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If I(n) = int(0)^(pi//4) tan^(n) x sec^(...

If `I_(n) = int_(0)^(pi//4) tan^(n) x sec^(2)x` dx, then `I_(1), I_(2), I_(3),….` are in

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

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The correct Answer is:
C
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. If I(n)=int(0)^(pi)(1-sin2nx)/(1-cos2x)dx then I(1),I(2),I(3),"….." ar...

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  2. If I(n) = int(0)^(pi//2) (sin^(2)nx)/(sin^(2)x)dx then I(1),I(2),I(3),...

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  3. If I(n) = int(0)^(pi//4) tan^(n) x sec^(2)x dx, then I(1), I(2), I(3),...

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  4. Let the roots alpha, beta of the equation ax^(2) + bx + c = 0 satisfy ...

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  5. If a, b, c be in A.P and a^(2), b^(2), c^(2) in H.P., then

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  6. If a, b, c are in H.P. then the value of ((1)/(b) + (1)/(c) - (1)/(a))...

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  7. The next term of the sequence 1,5,14,30,55,... is

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  8. If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove ...

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  9. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  10. The sum of first n terms of the series 1^(2) + 2.2^(2) + 3^(2) + 2.4^(...

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  11. The sum of first n terms of the series 3.1 + 2^(2) + 3.3^(2) + 4^(2)+…...

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  12. 1. If x ,y and z are respectively the p(th), q(th), and r(th) terms, r...

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  13. A.G.P. and H.P. have the same pth, qth and rth terms as a, b, c respec...

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  14. If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H...

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  15. Suppose a, b, c are in A.P. and a^(2), b^(2), c^(2) are in G.P. If a l...

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  16. If x, y, z are in A.P. then xth, yth and zth terms of any G.P. are in

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  17. If T(p), T(q), T(r) of an A.P. (G.P. or H.P.) are in A.P. (G.P. or H.P...

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  18. If x, y, z, w in N be four consecutive terms of an A.P., then T(x), T(...

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  19. If in any progressin the difference of any two consecutive terms bears...

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  20. In any progression, if (t(2)t(3))/(t(1)t(4)) = (t(2) + t(3))/(t(1) + t...

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