JEE Advanced 2020 Full Test 3 Paper 1

(A)

lim

x→0+

f(x)=

lim

x→0+

‌

ex+a

2x

=‌

1

2

⇒a=−1
If a=−1, then

lim

x→0+

f(x)=‌

1

2

,

lim

x→0−

f(x)=‌

1

2

∴f(x) is continuous at x=0, if a=−1,b=‌

1

2

(B) f(x) is discontinuous at x=0 if b≠‌

1

2

(C) ‌‌ If a≠−1, then

lim

x→0

‌

ex+a

2x

does not exist.
∴x=0 is a point of irremovable type of discontinuity.
(D) If a=−1, then

lim

x→0

f(x)=‌

1

2

∴b≠‌

1

2

⇒ removable type of discontinuity at x=0