1
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\alpha$$, $$\beta$$ and $$\gamma$$ are the angles which the vector OP (O being the origin) makes with positive direction of the coordinate axes, then which of the following are correct?

1. $${\cos ^2}\alpha + {\cos ^2}\beta = {\sin ^2}\gamma $$

2. $${\sin ^2}\alpha + {\sin ^2}\beta = {\cos ^2}\gamma $$

3. $${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma = 2$$

Select the correct answer using the code given below.
A
1 and 2 only
B
2 and 3 only
C
1 and 3 only
D
1, 2, and 3
2
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The point of intersection of the line joining the points ($$-$$3, 4, $$-$$8) and (5, $$-$$6, 4) with XY-plane is
A
$$\left( {{7 \over 3}, - {8 \over 3},0} \right)$$
B
$$\left( { - {7 \over 3}, - {8 \over 3},0} \right)$$
C
$$\left( { - {7 \over 3},{8 \over 3},0} \right)$$
D
$$\left( {{7 \over 3},{8 \over 3},0} \right)$$
3
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If the angle between the lines whose direction ratios are (2, $$-$$1, 2) and is $${\pi \over 4}$$, then the smaller value of x is
A
52
B
4
C
2
D
1
4
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B, and C respectively. The locus of the centre of the sphere OABC, O being the origin, is
A
$${x \over a} + {y \over b} + {z \over c} = 1$$
B
$${a \over x} + {b \over y} + {c \over z} = 1$$
C
$${a \over x} + {b \over y} + {c \over z} = 2$$
D
$${x \over a} + {y \over b} + {z \over c} = 2$$
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