A shopkeeper sells an item for Rs. 800 after giving a discount of 20% on its marked price. What is the marked price of the item?
A. Rs. 960
B. Rs. 1000
C. Rs. 900
D. Rs. 1020
Correct Answer: B Method 1 (Algebra): Let MP = x. 20% discount means SP = 80% of MP. So 0.80x = 800. x = 800/0.80 = Rs. 1000.
Method 2 (Unitary - Shortcut): If SP after 20% discount is Rs. 800, then 80% of MP = 800. So 1% of MP = 800/80 = 10. Therefore 100% (MP) = 10 x 100 = Rs. 1000.
Super Shortcut (1-Step): MP = SP x 100/(100 - discount%). MP = 800 x 100/80 = 800 x 5/4 = Rs. 1000. Just divide SP by (100 - discount%) and multiply by 100.
Verification: 20% of 1000 = 200. SP = 1000 - 200 = 800 OK
Common Mistake: Students often subtract 20% of 800 (160) and add it back, getting 960. Wrong! The discount is calculated on MP, not on SP. Always work with the formula: SP = MP x (100 - d%)/100.
Q2. Science
Which of the following is an example of a non-renewable resource?
A. Solar energy
B. Wind energy
C. Natural gas
D. Hydropower
Correct Answer: C Step 1: Understand the classification. Renewable resources replenish naturally within a human timescale (solar, wind, water). Non-renewable resources exist in fixed amounts and take millions of years to form (fossil fuels, minerals).
Step 2: Evaluate each option:
- Solar energy: Sun is practically infinite -> Renewable
- Wind energy: Caused by atmospheric pressure differences -> Renewable
- Natural gas: Fossil fuel formed from decomposed organic matter over millions of years -> Non-renewable
- Hydropower: Water cycle continuously replenishes it -> Renewable
Shortcut Trick: Remember the acronym 'FANC' for non-renewable: Fossil fuels, Atomic (nuclear), Natural gas, Coal. Anything ending in 'power' (solar, wind, hydro) is almost always renewable.
Common Mistake: Students think natural gas is 'cleaner' and therefore renewable. Clean != renewable. Natural gas is a fossil fuel and takes geological ages to form - it is definitely non-renewable.
Q3. Reasoning
Find the next number in the series: 2, 5, 8, 11, 14?
A. 15
B. 17
C. 18
D. 20
Correct Answer: B The series is formed by adding 3 to the previous term, hence the next number in the series would be: 14 + 3 = 17.
Q4. Mathematics
If the sum of the first 'n' odd natural numbers is 225, then what is the value of 'n'?
A. 10
B. 12
C. 15
D. 20
Correct Answer: C Step 1: Recall the formula - sum of the first n odd natural numbers = n^2. For example: 1 = 1^2, 1+3 = 4 = 2^2, 1+3+5 = 9 = 3^2, etc.
Step 2: Given sum = 225. So n^2 = 225.
Step 3: Take the square root: n = sqrt225 = 15.
Shortcut Trick: Learn the squares from 1 to 30. 225 is 15 squared - instantly tells you n = 15. No calculation needed if you know that 15^2 = 225 and 16^2 = 256.
Alternative Method: The nth odd number is (2n-1). Sum of first n odd numbers = n^2 (this is a fixed result - memorize it!).
Common Mistake: Some students use the formula for sum of n natural numbers (n(n+1)/2) instead of the odd number formula, getting the wrong answer. Always check: 'odd natural numbers' -> n^2; 'natural numbers' -> n(n+1)/2.
Q5. Reasoning
Complete the series: 2, 5, 10, 17, 26, ?
A. 37
B. 35
C. 39
D. 38
Correct Answer: A Method 1 (Difference Method):
2 -> 5 = +3
5 -> 10 = +5
10 -> 17 = +7
17 -> 26 = +9
26 -> ? = +11 (next odd number)
? = 26 + 11 = 37
The differences are consecutive odd numbers: 3, 5, 7, 9, 11.
Method 2 (Pattern Recognition - Shortcut):
The pattern follows n^2 + 1:
1^2 + 1 = 2
2^2 + 1 = 5
3^2 + 1 = 10
4^2 + 1 = 17
5^2 + 1 = 26
6^2 + 1 = 36 + 1 = 37
Super Shortcut: Once you identify the pattern as n^2 + 1, the next term is always (n+1)^2 + 1. Here n=5, so term 6 = 6^2 + 1 = 37. Takes 3 seconds!
Common Mistake: Students sometimes see the pattern but make calculation errors: 6^2 = 36, then forget to add 1, getting 36. Or they add 10 (instead of 11) to 26, getting 36. Always check your differences carefully.
Q6. General Knowledge
Who was the first Indian woman to win a medal at the Olympics?
A. P.T. Usha
B. Saina Nehwal
C. Mary Kom
D. Karnam Malleswari
Correct Answer: D Step 1: Karnam Malleswari won a bronze medal in weightlifting (69 kg category) at the 2000 Sydney Olympics.
Step 2: This made her the first Indian woman to win an Olympic medal.
Shortcut Trick: 'Malleswari' contains 'Mall' - think 'Mall-e-s-wari, Medal-e-First-wari'. Connect: Weightlifter -> heavy weights -> first woman to carry India's medal hopes. Also remember 2000 Sydney - the millennium Olympics.
Timeline for Indian Women at Olympics:
- 2000: Karnam Malleswari (Weightlifting) - FIRST ever
- 2012: Saina Nehwal (Badminton bronze)
- 2012: Mary Kom (Boxing bronze)
- 2016: P.V. Sindhu (Badminton silver)
- 2020: Mirabai Chanu (Weightlifting silver)
Common Mistake: Many confuse P.T. Usha ('Payyoli Express') as an Olympic medalist. She came 4th in 1984 by 1/100th of a second - famously missed the bronze!
Q7. Mathematics
What is the perimeter of a rectangle with a length of 6 cm and a width of 4 cm?
A. 16 cm
B. 18 cm
C. 20 cm
D. 22 cm
Correct Answer: C The perimeter of a rectangle is given by the formula: P = 2(length + width), P = 2(6 + 4), P = 2 * 10, P = 20 cm.
Q8. Science
What is the SI unit of electric current?
A. Volt
B. Ohm
C. Ampere
D. Watt
Correct Answer: C Step 1: The SI unit of electric current is the Ampere (symbol: A).
Step 2: 1 Ampere = flow of 1 Coulomb of charge per second through a conductor.
Shortcut Trick: Remember the SI units with the mnemonic 'VOW CA' - Volt (potential), Ohm (resistance), Watt (power) - and then Current = Ampere. Or simpler: 'Current is measured in Amps' -> 'A for Ampere, A for Amps'.
Complete SI Unit Table for Electricity:
- Current: Ampere (A)
- Potential Difference: Volt (V)
- Resistance: Ohm ()
- Power: Watt (W)
- Charge: Coulomb (C)
- Conductance: Siemens (S)
Common Mistake: 'Current is measured in Amperes' but many confuse it with Volts. Remember: Current = flow of electrons (Amps). Voltage = push/pull that causes flow (Volts). Think of a water pipe: current = water flow (Amps), voltage = water pressure (Volts).
Q9. General Knowledge
Which river is the longest in India?
A. Ganga
B. Brahmaputra
C. Yamuna
D. Godavari
Correct Answer: A The Ganga is the longest river in India, stretching approximately 2,525 kilometers from its source in the Himalayas to its delta in the Bay of Bengal.
Q10. General Knowledge
The 'Thomas Cup' is associated with which sport?
A. Badminton
B. Tennis
C. Table Tennis
D. Golf
Correct Answer: A Step 1: The Thomas Cup is the World Men's Team Badminton Championship, first held in 1949.
Step 2: It is named after Sir George Thomas, a former President of the International Badminton Federation.
Shortcut Trick: Remember the sports trophies with this association trick:
- Thomas Cup -> Badminton (Men's) -> Think 'Tom' plays badminton
- Uber Cup -> Badminton (Women's)
- Davis Cup -> Tennis
- Swaythling Cup -> Table Tennis (World Team)
- Ryder Cup -> Golf
More Badminton Trophies:
- Thomas Cup: Men's international team
- Uber Cup: Women's international team
- Sudirman Cup: Mixed team world championship
Common Mistake: 'Thomas' sounds like a tennis name (Wimbledon has a 'Gentlemen's' trophy), but Thomas Cup is definitely badminton. Similarly, Davis Cup is tennis, not badminton.
Q11. General Knowledge
Who is the author of the book 'India That Is Bharat'?
A. Jawaharlal Nehru
B. Abul Kalam Azad
C. Aruna Roy
D. J Sai Deepak
Correct Answer: D J Sai Deepak is the author of the book 'India That Is Bharat'.
Q12. Science
What is the process called when an organism's genetic information is passed from one generation to the next?
A. Mutation
B. Genetic Drift
C. Hereditary
D. Evolution
Correct Answer: C Hereditary refers to the passing of traits or genetic information from parents to their offspring through the transmission of genetic information.
Q13. Mathematics
If a = 2, b = 3, and c = 4, what is the value of a^2 + b^2 + c^2?
A. 25
B. 27
C. 29
D. 35
Correct Answer: C Substituting the given values: a^2 + b^2 + c^2 = 2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29.
Q14. Reasoning
Pointing to a photograph, a man said, "I have no brother or sister, but that man's father is my father's son." Whose photograph was it?
A. His own son
B. His father
C. His uncle
D. His nephew
Correct Answer: A Step 1: The man says 'I have no brother or sister' -> He is an only child.
Step 2: 'my father's son' - Since he has no siblings, 'my father's son' can only be HIMSELF.
Step 3: So the statement 'that man's father is my father's son' becomes: 'that man's father is ME'.
Step 4: Therefore, the man in the photograph is the son of the speaker. The photograph is of his son.
Shortcut Trick - Family Tree Method:
Draw a simple tree:
Speaker (no siblings) <- father
Speaker (only child) = 'my father's son'
That man's father = Speaker
-> That man = Speaker's son OK
Alternative Approach - Substitute Yourself:
Replace 'my father's son' with 'me' (since no siblings). The sentence becomes: 'that man's father is me.' If I am someone's father, that someone must be my child. Answer: his son.
Common Mistake: Many overcomplicate this by introducing cousins or uncles. The key phrase 'no brother or sister' eliminates all possibilities except the speaker himself. Always simplify 'my father's son' to 'me' when the person has no siblings.
Q15. General Knowledge
Who was the founder of the Maurya Empire?
A. Bindusara
B. Ashoka
C. Chandragupta Maurya
D. Samudragupta
Correct Answer: C Step 1: The Maurya Empire was founded by Chandragupta Maurya around 322 BCE after he overthrew the Nanda dynasty with the guidance of his mentor Chanakya (also known as Kautilya or Vishnugupta).
Shortcut Trick: Remember the chronological order: 'Chandra -> Bindu -> Ashoka' (Grandfather -> Son -> Grandson). Chandragupta = founder; Bindusara = his son (expanded empire); Ashoka = grandson (greatest Maurya ruler).
Key Fact: Chanakya authored the Arthashastra and was instrumental in Chandragupta's rise to power. The Maurya Empire was the largest empire in ancient India.
Common Mistake: Students confuse Chandragupta Maurya (founder of Maurya) with Chandragupta I (founder of Gupta dynasty). Remember: Maurya = Chandragupta Maurya (322 BCE); Gupta = Chandragupta I (320 CE) - nearly 650 years apart!