Mathematics

(1000)^0 equals 1 because any non-zero number raised to the power of zero is 1. 10^24 is a very large number (1 followed by 24 zeros). Adding 1 to 10^24 does not match any of the given numeric options, so the correct choice is 'None of these'.

The number series follows the pattern where each term is obtained by multiplying the previous term by 3 and then subtracting 3. Specifically: 3 × 3 - 3 = 6, 6 × 3 - 3 = 15, 15 × 3 - 3 = 42, 42 × 3 - 3 = 123, and 123 × 3 - 3 = 366. Therefore, the missing number in the series is 42, which corresponds to option C.

If 10% of the workers were fired, then 90% remained. Given that 540 workers survived, we can set up the equation 0.9 × total_workers = 540. Solving for total_workers gives 540 ÷ 0.9 = 600 workers originally.

Let Arif's share be x. Hafiz's share is 4x, and Arif's share is one-third of Haider's, so Haider's share is 3x. Total shares: x + 4x + 3x = 8x = 2560, so x = 2560/8 = 320. Therefore, Arif's share is Rs. 320.

The power set of a set with n elements contains 2^n elements. Since the set {1, 2, 3} has 3 elements, its power set has 2^3 = 8 elements.

5% of Rs. 100 is Rs. 5. Then, 5% of Rs. 5 is Rs. 0.25. Therefore, 5% of 5% of Rs. 100 equals Rs. 0.25.

If A's salary is 50% more than B's, then A = 1.5 × B. To find by what percent B's salary is less than A's, we calculate the percentage difference relative to A: ((A - B) / A) × 100 = ((1.5B - B) / 1.5B) × 100 = (0.5B / 1.5B) × 100 = 33 1/3%. This matches option C, which correctly represents 33 1/3%. Options A and B represent 33.25% and 33.5% respectively, which are incorrect. Therefore, the correct answer is option C.

Ali's current age is given as (x - 10) years. After 12 years, his age will be (x - 10) + 12 = x + 2 years. Therefore, the correct answer is option A: x + 2.

The phrase 'subtract eight times of the number b from ten times of the number c' means 10c minus 8b, which corresponds to option C. Option B reverses the order, which is incorrect.

If 20% of the bill is deducted, 80% remains to be paid. Since Rs. 100 is 80% of the original bill, the original bill = 100 ÷ 0.8 = Rs. 125.

Given the pth term is q and the qth term is p in an arithmetic progression, solving the equations shows the (p+q)th term equals zero.

In an arithmetic progression (A.P.) with first term 3 and common difference 0, all terms are equal to the first term. Therefore, the 5th term is also 3.

The population increased from 175,000 to 262,500 over 10 years, which is a total increase of 50%. The average annual percent increase is calculated as (50% ÷ 10) = 5%. However, since the question asks for average percent increase per year, it is more accurate to calculate the compound annual growth rate (CAGR): ((262500/175000)^(1/10) - 1) × 100 ≈ 4.75%. Therefore, option A is correct.

The nth term of an arithmetic progression (A.P.) is given by Tn = a + (n-1)d. Here, a = 3, d = 6, and n = 9, so T9 = 3 + (9-1)*6 = 3 + 48 = 51.

To express 1.14 as a percent of 1.9, divide 1.14 by 1.9 and multiply by 100: (1.14 / 1.9) × 100 ≈ 60%. Hence, option A is correct.

If x, y, and z are in proportion, it means the ratio of x to y is equal to the ratio of y to z, which is expressed as x : y :: y : z. Option B correctly represents this proportion.

To find what percent 90 is of 120, divide 90 by 120 to get 0.75, which is 75%. Among the options, 0.75 corresponds to 75%, making option C correct.

Using the principle of inclusion-exclusion, the percentage reading at least one magazine is 45% + 55% + 40% - 30% - 15% - 25% + 10% = 80%. Therefore, the percentage not reading any magazine is 100% - 80% = 20%. However, since 20% is option C, the correct answer is C, not A. Recalculating carefully: 45 + 55 + 40 = 140; subtract pairs: 30 + 15 + 25 = 70; add triple: 10; total = 140 - 70 + 10 = 80%. So 20% do not read any magazine, which matches option C.

An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

The expression as given is ambiguous, but interpreting it as (27 ÷ 32) + 4; 2 - 1 suggests two separate expressions: 27 divided by 32 plus 4, and 2 minus 1. The first evaluates to approximately 4.84375, and the second to 1, neither matching options A, B, or C. Therefore, 'None of these' is the correct choice.

Mr. A's work rate is 1/6 work per hour, and Mr. B's work rate is 1/12 work per hour. Together, their combined rate is 1/6 + 1/12 = 1/4 work per hour, so they will complete the work in 4 hours.

Amna's age three years ago is (x - 3). Five times this age is 5(x - 3), which corresponds to option B.

If Haroon uses 25% more petrol each day, the daily consumption increases by a factor of 1.25. The total petrol amount remains the same, so the new duration is 10 ÷ 1.25 = 8 days. However, this calculation is incorrect; let's re-examine: If the original daily usage is x, total petrol = 10x. New daily usage = 1.25x. Days = total petrol ÷ new daily usage = 10x ÷ 1.25x = 8 days. So the correct answer is 8 days, which corresponds to option C, not B. Correcting answer to C.

To solve the inequality 6x - 2 ≥ 3x + 10, subtract 3x from both sides to get 3x - 2 ≥ 10. Then add 2 to both sides: 3x ≥ 12. Dividing both sides by 3 (a positive number) gives x ≥ 4. Therefore, the solution interval is [4, ∞), which corresponds to option C.

The given arithmetic progression (A.P) has first term a = -15 and common difference d = -7. The nth term formula is a_n = a + (n-1)d. For the 11th term: a_11 = -15 + (11-1)(-7) = -15 - 70 = -85.