Determinants
If A = $\left[\begin{array}{cc}2& 3\\ 4& 1\end{array}\right],$ then adj (3A^{2} + 12A) is equal to
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JEE Mains 2017
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JEE Advanced 2012
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JEE 2010
Consider the following linear equations:
ax + by + cz = 0
bx + cy + az = 0
cx + ay + bz = 0
Match the conditions/ expressions in Column I with statements in Column II and indicate your answers by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
ax + by + cz = 0
bx + cy + az = 0
cx + ay + bz = 0
Match the conditions/ expressions in Column I with statements in Column II and indicate your answers by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
Column I 
Column II 

(A) 
a + b + c ≠ 0 and a^{2} + b^{2} + c^{2} = ab + bc + ca  (p) 
The equations represent planes meeting only at a single point.

(B) 
a + b + c = 0 and a^{2} + b^{2} + c^{2} ≠ ab + bc + ca  (q) 
The equations represent the line x = y = z.

(C)  a + b + c ≠ 0 and a + b + c ≠ ab + bc + ca  (r) 
The equations represent identical planes.

(D)  a + b + c = 0 and a^{2} + b^{2} + c^{2} = ab + bc + ca  (s) 
The equations represent the whole of the threedimensional space.

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JEE 2007