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The minimum integral value of `alpha` for which the quadratic equation `(cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0` has both positive roots

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VMC MODULES ENGLISH-INVERSE TRIGONOMETRY-LEVEL-2
  1. If x and y are positive integers such that tan^(-1)x+cot^(-1)y=tan^(-...

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  2. If cos^(-1)((7)/(|x|))+cos^(-1)((4sqrt(15))/(|x|))=(pi)/(2), then:

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  3. For the equation 2x=tan(2tan^(-1)a)+2 t a n(tan^(-1)a+tan^(-1)a^3) , w...

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  4. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to...

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  5. cos^(-1)x=tan^(-1)x then

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  6. Which of the following is/are correct?

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  7. Let x1,x2,x3,x4 be four non zero numbers satisfying the equation tan^...

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  8. The least value of n for which (n -2) x^(2) + 8 x + n + 4 gt sin^...

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  9. For x,y,z,t in R, if sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)*...

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  10. Let f(x)=(1)/(pi) (sin^(-1)x+cos^(-1)x+tan^(-1)x)+((x+1))/(x^(2)+2x+10...

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  11. The number of rational numbers in the domain of function y=sin^(-1)...

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  12. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2), then A=x^(2)+y^(2)+z^(2)....

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  13. Match the Column I with Column II and mark the correct option from the...

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  14. Let t(1)= (sin^(-1)x)^(sin^(-1)x),t(2)= (sin^(-1) x)^(cos^(-1)x),t(3) ...

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  15. If cos^(-1)(4x^3-3x)=a+bcos^(-1)x" for "-1 lt x lt -1/2, then [a + b+ ...

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  16. The minimum integral value of alpha for which the quadratic equation (...

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  17. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0 when...

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  18. The sum to infinite terms of the series cot^(- 1)(2^2+1/2)+cot^(- 1)(2...

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  19. Sum of infinite terms of the series cos^(-1) ( 1^(2) + 3/4) + cot^(-...

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

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