Let a be an integer such that all the real roots of the polynomial 2x 5 + 5x 4 + 10x 3 + 10x 2 + 10x + 10...

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Let a be an integer such that all the real roots of the poly: null (Mathematics) Question | DivineJEE | DivineJEE

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Let a be an integer such that all the real roots of the polynomial
2x⁵ + 5x⁴ + 10x³ + 10x² + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to ___________.

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Let P(S) denote the power set of S = { 1,2,3,...,10}. Define the relations R_{1} and R_{2} on P(S) as AR_{1}B if ( A cap B^{C} ) cup ( B cap A^{C} ) = phi and AR_{2}B if cup B^{C} = B cup A^{C},forall A,B in P(S). Then

The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

Consider the following relations: R = |(x,y)|x,y are real numbers and x = wy for some rational mumber w/; S = { ( frac{m}{n},frac{p}{q} )| m,n,p and q are integers such that n,q X 0 and qm = pm}. Then

Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

The integral int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} {dx}, where [.] denotes the greatest integer function is equal to

The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated, is

For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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