1
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Out of Syllabus
Let C be a curve given by y(x) = 1 + $$\sqrt {4x - 3} ,x > {3 \over 4}.$$ If P is a point on C, such that the tangent at P has slope $${2 \over 3}$$, then a point through which the normal at P passes, is :
A
(2, 3)
B
(4, $$-$$3)
C
(1, 7)
D
(3, $$-$$ 4),
2
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If the tangent at a point P, with parameter t, on the curve x = 4t2 + 3, y = 8t3−1, t $$\in$$ R, meets the curve again at a point Q, then the coordinates of Q are :
A
(t2 + 3, − t3 −1)
B
(4t2 + 3, − 8t3 −1)
C
(t2 + 3, t3 −1)
D
(16t2 + 3, − 64t3 −1)
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
The minimum distance of a point on the curve y = x2−4 from the origin is :
A
$${{\sqrt {19} } \over 2}$$
B
$$\sqrt {{{15} \over 2}}$$
C
$${{\sqrt {15} } \over 2}$$
D
$$\sqrt {{{19} \over 2}}$$
4
JEE Main 2016 (Offline)
+4
-1
A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then:
A
$$x=2r$$
B
$$2x=r$$
C
$$2x = \left( {\pi + 4} \right)r$$
D
$$\left( {4 - \pi } \right)x = \pi \,\, r$$
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