1
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $${\tan ^{ - 1}}\left( {{1 \over 2}} \right)$$. Water is poured into it at a constant rate of 5 cubic meter per minute. The the rate (in m/min.), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :-
A
$${1 \over {15\pi }}$$
B
$${1 \over {5\pi }}$$
C
$${1 \over {10\pi }}$$
D
$${2 \over \pi }$$
2
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
If ƒ(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then the set
S = {x $$\in$$ R : ƒ(x) = ƒ(0)}
Contains exactly :
A
four rational numbers.
B
four irrational numbers.
C
two irrational and one rational number.
D
two irrational and two rational numbes.
3
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
Let S be the set of all values of x for which the tangent to the curve
y = ƒ(x) = x3 – x2 – 2x at (x, y) is parallel to the line segment joining the points (1, ƒ(1)) and (–1, ƒ(–1)), then S is equal to :
A
$$\left\{ { {1 \over 3}, - 1} \right\}$$
B
$$\left\{ { - {1 \over 3}, 1} \right\}$$
C
$$\left\{ { - {1 \over 3}, - 1} \right\}$$
D
$$\left\{ { {1 \over 3}, 1} \right\}$$
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
If the tangent to the curve, y = x3 + ax – b at the point (1, –5) is perpendicular to the line, –x + y + 4 = 0, then which one of the following points lies on the curve ?
A
(2, –2)
B
(2, –1)
C
(–2, 2)
D
(–2, 1)
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