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

If $y=4 x-5$ is a tangent to the curve $y^2=p x^3+q$ at $(2,3)$, then the values of $p$ and $q$ are respectively

A
$-2,7$
B
$7,-2$
C
$2,-7$
D
$-7,-2$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{w}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$ where $\mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ is

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

$$\int_\limits0^a \frac{x-a}{x+a} d x=$$

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

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius $r$. If PS and RQ intersect at a point X on the circumference of the circle, then 2 r equals

A
$\sqrt{\mathrm{PQ} \cdot \mathrm{RS}}$
B
$\frac{\mathrm{PQ}+\mathrm{RS}}{2}$
C
$\frac{2 \cdot P Q \cdot R S}{P Q+R S}$
D
$\sqrt{\frac{\mathrm{PQ}^2+\mathrm{RS}^2}{2}}$
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