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Solution in the figure

Excepts for p=2 or 1 if we plot the curve we have one local minimum and one local maximum the region between whom is the one which does not come in range and hence if the local maximum> local...

What do you mean by dimension here ? Please specify so that i can help you in better way.

Alternatively , you can proceed this way. No. of elements in sample space = 10 x 9 x 8 for selection of 3 numbers one by one without replacement. According to the question 3 & 7 must get chosen and...

Possible Cases 4+4+3 3+4+4 4+3+4 Just place one male in each car first then place remaining 8 members on remaining seats in each case and then add.

Just place english books in 21! ways. Then between english books there are 23 gaps including ends so 19hindi book can pe placed in those 23gaps in 23P19 ways. So total ways is 21! * 23P19 ways.

Let O be origin, A be z1, B be z2 and C be the point corresponding to z1+z2 on the complex plane. Then OAZB is a rhombus and z1+z2 and z1-z2 are the diagonals. From geometry we know that the...

Let the A.P. be given by q = a + (p -1)d ... ( 1 ) p = a + (q -1)d ... ( 2 ) Subtracting ( 2 ) from ( 1 ), q - p = (p - q)d => d = -1 Putting d = -1 in ( 1 ), a = p + q - 1 nte term = a + (n - 1)d...

let the side of square be a and rectangle be of length l and width w perimiter equal gives 4a = 2(l+w) a = (l+w)/2 Now A1 = a 2 A2 = lw Then by AM>GM hence Option C

total ways = ways with square in single coloum or row = 64x14 Answer =

ok we have now as the w is a root of the ablove equation we have

First we arrange the boys. we remove 3 chairs there are 9 gaps in the 8 remaining chairs where the 3 chairs of the boys can be arranged in ways then the remaining girls can be arranged in so the total...

as every thing goes to infinity we can subtract the two sequences and we get

This is quite simlpe

A simple way to do it is to factorize now the factors should match f=3

omega given is the cube root of -1 1) conjugate 2) 3) The trick is to express this as now expanding them and using the properties mentioned above we get and hence the answer is 3

Solution here

It will be a circular region you can verify this by construction 1) Find points which lie on the perpendicular from O to P1P2 such that say N1 st ON1 = PN1 = PN2 2) Also find mid points of OP1’s...

now expanding the above by binomial theorm all except for the constant term will be containing 26 which is divisible by 13 hence the remainder is which is the same as remainder being 8

In a conic section, if P be point on a curve then the ratio between the distance of this point from focus and the distance from directrix is called ecentricity of this curve. Its use do determine the...

a+ b ) 2 a b a2 ab ab b2 The above diagram represents – a+ b is a line and the square are is a 2 + b2 +2ab Hence proved - (a+ b ) 2 = a 2 + b2 +2ab

-2............................................................................................................................

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse ...

dear frnd...., algebra is one of the branch in mathematics.......simply we say that the algebra is .... add...sub...multiplication...and division…....

Considering a+c and b+c are not equal to zero we cross multiply to get which gives

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