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If I(n) = int(0)^(pi//4) Tan^(n) x dx th...

If `I_(n) = int_(0)^(pi//4) Tan^(n) x dx` then `I_(2)+I_(4), I_(3)+I_(5), I_(4)+I_(6).....` 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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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. If a^(x) = b^(y) = c^(z) = d^(t) and a ,b ,c d are in G.P . Then x, y,...

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  2. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

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  3. If a,b,c are unequal numbers such that a,b,c are in A.P and b - a, c -...

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  4. If 2(y - a) is the H.M between y - x and y - z, then x - a, y -a, z - ...

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  5. Suppose a, b, c are positive resl numbers different from 1. If log(a) ...

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  6. If (1)/(a^(2)), (1)/(b^(2)), (1)/(c^(2)) are in H.P., then

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  7. If b +c, c + a, a + b are in H.P then

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  8. If a, 8, b are in A.P, a, 4 , b are in G.P, a , x, b are in H.P then x...

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  9. Three positive numbers form an increasing G.P. if the middle term in t...

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  10. If a,b,c are real

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  11. If p,q,r are three positive real numbers then the value of (p + q) (q ...

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  12. Suppose a, b, c are in A.P and a^(2), b^(2), c^(2) are in G.P if a lt ...

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  13. If I(n) = int(0)^(pi//4) Tan^(n) x dx then I(2)+I(4), I(3)+I(5), I(4)+...

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  14. If a,b,c are in A.P., p,q,r are in H.P and ap, bq, cr are in G.P., th...

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  15. If a ((1)/(b) + (1)/(c )), b ((1)/(c )+ (1)/(a)), c ((1)/(a) + (1)/(b)...

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  16. If a,b,c are in H.P., then the straight line (x)/(a) + (y)/(b) + (1)/(...

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  17. If x,y,z are in A.P and Tan^(-1) x, Tan^(-1) y and Tan^(-1) z are als...

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  18. The sum of the series 1 + (5)/(2) + (9)/(4) + (13)/(8) + ….. is

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  19. The sum of the series 1 + (5)/(2) + (9)/(4) + (13)/(8) + ….. is

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  20. If (10)^(9) + 2(11)^(1) (10)^(8) + 3(11)^(2) (10)^(7) + …. + 10(11)^(9...

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