MHT CET 2023 9th May Morning Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

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Let two non-collinear vectors $$\hat{a}$$ and $$\hat{b}$$ form an acute angle. A point $$\mathrm{P}$$ moves, so that at any time $$t$$ the position vector $$\overline{\mathrm{OP}}$$, where $$\mathrm{O}$$ is origin, is given by $$\hat{a} \sin t+\hat{b} \cos t$$, when $$P$$ is farthest from origin $$O$$, let $$M$$ be the length of $$\overline{\mathrm{OP}}$$ and $$\hat{\mathrm{u}}$$ be the unit vector along $$\overline{\mathrm{OP}}$$, then

$$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}+\hat{\mathrm{b}}}{|\hat{\mathrm{a}}+\hat{\mathrm{b}}|}$$ and $$\mathrm{M}=(1+\hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{\frac{1}{2}}$$

$$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}-\hat{\mathrm{b}}}{|\hat{\mathrm{a}}-\hat{\mathrm{b}}|}$$ and $$\mathrm{M}=(1+\hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{\frac{1}{2}}$$

$$\hat{u}=\frac{\hat{a}+\hat{b}}{|\hat{a}+\hat{b}|}$$ and $$M=(1+2 \hat{a} \cdot \hat{b})^{\frac{1}{2}}$$

$$\hat{u}=\frac{\hat{a}-\hat{b}}{|\hat{a}-\hat{b}|}$$ and $$M=(1-2 \hat{a} \cdot \hat{b})^{\frac{1}{2}}$$

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

The number of solutions in $$[0,2 \pi]$$ of the equation $$16^{\sin ^2 x}+16^{\cos ^2 x}=10$$ is