Determinants · Mathematics · NDA

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NDA Mathematics 21 April 2024
For what value of $n$ is the determinant $$\left|\begin{array}{ccc} C(9,4) & C(9,3) & C(10, n-2) \\ C(11,6) & C(11,5) & C(12, n) \\ C(m, 7) & C(m, 6)... NDA Mathematics 21 April 2024 If ABC is a triangle, then what is the value of the determinant$$ \left|\begin{array}{ccc} \cos C & \sin B & 0 \\ \tan A & 0 & \sin B \\ 0 & \tan (B+...
NDA Mathematics 21 April 2024
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 ...
NDA Mathematics 21 April 2024
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 $\begin{vmatrix} a & b & c \\... NDA Mathematics 3 September 2023 If$A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of det(I + AA'), where I is the 3 × 3 identity matrix?... NDA Mathematics 3 September 2023 If A, B and C are square matrices of order 3 and det(BC) = 2 det(A), then what is the value of det(2A-1BC)? NDA Mathematics 3 September 2023 Let A be a skew-symmetric matrix of order 3. What is the value of det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I) where I is the identit... NDA Mathematics 3 September 2023 If$A=\left[\begin{array}{rrr} 0 & 3 & 4 \\ -3 & 0 & 5 \\ -4 & -5 & 0 \end{array}\right]$, then which one of the following sta... NDA Mathematics 3 September 2023 If$\left|\begin{array}{ccc} x^2+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x \end{array}\right|$= a... NDA Mathematics 3 September 2023 If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is: NDA Mathematics 3 September 2023 If$A=\left[\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1 \end{array}\right]$, then what is the value of det[a... NDA Mathematics 3 September 2023 The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of deter... NDA Mathematics 3 September 2023 If$A_k=\left[\begin{array}{cc} k-1 & k \\ k-2 & k+1 \end{array}\right] $, then what is det(A1) + det(A2) + det(A3) + ... + det(A100... NDA Mathematics 3 September 2023 The function is decreasing on : NDA Mathematics 3 September 2023 The function attains local minimum value at : NDA Mathematics 16 April 2023 Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2α 3β, then what is the value of (α + β)? NDA Mathematics 16 April 2023 What is the sum of the roots of the equation$\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end...
NDA Mathematics 16 April 2023
If a, b, c are in AP, then what is \$\left|\begin{array}{lll} x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \\ x+a & x+b & x+c \end{a...
NDA Mathematics 16 April 2023
If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ?
NDA Mathematics 16 April 2023
If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ?
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