Class 12Mathematics3 and 4 .Determinants and MatricesRank of Matrices , Some special determinants, differentiation and integration of determinants
Difficultજો $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & \tan x \\ x^3 & x^2 & x \\ 2x & 1 & x \end{array} \right|$ હોય,તો $\lim_{x \to 0} \frac{f(x)}{x^2}$ ની કિંમત શોધો.
- A$0$
- B$3$
- C$2$
- D$1$
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જો $\left| \begin{array}{ccc} 1 + ax & 1 + bx & 1 + cx \\ 1 + a_1x & 1 + b_1x & 1 + c_1x \\ 1 + a_2x & 1 + b_2x & 1 + c_2x \end{array} \right| = A_0 + A_1x + A_2x^2 + A_3x^3$ હોય,તો $A_1$ ની કિંમત શોધો.
Difficult
View Solutionનીચે આપેલા શ્રેણિક $A$ નો નિશ્ચાયક (rank) શોધો:
$A = \begin{bmatrix} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{bmatrix}$
$A = \begin{bmatrix} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{bmatrix}$
જો $f(x) = \left| \begin{array}{ccc} \cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x \end{array} \right|$ હોય,તો $\lim_{x \rightarrow \pi} f(x)$ ની કિંમત શોધો.
MediumKCET 2021
View Solutionજો $\Delta (x) = \left| \begin{array}{ccc} x^n & \sin x & \cos x \\ n! & \sin \frac{n\pi}{2} & \cos \frac{n\pi}{2} \\ a & a^2 & a^3 \end{array} \right|$ હોય,તો $x = 0$ આગળ $\frac{d^n}{dx^n}[\Delta (x)]$ ની કિંમત શોધો.
Difficult
View Solutionશ્રેણિક $\left[\begin{array}{cccc}3 & 2 & 1 & -4 \\ 2 & 3 & 0 & -1 \\ 1 & -6 & 3 & -8\end{array}\right]$ નો નિશ્ચાયક (rank) શોધો.
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