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The logic followed here is:

Option 1) HN - TV

The letters are shifted by +12 and +8 respectively.

Option 2) YH - CE

Option 3) CL - GI

Option 4) AJ - EG

Thus, HN - TV is the odd one out.

Hence, the correct answer is "Option 1".

Shortcut Trick

The final Selling Price (SP) after successive discounts can be found directly using multiplying factors.

A 25% discount means the item is sold at 75% or 3/4 of its price.

A 15% discount means the item is sold at 85% or 17/20 of its price.

Final SP = 960 × (3/4) × (3/4) × (17/20)

Final SP = 960 × (153/320) = 3 × 153 = 459

∴ The correct answer is ₹459.

Alternate Method

Given:

Marked Price (MP) of the iPad = ₹960

Successive discounts: D₁ = 25%, D₂ = 25%, D₃ = 15%

Formula Used:

Final Selling Price (SP) = MP × (1 − D₁/100) × (1 − D₂/100) × (1 − D₃/100)

  Successive Discount Flow  -25%  -25%  -15%  ₹960 MP  ₹720 Price 1  ₹540 Price 2  ₹459 Final SP

Calculations:

⇒ SP = 960 × (1 − 25/100) × (1 − 25/100) × (1 − 15/100)

⇒ SP = 960 × (75/100) × (75/100) × (85/100)

⇒ SP = 960 × (3/4) × (3/4) × (17/20)

⇒ SP = 960 × (153/320)

⇒ SP = 3 × 153 = 459

∴ The correct answer is ₹459.

Additional Information

Effective Equivalent Discount

For two successive discounts of a% and b%, the single equivalent discount is calculated using the formula: Equivalent Discount = (a + b − ab/100)%.

Marked Price vs Cost Price

Discounts are always calculated on the Marked Price (MP) of the article. Meanwhile, Profit or Loss percentages are calculated on the Cost Price (CP).

Successive Percentage Change

Applying successive discounts of x%, y%, and z% is the same as finding the successive decrease of a value, meaning the order of discounts does not change the final selling price.

Given:

Seven boxes (H, I, J, K, Q, R, S) are kept in a vertical stack from 1 (bottom) to 7 (top).

1) H is kept second from the bottom.

2) Only three boxes are kept between H and S.

3) J is kept at one of the positions below H.

4) Only Q is kept between S and R.

5) K is kept at one of the positions above S.

S is on Floor 6. The only floor above it is Floor 7. K = Floor 7.

6) Placing the remaining box.

The only floor left is Floor 3, and the only box left is I. I = Floor 3.

Final Arrangement:

I is on Floor 3 and J is on Floor 1. The only box between them is H (Floor 2).

Hence, the correct answer is "Option 2".

The logic followed here is:

For TWSP to MPLI

For LOKH to EHDA

Applying the same logic to PSOL:

Thus, PSOL is related to ILHE.

Hence, the correct answer is "ILHE".

Shortcut Trick

Solve nested square roots systematically from the inside out:

√4 = 2 → 7 + 2 = 9

√9 = 3 → 97 + 3 = 100

√100 = 10 → 15 + 10 = 25

√25 = 5 → 31 + 5 = 36 → √36 = 6

∴ The correct answer is 6.

Alternate Method

Given:

√(31 + √(15 + √(97 + √(7 + √4))))

Calculation:

⇒ √(31 + √(15 + √(97 + √(7 + 2))))

⇒ √(31 + √(15 + √(97 + √9)))

⇒ √(31 + √(15 + √(97 + 3)))

⇒ √(31 + √(15 + √100))

⇒ √(31 + √(15 + 10))

⇒ √(31 + √25)

⇒ √(31 + 5)

⇒ √36

⇒ 6

∴ The correct answer is 6.

Additional Information

BODMAS Rule

Always follow the order of Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction.

Nested Radicals

When evaluating nested square roots, begin from the innermost radical and work outwards step by step.

Perfect Squares

Knowing perfect squares up to 30 helps in quickly solving square root simplification questions without writing down intermediate steps.

The correct answer is Wind Energy.

Key Points

• According to Energy Statistics India 2025, India's total estimated renewable power potential is approximately 2,109.66 GW.
• Among all renewable energy sources, Wind Energy has the highest estimated potential of about 1,163.86 GW, contributing nearly 55% of the total estimated renewable power potential.
• Solar Energy has an estimated potential of about 748.99 GW, accounting for nearly 36% of the total renewable power potential.
• Hence, the correct answer is Option 2 – Wind Energy.

Additional Information

• Estimated Renewable Power Potential in India:
• Wind Energy: ~1,163.86 GW (Largest share)
• Solar Energy: ~748.99 GW
• Large Hydro Power: ~133.41 GW
• Biomass Power: ~28.45 GW
• Small Hydro Power: ~21.13 GW
• Cogeneration (Bagasse): ~13.82 GW
• Rajasthan has the highest estimated renewable energy potential among Indian states, followed by Maharashtra, Gujarat, and Karnataka.

Important Points

• Largest estimated renewable power potential: Wind Energy (about 55%).
• Second-largest estimated potential: Solar Energy (about 36%).

Given:

Let us first decode the given symbols and then draw a family tree.

On checking: S + G & J # K × T

1. S + G - 'S + G' means 'S is the son of G'.

2. G & J - 'G & J' means 'G is the father of J'.

3. J # K- 'J # K' means 'J is the sister of K'.

4. K × T- 'K × T' means 'K is the wife of T'.

G S J K T

​Therefore, S is the brother of K, who is the wife of T → S is the Wife's brother of T.

Hence, the correct answer is "Option 4".

The logic follows here is:

Logic: (First Number × 2) + 4 = Second Number;

(First Number × 4) + 4 = Third Number

For (5, 14, 24):

(5 × 2) + 4 = 14

(5 × 4) + 4 = 24

For (3, 10, 16):

(3 × 2) + 4 = 10

(3 × 4) + 4 = 16

Option 1: (7, 18, 32)

(7 × 2) + 4 = 18

(7 × 4) + 4 = 32

Thus, (7, 18, 32) is related in the same way as the given sets.

Hence, the correct answer is "Option 1".

Shortcut Trick

Let the Cost Price (CP) be 100.

Marked Price (MP) = 100 + 90% = 190

Selling Price (SP) for 71% profit = 100 + 71% = 171

Discount = MP − SP = 190 − 171 = 19

Discount % = (Discount ÷ MP) × 100 = (19 ÷ 190) × 100 = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Mark-up Percentage = 90% above CP

Profit Percentage = 71%

Formula Used:

Ratio of CP to MP = (100 − Discount%) ÷ (100 + Profit%)

            CP = 100  SP = 171  MP = 190   +90% Markup   +71% Profit   −d% Discount

Calculations:

⇒ Let CP be 100

⇒ MP = 100 + 90 = 190

⇒ Using the formula: CP ÷ MP = (100 − D) ÷ (100 + P)

⇒ 100 ÷ 190 = (100 − D) ÷ (100 + 71)

⇒ 10 ÷ 19 = (100 − D) ÷ 171

⇒ 100 − D = (171 × 10) ÷ 19

⇒ 100 − D = 9 × 10

⇒ 100 − D = 90

⇒ D = 100 − 90 = 10%

∴ The correct answer is 10%.

Additional Information

Direct Relation Between CP and MP

The most efficient way to link Cost Price and Marked Price is using the ratio formula: CP/MP = (100 − Discount%) / (100 + Profit%).

Successive Discounts

When two consecutive discounts x% and y% are given on MP, the single equivalent discount = [x + y − (xy ÷ 100)]%.

Mark-up Percentage

It indicates how much more the Marked Price is compared to the Cost Price. Formula: Mark-up % = [(MP − CP) ÷ CP] × 100.

Shortcut Trick

Use the Assumed Mean Deviation method to solve it mentally.

Let the Assumed Mean be 10.

Sum of deviations = (+2) + (−7) + (+8) + (+7) + (−6) + (−1) + (+7) + (+9) + (+10) + (+5) + (−2) + (+7) + (−8) + (−7) + (+6) + (+1) + (−7) + (−9) + (−10) + (−5) = 0

Since the net deviation is 0, the Actual Mean is exactly equal to the Assumed Mean.

∴ The correct answer is 10.

Alternate Method

Given:

Data = 12, 3, 18, 17, 4, 9, 17, 19, 20, 15, 8, 17, 2, 3, 16, 11, 3, 1, 0, 5

Number of observations (n) = 20

Formula Used:

Mean = Sum of all observations ÷ Total number of observations

Total Sum of 20 observations = 200 Total Count (n) = 20 Mean = 200 ÷ 20 = 10

Calculations:

⇒ Sum = 12 + 3 + 18 + 17 + 4 + 9 + 17 + 19 + 20 + 15 + 8 + 17 + 2 + 3 + 16 + 11 + 3 + 1 + 0 + 5

⇒ Sum = 200

⇒ Mean = 200 ÷ 20

⇒ Mean = 10

∴ The correct answer is 10.

Additional Information

Assumed Mean Method

A shortcut to find the mean using an arbitrary value: Mean = A + (Σd ÷ n), where A is the assumed mean and d is the deviation of each value from A.

Median

The middle value when a data set is ordered from least to greatest. If the number of values is even, the median is the average of the two middle values.

Mode

The number that occurs most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

Range

The difference between the highest and lowest values in a set of numbers. Range = Maximum Value − Minimum Value.