1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The tangent to the curve y = x2 – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point :
A
$$\left\{ {{1 \over 4},{7 \over 2}} \right\}$$
B
$$\left( { - {1 \over 8},7} \right)$$
C
$$\left( {{7 \over 2},{1 \over 4}} \right)$$
D
$$\left( {{1 \over 8}, - 7} \right)$$
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let f(x) = $${x \over {\sqrt {{a^2} + {x^2}} }} - {{d - x} \over {\sqrt {{b^2} + {{\left( {d - x} \right)}^2}} }},\,\,$$ x $$\, \in$$ R, where a, b and d are non-zero real constants. Then :
A
f is an increasing function of x
B
f is neither increasing nor decreasing function of x
C
f ' is not a continuous function of x
D
f is a decreasing function of x
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
The maximum value of the function f(x) = 3x3 – 18x2 + 27x – 40 on the set S = $$\left\{ {x\, \in R:{x^2} + 30 \le 11x} \right\}$$ is :
A
$$-$$ 222
B
$$-$$ 122
C
$$122$$
D
222
4
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If y(x) is the solution of the differential equation $${{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x > 0,\,$$ where $$y\left( 1 \right) = {1 \over 2}{e^{ - 2}},$$ then
A
y(loge2) = loge4
B
y(x) is decreasing in (0, 1)
C
y(loge2) = $${{{{\log }_e}2} \over 4}$$
D
y(x) is decreasing in $$\left( {{1 \over 2},1} \right)$$
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