Home
Class 12
MATHS
IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,b...

`IfA_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,b_n=int_0^(pi/2)((sinn x)/(sinx))^2dxforn in N ,` Then (a) `A_(n+1)=A_n` (b) `B_(n+1)=B_n` (c) `A_(n+1)-A_n=B_(n+1)` (d) `B_(n+1)-B_n=A_(n+1)`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If A_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,B_n=int_0^(pi/2)((sinn x)/(sinx))^2 dx for n inN , Then (A) A_(n+1)=A_n (B) B_(n+1)=B_n (C) A_(n+1)-A_n=B_(n+1) (D) B_(n+1)-B_n=A_(n+1)

For any n in N, int_(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

For U_n=int_0^1x^n(2-x)^n dx ; V_n=int_0^1x^n(1-x)^ndxn in N , which of the following statement(s) is/are true? U_n=2^n V_n (b) U_n=2^(-n)V_n U_n=2^(2n)V_n (d) V_n=2^(-2n)U_n

If I_n=int_(pi/4)^(pi/2) (tanx)^-n dx(ngt1) , then I_n+I_(n+2)= (A) 1/(n-1) (B) 1/(n+1) (C) -1/(n+1) (D) 1/n-1

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 , then (a) b_(n) = 1+a_(n) (b) b_(n) = (-1)^(n)xxa_(n) (c) b_(n) = (-1)^(n-1) xxa_(n) (d) b_(n) + 1 = a_(n)

The value of int_0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

If sum_(r=1)^n r^4= a_n then sum_(r=1)^n(2r-1)^4)= (A) a_(2n)+a_n (B) a_(2n)-a_n (C) a_(2n)-16a_n (D) a_(2n)+16b_n

If n!=1, int_0^(pi/4) (tan^nx+tan^(n-2)x)d(x-[x])= (A) 1/(n-1) (B) 1/(n+1) (C) 1/n (D) 2/(n-1)

If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a. A_(n+1)=a A_n+b A_(n-1) b. A_(n+1)=b A_(n-1)+a A_n c. A_(n+1)=a A_n-b A_(n-1) d. A_(n+1)=b A_(n-1)-a A_n

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. The value of sin(pi/3-sin^(-1)(4/5)) is (a) (3sqrt(3)-4)/(10) (b) (3...

    Text Solution

    |

  2. "lim"(x->0)(ln(t a n(pi/4+a x)))/(sinb x),b!=0 is equal to (a)a/b (b...

    Text Solution

    |

  3. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

    Text Solution

    |

  4. Which of the following functions is periodic (a) cos^2x+sinx^3+"tan"...

    Text Solution

    |

  5. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  6. Projection of line (x+1)/2+(y+1)/(-1)=(z+3)/4 on the plane x+2y+z=6; h...

    Text Solution

    |

  7. Evaluate underset(xto0)lim(sin[cosx])/(1+[cosx]) ([.] denotes the grea...

    Text Solution

    |

  8. If [dot] represents the greatest integer function, then int4^(10)([x^2...

    Text Solution

    |

  9. Lim(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("sgn"x-cosx) (where {.} and sgn...

    Text Solution

    |

  10. int2^4((log)x2-(((log)2 2)^2)/(ln2))dx= 0 (b) 1 (c) 2 (d) 4

    Text Solution

    |

  11. The value of the integral int(-2)^2|1-x^2|dx is a.4 b. 2 c. -2 d. 0

    Text Solution

    |

  12. Prove that int(0)^(2)|x^(2)+2x-3|dx=4

    Text Solution

    |

  13. Let image of the line (x-1)/3=(y-3)/5=(z-4)/2 in the plane 2x-y+z+3=0 ...

    Text Solution

    |

  14. If f(x)={{:(e^(|x|+|x|-1)/(|x|+|x|),":",xne0),(-1,":",x=0):} (where [...

    Text Solution

    |

  15. Show that sin^(- 1)(sin((33pi)/7))+cos^(- 1)(cos((46pi)/7))+tan^-1(-ta...

    Text Solution

    |

  16. If [dot] denotes the greatest integer function, then (lim)(xvec0)x/a...

    Text Solution

    |

  17. prove "lim"(xvecoo)(ln x)/([x])="lim"(xvecoo)([x])/(ln x) where [.]...

    Text Solution

    |

  18. In which of the following function, range is not singleton set f(x)...

    Text Solution

    |

  19. If A is domain of f(x)=lntan^(-1)((x^3-6x^2+11 x-6)(x)(e^x-5) and B is...

    Text Solution

    |

  20. Let tan(2pi|sintheta|)=cot(2pi|costheta|) , where theta in R and f(x)...

    Text Solution

    |