1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let f : (–1, $$\infty$$) $$\to$$ R be defined by f(0) = 1 and
f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, x $$\ne$$ 0. Then the function f :
A
decreases in (–1, $$\infty$$)
B
decreases in (–1, 0) and increases in (0, $$\infty$$)
C
increases in (–1, $$\infty$$)
D
increases in (–1, 0) and decreases in (0, $$\infty$$)
2
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Out of Syllabus
The equation of the normal to the curve
y = (1+x)2y + cos 2(sin–1x) at x = 0 is :
A
y = 4x + 2
B
x + 4y = 8
C
y + 4x = 2
D
2y + x = 4
3
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Out of Syllabus
Let P(h, k) be a point on the curve
y = x2 + 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at P is :
A
x – 3y – 11 = 0
B
x – 3y + 22 = 0
C
x + 3y – 62 = 0
D
x + 3y + 26 = 0
4
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Out of Syllabus
If the tangent to the curve y = x + sin y at a point
(a, b) is parallel to the line joining $$\left( {0,{3 \over 2}} \right)$$ and $$\left( {{1 \over 2},2} \right)$$, then :
A
b = a
B
|b - a| = 1
C
$$b = {\pi \over 2}$$ + a
D
|a + b| = 1
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