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Question 1
The functionQuestion 2
The function
( ) ( ) ( )log 1 log 1ax bxf x
+ − −( ) ( ) ( )f xx
=
i d fi d h l hi his not defined at x = 0. The value which should be assigned to f at x = 0 so that it is gcontinuous at x = 0 is a) loga + logba) loga + logbb) 0) bc) a – b
d) a + b
If the function Question 3
1 cos x−⎧⎪ 2( ) 0f x for xx
k
⎪= ≠⎨⎪⎩
is continuous at x = 0 then the value of k is
k⎪⎩ X =0is continuous at x 0 then the value of k is
a)1 b)0c)1/2 d)-1
Question 4
− nxcos1=
→ mxnx
x cos1cos1lim
0 −→ mxx cos10
nma)
mnb)n m
c) 2m 2nd)c)2n
m2md)
2nd)22
mnd)m
Question 5
11
1a) b)x1− x1+
x
a) b)
c) d) 0x1x+
c) d) 0
C) xC) x1+
Question 6
a) b)e9 e3a) b)
c) d) 0e9 e3
ec) d) 0e
a)a)
Question 7
Question 8
If f:R→R is continuous such that f( + ) f( ) +f( ) ∀ R &f(x+y) = f(x) +f(y) ∀ x, y ∈R, &f(1) = 2 then f(100) =
a) b)0 100a) b)
c) d) 4000 100
200c) d) 400200
)200c)200
Question 9
where n is a non zero positive integer, th i l tthen a is equal to
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d) ‐yd) y
b)b) 0b) 0