Short Quiz

Question 1 of 5

NCERT Exemplar

The area of a triangle with vertices (-3, 0), \((3,0)\) and (0, k) is 9 sq. units. The value of \(k\) will be

A 9 B 3 C - 9 D 6

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Question 2 of 5

NCERT Exemplar

There are two values of \(a\) which makes determinant, \(\Delta=\left|\begin{array}{ccc}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a\end{array}\right|=86\), then sum of these number is

A 4 B 5 C - 4 D 9

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Question 3 of 5

NCERT Exemplar

If A and B are invertible matrices, then which of the following is not correct?

A \(\quad \operatorname{adj} \mathrm{A}=|\mathrm{A}| \cdot \mathrm{A}^{-1}\) B \(\quad \operatorname{det}(\mathrm{A})^{-1}=[\operatorname{det}(\mathrm{A})]^{-1}\) C \((\mathrm{AB})^{-1}=\mathrm{B}^{-1} \mathrm{~A}^{-1}\) D \(\quad(\mathrm{A}+\mathrm{B})^{-1}=\mathrm{B}^{-1}+\mathrm{A}^{-1}\)

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Question 4 of 5

The maximum value of \(\Delta=\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin \theta & 1 \\ 1+\cos \theta & 1 & 1\end{array}\right|\) is \((\theta\) is real number \()\)

A \(\frac{1}{2}\) B \(\frac{\sqrt{3}}{2}\) C \(\sqrt{2}\) D \(\frac{2 \sqrt{3}}{4}\)

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Question 5 of 5

CBSE Board Exam 2024

Let \(\mathrm{A}=\left[\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d}\end{array}\right]\) be a square matrix such that adj \(\mathrm{A}=\mathrm{A}\). Then, \((\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d})\) is equal to :

A 2a B 2b C 2c D 0

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