Home
Class 12
MATHS
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 `f(x) lt 0` for `-1 le x le 1`, then 'a' satisfies

A

`(-(pi)/(2), (pi)/(2))`

B

`(0, (3pi)/(2))`

C

`((pi)/(6), (7pi)/(6))`

D

`((7pi)/(6), (11pi)/(6))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Solved Examples : Single Option Correct Type Questions|2 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|10 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

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

If f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 then :

If "sin "3theta = 4"sin" theta("sin"^(2) x-"sin"^(2)theta), theta ne npi, n in Z . Then, the set of values of x, is

If f(x)=(2x)/(1+x^2)\ , show that f(tantheta)=sin2theta)

Let |f (x)| le sin ^(2) x, AA x in R, then

Solve the equation for 0 le x le 2pi. sin theta cos theta = (1)/(2)

If f(x)=|{:( sin^2 theta , cos^(2) theta , x),(cos^(2) theta , x , sin^(2) theta ),( x , sin^(2) theta , cos^2 theta ):}| theta in (0,pi//2), then roots of f(x)=0 are

If cos theta = (2x)/(1+x^2) , find the values of sin theta and cot theta [Given x^2 lt 1 ]

The tangents to the curve x=a(theta - sin theta), y=a(1+cos theta) at the points theta = (2k+1)pi, k in Z are parallel to :

If f(x)=(1-x^(2))/(1+x^(2)) , then prove that: f(tan theta)=cos 2theta

ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider, f(x)=(x+2a)(x+a-4)(a in R), g(x)=k(x^(2)+x)+3k+x(k in R) a...

    Text Solution

    |

  2. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  3. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

    Text Solution

    |

  4. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  5. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

    Text Solution

    |

  6. The number of all possible values of theta, where 0 lt theta lt pi, fo...

    Text Solution

    |

  7. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

    Text Solution

    |

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

    Text Solution

    |

  9. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)^(...

    Text Solution

    |

  10. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |