1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The function f defined by

f(x) = x3 $$-$$ 3x2 + 5x + 7 , is :
A
increasing in R.
B
decreasing in R.
C
decreasing in (0, $$\infty$$) and increasing in ($$-$$ $$\infty$$, 0)
D
increasing in (0, $$\infty$$) and decreasing in ($$-$$ $$\infty$$, 0)
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
A tangent to the curve, y = f(x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point :
A
$$\left( {{1 \over 3},24} \right)$$
B
$$\left( {{1 \over 2},4} \right)$$
C
$$\left( {2,{1 \over 8}} \right)$$
D
$$\left( {3,{1 \over 28}} \right)$$
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Out of Syllabus
The tangent at the point (2, $$-$$2) to the curve, x2y2 $$-$$ 2x = 4(1 $$-$$ y) does not pass through the point :
A
$$\left( {4,{1 \over 3}} \right)$$
B
(8, 5)
C
($$-$$4, $$-$$9)
D
($$-$$2, $$-$$7)
4
JEE Main 2017 (Offline)
+4
-1
Out of Syllabus
The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point :
A
$$\left( {{1 \over 2},{1 \over 2}} \right)$$
B
$$\left( {{1 \over 2}, - {1 \over 3}} \right)$$
C
$$\left( {{1 \over 2},{1 \over 3}} \right)$$
D
$$\left( { - {1 \over 2}, - {1 \over 3}} \right)$$
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