Jee 2014 Booklet5 Hwt Differential Calculus 1
Short Description
Jee 2014 Booklet5 Hwt Differential Calculus 1...
Description
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [1]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
4 x2 , where, [x] is the greatest integer function is x , 2 1, 2 x 2
Statement : 1
The domain of f x
Statement : 2
The domain of f x x 4 x 3 , where, [x] represents the greatest integer function x , 2 2
2 n 2 2 n 1 The domain of f x sin log 2 log3 x x 32 ,3 nI Choose the correct choice : (A) FTF (B) TFT (C) TTT (D)
Statement : 3
2.
If f x 2 x 3 2 x , then f (x) = 2
x2 2
(A)
3.
4.
If tan x tan y , then y
x2 5
x
log tan y log tan x
dy dx
(B)
log tan y 1 2 log tan x
(C)
x2 4 x 9
(D)
x 5 2 2 x 2
(C)
1
(D)
2
(C)
log (tan y )
(C)
24
(D)
43
(C)
19
(D)
1 + log 2
3a tan
(D)
a sin cos
2y (D) sin 2 x
log tan y 2 y cos ec 2 x log tan x 2 x cos ec 2 y
If log 4 log3 log 2 x 1 , then x is : (A)
6.
(B)
dy x 1 1 x 1 If y sec 1 sin x 1 , x 1 , then dx is : x 1 (A) 0 (B) 1
(A)
5.
FFF
4
23
(B)
9
3| x | 5 , If f : R R is defined by f x logx , x2 4 ,
x
2
1 2
1 x2 2 x2
1 1 2 3 The value of f f f f f 3 is : 3 3 3 2
(A)
7.
0
(B)
1
dy 2 1 dx 3 3 If x a cos , y a sin , then d2y
(A)
sec
VMC/Differential Calculus - 1
(B)
3/ 2
is equal to :
dx 2 3a sin cos
(C)
46
HWT/Mathematics
Vidyamandir Classes 8.
If f x (A)
9.
f x sin x sin x , 0 x
(A)
(C)
10.
6x 3 , then f 1 x is : 2x 4 2x 4 (B) 6x 3
lim
, 0 x 1 0 f x sin 1 , 1 x 2 3x | x |
(C)
4x 3 6 2x
(D)
Does not exist
, where [ ] represents the greatest integer function can also be represented as : 2
, 0 x 1 0 f x 1 sin 1 , 1 x 2
x 7 x 5| x |
(A)
6x 4 2x 3
4 , x 4 2
(B)
1 2 f x 1 1 2
(D)
, 0 x 0 4 f x 1 , x 1 4 sin 1 , 1 x 2
,
0 x
3/2
VMC/Differential Calculus - 1
(B)
3/7
(C)
47
3/5
(D)
2
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [2]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
x1 / 3 a1 / 3 dy If y tan 1 is : , x 0 , then 1 x1 / 3a1 / 3 dx 1 2 (A) (B) x2 / 3 1 x2 / 3 x1 / 3 1 x 2 / 3
2.
4.
(B)
2(x2 + 7)
a x log 1 x sin x cos 2 x
1 2
(B)
0
1
3x1 / 3 1 x 2 / 3
(C)
2(x2 + 11)
(D)
2(x2 + 10)
(C)
x2 2
(D)
1 x x
1 2
(D)
2
(C)
1 x 2 A function f is defined on 1, 1 as f x x 1 2
, 1 x 0 ,
f (x)
(B)
2f (x)
. Then value of f x f | x | is :
0 x 1 1 x 2 1 x 2 1 x 2
, 1 x
1 2
,
1 x0 2
,
0 x 1
(D)
1 , 1 x 10 4 2 x 1 , 0 x 1
(C)
, 2 2, 3
(D)
R 3, 2 , 2 , 3
Domain of the function f x 5| x | x 2 6 is : (A)
, 2 3,
(B)
3, 2 2 , 3
If [ ] denotes the greatest integer function,
lim x
(A) 8.
(D)
where, a > 0, is :
ex 1
x 0
(C)
7.
2x2 + 11
The value of lim
(A)
6.
1 1 If f x x 2 ; then f (x) is : x x2 1 (A) (B) x2 2 x x
(A)
5.
1
3x 2 / 3 1 x 2 / 3
If f x 2 x 2 5 x 11, f x f x is : (A)
3.
(C)
0
(B)
n
If 0 x y, lim y n x n (A)
e
VMC/Differential Calculus - 1
1/ n
2
5 sin cos x cos x 2
is :
1
(C)
(D)
Does not exist
x
(C)
y
(D)
nx n 1
is :
(B)
48
HWT/Mathematics
Vidyamandir Classes 9.
If 0.5 (A)
10.
4 log3 log1 / 3 x 2 5
1 then | x | belongs to :
1,
(B)
2 , 1 5
(C)
2 , 5
(D)
17 3 , 5 15
(D)
2 3
x 1 lim x sin 1 is : x 2x 1 6 (A)
1 2 3
VMC/Differential Calculus - 1
(B)
2 3
(C)
49
3 2
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [3]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
3.
A single formula that gives f (x) for all x 0 where, 3 x , 0 x 3 is : f x x3 3 x 3 , (A)
f x |2 x 1| 4 x
(B)
f x | x 3| 2 x
(C) (D)
6.
4 cos3 x sin x
f x |3 x 9 | x
(C)
4 sin3 x cos x
(D)
u
f x | x 3| 3x
x x log 1 log 1 2 2 If f x for x 0 x and f 0 a and f (x) is continuous at x = 0, then a is :
(A)
64 y
(B)
(C)
64y
(D)
ddx y x dydx equals : 2
7.
2
y 64 y 64
(A) (C)
8.
Let f x x x 1 where [ ] denotes the greatest 2
1 5 2 x=1 x
3
lim
x
(A) (C) 5.
The
dy is : dx
(B)
integer function. Then, in (0, 2), f (x) is discontinuous at the point :
4.
If y u 4 where u cos x,
[0, 1]
4u3
(C)
(D)
(A)
If y sin 8 sin 1 x then 1 x 2
(A)
5 2 ,
(C)
(D)
1 5 2 Both (A) and (C)
(B) (D)
2 2
(B)
x
2 x3 1
9.
(B) (D)
1 1/2
27 log x 2 2
x 9
x 3
(A)
12
(B)
8
(C)
9
(D)
e 1
x
e x 1 x 1 e x lim x 0 x
is :
4 1 domain
3
2
4x 8x 5x 2
x lim
0 1
of
the
10.
function
1/ 4
2 x 2 2 x 1 is x f x 9 x 27 3 219 3 (A) (B) 3, 3 3,
VMC/Differential Calculus - 1
(A)
12
(B)
8
(C)
9
(D)
e 1
If lim
x0
(A) (C)
50
x a cos x b sin x x a=b a=b–1
1 then : (B) (D)
a=b+1 None of these
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [4]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If f (x) is a thrice differentiable function such that lim
4.
5.
6.
x R, x 2
9
(D)
e 1
(D)
x , 1
(C)
21 8
(D)
21 8
(C)
2y 1 2y 1
(D)
cos x 2y 1
(C)
If y sin 1 cos x cos 1 sin x , 0 x
dy , then is : 2 dx (C)
3
2
Range of the function f x
,
(B)
(B)
2
5 sin log 5 12
15
(D)
15
1
(D)
0
(C)
1 1 4 , 2
(D)
5 , 5
(C)
1 1 4 , 2
(D)
5 , 5
(C)
cos
(D)
cos
1 is : 3 sin 5 x
(B)
11 1, 3
Range of the function f x x 1 x 3 x 5 is : (A)
10.
(C)
3
(A) 9.
8
dy 2x 3 If f x sin log x and y f , then dx at x 1 is equal to : 3 2x 12 (A) (B) (C) (D) cos log 5 cos log 5 sin log 5 5 x3 k 4 x 2.k , x 3 is continuous at x = 3, then k is : If the function f x x3 8 , x3
(A)
8.
(B)
7 dy 1 If x 2 xy y 2 , then at x = 1 and y is : 4 dx 2 3 5 (A) (B) 4 4 dy Let y sin x sin x sin x . . . . . , then is : dx 2y cos x (A) (B) cos x 2y 1
(A) 7.
12
12 , then f 0 is equal to :
Let f x x cos where, [ ] denotes the greatest integer function. Then, the domain of f is : x 2 (A) (B) x , 2 1, x R, x not an integer
(C) 3.
x3
x0
(A) 2.
f 4 x 3 f 3x 3 f 2 x f x
,
(B)
11 1, 3
If cos y x cos y then 1 x 2 2 x cos . (A)
sin
VMC/Differential Calculus - 1
(B)
sin
dy is : dx
37
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [5]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than one correct option. 1.
1 tan x log 2 1 is : lim 4x x sin x 4 4
(A) *2.
3.
(B)
1/4
(C)
0
(D)
does not exist
(B)
discontinuous when x n , n Z
The function f x 1 |tan x | is : (A)
continuous everywhere
(C)
not differentiable when x 2n 1
(D)
discontinuous at x 2n 1
If x sin and y cos3 then 2 y (A) (C)
4.
4
n , n Z and not differentiable at x ,nZ 2 2
d2y
2 2 2 3 cos cos 13 sin
dy 4 dx dx 2
2
is :
6 cos 2 7 sin 2 cos 2
x x 4 x9 . . . x x 1 x 1
n2
lim
(A)
,nZ 2
n n 1 n 2
n
(D)
cos 2 13 sin 2 cos 2 2
2
2
3 cos 17 sin cos
is :
n n 1 2n 1
(B)
6
(B)
6
(C)
n n 1 2n 1 6
(D)
n n 1 2n 1 6
1/ x
5.
sin x lim x 0 x (A)
is :
1
6.
sin x x If f x x x 1 (A) (C)
7.
1
(B)
, x0
0
(D)
e
, where [ ] denotes the greatest integer function, then :
, x0
lim f x sin 1
(B)
lim f x does not exist
(D)
x0
x0
If f p 2, f p 6 and lim
g x f p g p f x x p
x p
(A)
(C)
3:1
VMC/Differential Calculus - 1
(B)
1:3
0 then
(C)
38
lim f x 1
x0
lim f x exists but f (x) is not continuous at x = 0
x0
g p g p
1 : 12
is : (D)
12 : 1
HWT/Mathematics
Vidyamandir Classes 8.
x3 , x xn Let f x . If the two roots of px 2 qx r 0 are reciprocal to one another, then, the value of p, q, r 2 px qx r , x xn for which f (x) is continuous and differentiable at x = x0 are respectively : (A)
(C)
9.
pr
pr
2 x03 x02
1
2 x03 x02
1
,q
,q
x02 3 x02 1 x02
x02 3 x02 x02
, 0 x ,
,
pr
(D)
1
p 1 | cos x ||cos x| If f x q cot x 2 cot m x 2 e
pr
(B)
x
2 x03 1 x02 2 x03 1
x02
,q
,q
x02 3 x02 1 x02
x03 3 x02 1
x02
2
2
x 2
is a continuous function on 0, then the value of p and q are respectively : (A) 10.
m m/ ,e
(B)
em / ,
m
(C)
The set of all points of discontinuity of the inverse of f x (A)
VMC/Differential Calculus - 1
(B)
, 1
m , e m
(D)
e m / , m
(D)
R 1, 1
e x e x
is : e x e x (C) 1,
39
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [6]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than one correct option. 1.
*2.
In x (0, 1), f x 3 x 2 1 , where [x] stands for the greatest integer not exceeding x is : (A) continuous (B) continuous except at one point (C) continuous except at two points (D) continuous except at three points
lim 2 25 x 2 x 5 x is equal to :
x0
(A)
(B)
(D) 3.
6.
lim
2 x log e 1 x
lim
e x 1 x
x2 x sin 5 lim x0 x x0
2 1 cos x 2 (C)
lim
x0
(A) (C)
0 22
(D)
f (x) is not differentiable at x
e x x 4 x Let f x x x 3
5x4
7.
dx
*8.
12 22
(B) (D)
(A)
6x 6
(B)
36x11
(C)
6x5
(D)
3x 6
*5.
1
k 2
n 1 n 2 tan
(A)
tan
(B)
tan 1 n 1 tan 1 2
(C)
tan 1 2
1
(D)
9.
f (x) is continuous in 2 x 2 f (x) is not differentiable at x = 1
(C)
3 35 f 1 f 2 8
(D)
27 3 f 1 f 2 2
(A) (C)
Let f x |2 x 9| |2 x | |2 x 9|
10.
Which of the following are true ? (A)
9 f (x) is not differentiable at x 2
(B)
9 f (x) is not differentiable at x 2
VMC/Differential Calculus - 1
3x (A) (C)
40
3 x log 1 3 x 2 x 2 0 for x
2
n tan 1 2
Let f x max x, x 2 , x3 in 2 x 2 . Then :
k 1
2
None of these
du If u 3x12 and v x 6 , then is : dv
(A) (B)
tk is equal to where
cot 1 1 k k 1 tk = 2 k 1
, x0
x0
n
4.
9 9 , 0, 2 2
, x0
lim f x exists (D)
(C)
2 3d y If x 2 xy 3 y 2 1 then x 6 y is : 2
f (x) is not differentiable at x = 0
Where [ ] denotes the greatest integer function. Then, (A) f (x) is discontinuous at x = 0 (B) f (x) is continuous at x = 0
2
5x2
x0
(C)
1 0, 2 (0, 2)
(B)
(0, 1)
(D)
(0, 3)
5 2 x log 1 3 x 2 x 2 3 x in : 2 1 0, 2 (0, 2)
(B)
(0, 1)
(D)
(0, 3)
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [7]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If f x cos1
domain is : (A) 2 , 6
(B)
6, 2 2, 3
6 , 2
(D)
2, 2 2 , 3
(C) 2.
(A) (C) (D)
4.
1 6 3 x
4 2 10 3 , 3
cos ec
1 x 1
(B)
2
, x R , is :
7.
10 3, 3
2 10 , 3 3 , None of these
(B)
(C)
4
(D)
0
x5 243
x 3 x x aa
1 , then a is equal to :
(B) (D)
is continuous (B) is differentiable is non-differentiable
0 None
VMC/Differential Calculus - 1
is discontinuous
None
2
et
2
2t 2t 2 2t 1
et
dy dx
(B)
et
2
2t 2t 2 2t 1
2
t 2t 2 2t 1
4 x2 If f x sin log e 1 x
(D)
None of these
, x R , then domain and
range of f (x) are given by : (A) 2, 1 , 1, 1 (C)
, 1 1, , 0, 1 0, 1 , 1, 1
(D)
None of these
(B)
x 1 1 : f x x : 1 x 1 . Then f (x) at x = 0 : 1 : x 1 (A) (C) (D)
(D)
2 3
If x e t , y tan 1 2t 1 , then
(C)
9.
1 e
(A)
(A)
removable discontinuity infinite discontinuity no discontinuity essential discontinuity
1 If y log e x3 3 sin 1 x kx 2 and y 2 3 , then 2 k= (A) 6 (B) 6
(C) 8.
2
If lim
Let f x |2 sgn 2 x | 2 . Then f (x) has : (A) (B) (C) (D)
1 cos x 2 is equal to : lim x 1 1 x
(A) (C) 5.
6.
Domain of the function f x cos
3.
1 1 2 | x | loge 3 x , then its 4
10.
x x The function f x sin cos is : n! n 1 !
(A) (B) (C) (D)
37
non periodic periodic with period 2 n ! periodic with period 2 (n + 1) ! periodic with period of 2(n + 1)
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [8]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than one correct option. 1.
1 2 1 cos 2 x is : x x0
(A) (C)
2.
(A)
lim
1 Does not exist
b 2 lim 1 a x sin 2 x 1 a x
(B) (D)
(C)
1 None of these
, a, b, R, a 0 ,
6.
3.
b
(B)
(C)
a2/b
(D)
a R, b 0
*4.
is
7.
a 2b None
8.
If
dx
9.
10.
at
is : 2
VMC/Differential Calculus - 1
2, 1
Let f x
sin x
(D)
2
x 2x 4
None of these
, [.] G.I.F., then which one is
(B) (D)
f is even f is onto
1 Does not exist
(B) (D)
0 None of these
x a sinb x
, a, b, c R 0 , exists and is nonsinc x zero, then : (A) (B) abc 0 abc 0
If lim
x0
(C)
37
1 2
tan 1 x lim , [.] = G.I.F. is : x x 0
(A) (C)
2
(B) (D)
not true : (A) f is periodic (C) f is many-one
f (x) is continuous f (x) is differentiable Discontinuous None of these y a 1 cos , x a sin , then
1 2
If log0.3 x 1 log0.09 x 1 , then x lies in the interval : (A) (B) (1, 2) 2, (C)
None of these
d2y
(D)
t
If x e sin t, y e cos t
(A) (C)
1 x 1 If f x x ; ([.] = G.I.F.), then at x 2 : 2
(A) (B) (C) (D) 5.
(D)
Does not exist t
1 a 2 None of these
2
ax 2 b : x 0 If f x possesses derivative at x : x0 x 2 = 0, then : (A) (B) a 0, b 0 a 0, b 0 (C)
(B)
and y x y k xy y , then k =
equal to : (A)
4
abc 0
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [9]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have More than one correct option. 1.
Let
f x be continuous at x = 0 and f 0 k .
The value of lim
2 f x 3 f 2x f 4x x2 (B) (D)
x0
(A) (C) 2.
If
(C)
,
2
then
(B)
7 24 , 3 11
(C)
y y x log y x y log x x
y y x log y x x y log x
(B) (D)
2 f x2
2,
(A)
(C)
2
(t 1)
(B)
(t 1) (t 2 1)
(D)
f is odd f is periodic
(B) (D)
1 tan x lim x 0 1 sin x
7 24 , 3 11
y x y log x
*9.
x y log x y
lim
ax 1 ax 1 a x a x a x a x
n a sin 2 n! n 1
(A) (C)
1 0
f x x
(D)
f x sin x
ax 1
cos ec x
1/e 1
n
ax 1
(B)
(B) (D)
e None
, 0 a 1
(B) (D)
None
For a real number x, let [x] denote the greatest integer less than or equal to x. Then f x
None of these
tan x 2
1 x
is :
(A)
Continuous at some x
(B)
Continuous at all x but f x does not exist for some x
(t 2 1)
(C)
2
(t 1)
f x exists for all x but f x does not exist
for some x (D)
2t
f x exists for all x
(1 t 2 )
10.
f is even None of these
Which of the following functions is an even function ?
VMC/Differential Calculus - 1
f x
(A) (C)
If f x min| x 1|,| x |,| x 1| , then : (A) (C)
6.
is
None of these
2
5.
7.
1 1 If x t , y t , then dy/dx is equal to : t t
2t
(C) 2k None of these
8. (D)
f x
is :
If x y y x 1 , then dy/dx is : (A)
4.
1
f x
x 2 17 x 66 discontinuous at x = (A)
3.
k 3k
(A)
37
e1 / x 1 : x0 has at x = 0 : f x e1 / x 1 : x0 0 (A) Removable discontinuity (B) Non-removable discontinuity (C) No discontinuity (D) None of these
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : DC-1 [10]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If x
y
0
1
du , then
1 9u 2 1
(A)
1 9 y
d2y dx 2
2.
3.
9y
is equal to :
(B)
1 9 y2
(D)
None of these
2
(C)
6.
7.
If g is the inverse of f and f x sin x , then g x
(A)
cos ec g x
(C)
cos ec g x
sin g x
(D)
None of these
5.
f x sin x cos x , where denotes the greatest integer function, is : (A) {0} (B) {0, 1} (C) {1} (D) None Range
of
If p, q 0 and
lim
x
8.
9.
(B)
2 , 1
(C)
2 , 1
(D)
2, 1
Let f x max 2 sin x, 1 cos x , x 0, . Then set
(A)
(B)
2
(C)
1 3 cos 5
(D)
1 3 cos 5
(C)
(B) 2
q /p
2
VMC/Differential Calculus - 1
(D)
Let f x
10.
p 2 / q2
x 1 a cos x b sin x
, x 0, f 0 1 . If f x3 (x) is continuous at x = 0, a and b are given by : (A)
5 3 , 2 2
(B)
5 , 3
(C)
5 3 , 2 2
(D)
None of these
If xe xy y sin 2 x , then dy/dx at x = 0 is : (A) (C)
px q px q a, lim b, qx p x 0 qx p
1
b , then a and b, respectively,
2, 1
[.]
then a/b = (A)
x3
are : (A)
Period of the function f ( x ) sin 3 x tan x , where [.] & {.} denote the integral part and fractional parts respectively, is given by : (A) 1 (B) 2 (C) 3 (D)
4.
sin 2 x a sin x
x0
of points of non-differentiability is :
(B)
If lim
0
(B) (D)
1
Let f x log
u x v x
1 None
, u 2 4, v 2 2, u 2 2,
v 2 1 , f 2 is equal to :
None
(A) (C)
37
0
1
(B) (D)
1 None
HWT/Mathematics
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