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Let S1 , S2 , …. Be squares such that fo...

Let `S_1 , S_2` , …. Be squares such that for each `n ge 1 ` the length of a side of `S_n` equals the lengths of a diagonal of `S_(n+1)` . If the length of a sides of `S_1` is 10 cm, then for which of the following values of n is the area of `S_n` less than 1 square cm ?

A

7

B

8

C

9

D

10

Text Solution

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The correct Answer is:
B
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Let S_(1), S_(2)…., be squares such that for each n ge 1 , the length of a side of S_(n) equals the length of a side of S_(n) equals the length of a diagonal of S_(n+1) . If the length of a side S_(1) is 10 cm, then for which of the following value of n is the area of S_(n) less than 1 sq cm ?

ML KHANNA-PROGRESSIONS -PROBLEM SET - 2 (MULTIPLE CHOICE QUESTIONS)
  1. The minimum value of n such that 1 + 3 + 3^(2) +...+ 3^(n) gt 1000 is

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  2. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  3. Let S1 , S2 , …. Be squares such that for each n ge 1 the length of a...

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  4. If A and G be the A .M and G.M between two positive numbers, then the ...

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  5. If the A.M. and G.M. between two numbers are in the ratio m.n., then w...

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  6. If S = (2)/(3) + (8)/(9) + (26)/(27) + (30)/(81)+….+n terms, then the ...

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  7. Sum of n terms of the series (1)/(3) + (5)/(9) + (19)/(27) + (65)/(81)...

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  8. 8 + 88 + 888 +…n terms =

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  9. underset("n digits")((666…6)^(2)) + underset("n digits")((888…8)) is e...

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  10. The value of sum sum(n=1)^(13) ( i^(n) + i^(n+1)) where i= sqrt( -1) ,...

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  11. If |a| lt 1 and |b| lt 1 , then the sum of the series a(a+b) + a^2...

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  12. If S be the sum, P the product and R the sum of the reciprocals of n t...

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  13. If x = 1 + a + a^(2) + a^(3) +…"to" oo (|a| lt 1) and y = 1 b + b^(2) ...

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  14. If x is the first term of a G.P. with infinite number of terms and S(o...

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  15. If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)...

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  16. Given that 0 lt x lt (pi)/(4) and (pi)/(4) lt y lt (pi)/(2) and sum(k ...

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  17. If x = 1 + y + y^(2) + y^(3)+…"to"oo, then y is

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  18. (3)/(4)-(5)/(4^(2))+(3)/(4^(3))-(5)/(4^(4))+(3)/(4^(5))-(5)/(4^(6))+.....

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  19. If {:(x = a + a//r + a//r^(2)+......oo),(y = b - b//r + b//r^(2)-........

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  20. If S(1), S(2),…S(lambda) are the sums of infinite G.P.'s whose first t...

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