1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

A
$\mathrm{3+t}$
B
$3-\mathrm{t}$
C
$4-\mathrm{t}$
D
$1+\mathrm{t}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ such that $\overline{\mathrm{b}}+\lambda \overline{\mathrm{a}}$ is perpendicular to $\overline{\mathrm{c}}$, then $\lambda$ is

A
  $\frac{1}{2}$
B
$\frac{1}{4}$
C
$\frac{1}{6}$
D
$\frac{1}{8}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The number of integer values of $m$, for which $x$-coordinate of the point of intersection of the lines $3 x+4 y=9$ and $y=m x+1$ is also an integer, is

A
2
B
0
C
4
D
1
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\tan ^{-1}(x+2)+\tan ^{-1}(x-2)-\tan ^{-1}\left(\frac{1}{2}\right)=0$, then one value of $x$ is

A
$-$1
B
$\frac{1}{2}$
C
1
D
2
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