Find the derivative : f'(x) = 3-x-2x-12(x-1)(3-x) ≥ 0 ⇒ x ≤ 75 f(x) is increasing in : 1≤ x < 7/5 f(x) is decreasing in : 7/5 < x ≤3 f(7/5) is maximum and min at f(1) or f(3)

Suppose all the 12 pairs are different. Number of ways of selecting 4 socks is 24*23*22*21. Number of ways of selecting 4 socks of no pair is 24*22*20*18. Chances of not getting a pair, then is 18*20 / 23*21, or 120/161. (by removing the common factors 22*24. Chances of getting at least one pair isRead more

Using the identity sin^3(x)={3 sin(x)-sin(3x)}/4 and the identity sin(ax)sin(bx)=1/2(cos((a-b)x)-cos((a+b)x) we get sin^3(x)sin(3x) [{3sin(x)-sin(3x)}/4]sin(3x) 3/8 (cos(2x)-cos(4x))-1/8(cos(0x)-cos(6x)) Thus, $n=6$.

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## How to find the range of the function: f(x) =

## admin

Find the derivative : f'(x) = 3-x-2x-12(x-1)(3-x) ≥ 0 ⇒ x ≤ 75 f(x) is increasing in : 1≤ x < 7/5 f(x) is decreasing in : 7/5 < x ≤3 f(7/5) is maximum and min at f(1) or f(3)

## Probability : A bag contains 12 pair socks . Four socks are picked up at random. Find the probability that there is at least one pair.

## admin

Suppose all the 12 pairs are different. Number of ways of selecting 4 socks is 24*23*22*21. Number of ways of selecting 4 socks of no pair is 24*22*20*18. Chances of not getting a pair, then is 18*20 / 23*21, or 120/161. (by removing the common factors 22*24. Chances of getting at least one pair isRead more

## If where and are non zero complex numbers, then which one is correct

## admin

This answer was edited.{z_1}/{z_2}={a+ib}/{x+iy} ={(a+ib)(x-iy)}/{x^2+y^2} ={ax+by+i(bx-ay)}/{x^2+y^2} Therefore, you can find that Re({z_1} /{z_2})=0

## Given that is an identity . Find the value of n.

## admin

This answer was edited.Using the identity sin^3(x)={3 sin(x)-sin(3x)}/4 and the identity sin(ax)sin(bx)=1/2(cos((a-b)x)-cos((a+b)x) we get sin^3(x)sin(3x) [{3sin(x)-sin(3x)}/4]sin(3x) 3/8 (cos(2x)-cos(4x))-1/8(cos(0x)-cos(6x)) Thus, $n=6$.

## If |z-4/z|=2, then how to find the greatest value of |z| .

## admin

This answer was edited.|z| = |z - 4/z +4/z | ≤ |z - 4/z | + 4/|z| |z| ≤ 2 + 4/|z| ⇒ |z|^2 ≤ 2|z| + 4 ⇒ (|z| -1)^2 ≤ 5 ⇒ |z| ≤ 5 +1

## How to find the remainder of : 2^(85)/83 ?

## admin

This answer was edited.User Fermatt's theorem which states : ap-1p gives remainder 1, when a and p are both coprime numbers. 282×2383 which gives remainder 8.