Calculus - Study Mode

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[#166] At t = 0, the function [{ ext{f}}left( { ext{t}}
ight) = frac{{sin { ext{t}}}}{{ ext{t}}}] xa0 has

(A) a minimum

(B) a discontinuity

(C) a point of inflection

(D) a maximum

Correct Answer

(D) a maximum

[#167] A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x 4 - 16x 3 - 24x 2 + 37 is

(A) 0

(B) 1

(C) 2

(D) 3

Correct Answer

(D) 3

[#168] If P, Q and R are three points having coordinates (3, -2, -1), (1, 3, 4), (2, 1, -2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

(A) 3

(B) 5

(C) 7

(D) 9

Correct Answer

(A) 3

[#169] The value of the integral [intlimits_0^2 {frac{{{{left( {{ ext{x}} - 1}
ight)}^2}sin left( {{ ext{x}} - 1}
ight)}}{{{{left( {{ ext{x}} - 1}
ight)}^2} + cos left( {{ ext{x}} - 1}
ight)}}} { ext{dx}}] xa0 xa0 xa0is

(A) 3

(B) 0

(C) -1

(D) -2

Correct Answer

(B) 0

[#170] Stokes theorem connects

(A) a line integral and a surface integral

(B) a surface integral and a volume integral

(C) a line integral and a volume integral

(D) gradient of a function and its surface integral

Correct Answer

(A) a line integral and a surface integral