• Placement Questions

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(#M40020200) MATHS QUESTION Keep an EYE

Find all positive real numbers x such that both root x + 1/root x and cube root of x + 1/cube root of x are integers.

Asked In maths AISHWARYA (12 years ago)

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(#M40020198) MATHS QUESTION Keep an EYE

The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?

Asked In maths AISHWARYA (12 years ago)

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(#M40020197) MATHS QUESTION Keep an EYE

If the equation x4 − x3 + x + 1 = 0 has roots a, b, c, d, show that 1/a + 1/b is a root of x6 + 3x5 + 3x4 + x3 − 5x2 − 5x − 2 = 0.

Asked In maths AISHWARYA (12 years ago)

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(#M40020196) MATHS QUESTION Keep an EYE

For how many integers n > 1 is x49 congruent to x (modulo n) true for all integers x?

Asked In maths AISHWARYA (12 years ago)

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(#M40020195) MATHS QUESTION Keep an EYE

Show that, for all integers m and n, mn(m420 − n420) is divisible by 446617991732222310.

Asked In maths AISHWARYA (12 years ago)

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(#M40020194) MATHS QUESTION Keep an EYE

The terms of a sequence of positive integers satisfy an+3 = an+2(an+1 + an), for n = 1, 2, 3, ... .
If a6 = 8820, what is a7?

Asked In maths AISHWARYA (12 years ago)

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(#M40020193) MATHS QUESTION Keep an EYE

Let n be a positive integer. Prove that n! + 1 is composite for infinitely many values of n.

Asked In maths AISHWARYA (12 years ago)

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(#M40020192) MATHS QUESTION Keep an EYE

A triangle has two acute angles, A and B. Show that the triangle is right-angled if, and only if, sin2A + sin2B = sin(A + B).

Asked In maths AISHWARYA (12 years ago)

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(#M40020191) MATHS QUESTION Keep an EYE

how that, for each n greater than or equal to 3, n! can be represented as the sum of n distinct divisors of itself. (For example, 3! = 1 + 2 + 3.)

Asked In maths AISHWARYA (12 years ago)

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(#M40020190) MATHS QUESTION Keep an EYE

Let a, b, and c be positive real numbers such that abc = 1. Show that a2 + b2 + c2 less than or equal to a3 + b3 + c3.

Asked In maths AISHWARYA (12 years ago)

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