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If a. b, c are in A.P, then show that 1/...

If a. b, c are in A.P, then show that `1/(bc)`,`1/(ca)`,`1/(ab)` are also in A.P.

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If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

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If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b) are in A.P

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If a^(2), b^(2), c^(2) are in A.P., prove that (1)/(b+c), (1)/(c+a), (1)/(a+b) are also in A.P.

If (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) are in H.P.

If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4abc

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 14-EXERCISE
  1. How many solutions are there in the equation xyz = 2y where the soluti...

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  2. If n (> 1)is a positive integer, then show that 2^(2n)- 3n - 1 is divi...

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  3. If a. b, c are in A.P, then show that 1/(bc),1/(ca),1/(ab) are also in...

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  4. Find the perpendicular bisector of AB, where the co-ordinates of A and...

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  5. If the co-ordinate of three vertices of a- triangle are (9, 1, -3), (1...

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  6. Evaluate :lim(xrarrpi/2)(pi/2-x)tanx

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  7. If f(x + 2) = 2x^2 - 3x - 1, find the value of f(x + 1)

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  8. Three dice are thrown simultaneously. Find the probability that the su...

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  9. Two variables x and y are related by y=8+2x, if the S.D. of x is 3, th...

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  10. In three sets P,Q,R if Pcup R=Pcup Qand Pcap Q=PcapR,then show that Q=...

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  11. sintheta=ksin(theta+phi).show that tan(theta+phi)=(sinphi)/(cosphi-K)

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  12. In /\ABCif1/(a+c)+1/(b+c)=3/(a+b+c),show that angleC=pi/3

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  13. Using mathematical induction, prove that 1/5n^5+1/3n^3+7n/15 is a natu...

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  14. An equilateral triangle in the Argan plane has vertix as z1,z2and z3wh...

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  15. How many arragements can be made out of the letters of the word FAILUR...

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  16. Calcualte the sum of the series :1+3/2+7/4+15/8+31/16+….+tn

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  17. The equation of three sides of a triangle are x + 2y - 5 = 0, x +y = 6...

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  18. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  19. Find the equation, centre, and radius of a circle which is passes thro...

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  20. By using section formula, show that the points .(1, 2, 3), (-2, 4, 2) ...

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