AP EAPCET 2021 - 20th August Morning Shift | Matrices and Determinants Question 42 | Mathematics

If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z \cos A=0$$ and $$x \cos B+y \cos A-z=0$$

Only zero solution

A non-zero solution for all $$\Delta ABC$$

Only zero solution but for certain values of A, B and C

A non-zero solution if $$\Delta ABC$$ is an equilateral triangle and not for all triangles.

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

-0

If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]^{-1} =\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$$, then

$$a=1, b=1$$

$$a=\sin 2 \theta$$ and $$b=\cos 2 \theta$$

$$a=\cos 2 \theta$$ and $$b=\sin 2 \theta$$

$$a=0$$ and $$b=0$$

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

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What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ?

$$a^3+b^3+c^3+3 a b c$$

$$a^3+b^3+c^3-3 a b c$$

$$a^3+b^3+c^3-6 a b c$$

$$a^3+b^3+c^3+6 a b c$$

AP EAPCET 2021 - 19th August Evening Shift

MCQ (Single Correct Answer)

-0

The value of $$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$ is

$$a b c$$

$$(a+b)(b+c)(c+a)$$

$$4 a b c$$

$$(a-b)(b-c)(c-a)$$

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