1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If A is an invertible matrix of order n and k is any positive real number, then the value of $${[\det (kA)]^{ - 1}}\det (A)$$ is
A
k$$-$$ n
B
k$$-$$ 1
C
kn
D
nk
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If the value of the determinant $$\left| {\matrix{ a & 1 & 1 \cr 1 & b & 1 \cr 1 & 1 & c \cr } } \right|$$ is positive, where a $$\ne$$ b $$\ne$$ c, then the value of abc
A
cannot be less than 1
B
is greater than $$-$$ 8
C
is less than $$-$$ 8
D
must be greater than 8
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following statements in respect of the determinant $$\left| {\matrix{ {{{\cos }^2}{\alpha \over 2}} & {{{\sin }^2}{\alpha \over 2}} \cr {{{\sin }^2}{\beta \over 2}} & {{{\cos }^2}{\beta \over 2}} \cr } } \right|$$ where $$\alpha$$, $$\beta$$ are complementary angles.

1. The value of the determinant is $${1 \over {\sqrt 2 }}\cos \left( {{{\alpha - \beta } \over 2}} \right)$$.

2. The maximum value of the determinant is $${1 \over {\sqrt 2 }}$$.

Which of the above statement(s) is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If a, b, c are real numbers, then the value of the determinant $$\left| {\matrix{ {1 - a} & {a - b - c} & {b + c} \cr {1 - b} & {b - c - a} & {c + a} \cr {1 - c} & {c - a - b} & {a + b} \cr } } \right|$$ is
A
0
B
(a $$-$$ b) (b $$-$$ c) (c $$-$$ a)
C
(a + b + c)2
D
(a + b + c)3
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