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If x^(1/a)=y^(1/b)=z^(1/c)where a,b,c ar...

If `x^(1/a)=y^(1/b)=z^(1/c)`where a,b,c are in A.P,,than show that x,y,z are in G.P.

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If (y/z)^a.(z/x)^b.(x/y)^c=1 and a,b,c are in A.P ,show that x,y,z are in G.P.

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If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y) be (1)/(z) , then show that x, y, z are in G.P.

If a, b, c are in G.P. and a^(1//x) = b^(1//y) = c^(1//z) , show that x, y, z are in A.P.

Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a-z)/(r z) . If p, q, r are in A.P., show that (1)/(x), (1)/(y), (1)/(z) are in A.P.

UNITED BOOK HOUSE-HARE SCHOOL-EXERCISE
  1. Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc),1/(...

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  2. If a1,a2,a3,...,aaare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

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  3. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show...

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  4. Solve :barz=iz^2(z being a complex number)

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  5. if alpha,beta,gamma are in A>P show that cot=(sinalpha-singamma)/(cosg...

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  6. Prove that (1)/(2sin10^(@))-2sin70^(@)=1.

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  7. Prove that 0le3costheta+4sintheta+5le10

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  8. Show that 4(cos^3 10^@+sin^3 20^@)=3(cos10^@+sin20^@)

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  9. If the equation x^2-cx+d=0and x^2-ax+b=0 have a common root,and the ro...

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  10. If alphaand betaare roots of the equation qx^2+px+p=0,show that sqrt(a...

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  11. If z1 and z2 be two complex numbers show that Re(barz1z2)=1/2(z1barz2+...

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  12. Find the sum up to n terms :1+2/3+3/3^2+4/3^3+...

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  13. If x^(1/a)=y^(1/b)=z^(1/c)where a,b,c are in A.P,,than show that x,y,z...

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  14. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

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  15. IF A+B+C=pi,then prove that tan (A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2...

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  16. Prove that secx=2/(sqrt(2+sqrt(2+sqrt(2+2cos8x)))

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  17. Prove that tan20^@+4sin20^@=sqrt3

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  18. A(1,2)and B(5,-2)are two points. P is a point moving in such a way tha...

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  19. A variable straight line passes through the point of intersection of t...

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  20. For three mutually exclusive events X,Yand Zit is given that P(x)=2P(Y...

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