1
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $${x^2} - (1 - 2{a^2})x + (1 - 2{a^2}) = 0$$.
Under what condition does the above equation have real roots?
A
$${a^2} < {1 \over 2}$$
B
$${a^2} > {1 \over 2}$$
C
$${a^2} \le {1 \over 2}$$
D
$${a^2} \ge {1 \over 2}$$
2
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $${x^2} - (1 - 2{a^2})x + (1 - 2{a^2}) = 0$$.
Under what condition is $${1 \over {{\alpha ^2}}} + {1 \over {{\beta ^2}}} < 1$$?
A
$${a^2} < {1 \over 2}$$
B
$${a^2} > {1 \over 2}$$
C
$${a^2} > 1$$
D
$${a^2} \in \left( {{1 \over 3},{1 \over 2}} \right)$$ only
3
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Read the following information carefully and answer the questions given below.

2x2 + 3x $$-$$ $$\alpha$$ = 0 has roots $$-$$2 and $$\beta$$ while the equation x2 $$-$$ 3mx + 2m2 = 0 has both roots positive, where $$\alpha$$ > 0 and $$\beta$$ > 0.
What is the value of $$\alpha$$?
A
$${1 \over 2}$$
B
1
C
2
D
4
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Read the following information carefully and answer the questions given below.

2x2 + 3x $$-$$ $$\alpha$$ = 0 has roots $$-$$2 and $$\beta$$ while the equation x2 $$-$$ 3mx + 2m2 = 0 has both roots positive, where $$\alpha$$ > 0 and $$\beta$$ > 0.
If $$\beta$$, 2, 2 m are in GP, then what is the value of $$\beta$$$$\sqrt m $$?
A
1
B
2
C
4
D
6
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