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A person has a set of 5 keys, and only one of them opens a certain door. If the person tries the keys one by one, what is the probability that the person will open the door on the third attempt?
A. 1/5
B. 1/3
C. 2/5
D. 3/5
Correct Answer: A The probability of opening the door on the third attempt is the probability that the first two keys do not work and the third key works. Since there is only one correct key, the probability of not opening the door with the first key is 4/5, and the probability of not opening the door with the second key is 3/4 (given that the first key did not work). The probability of opening the door with the third key is 1/3 (given that the first two keys did not work). So, the probability of opening the door on the third attempt is (4/5) * (3/4) * (1/3) = 1/5.
Q2. [+2, -0.25]Reasoning
A bat and a ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?
A. $0.05
B. $0.10
C. $0.15
D. $0.20
Correct Answer: A Let's say the ball costs x cents. Since the bat costs $1.00 more than the ball, the bat costs x + $1.00. The total cost of the bat and the ball is $1.10, so we can set up the equation: x + (x + $1.00) = $1.10. Simplifying the equation, we get 2x + $1.00 = $1.10. Subtracting $1.00 from both sides, we get 2x = $0.10. Dividing both sides by 2, we get x = $0.05.
Q3. [+2, -0.25]Reasoning
If a car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h, what is the average speed of the car for the entire trip?
A. 45 km/h
B. 48 km/h
C. 50 km/h
D. 55 km/h
Correct Answer: B The average speed is calculated using the formula total distance / total time. Let the distance between city A and city B be d. The time taken to travel from A to B is d / 60, and the time taken to travel from B to A is d / 40. The total time is d / 60 + d / 40, which simplifies to (2d + 3d) / 120 = 5d / 120 = d / 24. The average speed is 2d / (d / 24) = 48 km/h.
Q4. [+2, -0.25]Science
What is the scientific term for the 'study of the structure, behavior, and properties of matter'?
A. Biology
B. Chemistry
C. Physics
D. Geology
Correct Answer: B Chemistry is the scientific study of the structure, behavior, and properties of matter, including the formation and reactions of chemical compounds.
Q5. [+2, -0.25]Mathematics
What is the value of x in the equation 2x - 5 = 11?
A. 6
B. 7
C. 8
D. 9
Correct Answer: C Add 5 to both sides of the equation to get 2x = 16, then divide both sides by 2 to get x = 8.
Q6. [+2, -0.25]Science
What is the process by which plants release water vapor into the air?
A. Respiration
B. Photosynthesis
C. Transpiration
D. Evaporation
Correct Answer: C Transpiration is the process by which plants release water vapor into the air through their leaves.
Q7. [+2, -0.25]Mathematics
What is the formula for the area of a circle?
A. A = 2πr
B. A = πr^2
C. A = 1/2 πr^2
D. A = 4πr
Correct Answer: B The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.
Q8. [+2, -0.25]Science
What is the process by which plants convert sunlight into energy?
A. Respiration
B. Photosynthesis
C. Decomposition
D. Fermentation
Correct Answer: B Photosynthesis is the process by which plants, algae, and some bacteria convert sunlight, carbon dioxide, and water into glucose and oxygen.
Q9. [+2, -0.25]Mathematics
What is the value of x in the equation 2x - 5 = 11?
A. 7
B. 8
C. 9
D. 10
Correct Answer: B To find the value of x, add 5 to both sides of the equation: 2x = 11 + 5, 2x = 16, x = 16/2, x = 8.
Q10. [+2, -0.25]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).
Q11. [+2, -0.25]General Knowledge
Who was the first President of the United States?
A. George Washington
B. Thomas Jefferson
C. Abraham Lincoln
D. Franklin D. Roosevelt
Correct Answer: A George Washington was the first President of the United States, serving from 1789 to 1797.
Q12. [+2, -0.25]Science
What is the process by which an organism's genetic information is passed from one generation to the next?
A. Mutation
B. Genetic Drift
C. Hereditary
D. Natural Selection
Correct Answer: C Hereditary is the process by which an organism's genetic information is passed from one generation to the next.
Q13. [+2, -0.25]Mathematics
What is the area of a triangle with a base of 5 cm and a height of 6 cm?
A. 12 cm^2
B. 13 cm^2
C. 15 cm^2
D. 18 cm^2
Correct Answer: C The area of a triangle is calculated as (base * height) / 2. So, area = (5 * 6) / 2 = 30 / 2 = 15 cm^2.
Q14. [+2, -0.25]Science
What is the largest mammal on Earth?
A. African Elephant
B. Blue Whale
C. Hippopotamus
D. Giraffe
Correct Answer: B The blue whale is the largest mammal on Earth, with some individuals reaching lengths of up to 33 meters and weighing up to 180 metric tons.
Q15. [+2, -0.25]General Knowledge
Which article of the Indian Constitution grants the 'Right to Equality'?
A. Article 19
B. Article 14
C. Article 21
D. Article 32
Correct Answer: B Step 1: The Right to Equality is covered under Articles 14 to 18 of the Indian Constitution.
Step 2: Article 14 specifically states: 'The State shall not deny to any person equality before the law or the equal protection of the laws within the territory of India.'
Shortcut Trick: Remember the Fundamental Rights with the mnemonic '14-18 Equality, 19-22 Freedom, 23-24 Against Exploitation, 25-28 Religious Freedom, 29-30 Cultural, 32 Constitutional Remedies'. Article 14 = starting point of equality - think '14 = for Equality'.
Detailed Breakdown of Right to Equality:
- Article 14: Equality before law
- Article 15: Prohibition of discrimination
- Article 16: Equality of opportunity in public employment
- Article 17: Abolition of untouchability
- Article 18: Abolition of titles
Common Mistake: Articles 19, 21, and 32 are very famous but belong to different rights. Article 19 = Right to Freedom (speech, expression), Article 21 = Right to Life, Article 32 = Right to Constitutional Remedies (heart and soul of the Constitution per Dr. Ambedkar).