This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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15. The slogan "Jai Jawan, Jai Kisan" was given by The slogan "Jai Jawan, Jai Kisan" was coined by Lal Bahadur Shastri, the second Prime Minister of India. The correct option is D. The final answer is D. Lal Bahadur Shastri. 16. If a nine-digit number 985x3678y is divisible by 72, then the value of (4x-3y) is Step 1: Apply the divisibility rule for 72. A number is divisible by 72 if it is divisible by both 8 and 9, since 72 = 8 × 9 and 8 and 9 are coprime. Step 2: Apply the divisibility rule for 8. For a number to be divisible by 8, its last three digits must be divisible by 8. In this case, the last three digits are 78y. We need to find a value for y (a digit from 0 to 9) such that 78y is divisible by 8. Let's test values for y: If y=0, 780 ÷ 8 = 97 with a remainder of 4. If y=1, 781 is not divisible by 8. If y=2, 782 is not divisible by 8. If y=3, 783 is not divisible by 8. If y=4, 784 ÷ 8 = 98. So, y=4. Step 3: Apply the divisibility rule for 9. For a number to be divisible by 9, the sum of its digits must be divisible by 9. The number is 985x3678y. Substituting y=4, the number becomes 985x36784. Sum of digits = 9 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 50 + x. For 50 + x to be divisible by 9, and x is a single digit (0-9): If x=0, 50+0=50 (not divisible by 9). If x=1, 50+1=51 (not divisible by 9). If x=2, 50+2=52 (not divisible by 9). If x=3, 50+3=53 (not divisible by 9). If x=4, 50+4=54 (divisible by 9, as 54 = 9 × 6). So, x=4. Step 4: Calculate the value of (4x-3y). Substitute the values x=4 and y=4 into the expression (4x-3y): 4x - 3y = 4(4) - 3(4) 4x - 3y = 16 - 12 4x - 3y = 4 The correct option is B. The final answer is B. 4. 17. SIR of electoral rolls by the Election Commission of India means The Election Commission of India (ECI) conducts various processes for updating electoral rolls. While "Special Summary Revision" (SSR) is a widely known process, among the given options, "Special Inclusive Registration" (SIR) refers to efforts to ensure that all eligible citizens, including marginalized groups, are registered in the electoral rolls. The correct option is A. The final answer is A. Special Inclusive Registration. 18. The phrase "Hobson's choice" means "Hobson's choice" is an idiom that refers to an apparently free choice where there is no real alternative. One must take what is offered or nothing at all. The correct option is A. The final answer is A. Only the choice offered and nothing else.