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If f(x)=4x^4-a x^3+b x^2-c x+5 (a,b,c in...

If `f(x)=4x^4-a x^3+b x^2-c x+5 (a,b,c in R)` has four positive real zeros `r_1,r_2,r_3,r_4` such that `r_1/2+r_2/4+r_3/5+r_4/8=1.` then a is equal to

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If f(x)=4x^(4)-ax^(3)+bx^(2)-cx+5(a,b,c in R) has four positive real zeros r_(1),r_(2),r_(3),r_(4) such that (r_(1))/(2)+(r_(2))/(4)+(r_(3))/(5)+(r_(4))/(8)=1. then a is equal to

In a DeltaABC, if r_(1)=2r _(2)=3r_(3), then show that a/b=5/4.

Let A= {(x,y) in R xx R |2x^(2)+2y^(2)-2x-2y=1}, B= {(x,y) in R xx R|4x^(2)+4y^(2)-16y+7=0} and C={(x,y) in R xx R |x^(2)+y^(2)-4x-2y+5 le r^(2)} . Then the minimum value of |r| such that A uu B sube C is equal to

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Let the straight line x=b divide the area enclosed by y=(1-x)^2, y=0 and x=0 into two parts R_1 (0 le x le b) and R_2 (b le x le 1) such that R_1-R_2=1/4 . Then b equals (A) 3/4 (B) 1/2 (C) 1/3 (D) 1/4

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

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MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
  1. If f(x)=4x^4-a x^3+b x^2-c x+5 (a,b,c in R) has four positive real zer...

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  2. Let Vr denote the sum of first r terms of an arithmetic progression (A...

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  3. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  4. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  5. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  6. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  7. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  8. A straight line through the vertex P of a triangle PQR intersects the ...

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  9. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

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  10. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

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  11. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

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  12. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

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  13. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

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  14. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

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  15. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

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  16. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  17. Let an denote the number of all n-digit positive integers formed by th...

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  18. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

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  19. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

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  20. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

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  21. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

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