Home
Class 12
MATHS
If Delta(x)=|[sin2x, e^x sinx+x cosx, si...

If `Delta(x)=|[sin2x, e^x sinx+x cosx, sinx+x^2 cosx] , [cosx+sinx, e^x+x, 1+x^2] , [e^x cosx, e^2x, e^x]|` then

A

f(x) is increasing for `forall x in (0,(pi)/(2))`

B

f(x) is non-increasing for `forall x in (0,(pi)/(2))`

C

f(x) is decreasing for `forall x in (0,(pi)/(2))`

D

f(x) is decreasing for `forall x in (0,(- pi)/(2),0)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -1 CONCEPT BUILDER|65 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

  • DIFFERENTIAL EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

((sinx - x cosx)/(x sinx + cos x ))

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

int_(0)^(pi//2) e^x(sinx+cosx) dx

inte^(x)(sinx-cosx)/(sin^(2)x)dx=

∫e^x (Cosx + Sinx) dx

lim_(x rarr0)(e^(x)-sinx + cosx - 2)/x^(2)

If delta(x)=|[1,cosx,1-cosx],[1+sinx,cosx,1+sinx-cosx],[sinx,sinx,1]|, then int_0^(pi/2)delta(x)dx is equal to

int(e^x(1-sinx))/(1-cosx)dx

Slove (2sinx-cosx)(1+cosx)=sin^2x

The value of 3(sinx - cosx)^4 + 6(sinx + cosx)^2 + 4 (sin^6 x + cos^6 x) is

DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
  1. If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

    Text Solution

    |

  2. The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...

    Text Solution

    |

  3. The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...

    Text Solution

    |

  4. If a^(2)+b^(2)+c^(2)=-2 and |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((...

    Text Solution

    |

  5. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  6. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  7. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

    Text Solution

    |

  8. the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...

    Text Solution

    |

  9. f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...

    Text Solution

    |

  10. If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then

    Text Solution

    |

  11. If the system of linear equations x1 + 2x2 + 3x3 = 6, x1 + 3x2 + 5x3 =...

    Text Solution

    |

  12. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

    Text Solution

    |

  13. Let A=[a(ij)](3xx3) be such that a(ij)=[{:(3, " when",hati=hatj),(0,,h...

    Text Solution

    |

  14. Let lambda "and" alpha be real. Let S denote the set of all values of ...

    Text Solution

    |

  15. Prove that the value of each the following determinants is zero: |s...

    Text Solution

    |

  16. For what value of p, is the system of equation p^3x+(p+1)^3y=(p+2)^3 a...

    Text Solution

    |

  17. If the sides of a DeltaABC and a, b, c and |{:(a^(2),b^(2),c^(2)),((a+...

    Text Solution

    |

  18. Supposealpha ,beta , gamma in R are such that sin alpha, sin beta , s...

    Text Solution

    |

  19. If Delta(x)=|[sin2x, e^x sinx+x cosx, sinx+x^2 cosx] , [cosx+sinx, e^x...

    Text Solution

    |

  20. Given that matrix A[(x,3,2),(1,y,4),(2,2,z)]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |