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If a,b,c are in A.P .then 3^a,3^band 3^c...

If a,b,c are in A.P .then `3^a`,`3^b`and `3^c`are in

A

a)A.P

B

b)G.P

C

c)both A.P and G.P

D

d)none of these.

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Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

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If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G.P. Prove that, a : b : c = 1 : 3 : 5 .

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a. a/c+c/a b. a/c-c/a c. b/q + q/b d. b/q - q/b

If in a triangle ABC, anglesA, B,C are in A.P, sides a,b,c are In G.P., then a^2,b^2,c^2 are in

Suppose a,b,c are in A.P and a^2 , b^2 , c^2 are in G.P if a

Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c and a+b+c=3/2 then the value of a is

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UNITED BOOK HOUSE-BETHUNE COLLEGIATE SCHOOL.-EXERCISE
  1. If Z=(sqrt3+i)/2,then the value of z^69is

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  2. if^nCr+^nC(r+1)=^(n+1)cxthen the value of x is

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  3. If a,b,c are in A.P .then 3^a,3^band 3^care in

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  4. If the slope of the line joining the points (3lambda,4)and (4,-3lambda...

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  5. If lim(xrarr3)(alphax^2-beta)/(x-3)=12,then find the value of alpha an...

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  6. For any three sets A,B and C,if AcapC=BcapCand AcapC^c=BcapC^cthen sho...

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  7. If f(x)=a(x-b)/(a-b)+b.(x-a)/(b-a)then show that f(a)+f(b)=f(a+b).

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  8. Prove that (1+sec2A)(1+sec2^2A)(1+sec2^3A).....(1+sec2^nA)=(tan2^nA)/(...

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  9. Prove that ,tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos...

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  10. How many 5 digit numbers can be formed using the digits 0,2,5,6,7 with...

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  11. Show that ,((1+i)/(1-i))^2+((1-i)/(1+i))^2is a real number.

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  12. Find the distance between the lines 3x+4y=9 and 6x+8y+15=0.

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  13. Find the value of :lim(xrarr0)(sin2x+sin6x)/(sin5x-sin3x)

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  14. In an examination 60% passed in mathematics,68% passes in statistics a...

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  15. If alpha!=betaand atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2),then sh...

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  16. For any three sets A,Band C show that :Acap(BcupC)=(AcapB)cup(AcapC)

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  17. Prove using principle of mathematical induction that sum of the cube t...

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  18. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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  19. Find the sum upto n terms of the following series 4+44+444+….n.

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  20. Show that the straight lines 5x-y=6,x+5y-22=0,5x-y-32=0 and x+5y+4=0 f...

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