Let f(x) = 5ˣ/(5ˣ + 5). Then the Sum of the Series f(1/20) + f(2/20) + f(3/20) + ⋯ + f(39/20) Is Equal To
JEE Main 2021 PYQ: for f(x)=5^x/(5^x+5), find the sum f(1/20)+f(2/20)+…+f(39/20) using the pairing identity f(x)+f(2-x)=1.
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Let the Centroid of an Equilateral Triangle ABC Be at the Origin and One of Its Sides Lie Along the Straight Line x + y = 3. If R and r Are the Radii of the Circumcircle and Incircle of Triangle ABC, Then R + r Is Equal To
JEE Main 2021 PYQ: an equilateral triangle has its centroid at the origin and one side along x+y=3. Find R+r using the R=2r relation for equilateral triangles.
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For p > 0, the Vector v₂ = 2i + (p+1)j Is Obtained by Rotating v₁ = √3 p i + j by an Angle θ About the Origin in a Counterclockwise Direction. If tan θ = (α√3 − 2)/(4√3 + 3), Then the Value of α Is Equal To
For p>0, vector v2=2i+(p+1)j is obtained by rotating v1=√3pi+j by angle θ. Given tanθ=(α√3−2)/(4√3+3), find α using the rotation-preserves-length property.
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Let p and q Be Two Positive Numbers Such That p + q = 2 and p⁴ + q⁴ = 272. Then p and q Are Roots of the Equation
Two positive numbers p, q satisfy p+q=2 and p^4+q^4=272. Find pq using power-sum identities, then write the quadratic having p, q as roots.
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If the Matrix A = [[1,0,0],[0,2,0],[3,0,−1]] Satisfies A²⁰ + αA¹⁹ + βA = [[1,0,0],[0,4,0],[0,0,1]] for Real Numbers α and β, Then β − α Is Equal To
Given a triangular matrix A satisfying A²⁰+αA¹⁹+βA equals a specific matrix, find β−α using the eigenvalues on A’s diagonal.