Mathematics · JEE

Online Practice: Evaluation of determinants for JEE

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Q1MathsUnit 3: Matrices and Determinants

STATEMENT 1: In a

\Delta A B C, a, b, c

denotes lengths of the sides and

\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|=\mathbf{0}

then the triangle is equilateral triangle. STATEMENT 2: Sum of three non- negative numbers

=0 \Rightarrow

each number is zero.

Q2MathsUnit 3: Matrices and Determinants

\operatorname{tet} f(\theta)=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & 1 & 1 \\ 1 & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & 1 & -1\end{array}\right|

f(\pi)+f(-\pi)

is equal to

Q3MathsUnit 3: Matrices and Determinants

\operatorname{Let} A=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right|

and suppose that det.

(A)=2

then the det.(B) equals, where

\boldsymbol{B}=\left|\begin{array}{ccc}\mathbf{4} \boldsymbol{x} & \mathbf{2} \boldsymbol{a} & -\boldsymbol{p} \\ \mathbf{4} \boldsymbol{y} & \mathbf{2} \boldsymbol{b} & -\boldsymbol{q} \\ \boldsymbol{4} \boldsymbol{z} & \boldsymbol{2} \boldsymbol{c} & -\boldsymbol{t}\end{array}\right|

Q4MathsUnit 3: Matrices and Determinants

f\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \mathbf{3} & \mathbf{5} \\ \mathbf{2} & \boldsymbol{x}+\mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \boldsymbol{x}+\mathbf{4}\end{array}\right|=\mathbf{0},

then

\boldsymbol{x}=?

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