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int(0)^(pi//2)(sin^(1000)xdx)/(sin^(1000...

`int_(0)^(pi//2)(sin^(1000)xdx)/(sin^(1000)x+cos^(1000)x)` is equal to

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The correct Answer is:
C
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HIMALAYA PUBLICATION-COMMON ENTRANCE TEST -2016-QUESTION BANK
  1. If x^(m)y^(n) = (x + y)^(m +n) then (dy)/(dx) is equal to

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  2. The differential coefficient of log(10)x with respect to log(x)10 is

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  3. int(0)^(pi//2)(sin^(1000)xdx)/(sin^(1000)x+cos^(1000)x) is equal to

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  4. The value of fe^(x)(x^(2)tan^(-1) x + tan^(-1) x + 1)/(x^(2) + 1) dx ...

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  5. The 11^(th) term in the expansion of (x+(1)/(sqrt(x)))^(14) is

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  6. The general solution of cot theta + tan theta = 2 is

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  7. If A = [{:(cos 2thet,,-sin 2theta),(sin 2theta,, cos 2theta):}] and A ...

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  8. If A is matrix of order m xx n and B is a matrix such that AB' and B'A...

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  9. The value of 1sin^(-1)(cos(53pi)/(5)) is

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  10. If 2 vec a . vec b = |vec a|.|vec b| then the between vec a and vec b ...

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  11. If 1 + sin theta + sin^(2)theta + … upto oo 2sqrt(3) + 4, then theta =

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  12. The function f(x) = [x] where [x] is the greatest integer function is ...

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  13. Let f: R rarrR be defined by f(x)=2x+6 which is bijective mapping then...

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  14. If cos alpha, cos beta, cos gamma are the direction cosines fo a vecto...

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  15. Write the converse and contrapositive of the statement " If x ...

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  16. The value of int(-pi//4)^(pi//4) sin^(103) x*cos^(101) xdx is

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  17. If a = 3,b = 4, c = 5 each one of vec a, vec b and vec c is perpendicu...

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  18. Suppose vec a + vec b + vec c = 0, |vec a| = 3, |vec b| = 5, |vec c| =...

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  19. If x^(y) = e^(x-y) then (dy)/(dx) is equal to

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  20. If P(AnnB)=7//10andP(B)=17//20, where P stands for probability then P(...

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