1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$\widehat a$$ and $$\widehat b$$ of two unit vectors and $$\theta$$ be the angle between them.
What is $$\cos \left( {{\theta \over 2}} \right)$$ equal to ?
A
$${{\left| {\widehat a - \widehat b} \right|} \over 2}$$
B
$${{\left| {\widehat a + \widehat b} \right|} \over 2}$$
C
$${{\left| {\widehat a - \widehat b} \right|} \over 4}$$
D
$${{\left| {\widehat a + \widehat b} \right|} \over 4}$$
2
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$\widehat a$$ and $$\widehat b$$ of two unit vectors and $$\theta$$ be the angle between them.
What is $$\sin \left( {{\theta \over 2}} \right)$$ equal to ?
A
$${{\left| {\widehat a - \widehat b} \right|} \over 2}$$
B
$${{\left| {\widehat a + \widehat b} \right|} \over 2}$$
C
$${{\left| {\widehat a - \widehat b} \right|} \over 4}$$
D
$${{\left| {\widehat a + \widehat b} \right|} \over 4}$$
3
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$\alpha = \widehat i + 2\widehat j - \widehat k$$, $$\beta = 2\widehat i - \widehat j + 3\widehat k$$ and $$\gamma = 2\widehat i + \widehat j + 6\widehat k$$ be three vectors. If $$\alpha$$ and $$\beta$$ are both perpendicular to the vector $$\delta$$ and $$\delta \,.\,\gamma = 10$$, then what is the magnitude of $$\delta$$ ?
A
$$\sqrt 3 $$ units
B
$$2\sqrt 3 $$ units
C
$${{\sqrt 3 } \over 2}$$ unit
D
$${1 \over {\sqrt 3 }}$$ unit
4
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\widehat a$$ and $$\widehat b$$ are two unit vectors then the vector ($$\widehat a$$ + $$\widehat b$$) $$\times$$ ($$\widehat a$$ $$\times$$ $$\widehat b$$) is parallel to
A
($$\widehat a$$ $$-$$ $$\widehat b$$)
B
($$\widehat a$$ + $$\widehat b$$)
C
(2$$\widehat a$$ $$-$$ $$\widehat b$$)
D
(2$$\widehat a$$ + $$\widehat b$$)
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