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IPMAT indore 2023 Complete Paper Solution

Instructions

For the following questions answer them individually

Question 1.

If f(1) = 1 and f(n) = 3n - f(n - 1) for all integers n 1 , then the value of f(2023) is _________

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Question 2.

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be ______.

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Question 3.

If f(n)= 1 + 2 + 3 +∙∙∙+(n+1) and g(n)g(n) =k=1k=n1f(k)\sum_{k=1}^{k=n}\frac{1}{f(k)} then the least value of nn for which g(n)g(n) exceeds the value 99100\frac{99}{100} is ____________.

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Question 4.

In an election with only two contesting candidates, 15% of the voters did not turn up to vote, and 50 voterscast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting list is_________.

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Question 5.

The total number of positive integer solutions of 21a+b+c2521 \leq a + b + c \leq 25 is __________.

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Question 6.

If three consecutive coefficients in the expansion of (x+y)n(x + y)^{n} are in the ratio 1 : 9 : 63, then the value of n is ___________.

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Question 7.

The polynomial 4x10x9+3x85x7+cx6+2x5x4+x34x2+6x24x^{10} − x^{9} + 3x^{8} − 5x^{7} + cx^{6} + 2x^{5} − x^{4} + x^{3} − 4x^{2} + 6x − 2 when divided by x1x - 1 leaves a remainder 2. Then the value of c+6c + 6 is________.

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Question 8.

The product of the roots of the equation log22(log2x)25log2x+6=0\log_{2}2^{(\log_{2}x)^{2} }− 5\log_{2}x + 6 = 0 is ________

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Question 9.

The remainder when 1! + 2! + 3! +∙∙∙+95! is divided by 15 is _____________.

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Question 10.

Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed inthe first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be______.

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