RRB Group D Previous Year Paper (Held on: 18 Aug 2022 Shift 1)

The correct answer is 4 Only.

Key Points

• Reduction is a chemical reaction that involves the loss of oxygen or the gain of hydrogen by a substance.
• In the context of redox (reduction-oxidation) reactions:
• Statement I: If a substance loses oxygen during a reaction, it is said to be reduced. This is correct because the loss of oxygen is one of the criteria for reduction.
• Statement II: If a substance gains hydrogen during a reaction, it is said to be reduced. This is also correct because the gain of hydrogen is another criterion for reduction.
• Thus, both statements are true and accurately describe the process of reduction in a chemical reaction.

The correct answer is Odisha

Key Points

• Odisha became the first state in India to launch 'Air Health Service' in rural areas in March 2022.
• The initiative aims to provide advanced healthcare services in remote and rural areas using air transportation.
• This service will help in reducing the time taken to reach medical facilities and provide timely treatment to patients in need.
• The 'Air Health Service' initiative is expected to significantly improve the healthcare infrastructure and accessibility in the rural regions of Odisha.

Additional Information

• Odisha has been at the forefront of implementing various innovative healthcare programs to improve the health and well-being of its citizens.
• The state government has also been focusing on building robust healthcare infrastructure and ensuring that medical services reach the most remote areas.
• Other states are expected to follow Odisha's example and implement similar services to enhance healthcare delivery in rural regions.

Shortcut Trick

Since AB || QP, by the Basic Proportionality Theorem, the triangles ΔRAB and ΔRQP are similar.

Therefore, the ratio of their corresponding sides is equal:

AB ÷ QP = RB ÷ RP

⇒ x ÷ (x + 10) = (x/2) ÷ (x/2 + x + 1)

⇒ 1 ÷ (x + 10) = 1 ÷ (3x + 2) ⇒ 3x + 2 = x + 10 ⇒ 2x = 8 ⇒ x = 4

⇒ PQ = x + 10 = 4 + 10 = 14 units

∴ The correct answer is 14 units.

Alternate Method

Given:

AB || QP

AB = x

PQ = x + 10

RB = x/2

BP = x + 1

Formula Used:

In similar triangles, the ratio of corresponding sides is equal. Since AB || QP, we have ΔRAB ∼ ΔRQP, which gives:

AB ÷ QP = RB ÷ RP

Calculations:

⇒ RP = RB + BP

⇒ RP = (x/2) + (x + 1)

⇒ RP = (3x + 2)/2

Using the similarity ratio:

⇒ AB ÷ QP = RB ÷ RP

⇒ x ÷ (x + 10) = (x/2) ÷ ((3x + 2)/2)

⇒ x ÷ (x + 10) = x ÷ (3x + 2)

Since x cannot be 0, we divide both sides by x:

⇒ 1 ÷ (x + 10) = 1 ÷ (3x + 2)

⇒ 3x + 2 = x + 10

⇒ 2x = 8

⇒ x = 4

Substitute the value of x to find the length of PQ:

⇒ PQ = x + 10

⇒ PQ = 4 + 10 = 14 units

Verification of other options:

If PQ = 13 units (Option 1): x + 10 = 13 ⇒ x = 3. Then AB = 3, RB = 1.5, BP = 4, RP = 5.5. The ratio AB/QP = 3/13 ≈ 0.23, while RB/RP = 1.5/5.5 ≈ 0.27. Since the ratios are not equal, this option is incorrect.

If PQ = 18 units (Option 3): x + 10 = 18 ⇒ x = 8. Then AB = 8, RB = 4, BP = 9, RP = 13. The ratio AB/QP = 8/18 = 4/9 ≈ 0.44, while RB/RP = 4/13 ≈ 0.31. Since the ratios are not equal, this option is incorrect.

If PQ = 12 units (Option 4): x + 10 = 12 ⇒ x = 2. Then AB = 2, RB = 1, BP = 3, RP = 4. The ratio AB/QP = 2/12 = 1/6 ≈ 0.17, while RB/RP = 1/4 = 0.25. Since the ratios are not equal, this option is incorrect.

∴ The correct answer is 14 units.

Additional Information

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

Similarity of Triangles

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (proportional).

The correct answer is Option 2.

Key Points

• Statement a: Plants do not move, whereas animals move in search of food, mate, and shelter. This statement is correct.
• Statement b: Most tissues are dead in plants, whereas most tissues are living in animals. This statement is correct.
• Statement c: Plants need less energy, whereas animals need more energy. This statement is correct.
• Statement d: Growth is limited to certain regions in both plants and animals. This statement is incorrect. Growth is limited to certain regions in plants but not in animals.

Additional Information

• Plants:
• Plants are generally stationary and do not move from place to place.
• Most of the plant tissues are dead at maturity, which provides structural support.
• Plants require less energy as they produce their own food through photosynthesis.
• Growth in plants is typically restricted to meristematic regions (e.g., root and shoot tips).
• Animals:
• Animals are mobile and move in search of food, mate, and shelter.
• Most of the animal tissues are living, which supports various functions like movement, digestion, and reproduction.
• Animals require more energy as they have to perform various activities and obtain food from external sources.
• Growth in animals is not limited to certain regions and occurs throughout the body.

The logic followed here is:

Logic: (1st number)² + 9 = 2nd number.

Now,

For, 11 : 130

⇒ 11² + 9 = 121 + 9 = 130.

For, 7 : 58

⇒ 7² + 9 = 49 + 9 = 58.

Similarly, for 15 : ?

⇒ 15² + 9 = 225 + 9 = 234.

Hence, the correct answer is "Option 2".

The correct answer is Prophet Muhammad

Key Points

• Prophet Muhammad is considered the founder of Islam.
• He is believed to be the last prophet sent by God to guide humanity.
• Prophet Muhammad's teachings are compiled in the holy book of Islam, the Quran.
• He was born in Mecca in 570 CE and began receiving revelations from God at the age of 40.
• His teachings emphasized monotheism, social justice, and moral conduct.

Additional Information

• Islam is one of the world's major religions, with over a billion followers globally.
• The word "Islam" means "submission to the will of God."
• Muslims follow the Five Pillars of Islam, which are the basic acts of worship and the foundation of a Muslim's faith and practice.
• The life and teachings of Prophet Muhammad have had a profound impact on the world and continue to influence the lives of many people today.
• His migration from Mecca to Medina in 622 CE, known as the Hijra, marks the beginning of the Islamic calendar.

The correct answer is option 3

Key Points

• The movement of food in phloem is represented by figure C.
• Phloem is responsible for the translocation of nutrients, particularly sugar, from the leaves to other parts of the plant.
• This process is known as source to sink movement, where the source is the part of the plant where the food is produced (usually the leaves), and the sink is where the food is consumed or stored (such as roots, fruits, and seeds).
• The correct diagram would illustrate the flow from the source (leaves) to the sink (roots, fruits, etc.) via the phloem vessels.

Additional Information

• Phloem is one of the two types of vascular tissue in plants, the other being xylem.
• While xylem transports water and minerals from roots to other parts of the plant, phloem distributes the products of photosynthesis.
• The movement in phloem is bidirectional, meaning it can move substances up or down the plant as needed.
• This process is energy-dependent and involves active transport mechanisms.
• Phloem tissues consist of sieve tube elements, companion cells, phloem fibers, and phloem parenchyma.

The correct answer is First attempt to relate the properties of elements with atomic mass.

Key Points

• Dobereiner's triads were an early attempt to classify elements based on their properties and atomic masses.
• He grouped elements in sets of three (triads) where the atomic mass of the middle element was approximately the average of the other two.
• This classification showed a relationship between the atomic masses and the properties of elements, paving the way for future periodic table developments.
• Examples of Dobereiner's triads include lithium, sodium, and potassium; calcium, strontium, and barium.

Additional Information

• Johann Wolfgang Döbereiner was a German chemist who made significant contributions to the development of the periodic classification of elements.
• His work on triads in the early 19th century was among the first systematic attempts to identify patterns in the properties of elements.
• Döbereiner's observations contributed to the later development of the periodic law by Dmitri Mendeleev.
• The concept of triads eventually evolved into the modern periodic table, where elements are arranged based on increasing atomic number and recurring chemical properties.
• Despite the limitations of his triads, Döbereiner's work highlighted the importance of atomic mass in the study of chemical elements.

Given: Eight friends Kriti, Durga, Manasi, Surya, Tahira, Vritti, Ahana, and Yoshita are sitting around a square table and all are facing the centre of the table.

1. Surya is sitting at the third place to right of Durga. 2. Manasi is second to left of Durga. 3. Vritti is second to left of Manasi.

4. Only Tahira is between Kriti and Durga. 

5. Only Vritti is sitting between Surya and Yoshita. 6. Yoshita is second to left of Ahana.

So, 'Manasi' is sitting third to the left of Tahira.

Hence, the correct answer is "Option 4".

The correct answer is They are not soluble in an organic solvent.

Key Points

• Covalent compounds are formed by the sharing of electrons between atoms.
• They generally do not form ions.
• Covalent compounds are usually soluble in organic solvents but not in water.
• They are typically bad conductors of electricity and heat due to the absence of free ions or electrons.

Additional Information

• Covalent compounds often have low melting and boiling points compared to ionic compounds.
• They can exist in all three physical states: solid, liquid, and gas, at room temperature.
• The bond formed in covalent compounds is directional, which affects their physical properties.
• Examples of covalent compounds include methane (CH₄), water (H₂O), and carbon dioxide (CO₂).

The correct answer is Tenth Five Year Plan

Key Points

• Bharat Nirman was launched during the Tenth Five Year Plan period (2002-2007).
• The initiative aimed at improving rural infrastructure, including areas such as irrigation, roads, housing, water supply, electrification, and telecommunication connectivity.
• The program sought to provide basic amenities and bridge the gap between rural and urban areas.
• It was a time-bound business plan for action in rural infrastructure for a period of four years (2005-2009).

Additional Information

• The Tenth Five Year Plan aimed at achieving a GDP growth rate of 8% per annum.
• It emphasized the importance of social development and poverty reduction.
• The plan also focused on increasing employment opportunities and improving the quality of education and healthcare services.
• Other major initiatives during the Tenth Plan included the National Rural Employment Guarantee Act (NREGA), now known as MGNREGA, aimed at providing employment to rural households.

Shortcut Trick

The Marked Price (MP) is Rs. 10,490 and the Selling Price (SP) is Rs. 9,441.

Discount = MP − SP = 10,490 − 9,441 = Rs. 1,049.

Discount % = (Discount ÷ MP) × 100.

Discount % = (1,049 ÷ 10,490) × 100 = 1/10 × 100 = 10%.

∴ The correct answer is 10%.

Alternate Method

Given: Marked Price (MP) = Rs. 10,490, Selling Price (SP) = Rs. 9,441.

Formulas: Discount = MP − SP | Discount % = (Discount ÷ MP) × 100

⇒ Discount = Rs. 10,490 − Rs. 9,441 = Rs. 1,049

⇒ Discount % = (1,049 ÷ 10,490) × 100

⇒ Discount % = 0.1 × 100 = 10%

∴ The correct answer is 10%.

Additional Information

Marked Price & Discount

The price listed on the label is the Marked Price. Discount is always calculated on the MP unless stated otherwise. SP = MP − Discount.

Selling Price Formula

To find SP when discount % is given: SP = MP × (100 − Discount%) ÷ 100.

The correct answer is (3)/(2) R

Key Points

• Given a wire of length 'l' and resistance 'R', we need to find the resistance of another wire of the same material with three times the length and twice the cross-sectional area.
• Resistance (R) is directly proportional to the length (l) of the wire and inversely proportional to its cross-sectional area (A), given by the formula: R = ρ(l/A), where ρ is the resistivity of the material.
• For the second wire, the length becomes 3l and the cross-sectional area becomes 2A.
• Substituting these values into the resistance formula, we get the new resistance R' as: R' = ρ(3l/2A).
• This simplifies to: R' = (3/2) * (ρ(l/A)).
• Since ρ(l/A) is the original resistance R, we get: R' = (3/2) * R.
• Thus, the resistance of the second wire is (3)/(2) R.

Additional Information

• This problem uses the fundamental concept of resistance in electrical circuits, which is crucial for understanding the behavior of electrical components.
• Understanding how resistance changes with length and cross-sectional area is important for designing electrical systems and components.
• This principle is widely applied in electrical engineering and physics to solve practical problems related to electrical resistance and conductivity.

Given:

2.666 ... + 2.77 ...

Calculation:

Let x = 2.666666...  ----(1)

Multiply by 10 on both sides,

⇒ 10x = 26.666...    ----(2)

Subtracting equation 2 from 1, we get,

⇒ 9x = 24

⇒ $x={24\over9}$

Now

Let y = 2.7777.....   ------ (3)

Multiply by 10 on both sides,

⇒ 10y = 27.7....      -------(4)

Subtracting equation 4 from 3, we get,

⇒ 9x = 25

⇒ $y={25\over9}$

⇒  $x+y={24\over9}+{25\over9}$

⇒ $x+y={49\over9}$

Hence, the required answer is '${49\over9}$'.

Given: Six persons P, Q, R, S, T, and U each have a different weight.

1. The weight of Q is more than only two other persons.

⇒ Q > _ > _

2. The weight of P is more than U’s weight.

P > U

3. The weight of S is more than Q’s weight.

S > Q

4. The weight of R is less than the weight of T.

T > R

5. The weight of Q is more than the weight of T.

Q > T

6. U has the second-highest weight among all the six persons.

_ > U > _ >  Q > _ > _

So, combine all the given information:

P > U > S > Q > T > R

Therefore, the person with the third highest weight is S.

Hence, the correct answer is "Option 1: S".

The correct answer is Ca(OH)2 + Cl2 → CaOCl2 + H2O

Key Points

• Ca(OH)2 + Cl2 → CaOCl2 + H2O is the correct chemical reaction for the preparation of bleaching powder.
• Bleaching powder, also known as calcium hypochlorite, is widely used for disinfecting drinking water and in the textile industry for bleaching fabrics.
• This reaction involves the chlorination of calcium hydroxide, resulting in the formation of bleaching powder and water.
• The chemical formula for bleaching powder is Ca(OCl)2.

Additional Information

• Chlorine is a powerful oxidizing agent and is used in various industrial and household applications.
• Calcium hydroxide, also known as slaked lime, is used in the preparation of bleaching powder due to its alkaline nature.
• Bleaching powder should be stored in a dry and cool place to prevent it from decomposing and losing its effectiveness.
• It is important to handle bleaching powder with care, as it can be irritating to the skin and eyes and is harmful if inhaled.

Shortcut Trick

Calculate the Effective Interest Rate by multiplying Rate and Time.

Effective Rate = 5% × 3 = 15%

Simple Interest = 15% of ₹1,280

⇒ 0.15 × 1280 = ₹192

∴ The correct answer is ₹192.

Alternate Method

Given:

Principal (P) = ₹1,280

Rate (R) = 5% per annum

Time (T) = 3 years

Formula Used:

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

Calculations:

⇒ SI = (1280 × 5 × 3) ÷ 100

⇒ SI = (1280 × 15) ÷ 100

⇒ SI = 19200 ÷ 100

⇒ SI = ₹192

∴ The correct answer is ₹192.

Additional Information

Total Amount Formula

The total amount (A) after T years is the sum of the Principal and the Simple Interest: A = P + SI.

Interest Rate Finding

To find the annual rate when SI, P, and T are known: R = (SI × 100) ÷ (P × T).

Constant Interest Property

In Simple Interest, the interest earned remains the same every year because it is always calculated on the original Principal.

The correct answer is Ca

Key Points

• Calcium (Ca) is the most reactive element among the options provided.
• Reactivity of elements is determined by their ability to lose or gain electrons easily, which is influenced by their position in the periodic table.
• Calcium is an alkaline earth metal, which are known for their high reactivity, especially with water and oxygen.
• Calcium reacts more vigorously with water compared to other elements listed, forming calcium hydroxide and hydrogen gas.

Additional Information

• Lead (Pb) is a post-transition metal with low reactivity.
• Magnesium (Mg) is also reactive, but not as much as calcium.
• Aluminum (Al) forms a protective oxide layer that reduces its reactivity.
• Reactivity generally increases as you move down a group in the periodic table, which is why calcium is more reactive than magnesium.
• Calcium is widely used in various applications due to its reactive properties, including in the production of cement, steel, and as a reducing agent in chemical reactions.

The correct answer is By photosynthesis during the day

Key Points

• Oxygen is produced as a waste product during the process of photosynthesis.
• Photosynthesis occurs in the chloroplasts of plant cells, where light energy is converted into chemical energy.
• During the day, sunlight provides the energy required for photosynthesis.
• In this process, plants take in carbon dioxide (CO₂) and water (H₂O) and convert them into glucose (C₆H₁₂O₆) and oxygen (O₂).
• The oxygen produced is released into the atmosphere as a byproduct.

Additional Information

• Photosynthesis can be summarized by the equation: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂.
• Photosynthesis primarily occurs in the leaves of plants, which contain the most chlorophyll.
• While oxygen is a waste product for the plant, it is essential for the survival of most other living organisms on Earth.
• At night, plants switch to respiration, a process in which they consume oxygen and produce carbon dioxide.

Given: A, B, C, D, E, and F were six friends playing games around a circular table. They were standing facing the center of the table.

1. E was standing to the immediate left of A. 2. B was at the immediate right of A.

3. There were exactly two people between D and A.

4. C was second to the left of F.

So, 'E' is standing immediately right of F.

Hence, the correct answer is "Option 3".

Shortcut Trick

Cost Price (CP) of item = 5,000 − 2,000 = Rs. 3,000.

Successive discounts of 10% and 5% are applied.

Effective Multiplier = (90 ÷ 100) × (95 ÷ 100) = 0.9 × 0.95 = 0.855.

Final Selling Price (SP) = 3,000 × 0.855 = Rs. 2,565.

∴ The correct answer is Rs. 2,565.

Alternate Method

Given: Initial Price = Rs. 5,000 − Rs. 2,000 = Rs. 3,000; Discount 1 = 10%; Discount 2 = 5%.

Formulas: SP = CP × (100 − D₁)% × (100 − D₂)% | Successive Discount = a + b − (ab ÷ 100).

⇒ Cost Price (CP) = 5,000 − 2,000 = Rs. 3,000.

⇒ Price after Dealer Discount (10%) = 3,000 − (10% of 3,000) = 3,000 − 300 = Rs. 2,700.

⇒ Price after Retailer Discount (5%) = 2,700 − (5% of 2,700) = 2,700 − 135 = Rs. 2,565.

⇒ Final Selling Price (SP) = Rs. 2,565.

∴ The correct answer is Rs. 2,565.

Additional Information

Successive Discounts

When two discounts a% and b% are given, the total equivalent discount is (a + b − ab ÷ 100)%.

Selling Price Calculation

The selling price after multiple discounts is calculated as: SP = MP × (1 − d₁/100) × (1 − d₂/100).

Given information,

Six girls decided to record a video of their talks, one on each separate day of the same week.

Sunday will be a rest day.

1. P said Friday will suit her.

2. U will start the process and record on Monday.

3. S will record immediately before T.

4. Q will record on a day exactly between the days of U and S.

5. T selected Thursday.

 

So,, the day left for R is Saturday.

The final arrangement is as follows:

Hence, the correct answer is "Option 2: Saturday".

Given Statements:

I. All grasses are shrubs.

II. All roots are fruits.

III. All fruits are flowers.

Conclusions:

I. All grasses are flowers - False (No direct relationship given between grasses and flowers).

II. All roots are flowers - True (Because all roots are fruits and all fruits are flowers So, all roots are also flowers).

III. Some flowers are fruits - True (Because all fruits are flowers So, some flowers are also fruits).

Hence, the correct answer is "Option 1".

The correct answer is 1.

Key PointsPrincipal Focus of a Lens:

• The first principal focus of a lens is the point on the principal axis where light rays parallel to the principal axis converge (in case of a convex lens) or appear to diverge from (in case of a concave lens) after passing through the lens. Hence, for a lens, the first principal focus is the position of the object whose image is at infinity. Thus, statement (a) is correct.
• The second principal focus of a lens is the point on the principal axis where light rays that are converging towards (for a convex lens) or diverging from (for a concave lens) appear to come from or converge to after passing through the lens. Hence, for a lens, the second principal focus is the position of the real image whose object is at infinity. Thus, statement (c) is correct.
• Statement (b) is incorrect because the first principal focus is not related to the image being formed at twice the focal length. It is related to the image being at infinity.
• Statement (d) is also incorrect because the second principal focus is not related to the image being formed at twice the focal length.

Therefore, the correct answer is 1) Both (a) and (c).

Shortcut Trick For the given quadratic equation, sum (a + b) = −1 and product (ab) = −2. The new roots are (a + b)/ab = −1/−2 = 1/2 and ab = −2. New sum of roots = 1/2 − 2 = −3/2 and product of roots = 1/2 × (−2) = −1. Required equation: x2 − (sum)x + product = 0 ⇒ x2 + (3/2)x − 1 = 0. ∴ The correct answer is 2x2 + 3x − 2 = 0.

Alternate Method Given: a and b are the roots of the equation x2 + x − 2 = 0. Formula Used: For Ax2 + Bx + C = 0, Sum = −B/A and Product = C/A. The quadratic equation is x2 − (Sum)x + Product = 0. ⇒ Sum of original roots (a + b) = −1 / 1 = −1 ⇒ Product of original roots (ab) = −2 / 1 = −2 ⇒ New roots are α = (1/a + 1/b) and β = ab ⇒ α = (a + b) / ab = −1 / −2 = 1/2 ⇒ β = −2 ⇒ Sum of new roots (α + β) = 1/2 + (−2) = −3/2 ⇒ Product of new roots (α × β) = (1/2) × (−2) = −1 ⇒ The required quadratic equation is x2 − (−3/2)x + (−1) = 0 ⇒ x2 + (3/2)x − 1 = 0 ⇒ 2x2 + 3x − 2 = 0 ∴ The correct answer is 2x2 + 3x − 2 = 0.

Additional Information Nature of Roots The nature of roots depends on the discriminant (D = B2 − 4AC). If D > 0 roots are real and distinct; if D = 0 roots are real and equal; if D < 0 roots are imaginary. Relation between Roots and Coefficients For any quadratic equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. Symmetric Functions of Roots Expressions like 1/a + 1/b, a2 + b2, and a/b + b/a can always be expressed in terms of (a+b) and (ab) to find their values without calculating the individual roots.

The logic followed here is:

Given Sequence: B _ M _ Q _ V M W _ B V M W _ B V _ _ T

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) V, W, V, R, R, M, W → B V M W Q / V V M W R / B V M W R / B V M W T

Option 2) V, W, V, R, S, M, R → B V M W Q / V V M W R / B V M W S / B V M R T

Option 3) V, W, B, V, S, W, M → B V M W Q / B V M W V / B V M W S / B V W M T

Option 4) V, W, B, R, S, M, W → B V M W Q / B V M W R / B V M W S / B V M W T

• Q + 1 = R, R + 1 = S, S + 1 = T

Here, 'Option 4' followed a pattern.

Hence, the correct answer is "Option 4".

Given Statement: H = W > F ≥ S ≥ T > Y

Now,

Conclusions:

Option 1: Y < S → True (S ≥ T > Y, it gives Y < S)

Option 2: T ≥ F → False (F ≥ S ≥ T, it gives F > T, so T < F)

Option 3: H < F → False (H = W > F, it gives H > F)

Option 4: W < T → False (W > F ≥ S ≥ T, it gives W > T)

Hence, the correct answer is "Option 1".

Given:

 

Now, the group of numbers and symbols is: '5 # % 6 7 # 3 8'

Following the conditions:

Condition (i) is applied: The first element (5) is odd, and the last element (8) is even. So, the codes for these two elements are interchanged.

After applying Condition (i):

Hence, the correct answer is "Option 2".

The correct answer is i - c, ii - b, iii - a.

Key Points

• Red cabbage leaves contain a pigment called anthocyanin, which changes color in response to changes in pH. This makes it a natural acid base indicator. Hence, i matches with c.
• Methyl orange is a synthetic indicator commonly used in titrations because it changes color at a pH range of 3.1 to 4.4. It is an acid base indicator. Hence, ii matches with b.
• Onion and clove are used as olfactory indicators in chemistry to detect the presence of acids or bases by their smell. Hence, iii matches with a.

Additional Information

• Natural Acid Base Indicator:
• Natural indicators are substances found in nature that change color when they come in contact with an acid or a base. Examples include red cabbage juice, turmeric, and litmus.
• Red cabbage leaves contain anthocyanin, which can indicate pH changes by changing colors.
• Acid Base Indicator:
• Acid-base indicators are substances that change color in response to changes in pH, which makes them useful for determining the acidity or basicity of a solution.
• Methyl orange is an example of a synthetic acid-base indicator that changes color at different pH levels.
• Olfactory Indicator:
• Olfactory indicators are substances that change their smell in the presence of an acid or a base. They are used to detect the presence of acids and bases through the sense of smell.
• Onion and clove are examples of olfactory indicators.

The correct answer is The Sun

Key Points

• The Sun is worshipped by people during the festival of Pongal.
• Pongal is a popular harvest festival celebrated in Tamil Nadu, India.
• The festival marks the end of the winter solstice and the start of the sun's six-month-long journey northwards (Uttarayana).
• It is a four-day festival that includes Bhogi Pongal, Surya Pongal, Mattu Pongal, and Kaanum Pongal.
• Surya Pongal, the second day of the festival, is dedicated to the Sun God (Surya) and is the most important day of the festival.
• During Surya Pongal, people prepare a special dish called 'Pongal' and offer it to the Sun God as a token of gratitude for a bountiful harvest.

Additional Information

• Pongal is celebrated in the month of Thai (January-February) according to the Tamil calendar.
• The word "Pongal" means "to boil" and refers to the traditional dish prepared from the new harvest of rice boiled in milk with jaggery.
• The festival is similar to other harvest festivals celebrated in different parts of India, such as Makar Sankranti in North India, Lohri in Punjab, and Bihu in Assam.
• It is a time of joy, family reunions, and thanksgiving for the agricultural abundance.
• Pongal is also celebrated with traditional music, dance, and cultural performances.

Shortcut Trick

Parallel lines properties: Corresponding angles are equal, Alternate interior angles are equal, and Vertically opposite angles are always equal.

Consecutive interior angles (on the same side) are supplementary (sum = 180°), not necessarily equal.

They are equal only if the transversal is perpendicular to the parallel lines (90° + 90° = 180°).

∴ The correct answer is A pair of interior angles on the same side of the transversal have the same measure.

Alternate Method

Given: Two parallel lines l and m, and a transversal t.

Formula Used: Parallel line theorems (Corresponding, Alternate, and Co-interior angles).

⇒ Option A: Corresponding angles (e.g., ∠1 and ∠5) are always equal when lines are parallel.

⇒ Option C: Vertically opposite angles (e.g., ∠1 and ∠3) are always equal regardless of parallelism.

⇒ Option D: Alternate interior angles (e.g., ∠4 and ∠6) are always equal when lines are parallel.

⇒ Option B: Interior angles on the same side (Co-interior angles, e.g., ∠3 and ∠6) are supplementary.

⇒ ∠3 + ∠6 = 180°. They are equal only if ∠3 = ∠6 = 90°.

⇒ Therefore, they are not necessarily equal in all cases.

∴ The correct answer is A pair of interior angles on the same side of the transversal have the same measure.

Additional Information

Supplementary Angles

Two angles are supplementary if their sum is exactly 180°. Co-interior angles formed by parallel lines are always supplementary.

Alternate Exterior Angles

When two parallel lines are cut by a transversal, the pairs of alternate exterior angles (e.g., ∠1 and ∠7) are equal in measure.

Linear Pair Postulate

If a ray stands on a line, then the sum of two adjacent angles so formed is 180° (e.g., ∠1 + ∠2 = 180°).

Given Equation: [{(23 × 15) - (1 ÷ 4)} + (2 - 2)] ÷ 2

Decoding the given information:

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Now replacing the signs from left to right using the given decoding information, we get:

New Equation: [{(23 - 15) + (1 × 4)} ÷ (2 + 2)] × 2

Calculation:

= [{8 + 4} ÷ 4] × 2

= [12 ÷ 4] × 2

= 3 × 2

= 6

Hence, the correct answer is 'Option 3'.

Calculation:

⇒ Total units sold by Mr. P = 80 + 30 + 50 + 90

⇒ Total units sold by Mr. P = 250

⇒ Total units sold by Mr. Q = 60 + 40 + 70 + 60

⇒ Total units sold by Mr. Q = 230

⇒ Ratio of units sold by Mr. P to Mr. Q = Total units sold by Mr. P / Total units sold by Mr. Q

⇒ Ratio = 250 / 230

⇒ Ratio = 25 / 23

∴ The respective ratio of the total units sold by Mr. P and Mr. Q during the 4 months is 25 : 23.

The correct answer is Ferns

Key Points

• Ferns reproduce via spores, which are typically found on the underside of their fronds.
• Spores are a common reproductive method for non-flowering plants such as ferns, mosses, and fungi.
• Unlike seeds, spores are usually single-celled and do not contain stored food resources.
• Spores can be dispersed by wind, water, or animals, allowing the plant to spread to new locations.

Additional Information

• Yeast reproduces primarily through budding, a form of asexual reproduction.
• Amoeba reproduces by binary fission, another form of asexual reproduction.
• Mango trees reproduce through seeds and vegetative propagation, not spores.
• Spores are a key feature of the life cycle of many plants and fungi, enabling them to survive in various environments and conditions.

The correct answer is Ministry of External Affairs

Key Points

• The Weapons of Mass Destruction and their Delivery Systems (Prohibition of Unlawful Activities) Amendment Bill, 2022, was introduced in the Lok Sabha on 5 April 2022.
• The bill was introduced by the Ministry of External Affairs.

Additional Information

• The bill aims to amend the existing Weapons of Mass Destruction and their Delivery Systems (Prohibition of Unlawful Activities) Act, 2005.
• The amendment seeks to prohibit the financing of activities related to weapons of mass destruction and their delivery systems.
• This move aligns with India's international obligations under various treaties and conventions.
• The amendment enhances the regulatory framework to prevent the proliferation of weapons of mass destruction.

Given word: DIRECT 

Now, arranged in alphabetical order:

Here, 'T' will remain unchanged if each of the letters in the word DIRECT is arranged in alphabetical order.

Hence, the correct answer is "Option 1".

Shortcut Trick

Efficiency of A = 100 ÷ 4 = 25 eggs/min

Efficiency of B = 100 ÷ 5 = 20 eggs/min

Combined Efficiency = 25 + 20 = 45 eggs/min

Total Time = 450 ÷ 45 = 10 minutes

∴ The correct answer is 10 min.

Alternate Method

Given:

Time taken by A to count 100 eggs = 4 minutes

Time taken by B to count 100 eggs = 5 minutes

Total eggs to be counted = 450 eggs

Formula Used:

Efficiency = Total Work ÷ Time

Time Taken = Total Work ÷ Combined Efficiency

Calculations:

⇒ Total combined efficiency of A and B = 25 + 20 = 45 eggs per minute

⇒ Total eggs to count = 450 eggs

⇒ Time required = 450 ÷ 45

⇒ Time = 10 minutes

∴ The correct answer is 10 min.

Additional Information

Unitary Method for Efficiency

Work done by a person in one unit of time (1 minute/1 hour/1 day) is called efficiency. If total work remains constant, efficiency is inversely proportional to time taken.

Time & Work Relation

When multiple people work together, their individual efficiencies are added to get the total efficiency of the group. Total Time = Total Work ÷ (Sum of individual efficiencies).

The correct answer is 2 Ω

Key Points

• The equivalent resistance between points A and B is 2 Ω.
• To find the equivalent resistance, resistors in series and parallel combinations need to be identified and simplified step-by-step.
• R_series= R₁ + R₂ = 3 + 3 = 6 Ω
• 1/R_parallel = 1/R₁ + 1/R₂ = 1/3 + 1/6 = 3/6 = 1/2
• Rparallel = 2 Ω
• In the given circuit, the combination of resistors simplifies to an equivalent resistance of 2 Ω between points A and B.

Additional Information

• Resistors in series add up directly:
• $Rseries=R1+R2+…+Rn$
• Resistors in parallel combine as:
• 1Rparallel=1R1+1R2+…+1Rn1Rparallel=1R1+1R2+…+1Rn $\frac{1}{Rparallel} = \frac{1}{R1} + \frac{1}{R2} + ...+\frac{1}{Rn}$
• Understanding the configuration of resistors in a circuit is crucial for calculating equivalent resistance accurately.
• The given problem is a common type of question in electrical circuit analysis, often found in exams and practical applications.

The logic followed here is:

'GLEPK’ is written as 'DIBMH'

'QRYHN' is written as 'NOVEK'

Similarly, for 'POTER’

So, 'POTER’ is written as 'MLQBO'.

Hence, the correct answer is "Option 3".

The Given Series: 158, 438, 182, 325, 230

Now, If 5 is added to the first digit of every number:

Series becomes: 658, 938, 682, 825, 730.

There are 2 Numbers in which the first digit is exactly divisible by the second digit: 938, 825.

As 9 is completely divisible by 3.

And, 8 is completely divisible by 2.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

So, '30' will come next in the given series.

Hence, the correct answer is "Option 4".

The correct answer is option 3

Key Points

• Option 3: 2-ethyl pentane is not a possible isomer of hexane.
• Hexane (C₆H₁₄) has several isomers, including different structural forms such as straight-chain and branched-chain alkanes.
• Possible isomers of hexane include n-hexane, 2-methyl pentane, 3-methyl pentane, 2,2-dimethyl butane, and 2,3-dimethyl butane.
• 2-ethyl pentane is not a valid isomer because it would imply a seven-carbon chain, which does not match the molecular formula of hexane.

Additional Information

• Isomers are compounds with the same molecular formula but different structural formulas.
• Structural isomers differ in the connectivity of their atoms, while stereoisomers differ in the spatial arrangement of atoms.
• Hexane's structural isomers include different arrangements of the carbon atoms, leading to variations in the branching of the carbon chain.

Given Statements:

1. All couriers are shipments.
2. All shipments are transports.
3. No haul is transport.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No transport is shipment → False (Because it is given that all shipments are transports which means some part of transport is definitely shipment.)

II. All couriers are transports → True (Because it is given that all couriers are shipments and all shipments are transports which gives all couriers are transports)

III. Some transports are shipments → True (Because it is given that all shipments are transports which means some part of transport is definitely shipment.)

IV. No courier is haul → True (Because there is no relation given between courier and haul, so it can be possible but not definitely true)

So, conclusion II, III, and IV follows.

Hence, the correct answer is "Option 4".

Given: P, Q, R, S, T, U, and V live on seven different floors of the same building.

1. U lives on the top floor. 2. Q is on floor number 3.

3. Q lives on the floor immediately below R’s floor. 4. S lives on the floor immediately above R’s floor.

5. Only two persons live between T and Q. 6. V lives on the floor immediately above P’s floor.

So, 'T' lives on the sixth floor.

Hence, the correct answer is "Option 3".

Given word: LAMENT

Now, arranged in alphabetical order:

Here, 'N' and 'T' will remain unchanged if each of the letters in the word LAMENT is arranged in alphabetical order.

Hence, the correct answer is "Option 4".

Given:

Janhvi starts walking from her home and goes 45 m towards the west.

She then turns right and walks 32 m.

Then, she turns right and walks 88 m.

After that, she turns right and walks 50 m.

Finally, she turns right again and walks 43 m.

So, at the end, she is 18 m and in South direction from home.

Hence, the correct answer is "Option 1".

Given Statements:

All donkeys are zebras.

Some bulls are cats.

Some donkeys are apes.

The least possible Venn diagram for the given statement is:

Conclusions:

(I) Some zebras are bulls → False (Because there is no relation given between zebras and bulls, so it can be possible but not definitely true)

(II) Some zebras are apes → True (Because it is given that some donkeys are apes and all donkeys are zebras, the part which is common in donkeys and apes is also zebra.)

(III) Some donkeys are cats → False (Because there is no relation given between donkeys and cats, so it can be possible but not definitely true)

So, only conclusion II follows.

Hence, the correct answer is "Option 3".

Shortcut Trick For a quadratic equation ax2 + bx + c = 0, the sum of roots is given by −b/a. In the equation x2 − 12x + k = 0, the sum of roots = −(−12)/1 = 12. Given one root is 3, the other root = Total Sum − Given Root. Other root = 12 − 3 = 9. ∴ The correct answer is x = 9.

Alternate Method Given: Quadratic equation: x2 − 12x + k = 0 One root (x) = 3 Formula Used: If x = r is a root of a quadratic equation, it must satisfy the equation. Calculations: Substitute x = 3 in the equation: ⇒ (3)2 − 12(3) + k = 0 ⇒ 9 − 36 + k = 0 ⇒ −27 + k = 0 ⇒ k = 27 Now, substitute k = 27 back into the original equation: ⇒ x2 − 12x + 27 = 0 Factorize the quadratic equation by splitting the middle term: ⇒ x2 − 9x − 3x + 27 = 0 ⇒ x(x − 9) − 3(x − 9) = 0 ⇒ (x − 3)(x − 9) = 0 ⇒ x = 3 or x = 9 Since one root is 3, the other root is 9. ∴ The correct answer is x = 9.

Additional Information Sum and Product of Roots For ax2 + bx + c = 0, sum of roots (α + β) = −b/a and product of roots (αβ) = c/a. Nature of Roots The nature depends on the Discriminant (D = b2 − 4ac). If D > 0, roots are real and distinct; if D = 0, roots are real and equal. Forming an Equation If roots α and β are known, the quadratic equation is x2 − (α + β)x + (αβ) = 0.

The correct answer is 22 languages

Key Points

• As of June 2022, there are 22 languages listed in the Eighth Schedule of the Indian Constitution.
• The Eighth Schedule to the Indian Constitution lists the official languages recognized by the Indian government.
• The original constitution included 14 languages in the Eighth Schedule, but several amendments have increased this number to 22.
• The languages included are Assamese, Bengali, Gujarati, Hindi, Kannada, Kashmiri, Konkani, Malayalam, Manipuri, Marathi, Nepali, Odia, Punjabi, Sanskrit, Sindhi, Tamil, Telugu, Urdu, Bodo, Santhali, Maithili, and Dogri.
• Recognition in the Eighth Schedule means that these languages can be used for official purposes such as parliamentary proceedings, judiciary, and communications between the central government and states.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Eighth Schedule of the Constitution has been amended several times to include more languages as per the evolving linguistic diversity of the nation.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The inclusion of languages in the Eighth Schedule is significant for the cultural and linguistic recognition of the diverse population of India.

Shortcut Trick

For continued proportion a : b : b : c, the formula is b² = ac.

For first series: x = 12² ÷ 9 = 144 ÷ 9 = 16.

For second series: y = 42² ÷ 28 = (42 × 42) ÷ 28 = 63.

Required value: 2x + y = 2(16) + 63 = 32 + 63 = 95.

∴ The correct answer is 95.

Alternate Method

Given: 9 : 12 :: 12 : x and 28 : 42 :: 42 : y

Formula Used: Product of Extremes = Product of Means (ad = bc)

⇒ 9 × x = 12 × 12

⇒ x = 144 ÷ 9 = 16

⇒ 28 × y = 42 × 42

⇒ y = (42 × 42) ÷ 28 = 1764 ÷ 28 = 63

⇒ 2x + y = 2(16) + 63

⇒ 2x + y = 32 + 63 = 95

∴ The correct answer is 95.

Additional Information

Fourth Proportional

If a, b, c, d are in proportion, then a/b = c/d, where d is the fourth proportional (d = bc/a).

Third Proportional

In a continued proportion a : b :: b : c, the term c is called the third proportional (c = b²/a).

Mean Proportional

The mean proportional between a and b is √(a × b).

The correct answer is f

Key Points

• When a boy focuses a sharp image of a distant object using a lens, the distance between the lens and the screen is approximately equal to the focal length (f) of the lens.
• This is because, for distant objects, the light rays coming into the lens are parallel, and they converge at the focal point of the lens.
• The focal length is the distance between the center of the lens and the point where the parallel rays converge to form a sharp image.

Additional Information

• The focal length (f) of a lens is a crucial parameter in determining its optical power.
• Lens makers use the focal length to design lenses for various applications, including cameras, eyeglasses, microscopes, and telescopes.
• In practical scenarios, the focal length can be determined using lens formulas or experimental setups.

The correct answer is Pops

Key Points

• Pops is the name of India's first intelligent messenger launched by Paytm Money in January 2022.
• This innovative feature aims to provide users with personalized updates, insights, and important information related to their investments.
• The messenger is designed to enhance the user experience by offering timely and relevant notifications directly within the Paytm Money app.
• With Pops, Paytm Money continues to leverage technology to simplify and improve the investment process for its users.

Additional Information

• Paytm Money is a subsidiary of One97 Communications, which owns the brand Paytm.
• It provides a comprehensive suite of investment and wealth management services, including mutual funds, stocks, and digital gold.
• Paytm Money aims to democratize wealth management services and make investing more accessible to the general public.
• Since its inception, Paytm Money has continually introduced new features and services to cater to the evolving needs of its users.
• The launch of Pops is part of Paytm Money's ongoing efforts to integrate advanced technology into its platform to provide a seamless and efficient user experience.

Shortcut Trick

By definition, co-prime numbers do not share any common factor other than 1.

Therefore, the highest common factor (HCF) of any set of co-prime numbers, regardless of the number of elements in the set, is always 1.

∴ The correct answer is 1.

Alternate Method

Given: A set of 10 co-prime numbers.

Formula/Property Used: Two or more numbers are said to be co-prime if their Highest Common Factor (HCF) is 1.

⇒ Let the set of 10 co-prime numbers be {a₁, a₂, a₃, ..., a₁₀}.

⇒ Since they are co-prime to each other, there is no common prime factor among all of them.

⇒ Thus, the only common divisor for all the 10 numbers is 1.

⇒ HCF(a₁, a₂, a₃, ..., a₁₀) = 1.

∴ The correct answer is 1.

Additional Information

Co-prime Numbers

Two or more numbers are co-prime if they share no common positive factors other than 1. They do not need to be prime numbers themselves (e.g., 8 and 9 are co-prime).

HCF of Prime Numbers

The HCF of any set of distinct prime numbers is always 1, as prime numbers only have 1 and themselves as factors.

LCM of Co-prime Numbers

The Least Common Multiple (LCM) of any set of co-prime numbers is always equal to the product of those numbers.

The correct answer is Option 4

Key Points

• Option 4 is the correct answer for the given question.
• The refractive index of medium A with respect to medium B is equal to $\frac{1}{\sqrt2}$
• This is determined based on the path of the light ray incident on the interface separating the two media as shown in the figure.
• The refractive index is a measure of how much the speed of light is reduced inside a medium compared to the vacuum.

To determine the refractive index of medium A with respect to medium B, you can use Snell's law, which states:$\ n_A \sin(\theta_A) = n_B \sin(\theta_B)$

Where:

$n_A$ is the refractive index of medium A,

$n_B$ is the refractive index of medium B,

$\theta_A$ is the angle of incidence in medium A,

$\theta_B$ is the angle of refraction in medium B.

The refractive index of medium A with respect to medium B can be calculated using the formula:

$\ \text{Refractive Index} , (n_{A/B}) = \frac{n_A}{n_B} = \frac{\sin(\theta_B^\circ)}{\sin(\theta_A^\circ)} \ = \frac{\sin(30^\circ)}{\sin(45^\circ)} \ =\frac{1}{2} \times \frac {\sqrt2}{1} =\frac{1}{\sqrt{2}}$

The correct answer is Do not overuse air conditioning or heating systems.

Key Points

• Do not overuse air conditioning or heating systems as these appliances consume a significant amount of energy, which is often generated from coal and petroleum resources.
• Using energy-efficient appliances and adopting energy-saving practices can help reduce the consumption of these fossil fuels.
• Promoting the use of public transportation or joining a carpool can significantly decrease the reliance on petroleum products.
• Utilizing renewable energy sources like solar cookers can reduce the dependency on coal and petroleum.

Additional Information

• Coal and petroleum are non-renewable resources, meaning they cannot be replenished on a human time scale once depleted.
• The burning of these fossil fuels releases greenhouse gases, contributing to climate change and environmental pollution.
• Adopting energy conservation techniques and promoting renewable energy sources are crucial steps toward sustainable development.
• Energy conservation not only helps in preserving these resources but also reduces energy costs and environmental impact.

Shortcut Trick

The vertices A(0, −2) and C(0, 4) lie on the y-axis, forming a vertical diagonal AC of length 4 − (−2) = 6 units.

The vertices B(2, 1) and D(−2, 1) lie on the horizontal line y = 1, forming a horizontal diagonal BD of length 2 − (−2) = 4 units.

Since the diagonals are perpendicular to each other, the area of the quadrilateral ABCD is given by:

Area = (1/2) × d₁ × d₂ = (1/2) × 6 × 4 = 12 square units.

∴ The correct answer is 12 square units.

Alternate Method

Given:

Vertices of the quadrilateral ABCD are A(0, −2), B(2, 1), C(0, 4), and D(−2, 1).

Formula Used:

The area of a polygon with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄) can be calculated using the Shoelace Formula:

Area = (1/2) × |(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) − (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)|

Calculations:

Let the coordinates be:

(x₁, y₁) = (0, −2)

(x₂, y₂) = (2, 1)

(x₃, y₃) = (0, 4)

(x₄, y₄) = (−2, 1)

⇒ Sum₁ = x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁

⇒ Sum₁ = (0 × 1) + (2 × 4) + (0 × 1) + (−2 × −2)

⇒ Sum₁ = 0 + 8 + 0 + 4 = 12

⇒ Sum₂ = y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁

⇒ Sum₂ = (−2 × 2) + (1 × 0) + (4 × −2) + (1 × 0)

⇒ Sum₂ = −4 + 0 − 8 + 0 = −12

⇒ Area = (1/2) × |Sum₁ − Sum₂|

⇒ Area = (1/2) × |12 − (−12)|

⇒ Area = (1/2) × |12 + 12|

⇒ Area = (1/2) × 24 = 12 square units.

Since the calculated area is exactly 12 square units, Option (1) is correct. The other options (14, 15, and 13 square units) are incorrect because they do not match the geometric area computed from the given coordinates.

∴ The correct answer is 12 square units.

Additional Information

Area of a Rhombus / Kite

When the diagonals of a quadrilateral are perpendicular, the area is always half the product of the lengths of the diagonals: Area = (1/2) × d₁ × d₂.

Shoelace Formula (Gauss's Area Formula)

A mathematical algorithm to determine the area of a simple polygon whose vertices are described by ordered pairs in the coordinate plane.

Distance Formula

The distance between any two points (x₁, y₁) and (x₂, y₂) is given by d = √((x₂ − x₁)² + (y₂ − y₁)²).

Shortcut Trick

Ratio of cost of Printer to Television = 2 : 1

Difference in ratio parts = 2 − 1 = 1 unit

Given difference in price = Rs. 35,000

∴ 1 unit = Rs. 35,000

Cost of Television (1 unit) = Rs. 35,000

∴ The correct answer is Rs. 35,000.

Alternate Method

Given:

Difference between cost of printer and television = Rs. 35,000

Cost of printer = 2 × Cost of television

Let the cost of the television be x.

Then, the cost of the printer = 2x

According to the question, the television costs Rs. 35,000 less than the printer:

⇒ 2x − x = 35,000

⇒ x = 35,000

Thus, the cost of the television is Rs. 35,000, which corresponds to Option (3).

∴ The correct answer is Rs. 35,000.

Additional Information

Ratio and Proportions

When one value is a multiple of another, representing them as ratio units (e.g., 2:1) simplifies the calculation of differences.

Unitary Method

If 1 unit represents a certain value, any number of units can be found by direct multiplication: Value = Number of units × Value of 1 unit.

Linear Equations

For problems involving 'more than' or 'less than', setting up a linear equation x = y ± constant is a reliable algebraic approach.

Shortcut Trick

Sum of ages 5 years ago = 39 years.

Sum of present ages = 39 + (5 × 2) = 49 years.

Age of child = (Sum − Difference) ÷ 2 = (49 − 25) ÷ 2 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given: Difference between father and child = 25 years. Sum 5 years ago = 39 years.

Formula Used: Present Sum = Past Sum + (n × number of people).

Let my present age be x years.

Father's present age = x + 25 years.

⇒ (x − 5) + (x + 25 − 5) = 39

⇒ 2x + 15 = 39

⇒ 2x = 39 − 15

⇒ 2x = 24

⇒ x = 12 years.

∴ The correct answer is 12 years.

Additional Information

Age Difference Property

The difference between the ages of two people always remains constant, regardless of the number of years passed.

Sum of Ages Change

If there are n people, the sum of their ages increases or decreases by n × t years after a time period of t years.

Ratio of Ages

Unlike age difference, the ratio of ages changes over time as years are added to both the numerator and denominator.

Shortcut Trick

For a number to be divisible by 90, it must be divisible by both 10 and 9 (since 90 = 9 × 10).

Divisibility by 10 ⇒ last digit y = 0.

Divisibility by 9 ⇒ sum of digits (1 + 1 + 5 + x + 0) = 7 + x must be a multiple of 9.

The nearest multiple of 9 is 9, so 7 + x = 9 ⇒ x = 2.

Therefore, x + y = 2 + 0 = 2.

∴ The correct answer is 2.

Alternate Method

Given: Number = 115xy, Divisor = 90.

Condition: The number is perfectly divisible by 90.

Step 1: Apply Divisibility Rule of 10

⇒ For a number to be divisible by 10, the unit digit must be 0.

⇒ In 115xy, the unit digit is y.

⇒ y = 0.

Step 2: Apply Divisibility Rule of 9

⇒ A number is divisible by 9 if the sum of its digits is divisible by 9.

⇒ Sum of digits of 115x0 = 1 + 1 + 5 + x + 0

⇒ Sum = 7 + x

⇒ For (7 + x) to be divisible by 9, where x is a single digit (0-9):

⇒ 7 + x = 9

⇒ x = 2.

Step 3: Calculate the required value

⇒ x + y = 2 + 0

⇒ x + y = 2

∴ The correct answer is 2.

Additional Information

Divisibility Rule of 9

A number is divisible by 9 if and only if the sum of its digits is a multiple of 9.

Divisibility Rule of 10

A number is divisible by 10 if its unit digit (the last digit) is exactly 0.

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, it is also divisible by their product (a × b). Here, 9 and 10 are co-prime.

The correct answer is electromagnetic induction

Key Points

• An AC generator works on the principle of electromagnetic induction.
• Electromagnetic induction refers to the process of generating electric current by changing the magnetic field enclosed by an electrical circuit.
• This principle was discovered by Michael Faraday in 1831.
• The changing magnetic field induces an electromotive force (EMF) in the conductor, which causes the current to flow.
• AC generators are widely used in power plants to produce electricity.

Additional Information

• Michael Faraday's Law of electromagnetic induction states that the induced EMF in any closed circuit is equal to the rate of change of the magnetic flux through the circuit.
• AC generators convert mechanical energy into electrical energy using this principle.
• They consist of a rotating coil within a stationary magnetic field or a rotating magnetic field within a stationary coil.
• AC generators are also known as alternators.
• The frequency of the generated AC voltage depends on the speed of rotation of the coil or the magnetic field.

The correct answer is Knowing about their body changes, teenagers start making fun of each other.

Key Points

• Sex education is crucial in providing teenagers with accurate information about their bodies and sexuality, which can help them make informed decisions.
• It helps in preventing sexual abuse by educating teenagers about consent and boundaries (Option 1).
• Sex education is essential for dispelling myths and misconceptions related to sexual health and puberty (Option 2).
• It provides knowledge about the changes that occur during puberty, helping teenagers understand and cope with these changes (Option 4).
• However, the idea that knowing about body changes leads teenagers to make fun of each other is a misconception and counterproductive to the goals of sex education (Option 3).

Additional Information

• Comprehensive sex education includes topics such as human development, relationships, decision-making, abstinence, contraception, and disease prevention.
• It aims to equip young people with knowledge, skills, and values to make responsible choices about their sexual and social relationships.
• Studies have shown that comprehensive sex education can lead to reduced rates of teen pregnancy and sexually transmitted infections (STIs).

Shortcut Trick

Ratio of numbers = 5 : 6 : 8

Sum of squares of ratio parts = 5² + 6² + 8² = 25 + 36 + 64 = 125

Common factor x² = Total Sum of Squares ÷ Ratio Sum = 1250 ÷ 125 = 10 ⇒ x = √10

Product = (5 × 6 × 8) × x³ = 240 × (√10)³ = 240 × 10√10 = 2400√10

∴ The correct answer is 2400√10.

Alternate Method

Given: Ratio = 5 : 6 : 8, Sum of squares = 1250

Formula: Let numbers be ax, bx, cx; then (ax)² + (bx)² + (cx)² = S

⇒ Let the numbers be 5x, 6x, and 8x.

⇒ (5x)² + (6x)² + (8x)² = 1250

⇒ 25x² + 36x² + 64x² = 1250

⇒ 125x² = 1250

⇒ x² = 10

⇒ x = √10

⇒ Product = 5x × 6x × 8x = 240x³

⇒ Product = 240 × (√10)³ = 240 × 10√10 = 2400√10

∴ The correct answer is 2400√10.

Additional Information

Ratio and Proportion Basics

When terms are in ratio a:b:c, they can be represented as ax, bx, and cx where x is a common constant.

Compound Ratio

The product of multiple ratios a:b and c:d is given by the compound ratio (ac):(bd).

Square Root Property

For any positive number n, (√n)³ = n√n. This is essential for volumetric or product calculations involving square roots.

Shortcut Trick

Ratio of chocolates = 7 : 5

Difference in ratio units = 7 − 5 = 2 units

According to the question, 2 units = 28 chocolates ⇒ 1 unit = 14 chocolates

Larger number = 7 units = 7 × 14 = 98 chocolates

∴ The correct answer is 98 chocolates.

Alternate Method

Given:

Ratio of chocolates in two boxes = 7 : 5

Difference in number of chocolates = 28

Calculations:

⇒ Let the number of chocolates in the boxes be 7x and 5x respectively.

⇒ According to the problem, 7x − 5x = 28

⇒ 2x = 28

⇒ x = 28 ÷ 2

⇒ x = 14

⇒ Number of chocolates in the larger box = 7x = 7 × 14

⇒ Total chocolates = 98

∴ The correct answer is 98 chocolates.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a : b is the ratio, the actual values are ax and bx where x is the common multiplier.

Difference and Sum in Ratios

If the ratio is a : b and the sum is S, then 1 unit = S / (a + b). If the difference is D, then 1 unit = D / |a − b|.

Calculation:

53 × 54 × 52 = ?

Since, a^m × aⁿ = a^m+n

53 × 54 × 52 = 5³⁺⁴⁺²

53 × 54 × 52 = 59

∴ The correct answer is option 2.

The correct answer is Dhruv Sitwala

Key Points

• Pankaj Advani secured his 41st title by defeating Dhruv Sitwala in the final match.
• This victory marked his 8th title at the Asian 100 UP Billiards Championship 2022.
• Pankaj Advani is a renowned Indian billiards and snooker player with multiple world titles to his name.
• He has been a dominant force in both national and international billiards and snooker tournaments.

Additional Information

• Pankaj Advani has won numerous titles across different formats, including both the long and short formats of billiards and snooker.
• He has been awarded several prestigious honors in India, including the Padma Bhushan, Padma Shri, and the Rajiv Gandhi Khel Ratna Award.
• Advani's consistent performance has contributed significantly to India's reputation in the global billiards and snooker community.

The correct answer is International Monetary Fund (IMF)

Key Points

• The 'World Economic Outlook-April 2022' report raised India's GDP growth estimate to 9% for 2022-23 and forecasted the economy to grow by 7.1% for 2023-24.
• This report was released by the International Monetary Fund (IMF).
• The IMF is an international organization that aims to promote global economic growth and financial stability, encourage international trade, and reduce poverty.
• The IMF publishes the World Economic Outlook report biannually, providing analysis and projections of economic developments globally.

Additional Information

• The IMF was established in 1944 during the Bretton Woods Conference and has its headquarters in Washington, D.C.
• The organization currently has 190 member countries.
• The primary purpose of the IMF is to ensure the stability of the international monetary system—the system of exchange rates and international payments that enables countries to transact with each other.
• IMF provides policy advice, financial assistance, and technical assistance to its member countries.
• It also monitors global economic trends and performance, providing regular assessments in its World Economic Outlook report.

The correct answer is 73rd

Key Points

• The 73rd Amendment of the Constitution of India envisages the Gram Sabha as the foundation of the Panchayat Raj System.
• This amendment was enacted in 1992 and came into effect on 24th April 1993.
• It added Part IX to the Constitution, titled "The Panchayats", and consists of provisions from Article 243 to Article 243O.
• The amendment aims to provide constitutional status to the Panchayati Raj institutions and ensure more participation of people in the administration of local affairs.
• The Gram Sabha is entrusted with powers and functions by the state legislatures to ensure effective governance at the grassroots level.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The 73rd Amendment has played a significant role in empowering local governance and decentralizing administration in India.

Shortcut Trick

When the distance traveled is the same for two speeds S₁ and S₂, the Average Speed is given by the Harmonic Mean formula.

Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂)

⇒ Average Speed = (2 × 60 × 100) ÷ (60 + 100) = 12000 ÷ 160 = 75 km/h.

∴ The correct answer is 75 km/h.

Alternate Method

Given:

Speed from P to Q (S₁) = 60 km/h

Speed from Q to P (S₂) = 100 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

Let the distance between P and Q be the LCM of 60 and 100 = 300 km.

⇒ Time taken from P to Q (t₁) = 300 ÷ 60 = 5 hours

⇒ Time taken from Q to P (t₂) = 300 ÷ 100 = 3 hours

⇒ Total Distance = 300 + 300 = 600 km

⇒ Total Time = 5 + 3 = 8 hours

⇒ Average Speed = 600 ÷ 8 = 75 km/h

∴ The correct answer is 75 km/h.

Additional Information

Average Speed for Different Distances

If distances d₁, d₂ are covered with speeds v₁, v₂, use Average Speed = (d₁ + d₂) ÷ (d₁/v₁ + d₂/v₂).

Relative Speed

For two objects moving in the opposite direction, Relative Speed = S₁ + S₂. For same direction, Relative Speed = |S₁ − S₂|.

Speed-Time Relation

When distance is constant, speed is inversely proportional to time (S ∝ 1/T). Ratio of speeds S₁:S₂ = Ratio of times T₂:T₁.

The correct answer is Israel

Key Points

• India launched a commemorative logo to mark her 30th anniversary of diplomatic ties with Israel.
• The logo was unveiled in a virtual ceremony attended by the ambassadors of both countries.
• The logo features the Star of David and the Ashoka Chakra, symbolizing the strong friendship and deep-rooted ties between the two nations.
• India and Israel established full diplomatic relations on January 29, 1992, and have since developed a multi-faceted partnership across various sectors including defense, agriculture, and technology.

Additional Information

• India was among the 164 nations that voted in favor of the UN resolution for the partition of Palestine and the creation of Israel in 1947.
• Despite early support, India did not establish full diplomatic relations with Israel until 1992.
• Since the establishment of full diplomatic ties, India and Israel have significantly expanded cooperation in areas such as defense, agriculture, water management, and cybersecurity.
• The two countries have also increased people-to-people contacts through cultural exchanges and tourism.
• India is one of Israel's largest trading partners in Asia, and both countries continue to explore new avenues for collaboration.

Shortcut Trick

Distance in first 2 hours = 60 × 2 = 120 km

Distance in next 2 hours (at 75 km/h) = 75 × 2 = 150 km

Total distance covered in 4 hours = 120 + 150 = 270 km

Remaining distance = 360 − 270 = 90 km

Time for remaining distance (at 90 km/h) = 90 ÷ 90 = 1 hour

Total time = 2 + 2 + 1 = 5 hours

∴ The correct answer is 5 hr.

Alternate Method

Given: Initial Speed = 60 km/h, Increase = 15 km/h every 2 hours, Total Distance = 360 km.

Formula Used: Distance = Speed × Time

⇒ Distance in first interval (0 to 2 hrs) = 60 km/h × 2 hr = 120 km

⇒ Speed for second interval (2 to 4 hrs) = 60 + 15 = 75 km/h

⇒ Distance in second interval = 75 km/h × 2 hr = 150 km

⇒ Cumulative distance after 4 hours = 120 + 150 = 270 km

⇒ Remaining distance = 360 − 270 = 90 km

⇒ Speed for third interval (after 4 hrs) = 75 + 15 = 90 km/h

⇒ Time to cover remaining distance = 90 km ÷ 90 km/h = 1 hr

⇒ Total time taken = 2 + 2 + 1 = 5 hours

∴ The correct answer is 5 hr.

Additional Information

Uniform Speed vs. Variable Speed

In uniform speed, the distance covered per unit time remains constant. In variable speed problems, calculate distance separately for each time interval where the speed is constant.

Average Speed

Average Speed = Total Distance ÷ Total Time. For this journey, Average Speed = 360 ÷ 5 = 72 km/h.

Arithmetic Progression in Speed

When speed increases by a fixed amount (d) over fixed time intervals, the speeds form an Arithmetic Progression (AP): a, a+d, a+2d, ...

Given equation: 7 × 8 + 9 - 6 ÷ 3 = 59

Let's check each option one by one.

Option 1) 8 and 9 

Given: 7 × 8 + 9 - 6 ÷ 3 = 59

After interchanging 8 and 9 we get;

⇒ 7 × 9 + 8 - 6 ÷ 3 = 59

⇒ 63 + 8 - 2 = 59

⇒ 71 - 2 = 69

⇒ 69 ≠ 59

⇒ LHS ≠ RHS

Option 2) 6 and 9

Given: 7 × 8 + 9 - 6 ÷ 3 = 59

After interchanging 6 and 9 we get;

⇒ 7 × 8 + 6 - 9 ÷ 3 = 59

⇒ 56 + 6 - 3 = 59

⇒ 62 - 3 = 59

⇒ 59 = 59

⇒ LHS = RHS

Option 3) 3 and 6

Given: 7 × 8 + 9 - 6 ÷ 3 = 59

After interchanging 3 and 6 we get;

⇒ 7 × 8 + 9 - 3 ÷ 6 = 59

⇒ 56 + 9 - 0.5 = 59

⇒ 65 - 0.5 = 64.5

⇒ 64.5 ≠ 59

⇒ LHS ≠ RHS

Option 4) 7 and 3

Given: 7 × 8 + 9 - 6 ÷ 3 = 59

After interchanging 7 and 3 we get;

⇒ 3 × 8 + 9 - 6 ÷ 7 = 59

⇒ 24 + 9 - 0.857 ≈ 59

⇒ 33 - 0.857 ≈ 32.143

⇒ 32.143 ≠ 59

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 2".

Shortcut Trick

Put a standard angle, let θ = 60°.

Expression = √((1 − 1/2) ÷ (1 + 1/2)) = √((1/2) ÷ (3/2)) = √(1/3) = 1/√3.

Check options: cosec 60° − cot 60° = 2/√3 − 1/√3 = 1/√3. (Matches)

∴ The correct answer is cosec θ − cot θ.

Alternate Method

Given: √((1 − cos θ) ÷ (1 + cos θ))

Formula Used: Rationalization of denominator and Identity: sin² θ + cos² θ = 1

⇒ √[((1 − cos θ) × (1 − cos θ)) ÷ ((1 + cos θ) × (1 − cos θ))]

⇒ √[(1 − cos θ)² ÷ (1 − cos² θ)]

⇒ √[(1 − cos θ)² ÷ sin² θ]

⇒ (1 − cos θ) ÷ sin θ

⇒ (1 ÷ sin θ) − (cos θ ÷ sin θ)

⇒ cosec θ − cot θ

∴ The correct answer is cosec θ − cot θ.

Additional Information

Trigonometric Identities

Standard identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ = cos θ/sin θ.

Rationalization Rule

When simplifying square roots involving (1 ± cos θ) or (1 ± sin θ), multiply numerator and denominator by the conjugate to create a perfect square.

The correct answer is 11

Key Points

• The first round of Mission Indradhanush (IMI) 4.0 was organised by the Union Ministry of Health and Family Welfare in 11 states in February 2022.
• The aim of the initiative was to increase the full immunisation coverage across these states.
• Mission Indradhanush aims to vaccinate all unvaccinated and partially vaccinated children and pregnant women by 2022 against vaccine-preventable diseases.
• The campaign is conducted in rounds, with each round focusing on identified high-risk areas.
• IMI 4.0 is a strategic endeavor to ensure that the benefits of vaccination reach every child and pregnant woman in the country.

Additional Information

• Mission Indradhanush was first launched in December 2014 to achieve full immunisation coverage for all children and pregnant women at a rapid pace.
• The mission focuses on districts and urban areas with low immunisation coverage to ensure that no child is left out.
• It includes vaccines for diseases such as diphtheria, whooping cough, tetanus, polio, tuberculosis, measles, and hepatitis B, among others.
• Special attention is given to marginalized and under-served populations, including those living in remote and inaccessible areas.
• The initiative has been praised for its contribution to reducing child mortality and improving maternal health in India.

Calculation:

⇒ B₂₀₁₃ = 45 (Assumed from graph)

⇒ B₂₀₁₇ = 90 (Assumed from graph)

⇒ Percentage = (B₂₀₁₃ / B₂₀₁₇) × 100

⇒ Percentage = (45 / 90) × 100

⇒ Percentage = 50%

Given:

The value of 0.0486 ÷ 0.002

Concept:

To divide two decimal numbers, adjust the decimal places to convert the divisor into a whole number and then perform the division.

Formula Used:

Division of decimals: Move the decimal point of both numbers to the right until the divisor is a whole number.

Calculation:

We have,

⇒ 0.0486 ÷ 0.002

Move the decimal point three places to the right for both numbers:

⇒ 48.6 ÷ 2

Now, perform the division:

⇒ 48.6 ÷ 2 = 24.3

∴ The correct answer is option 2.

Given:

Anita is standing facing the north direction.

Then, she turns 135° anticlockwise.

After that, she turns 90° clockwise.

So, Anita is facing 'North west' direction.

Hence, the correct answer is "Option 3".

Statement:

"Essay writing is an art. It requires an understanding of the subject as well as a command over the language to be able to write a good essay."

Analysis:

Assumption I: The statement mentions that essay writing requires an understanding of the subject. However, it does not state that complete mastery is necessary. It implies that some level of understanding is required but does not suggest that mastery is mandatory. Therefore, Assumption I is not implicit.

Assumption II: The statement indicates that both an understanding of the subject and a command over the language are needed to write a good essay. Thus, having only a good command over the language is not sufficient on its own. Therefore, Assumption II is not implicit.

Neither Assumption I nor Assumption II is implicit in the statement.

Hence, the correct answer is "Option (1)".

The correct answer is Number 4

Key Points

• Number 4 indicates the spinal cord's location in the human brain.
• The spinal cord is an essential part of the central nervous system that extends from the brainstem and continues down the vertebral column.
• It plays a crucial role in transmitting nerve signals between the brain and the rest of the body.
• Understanding the location and function of the spinal cord is vital for studying human anatomy and neurobiology.

Additional Information

• The spinal cord starts at the medulla oblongata in the brainstem and extends down to the lumbar region of the vertebral column.
• It is protected by the vertebral bones and is surrounded by cerebrospinal fluid, which cushions it against impacts.
• The spinal cord is responsible for reflex actions and transmitting sensory and motor information to and from the brain.
• Damage to the spinal cord can result in loss of sensation and motor function below the level of injury.
• Medical imaging techniques like MRI and CT scans are often used to diagnose spinal cord injuries and diseases.

The correct answer is Credit Control.

Key Points

• Credit control is NOT included in the financial budget of India.
• The financial budget primarily includes revenue deficit, primary deficit, and fiscal deficit.
• Revenue deficit occurs when the net income generated (revenue receipts) is less than the projected net income.
• Primary deficit is the fiscal deficit of the current year minus the interest payments on previous borrowings.
• Fiscal deficit is the difference between the government's total expenditure and its total receipts (excluding borrowing).

Additional Information

• Credit control refers to the measures taken by the central bank to control the amount of credit in the economy.
• The financial budget is presented annually by the Finance Minister and outlines the government's revenue and expenditure for the upcoming fiscal year.
• The budget aims to allocate resources efficiently, manage public finances, and achieve economic stability and growth.
• India's financial budget includes various components such as tax revenue, non-tax revenue, capital receipts, and expenditure on different sectors.
• Understanding the components of the financial budget is crucial for analyzing the government's fiscal policy and economic strategy.

Given: BEING : YVRMT : : PRIDE : KIRWV : : CLEAN:  ?

The logic followed here is:

→ BEING : YVRMT

→ PRIDE : KIRWV

→ CLEAN:  ?

Hence, the correct answer is "Option 3".

The correct answer is Shaili Singh

Key Points

• Shaili Singh is an Indian athlete specializing in the long jump.
• She won a silver medal at the U-20 World Athletics Championships in 2021.
• Shaili Singh is considered one of India's most promising young athletes in track and field.
• Her achievement at the U-20 World Athletics Championships has brought her significant recognition in the sports community.

Additional Information

• Mercy Kuttan is a former Indian long jumper who later switched to sprinting and is the first Indian woman to qualify for the Olympics in long jump.
• Nayana James is another Indian long jumper who has represented India in various international competitions.
• Seema Punia is an Indian discus thrower and has won medals in several Commonwealth and Asian Games.

The correct answer is Only Statement I is Correct..

Key Points

• Statement I: Dobereiner gave the law of triads.
• Statement II: Dobereiner tried to arrange the elements with different properties into groups, having three elements each.
• Explanation:
• Johann Wolfgang Döbereiner was a German chemist who is best known for his work that led to the development of the periodic classification of elements.
• The Law of Triads, proposed by Döbereiner in 1817, states that the atomic weight of the middle element of a triad is approximately the arithmetic mean of the atomic weights of the other two elements.
• Statement I is correct because it accurately describes Döbereiner's contribution to chemistry.
• However, Statement II is incorrect because it suggests that Döbereiner tried to arrange elements with different properties into groups. In reality, Döbereiner grouped elements with similar properties into triads.
• Therefore, only Statement I is correct, making Option 2 the correct answer.