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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 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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  2. int1^2 1/(x(x^4+1))dx =

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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. The area {(x ,y); x^2lt=ylt=sqrt(x)} is equal to 1/3 b. 2/3 c. 1/6 d. ...

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  5. "I f"|(z1-3z2)/(3-z1 bar(z2))|=1"and"|z2|!=1,t h e n|z1|"i s" 3 (b) ...

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  6. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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  7. If alpha and beta are the roots of x^2-2x+4=0 , then alpha^n+beta^n is...

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  8. Let |z1|=|"z"2|="p"/2 then "|z1+z2|^2+|z1-z2|^2= a.p^2 b. (p^2)...

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  9. If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z...

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  10. Show that the relation geq on the set R of all real numbers is r...

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  11. The polar form of the complex number (i^(25))^3 is (a) cos(pi/2)+isin(...

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  12. ((1+sintheta+i costheta)/(1+sintheta-i costheta))^n is equal to

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  13. If 3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100) and x=k y then k is: a.-...

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  14. If(5z2)/(7z1) is purely imaginary, then |(2z1+3z2)/(2z1-3z2)|= (A)...

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  15. If complex number (3+2i sin x)/(1-2i sin x) is purely imaginary then ...

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  16. Let z be a complex number having the argument theta,0<theta<pi//2,a n ...

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  17. If the area of the triangle on the complex plane formed by the points ...

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  18. If alpha + beta + gamma = pi, then the value of the determinant |(e^...

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  19. If vec a is perpendicular to vec b and vec r is non-zero vector suc...

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  20. int(1+x^4)/((1-x^4)^(3/2))dx i s e q u a l to 1/(sqrt(...

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