જેના માટે left|begin{array}{ccc}1 & frac{3}{2} & alpha+frac{3}{2} 1 & frac{1}{3} & alpha+frac{1}{3} 2 alpha+3 & 3 alpha+1 & 0end{array}right|=0 થાય તેવી alpha ની કિંમત..................... અંતરાલમાં

Q: જેના માટે $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$ થાય તેવી $\alpha$ ની કિંમત..................... અંતરાલમાં આવે છે.

b $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$ $ \Rightarrow(2 \alpha+3)\left\{\frac{7 \alpha}{6}\right\}-(3 \alpha+1)\left\{\frac{-7}{6}\right\}=0 $ $ \Rightarrow(2 \alpha+3) \cdot \frac{7 \alpha}{6}+(3 \alpha+1) \cdot \frac{7}{6}=0 $ $ \Rightarrow 2 \alpha^2+3 \alpha+3 \alpha+1=0 $ $ \Rightarrow 2 \alpha^2+6 \alpha+1=0 $ $ \Rightarrow \alpha=\frac{-3+\sqrt{7}}{2}, \frac{-3-\sqrt{7}}{2}$ Hence option $(2)$ is correct.

MCQ

ગુજરાતી માધ્યમ

જેના માટે $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$ થાય તેવી $\alpha$ ની કિંમત..................... અંતરાલમાં આવે છે.

A $(-2,1)$
B $(-3,0)$
C $\left(-\frac{3}{2}, \frac{3}{2}\right)$
D $(0,3)$

JEE MAIN 2024, Diffcult

ધોરણ 12 સાયન્સ
ગણિત
3 and 4 . determinant and metrices
JEE

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