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For the equation (e ^(-x))/(1+x)= lamda ...

For the equation `(e ^(-x))/(1+x)= lamda` which of the following statement (s) is/are correct ?

A

When `lamda in (0,oo)` equation has 2 real and distinct roots

B

When `lamda , in (-oo,- e^(2))` equation has 2 real and istinct roots

C

When `lamda in (0,oo) ` equation hs 1 real root

D

When `lamda in (-e,0)` equation has no real root

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The correct Answer is:
B, C, D
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VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )
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  6. Find the gradient of the line passing through the point (2,8) and touc...

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  7. The equation x + cos x = a has exactly one positive root. Complete set...

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  8. Given that f (x) is a non-constant linear function. Then the curves :

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  9. f (x) = int (0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt ...

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  11. Which of the following graphs represent function whose derivatives hav...

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  12. Consider f (x)= sin ^(5) x-1, x in [0, (pi)/(2)], which of the followi...

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  13. If f(x)=x^(alpha)log x and f(0)=0, then the value of 'alpha' for which...

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  14. Which of the following is/are true for the function f(x)= int (0) ^(x)...

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  15. Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a ...

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  16. Let f (x) = {{:(x ^(3)+x^(2)-10x,,, -1 le x lt 0),( sin x ,,, 0 le x l...

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  17. Minimum distance between the curves y ^(2) =x-1 and x ^(2) =y -1 is eq...

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  18. For the equation (e ^(-x))/(1+x)= lamda which of the following stateme...

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  19. If y = m x +5 is a tangent to the curve x ^(3) y ^(3) = ax ^(3) +by^(...

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  20. If (f(x)-1) (x ^(2) + x+1)^(2) -(f (x)+1) (x^(4) +x ^(2) +1) =0 AA x...

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