹

⇒ 15 = 3 × 5

⇒ LCM = 2² × 3² × 5 × 13 = 4 × 9 × 5 × 13 = 2340.

Step 2: Divide the largest 4-digit number (9999) by the LCM.

⇒ 9999 ÷ 2340

⇒ Quotient = 4

⇒ Remainder = 9999 − (2340 × 4) = 9999 − 9360 = 639.

Step 3: Subtract the remainder from 9999.

⇒ Required Number = 9999 − 639 = 9360.

∴ The correct answer is 9360.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is perfectly divisible by a given set of numbers.

Divisibility Rules

A number is divisible by 9 if the sum of its digits is divisible by 9. In 9360, 9+3+6+0 = 18 (divisible by 9).

Finding Multiples

Any number divisible by a set of numbers must be a multiple of their LCM.

The correct answer is Saba Karim.

• Former India wicketkeeper Saba Karim has been asked to resign from the post of BCCI General Manager – Cricket Operations.
• He played one Test and 34 ODIs for India, was appointed by the Board of Control for Cricket in India in December 2017.
• He was responsible for implementing operational plans, budgeting, monitoring the match playing conditions, and administration of the Domestic program.

Important Points

Additional Information

• Sourav Ganguly is the president of BCCI 2020.

Shortcut Trick

In same direction problems involving a moving object passing two others, use the constant train length property.

Let Train Speed = S km/h.

(S − 9) × 8 = (S − 12) × 8.4

8S − 72 = 8.4S − 100.8

0.4S = 28.8

S = 28.8 ÷ 0.4 = 72 km/h

∴ The correct answer is 72 km/h.

Alternate Method

Given: Speed of 1^st person = 9 km/h, Time taken = 8 s. Speed of 2^nd person = 12 km/h, Time taken = 8.4 s.

Formula Used: Distance = Relative Speed × Time

⇒ Let the speed of the train be S km/h and length be L meters.

⇒ Conversion factor: 1 km/h = 5/18 m/s.

⇒ L = (S − 9) × (5/18) × 8 --- (Equation 1)

⇒ L = (S − 12) × (5/18) × 8.4 --- (Equation 2)

⇒ (S − 9) × 8 = (S − 12) × 8.4

⇒ 8S − 72 = 8.4S − 100.8

⇒ 100.8 − 72 = 8.4S − 8S

⇒ 28.8 = 0.4S

⇒ S = 72 km/h

∴ The correct answer is 72 km/h.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction with speeds u and v ( v), their relative speed is (u − v).

Relative Speed in Opposite Direction

When two objects move in opposite directions, their relative speed is (u + v).

Speed Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Given,

 

 

Here we see the person is facing North-West direction.

Hence, the correct answer is North-West.

Given,

Statement: There are many aspects to a person.

Argument:

1. Yes, everyone responds to a situation that is different from the other → Correct as everyone's response to a situation is different from the other.
2. No, we are responsible for what we create all around us. What we produce happiness or sorrow is up to us.

→ Incorrect as we are not always responsible for what we create all around us.

∴ Only argument 1 is correct.

Hence the correct answer is, Only argument 1 is correct.