IPM Indore 2019


For the following questions answer them individually

Question 21

If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent

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Question 22

The maximum value of the natural number n for which $$21^{n}$$ divides 50! is

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Question 23

The remainder when $$(29^{29})^{29}$$ is divided by 9 is

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Question 24

Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6,7 and 9?

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Question 25

In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then

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Question 26

In a class of 65 students 40 like cricket, 25 like football and 20 like hockey. 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least one sport, then the number of students who like both cricket and hockey is

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Question 27

If x ∈ (a, b) satisfies the inequality, $$\frac{x-3}{x^{2} + 3x + 2}$$ then the largest possible value of b - a is

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Question 28

If a, b, c are real numbers $$a^{2} + b^{2} + c^{2} = 1$$, then the set of values ab + bc + ca can take is:

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Question 29

The inequality $$\log_{2} \frac{3x - 1}{2 - x} < 1$$ holds true for

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Question 30

The set of values of x which satisfy the inequality $$0.7^{2x^{2}-3x+4} < 0.343$$ is

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