Calculus - Study Mode
[#91] Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant det [left[ {x08egin{array}{*{20}{c}}
{ < { ext{x}},{ ext{x}} > }&{ < { ext{x}},{ ext{y}} > } \
{ < { ext{y}},{ ext{x}} > }&{ < { ext{y}},{ ext{y}} > }
end{array}}
ight].]
Correct Answer
(B) is positive when x and yare linearly independent
[#92] $$mathop {{ ext{Lim}}}limits_{{ ext{x}} o infty } left( {frac{{{ ext{x}} + sin { ext{x}}}}{{ ext{x}}}}
ight)$$ xa0 xa0equal to
Correct Answer
(C) 1
[#93] For a vector E, which one of the following statements is NOT TRUE ?
Correct Answer
(D) If $$
abla $$ · E = 0, E is called irrotational
[#94] Which one of the following functions is continuous at x = 3?
Correct Answer
(A) [{ ext{f}}left( { ext{x}}
ight) = left{ {x08egin{array}{*{20}{c}}
{2,}&{{ ext{if}}}&{{ ext{x}} = 3} \
{{ ext{x}} - 1,}&{{ ext{if}}}&{{ ext{x}} > 3} \
{frac{{{ ext{x}} + 3}}{3},}&{{ ext{if}}}&{{ ext{x}} < 3}
end{array}}
ight.]
[#95] If A(0, 4, 3), B(0, 0, 0) and C(3, 0, 4) are three points defined in x, y, zeo-ordinate system, then which of the following vector is perpendicular to both vectors [overrightarrow {{ ext{AB}}} ] xa0and [overrightarrow {{
m{BC}}} .]
Correct Answer
(C) [16{
m{hat i}} - 9{
m{hat j}} - 12{
m{hat k}}]