1
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices are lie on the line $y=2 x+\mathrm{c}$ where c is the constant, then co-ordinates of other two vertices are

A
$(4,4),(2,0)$
B
$(4,4),(1,0)$
C
$(2,0),(4,1)$
D
$(2,0),(1,-1)$
2
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\mathrm{a}^x \cdot \mathrm{~b}^{2 x-1}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is equal to

A
$\quad y\left(\log \left(a b^2\right)\right)$
B
$\quad y^2\left(\log \left(a \mathrm{~b}^2\right)\right)$
C
$\quad y\left(\log \left(a b^2\right)\right)^2$
D
$\quad y^2(\log (a b))^2$
3
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a culture bacteria count is $1,00,000$ initially. The number increases by $10 \%$ in first 2 hours. In how many hours will the count reach $2,00,000$, if the rate of growth of bacteria is proportional to the number present?

A
$\frac{2 \log \left(\frac{11}{10}\right)}{\log 2}$
B
$\frac{\log \left(\frac{11}{10}\right)}{\log 2}$
C
$\frac{2 \log 2}{\log \left(\frac{11}{10}\right)}$
D
$\frac{\log (2)}{\log \left(\frac{11}{10}\right)}$
4
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+1
-0

Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is

A
$3 \%$
B
$2 \%$
C
$6 \%$
D
$9 \%$
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