Explanation

√(x - 1)^2 + √(3 - x)^2

Since 1 < x < 2, we can simplify the expressions inside the square roots:

(x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 1

(3 - x)^2 = (3 - x)(3 - x) = 9 - 6x + x^2

Now, add the two expressions:

x^2 - 2x + 1 + 9 - 6x + x^2

= 2x^2 - 8x + 10

Take the square root of the result:

√(2x^2 - 8x + 10)

Since 1 < x < 2, we can plug in x = 1 and x = 2 to find the maximum and minimum values:

At x = 1: √(2 - 8 + 10) = √4 = 2

At x = 2: √(8 - 16 + 10) = √2

So, the minimum value of the expression is 2, which occurs when x = 1.

Therefore, the correct answer is: 2

Explanation

Hour hand moves 225° (7.5 hours).

Minute hand moves 180° (30 minutes).

Angle between them: 45° (difference) + 30° (hour hand's extra move) = 75°.

OR

= 8h x 30 - 30 x 11/2

= 240 - 165

= 75°

Explanation

The player's average runs in 10 innings is 32, so the total runs scored is: 10 x 32 = 320 runs.

To increase the average by 4, the new average will be: 32 + 4 = 36 runs.

Since the player has played 11 innings now (10 previous + 1 next), the total runs required to achieve the new average is: 11 x 36 = 396 runs.

To find out how many runs the player needs to score in the next innings, subtract the runs already scored from the total runs required: 396 - 320 = 76 runs.

So, the correct answer is: 76

Explanation

60 women spin 48 kg of cotton in 8 hours.

First, find the total hours worked by 60 women: 60 women x 8 hours = 480 hours.

Now, find the total cotton spun per hour: 48 kg ÷ 480 hours = 0.1 kg/hour.

Since 30 women work 12 hours daily, find their total hours: 30 women x 12 hours = 360 hours.

Finally, find the total cotton spun by 30 women: 360 hours x 0.1 kg/hour = 36 kg.

So, the correct answer is: 36 kg

Explanation

The sum of money doubles in 3 years, which means it becomes 2 times itself.

Since it's compounded annually at the same rate, the interest rate is consistent.

To become 4 times itself, it needs to double twice more (2 × 2 = 4).

Since it doubles every 3 years, it will double twice more in 2 × 3 = 6 years.

So, the correct answer is: 6 years

Explanation

The average of 50 numbers is 30, so the sum of all 50 numbers is 50 x 30 = 1500.

If we discard 35 and 40, we subtract these from the total sum: 1500 - 35 - 40 = 1425.

Now, we have 48 numbers left (50 - 2 = 48).

To find the new average, we divide the remaining sum by the number of remaining numbers: 1425 ÷ 48 ≈ 29.68.

So, the correct answer is: 29.68

Explanation

It was a mistake that I didn't look through the contract before signing it.

یہ ایک غلطی تھی کہ میں نے معاہدے پر دستخط کرنے سے پہلے اسے نہیں دیکھا۔

"Look through" means to carefully examine or review something.

It would have been the appropriate action to avoid mistakes in signing the contract.

Explanation

The correct phrase is "pride in."

"In" is the appropriate preposition used to indicate pride regarding something, like qualifications.

Explanation

Chivalrous means بہادر

Gallant means بہادر

Explanation

Kith means دوست

Stranger means اجنبی