If Δ = \(\left[\begin{array}{cc}10 & 2 \\30 & 6\end{array}\right]\) then A =
  • 0
  • 10
  • 12
  • 60
A = \(\left[\begin{array}{ll}\alpha & q \\q & \alpha\end{array}\right]\) |A³| = 125 then α =
  • ±3
  • ±2
  • ±5
  • 0
The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be
  • 9
  • 3
  • -9
  • 6
Let f(t) = \(\left[\begin{array}{ccc}cot t & t & 1 \\2 sin t & t & 2t \\sin t & t & t\end{array}\right]\) then \(_{t→0}^{lim}\) \(\frac{f(t)}{t^2}\) is equal to
  • 0
  • -1
  • 2
  • 3
If A and B are invertible matrices, then which of the following is not correct?
  • adj A = |A|.A
  • det (a)= [det (a)]
  • (AB)= BA
  • (A + B)= B+ A
Evaluate the determinant Δ = \(\left|\begin{array}{cc}log_{3}512 & log_{4}3 \\log_{3}8 & log_{4}9\end{array}\right|\)
  • \(\frac{15}{2}\)
  • 12
  • \(\frac{14}{3}\)
  • 6
\(\left|\begin{array}{cc}x & -7 \\x & 5 x+1\end{array}\right|\)
  • 3x² + 4
  • x(5x + 8)
  • 3x + 4x²
  • x(3x + 4)
\( \left|\begin{array}{cc}\cos \theta & -\sin \theta \\\sin \theta & \cos \alpha\end{array}\right|\)
  • 0
  • 1
  • 2
  • 3
\( \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\\sin 75^{\circ} & \cos 75^{\circ}\end{array}\right|\)
  • 0
  • 5
  • 3
  • 7
\(\left|\begin{array}{cc}a+i b & c+i d \\-c+i d & a-i b\end{array}\right|\)
  • (a + b)²
  • (a + b + c + d)²
  • (a² + b² – c² – d²)
  • a² + b² + c² + a²
If \(\left|\begin{array}{ccc}a-b-c & 2 a & 2 a \\2 b & b-c-a & 2 b \\2 c & 2 c & c-a-b\end{array}\right|\) = k (a + b + c)³ then k is
  • 0
  • 1
  • 2
  • 3
\(\left|\begin{array}{lll}a+1 & a+2 & a+4 \\a+3 & a+5 & a+8 \\a+7 & a+10 & a+14\end{array}\right|\) =
  • 2
  • -2
  • 4
  • -4
\(\left|\begin{array}{lll}b-c & c-a & a-b \\c-a & a-b & b-c \\a-b & b-c & c-a\end{array}\right|\) =
  • 0
  • 1
  • 2
  • 3
The value of the determinant \(\left|\begin{array}{ccc}\alpha & \beta & \gamma \\\alpha^{2} & \beta^{2} &\gamma^{2} \\\beta+\gamma & \gamma+\alpha & \alpha+\beta\end{array}\right|\)
  • (α + β)(β + γ)(γ + α)
  • (α – β)(β – γ) (γ – α) (α + β + γ)
  • (α + β + γ)² (α – β – γ)²
  • αβγ (α + β + γ)
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