1
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
2
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
$3 x+20 y=332$
3
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
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the function $f(x)=x^3+a x^2+b x+40$ satisfies the conditions of Rolle's theorem on the interval $[-5,4]$ and $-5,4$ are two roots of the equation $f(x)=0$, then one of the values of $c$ as stated in that theorem is
A
3
B
$\frac{1+\sqrt{67}}{3}$
C
$\frac{1+\sqrt{65}}{3}$
D
-2
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