1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$$

A
104
B
100
C
102
D
103
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$[(\bar{a}+2 \bar{b}+3 \bar{c}) \times(\bar{b}+2 \bar{c}+3 \bar{a})] \cdot(\bar{c}+2 \bar{a}+3 \bar{b})=54$$ then the value of $$\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$$ is

A
0
B
1
C
3
D
2
3
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is $$3 \mathrm{~mm}$$ and 1 hour later it reduces to $$2 \mathrm{~mm}$$, then the expression for the radius $$R$$ of the raindrop at any time $$t$$ is

A
$$6 \mathrm{R}=\mathrm{t}+2$$
B
$$\mathrm{R}(\mathrm{t}+2)=6$$
C
$$\mathrm{R}=6(\mathrm{t}+2)$$
D
$$6 \mathrm{R}=\mathrm{t}$$
4
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the Cartesian equation of a line is $$6 x-2=3 y+1=2 z-2$$, then the vector equation of the line is

A
$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
B
$$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
C
$$\overline{\mathrm{r}}=\left(\frac{-1}{3} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
D
$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}-\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$$
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