1
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
2
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
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Out of Syllabus
The tangent to the curve, y = xex2 passing through the point (1, e) also passes through the point
A
$$\left( {{4 \over 3},2e} \right)$$
B
(3, 6e)
C
(2, 3e)
D
$$\left( {{5 \over 3},2e} \right)$$
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
A helicopter is flying along the curve given by y – x3/2 = 7, (x $$\ge$$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -
A
$${1 \over 6}\sqrt {{7 \over 3}}$$
B
$${{\sqrt 5 } \over 6}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$$$\sqrt {{7 \over 3}}$$
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