Exam Details
2022 Mathematics
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Questions
120
Duration
180 mins
Package
Combined SO (Grade B) LDC Examination - Previous Year Papers
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120questions
Medium
40
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40
33.3%
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120questions
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2022 · Unclassified
2022 Mathematics
If \( \Delta₁ = \begin{vmatrix} 1 & p & q \\ 1 & q & r \\ 1 & r & p \end{vmatrix} \) and \( \Delta₂ = \begin{vmatrix} 1 & 1 & 1 \\ q & r & p \\ r & p & q \end{vmatrix} \) where \( p \neq q \neq r \), then \( \Delta₁ + \Delta₂ \) is
2022 · Unclassified
2022 Mathematics
If \( (a - b)(b - c)(c - a) = 2 \) and \( abc = 6 \), then what is the value of \( \begin{vmatrix} a & b & c \\ a² & b² & c² \\ a³ & b³ & c³ \end{vmatrix} \) ?
2022 · Unclassified
2022 Mathematics
Under which of the following conditions does the determinant \( \begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix} \) vanish ?
1. \( a + b + c = 0 \)
2. \( a³ + b³ + c³ = 3abc \)
3. \( a² + b² + c² - ab - bc - ca = 0 \)
Select the correct answer using the code given below :
2022 · Unclassified
2022 Mathematics
Consider the following in respect of the matrices :
\( A = [m \ n], B = [-n \ -m] \) and \( C = \begin{bmatrix} m \\ -m \end{bmatrix} \)
1. \( CA = CB \)
2. \( AC = BC \)
3. \( C(A + B) = CA + CB \)
Which of the above statements is/are correct ?
2022 · Unclassified
2022 Mathematics
If \( A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2 \cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix} \), then what is \( A(adjA) \) equal to ?
where \( I \) is the identity matrix.
2022 · Unclassified
2022 Mathematics
For what value of \( k \) is the matrix \( \begin{bmatrix} 2 \cos 2\theta & 2 \cos 2\theta & 6 \\ 1 - 2 \sin² \theta & 2 \cos² \theta - 1 & 3 \\ k & 2k & 1 \end{bmatrix} \) singular ?