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

The minimum distance and maximum distance of the point $\mathrm{P}(2,-7)$ from the circle $x^2+y^2-14 x-10 y-151=0$ are respectively _______units

A
2,28
B
5,25
C
6,24
D
3,27
2
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The lines $\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ and $\overline{\mathrm{r}}=\overline{\mathrm{c}}+\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ will intersect if

A

$\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\overline{\mathrm{b}} \times \overline{\mathrm{c}}$

B

$\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}$

C

$\bar{a} \cdot \bar{c}=|\bar{b}|^2$

D

$\bar{a} \times \bar{b}=\bar{c} \times \bar{a}$

3
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ 3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}= $$

A
0
B
1
C
2
D
3
4
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10 lakhs and due to loss they reduce to ₹ 10000 after 3 years, then the number of years required for the person to be bankrupt will be

A
$\frac{20}{3}$ years
B
$\frac{10}{3}$ years
C
$\frac{10}{9}$ years
D
$\frac{20}{9}$ years
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