1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
For what value of $n$ is the determinant

$$ \left|\begin{array}{ccc} C(9,4) & C(9,3) & C(10, n-2) \\ C(11,6) & C(11,5) & C(12, n) \\ C(m, 7) & C(m, 6) & C(m+1, n+1) \end{array}\right|=0 $$

for every $m>n$ ?
A

4

B

5

C

6

D

7

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If ABC is a triangle, then what is the value of the determinant

$$ \left|\begin{array}{ccc} \cos C & \sin B & 0 \\ \tan A & 0 & \sin B \\ 0 & \tan (B+C) & \cos C \end{array}\right| ? $$

A

-1

B

0

C

1

D

3

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If $a, b, c$ are the sides of a triangle $ABC$, then what is $$ \begin{vmatrix} a^2 & b \sin A & c \sin A \\ b \sin A & 1 & \cos A \\ c \sin A & \cos A & 1 \end{vmatrix}$$ equal to?

A

Zero

B

Area of triangle

C

Perimeter of triangle

D

$a^2 + b^2 + c^2$

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If in a triangle $ABC$, $\sin^3A + \sin^3B + \sin^3C = 3\sin A \sin B \sin C$, then what is the value of the determinant $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$, where $a$, $b$, $c$ are sides of the triangle?

A

$a + b + c$

B

$ab + bc + ca$

C

$(a + b)(b + c)(c + a)$

D

0

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