Arunchal Pradesh

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229 Arunchal Pradesh MCQ Questions in english हिन्दी

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In which sport would you use a pommel horse?

Who is the only boxer to retire undefeated as a professional?

Which sport is played at Wimbledon?

What is the length of a standard Olympic swimming pool?

Which country won the most medals in the 2024 Paris Olympics?

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In which sport is the term "checkmate" used?

Who is known as the "Lightning Bolt" in athletics

Which sport is associated with the Ryder Cup

In which year were the first modern Olympic Games held?

Which sport uses a shuttlecock?

What is the maximum score in a single frame of ten-pin bowling?

Which country has won the most Cricket World Cups?

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In which sport would you perform a "slam dunk"?

Who holds the record for the most Olympic gold medals?

Which country hosts the Tour de France?

In tennis, what is the term for a score of zero?

Which sport is known as the "king of sports"?

How many players are there in a standard soccer team on the field?

In which sport is the term "hole-in-one" used?

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If $ \frac{1}{x} + \frac{1}{y} = 1 $ and $ xy = 12 $, what is the value of $ x + y $?

Given $ \frac{1}{x} + \frac{1}{y} = 1 $, we have $ \frac{x + y}{xy} = 1 $. Since $ xy = 12 $, it follows that $ x + y = 12 $. Check with roots of $ t^2 - (x+y)t + xy = 0 $: $ t^2 - 12t + 12 = 0 $. Discriminant = $ 144 - 48 = 96 $, roots are $ t = \frac{12 \pm \sqrt{96}}{2} $. However, directly, $ x + y = 12 $, but testing pairs (e.g., 3, 4) gives $ x + y = 7 $,

What is the value of $ x $ if $ 2x + 3 = 7x - 2 $?

Solve $ 2x + 3 = 7x - 2 $. Rearrange: $ 3 + 2 = 7x - 2x $, so $ 5 = 5x $, and $ x = 1 $.

If $ 2x + 3y = 12 $ and $ 3x - 2y = 5 $, what is the value of $ x + y $?

Add the equations: $ (2x + 3y) + (3x - 2y) = 12 + 5 $, giving $ 5x + y = 17 $. Subtract: $ (2x + 3y) - (3x - 2y) = 12 - 5 $, giving $ -x + 5y = 7 $. Solve the system: multiply the first by 5 ($ 25x + 5y = 85 $) and subtract the second: $ (25x + 5y) - (-x + 5y) = 85 - 7 $, so $ 26x = 78 $, and $ x = 3 $. Substitute into $ 5x + y = 17 $: $ 5(3) + y = 17 $, so $ y = 2 $. Thus, $ x + y = 3 + 2 = 4 $.

The difference between two numbers is 30, and the smaller number is 13 more than half of the greater number. What is the greater number?

Let the greater number be $ x $, and the smaller number be $ y $. Given $ x - y = 30 $ and $ y = \frac{x}{2} + 13 $. Substitute $ y $ in the first equation: $ x - \left( \frac{x}{2} + 13 \right) = 30 $. Solving, $ \frac{x}{2} - 13 = 30 $, so $ \frac{x}{2} = 43 $, and $ x = 86 $.

If $ x + y + z = 0 $, then what is the value of $ \frac{x^2}{yz} + \frac{y^2}{xz} + \frac{z^2}{xy} $?

Given $ x + y + z = 0 $, the expression is $ \frac{x^2}{yz} + \frac{y^2}{xz} + \frac{z^2}{xy} $. This simplifies to $ \frac{x^3 + y^3 + z^3}{xyz} $. Since $ x + y + z = 0 $, we use the identity $ x^3 + y^3 + z^3 = 3xyz $. Thus, $ \frac{3xyz}{xyz} = 3 $.

A shopkeeper mixes two varieties of pulses worth Rs. 50/kg and Rs. 75/kg to get a mixture worth Rs. 65/kg. In what ratio should they be mixed?

Using the alligation rule: $ (75 - 65) : (65 - 50) = 10 : 15 = 2 : 3 $. Thus, the ratio of cheaper (50/kg) to dearer (75/kg) is 3:2, or dearer to cheaper is 2:1

If the cost of apples increases by 20% and then decreases by 20%, what is the net percentage change?

Let the original price be 100. After a 20% increase, price = $ 100 \times 1.2 = 120 $. After a 20% decrease, price = $ 120 \times 0.8 = 96 $. Net change = $ \frac{96 - 100}{100} \times 100 = -4\% $.

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A car travels 275 km at 50 km/h and 315 km at 70 km/h. What is the average speed for the entire journey

Total distance = 275 + 315 = 590 km. Time for the first part = $ \frac{275}{50} = 5.5 $ hours; second part = $ \frac{315}{70} \approx 4.5 $ hours. Total time = $ 5.5 + 4.5 = 10 $ hours. Average speed = $ \frac{590}{10} = 59 $ km/h (approximately 58.33 km/h for precision).

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