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Using the relation A.M ge G.M. Prove tha...

Using the relation `A.M ge G.M`. Prove that
(i) `tan theta +cot theta ge 2`, if `0 lt theta lt (pi)/(2)`
(ii) `(x^2y+y^2z+z^x)(xy^2+yz^2+zx^2) gt 9x^2y^2z^2`. Where x,yz are different real no.
(iii) `(a+b).(b+c).(c+a) ge 8abc`, if a,b,c are positive real numbers.

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MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
  1. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  2. In a set of four number, the first three are in GP & the last three ar...

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  3. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

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  4. Find the sum of the n terms of the series whose nth term is (i) n(n+...

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  5. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

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  6. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

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  7. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

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  8. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

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  9. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

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  10. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  11. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  12. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

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  13. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

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  14. Using the relation A.M ge G.M. Prove that (i) tan theta +cot theta g...

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  15. Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c), where a,b,c gt 0 .

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  16. The arithmetic mean of two numbers is 6 and their geometric mean G and...

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  17. In a circle of radius R a square is inscribed, then a circle is inscri...

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  18. 9. Find three numbers a,b,c between 2 & 18 such that; (G) their sum is...

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  19. Two distinct, real infinite geometric series each have a sum of 1 and ...

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  20. One of the roots of the equation 2000x^6 +100x^5 +10x^3+x-2=0 is the f...

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