1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$y=f(x)$ and $x=g(y)$ are two curves and $P(x, y)$ is a common point of the two curves. If at $P$ on the curve $y=f(x), \frac{d y}{d x}=Q(x)$ and at the same point $P$ on the curve $x=g(y), \frac{d x}{d y}=-Q(x)$, then
A
the two curves have common tangent
B
the angle between two curves is $45^{\circ}$
C
tangent drawn at $P$ to one curve is normal to the other curve at $P$
D
the two curves never intersect orthogonally
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the expression $7+6 x-3 x^2$ attains its extreme value $\beta$ at $x=\alpha$, then the sum of the squares of the roots of the equation $x^2+\alpha x-\beta=0$ is
A
21
B
-19
C
19
D
-21
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The equation of the normal drawn to the curve $y^3=4 x^5$ at the point $(4,16)$ is
A
$20 x+3 y=128$
B
$20 x-3 y=32$
C
$3 x-20 y+308=0$
D
$3 x+20 y=332$
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A point $P$ is moving on the curve $x^3 y^4=2^7$. The $x$-coordinate of $P$ is decreasing at the rate of 8 units per second. When the point $P$ is at $(2,2)$, the $y$-coordinate of $P$
A
increases at the rate of 6 units per second
B
decreases at the rate of 6 units per second
C
increases at the rate of 4 units per second
D
decreases at the rate of 4 units per second
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