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Mathematics: Post your doubts here!

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Help:
If the letters of the word 'MINIMUM' are arranged in a line at random. What is the probability that the arrangement begins with MMM?
 
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Again:
In how many ways can 10 students be arranged in a way that 2 youngest are separated?
 
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I. How many 4 digit numbers can be formed from the digits 1,2,3 and 5 If repetitions are not allowed?

II. How many 4 digit numbers divisible by 5 can be formed from the digits above?
 
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find normal (n hat) by doing cross product with the direction of line l and the directon vector A.

replace in the formula r. n hat = a . n hat

a can be the point in line equation (4,-2,2)

replace n u get the answer.
That's the normal to the plane right? How do you find it?
 
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cross product of direction of line n direction vector A
i mentioned it there :)
Yeah what's the general equation for it? Is it the cross product of the position vector of any point on a plane and the direction vector? Isn't the direction of line l the same as the direction vector A?
 
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When it says , Find all the roots in the interval (-180 < x <180) of the following equations : 1) 4 sin X = 5 cosX 2) cos3X =2/3
Now what is the difference between cos3X and 3cos X? Are they both same? . And which roots lie in the interval ( -180 < x < 180)??????...What does -180 means? Plzzz solve both question step by step.Thanks
 
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