41
MCQ (Single Correct Answer)
The equation of tangent to the curve $y\left(1+x^2\right)=2-x$, where it crosses $X$-axis, is
A
$x+5 y=2$
B
$x-5 y=2$
C
$5 x-y=2$
D
$5 x+y=2$
42
MCQ (Single Correct Answer)
The points at which the tangents to the curve $y=x^3-12 x+18$ are parallel to $X$-axis are
A
$(2,-2),(-2,-34)$
B
$(2,34),(-2,0)$
C
$(0,34),(-2,0)$
D
$(2,2),(-2,34)$
43
MCQ (Single Correct Answer)
The tangent to the curve $y=e^{2 x}$ at the point $(0,1)$ meets $X$-axis at
A
$(0,1)$
B
$\left(-\frac{1}{2}, 0\right)$
C
$(2,0)$
D
$(0,2)$
44
MCQ (Single Correct Answer)
The slope of tangent to the curve $x=t^2+3 t-8$ and $y=2 t^2-2 t-5$ at the point $(2,-1)$ is
A
$\frac{22}{7}$
B
$\frac{6}{7}$
C
$-\frac{6}{7}$
D
$-6$
45
MCQ (Single Correct Answer)
Two curves $x^3-3 x y^2+2=0$ and $3 x^2 y-y^3-2=0$ intersect at an angle of
A
$\frac{\pi}{4}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{6}$