Recently Active Mathematics Questions

Show that in any set of eleven integers there are six whose sum is divisible by 6 . ...

Evaluate \int_{-1}^1\dfrac{\ln(13-6x)}{\sqrt{1-x^2}}\ \mathrm dx ...

find : \frac{29\int_{0}^{1}{\left(1-x^4 \right)^{7}}\mathrm{dx}}{4\int_{0}^{1}{\left(1-x^4 \right)^{6}}\mathrm{dx}} ...

1. Two rods of lengths a and b side along coordinate axis in a manner that their ends are always concyclic. Find the locus of the centre of the circle passing throw these ends. 2.The base of a triangle passes throw a fixed po ...

*Image* Explain the approach,no need to solve. ...

if α, β, γ are connected by the relation 2 tan2α tan2β tan2γ + tan2α tan2β + tan2β tan2γ +tan2γ tan2α =1, then the value of cos2α +cos2β +cos2γ is ________ answer: 1 ...

*Image* *Image* Prove it from both Sides : 1. Co ordinate Geometry 2 . Euclidean Geometry (Normal Geometry) Separately ...

tanθ+tan(θ+60)+tan(θ-60)=k tan 3θ,where k is equal to: a)1 b)2 c)3 d)4 ...

Given are Positive integers not exceeding a fixed integer constant M. If the LCM of every 2 of them is greater than M,prove that the sum of the reciprocals of these numbers is less than 3/2 ...

1) show that the normal at the point (3t , 4/t ) of the curve xy = 12 cuts the curve again at the point whose parametr t1 is given by t1 = -16/9t3 ...

find all the tangents to the curve y = cos ( x+y ) ,-2pi≤x≤2pithat are parallel to the line x + 2y = 0 ...

Q.1. The number of terms of an A.P. is even;the sum of the odd terms is 24,of the even terms is 30,and the last term excceds the first term by10 1/2 ,find the number of terms and the sries. ...

Let θ[0,45] and t1=tanθtanθ, t2=tanθcotθ, t3=cotθtanθ, t4=cotθcotθ, then: a)t1>t2>t3>t4 b)t4>t3>t1>t2 c)t3>t1>t2>t4 d)t2>t3>t1>t4 ...

1.Prove that sin(3x) = 4sinx.sin2x.sin4x 2.Solve : cosx(1+sin x/4 - 2cosx) + sinx (cosx/4 - 2sinx) = 0 3.solve : cos 3x + cos 2x = sin 3x/2 + sin x/2 , x=(0,pi) 4.solve for x and y : cos2x + cosx.cosy + cos2y = 0 ...

What is the minimum value of 9sec2x + 10cosec2x for all x belongs to R?? ...

Prove: sinx/cos3x + sin3x/cos9x + sin9x/cos27x = 1/2 (tan27x-tanx) ...

If the first and the (2n-1)the terms of an A.P. , G.P. and H.P. are equal an their nth terms are a, b, c respectively, then (a) a=b=c (b) a≥b≥c (c) a+c=b (d) ac-b2 = 0 ...

( 2 +1)x+( 2 -1)x =6x/2 ...

1)) \lim_{x\rightarrow \propto } sinx/x 2) \lim_{x\rightarrow 0} \frac{\sqrt{(1-cos2x)/2}}{x} ...

solve 1) | x2+x+1|=3 2) |x|x2-x-2=1 ...

Find the values of α and β, 0<α, β < Π/2, satisfying the eqn - cos α cos β cos (α+β) = -1/8. ...

If cos π/7 , cos 3π/7 , cos 4π/7 are the roots of the equation 8x3-4x2-4x+1 = 0 then the What are the values of expressions sin π/14 sin 3π/14 sin 5π/14 and cos π/14 cos 3π/14 cos 5π/14 ???? ...

Find: limn→∞Σ 1 to n: r/(4r2+1) ...

x+ log10(2x+1) =log106 +xlog105 ...

If f(x)= \sqrt{\frac{x-sinx}{x+cos^{2}x}} then find \lim_{x\rightarrow \propto } f(x) ...

find the no. of solutions of the triplet (a,b,c) for which acos 2x+bcos2x+c=0 is satisfied for all values of x. ...

Find the values of x; y for which x2 + y2 takes the minimum valuewhere (x + 5)2 + (y-12)2 = 142. ...

solve 1) (x+4)(x+7)(x+8)(x+11) +20=0 2) 2x3+5x2-2x+3=0 ...

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Find coordinates of a set of eight non-collinear planar points so that each has an integral distance from others. ...