Mathematics

The number of ways to select 2 men from 5 is C(5,2) = 10, and the number of ways to select 3 women from 6 is C(6,3) = 20. Multiplying these gives 10 × 20 = 200 ways. However, the options given do not include 200 as the correct answer; option B is 200 but the calculation shows 10 × 20 = 200, so the correct answer is B, not D. Rechecking: C(5,2) = 10, C(6,3) = 20, total = 200, so correct answer is B.

The total number of ways to arrange four distinct books A, B, C, and D is 4! = 24. To find the number of arrangements where A and B are consecutive, treat A and B as a single block. This block and the other two books C and D can be arranged in 3! = 6 ways. Inside the block, A and B can be arranged in 2! = 2 ways. So, the total number of arrangements with A and B together is 2! × 3! = 12. Therefore, the number of arrangements where A and B are never consecutive is 24 - 12 = 12. Hence, the correct answer is option B (12).

Let x be the liters of oil at Rs.40 per liter. The total cost of the mixture is (40x + 60*240) and the total volume is (x + 240). The cost per liter of the mixture is Rs.52, so (40x + 14400)/(x + 240) = 52. Solving gives x = 120 liters.

The selling price of the mixture is Rs. 68.20 per kg with a gain of 10%. To find the cost price of the mixture, use the formula: Cost Price = Selling Price / (1 + Gain%) = 68.20 / 1.10 = Rs. 62 per kg. Using the allegation method to mix teas worth Rs. 60 and Rs. 65 to get a mixture costing Rs. 62, the ratio is calculated as (65 - 62) : (62 - 60) = 3 : 2. Therefore, the grocer must mix the teas in the ratio 3:2 to achieve the desired gain.

The word MATERIAL has 8 letters with vowels A, A, E, I (4 vowels) and consonants M, T, R, L (4 consonants). Treating all vowels as a single unit, we have 5 units to arrange (the vowel block + 4 consonants), which can be arranged in 5! = 120 ways. The vowels inside the block can be arranged among themselves in 4!/2! = 12 ways (dividing by 2! for the two identical A's). Therefore, total arrangements = 120 × 12 = 1440. However, the correct calculation is 5! × (4!/2!) = 120 × 12 = 1440, which corresponds to option B. But the original correct_answer was B, so the original answer is correct. On rechecking, the original answer B (1440) is correct. So the correct_answer remains B.

The problem states that a delegation of 5 members is to be formed from 3 ladies and 5 gentlemen, with 2 particular ladies always included. Since these 2 ladies are fixed, we need to select the remaining 3 members from the remaining 1 lady and 5 gentlemen, totaling 6 people. The number of ways to choose 3 members from these 6 is given by the combination formula C(6,3) = 20. Therefore, the correct answer is option A (20).

The total number of ways to arrange 6 players in a line is 6! = 720. To find the number of arrangements where two specific players (Asim and Raheem) are together, treat them as a single unit. This gives 5 units to arrange, which can be done in 5! ways. Since Asim and Raheem can switch places within this unit, multiply by 2!. So, the number of arrangements with Asim and Raheem together is 2! × 5! = 240. Therefore, the number of arrangements where Asim and Raheem are never together is 720 - 240 = 480. Hence, the correct answer is 480, which corresponds to option D.

The word 'NOKIA' has 5 letters. Fixing 'N' at the start and 'A' at the end leaves 3 letters (O, K, I) to arrange in the middle. The number of such arrangements is 3! = 6.

Using the allegation method: The difference between the price of the first rice and the mixture price is 7.20 - 6.30 = 0.90, and the difference between the mixture price and the second rice price is 6.30 - 5.70 = 0.60. The ratio in which the two types of rice should be mixed is the inverse of these differences, i.e., 0.60 : 0.90 = 2 : 3. Therefore, rice at Rs. 7.20 should be mixed with rice at Rs. 5.70 in the ratio 2 : 3, which corresponds to option B.

Let the cost of a chair be C and a table be T. From the equations: 2C + 3T = 1300 and 3C + 2T = 1200, solving these simultaneously gives C = 160 and T = 230. The difference T - C = 70, so each table costs Rs.70 more than each chair.