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If `f` is continuous on `[0,1]` such that `f(x)+f(x+1/2)=1` and `int_0^1f(x)dx=k ,` then value of `2k` is 0 (2) 1 (3) 2 (4) 3

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. A tangent drawn to hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1at P((p...

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  2. Write the following sets in set-builder form (i) C={1,-1,i,-i}

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  3. If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int0^1f(x)dx...

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  4. If A & B are two rational numbers and AB, A + B and A -B are rational ...

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  5. Write the following sets in the set builder form: S={1,3,9, 27}

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  6. The distance of the point (1, -5, 9) from the plane x-y+z=5 measured a...

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  7. Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is...

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  8. Write the following sets in the set builder form: R={2,3,5,7}

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  9. Two concentric ellipses are such that the foci of one are on the other...

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  10. Write the relation R={(x , x^3): x is a prime number less than 10} in ...

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  11. Using laws of set algebra, show that If A 'uuB^=U , show that AsubB

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  12. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is such that its has th...

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  13. about to only mathematics

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  14. Using laws of set algebra, show that If AnnB^(prime)=varphi, show that...

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  15. If f(x)={x^2}, where {x} denotes the fractional part of x , then (a)f(...

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  16. Using properties of sets, show that(i) A uu( A nnB) = A (ii) A nn(A...

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  17. The coefficient of x^(24) in (1+x^(2))^(12)(1+x^(12))(1+x^(24)) is

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  18. Which of the following when simplified reduces to unity ?

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  19. For the ellipse (x^(2))/(4) + (y^(2))/(3) = 1 , the ends of the two ...

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  20. Determine the empty sets, singleton sets and pair sets in the followin...

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