91
Minimum of the real valued function \[{\rm{f}}\left( {\rm{x}} \right) = {\left( {{\rm{x}} - 1} \right)^{\frac{2}{3}}}\] occurs at x equal to
A)
\[ - \infty \]
B)
0
C)
1
D)
\[\infty \]
Answer & Solution
Answer: Option
C
92
Given the following statements about a function f : R → R , select the right option:0 , then it is differential at x = x0 .0 , then it may not be differentiable at x = x0 .0 , then it is also continuous at x = x0 .
A)
P is true, Q is false, R is false
B)
P is false, Q is true, R is true
C)
P is false, Q is true, R is false
D)
P is true, Q is false, R is true
Answer & Solution
Answer: Option
B
93
The integral \[\frac{1}{{\sqrt {2\pi } }}\int\limits_{ - \infty }^\infty {{{\rm{e}}^{ - \frac{{{x^2}}}{2}}}} {\rm{dx}}\] is equal to
A)
\[\frac{1}{2}\]
B)
\[\frac{1}{{\sqrt 2 }}\]
C)
1
D)
\[\infty \]
Answer & Solution
Answer: Option
C
94
The area of a triangle formed by the tips of vectors \[\overline {\rm{a}} {\rm{,}}\,\overline {\rm{b}} \] and \[\overline {\rm{c}} \] is
A)
\[\frac{1}{2}\left( {\overline {\rm{a}} - \overline {\rm{b}} } \right) \cdot \left( {\overline {\rm{a}} - \overline {\rm{c}} } \right)\]
B)
\[\frac{1}{2}\left| {\left( {\overline {\rm{a}} - \overline {\rm{b}} } \right) \times \left( {\overline {\rm{a}} - \overline {\rm{c}} } \right)} \right|\]
C)
\[\frac{1}{2}\left| {\overline {\rm{a}} \times \overline {\rm{b}} \times \overline {\rm{c}} } \right|\]
D)
\[\frac{1}{2}\left( {\overline {\rm{a}} \times \overline {\rm{b}} } \right) \cdot \overline {\rm{c}} \]
Answer & Solution
Answer: Option
B
95
For real x the maximum value of \[\frac{{{{\text{e}}^{\sin {\text{x}}}}}}{{{{\text{e}}^{\cos {\text{x}}}}}}\] is
A)
1
B)
e
C)
\[{{\text{e}}^{\sqrt 2 }}\]
D)
\[\infty \]
Answer & Solution
Answer: Option
C
96
Which of the following is not associated with vector calculus?
A)
Stoke's theorem
B)
Gauss Divergence theorem
C)
Green's theorem
D)
Kennedy's theorem
Answer & Solution
Answer: Option
D
97
The series \[\sum\limits_{{\text{m}} = 0}^\infty {\frac{1}{{{4^{\text{m}}}}}{{\left( {{\text{x}} - 1} \right)}^{2{\text{m}}}}} \] converges for
A)
-2 < X < 2
B)
-1 < X < 3
C)
-3 < X < 1
D)
X < 3
Answer & Solution
Answer: Option
B
98
f(x, y) is a continuous function defined over (x, y) \[ \in \] [0, 1] × [0, 1]. Given the two constraints, x > y2 and y > x2 , the volume under f(x, y) is
A)
\[\int\limits_{{\text{y}} = 0}^{{\text{y}} = 1} {\int\limits_{{\text{x}} = {{\text{y}}^2}}^{{\text{x}} = \sqrt {\text{y}} } {{\text{f}}\left( {{\text{x,}}\,{\text{y}}} \right){\text{dx dy}}} } \]
B)
\[\int\limits_{{\text{y}} = {{\text{x}}^2}}^{{\text{y}} = 1} {\int\limits_{{\text{x}} = {{\text{y}}^2}}^{{\text{x}} = 1} {{\text{f}}\left( {{\text{x,}}\,{\text{y}}} \right){\text{dx dy}}} } \]
C)
\[\int\limits_{{\text{y}} = 0}^{{\text{y}} = 1} {\int\limits_{{\text{x}} = 0}^{{\text{x}} = 1} {{\text{f}}\left( {{\text{x,}}\,{\text{y}}} \right){\text{dx dy}}} } \]
D)
\[\int\limits_{{\text{y}} = 0}^{{\text{y}} = \sqrt {\text{x}} } {\int\limits_{{\text{x}} = 0}^{{\text{x}} = \sqrt {\text{y}} } {{\text{f}}\left( {{\text{x,}}\,{\text{y}}} \right){\text{dx dy}}} } \]
Answer & Solution
Answer: Option
A
99
The value of \[\int\limits_0^{\frac{\pi }{6}} {{{\cos }^4}3\theta \,{{\sin }^3}6\theta \,{\text{d}}\theta } \] is
A)
0
B)
\[\frac{1}{{15}}\]
C)
1
D)
\[\frac{8}{3}\]
Answer & Solution
Answer: Option
B
100
Which one of the following is NOT a correct statement?
A)
The function \[\sqrt[{\text{x}}]{{\text{x}}}\],(x > 0), has the global minima at x = e
B)
The function \[\sqrt[{\text{x}}]{{\text{x}}}\],(x > 0), has the global maxima at x = e
C)
The function x3 has neither global minima nor global maxima
D)
The function |x| has the global minima at x = 0
Answer & Solution
Answer: Option
A
