36
MCQ (Single Correct Answer)
A ladder, 5 m long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of $10 \mathrm{~cm} / \mathrm{s}$, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 m from the wall is
A
$\frac{1}{10} \mathrm{rad} / \mathrm{s}$
B
$\frac{1}{20} \mathrm{rad} / \mathrm{s}$
C
$20 \mathrm{rad} / \mathrm{s}$
D
$10 \mathrm{rad} / \mathrm{s}$
37
MCQ (Single Correct Answer)
The curve $y=x^{1 / 5}$ has at $(0,0)$
A
a vertical tangent (parallel to $Y$-axis)
B
a horizontal tangent (parallel to $X$-axis)
C
an oblique tangent
D
no tangent
38
MCQ (Single Correct Answer)
The equation of normal to the curve $3 x^2-y^2=8$ which is parallel to the line $x+3 y=8$ is
A
$3 x-y=8$
B
$3 x+y+8=0$
C
$x+3 y \pm 8=0$
D
$x+3 y=0$
39
MCQ (Single Correct Answer)
If the curve $a y+x^2=7$ and $x^3=y$, cut orthogonally at $(1,1)$, then the value of $a$ is
A
1
B
0
C
$-6$
D
6
40
MCQ (Single Correct Answer)
If $y=x^4-10$ and $x$ changes from 2 to 1.99, then what is the change in $y$ ?
A
0.32
B
0.032
C
5.68
D
5.968