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1
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$y = {(\cos x)^{{{(\cos x)}^{(\cos x)\infty }}}}$$, then $${{dy} \over {dx}}$$ is equal to
A
$$ - {{{y^2}\tan x} \over {1 - y\ln (\cos x)}}$$
B
$${{{y^2}\tan x} \over {1 + y\ln (\cos x)}}$$
C
$${{{y^2}\tan x} \over {1 - y\ln (\sin x)}}$$
D
$${{{y^2}\tan x} \over {1 + y\ln (\sin x)}}$$
2
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following statements

1. Derivative of f(x) may not exist at some point.

2. Derivative of f(x) may exist finitely at some point.

3. Derivative of f(x) may be infinite (geometrically) at some point.

Which of the above statements are correct?
A
1 and 2 only
B
2 and 3 only
C
1 and 3 only
D
1, 2 and 3
3
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$y = {\cos ^ - }\left( {{{2x} \over {1 + {x^2}}}} \right)$$, then $${{dy} \over {dx}}$$ is equal to
A
$$ - {2 \over {1 + {x^2}}}$$ for all | x | < 1
B
$$ - {2 \over {1 + {x^2}}}$$ for all | x | > 1
C
$${2 \over {1 + {x^2}}}$$ for all | x | < 1
D
None of the above
4
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $${{{d^2}x} \over {d{y^2}}}$$ equal to ?
A
$$ - {\left( {{{{d^2}y} \over {d{x^2}}}} \right)^{ - 1}}{\left( {{{dy} \over {dx}}} \right)^{ - 3}}$$
B
$${\left( {{{{d^2}y} \over {d{x^2}}}} \right)^{ - 1}}{\left( {{{dy} \over {dx}}} \right)^{ - 2}}$$
C
$$ - \left( {{{{d^2}y} \over {d{x^2}}}} \right){\left( {{{dy} \over {dx}}} \right)^{ - 3}}$$
D
$${\left( {{{{d^2}y} \over {d{x^2}}}} \right)^{ - 1}}$$
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