RRC Group D Previous Year Paper 41 (Held On: 16 Oct 2018 Shift 2)

According to the given information,

Latika is facing west and waiter stands at 90° to the right of Latika and facing her. So the waiter is facing the south direction as shown in the diagram.

Hence, “South” is the correct answer.

After changing the signs in the equation 84 + 2 ÷ 4 – 6 × 12 the equation becomes 84 ÷ 2 – 4 × 6 + 12

Now solving according to BODMAS rule the equation

42 - 24 + 12 = 30

Hence, “30” is the correct answer.

The correct answer is Dipa Karmakar.

Key Points

• Dipa Karmakar, India’s premier gymnast clinched the gold medal in the vault event of FIG Artistic Gymnastics World Challenge Cup at Mersin, Turkey.
• She created history by becoming the first Indian woman to qualify in the individual Vault finals in the Rio Olympics 2016.
• Dipa won a bronze medal at the 2014 Commonwealth Games in Glasgow.
• She becomes the first Indian female gymnast to do so in the history of the Games.
• She is only the fifth woman in gymnastics history to land the Produnova vault.

Important Points

Shortcut Trick

Average Speed for equal distance segments = (2 × S₁ × S₂) ÷ (S₁ + S₂)

Average Speed = (2 × 40 × 60) ÷ (40 + 60) = 4800 ÷ 100 = 48 kmph

Total Distance = Average Speed × Total Time = 48 × 8 = 384 km

∴ The correct answer is 384 kms.

Alternate Method

Given:

Speed 1 (S₁) = 40 km/hr

Speed 2 (S₂) = 60 km/hr

Total Time (T) = 8 hours

Formula Used:

Time = Distance ÷ Speed

Calculations:

Let the total distance be 2D. Then each half is D.

⇒ Time taken for first half (t₁) = D / 40

⇒ Time taken for second half (t₂) = D / 60

⇒ t₁ + t₂ = 8

⇒ (D / 40) + (D / 60) = 8

⇒ (3D + 2D) / 120 = 8

⇒ 5D / 120 = 8

⇒ D / 24 = 8

⇒ D = 24 × 8 = 192 km

⇒ Total Distance = 2D = 2 × 192 = 384 km

∴ The correct answer is 384 kms.

Additional Information

Average Speed (Equal Distances)

When a journey is divided into two equal distances with speeds x and y, the average speed is given by (2xy) ÷ (x + y).

Average Speed (General Formula)

Average Speed = Total Distance Covered ÷ Total Time Taken.

Relative Speed

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

The correct answer is Gujarat.

Key Points

• Vansda National Park is located in the Navsari district, Gujarat.
• The total area of the park is about 23.99 Km².
• The park got its name Vansda as the area was privately owned by the Maharaja of Vansda.
• It was established as a National park in the year in 1979.
• The area having groves of “Katas” bamboo owes its beauty to no felling of trees since 1952.

Important Points

The correct answer is John Dalton.

Key Points

• The postulates of Dalton’s atomic theory:
• The matter is composed of exceedingly small particles called atoms.
• An atom is the smallest unit of an element that can participate in a chemical change.
• An element consists of only one type of atom, which has a mass that is characteristic of the element and is the same for all atoms of that element.
• Atoms of one element differ in properties from atoms of all other elements.
• Atoms are neither created nor destroyed during a chemical change.
• Dalton used three laws of chemical reactions as a basis for his theory:
• The Law of Conservation of Mass.
• The Law of Definite Proportions.
• The Law of Multiple Proportions.

Important Points

The correct answer is Oxalic Acid.

• Oxalic acid is present in tomatoes.
• Tomatoes are a good source of vitamin C and potassium.
• Other acids like citric acid and ascorbic acid are also present in tomatoes.

Important Points

The correct answer is Amit V. Masurkar.

Key Points

• Newton is a 2017 Indian comedy-drama film directed by Amit V. Masurkar.
• He directed the independent comedy film Sulemani Keeda in 2013.
• Newton' is India's official entry for Oscars 2018.
• The National Award-winning actor Rajkummar Rao plays the lead in this movie.

Important Points

The correct answer is Copper.

Key Points

• Copper has been used in electrical wiring since the invention of the electromagnet and the telegraph in the early 1800s.
• Copper electrical connectors are still used in telecommunications, as well as power generation, distribution, and transmission.
• The lower the level of resistivity, the more electrical conductivity a metal has.
• Copper has low resistivity and therefore is an excellent conductor.
• Copper is less oxidative than other metals, this is another reason.

Important Points

• The electrical resistivity of particular conductor material is a measure of how strongly the material opposes the flow of electric current through it.

Shortcut Trick

Apply Remainder Theorem: If a polynomial P(x) is divided by (x − a), the remainder is P(a).

Here, divisor is (x − 2), so a = 2.

Remainder = 4(2)³ − 2(2)² + 5(2) − 8

Remainder = 32 − 8 + 10 − 8 = 26.

∴ The correct answer is 26.

Alternate Method

Given:

Polynomial P(x) = 4x³ − 2x² + 5x − 8

Divisor D(x) = x − 2

Formula Used:

For a divisor (x − a), the Remainder R = P(a).

Calculations:

⇒ To find the remainder, substitute x = 2 into P(x).

⇒ P(2) = 4(2)³ − 2(2)² + 5(2) − 8

⇒ P(2) = 4(8) − 2(4) + 10 − 8

⇒ P(2) = 32 − 8 + 10 − 8

⇒ P(2) = 24 + 2

⇒ P(2) = 26

∴ The correct answer is 26.

Additional Information

Remainder Theorem

It states that the remainder of the division of a polynomial f(x) by a linear invariant (x − a) is equal to f(a).

Factor Theorem

A special case of the remainder theorem where if f(a) = 0, then (x − a) is a factor of the polynomial f(x).

Synthetic Division

A shorthand method of polynomial division, especially for division by a linear factor, useful for finding roots and remainders quickly.

In diagram A, B, C half of the area is black and other half area is white but in diagram D one fourth of the area is white and three fourth of the area is black. So, diagram D is the odd one out.

Hence, “Figure D” is the correct answer.

The correct answer is 1857.

Important Points

• The revolt of 1857 started on 10th May when the Company’s Indian soldiers at Meerut rebelled.
• It is also called the Sepoy Mutiny by the British.
• It is now also known as the 'First War of Independence' against the British rulers.
• Their policy of annexation called Doctrine of Lapse led to many independent kingdoms being annexed to the British Empire.
• Lord Dalhousie annexed the Maratha States of Satara, Nagpur, Jhansi, and several other minor kingdoms.
• The main event which became the immediate cause of the war was the refusal of the Sepoys to use the grease-covered cartridges (greased with the fat of pig and cow) on January 23, 1857.
• At the same time, an Indian sepoy killed two British officers at Barrackpore, when he was forced to use greased cartridges.
• First came the desperate struggles at Delhi, Kanpur, and Lucknow during the summer; then the operations around Lucknow in the winter of 1857–58, directed by Sir Colin Campbell; and finally the “mopping up” campaigns of Sir Hugh Rose in early 1858.

The correct answer is NDTV.

Key Points

• Ravish Kumar is New Delhi Television Network (NDTV) India's senior executive editor and one of India's most influential TV journalists.
• He has been reporting real-life and under-reported problems of ordinary common people.
• He hosts many programs include Prime Time, Hum Log, Ravish Ki Report, and Des Ki Baat.
• Television journalist Ravish Kumar was honored with the prestigious Ramon Magsaysay Award 2019 for giving "voice to the voiceless".
• He was awarded Red Ink Award for Journalist of the Year in 2016.

The correct answer is Dog fish.

Key Points

• Dogfish is a true fish, amongst Jellyfish, Snake, Dogfish, and Cattle fish.
• Dogfish has all character of fish has, like a cartilaginous skeleton, vertebra, gill slits, fins, etc.
• Jellyfish can not be listed as a fish because it does not meet the requirements of being a fish.
• Cuttlefish are the mollusc of the order Sepiida, belonging to the class Cephalopoda.

Additional Information

• Flying fish, Skatefish, Sturgeon are true fish.
• Silverfish, Starfish, Shrimp fish are not true fish.

The correct answer is 8 elements.

Key Points

• The second and third periods contain 8 elements each and are called short periods.
• The 2nd-period elements: lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, and neon.
• The 3rd-period elements: sodium, magnesium, aluminum, silicon, phosphorus, sulfur, chlorine, and argon.
• The First period contains 2 elements (Hydrogen, Helium) and is called a very short period.

Important Points

• All the elements in the periodic table are arranged in the order of their increasing atomic number.
• Each period in the periodic table starts with the beginning of a new energy level.
• The first period begins with the filling of the first energy shell (K-shell).
• The first energy shell can accommodate only 2 electrons in it.
• The second period begins with the filling of the second energy shell (L-shell).
• The second energy shell can accommodate only 8 electrons in it.

• The statement says that I have made the decision to become a pilot.
• So, this is implicit that you would decide to become a pilot only if you are not one.
• Thus, assumption I is implicit.
• Assumption II contradicts assumption I. Thus, only one of the two assumptions can be implicit.

Hence, “Only assumption I is implicit” is the correct answer.

The correct answer is the average speed.

Key Points

• Speed is the scalar measure of the rate of movement of a body expressed either as the distance traveled divided by the time taken.
• Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
• Displacement is a vector quantity that refers to "how far out of place an object is".
• It is the object's overall change in position.
• Average speed is the average of all instantaneous speeds. It is found simply by a distance/time ratio.
• Velocity is defined as a vector measurement of the rate and direction of motion of an object.
• Velocity formula when an object moving in a straight line: r = d / t.
• r is the rate or speed, d is the distance moved, t is the time it takes to complete the movement.
• A body moving with a constant speed has velocity without acceleration.

Hence, “Diagram B” is the correct answer**.**

As Blood flows in Veins and Veins are inside the body so the Body is represented by the larger circle and in which the middle circle and the smaller circle represents Veins and Blood respectively. Hence, the answer is figure A.

Shortcut Trick

To find the sum of natural numbers, we need the specific value of n.

Statement I provides both the formula and the exact value of n (n = 50).

Statement II is a general property of numbers and does not provide any numerical value to calculate a sum.

∴ The correct answer is Only statement I is sufficient.

Alternate Method

Given:

Target: Find the sum of the first n natural numbers.

Statement I: $s_n = \frac{n(n + 1)}{2}$ and n = 50.

Statement II: Some numbers are even and some are odd.

Calculation:

Using Statement I:

⇒ Sum S₅₀ = [50 × (50 + 1)] ÷ 2

⇒ S₅₀ = [50 × 51] ÷ 2

⇒ S₅₀ = 25 × 51 = 1275

⇒ Statement I alone is sufficient to give a unique value.

Using Statement II:

⇒ Knowing that numbers are even or odd is a universal fact but provides no numerical limit for n.

⇒ Statement II alone is not sufficient.

∴ The correct answer is Only statement I is sufficient.

Additional Information

Sum of First n Natural Numbers

The formula for the sum of the first n natural numbers is always S_n = n(n + 1) ÷ 2.

Sum of Squares and Cubes

Sum of squares of first n numbers = [n(n + 1)(2n + 1)] ÷ 6. Sum of cubes = [n(n + 1) ÷ 2]².

Data Sufficiency Tip

In data sufficiency, if one statement provides a definite numerical value for the variable required in the formula, it is usually sufficient.

Shortcut Trick

Larger number = (Sum + Difference) ÷ 2 = (90 + 16) ÷ 2 = 106 ÷ 2 = 53

Smaller number = (Sum − Difference) ÷ 2 = (90 − 16) ÷ 2 = 74 ÷ 2 = 37

Verification: 53 + 37 = 90 and 53 − 37 = 16.

∴ The correct answer is 53, 37.

Alternate Method

Given:

Sum of two numbers = 90

Difference between numbers = 16

Let the two numbers be x and y, where x > y.

⇒ x + y = 90 — (Equation 1)

⇒ x − y = 16 — (Equation 2)

Adding Equation 1 and Equation 2:

⇒ (x + y) + (x − y) = 90 + 16

⇒ 2x = 106

⇒ x = 106 ÷ 2 = 53

Substitute the value of x in Equation 1:

⇒ 53 + y = 90

⇒ y = 90 − 53

⇒ y = 37

∴ The correct answer is 53, 37.

Additional Information

Linear Equations in Two Variables

When two variables are related by two linear conditions, they can be solved using Elimination or Substitution methods.

Sum and Difference Formula

If A + B = S and A − B = D, then the larger value A = (S + D) ÷ 2 and the smaller value B = (S − D) ÷ 2.

Verification Rule

Always verify the results by putting the values back into the original sum and difference conditions to ensure accuracy.

Shortcut Trick

Speed = 82 km/hr, Time = 24 min = 24/60 hr = 0.4 hr

Distance = 82 × 0.4 = 32.8 km

∴ The correct answer is 32.8 km.

Alternate Method

Given:

Average Speed of the train = 82 km/hr

Time duration = 24 minutes

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Convert Time from minutes to hours: 24 ÷ 60 hours

⇒ Time = 2/5 hours

⇒ Distance = 82 × (2/5)

⇒ Distance = 164 ÷ 5

⇒ Distance = 32.8 km

∴ The correct answer is 32.8 km.

Additional Information

Unit Conversion

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy/(x+y).

Relative Speed

Same direction: subtract speeds (s₁ − s₂). Opposite direction: add speeds (s₁ + s₂).

Shortcut Trick

If sugar is 6%, then water must be 100% − 6% = 94%.

Water volume = 94% of 350 ml.

⇒ 350 − (6% of 350) = 350 − 21 = 329 ml.

∴ The correct answer is 329 ml.

Alternate Method

Given: Total volume = 350 ml, Sugar concentration = 6%.

Formula Used: Volume of Component = Total Volume × Percentage Concentration.

⇒ Sugar volume = (6 ÷ 100) × 350

⇒ Sugar volume = 0.06 × 350 = 21 ml

⇒ Water volume = Total volume − Sugar volume

⇒ Water volume = 350 − 21 = 329 ml

∴ The correct answer is 329 ml.

Additional Information

Percentage Composition

The sum of percentages of all components in a mixture or solution is always 100%.

Dilution Formula

When more solvent (water) is added, the amount of solute (sugar) remains constant: C₁V₁ = C₂V₂.

Concentration by Mass/Volume

Concentration % = (Mass or Volume of Solute ÷ Total Volume of Solution) × 100.

CONCEPT:

• Resistance (R): The resistance offered to the flow of current is known as the resistance.
• SI unit of resistance is the ohm (Ω).
• Mathematically resistance can be written as

$⇒ R = \frac{{\rho l}}{A}$

Where R = resistance, l = length, A = area of cross-section and ρ = resistivity

EXPLANATION:

• That wire is doubled on it means to fold the length of wire. That is its length will get half and the area of the cross-section will get doubled.

Given: R1 = R = 5 Ω 

As we know that the resistance of the wire is,

$\Rightarrow R = \frac{{\rho l}}{A}$

When the wire is doubled then, then its area will increase automatically. But the volume of the wire will be the same.

∴ The volume of original wire = volume of new wire

⇒ A1l1 = A2l2

⇒ A1l1 = A2 l1/2

⇒ A2 = 2A1

• The resistance of the wire in 1st case

$\Rightarrow {R_1} = R = \frac{{\rho {l_1}}}{{{A_1}}}$       ----(1)

• The resistance of the wire in 2nd case

$\Rightarrow {R_2} = \frac{{\rho {l_2}}}{{{A_2}}} = \frac{{\rho {\frac{l_1}{2}}}}{{{2A_1}}} = \frac{{\rho {l_1}}}{{{4A_1}}}$         -----(2)

Divide equation 1 and 2, we get

$\Rightarrow \frac{R}{{{R_2}}} = \frac{{\frac{{\rho {l_1}}}{{{A_1}}}}}{ \frac{{\rho {l_1}}}{{{4A_1}}}} = 4$

⇒ R2 = 5/4 Ω = 1.25 Ω

The correct answer is The weight of a body in an elevator moving downwards decreases while its Mass remains the same.

Key Points

• This force exerted by the scale is known as apparent weight.
• When the lift accelerates and decelerates the force that the cables and motors exert on the lift is either added to or subtracted from, the force with which the floor of the lift pushes up on you.
• This is what makes the body feel heavier and lighter.
• Consider the normal force (N) acting on the body (mass = m) from the elevator:
• If the elevator is at rest or moving at a constant velocity.
• N = mg
• If the elevator has an upward acceleration (a).
• N = mg + ma
• If the elevator has a downward acceleration (a).
• N = mg - ma
• When a lift accelerates downwards at the same rate as gravity (9.81 m/s²) the body would feel weightless.
• When a lift accelerates upwards at the same rate as gravity (9.81 m/s²) the body would feel twice weighed as much.

The pattern followed here is:

This is an alternating series of multiplication and addition. First number is multiplied by 2 to get the second number and then 2 is added to the second number to get the third number and so on.

Hence, “60” is the correct answer.

It is clear from the statement that Co-curricular activities are important to children.

Assumption I: “Holistic development occurs through various co-curricular activities” is implicit.

Assumption II: “Schools don’t admit without co-curricular activities” is irrelevant.

Hence, “Only assumption I is implicit” is the correct answer.

CONCEPT:

Here we need to make the denominators same by taking LCM so that we can compare to find the greatest fraction.

CALCULATION:

LCM of 14, 77, 66, 21 = 462

5/14 can be written as (5 × 33)/(14 × 33) = 165/462

29/77 can be written as (29 × 6)/(77 × 6) = 174/462

25/66 can be written as (25 × 7)/(66 × 7) = 175/462

8/21 can be written as (8 × 22)/(21 × 22) = 176/462

Comparing these we know that 8/21 is the greatest

∴ 8/21 is the greatest fraction.

The correct answer is positive.

Key Points

• The distance from the lens to the focal point is called the focal length.
• For diverging or convex mirrors, the focal length is always positive.
• For a converging or concave mirror, the focal length is always negative.
• The focal length of a convex mirror is half of its radius of curvature.

Important Points

• The definitions of the principal axis, center of curvature C, the radius of curvature R, and the vertex V, of a convex mirror, are analogous to the corresponding definitions for a concave mirror.

• When parallel light-rays strike a convex mirror they are reflected such that they appear to emanate from a single point F located behind the mirror, as shown in fig below.
  

• This point is called the virtual focus of the mirror. The focal length f of the mirror is simply the distance between V and F. In the paraxial approximation, the focal length of a convex mirror is half of its radius of curvature.

• The power of an optical element is calculated by 1/focal length and the unit is dioptre (1/m).

Shortcut Trick

Use the direct formula for two pipes: Time = (X × Y) ÷ (X + Y)

X = 10 hrs, Y = 15 hrs

Time = (10 × 15) ÷ (10 + 15) = 150 ÷ 25 = 6 hrs

∴ The correct answer is 6 hrs.

Alternate Method

Given:

Time taken by Pipe A = 10 hrs

Time taken by Pipe B = 15 hrs

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time

Calculations:

⇒ Combined Efficiency of A + B = 3 + 2 = 5 units/hr

⇒ Total Time taken together = Total Work ÷ Combined Efficiency

⇒ Time = 30 ÷ 5

⇒ Time = 6 hrs

∴ The correct answer is 6 hrs.

Additional Information

Pipes and Cisterns

If an inlet pipe fills in X hours and an outlet pipe empties in Y hours, the net work done in 1 hour is (1/X − 1/Y).

Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a task. If the ratio of time is a:b, the ratio of efficiency is b:a.

CONCEPT:

Here we need to make the denominators same by taking LCM so that we can compare to find the smallest fraction.

CALCULATION:

LCM of (9, 4, 8 7) = 504

4/9 can be written as (4 × 56)/(9 × 56) = 224/504

5/4 can be written as (5 × 126)/(4 × 126) = 630/504

3/8 can be written as (3 × 63)/(8 × 63) = 189/504

6/7 can be written as (6 × 72)/(7 × 72) = 432/504

∴ 3/8 is the smallest fraction

Shortcut Trick For Inverse Trigonometric Functions, find the value in the principal range. Since 4 radians is in Quadrant III (π < 4 < 3π/2), x = cos−1(cos 4) = 2π − 4. Since 3 radians is in Quadrant II (π/2 < 3 < π), y = sin−1(sin 3) = π − 3. Sum: x + y = (2π − 4) + (π − 3) = 3π − 7. Taking tan: tan(x + y) = tan(3π − 7) = tan(−7) = −tan 7. ∴ The correct answer is tan (x + y) = − tan 7. Alternate Method Given: x = cos−1(cos 4) and y = sin−1(sin 3). Formula Used: cos−1(cos θ) = 2nπ ± θ and sin−1(sin θ) = nπ + (−1)nθ, such that the result lies in the Principal Value Branch.

⇒ For x = cos−1(cos 4), since 4 ∈ (π, 2π), we use 2π − 4 ≈ 6.28 − 4 = 2.28 (lies in [0, 3.14]). ⇒ x = 2π − 4 ⇒ For y = sin−1(sin 3), since 3 ∈ (π/2, 3π/2), we use π − 3 ≈ 3.14 − 3 = 0.14 (lies in [−1.57, 1.57]). ⇒ y = π − 3 ⇒ x + y = (2π − 4) + (π − 3) = 3π − 7 ⇒ tan(x + y) = tan(3π − 7) ⇒ tan(x + y) = tan(π − 7) = −tan 7 ∴ The correct answer is tan (x + y) = − tan 7. Additional Information Principal Value Branch For sin−1x, range is [−π/2, π/2]. For cos−1x, range is [0, π]. All input values must be mapped to these intervals. Periodicity of Tangent tan(θ) has a period of π, meaning tan(nπ + θ) = tan θ. Also, tan(−θ) = −tan θ. Quadrant Rules cos(2π − θ) = cos θ (Quadrant IV) and sin(π − θ) = sin θ (Quadrant II). These help in shifting values to the principal range.

Shortcut Trick

Use the direct identity: 2xy = (x² + y²) − (x − y)²

2xy = 156 − 12²

2xy = 156 − 144 = 12

xy = 12 ÷ 2 = 6

∴ The correct answer is 6.

Alternate Method

Given:

x² + y² = 156

x − y = 12

Formula Used:

Using the algebraic identity: (a − b)² = a² + b² − 2ab

Calculations:

⇒ (x − y)² = x² + y² − 2xy

⇒ (12)² = 156 − 2xy

⇒ 144 = 156 − 2xy

⇒ 2xy = 156 − 144

⇒ 2xy = 12

⇒ xy = 12 ÷ 2

⇒ xy = 6

∴ The correct answer is 6.

Additional Information

Square of Sum Identity

The square of the sum of two numbers is given by (x + y)² = x² + y² + 2xy.

Difference of Squares

The difference between the squares of two numbers is factorized as x² − y² = (x − y)(x + y).

Relation between (x+y) and (x-y)

The two identities are related as (x + y)² = (x − y)² + 4xy.

∴ Y is facing the North-east direction.

So, “North-East” is the correct answer.

The correct answer is Janata Party.

Key Points

• On June 25 in 1975, former Prime Minister of India, Indira Gandhi, took the most controversial decision and imposed an Emergency across the country.
• The Emergency remained intact for 21 months and changed the dynamics of the country’s political system.
• The Emergency was imposed on 25 June 1975, its foundation was laid on June 12 that year.
• After the national emergency was imposed, political leaders of opposition parties including Lal Krishna Advani, Atal Bihari Vajpayee, Morarji Desai, and Jayaprakash Narayan were sent to jail.
• On March 21, 1977, the Emergency ended.
• The Janata Party and its allies came to power at the center by defeating Congress Party in 1977.
• Janata Party and its allies won 330 out of 542 seats in the Lok Sabha. Janata Party itself won 295 seats.

Additional Information

• Railway Strike of 1974 was led by George Fernandes. Its main demand was related to bonuses and service conditions.
• The magazines like ‘Seminar’ and ‘Mainstream’ chose to close down after the declaration of emergency in 1975.

The correct answer is Kangaroos.

Key Points

• Kangaroos give birth to poorly developed young ones.
• Kangaroos are called marsupials.
• They Terrifically grow their babies, Kangaroos babies were very tiny when they gave birth.
• They were staying inside the mother’s pouch until they have grown up for about 9 months.
• They can stay for three months in the pouch, after three months they can start to out their head from the pouch.

The correct answer is Jammu and Kashmir.

Key Points

• Dachigam National Park is located in Jammu and Kashmir.
• The park is best known as the home of the hangul, or Kashmir stag.
• 'Dachigam' means “Ten Villages”, which stands for the number of villages that were relocated to facilitate its creation.
• Dachigam was declared a National Park in 1981.

Important Points

Shortcut Trick

Using the Assumed Mean Method, let the assumed mean (A) = 35 and class width (h) = 10.

The deviations (u_i) for the midpoints (15, 25, 35, 45, 55) are −2, −1, 0, 1, 2 respectively.

Σf_iu_i = (8 × −2) + (12 × −1) + (16 × 0) + (11 × 1) + (13 × 2) = −16 − 12 + 0 + 11 + 26 = 9.

Mean = A + (Σf_iu_i ÷ Σf_i) × h = 35 + (9 ÷ 60) × 10 = 35 + 1.5 = 36.5.

∴ The correct answer is 36.5.

Alternate Method

Given:

The frequency distribution of the given class intervals.

Formula Used:

Mean = Σ(f_i × x_i) ÷ Σf_i

where x_i is the midpoint of each class interval and f_i is the corresponding frequency.

Calculations:

Find the midpoints (x_i) of each class interval:

⇒ For 10 - 20: x₁ = (10 + 20) ÷ 2 = 15

⇒ For 20 - 30: x₂ = (20 + 30) ÷ 2 = 25

⇒ For 30 - 40: x₃ = (30 + 40) ÷ 2 = 35

⇒ For 40 - 50: x₄ = (40 + 50) ÷ 2 = 45

⇒ For 50 - 60: x₅ = (50 + 60) ÷ 2 = 55

Calculate the product of frequency and midpoint (f_i × x_i):

⇒ f₁ × x₁ = 8 × 15 = 120

⇒ f₂ × x₂ = 12 × 25 = 300

⇒ f₃ × x₃ = 16 × 35 = 560

⇒ f₄ × x₄ = 11 × 45 = 495

⇒ f₅ × x₅ = 13 × 55 = 715

Calculate the sum of frequencies (Σf_i) and sum of products (Σf_ix_i):

⇒ Σf_i = 8 + 12 + 16 + 11 + 13 = 60

⇒ Σf_ix_i = 120 + 300 + 560 + 495 + 715 = 2190

Calculate the mean:

⇒ Mean = Σf_ix_i ÷ Σf_i = 2190 ÷ 60 = 36.5

Why other options are incorrect:

⇒ Option (1) 12 is incorrect because it lies at the extreme lower end of the first interval and does not represent the central tendency of the dataset.

⇒ Option (2) 23.4 is incorrect because the higher frequencies are concentrated in the 30-60 range, pulling the mean significantly higher than 23.4.

⇒ Option (4) 42.7 is incorrect because it is higher than the actual weighted average of 36.5.

∴ The correct answer is 36.5.

Additional Information

Direct Method for Grouped Mean

The standard formula is Mean = Σf_ix_i ÷ Σf_i, where x_i is the class mark (midpoint) of the i-th class interval.

Assumed Mean Method

Used to simplify calculations: Mean = A + Σf_id_i ÷ Σf_i, where A is the assumed mean and d_i = x_i − A is the deviation.

Step-Deviation Method

Further simplifies calculations when class widths are equal: Mean = A + h × (Σf_iu_i ÷ Σf_i), where u_i = (x_i − A) ÷ h and h is the class width.

The correct answer is Deepika Kumari.

Key Points

• Indian archer Deepika Kumari as a documentary on her life, Ladies First was released on Netflix.
• The documentary was directed by Uraaz Bahl and produced by his wife Shaana Levy-Bahl.
• Deepika is the daughter of Shivnarayan Mahato and Geeta Mahato.
• Shivnarayan is an auto-rickshaw driver while Geeta is a nurse at Ranchi medical college.
• She won her first World Cup individual stage recurve gold medal in May 2012.
• She won two gold medals in the Commonwealth Games in Delhi in 2010.

Important Points

• Rahul Banerjee is an Indian Olympic archer.
• He won a team silver medal, which was the first world-level medal for Indian archers.
• At the 2010 Commonwealth Games in Delhi, he won a gold medal.
• He won a team bronze at the 2010 Asian Games.
• Tarundeep Rai is an Indian archer.
• He has already represented the country at two Olympic Games - Athens 2004 and London 2012.
• Jayanta Talukdar is an Indian archer.
• He won the silver medal at the 2004 Junior World Championships.
• In 2006 he also won a gold medal at the South Asian Games.

Shortcut Trick

Use the direct formula for Time (T) = (SI × 100) ÷ (P × R)

T = (390 × 100) ÷ (1800 × 5) = 390 ÷ 90 years

T = 13 ÷ 3 = 4 (1/3) years

T = 4 years + (1/3 × 12) months = 4 years 4 months.

∴ The correct answer is 4 years, 4 months.

Alternate Method

Given:

Principal (P) = ₹ 1,800

Simple Interest (SI) = ₹ 390

Rate (R) = 5% per annum

Formula Used:

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

Calculations:

⇒ 390 = (1800 × 5 × T) ÷ 100

⇒ 390 = 18 × 5 × T

⇒ 390 = 90 × T

⇒ T = 390 ÷ 90 = 39/9 years

⇒ T = 4 (3/9) years = 4 (1/3) years

⇒ T = 4 years + (1/3 × 12) months = 4 years 4 months

∴ The correct answer is 4 years, 4 months.

Additional Information

Amount in Simple Interest

The total sum payable at the end of the period is the Amount (A), calculated as A = P + SI = P(1 + RT/100).

Rate of Interest Formula

To find the annual rate of interest: R = (SI × 100) ÷ (P × T).

Principal Formula

To find the initial sum invested: P = (SI × 100) ÷ (R × T).

The correct answer is the Density of the fluid and the volume of the body immersed in it.

Key Points

• The buoyant force depends on the volume of the liquid displaced. The buoyant force depends on the mass of the object, the weight of the object, and its density.
• The buoyant force depends directly upon:
• The volume of the fluid displaced.
• The density of the fluid in which the body is immersed.
• Acceleration due to gravity at the place.

Important Points

• The three types of buoyancy are positive buoyancy, negative buoyancy, and neutral buoyancy.
• Positive buoyancy is when the immersed object is lighter than the fluid displaced and this is the reason why the object floats.
• Negative buoyancy is when the immersed object is denser than the fluid displaced which results in the sinking of the object.
• Neutral buoyancy takes place when the weight of an immersed object is equal to the fluid displaced.

Shortcut Trick

Net efficiency = 1/4 + 1/6 − 1/8

LCM of 4, 6, 8 = 24. Efficiencies: A = 6, B = 4, C = −3.

Combined efficiency = 6 + 4 − 3 = 7 units/hr.

Time = 24 ÷ 7 = 3.428 hours ≈ 3 hours 26 minutes.

∴ The correct answer is 3 hr, 26 min.

Alternate Method

Given: Filling time Tap A = 4 hrs, Tap B = 6 hrs. Emptying time Tap C = 8 hrs.

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

⇒ Total Efficiency when all open = 6 + 4 − 3 = 7 units/hr

⇒ Time taken = 24 ÷ 7 hours

⇒ Time = 3 ³⁄₇ hours

⇒ Time = 3 hr + (3/7 × 60) min ≈ 3 hr + 25.7 min ≈ 3 hr 26 min

∴ The correct answer is 3 hr, 26 min.

Additional Information

Pipes and Cisterns Convention

Inlet pipes have positive efficiency (work to fill), whereas outlet/leak pipes have negative efficiency (work to empty).

Total Time Formula

If two pipes fill in x and y hours and one empties in z hours, Net Work in 1 hour = (1/x + 1/y − 1/z).

Work and Wages

Wages are distributed in the direct ratio of efficiency or work done by each pipe/tap if they work for the same duration.

The Correct Answer is Option 2 i.e Neutrons.

• The atom is composed of the proton, the neutron, and the electron.
• Protons and neutrons make up the nucleus of the atom, whereas the negatively charged electrons revolve around the nucleus.
• The number of protons found in the nucleus equals the number of electrons that surround it
• Protons and neutrons have nearly equal masses, but they differ in charge.
• Protons:
• The number of protons within the nucleus of a given atom is equal to the atomic number of the corresponding element. 
• For example, the atomic number of helium is two. Therefore, the number of protons is also two.
• Neutrons:
• The number of neutrons within the nucleus of a given atom can be found by subtracting the atomic number from the atomic mass i.e difference between the mass number of the atom and the atomic number.
• The mass number is equal to the sum of protons and neutrons in an atom.
• Example Sodium, Na has Atomic Number is 11 and the Mass number is 23.
• So Protons are 11, Neutrons are 12, and electrons are 11.

The pattern followed here is:

4 + 13 × 1 = 17

17 + 13 × 2 = 43

43 + 13 × 3 = 82

82 + 13 × 4 = 134

Hence, “134” is the correct answer.

The correct answer is Rhizopus.

Key Points

• Spore formation is a method of asexual reproduction.
• Plants like ferns, moss, fungi reproduce by this method.
• Spores are unicellular reproductive bodies present in a sac called sporangia.
• Rhizopus is a saprophytic fungus and grows on substrates like bread, jelly, leather, decaying vegetables, and fruits.
• It is commonly called ‘Bread mold’.

Important Points

CONCEPT:

Here we need to use BODMAS, firstly divide, then multiply and then add and lastly subtract.

CALCULATION:

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

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

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

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

calculated,

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

should be calculated.

Now,

8.53 + 6.6 × 0.8 - 1.17 ÷ 0.09

⇒ 8.53 + 6.6 × 0.8 – (1.17/0.09)

⇒ 8.53 + 5.28 – 13

∴ 13.81 – 13 = 0.81

1. In figure A white area is on the left side of both the shapes and black area is on the right side of both the shapes.

 2) In figure B white area is on the right side of both the shapes and black area is on the left side of both the shapes.

3. In figure C white area is on the bottom side of both the shapes and black area is on the top side of both the shapes.

4. In figure D white area in both shapes is on different side (in circle white area is on top side and in rectangle white area is in bottom side) and black area in both shapes is also on different side (in circle black area is on bottom side and in rectangle black area is in top side).

So Figure D is the odd one out.

Hence, “Figure D” is the correct answer.

Total Seconds in a day =  86400

Total seconds in  7 minutes 12 seconds = 420 + 12 = 432 

fraction of a day are 7 minutes 12 seconds = 432/86400 = 1/200

Hence, 1/200 is the correct answer.

Age order according to given question:

Beena > Meena

Kavi > Swathi

Statement I:

“Swathi is younger than Beena” (i.e Beena > Swathi)

There are two possibilities of the age order according to this statement:

1. Beena > Meena > Kavi > Swathi

2. Beena > Kavi > Swathi > Meena

So, “Statment I” is not sufficient to answer the question.

Statement II:

“Kavi is younger than Meena” (i.e Meena > Kavi)

There is only one possibility of the age order according to this statement:

Beena > Meena > Kavi > Swathi

So, Swathi is the youngest.

 ∴ Data in Statement II alone is sufficient to answer the given question.

Hence, “Data in II alone is sufficient” is the correct answer.

The pattern here is as follows:

Similarly, 

Hence, “Diagram D” is the correct answer.

From the given statements we can draw the least possible Venn diagram for the given question and answer the conclusions according to Venn diagram:

Conclusion 1: “All rats are cats”.

It is possible but not definite. Hence, conclusion “All rats are cats” is false.

Conclusion 2: “Some of the tigers are rats”.

As some tiger are cats and all cats are rats.

So, the conclusion “Some of the tigers are rats” is true.

Hence, “Only conclusion 2 follows” is the correct answer.

The correct answer is Evolution.

Key Points

• Evolution in its contemporary meaning in biology typically refers to the changes in the proportions of biological types in a population over time.
• Evolution is the change in the characteristics of a species over several generations and relies on the process of natural selection.
• Evolution relies on there being genetic variation? in a population which affects the physical characteristics (phenotype) of an organism.
• Charles Darwin is usually the starting point for contemporary understandings of evolution.
• Charles Darwin’s theory of evolution states that evolution happens through natural selection.
• Individuals in a species show variation in physical characteristics.
• This variation is because of differences in their genes.

Important Points

Shortcut Trick

Efficiency Ratio is the inverse of Time Ratio when work is constant.

Ratio of time (A : B) = 5 : 8 → Ratio of efficiency (A : B) = 8 : 5

Total ratio parts = 8 + 5 = 13 units → ₹6760

A’s share = (8 ÷ 13) × 6760 = 8 × 520 = ₹4160

∴ The correct answer is ₹4160.

Alternate Method

Given: Time taken by A = 5 days, Time taken by B = 8 days, Total Wages = ₹6760.

Formula Used: Wages are distributed in the ratio of Efficiency when people work for the same duration. Efficiency = Total Work ÷ Time.

⇒ Ratio of efficiency of A : B = 8 : 5

⇒ Sum of ratios = 8 + 5 = 13

⇒ 13 units = ₹6760

⇒ 1 unit = 6760 ÷ 13 = ₹520

⇒ A’s share = 8 units = 8 × 520

⇒ A’s share = ₹4160

∴ The correct answer is ₹4160.

Additional Information

Work and Wages Rule

Wages are directly proportional to the work done. If time is same for all, Wages ∝ Efficiency. If work is done for different durations, Wages ∝ (Efficiency × Time).

Pipes & Cisterns Wage Analogy

Similar to men working, the rate of flow (efficiency) of a pipe determines its contribution to the total volume filled/emptied.

Shortcut Trick

Identify complementary angles: tan θ × tan (90° − θ) = 1.

Pairing: (tan 8° × tan 82°) = 1 and (tan 22° × tan 68°) = 1.

The expression simplifies to: 1 × 1 × cot 60°.

Value of cot 60° = 1/√3.

∴ The correct answer is 1/√3.

Alternate Method

Given: tan 8° tan 22° cot 60° tan 68° tan 82°

Formula Used: tan (90° − θ) = cot θ and tan θ × cot θ = 1

⇒ Expression = tan 8° × tan 22° × cot 60° × tan (90° − 22°) × tan (90° − 8°)

⇒ Expression = tan 8° × tan 22° × cot 60° × cot 22° × cot 8°

⇒ Expression = (tan 8° × cot 8°) × (tan 22° × cot 22°) × cot 60°

⇒ Expression = 1 × 1 × (1/√3)

⇒ Expression = 1/√3

∴ The correct answer is 1/√3.

Additional Information

Complementary Angle Identities

For any angle θ, sin (90° − θ) = cos θ, tan (90° − θ) = cot θ, and sec (90° − θ) = cosec θ.

Standard Trigonometric Values

tan 30° = 1/√3, tan 45° = 1, tan 60° = √3. Note that cot θ = 1/tan θ, so cot 60° = 1/tan 60° = 1/√3.

Product Rule for Tangents

If A + B = 90°, then tan A × tan B = 1 and cot A × cot B = 1.

The correct answer is Shivangi Pathak.

• India's Shivangi Pathak has become the youngest woman in the country to scale Mt Everest from the Nepal side.
• She was 16 years old when she got this achievement.

Important Points

Additional Information

• Raghav Joneja from Moradabad became the youngest Indian to scale Mount Everest when he along with his five schoolmates climbed the first highest peak in the world.
• He set his record at age of 15 years and 7 months.

The correct answer is Lead and tin.

• Solder is a metal alloy usually made of tin (60%) and lead (40%) which is melted using a hot iron.
• Soldering is a joining process used to join different types of metals together by melting solder.

Important Points

• List of Important Alloys and their Uses:

Shortcut Trick

Use the chain rule for successive profits: Initial CP × (100 + P₁)% × (100 + P₂)% = Final Price.

Let the cost price for M be x.

x × (110 ÷ 100) × (104 ÷ 100) = 14,300.

x × 1.1 × 1.04 = 14,300 ⇒ x × 1.144 = 14,300.

x = 14,300 ÷ 1.144 = 12,500.

∴ The correct answer is Rs. 12,500.

Alternate Method

Given: Profit of M = 10%, Profit of N = 4%, Price paid by P = Rs. 14,300.

Formulas: SP = CP × (100 + P%) ÷ 100

⇒ Let CP of M = Rs. x.

⇒ Selling Price of M (which is CP for N) = x × (110 ÷ 100) = 1.1x.

⇒ Selling Price of N (which is CP for P) = 1.1x × (104 ÷ 100) = 1.144x.

⇒ According to the question: 1.144x = 14,300.

⇒ x = 14,300 ÷ 1.144.

⇒ x = 12,500.

∴ The correct answer is Rs. 12,500.

Additional Information

Successive Percentage Change

When a value is changed by a% and then b%, the net effective change is given by (a + b + ab ÷ 100)%.

Cost Price vs Selling Price

The Selling Price for the first person becomes the Cost Price for the next person in a chain of transactions.

From the given statements we can draw the least possible Venn diagram for the given question and answer the conclusions according to the Venn diagram:

Conclusion 1: “Some bulbs are lamps” (True)

As some bulbs are lights and all lights are lamps.

So, the conclusion “Some bulbs are lamps” is true.

Conclusion 2: “No light is a bulb”.

It is not possible as some bulbs are lights. Hence, conclusion “No light is a bulb” is false.

Hence, “only conclusion 1 follows” is the correct answer.

In the figure A, B, C there is a similarity that embedded figure is same as the outer figure.

But in figure D, the embedded figure is not same as the outer figure. Figure D is the odd one out.

Hence, “Figure D” is the correct answer.

Shortcut Trick CP = 100% | Given loss = 7% ⇒ SP1 = 93% 93% ≡ Rs. 31 ⇒ 1% ≡ 31 ÷ 93 = 1/3 SP2 = Rs. 35 ⇒ Percentage value = 35 × 3 = 105% Profit% = 105% − 100% = 5% ∴ The correct answer is 5% profit.

Alternate Method Given: SP1 = Rs. 31, Loss% = 7%, SP2 = Rs. 35 Formulas: CP = [SP × 100] ÷ [100 − Loss%], Profit% = [(SP − CP) ÷ CP] × 100

⇒ Cost Price (CP) = (31 × 100) ÷ (100 − 7) = 3100 ÷ 93 = Rs. 100/3 ⇒ New Selling Price (SP2) = Rs. 35 ⇒ Profit = 35 − 100/3 = (105 − 100) ÷ 3 = Rs. 5/3 ⇒ Profit% = [(5/3) ÷ (100/3)] × 100 = (5 ÷ 100) × 100 = 5% ∴ The correct answer is 5% profit.

Additional Information Cost Price and Outlay The term outlay refers to the total Cost Price (CP) including any overhead expenses incurred on the article. Relationship between SP and CP If SP > CP, it is a Profit. If SP < CP, it is a Loss. Profit or Loss is always calculated on the CP unless stated otherwise.

The correct answer is Agriculture & farmers.

Important Points

• Ministry of Agriculture funding start-ups under the innovation and agripreneurship component of Rashtriya Krishi Vikas Yojana in 2020-21.
• A component, Innovation and Agri-entrepreneurship Development program has been launched under this program.
• These start-ups are in various categories such as:
• Agro-processing, artificial intelligence, digital agriculture, farm mechanization, waste to wealth, dairy, fisheries, etc.
• The Cabinet has approved (1st November 2017) for the continuation of the ongoing Centrally Sponsored Scheme (State Plans) – Rashtriya Krishi Vikas Yojana (RKVY) as Rashtriya Krishi Vikas Yojana- Remunerative Approaches for Agriculture and Allied Sector Rejuvenation (RKVY-RAFTAAR).
• In the first phase, 112 startups in the area of agro-processing, food technology and value addition will be funded for a sum of Rs. 1185.90 lakhs.
• The Rashtriya Krishi Vikas Yojna (RKVY) which aims at strengthening infrastructure in agriculture and allied areas,

The correct answer is Mukesh Ambani.

Key Points

• Reliance Industries Chairman Mukesh Ambani has topped the Forbes Global Game Changers list in 2017.
• The top 5 spots in the list have been occupied by:

1. Mukesh Ambani of India
2. Ziv Aviram, Amnon Shashua of Israel
3. Stewart Butterfield of United States
4. John and Patrick Collison of the United States
5. James Dyson of United Kingdom

Additional Information 

• Kumar Mangalam Birla, the chairman of the Aditya Birla Group.
• He received the honour of 'The Ernst & Young Entrepreneur of the Year-India' in 2005.

Shortcut Trick

In an Arithmetic Progression (A.P.), the n^th term is calculated as: a + (n − 1)d.

Here, the first term (a) = √2 and the common difference (d) = 2√2.

For the 10^th term, we need to add 9 common differences to the first term.

Calculation: √2 + (9 × 2√2) = √2 + 18√2 = 19√2.

∴ The correct answer is 19√2.

Alternate Method

Given:

Arithmetic Progression: √2, 3√2, 5√2, 7√2, ...

First term (a) = √2

Common difference (d) = 3√2 − √2 = 2√2

Term to find (n) = 10

Formula Used:

n^th term of A.P. (T_n) = a + (n − 1)d

Calculations:

⇒ T₁₀ = √2 + (10 − 1) × (2√2)

⇒ T₁₀ = √2 + 9 × 2√2

⇒ T₁₀ = √2 + 18√2

⇒ T₁₀ = 19√2

∴ The correct answer is 19√2.

Additional Information

Arithmetic Progression (A.P.) General Term

The general term is T_n = a + (n − 1)d, where 'a' is the first term and 'd' is the common difference.

Common Difference

It is obtained by subtracting any term from its succeeding term: d = T₂ − T₁ = T₃ − T₂.

Sum of First n Terms

The sum S_n is given by (n/2)[2a + (n − 1)d] or (n/2)[a + l], where 'l' is the last term.

Number of odd days from 22 feburary 2002 to 22 feburary 2008 = 1 + 1 + 2 + 1 + 1 + 1 = 7 (0 odd day)

Number of odd days from 22 feburary 2008 to 15 march 2008 = 7 + 15 = 22 (1 odd day)

So total number of odd days from 22 feburary 2002 to 15 march 2008 = 1

So, the day on 15 march 2008 was “Saturday”.

Hence, **“Saturday”**is the correct answer.

CONCEPT:

A normal year has 365 days (i.e.) 52 weeks plus 1 odd day. When we proceed forward by one year, then 1 day is gained and vice-versa.

Leap years have 366 days. The extra day is added to February which has 29 days in a leap year.

When we proceed forward by one leap year, then 2 odd days are gained 

A year is considered to be a leap year if:

a) The year can be evenly divided by 4.

b) If the year can be evenly divided by 100, it is NOT a leap year, unless;

c) The year is also evenly divisible by 400. Then it is a leap year

Number of odd days in each month in a normal year:

Number of odd days in each month in a leap year:

DIAGRAM

So, “diagram A” is the correct answer.

The pattern is as follows:

Outer rectangle symbols are turned anticlockwise and placed in inner rectangle and inner rectangle symbols are turned clockwise and placed in the inner rectangle

 Hence “Figure 3” is the correct answer.

Alternate MethodThe outer shape of the rectangle is placed in the inner rectangle, and the inner shape of the rectangle is placed in the outer rectangle:

Similarly,

Hence, the correct answer is "Option 3".

The correct answer is Rs. 2.11 lakh crore.

Key Points

• The Indian government announced an allocation of Rs 2.11 lakh crore over two years for the recapitalization of public sector banks.
• The deficit target of 3.2 percent of GDP for the year.
• The plan is intended to help banks make adequate provisions against bad loans and revive lending.
• It may help support a recovery in the economy and private investment.
• The recapitalization plan is split into two parts:
• Rs 1.35 lakh crore - will come via the issue of recapitalization bonds.
• Rs 76,000 crore, which includes Rs 18,000 crore allocated under the Indradanush Recapitalisation Scheme, will come through budgetary support over two fiscal years.

Number of odd days from 17 January 2004 to 17 January 2013 = 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 +

2 = 12 (5 odd days)

Number of odd days from 17 January 2013 to 10 April 2013 = 14 + 0 + 3 + 10 = 27 (6 odd days)

Number of odd days from 17 January 2004 to 10 April 2013 = 6 + 5 = 11 (4 odd days)

So, on 10 April 2013 will be Wednesday.

Hence, “Wednesday” is the correct answer.

CONCEPT:

A normal year has 365 days (i.e.) 52 weeks plus 1 odd day. When we proceed forward by one year, then 1 day is gained and vice-versa.

Leap years have 366 days. The extra day is added to February which has 29 days in a leap year.

When we proceed forward by one leap year, then 2 odd days are gained 

A year is considered to be a leap year if:

a) The year can be evenly divided by 4.

b) If the year can be evenly divided by 100, it is NOT a leap year, unless;

c) The year is also evenly divisible by 400. Then it is a leap year

Number of odd days in each month in a normal year:

Number of odd days in each month in a leap year:

The correct answer is The Conference of Asian Countries, New Delhi in 1947.

Key Points

• The Asian Games are the oldest and most prestigious event on the Olympic Council of Asia (OCA) calendar, dating back to the inaugural edition in 1951.
• The 2018 Asian Games in Jakarta and Palembang, Indonesia was the 18th edition.
• The flag bearer of this event from the Indian side was Javelin Thrower "Neeraj Chopra".
• The first edition of the Asian Games was held in New Delhi in March 1951.
• The hosted country of the 2022 Asian Games will be Hangzhou, China.

Important Points

• India stood second in the first Asian Games in 1951.
• The Asian Games had been held the most number of times in Bangkok - 4 times.
• Kamaljit Sandhu (Runner) is the first Indian woman to win a gold medal at the Asian Games.

It is clear from the statement that he want to become a school teacher.

Assumption 1: “I am not a school teacher” is implicit.

Assumption 2: “I am a school teacher” is false.

Hence, **“Only assumption I is implicit”**is the correct answer

The correct answer is Abscisic acid.

Key Points

• The plant hormone, Abscisic acid inhibits the growth of the plant.
• Auxin, Gibberellins, and cytokinins promote the growth of the plant.
• Abscisic Acid (ABA) is involved in the closure of stomata, seeds dormancy, and inhibit other hormonal actions.
• It plays an important role in seed maturation.
• It also has an important role in the synthesis of proteins and compatible osmolytes, which enable plants to tolerate stresses due to environmental or biotic factors.

Additional Information

• Cytokinins, Gibberellins, Auxins are responsible for plant growth.
• They are produced within the plant and occur in very low concentrations.
• They control all aspects of plant growth and development, regulation of organ size, embryogenesis, stress tolerance, etc.

The correct answer is 4 mgh.

Key Points

• Potential energy is the stored energy of position possessed by an object.
• Potential Energy (P_e) = m × g × h
• m represents the mass of the object.
• h represents the height of the object.
• g represents the gravitational field strength (9.8 N/kg on Earth).
• Here given height is 4h.
  

So the P_e of the object = m × g × 4h = 4 mgh.

Thus, ([(25 < 15)] × 4) < 1 will be decoded as ([(25 + 15)] ÷ 4) + 1

Solving

([(25 + 15)] ÷ 4) + 1)

= ([(40)] ÷ 4) + 1

= (10) + 1

= 11

Hence, ‘11’ is the correct answer.

The correct answer is Methanoic acid.

• The acid present in an ant sting is Formic acid.
• Formic acid (systematically called methanoic acid) is the simplest carboxylic acid.
• Molecular formula: HCOOH
• It is quite fatal for those ants as after stinging, their stinger is lost and they forcibly release formic acid from their poison gland.

Important Points

• Oxalic acid is an organic compound found in many plants. These include leafy greens, vegetables, fruits, cocoa, nuts, and seeds
• Lactic acid is a natural organic acid, found in milk and other food products such as meat and beer.
• It is used in the food industry as a preservative, flavor enhancer, and acid adjustment.
• Citric acid is found naturally in citrus fruits, like lemons and limes.
• It gives them their tart, sour taste.

In this coding each word is divided into various set of two alphabets and each set is reversed and then merged respectively.

Like “VISITORS” is divided into sets of VI, SI, TO, RS and each set is reversed IV, SI, OT, SR and then these sets are merged respectively IVSIOTSR.

Similarly, “STATUS” is divided into sets of ST, AT, US and each set is reversed TS, TA, SU and then these sets are merged respectively TSTASU.

Hence, “TSTASU” is the correct answer.

Each alphabet in second word is obtained by “alphabet position value in first word -1”.

So the word “CREATION” is coded as:

Similarly the word “PRODUCTION” is coded as:

Hence, “OQNCTBSHNM” is the correct answer.

Difference between the consecutive terms,

⇒ 12 - 6 = 6

⇒ 20 - 12 = 8

⇒ 30 - 20 = 10

⇒ ? - 30 = 12

⇒ 56 - ? = 14

⇒ 72 - 56 = 16

∴ ? = 12 + 30 = 42

The correct answer is Meerut.

Key Points

• With a daily earning of nearly Rs 10 crore, Meerut is the largest jewellery market in Uttar Pradesh and among the top ten in the country.
• With over 40,000 artisans and 2,000 jewelry shop owners in the city depending on the industry.
• The gems and jewelry sector plays a significant role in the Indian economy, contributing around 7% of the country’s GDP and 15% to India’s total merchandise export.
• India’s gems and jewelry sector is one of the largest in the world, contributing 29% to global jewelry consumption.
• The sector is home to more than 300,000 gems and jewelry players.
• Its market size will grow by US$ 103.06 billion during 2019–2023.

The correct answer is Group 18.

Important Points

• The periodic table was first given by Mendeleev of 63 elements and defined as " physical and chemical properties of the elements are the periodic function of their atomic masses".
• After Mendeleev due to some demerits, a Modern Periodic table was given by Henry Moseley which is defined as "physical and chemical properties of elements are the periodic function of their atomic number".
• In the periodic table, vertical columns are called groups, and horizontal rows are called periods.
• In the periodic table, 18 groups and 7 periods are given and 118 elements discovered till now.

Key Points

• In the periodic table, group 18 called as Inert gases group or noble gases group because all elements are in a gaseous state of this group and all elements are stable in nature.
• It includes helium, neon, argon, krypton, xenon, and radon.
• The characterized of Noble gases are:
• Low reactivity
• Low boiling point
• Very low electronegativity
• High ionization energy
• Colourless and odourless

Shortcut Trick

Simplify both factors to the form (a − b) and (a + b).

First part: 3√9 − 3√8 = 9 − 6√2

Second part: 9 + 2√18 = 9 + 6√2

Product inside the root: (9 − 6√2)(9 + 6√2) = 9² − (6√2)² = 81 − 72 = 9

The result is √9 = 3.

∴ The correct answer is 3.

Alternate Method

Given:

Expression: √((3√9 − 3√8)(9 + 2√18))

Formula Used:

1. (a − b)(a + b) = a² − b²
2. √x² = x

Calculations:

⇒ √((3 × 3 − 3 × √(4 × 2)) × (9 + 2 × √(9 × 2)))

⇒ √((9 − 3 × 2√2) × (9 + 2 × 3√2))

⇒ √((9 − 6√2) × (9 + 6√2))

Using the algebraic identity (a − b)(a + b) where a = 9 and b = 6√2:

⇒ √(9² − (6√2)²)

⇒ √(81 − 36 × 2)

⇒ √(81 − 72)

⇒ √9

⇒ 3

∴ The correct answer is 3.

Additional Information

Algebraic Identities

The identity (a − b)(a + b) = a² − b² is used to simplify the product of conjugate surds.

Simplifying Surds

A surd √(m²n) can be simplified to m√n by extracting the perfect square factor from the radicand.

Square Root Property

For any positive real number x, the principal square root √x is always positive.

The correct answer is Hindi Medium.

Key Points

• The Irfan khan and Saba Qamar starrer 'Hindi Medium' was named the best film at the 63rd edition of the Filmfare Awards.
• Irfan won the Best Actor award at the 63rd Jio Filmfare Awards 2018  for 'Hindi Medium' while
• Vidhya Balan won the Best Actress award at the 63rd Jio Filmfare Awards 2018 for 'Tumahri Sulu'.

Additional Information

• Toilet Ek Prem Katha was a movie directed by Shree Narayan Singh
• ​This film is Co-produced by Akshay Kumar and Neeraj Pandey, the film stars Akshay Kumar and Bhumi Pednekar in the lead roles.
• ​This film is a satirical comedy in support of governmental campaigns to improve sanitation conditions in India, with an emphasis on the eradication of open defecation, especially in rural areas.
• Rustom is a movie in which Akshay Kumar and Illeana D'Cruz in a leading role.
• Rajkumar Rao starrer 'Newton' won the Best Film ( critics) Filmfare Award.
• This Movie has been selected as India's official entry to the Oscars.

The correct answer is Affordable housing.

Key Points

• Pradhan Mantri Awas Yojana (Urban) mission launched on 25th June 2015.
• Its aim is to provide housing for all in urban areas by the year 2022.
• The Yojana involves the construction of around 20 million houses at an affordable price by March 31, 2022.
• The Mission provides Central Assistance to the implementing agencies through States/ Union Territories (UTs) and central nodal agencies for providing houses to all eligible families/ beneficiaries against the validated demand for houses for about 1.12cr.
• As per PMAY(U) Guidelines, the size of the house for the Economically Weaker Section( EWS) could be up to 30 sq. mt. carpet area, States/UTs have the flexibility to enhance the size of houses in consultation and approval of the ministry.
• This is the government's effort towards the (**PMAY)**empowerment of women from EWS and LIG unlike earlier schemes, PMAY(U) has made a mandatory provision for the female head of the family to be the owner or co-owner of the house under this mission.

CONCEPT:

Here we need to take common and then calculate the square root.

FORMULAE USED:

 (A^x)^y = A^xy

CALCULATION:

 (3³⁸ + 3³⁹)^1/2 = (3³⁸ (1 + 3) )^1/2 = (3³⁸ × 4)^0.5 = 3¹⁹ × 2

∴ The answer is 2 × 3¹⁹

Key Points ​

• Reflection- When the light rays fall on the plane surface it deviates from its path in the same medium. 
• or When a ray of light is incident on the plane surface is reflected back into the same medium it is termed as Reflection.
• Example - Plane Mirror.

​

Important Points

• The angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.
• Laws of reflection
• The angle of incidence is equal to the angle of reflection.
• The Normal, Incident ray, reflected ray lie on the same plane at the point of Incidence.
• Refractive Index- It is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density.
• formula, n= c/v  where n= refractive index, c= speed of light, v= phase velocity of a light.

Additional Information

• Refraction- When a light ray travels from one transparent medium to another transparent medium then it deviates from its original path and this phenomenon is called Refraction.
• For example- when light travels from the Rarer medium (Air) to the Denser medium (Water) is deviates towards the Normal.
• Laws of refraction
• The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
• The Normal, Incident ray, Refracted ray lie on the same plane at the point of Incidence.

Mistake Points

• For refraction- 
• The Normal, Incident ray, Refracted ray lie on the same plane at the point of Incidence.
• For reflection 
• The Normal, Incident ray, reflected ray lie on the same plane at the point of Incidence