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For some integer k, i^(4k)+i^(4k+1)+i^(4...

For some integer `k, i^(4k)+i^(4k+1)+i^(4k+2)+i^(4k+3)` = ..........

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The correct Answer is:
zero
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Knowledge Check

  • The distance between the line bar r = 2 hat i - 2 hat j + 3 hat k + lambda(hat i - hat j + 4 hat k) and the plane bar r. (hat i + 5 hat j + hat k) = 5 is..........

    A
    `3/10`
    B
    `10/3`
    C
    `10/9`
    D
    `10/(3(sqrt(3)))`

  • hat(i). ( hat(k) xx hat(j)) + hat(j) .(hat(i) xx hat(k) ) + hat(k). ( hat(j) xx hat(i) ) + hat(i). (hat(i) xx hat(j) ) + hat(j) . ( hat(j) xx hat(k) ) =...........

    A
    `-1`
    B
    `1`
    C
    `3`
    D
    `-3`

  • The equation of the plane passing through the point hat i + 2 hat j + - hat k and perpendicular to the intersection line of the planes bar r . ( 3 hat i - hat j + hat k) = 1 and bar (hat i + 4 hat j - 2 hat ) = 2 is.............

    A
    `bar(r) . (2 hat i - 7 hat j - 13 hat k) = 1`
    B
    `bar r. (2 hat i - 7 hat j - 13 hat k) = 1`
    C
    `bar r. (2 hat i - 7 hat j -13 hat) = 1`
    D
    None of these

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    Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : If k + 2, 4k - 6, 3k - 2 are three consecutive terms of an AP, then k = ..........

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