Class 12Mathematics3 and 4 .Determinants and MatricesExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Easyयदि $\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1+y & 1+2 y & 1 \\ 1+z & 1+z & 1+3 z\end{array}\right| = 10 k x y z \left(3+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ है,तो $k = \text{ . . . . . . }$ (जहाँ $x, y, z \neq 0$ और $3+\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \neq 0$).
- A$\frac{1}{5}$
- B$2$
- C$5$
- D$1$
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$(4, 4)$,$(3, -2)$ और $(3, -16)$ शीर्षों वाले त्रिभुज का क्षेत्रफल क्या है?
Easy
View Solutionयदि $\Delta_k=\left|\begin{array}{ccc}1 & 0 & 0 \\ 0 & k & k-1 \\ 0 & k-1 & k\end{array}\right|$ है,तो $\Delta_1+\Delta_2+\ldots+\Delta_{20}$ का मान ज्ञात कीजिए।
$\left|\begin{array}{rr}\sin 35^{\circ} & -\cos 35^{\circ} \\ \sin 55^{\circ} & \cos 55^{\circ}\end{array}\right|=$ . . . . . .
$c \in R$ का वह अधिकतम मान ज्ञात कीजिए जिसके लिए रैखिक समीकरण निकाय $x - cy - cz = 0$,$cx - y + cz = 0$,$cx + cy - z = 0$ का एक अशून्य हल (non-trivial solution) हो।
DifficultJEE MAIN 2019
View Solutionयदि $A = \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{vmatrix}$,$B = \begin{vmatrix} 1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix}$,और $C = \begin{vmatrix} a & b & c \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix}$ है,तो कौन सा संबंध सही है?
Easy
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