The correct answer is current.

Key Points 

Magnetic field lines:

• A magnetic field line is an imaginary line such that tangent to it at any point gives the direction of the magnetic field at that point in space.
• Magnetic field lines are drawn to represent the magnetic fields.
• Magnetic field lines can be drawn with the help of a magnetic compass.
• Magnetic field lines are also called magnetic lines of force.

Properties of magnetic field lines:

• The magnetic field lines of a magnet (or a solenoid) form continuous closed loops.
• The magnetic field lines start from the north pole and end on a south pole outside the magnet. Inside the magnet, the magnetic field lines start from the south pole and end on the north pole.
• The tangent to the field line at a given point represents the direction of the net magnetic field B at that point.
• The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
• The magnetic field lines do not intersect with each other if they did, there will be two directions of the magnetic field at that point which is not possible.

EXPLANATION:

• The magnetic field lines of a magnet (or a solenoid) form continuous closed loops. Hence, option 2 is correct.

Shortcut Trick

Ratio of Amount to Principal → A/P = 2809/2500

Convert Rate to Fraction: 6% = 6/100 = 3/50, so Growth Multiplier = 53/50

Identify the power: (53/50)ⁿ = 2809/2500

Since 50² = 2500 and 53² = 2809, the power n must be 2.

∴ The correct answer is 2 years.

Alternate Method

Given:

Principal (P) = ₹2500

Maturity Amount (A) = ₹2809

Rate of Interest (R) = 6% per annum

Formula Used:

A = P(1 + R/100)ⁿ, where n is the Time Period.

Calculations:

⇒ 2809 = 2500(1 + 6/100)ⁿ

⇒ 2809/2500 = (106/100)ⁿ

⇒ 2809/2500 = (53/50)ⁿ

⇒ (53)² / (50)² = (53/50)ⁿ

⇒ (53/50)² = (53/50)ⁿ

⇒ Comparing the powers on both sides:

⇒ n = 2 years

∴ The correct answer is 2 years.

Additional Information

Compound Interest (CI) Formula

The interest earned is given by CI = A − P = P[(1 + R/100)ⁿ − 1].

Compounding Frequencies

If interest is compounded half-yearly, the rate becomes R/2 and the time period becomes 2n.

CI vs SI Difference for 2 Years

The difference between CI and SI for 2 years is given by D = P × (R/100)².

Shortcut Trick

Total items after change = 60 + 25 − 5 = 80

New ratio of Pens to Pencils = 3 : 1 (Total 4 units)

4 units = 80 ⇒ 1 unit = 20

New Pens = 60, New Pencils = 20

Original Pens = 60 − 25 = 35; Original Pencils = 20 + 5 = 25

Difference = 35 − 25 = 10

∴ The correct answer is 10.

Alternate Method

Given: Total pens and pencils = 60

Let the original number of pens be x and pencils be (60 − x).

⇒ New number of pens = x + 25

⇒ New number of pencils = (60 − x) − 5 = 55 − x

⇒ According to the question: (x + 25) = 3 × (55 − x)

⇒ x + 25 = 165 − 3x

⇒ 4x = 165 − 25

⇒ 4x = 140 ⇒ x = 35

⇒ Original pens = 35, Original pencils = 60 − 35 = 25

⇒ Difference = 35 − 25 = 10

∴ The correct answer is 10.

Additional Information

Ratio and Proportion

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

Linear Equations

In word problems, define a single variable to represent one unknown to simplify the calculation steps.

The correct answer is -15.0 m

Key Points

• Given Information:
• Object height (h₀) = 10.0 m
• Image height (hᵢ) = 30.0 m (real image, so it's inverted, meaning we'll use -30m in the magnification calculation)
• Object distance (u) = -20.0 m (negative because the object is in front of the mirror)
• Magnification Formula:
• Magnification (M) is given by:
• M = hᵢ / h₀ = -v/u
• Calculating Magnification:
• M = (-30.0 m) / (10.0 m) = -3
• Finding Image Distance (v):
• Using M = -v/u:
• -3 = -v / (-20.0 m)
• -3 = v / 20.0 m
• v = -60.0 m (negative because it's a real image formed in front of the concave mirror)
• Mirror Formula:
• The mirror formula relates object distance (u), image distance (v), and focal length (f):
• 1/f = 1/v + 1/u
• Calculating Focal Length (f):
• 1/f = 1/(-60.0 m) + 1/(-20.0 m)
• 1/f = -1/60 - 3/60
• 1/f = -4/60
• 1/f = -1/15
• f = -15.0 m
• Therefore, the principal focus of the mirror is at -15.0 m.

Additional Information

The logic followed here is:

Numbers are Decreasing in Prime number order.

Here, 43, 41, 37,31, ? ,23

Next prime number in place of Question mark = 29 

So, 29 will complete the given series.

Hence, the correct answer is 'Option 1'.

Additional Information Prime number between 1 to 100.

The correct answer is Strontium (atomic mass = 87.62).

Key Points

• Strontium
• Atomic number: 38
• Atomic mass: 87.62 u
• Symbol: Sr
• Group: 2
• Period: 5
• Strontium is an alkaline earth metal that is soft, silvery-white, and highly reactive. It is found in nature in the minerals celestite and strontianite. Strontium is used in fireworks to produce a bright red color, in signal flares, and in some medical applications.

Additional Information

• Nitrogen
• Atomic number: 7
• Atomic mass: 14.007 u
• Symbol: N
• Group: 15
• Period: 2
• Nitrogen is a colorless, odorless, and tasteless gas that is essential for life. It makes up about 78% of the Earth's atmosphere. Nitrogen is used in the production of fertilizers, explosives, and other industrial products.
• Phosphorus
• Atomic number: 15
• Atomic mass: 30.974 u
• Symbol: P
• Group: 15
• Period: 3
• Phosphorus is a nonmetal that is essential for life. It is found in bones, teeth, and DNA. Phosphorus is used in the production of fertilizers, matches, and other products.
• Chlorine
• Atomic number: 17
• Atomic mass: 35.45 u
• Symbol: Cl
• Group: 17
• Period: 3

Shortcut Trick

Total Work (LCM of 18, 24, 60) = 360 units.

Efficiencies: A = 20, B = 15, C = 6.

Cycle: Day 1 (A+B) = 35; Day 2 (A+C) = 26. Total units in 2 days = 61.

5 cycles (10 days) = 305 units. Remaining = 55 units. Day 11 (A+B) takes 35 units.

Remaining 20 units done by (A+C) in 20/26 = 10/13 days. Total = 11¹⁰/₁₃ days.

∴ The correct answer is 11¹⁰/₁₃ days.

Alternate Method

Given: Time taken by A = 18 days, B = 24 days, C = 60 days.

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

⇒ Work on Day 1 (A + B) = 20 + 15 = 35 units.

⇒ Work on Day 2 (A + C) = 20 + 6 = 26 units.

⇒ Work in 1 cycle (2 days) = 35 + 26 = 61 units.

⇒ Work in 5 cycles (10 days) = 61 × 5 = 305 units.

⇒ Remaining Work = 360 − 305 = 55 units.

⇒ Day 11 (A + B) completes 35 units. Remaining = 55 − 35 = 20 units.

⇒ Day 12 (A + C) time for remaining work = 20 ÷ 26 = 10/13 days.

⇒ Total Time = 10 + 1 + 10/13 = 11¹⁰/₁₃ days.

∴ The correct answer is 11¹⁰/₁₃ days.

Additional Information

Alternate Day Work

When people work on alternate days, calculate the work done in one complete cycle and then multiply to reach closest to the total work.

Combined Efficiency

If multiple persons work together, their combined efficiency is the sum of their individual efficiencies: E_total = E₁ + E₂ + ... + E_n.

Work and Time Relationship

Time taken to complete the work is inversely proportional to the efficiency: Time = Work ÷ Efficiency.

Shortcut Trick

Given a sin q = b cos q.

Substitute b cos q for a sin q in the second equation: (b cos q) sin² q + b cos³ q = sin q cos q.

Factor out b cos q: b cos q (sin² q + cos² q) = sin q cos q ⇒ b cos q (1) = sin q cos q ⇒ b = sin q.

Similarly, substituting a sin q for b cos q gives a = cos q.

Calculate a² + b² = cos² q + sin² q = 1.

∴ The correct answer is 1.

Alternate Method

Given:

1. a sin q = b cos q

2. a sin³ q + b cos³ q = sin q cos q

Calculations:

⇒ (a sin q) sin² q + (b cos q) cos² q = sin q cos q

⇒ (b cos q) sin² q + (b cos q) cos² q = sin q cos q [Using eq 1]

⇒ b cos q (sin² q + cos² q) = sin q cos q

⇒ b cos q (1) = sin q cos q ⇒ b = sin q

⇒ From eq 1: a sin q = (sin q) cos q ⇒ a = cos q

⇒ a² + b² = (cos q)² + (sin q)²

⇒ a² + b² = 1

∴ The correct answer is 1.

Additional Information

Fundamental Trigonometric Identities

The three basic identities are: sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

Complementary Angles

For 0 < θ < 90°, sin(90°−θ) = cos θ and cos(90°−θ) = sin θ.

Ratio Relation

tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

Given number: 36275918

Each of the digits in the number 36275918 is arranged in ascending order from left to right.

All digits changed their position as compared to that in the original number.

Hence, the correct answer is 'Option 4'.

Shortcut Trick

Substitute x = 5 into the terms: 7(5) + 5 = 40, 7(5) + 4 = 39, 5(5) + 5 = 30.

Since the terms are in proportion: 40 ÷ 39 = 30 ÷ y.

y = (39 × 30) ÷ 40 = 39 × 0.75 = 29.25.

∴ The correct answer is 29.25.

Alternate Method

Given: x = 5 and terms are 7x + 5, 7x + 4, 5x + 5, y.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d or ad = bc.

⇒ First term = 7(5) + 5 = 35 + 5 = 40

⇒ Second term = 7(5) + 4 = 35 + 4 = 39

⇒ Third term = 5(5) + 5 = 25 + 5 = 30

⇒ 40/39 = 30/y

⇒ 40 × y = 39 × 30

⇒ y = (39 × 30) ÷ 40

⇒ y = 1170 ÷ 40

⇒ y = 29.25

∴ The correct answer is 29.25.

Additional Information

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is calculated as d = (b × c) ÷ a.

Continued Proportion

Three quantities a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

Mean Proportional

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

The correct answer is gypsum at 373 K.

Key Points

• It is also known as the Plaster of Paris because for the preparation of POP, the abundant gypsum was first found near the capital city of France i.e. Paris.
• The chemical formula of the Plaster of Paris is (CaSO4)2. H2O.

Application of Plaster of Paris is as follows

• It is used as a building material as a protective coating on walls and ceilings.
• It is used as a moulding and vesting agent for decorative elements.
• It is also used for aesthetic touch to the construction elements.
• It is also field as plaster in orthopaedics and as a filling material by dentists, etc.
• we can conclude that Plaster of Paris is chemically (CaSO4)2 H2O.​

Additional Information

• Gypsum is an ore of Calcium (Ca). The chemical formula of Gypsum is CaSO4. 2H2O.
• Gypsum is mainly used as a fertilizer, as the main constituent in plaster, chalk etc.
• The plaster of Paris on mixing with water produces gypsum.
• Calcium Sulphate Hemihydrate (CaSO4·1/2 H2O) on hydration leads to the crystallization of gypsum calcium sulphate dihydrate (CaSO4·2H2O).

Shortcut Trick

Convert all coefficients to simple fractions: 60% = 3/5, 1.2 = 6/5, and the third is 2/5.

Equation: (3/5)A = (6/5)B = (2/5)C ⇒ 3A = 6B = 2C.

Divide by LCM of (3, 6, 2) which is 6: (3A/6) = (6B/6) = (2C/6).

Result: A/2 = B/1 = C/3 → A ∶ B ∶ C = 2 ∶ 1 ∶ 3.

∴ The correct answer is 2 ∶ 1 ∶ 3.

Alternate Method

Given: 60% of A = 1.2 of B = 2/5 of C

60% A

1.2 B

2/5 C

=

A : B : C = 2 : 1 : 3

Calculation:

⇒ 60% of A = (60/100)A = (3/5)A

⇒ 1.2 of B = (12/10)B = (6/5)B

⇒ (3/5)A = (6/5)B = (2/5)C

⇒ Multiplying by 5: 3A = 6B = 2C = k

⇒ A = k/3, B = k/6, C = k/2

⇒ A ∶ B ∶ C = (k/3) ∶ (k/6) ∶ (k/2)

⇒ Multiply by LCM(3, 6, 2) = 6: (6/3) ∶ (6/6) ∶ (6/2) = 2 ∶ 1 ∶ 3

∴ The correct answer is 2 ∶ 1 ∶ 3.

Additional Information

Ratio from Coefficients

If xA = yB = zC, then A ∶ B ∶ C = (1/x) ∶ (1/y) ∶ (1/z). Multiply by the LCM of denominators to simplify.

Percentage and Decimal Conversion

To compare ratios, convert percentages (x% = x/100) and decimals (0.x = x/10) into simplified fractions first.

Compound Ratio

The ratio of ratios (a/b) ∶ (c/d) can be solved by cross-multiplication or multiplying by the LCM of b and d.

Shortcut Trick

Arrange the observations in ascending order: 12, 15, 16, 17, 18, 24, 25, 26, 73, 74.

Total number of terms (n) = 10 (an even number).

For even n, Median = Average of (n/2)^th and (n/2 + 1)^th terms.

Median = Average of 5^th (18) and 6^th (24) terms.

Median = (18 + 24) ÷ 2 = 21.

∴ The correct answer is 21.

Alternate Method

Given Data: 12, 16, 26, 15, 17, 18, 73, 74, 25, 24

Formula: Median (for even n) = [ (n/2)^th term + (n/2 + 1)^th term ] ÷ 2

⇒ Arrange in Ascending Order: 12, 15, 16, 17, 18, 24, 25, 26, 73, 74

⇒ Total observations (n) = 10

⇒ Median = [ (10/2)^th value + (10/2 + 1)^th value ] ÷ 2

⇒ Median = [ 5^th value + 6^th value ] ÷ 2

⇒ Median = (18 + 24) ÷ 2

⇒ Median = 42 ÷ 2 = 21

∴ The correct answer is 21.

Additional Information

Median for Odd Number of Terms

If n is odd, the Median is exactly the (n + 1) ÷ 2^th term of the sorted data.

Empirical Relation between Mean, Median, and Mode

For a moderately skewed distribution: Mode = 3 × Median − 2 × Mean.

Effect of Outliers

The Median is a more robust measure of central tendency than the Mean because it is not significantly affected by extreme values (outliers).

Given word: KINDLE

Vowels is to be changed to the next letter KINDLE → KJNDLF

Consonant to be changed to letter preceding in English alphabetical order KJNDLF → JJMCKF

the new word formed is JJMCKF.

Here, J is being repeated twice

Hence, the correct answer is "Option 4".

The correct answer is Tamil.

Key Points

• Languages that have a long history, whose grammar has been the subject of many studies and in which much literature has been written are referred to as classical languages.
• The classical languages are considered dead languages as they lose their importance in the modern world and their speakers shift to another language. A language becomes dead when the language has no more native speakers.
• As per the requirements set by the Government of India in 2004, a language is accorded the status of "Classical Language of India" if it fulfills the following criteria:
• It should have a recorded history of existing for over a period of 1500-2000 years.
• It would have an original literature tradition and would not borrow anything from any other language family.
• It should have some ancient literature or epics in it.
• The language should be different from its modern/later forms.
• Currently, there are six languages mentioned in the 8th schedule of the Indian constitution that enjoy the "Classical" status in India that are Tamil (declared in 2004), Sanskrit (2005), Kannada (2008), Telugu (2008), Malayalam (2013), and Odia (2014).

 Additional Information The Union Cabinet recently declared five Indian languages in 2024 - Marathi, Assamese, Pali, Prakrit, and Bengali - as classical languages. This decision aims to preserve the rich heritage of these languages and bring the total number of classical languages in India to eleven.

Shortcut Trick

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

986: Even number, divisible by 2.

319: 11 × 29 = 319 (divisible by 11).

153: Sum of digits (1+5+3=9) is divisible by 9, so the number is divisible by 9.

983: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 (primes up to √983 ≈ 31.3).

∴ The correct answer is 983.

Alternate Method

Check each option for divisibility using standard rules:

Option 1: 986

⇒ Ends in 6 (even), so it is divisible by 2.

⇒ 986 = 2 × 493 (Not a prime).

Option 2: 319

⇒ Divisibility by 11: (3 + 9) − 1 = 11. Since 11 is divisible by 11, the number is divisible by 11.

⇒ 319 = 11 × 29 (Not a prime).

Option 3: 153

⇒ Sum of digits = 1 + 5 + 3 = 9. Since 9 is divisible by 3 and 9, the number is divisible by 3 and 9.

⇒ 153 = 9 × 17 (Not a prime).

Option 4: 983

⇒ √983 is approx 31.3. Testing primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.

⇒ 983 is not divisible by any of these primes.

∴ The correct answer is 983.

Additional Information

Prime Number Definition

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Primality Test Rule

To check if n is prime, verify if any prime p ≤ √n divides n. If no such p exists, n is prime.

Composite Numbers

Numbers that have more than two factors are called composite numbers. 1 is neither prime nor composite.

Given:

?² + 53.99 = 206.01 ÷ 1.99

Formula Used:

To find ?, isolate ?² and then take the square root.

Calculation:

Start by simplifying the right-hand side:

⇒ 206.01 ÷ 1.99 ≈ 103

Now, isolate ?²:

⇒ ?² + 53.99 = 103

⇒ ?² ≈ 103 - 54

⇒ ?² ≈ 49

⇒ ? = 7

The correct answer is option 4.

The correct answer is Sarpanch.

Key Points

• Nyaya Panchayat consists of at least 10 members.
• The number of members in each Nyaya Panchayat is such that it is completely divisible by five.
• The number of Panches of Nyaya Panchayat having 1 to 6 village councils will be 15, 7 to 9 will be 20 and if more than 9 will be 25.

Given:

Total cost of house and garden = ₹51 lakh

Cost of the garden = $\frac{5}{{12}}$ of the cost of the house

Formula Used:

Let the cost of the house be H.

Then, cost of the garden = $\frac{5}{{12}}$ H

Total cost = Cost of the house + Cost of the garden

Total cost = H + $\frac{5}{{12}}$ H

Calculation:

Let the cost of the house be H.

Total cost = H + $\frac{5}{{12}}$ H

⇒ ₹51 lakh = $\frac{12H + 5H}{12}$

⇒ ₹51 lakh = $\frac{17H}{12}$

⇒ 51 × 12 = 17H

⇒ 612 = 17H

⇒ H = $\frac{612}{17}$

⇒ H = 36 lakh

Cost of the garden = $\frac{5}{12}$ × 36 lakh

⇒ Cost of the garden = 15 lakh

The cost of the garden is ₹15 lakh.

The Position and positional values of English Alphabets are:

Given Word: DEHRAZUN

Now, If each of the letter of the letter cluster 'DEHRAZUN' is arranged in alphabetical order,

The Word becomes, ADEHNRUZ

Vowels are: A, E, I, O, U

Now, vowels immediately preceded by a consonant in newly formed Word Cluster are: DE and RU.

There are 2 Vowels in the newly formed word cluster which are preceded by a consonant.

Hence, the correct answer is "Option 3".

The logic followed here is:

Given series: Q_T_T_BT_TQB_RT

 

Here, 'QBTRT / QBTRT / QBTRT ' - The Pattern "QBTRT" is repeated in the series.

Hence, the correct answer is "Option 3".

Shortcut Trick

Sum of ratio parts = 3 + 4 + 5 = 12 units.

Total internal angles of triangle = 180°.

Internal angle ∠ABC corresponds to the second part of the ratio = (4 ÷ 12) × 180° = 60°.

Exterior angle ∠CBX = 180° − ∠ABC = 180° − 60° = 120°.

∴ The correct answer is 120°.

Alternate Method

Given: Ratio of angles ∠A : ∠B : ∠C = 3 : 4 : 5.

Formula Used: Sum of angles in a triangle = 180° | Exterior angle = 180° − Adjacent interior angle.

⇒ Let the angles be 3k, 4k, and 5k.

⇒ 3k + 4k + 5k = 180°

⇒ 12k = 180°

⇒ k = 15°

⇒ Angle ∠ABC (Angle B) = 4 × 15° = 60°.

⇒ Since AB is extended to X, ∠ABC and ∠CBX form a linear pair.

⇒ ∠CBX = 180° − 60° = 120°.

∴ The correct answer is 120°.

Additional Information

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Here, ∠CBX = ∠A + ∠C = 45° + 75° = 120°.

Linear Pair Postulate

When a side of a triangle is extended, the resulting exterior angle and the adjacent interior angle are supplementary (sum is 180°).

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon (including a triangle), taking one at each vertex, is always 360°.

The correct answer is Households should separate non-biodegradable items from biodegradable items in the trash.

Key Points

• Segregation at source for non-biodegradable waste refers to the practice of separating different types of non-biodegradable materials at the point of generation.
• This means sorting waste like plastic, paper, glass, metal, and e-waste into separate containers before it is collected for disposal.
• This process is crucial for effective waste management and recycling.
• By segregating waste at the source, we can prevent contamination, increase the efficiency of recycling processes, and reduce the amount of waste that ends up in landfills.
• It also helps to conserve natural resources and reduce pollution.

The correct answer is XE.

Key Points

COVID-19

• Coronavirus disease (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus.
• Most people infected with the virus will experience mild to moderate respiratory illness and recover without requiring special treatment. However, some will become seriously ill because of Acute Respiratory Distress Syndrome (ARDS) and require medical attention.
• Older people and those with underlying medical conditions like cardiovascular disease, diabetes, chronic respiratory disease, or cancer are more likely to develop serious illnesses.
• Anyone can get sick with COVID-19 and become seriously ill or die at any age.
• The best way to prevent and slow down transmission is
• To be well informed about the disease and how the virus spreads.
• Protect yourself and others from infection by staying at least 1 meter apart from others, wearing a properly fitted mask, and washing your hands or using an alcohol-based rub frequently.
• Get vaccinated when it’s your turn and follow local guidance.
• The virus can spread from an infected person’s mouth or nose in small liquid particles when they cough, sneeze, speak, sing or breathe.
• These particles range from larger respiratory droplets to smaller aerosols.
• It is important to practice respiratory etiquette, for example by coughing into a flexed elbow, and to stay home and self-isolate until you recover if you feel unwell.

COVID-19 affects different people in different ways. Most infected people will develop mild to moderate illness and recover without hospitalization.

Most common symptoms:

• fever
• cough
• tiredness
• loss of taste or smell.

Less common symptoms:

• sore throat
• headache
• aches and pains
• diarrhea
• a rash on the skin, or discoloration of fingers or toes
• red or irritated eyes.

Serious symptoms:

• difficulty breathing or shortness of breath
• loss of speech or mobility, or confusion
• chest pain.

The logic followed here is: 

Logic: (1st number × 3) + 2nd number = 3rd number.

Now,

For (7, 19, 40):

⇒ (7 × 3) + 19

= 21 + 19 = 40.

For (12, 11, 47)

⇒ (12 × 3) + 11

= 36 + 11 = 47.

Similarly, for Option 2: (16, 5, 53)

⇒ (16 × 3) + 5

= 48 + 5 = 53.

Hence, the correct answer is Option 2.

The correct answer is Starch was digested by salivary amylase in the saliva.

Key Points

• Starch: A complex carbohydrate found in various plant-based foods like potatoes, rice, and bread. It's a long chain of glucose molecules.
• Salivary Amylase: An enzyme present in saliva, produced by the salivary glands. Enzymes are biological catalysts that speed up chemical reactions.
• Digestion: The process of breaking down complex food molecules into simpler ones that can be absorbed by the body.
• Process: When you chew food, it mixes with saliva. Salivary amylase in the saliva starts breaking down the long chains of glucose molecules in starch into smaller units, primarily maltose (a disaccharide).
• Significance: This initial digestion in the mouth is crucial as it prepares the food for further breakdown in the digestive system.
• Maltose: A simpler sugar molecule formed from two glucose units.
• Continued Digestion: The partially digested starch then travels to the stomach and eventually the small intestine, where further enzymes (like pancreatic amylase) continue the breakdown process.
• Absorption: The final products of starch digestion (mainly glucose) are then absorbed into the bloodstream through the walls of the small intestine.
• Energy: Glucose is the primary source of energy for the body's cells.

Given: (LEFT) 2 8 3 6 0 8 1 5 3 7 3 4 9 6 2 4 3 2 5 6 4 0 7 (RIGHT)

Now,

Option 1: (LEFT) 2 8 3 6 0 8 1 5 3 7 3 4 9 6 2 4 3 2 5 6 4 0 7 (RIGHT)

Here, all the digits are placed continuously.

Option 2: (LEFT) 2 8 3 6 0 8 1 5 3 7 3 4 9 6 2 4 3 2 5 6 4 0 7 (RIGHT)

Here, 7, 4, and 6 are in the alternate sequence.

Option 3: (LEFT) 2 8 3 6 0 8 1 5 3 7 3 4 9 6 2 4 3 2 5 6 4 0 7 (RIGHT)

Here, 0, 1, and 3 are in the alternate sequence.

Option 4: (LEFT) 2 8 3 6 0 8 1 5 3 7 3 4 9 6 2 4 3 2 5 6 4 0 7 (RIGHT)

Here, 2, 3, and 0 are in the alternate sequence.

So, 'Option 1' does not belong to the group.

Hence, the correct answer is "Option 1".

The correct answer is Republic Day.

Key Points

• Republic Day:
• Celebrated on January 26th, commemorating the adoption of the Indian Constitution in 1950. It features a grand parade in New Delhi showcasing India's cultural and military heritage.Republic Day parade in India
• Independence Day:
• ​Celebrated on August 15th, commemorating India's independence from British rule in 1947. The Prime Minister hoists the national flag at the Red Fort in Delhi, followed by a speech and various cultural performances.
• Gandhi Jayanti:
• Celebrated on October 2nd, commemorating the birthday of Mahatma Gandhi, the Father of the Nation. It is a day of non-violence and peace, marked by prayer services and inspirational programs.

The correct answer is Bethlehem.

Key Points

• Christmas is celebrated by Christians around the world as the birth of Jesus Christ.
• This festival is observed on December 25th each year.
• Christmas is marked by various traditions including gift-giving, decorating Christmas trees, attending church services, and sharing meals with family and friends.
• The holiday holds significant religious importance as well as cultural significance in many countries.

 Additional Information

• Easter is another major Christian holiday, celebrating the resurrection of Jesus Christ, but it is not related to his birth.
• Good Friday commemorates the crucifixion of Jesus Christ and is observed during the Holy Week preceding Easter.
• Eid ul Fitr is an Islamic festival marking the end of Ramadan, the holy month of fasting.
• Christmas has been celebrated for centuries and has evolved to include various customs and traditions unique to different cultures around the world.
• In many countries, Christmas is a public holiday, allowing people to celebrate with their loved ones.

Given:

Statement :

Segregation of garbage into wet and dry waste will help in recycling it.

Now,

Arguments :

I. Wet waste can be converted to organic compost or biogas when managed the right way - True (As the statement suggests, segregation of wet waste allows for better management, such as converting it into compost or biogas, which supports recycling).

II. Recycled plastic can be remanufactured for a wide array of products including carpet, upcycled polyester for clothing, recycled plastic building materials - True (This argument highlights that dry waste, particularly plastic, can be recycled into various products, which is a valid part of the recycling process).

So, Both I and II strengthen the statement.

Hence, the correct answer is "Option 3".

The Logic follows here is:

1. Madhav starts from Point A and drives 16 km towards the east.

2. He then takes a right turn, drives 4 km, turns right and drives 12 km.

3. He then takes a right turn and drives 11 km,

4. takes a left turn and drives 4 km and stops at Point B. 

Drawing the Diagram as per the given information:

Distance between point B to point A is 7KM.

Thus, Madhav should drive 7KM in south direction to reach point A from Point B.

Hence, the correct answer is "Option 1"

Given Statements:

Some Buses are Vans.

All Vans are Trucks.

Some Buses are Cars.

The least possible Venn diagram for the given statement is:

Conclusion:

(I) Some Trucks are Buses → TRUE (Those trucks which are Vans are also bus, so Some Trucks are Buses).

(II) Some Cars are Trucks → FALSE (There is no definite relation given between Cars and Trucks, so it can be possible only).

So, Only conclusion (I) follows.

Hence, the correct answer is "Option 3".

Here BODMAS Table applies:

Given Equation: 47 + 56 ÷ 6 - 2 × 3

If '2' is interchanged with the position of the digit '4'

And, '5' is interchanged with the position of the digit '3' 

Equation becomes:  27 + 36 ÷ 6 - 4 × 5

⇒ 27 + 36 ÷ 6 - 4 × 5 

⇒ 27 + 6 - 4 × 5

⇒ 27 + 6 - 20

⇒ 33 - 20 = 13.

Hence, the correct answer is "Option 2".

Shortcut Trick

Convert mixed recurring decimal 0.372 directly to a fraction:

Numerator = Total digits − Non-repeating digits = 372 − 3 = 369

Denominator = 99 (for two repeating digits) followed by 0 (for one non-repeating digit) = 990

Fraction = 369 ÷ 990 = 41 ÷ 110

Since x and y are coprime, x = 41 and y = 110, giving (x + y) = 151.

∴ The correct answer is 151.

Alternate Method

Given:

x ÷ y = 0.372

Let N = 0.3727272...

⇒ 10N = 3.727272... (Equation 1)

⇒ 1000N = 372.727272... (Equation 2)

Subtracting Equation 1 from Equation 2:

⇒ 1000N − 10N = 372.727272... − 3.727272...

⇒ 990N = 369

⇒ N = 369 ÷ 990

⇒ N = 41 ÷ 110

Since x and y are coprime, we can equate x = 41 and y = 110.

⇒ (x + y) = 41 + 110 = 151

∴ The correct answer is 151.

Additional Information

Pure Recurring Decimal

A decimal where all digits after the decimal point are repeated. To convert, place the repeating digits in the numerator and an equal number of 9s in the denominator (e.g., 0.4545... = 45 ÷ 99).

Mixed Recurring Decimal

A decimal where some digits after the decimal point do not repeat. The denominator will have 9s equal to the repeating digits and 0s equal to the non-repeating digits.

Coprime Numbers

Two numbers are coprime if their highest common factor (HCF) is 1. They do not necessarily need to be prime numbers themselves (e.g., 8 and 15 are coprime).

The correct answer is 2022.

Key Points

• Earth Observation Satellite (EOS-04)
• ​​The EOS-04, formerly known as RISAT-1A, is a land-based earth observation satellite that images using radar.
• On 14 February 2022, it was inserted into a sun-synchronous orbit at an altitude of 529 km from the surface.
• EOS-04 is the sixth satellite to be launched under the RISAT (Radar Imaging Satellite) programme in the last decade.
• Built at ISRO’s UR Rao Satellite Centre in Bengaluru, EOS-04 carries synthetic aperture radar (SAR) that can peer through all kinds of weather and clouds, during night-time as well.
• It will be used in the fields of plantations, flood mapping, hydrology and more. The satellite weighs 1,710 kg and will function for at least 10 years.
• INS-2TD
• ​INS-2TD is a precursor to the India-Bhutan joint satellite, INS-2B, built by Bhutanese engineers who were trained at UR Rao Satellite Centre.
• INS-2TD is a tech demonstrator carrying a thermal imaging camera. The satellite weighs 17.5 kg and has a mission life of six months.
• It will assess and monitor land temperature, the surface temperature of water bodies like lakes and wetlands, delineation of vegetation of crops and forests, and thermal inertia or temperature variation between day and night times.
• INSPIREsat-1
• ​INSPIRE stands for the International Space Program in Research and Education, and was launched in 2017.
• The CubeSat carries two scientific payloads, one each to study the earth’s ionosphere and to observe the solar flares.

 Additional Information The Indian Space Research Organisation (ISRO) successfully launched the earth observation satellite EOS-04, along with two other satellites, on the PSLV-C52 mission.

According to the given information - 

1) L is fifth from the bottom in the stack.

 

2) M is immediately above L. 

 

3. Only three boxes are there between O and L.

 

4. Only two boxes are there between P and N. N is immediately above Q.

 

5) P is at one of the positions above N.

 

Thus, the box placed at sixth from the bottom 'M'.

Hence, the correct answer is "Option 4".

The correct answer is submerged.

Key Points

• Western Coastal Plains of India-
• Western Coastal Plains stretches from Kerala in the south to Gujarat in the north passing through Karnataka, Goa and Maharashtra.
• The western coast is further divided into four categories:
• Kachchh and Kathiawar coast- Kachchh, formerly a gulf is formed by the deposition of silt by the Indus. Kathiawar is situated to the south of Kachchh.
• Konkan coast-  It extends between Daman in the north to Goa in the south.
• Rice and cashew are the two important crops of this region.
• Kannada coast- It extends between Marmagaon and Mangalore and is rich in iron deposits.
• Malabar coast- Extending between Mangalore to Kanyakumari, the Malabar coast is relatively broad.
• This region also consists of lagoons running parallel to the coast in southern Kerala.

The correct answer is Because they don't form any ions.

Key Points

• Carbon compounds don't have a free electron that is required for electricity transfer thus making them bad conductors.
• Carbon compounds consist of molecules in which the atoms are joined by strong covalent bonds. However, the molecules in the compounds are held together by weak forces so these substances have low melting and boiling points.

Additional Information

• Due to the strong carbon-carbon single bonds, saturated carbon compounds are often not very reactive.
• Alkanes are single-bond C-C saturated carbon compounds.
• A general inertness to various chemical reagents is one of the characteristics of alkanes as a class.
• Strong connections between C and H can be found.
• Unless alkanes are heated to extremely high temperatures, they do not break.
• The bonds between carbon and hydrogen are only marginally polarised because carbon and hydrogen have approximately identical electronegativities.
• They are hence typically unaffected by the majority of bases.

Given:

Simplify the expression:

$\frac{{{{\left[ {\left( {34.45} \right)} \right]}^2} - {{\left( {11.75} \right)}^2}],, × ,,5.15}}{{\left[ {{{\left( {25.75} \right)}^2} + \left( {25.75, × ,20.45} \right)} \right],, × 22.7}}$

Solution:

We use the identity a² - b² = (a - b)(a + b):

(34.45)² - (11.75)² = (34.45 - 11.75)(34.45 + 11.75) = 22.7 × 46.2

Numerator : 22.7 × 46.2 × 5.15

Simplify the denominator:

⇒ $[(25.75)^2 + (25.75×20.45)] × 22.7$

⇒ $[(25.75 (25.75 + 20.45)] × 22.7$

⇒ $25.75 \times 46.2 × 22.7$

Combine numerator and denominator and Divide the numerator by the denominator:

$\frac{22.7 × 46.2 × 5.15}{25.75 \times 46.2 × 22.7}$

⇒ $\frac{5.15}{25.75} = \frac{1}{5}$

∴ The correct answer is option 3.

Shortcut Trick

Since −2 is a root of 3x² + px + 2 = 0, substitute x = −2 to find p = 7.

For the equation 7x² + 7x + k = 0 to have equal roots, the constant term k must satisfy the condition k = b² ÷ 4a.

k = 7² ÷ (4 × 7) = 49 ÷ 28 = 7/4.

∴ The correct answer is 7/4.

Alternate Method

Given:

Equation 1: 3x² + px + 2 = 0 (One root is −2)

Equation 2: 7x² + px + k = 0 (Has equal roots)

Step 1: Find the value of p.

Since −2 is a root of the first quadratic equation, it must satisfy the equation:

⇒ 3(−2)² + p(−2) + 2 = 0

⇒ 3(4) − 2p + 2 = 0

⇒ 12 − 2p + 2 = 0

⇒ 14 − 2p = 0

⇒ 2p = 14

⇒ p = 7

Step 2: Find the value of k.

Substitute p = 7 in the second equation:

⇒ 7x² + 7x + k = 0

For equal roots, the discriminant (D) must be zero:

⇒ D = b² − 4ac = 0

⇒ 7² − 4 × 7 × k = 0

⇒ 49 − 28k = 0

⇒ 28k = 49

⇒ k = 49 ÷ 28

⇒ k = 7/4

The value of k is 7/4, which matches the required result.

∴ The correct answer is 7/4.

Additional Information

Nature of Roots

For a quadratic equation ax² + bx + c = 0, if D = b² − 4ac > 0 roots are real and distinct; if D = 0 roots are real and equal; if D < 0 roots are imaginary.

Root Substitution

If α is a root of f(x) = 0, then f(α) = 0 always holds true. This is used to find unknown coefficients in the equation.

Sum and Product of Roots

For ax² + bx + c = 0, Sum of roots (α + β) = −b/a and Product of roots (αβ) = c/a.

The correct answer is intestinal juice.

Key Points

• Source: Intestinal juice, or succus entericus, is secreted by the intestinal glands found in the lining of the small intestine.
• Proteases: It contains proteases like peptidases which break down proteins into amino acids.
• Carbohydrases: Enzymes such as maltase, lactase, and sucrase convert complex carbohydrates into simple sugars like glucose.
• Lipases: Intestinal juice contains lipases that catalyze the breakdown of fats into fatty acids and glycerol.
• Optimal pH: These enzymes function optimally in the slightly alkaline pH of the small intestine, ensured by the bicarbonate ions present in the intestinal juice.
• Absorption Ready: The conversion to amino acids, glucose, and fatty acids and glycerol makes nutrients ready for absorption into the bloodstream.
• Pancreatic Enzymes Support: Intestinal enzymes work in conjunction with pancreatic enzymes to complete digestion.
• Vital Role: These enzymes play a crucial role in the final steps of digestion, ensuring that nutrients from food are in a form that the body can absorb and utilize.
• Nutrient Uptake: The small intestine is the main site for nutrient uptake, facilitated by the action of these enzymes.
• Health Importance: Efficient functioning of these enzymes is key to good health and nutrient availability to the body.

The correct answer is Forty-Second.

Key Points

• The Forty-second Amendment Act, 1976, added the words "Socialist" and "Secular" to the Preamble of the Indian Constitution.
• This amendment is known as the Constitution (Forty-second Amendment) Act, 1976.
• The aim was to reflect the socialist and secular ideals of the Indian nation and to reinforce the commitment of the state to these principles.
• This amendment was introduced during the tenure of Prime Minister Indira Gandhi.

 Additional Information

• Preamble of the Indian Constitution
• The Preamble is an introductory statement that outlines the guiding principles and philosophy of the Indian Constitution.
• It reflects the values of justice, liberty, equality, and fraternity.
• The Preamble begins with the words "We, the people of India," signifying that the power and authority of the government are derived from the people.
• It was adopted on 26th November 1949 and came into effect on 26th January 1950.
• Forty-second Amendment Act, 1976
• This amendment is often referred to as the "Mini-Constitution" because of its wide-ranging impact on the Indian Constitution.
• It made significant changes to the Preamble, Fundamental Rights, Directive Principles of State Policy, and other parts of the Constitution.
• One of the key changes was the addition of the words "Socialist" and "Secular" to the Preamble.
• The amendment also aimed to reduce the power of the judiciary and increase the power of the Parliament.
• Socialist
• The term "Socialist" in the Preamble signifies the commitment of the Indian state to social and economic equality.
• It implies that the government will strive to reduce inequalities in income and wealth and ensure a fair distribution of resources.
• It also emphasizes the state's role in providing social security and welfare to its citizens.
• Secular
• The term "Secular" in the Preamble signifies that the Indian state does not have an official religion and treats all religions equally.
• It implies that the government will not favor or discriminate against any religion.
• It also emphasizes the state's commitment to maintaining religious harmony and ensuring the freedom of religion for all citizens.

The correct answer is BaBr₂.

Key Points

• BaBr₂ stands for Barium Bromide, which is a chemical compound composed of barium and bromine.
• In the above reaction, Barium Bromide is insoluble in water which is why it precipitates out of the solution.
• In the reaction, 2KBr + Bal₂ → 2KI + BaBr₂, BaBr₂ does not dissolve in water and remains as a solid.
• The formation of an insoluble precipitate like BaBr₂ is a common occurrence in double displacement reactions.

Additional Information

• Solubility
• Solubility is a chemical property referring to the ability of a given substance, the solute, to dissolve in a solvent.
• It is measured in terms of the maximum amount of solute dissolved in a solvent at equilibrium.
• Barium Bromide (BaBr₂) has low solubility in water, leading to its precipitation in the reaction.
• Double Displacement Reaction
• A double displacement reaction, also known as a metathesis reaction, occurs when parts of two ionic compounds are exchanged and make two new compounds.
• These reactions are generally written as AB + CD → AD + CB.
• In this particular reaction, KBr and Bal₂ exchange ions to form KI and BaBr₂.
• Precipitation
• Precipitation is the process of a substance being separated from a solution as a solid.
• In the reaction provided, BaBr₂ forms a solid precipitate because it is insoluble in water.
• Precipitation reactions are a type of double displacement reaction where an insoluble solid forms and separates from the solution.

The position and positional values of English Alphabets are:

The logic followed here is

For, 'ARMOR' is written as 'CVOST'

For, 'Gland' is written as 'IPCRF' 

Similarly, 'FARMS' will be:

Thus, 'FARMS' is coded as 'HETQU'

Hence, the correct answer is "Option 1".

Given:

$\frac{{{9^4}, \times ,{{10}^3}, \times {4^{ - 4}} \times {{16}^{^{\frac{1}{2}}}}}}{{{5^6} \times {3^6}}}$

Calculation:

Step 1: Break down the components

$9^4 = (3^2)^4 = 3^8$

$10^3 = (2 × 5)^3 = 2^3 × 5^3$

$4^{-4} = (2^2)^{-4} = 2^{-8}$

$16^{1/2} = (2^4)^{1/2} = 2^2$

Substituting these into the expression:

$\frac{(3^8 × (2^3 × 5^3) × 2^{-8} × 2^2)}{(5^6 × 3^6)}$

Step 2: Simplify the numerator

Combine the powers of 2:

$2^3 × 2^{-8} × 2^2 = 2^{-3}$

The numerator becomes:

$3^8 × 5^3 × 2^{-3}$

Step 3: Simplify the denominator

The denominator remains:

$5^6 × 3^6$

Step 4: Combine the terms

$\frac{3^8 × 5^3 × 2^{-3}}{5^6 × 3^6} = \frac{3^2}{5^3 \times 2^3}$

⇒ 9 × (1 / 8) × (1 / 125) = 9 / 1000

The simplified value is 9 / 1000.

The correct answer is 2.0

Key Points

• Lens Formula:
• The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens:
• 1/v - 1/u = 1/f
• Given Values:
• Object height (h₀) = 3 cm
• Object distance (u) = -1.5f (negative because the object is in front of the lens)
• Focal length (f) = f
• Applying the Lens Formula:
• 1/v - 1/(-1.5f) = 1/f
• 1/v + 1/(1.5f) = 1/f
• 1/v = 1/f - 1/(1.5f)
• 1/v = (1.5 - 1) / 1.5f
• 1/v = 0.5 / 1.5f
• 1/v = 1 / 3f
• v = 3f
• Magnification Formula:
• Magnification (M) is given by:
• M = -v/u
• Calculating Magnification:
• M = -(3f) / (-1.5f)
• M = 2
• Therefore, the magnification will be 2.

Additional Information

• Convex Lens
• In most instances, an optical lens is composed of two spherical surfaces.
• This lens has thinner margins and a thicker centre than its edges.
• If those surfaces are curved outwards, the lens is referred to as a biconvex lens or just a convex lens.
• The image formed by a convex lens can be both real and virtual images based on the object's position.
• The erect image by convex lens is always virtual and diminished image of the object.
• A beam of light coming from the outside can be focused by these lenses to a place on the other side.
• The focal length of a convex lens is the distance from the lens’s centre to the focus.
• The focus is at this point. On the other hand, a plano-convex lens is created when one of the surfaces is convex and the other is flat.

Given: Six friends A, B, C, D, E, and F.

1) Only one person is shorter than E. 

__ > __ > __ > __ > E > __.

2)  Only two people are taller than D.

__ > __ > D > __ > E > __.

3)  A is shorter than F but taller than C. F is not the tallest.

__ > F > D > A > E > C.

After combining all the arrangements, we get:

B > F > D > A > E > C.

Here, C is the shortest among all the friends.

Hence, the correct answer is 'Option 4'.

Person: M, N, O, P, Q, R lives on a six-floor building

M lives two floors above R, on an odd-numbered floor

 

Q lives immediately below M

 

There are only two people living between O and Q. 

 

O is not living on the lowermost floor, thus CASE 1 will not be possible.

N lives immediately above M.

 

Thus, there are 3 people living between Q and P

Hence, the correct answer is "Option 2".

Shortcut Trick

Apply the Empirical Relation: 3 × Median = Mode + 2 × Mean.

3 × Median = 45 + 2 × 46

3 × Median = 45 + 92 = 137

Median = 137 ÷ 3 = 45.66...

Rounding to one decimal place, we get 45.7.

∴ The correct answer is 45.7.

Alternate Method

Given:

Mean of the data = 46

Mode of the data = 45

Formula Used:

The relationship between Mean, Median, and Mode is given by:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 45 = 3 × Median − 2 × 46

⇒ 45 = 3 × Median − 92

⇒ 3 × Median = 45 + 92

⇒ 3 × Median = 137

⇒ Median = 137 ÷ 3

⇒ Median = 45.666...

⇒ Median ≈ 45.7 (Rounded to one decimal place)

∴ The correct answer is 45.7.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is Mode = 3 Median − 2 Mean. This was first suggested by Karl Pearson.

Symmetrical Distribution

In a perfectly symmetrical distribution (like the Normal distribution), the Mean, Median, and Mode are all identical (Mean = Median = Mode).

Types of Skewness

If Mean > Median > Mode, the distribution is positively skewed. If Mean < Median < Mode, the distribution is negatively skewed.

The logic followed here is:

logic: (1st number - 3rd number) × 6 = 2nd number.

Now, 

For (85, 198, 52)

→ (85 - 52) × 6

→ 33 × 6 = 198.

For (77, 270, 32)

→ (77 - 32) × 6

→ 45 × 6 = 270.

Similarly, for (62, 90, 47)

→ (62 - 47) × 6

→ 15 × 6 = 90.

Hence, the correct option is "Option 4".

The correct answer is Gender Equality Today for a Sustainable Tomorrow

Key Points

• The United Nations theme for International Women's Day in 2022 was "Gender equality today for a sustainable tomorrow".
• This theme recognized the contributions of women and girls around the world in addressing climate change.
• The campaign theme for International Women's Day 2022 was #BreakTheBias.
• The International Women's Day website asked people to imagine a world free of bias, stereotypes, and discrimination.
• International Women's Day (IWD) is a worldwide event celebrating women's cultural, political, and economic achievements.
• Every year on March 8th, it is commemorated.

Additional Information

• IWD arose from early twentieth-century labour movements in North America and Europe.
• The first edition was supposedly a "Women's Day" organized by the Socialist Party of America on February 28, 1909, in New York City.
• International Women's Day is celebrated in a number of forms around the world, in certain nations, it is a public holiday, and it is observed socially or politically.
• International Women's Day is celebrated in a number of ways around the world; in some nations, it is a national holiday, whereas, in others, it is observed socially or locally.
• The UN commemorates the holiday in celebration of a specific topic, movement, or theme related to women's rights.

The position and positional values of English Alphabets are:

The logic follows here is:

QJD : TMG

GMS : JPV

Similarly, for RPH :USK

Hence, the correct answer is "Option 1".

The correct answer is revenue deficit.

Key Points

• When a government's revenue expenditure exceeds revenue receipts, it is termed as a revenue deficit.
• Revenue expenditure refers to the day-to-day operational expenses incurred by the government, such as salaries, pensions, and interest payments on debt. Revenue receipts are the funds that the government receives from tax collections and other sources during the normal course of operations.
• A revenue deficit essentially means that the government's own earnings are insufficient to meet the operational costs of running government departments and provision of services.
• To cover this deficit, the government may need to borrow or sell assets, which could further affect its fiscal position. It may also hint at the possibility of structural economic imbalances.​

Additional Information

• Primary Deficit:
• Primary deficit refers to the difference between the current year's fiscal deficit and interest payments on previous borrowings.
• It shows how much of the government's expenses, other than interest payments, exceed revenue.
• If the primary deficit is zero, it means that the current borrowings of the government are being used only for making interest payments.
• Capital Receipt:
• A capital receipt is a cash inflow that a government or organization receives from non-routine sources, such as the sale of assets, loans, or equity investments.
• Capital receipts are different from revenue receipts, which are generated from regular business activities.
• Capital receipts are important for an organization's financial stability because they: Fund long-term investments, Repay long-term debts, and Ensure sufficient funds for future growth
• Capital Expenditure:
• ​Capital expenditures, or CapEx, are funds a company uses to purchase, maintain, or upgrade its capital assets.
• Capital assets are long-term investments, such as buildings, equipment, vehicles, land, or software.
• CapEx is different from operating expenses (OpEx), which are the day-to-day costs of running a business

The correct answer is Plaster of Paris

Key Points

• Calcium sulphate hemihydrate is also known as plaster of Paris.
• Plaster of Paris
• It is chemically calcium sulphate hemihydrate, i.e. CaSO4. 1/2 H2O.
• It is formed from gypsum, that is, CaSO4. 2H2O.
• It is used to plaster fractured bones, for making toys, materials for decoration, and for making surfaces smooth.

Additional Information

• Gypsum​
• Gypsum is mainly used as a fertilizer, as the main constituent in plaster, chalk, etc.
• Rapid setting of cement is the function of gypsum in cement.
• It is a crystalline mineral composed of calcium sulfate dihydrate.
• Gypsum helps in controlling the rate of hardening of the cement.
• It also prevents early hardening allowing long working time, hence we can say that it helps in the rapid setting of cement.
• The Bikaner district of Rajasthan has the maximum quantity of Gypsum.
• Rajasthan produces 90% of total production in India.
• Limestone
• ​Limestone is primarily composed of calcium carbonate (CaCO₃).
• It forms from the remains of marine organisms like corals and shells, or through the precipitation of calcium carbonate from water.
• Used as building material (blocks and slabs).
• Limestone is a key ingredient in the production of cement
• Quike lime
• ​Quicklime is produced by heating limestone in a kiln at high temperatures (around 900–1000°C)
• Quicklime is a highly reactive substance.
• It appears as a white, granular or powdery material.
• Used in steel manufacturing, water treatment, and in the production of chemicals like calcium hydroxide (slaked lime).
• It is  Often used in the production of mortar and plasters.

The logic followed here is:

Given Series: 2, 3, 6, 12, ?, 37, 58

The series follows the pattern of double difference. 

So, '22' will complete the given series.

Hence, the correct answer is "Option 4".

Shortcut Trick

Identify ΔBCD as a right-angled triangle at B with BC = 8 cm and hypotenuse CD = 17 cm.

Using Pythagorean triplet (8, 15, 17), BD = 15 cm.

In ΔABD (right-angled at A), BD = 15 cm (hypotenuse) and AD = 9 cm, so AB = 12 cm (triplet 9, 12, 15).

Area = Area(ΔABD) + Area(ΔBCD) = (1/2 × 9 × 12) + (1/2 × 8 × 15) = 54 + 60 = 114 cm².

∴ The correct answer is 114 cm².

Alternate Method

Given: AD = 9 cm, BC = 8 cm, CD = 17 cm, ∠DAB = 90°, ∠DBC = 90°.

Formula Used: Area of right-angled triangle = 1/2 × base × height; Pythagoras Theorem: a² + b² = c².

⇒ In ΔDBC, CD² = BD² + BC²

⇒ 17² = BD² + 8² ⇒ 289 = BD² + 64

⇒ BD² = 225 ⇒ BD = 15 cm

⇒ In ΔABD, BD² = AB² + AD²

⇒ 15² = AB² + 9² ⇒ 225 = AB² + 81

⇒ AB² = 144 ⇒ AB = 12 cm

⇒ Area of ΔABD = 1/2 × 12 × 9 = 54 cm²

⇒ Area of ΔBCD = 1/2 × 15 × 8 = 60 cm²

⇒ Total Area = 54 + 60 = 114 cm²

∴ The correct answer is 114 cm².

Additional Information

Pythagorean Triplets

Common triplets like (8, 15, 17) and (9, 12, 15) help solve right-triangle geometry questions faster without full calculations.

Area of General Quadrilateral

If no angles are 90°, the area can be found using Heron's Formula for both triangles: Area = √[s(s−a)(s−b)(s−c)].

The correct answer is the seventh

Key Points

• India’s total geographical area:
• India's total geographical area is about 3.28 million square kilometers.
• This area accounts for approximately 2.4 per cent of the total geographical area of the world.
• India is the seventh-largest country in the world by land area.
• Despite its relatively small size compared to other large nations, India has a significant population, making it the second most populous country in the world.

Additional Information

• Other comparative statistics:
• Canada: The second-largest country by area, Canada accounts for about 6.1% of the world’s total land area.
• Brazil: The fifth-largest country by area, Brazil accounts for about 5.7% of the world’s total land area.
• Australia: The sixth-largest country by area, Australia accounts for about 5.3% of the world’s total land area.
• India: The seventh-largest country by area, India accounts for about 2.3% of the world’s total land area.
• Argentina: The eighth-largest country by area, Argentina accounts for about 1.7% of the world’s total land area.
• Kazakhstan: The ninth-largest country by area, Kazakhstan accounts for about 1.6% of the world’s total land area.
• Algeria: The tenth-largest country by area, Algeria accounts for about 1.5% of the world’s total land area.

Shortcut Trick

For a quadratic equation of the form x² ± kx + c = 0 to have equal roots, the middle coefficient k must be equal to ± 2√c.

In the given equation x² − kx + 169 = 0, we have c = 169.

⇒ k = ± 2 × √169

⇒ k = ± 2 × 13 = ± 26.

∴ The correct answer is ±26.

Alternate Method

Given:

The quadratic equation is x² − kx + 169 = 0.

Formula Used:

For a quadratic equation ax² + bx + c = 0, the roots are equal if the Discriminant (D) is equal to zero.

D = b² − 4ac = 0

Calculations:

Comparing x² − kx + 169 = 0 with ax² + bx + c = 0:

⇒ a = 1, b = −k, c = 169

Substituting these values into the discriminant formula:

⇒ (−k)² − 4 × 1 × 169 = 0

⇒ k² − 676 = 0

⇒ k² = 676

⇒ k = √676

⇒ k = ± 26

∴ The correct answer is ±26.

Additional Information

Nature of Roots

The nature of roots depends on the Discriminant (D): if D > 0, roots are real and unequal; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Perfect Square Condition

A quadratic expression is a perfect square if and only if its discriminant is zero (b² = 4ac).

Sum and Product of Roots

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

The correct answer is that It will discourage teen pregnancies

Key Points

• The primary benefits of raising the age of marriage for girls to 21 are related to improving women's health, education, and overall well-being.
• It will discourage teen pregnancies:
• This is one of the significant benefits.
• By delaying marriage, the law can reduce the likelihood of early pregnancies, which often carry health risks for both mothers and babies.
• It can also encourage girls to focus on education and career opportunities before starting a family.
• Early marriage is one of the most common reasons cited for girls leaving school.
• Supporters of the law believe that a greater age at marriage will make more time available to girls for completing their education, gaining skills, and potentially entering the workforce.
• This may lead to greater economic independence

Additional Information

• History Of Child Marriage
• Ancient Period:
• Child marriage was prevalent in ancient India during the Vedic period.
• Girls as young as 8-10 years were married off to older men.
• The main reason was to ensure the security of daughters and the continuity of lineage through sons.
• Medieval Period:
• The practice of child marriage continued and even spread during the medieval period.
• The age of marriage for girls decreased to 7-8 years.
• British Rule:
• Though British officials tried to curb child marriage in India, they faced resistance due to cultural and religious beliefs.
• The minimum age of marriage for girls was raised to 12 through the Child Marriage Restraint Act of 1929, but it was ineffective.
• Post-Independence:
• After independence, the government raised the legal age of marriage for girls to 18 through the Child Marriage Restriction Act of 1976.
• However, this failed to curb the practice successfully.
• Poverty, lack of education and cultural norms continue to fuel child marriage in India.
• Current Scenario:
• While the legal age of marriage is 18, child marriage continues in India, especially in rural and tribal areas.
• Girls below 18 years account for about 25% of married women in India, according to UNICEF.
• Lack of policy implementation and socio-economic factors are significant hurdles in eradicating child marriage.
• The need of the hour is the stricter implementation of laws against child marriage along with social reforms, better access to education and empowerment of women.
• NGOs and government schemes are working to curb this social evil.
• With continued efforts and awareness, child marriage can hopefully be eradicated from India over time.

The correct answer is electric dynamo

Key Points

• A dynamo is a device that converts mechanical energy into electrical energy
• Dynamos use electromagnetic induction to produce electric current.
• They work by using revolving wire coils and magnetic fields to convert mechanical revolutions into a pulsed direct electric current.
• Dynamos were the first electrical generators to power industries.
• They were the basis for many other electric-power conversion devices, including electric motors, alternating-current alternators, and rotary converters

Additional Information

• Electric motor​

• An electric motor converts electrical energy into mechanical energy.

• Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate force in the form of torque applied on the motor's shaft.

• Compass needle​

• A compass is a device that uses a small, magnetized needle that aligns itself with the Earth's magnetic field.

• The needle points towards the Magnetic North Pole, which is the point where the Earth's magnetic field lines converge in the Northern Hemisphere.

• Dry Cell

• A dry cell has the electrolyte immobilized as a paste, with only enough moisture in it to allow current to flow.

• Unlike a wet cell, a dry cell can operate in any orientation without spilling, as it contains no free liquid.

• This versatility makes it suitable for portable equipment.

• A dry cell consists of a metal container in which a low moisture electrolyte paste covers the graphite rod or a metal electrode.

Shortcut Trick

In a congruence statement like ΔXYZ ≅ ΔABC, the position of letters indicates corresponding parts.

Position 1 & 2: XY = AB

Position 2 & 3: YZ = BC

Position 1 & 3: XZ = AC

Since XZ and AC occupy the same relative positions (1st and 3rd), their measures must be equal.

∴ The correct answer is m(XZ) = m(AC).

Alternate Method

Given: ΔXYZ ≅ ΔABC

Formula Used: CPCT (Corresponding Parts of Congruent Triangles)

⇒ When two triangles are congruent, their corresponding sides and angles are equal.

⇒ From the congruence statement ΔXYZ ≅ ΔABC, we establish the following correspondence:

⇒ Vertex X corresponds to Vertex A

⇒ Vertex Y corresponds to Vertex B

⇒ Vertex Z corresponds to Vertex C

⇒ Therefore, the side XZ (joining 1st and 3rd vertices) must be equal to side AC (joining 1st and 3rd vertices).

∴ The correct answer is m(XZ) = m(AC).

According to the given information, we have the following diagram.

Town P is west of town Q.

Town P is south-west of town S.

Town S is north of town Q.

If town R is south-east of town Q and town M is east of town R.

Here, position of P is in the North-West direction with respect of point M.

Hence, the correct answer is "Option 2".

The correct answer is 4 cm

Key Points

• Calculate the focal length (f):
• Power (P) = 1/f (where f is in meters)
• Given
• P = -2.5 D
• f = 1/(-2.5) = -0.4 m = -40 cm​
• Use the lens formula:
• 1/f = 1/v - 1/u
• Where:
• f = focal length (-40 cm)
• v = image distance (what we want to find)
• u = object distance (-20 cm, negative as it's on the left side)
• 1/-40 = 1/v - 1/-20
• 1/-40 = 1/v + 1/20
• 1/v = 1/-40 - 1/20
• 1/v = (-1 - 2)/40
• 1/v = -3/40
• v = -40/3 cm
• Calculate magnification (M):
• M = -v/u
• M = -(-40/3) / (-20)
• M = (40/3) / (-20)
• M = -2/3
• Calculate image height (h'):
• M = h'/h
• Where:
• h' = image height (what we want to find)
• h = object height (6 cm)
• -2/3 = h'/6
• h' = (-2/3) * 6
• h' = -4 cm
• The height of the image is 4 cm.
• The negative sign indicates the image is inverted.

Additional Information

• Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
• Convex lens: ​A lens having two spherical surfaces, bulging outwards is called a double convex lens (or simply convex lens).
• It is thicker in the middle as compared to the edges.
• Convex lenses converge light rays and hence, convex lenses are also called converging lenses.
• The lens formula is given by:

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Where V = Distance of image from the optical center, U = Distance of object from the optical center.

The correct answer is 2022

Key Points

• Taking another step in the direction of making India one of the top air sports nations by 2030, the Union Ministry of Civil Aviation announced the country’s first 'National Air Sports Policy' in June 2022.
• The policy will cover air sports such as aerobatics, aeromodelling, model rocketry, amateur-built and experimental aircraft, ballooning, drones, gliding, and powered gliding, hang-gliding and powered hang-gliding, parachuting (including skydiving, Base jumping, and wingsuit flying), paragliding and paramotoring (including powered parachute trikes), powered aircraft and rotorcraft.
• The Air Sports Federation of India (ASFI) will be the apex governing body for this initiative.
• This federation will be chaired by Civil Aviation Ministry Secretary Rajiv Bansal.
• The ASFI is an autonomous body and will present India at the Fédération Aéronautique Internationale (FAI) and other global platforms related to air sports.​

Additional Information

• World Air Sports Federation.
• The World Air Sports Federation (FAI) is responsible for establishing rules and regulations for air sports and aeronautical records.
• The FAI also promotes safety, proficiency, and skill in aeronautics.
• The FAI awards awards to those who work on restoring old aircraft.
• Founded on 14 October 1905.
• Headquarters are located in Lausanne, Switzerland.
• President is David Monks.

Shortcut Trick

Petrol expense = 20% = ₹7,500.

Remaining income = 80%.

Household expenditure = 1/3 × 80% = 80/3 %.

Value = (7500 ÷ 20) × (80/3) = 375 × (80/3) = 125 × 80 = ₹10,000.

∴ The correct answer is ₹10,000.

Alternate Method

Given:

Petrol expenditure = 20% of Income = ₹7,500.

Household expenditure = 1/3 of (Income − Petrol expenditure).

Calculations:

⇒ Let Total Income be I.

⇒ 20% of I = 7,500

⇒ (20/100) × I = 7,500

⇒ I = 7,500 × 5 = ₹37,500

⇒ Remaining Income = 37,500 − 7,500 = ₹30,000

⇒ Household Expenditure = 1/3 × 30,000

⇒ Household Expenditure = ₹10,000

∴ The correct answer is ₹10,000.

Additional Information

Percentage Change

To find the original value when a percentage is known: Original = (Given Value ÷ Percentage) × 100.

Successive Deductions

When spending from the 'remaining' amount, always subtract the previous expenses from the total before calculating the next portion.

Ratio Method

Income components can be expressed as ratios. If petrol is 1 part out of 5, then 4 parts remain, and household is 1/3 of those 4 parts.

The correct answer is 90°

Key Points

• Fleming's Right Hand Rule can be applied only if the directions of the applied magnetic field, the motion of the conductor, and the induced current are mutually at 90° with respect to each other.
• Fleming right-hand thumb rule:
• When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction.
• Fleming's right-hand rule (for generators) shows the direction of induced current when a conductor attached to a circuit moves in a magnetic field.
• The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.
• The first finger is pointed in the direction of the magnetic field. (north to south)
• Then the second finger represents the direction of the induced or generated current within the conductor (from the terminal with lower electric potential to the terminal with higher electric potential, as in a voltage source)

Additional Information

• Fleming's right-hand rule is used to determine the direction of induced current in a conductor moving in a magnetic field.
• It is particularly useful in the context of generators and other devices where mechanical motion is converted into electrical energy.
• Conversely, Fleming's left-hand rule is used for electric motors where electrical energy is converted into mechanical motion.
• Both rules are fundamental principles in electromagnetism and are widely used in physics and engineering.

The correct answer is the Linear curve.

Key Points

• The current-voltage graph of ohmic devices is of the form linear curve.
• Ohm’s Law
• The electric current flowing through a conductor is directly proportional to the potential difference across its ends.
• It is given by the formula:
• V=IR
• The device which follows ohm's law for all voltages across it is called an ohmic device.
• The current-voltage graph of ohmic devices is a linear curve.

Additional Information

• Zig-Zag:
• This type of graph suggests a non-smooth, alternating pattern.
• While some materials, such as semiconductors or conductors under varying external conditions, might exhibit irregularities in their behaviour,
• It is more associated with irregular, fluctuating behaviours
• Parabolic:
• A parabolic graph suggests that the relationship between voltage and current is quadratic.
• This can occur in certain non-ohmic materials, where the resistance is not constant but changes with the applied voltage.
• For example, in materials like diodes or thermistors (at higher voltages), the current may increase more rapidly than the voltage, resulting in a parabolic relationship.
• This is often seen in semiconductor devices
• Exponential:
• An exponential relationship indicates that the current increases (or decreases) exponentially with voltage.
• This type of behaviour is typical in certain non-linear devices, like diodes or transistors.
• In these devices, small changes in voltage lead to large changes in current, especially when they are forward-biased.
• The voltage-current graph in such cases often has an exponential shape.

The correct answer is 100 cm

Key Points

• Concave Mirror:
• Imagine a spoon. The inside curved surface of the spoon is like a concave mirror. It curves inwards.
• Pole (P):
• The centre point of the mirror's surface.
• Center of Curvature (C):
• ​The centre of the sphere from which the mirror is a part.
• If you were to extend the concave mirror into a full sphere, C would be the sphere's centre.
• Radius of Curvature (R):
• ​The distance between the pole (P) and the centre of curvature (C).
• It's essentially the radius of that imaginary sphere.
• It states that the radius of curvature (R) of the concave mirror is 100 cm
• By definition, the radius of curvature is the distance between the pole and the center of curvature.
• Therefore, if the radius of curvature is 100 cm, the distance between the pole and the center of curvature is also 100 cm.

Additional Information

• Difference between Concave and Convex Mirror
• | Feature | Concave Mirror | Convex Mirror | | --- | --- | --- | | Type | Rounded or hollowed inwards | Rounded or curved outwards | | Other Name | Converging mirror | Fish Eye or Diverging mirror | | Mirror Coating | On the outer edge of the spherical surface | On the inner side of the spherical surface | | Center of Curvature | On the same side as the reflecting surface | On the opposite side of the reflecting surface | | Focus & Focal Length | In front of the mirror; the focal length is positive | Behind the mirror; the focal length is negative | | Image Formed | Real, inverted, and expanded | Virtual, straight, and diminished | | Image on Screen | Yes, as they are real | No, since they are virtual | | Uses | Reflective telescopes, grooming mirrors, torchlights, etc. | Cars as side or rearview mirrors |

Shortcut Trick

Let the Cost Price (CP) for X be 100 units.

X profit = 20% of 100 = 20 units. CP for Y = 120 units.

Y sells to Z at 12% loss ⇒ CP for Z = 120 × 0.88 = 105.6 units.

Z profit = 30% of 105.6 = 31.68 units.

Difference in profits (Z − X) = 31.68 − 20 = 11.68 units.

11.68 units = 87.60 ⇒ 1 unit = 7.5. CP for Y = 120 × 7.5 = 900.

∴ The correct answer is ₹900.

Alternate Method

Given → X profit = 20%, Y loss = 12%, Z profit = 30%, Profit difference (Z − X) = 87.60. Formulas → Profit = SP − CP | SP = CP × (100 ± Change%) ÷ 100.

⇒ Let X CP = 100x. X profit = 20x. ⇒ Y CP = 120x. Z CP = 120x × 0.88 = 105.6x. ⇒ Z profit = 30% of 105.6x = 31.68x. ⇒ Difference = 31.68x − 20x = 11.68x. ⇒ 11.68x = 87.60 ⇒ x = 87.60 ÷ 11.68 = 7.5. ⇒ Price Y bought (Y CP) = 120x = 120 × 7.5 = 900.

∴ The correct answer is ₹900.

Additional Information

Chain Sale Calculations

In a series of transactions, the Selling Price (SP) of the previous seller becomes the Cost Price (CP) for the next buyer.

Profit and Loss Multipliers

For a profit of p%, multiply CP by (1 + p/100). For a loss of l%, multiply CP by (1 − l/100).