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
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
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?
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?
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
Questions Asked from Determinants (Marks 2.5)
Number in Brackets after Paper Indicates No. of Questions
NDA Subjects
Mathematics
Algebra
Sets, Relations and Functions Logarithms Quadratic Equations and Inequalities Sequence And Series Binomial Theorem Matrices Determinants Permutations and Combinations Probability Complex Numbers Vector Algebra Three Dimensional Geometry Statistics
Trigonometry
Trigonometric Angles and Equations Inverse Trigonometric Function Height and Distance Properties of Triangles
Coordinate Geometry
Calculus
English
General Studies