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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_(n+1)=A_n` (b) `B_(n+1)=B_n` `A_(n+1)-A_n=B_(n+1)` (d) `B_(n+1)-B_n=A_(n+1)`

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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)

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

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot

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

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 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 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 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

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Consider I1=int0^(pi//4)e^(x^2)dx ,I2=int0^(pi//4)e^x dx ,I3=int0^(pi/...

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  2. lim(xto0)(sinx^(4)-x^(4)cosx^(4))/(x^(4)(e^(2x^(4))-1-2x^(4))) is

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

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  4. If A , B ,C are angles of a triangles, then the value of e^(2i A)e^(-i...

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  5. Sum of all the solutions of the equation : tan^2 33x = cos2x - 1 which...

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  6. Statement-1 : Let z be a complex number satisfying |z-3|lt=|z-1|,|z-3|...

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  7. If 0ltaltbltc and the roots alpha,beta of equation a"" x^2+b""x+c="0 a...

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  8. If a^2+b^2=1t h e n(1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

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  9. The graph of the function y=cos xcos(x+2)-cos^2(x+1) is: (A) &n...

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  10. If in a triangle A B C ,(a+b+c)(b+c-a)=kdotb c ,t h e n:

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  11. A round balloon of radius r subtends an angle at the eye of the observ...

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  12. If f^(prime)(1)=-2sqrt(2) and g^(prime)(sqrt(2))=4 , then the derivati...

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  13. Let a(n) be the nth term of an AP, if sum(r=1)^(100)a(2r)= alpha " and...

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  14. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx...

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  15. The fourth term of the sequence 1/(1+sqrt(x)),1/(1-x),1/(1-sqrt(x)), ...

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  16. At the point P (a,a^(n)) on the graph of y=x^(n),(n in N), in the firs...

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  17. Sum of all the numbers between 1 and 1000 which are divisible by 3 i...

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  18. int(cos^3x)/(sqrt(sin^7x))dx= (a) 2/5dotcos e c^(7/2)x+2sqrt(cose c ...

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  19. Given an A.P. whose terms are all positive integers. The sum of its fi...

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  20. Evaluate: int1/(sin^4x+cos^4x)dx

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