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Evaluation of determinants Previous Year Questions for JEE

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Part of Matrices and Determinants in JEE Main Mathematics.

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Q1MathsUnit 3: Matrices and Determinants
STATEMENT 1: In a ΔABC,a,b,c\Delta A B C, a, b, c denotes lengths of the sides and ∣abcbcacab∣=0\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⇒=0 \Rightarrow each number is zero.
Q2MathsUnit 3: Matrices and Determinants
tet⁡f(θ)=∣cos⁡θ2111cos⁡θ2−cos⁡θ2−cos⁡θ21−1∣\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(π)+f(−π)f(\pi)+f(-\pi) is equal to
Q3MathsUnit 3: Matrices and Determinants
Let⁡A=∣abcpqrxyz∣\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(A)=2 then the det.(B) equals, where B=∣4x2a−p4y2b−q4z2c−t∣\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∣x+1352x+2523x+4∣=0,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 x=?\boldsymbol{x}=?
Q5MathsUnit 3: Matrices and Determinants
If each row of a determinant of third order of value Δ\Delta is multipled by 3,3, then the value of new determinant is
Q6MathsUnit 3: Matrices and Determinants
∣1!2!3!2!3!4!3!4!5!∣=2016K\left|\begin{array}{ccc}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right|=2016 K then value of K\boldsymbol{K} is

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