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Consider I1=int0^(pi/4)e^x^2dx ,I2=int0^...

Consider `I_1=int_0^(pi/4)e^x^2dx ,I_2=int_0^(pi/4)e^x dx ,I_3=int_0^(pi/4)e^x^2cosxdx ,I_4=int_0^(pi/4)e^x^2sinxdxdot` STATEMENT 1 : `I_2> I_1> I_3> I_4` STATEMENT 2 : For `x in (0,1),x > x^2a n dsinx >cosxdot`

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Let I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).sin x dx , then :

(i) int_0^(pi/2) sin^2 x dx (ii) int_0^(pi//2) cos^2 x dx

I=int_(0)^(1)e^(x^(2)-x)dx then

If I_(1)=int_(0)^(pi//2)"x.sin x dx" and I_(2)=int_(0)^(pi//2)"x.cos x dx" , then

(i) int_0^(pi//4) tan x dx (ii) int_(pi//4)^(pi//2) cot x dx

I_(1)=int_(0)^((pi)/2)In (sinx)dx, I_(2)=int_(-pi//4)^(pi//4)In(sinx+cosx)dx . Then

(i) int_0^(pi//4) sec x dx (ii) int_(pi//6)^(pi//4) cosec x dx

If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx. then

RESONANCE DPP-JEE MAINS-All Questions
  1. If z1,z2,z3,z4 be the vertices of a parallelogram taken in anticlockwi...

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  2. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

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  3. Consider I1=int0^(pi/4)e^x^2dx ,I2=int0^(pi/4)e^x dx ,I3=int0^(pi/4)e^...

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  4. (lim)(xvec0)(s in x^4-x^4cos x^4)/(x^4(e^(2x)^4-1-2x^4)) 1/3 b. 1/2 c...

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  5. If An=int0^(pi/2)(sin(2n-1)x)/(s in x)"dx";"B""n"=int0^("pi"/2)(("s i ...

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

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

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

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

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

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

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  12. If in a triangle A B C ,(a+b+c)(b+c-a)=kdotb c ,t h e n : k<0 b. k >6...

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  13. A round balloon of radius r subtends an angle alpha at the eye of the ...

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  14. If f^(prime)(1)=-2sqrt(2)a n dg^(prime)(sqrt(2))=4 , then the derivati...

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  15. Let an be the n^(t h) term of an A.P. If sum(r=1)^(100)a(2r)=alpha&su...

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  16. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec ax...

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  17. A normal is drawn at point P(a ,a^n) on the curve =x^n in the first qu...

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

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

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

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