In base-4, 'XYZ' = 4^2*X + 4^1*Y + 4^0*Z = 27. The only valid combination is X=3, Y=3, Z=3.

30% of 10 liters = 0.3 * 10 = 3 liters of salt.

Since 1000 can be expressed as 10^3, we have 10^x = 10^3, thus x = 3.

Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.

The percentage who like only tea is 25% - 10% = 15%.

Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.

The number of students who like only Mathematics is 40 - 10 = 30.

Dividing both sides by 4 gives x ≡ 2 (mod 3), so the smallest non-negative solution is 2.

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

Total salt = (0.2*5) + (0.3*15) = 1 + 4.5 = 5.5 liters. Total volume = 5 + 15 = 20 liters. Concentration = (5.5/20)*100 = 27.5%.

The number of arrangements of 6 different colored balls is 6! = 720.

The percentage of students who like only writing is 40% - 10% = 30%.

The percentage playing only cricket is 60% - 10% = 50%, and only football is 40% - 10% = 30%. Thus, total playing only one sport is 50% + 30% = 80%.

To solve 7x ≡ 3 (mod 5), we first reduce 7 mod 5 to get 2x ≡ 3 (mod 5). The solution is x ≡ 4 (mod 5), which corresponds to 2.

Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

Dividing both sides by 4 gives 2x ≡ 1 (mod 3). The solution is x = 2.

Total balls = 3 + 2 = 5. Probability of selecting a red ball = Number of red balls / Total balls = 3/5.

The total time taken is 1.5 hours. Average speed = total distance / total time = 60 km / 1.5 h = 40 km/h.

The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.

The number of ways to choose 3 people from 5 is given by 5C3 = 10.

The number of ways to choose 3 members from 5 is given by 5C3 = 10.

Total Price = $50 + $70 = $120. Discount = 20% of $120 = $24. Amount Paid = $120 - $24 = $96.

To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.

In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 2.

In the linear function f(x) = mx + b, 'm' represents the slope. Here, m = 2.

To find the y-intercept, set x = 0. The equation becomes -4y = 12, thus y = -3. The y-intercept is (0, -3).

Using the simple interest formula, SI = (Principal * Rate * Time) / 100 = (5000 * 6 * 4) / 100 = $1200.

20% of 50 liters = 0.2 * 50 = 10 liters of sugar.

Water in the mixture = 60% of 15 liters = 0.6 * 15 = 9 liters.

40% of 200 grams = 0.4 * 200 = 80 grams of sugar.