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If cot ^(-1) ((n^(2) - 10n + 21*6)/pi) g...

If `cot ^(-1) ((n^(2) - 10n + 21*6)/pi) gt pi/6 , n in N `, then find the minimum value of n.

A

4

B

3

C

5

D

2

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-ASSIGNMENT (SECTION - B)(OBJECTIVE TYPE QUESTIONS (ONE OPTION IS CORRECT))
  1. Prove that: sin^(-1)4/5+sin^(-1)5/(13)+sin^(-1)(16)/(65)=pi/2

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  2. If alpha=tan^(-1)((sqrt(3)x)/(2y-x)) , beta=tan^(-1)((2x-y)/(sqrt(3)y)...

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  3. Evaluate: {(2tan^(-1)1)/5-pi/4} (ii) tan{1/2cos^(-1)(sqrt(5))/3}

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  4. If -1 le x le -1/2, then sin^(-1)(3x-4x^3) equals

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  5. The value of cos (2Cos^-1 0.8) is

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  6. Find the value of 4 tan^-1 (1/5) - tan^-1 (1/239)

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  7. If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is ...

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  8. If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3), then

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  9. The set of values of x satisfying |sin^(- 1)x|lt|cos^(- 1)x|,is

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  10. Let f(x)=sec^-1(x-10)+cos^-1(10-x). Then range of f(x) is

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  11. Let f(x) = cosec^-1[1 + sin^2x], where [*] denotes the greatest intege...

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  12. The sum sum (n=1)^ootan^(-1)(1/(2^n+2^(1-n))) equals

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  13. tan ((pi)/(4) + (1)/(2) cos^(-1) x) + tan ((pi)/(4) - (1)/(2) cos^(-1)...

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  14. The sum sum(k=1)^oocot^(-1)(2k^2) equals

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  15. The sum tan^(-1).(1)/(1+x+x^2)+tan^(-1).(1/(3+3x+x^2))+tan^(-1).(1/(7+...

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  16. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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  17. If cot ^(-1) ((n^(2) - 10n + 21*6)/pi) gt pi/6 , n in N , then find t...

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  18. Find the set of values of k for which x^(2) - kx + sin^(-1) ( sin 4) ...

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  19. Ifp > q > 0a n dp r < -1 < q r , then find the value of tan^(-1)((p-...

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  20. Number of solutions of the equation 2(sin^(-1)x)^2-sin^(-1)x-6=0 is

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