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Engineering Maths · all questions

Calculus
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What is the value of the definite integral,

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The direction of vector A is radially outward from the origin, with |A| = krn where r2 = x2 + y2 + z2 and k is a constant. The value of n for which   is

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The angle of intersection of the curves x2 = 4y and y2 = 4x at point (0, 0) is

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The expression e-n x for x > 0 is equal to

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While minimizing the function f(x), necessary and sufficient conditions for a point x0 to be a minima are

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The function f(x) = x2 = x + x ...... x times, is defined

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The position vector  of P(20, 10) is rotated anti-clockwise in X-Y plane by an angle θ = 30° such that the point P occupies position Q, as shown in the figure. The coordinates (x, y) of Q are
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If z = xy n(xy), then

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If and are two arbitrary vectors with magnitudes a and b, respectively,  will be equal to

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The value of the integral given below is

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Velocity vector of a flow field is given as   The vorticity vector at (1, 1, 1) is

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If is the position vector of any point on a closed surface S that encloses volume V then  is equal to

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