1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let C be a curve given by $y(x)=1+\sqrt{4 x-3}$, $x>\frac{3}{4}$. If P is a point on C , such that the tangent at P has slope $\frac{2}{3}$, then a point through which the normal at P passes, is

A
$(1,7)$
B
$(4,-3)$
C
$(3,-4)$
D
$(2,3)$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the circle, the end points of whose diameter are the centres of the circles $x^2+y^2+6 x-14 y+5=0$ and $x^2+y^2-4 x+10 y-4=0$ is

A
$x^2+y^2-x-2 y+41=0$
B
$x^2+y^2+x-2 y-41=0$
C
$x^2+y^2+x-2 y-41=0$
D
$x^2+y^2-x+2 y-41=0$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane, passing through the point $(1,1,1)$ and perpendicular to the planes $2 x+y-2 z=5$ and $3 x-6 y-2 z=7$, is

A
$14 x+2 y-15 z=1$
B
$14 x-2 y+15 z=27$
C
$14 x+2 y+15 z=31$
D
$-14 x+2 y+15 z=3$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^3}\right)$ is $\sqrt{x} \cdot g(x)$, then $g(x)$ equals

A
$\frac{3 x \sqrt{x}}{1-9 x^3}$
B
$\frac{3 x}{1-9 x^3}$
C
$\frac{3}{1+9 x^3}$
D
$\frac{9}{1+9 x^3}$
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