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Consider, f(x)=(x+2a)(x+a-4)(a in R), ...

Consider, `f(x)=(x+2a)(x+a-4)(a in R)`,
`g(x)=k(x^(2)+x)+3k+x(k in R)` and
`h(x)=(1-sin theta)x^(2)+2(1-sin theta)x-3 sin theta`
`( theta in R-(4n+1)(pi)/(2), n in I)`
If `g(x) gt-3` for all real x, then the values of k are given by

A

`-1 lt k lt 1/11`

B

`-1 lt k lt 0`

C

`0 lt k lt 1/22`

D

`k lt 1/11`

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
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  7. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

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  8. If sin^ 4 x/2+cos^4 x/3 =1/5 then

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  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

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  12. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

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  13. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

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  14. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

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  15. If A = sin^2x + cos^4 x, then for all real x :

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  16. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

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  18. A triangular park is enclosed on two sides by a fence and on the third...

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  19. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

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  20. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

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