Jee 2014 Booklet3 Hwt Functions
Short Description
Jee 2014 Booklet3 Hwt Functions...
Description
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : FNC [1]
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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, question marked with ‘*’ may have More than One correct option. 1.
Let f x 6 x 7 cos x 6 x where [ ] is greatest integer function, then : (A)
Period of the function is 1 1 Period of the function is 2
(C) 2.
1, f a b e
6.
9.
0,
(D)
1,
(B)
f a b e2
(C)
f a b
(D)
None of these
x2 , x 2 is : x2
1
(C)
1, 1
(D)
1, 0, 1
2 x 2 x is : sin 2 x 2 x (A) Even function
(B)
Has domain R
(C)
Odd function
(D)
None of these
If f x 2 y, x 2 y xy then f (x, y) is : x2 y2 8
(B)
x2 y2 4
(C)
x2 y2 4
(D)
x2 y2 2
If x 5 x 6 0 (where [ ] denotes greatest integer function) then x belongs to : 2
[2, 4)
(B)
[2, 4) – {3}
(C)
{3}
(D)
{2}
(C)
[0, 1)
(D)
(0, 1]
, 1
(C)
1,
(D)
1,
odd
(C)
neither even nor odd
x2 e , then range of f (x) is : If f x ln x2 1 (A) (0, 1) (B) [0, 1]
Range of y (A)
10.
(C)
(B)
(A) 8.
0,
{1}
(A) 7.
Function is non periodic
(B)
Range of the function f x (A)
*5.
(D)
If f x e px 2 then f a f b is : (A)
4.
Period of the function is 2
Domain of f x log10 log10 1 x 3 is : (A)
3.
(B)
ex ,x 0 : x 1
0,
(B)
If f x x 2 sin x , then f (x) is : (A)
even
VMC/Functions
(B)
61
(D)
None of these
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
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TIME : 25 MINUTES
TEST CODE : FNC [2]
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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, question marked with ‘*’ may have More than One correct option. 1.
2.
x , x 0 [{ } denotes fractional part] f x x , x 0 Then f (x) is : (A) even (B) both even and odd (C)
*8.
2
(D)
3
even
(C)
both
(D)
None of these
periodic
(C)
odd
(D)
None of these
(B)
even
(B)
even natural number irrational number
(B) (D)
odd natural number zero
If f x cos 2 x cos 2 x , where [ ] stands for greatest integer function, then :
f 1 2
(B)
f 1
(C)
f 0
(B)
f x y f x f y
(D)
f 1 4
Let f x x 1 then :
(A)
f x2 f x
(C)
f
2
x f x
(D)
None of these
(B) (D)
periodic with period 2 odd function
0, 1
(C)
e,
(D)
1,
R 0 , 1, 1
(C)
R 0
(D)
None of these
ln sin x tan3 x cos ec 3x 5 is : Function f x e
periodic with period non periodic
Domain of f x log e log e x is : (A)
10.
(C)
1
If f (x) is odd and even simultaneously then f 3 f 2 is :
(A) (C) 9.
odd
(A) 7.
(B)
Function f x x tan x is :
(A) (C) *6.
0
(A) 5.
None of these
If h x f x f x g x g x , then h (x) is : (A)
4.
(D)
Number solution of : x 2 4 x 0 (A)
3.
odd
1,
(B)
Domain of f x log e x 2 is : (A)
R
VMC/Functions
(B)
62
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : FNC [3]
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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 x x x is satisfied by k values of x. Then k is :
(A) 2.
f x (A)
3.
9.
10.
2
(D)
3
(B)
Odd
(C)
Period
(D)
Positive always
(B) (D)
Periodic but with the fundamental period None of these
(C)
x 2 2
(D)
x2 2
(C)
R 0
(D)
R 1
(D)
None of these
x 1 is : 2
Periodic with period Non periodic
x 2 2 3
R+
x2
x 2 2
(B)
2
4
x then domain of f (x) is : (B)
R 1
(C)
2
1
(B)
0
(B) (D)
Periodic with different period Periodic with same or different period
If log x x ; then number of such value of x are : (A) 0 (B) 1
(C)
2
(D)
3
The number of solutions of 2 x 4 x 5 x 0 are : (A) 0 (B) 1
(C)
2
(D)
3
Total number solutions of 2 x 4 x 5 x 0 are : (A) 0 (B) 1
(C)
2
(D)
3
If f (x) is periodic then f x is : (A) (C)
8.
(C)
If f x e x and g x e x , then f x g x has how many solutions : (A)
7.
e 1 Even
If f x log (A)
6.
1
f x 2 f 1 x x 2 2, x R , then f (x) is :
(A)
5.
x x
(B)
f x sin x x is :
(A) (C) 4.
0
Periodic with same period Non periodic
VMC/Functions
63
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : FNC [4]
ROLL NO.
START TIME :
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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, question marked with ‘*’ may have More than One correct option. 1.
Period of sin x cos x is :
2
(A) 2.
4.
1 sq. unit
, 2 4,
*10.
(B)
2 sq. unit
1
4
(C)
No point
(D)
None of these
(C)
f (1) = 2
(D)
f (x) = 0 has 1 real solution
(C)
3 sq. unit
(D)
4 sq. unit
(C)
, 2 4,
(D)
None of these
(C)
2
(D)
3
is :
2
x x 6
, 2 4,
Number of integers in the range of f x 1
(B)
x 1 x2
0
are :
Domain of the function f x x 2 x is : 2
R
(B)
0,
(C)
, 0
(D)
None of these
(B)
4
(C)
2
(D)
2
7
(D)
4
Period of sin 4 x cos 4 x is :
(A) 9.
2 points
(B)
Domain of the function f x
(A) 8.
(D)
Area bounded by the curve x y 1 is :
(A) 7.
(B)
1 1 If f x f f x f and f 3 28 then : x x (A) f (x) is even (B) f (x) is odd
(A) 6.
2
1 point
(A) 5.
(C)
f x sgn e x 1 is discontinuous at : (A)
*3.
(B)
Number of break points in the curve f x 2 sin x in 0 , 2 : (A) 6 (B) 5 (C) f x
e e If e Choose correct statements : (A) Only 1 natural number is in domain of the function (B) Only 1 natural number is in range of the function (C) Only 1 whole number is in the domain of the function (D) Only 1 whole number is in the range of the function
VMC/Functions
x
64
HWT/Mathematics
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : FNC [5]
ROLL NO.
START TIME :
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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, question marked with ‘*’ may have More than One correct option. 1.
(A)
If f (x) is defined for x 0 , 1 , then function f 2 x 3
(C)
is defined for :
*2.
3.
(A)
x 0 , 1
(B)
3 x , 1 2
(C)
xR
(D)
3 x , 1 2
Which of the following is(are) odd function : (A) f (x) = constant (B) f (x) = sin x + cos x (C)
f x sin log x x 2 1
(D)
f x 1 x 2 x3
If f x (A)
f x 3
Domain set of definition of f x
6.
3 f x 1 f x 3 f x 3
1 x 2 x
(C) (D)
None of these
Domain of f x log10 (A)
[4, 6]
(C)
(2, 3)
x4 6 x (B)
(D) 1 sin x sin x Function f x 2 cos x cos x
9.
3 f x 1
, 2, 2 (B) , 1, 1 1, 1 , 2 2 ,
(A)
5.
(D)
f x 1
(D)
2 4
2 x 2 lies in Value of the function f x 3 sin 16 the interval : 3 (A) (B) 0, 4 , 4 2 (C)
8.
(B)
3, 3
Range of the function f x
(D)
None of these
1 is : 2 cos 3 x
1 (B) R 3 , 0 1 (C) (D) None of these 3 , 1 A polynomial function satisfies the condition 1 1 f x f f x f . If f 10 1001 , then x x f (20) is : (A) 2002 (B) 8008 (C) 8001 (D) None of these (A)
x 1 , then f (2x) is : x 1 f x 1 (B) f x 3
(C)
4.
7.
2
10.
:
, 6 (4, 6) is periodic with
1 x The function f x log satisfies the equation : 1 x (A) f x 2 2 f x 1 f x 0
(B)
f x 2 f x f x x 1
(C)
f x1 f x2 f x1 x2
(D)
x x f x1 f x2 f 1 2 1 x1 x2
period :
VMC/Functions
65
HWT/Mathematics
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : FNC [6]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
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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, question marked with ‘*’ may have More than One correct option. 1.
2.
If a function f (x) satisfies the condition 1 1 f x x 2 2 , x 0 , then f (x) equals : x x (A)
x 2 2 for x 0
(B)
x 2 2 for x 2
(C)
x 2 2 for x 2
(D)
None of these
4.
5.
6.
7.
1 The function f x is : 2 (A) Periodic (B) An odd function (C) Expressible as the sum of an even function and an odd function (D) None of these
(B)
5,
(C)
(D)
None of these
Domain definition of the function f x tan x 2 is :
VMC/Functions
[8, 10] [1, 10]
None of these
(B) (D)
(A) (C) 8.
12
One Zero
64 1 7 x is equals to : 3 (B) Two (D) None of these
Minimum value of f x x 1 x 2 x 3 is equal to : (A) 1 (C) 3
9.
(B) (D)
1 If 2 f x 2 3 f 2 x
1 x
(A) (C)
1 x 2
(B)
5x
2
1 x 4
(D)
None of these
Domain of the function a x a y a a 1 is : (A) (C)
66
5x2
5x
2 zero
2 2 x 1 then f (x ) is :
4
10.
(8, 10) None of these
Total number of real values of x such that
x
is defined for all x
belonging to : (A) 5,
, 5
(D)
12 x 1 7 12 x 1 7
f (x) is periodic with period 4k f (x) is periodic with period 2k f (x) is periodic with period k f (x) is not periodic but an odd function
f x log 2 x 5 x 2 3x 10
2, 1
Domain definition of the function
(A) (C)
sin x
*3.
(C)
(B)
f x log 4 log5 log3 18 x x 2 77 is :
If f x k f x 0 for x 0 then : (A) (B) (C) (D)
2 , 1 R 2 , 1
(A)
0 x 1 x 1
(B) (D)
0 x 1 x 0
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : FNC [7]
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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.
If f x 3 y, x 3 y 12 xy , then f x, y is : (B)
2 x2 y 2
(C)
x2 y 2
(D)
None of these
7.
(B)
f (x) is periodic with period
(C) (D)
f (x) is periodic with period 42 f (x) is non periodic
8.
, 1 1,
(B) (D)
Domain of the function : f x
(C)
(B) (D)
Domain of the function f x
x x
9.
, , 0 log0.3 x 1
(B)
2, 4
(C)
(2, 4)
(D)
None of these
f x x x
(B)
1 if x is a rational number f x 0 if x is a irrational number
(A)
f x sin 2 x and g x x
(B)
f x sin x, g x x
(C)
f x x 2 , g x sin x
2
then :
f and g cannot be determined
If f x a x n
(A) (C) 10.
1n
, where a > 0 and n N , then
a xn
(B) (D)
x an
Let f x x and g x x for all x R . Then the function x satisfying
x f x x g x 0 is : 2
Which of the following is non-periodic : (A)
fof x is equal to :
x2 2 x 8
(1, 4)
2 –1
(B) (D)
2
1
If g f x sin x and f g x sin x
(D)
1
(A)
VMC/Functions
x , x 1 . Then, for what value of is x 1
(A) (C)
ex ,x 0 : Range of y x 1
, 0 0,
Let f x
f (x) is periodic with period 2
0, 1,
None of these
f f x x ?
(A)
(A)
6.
(D)
f x sin x , then :
(C)
5.
2xy
(A)
4.
(A)
8 8 1 cos x 1 cos x
f x
(C)
67
2
(A)
x x, x 0 ,
(B)
x x, x R
(C)
x x, x , 0
(D)
x x x , x R
HWT/Mathematics
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : FNC [8]
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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.
1
f x
x x
5.
1 x x
then :
(A)
dom f and dom g
(B)
dom f and dom g
(C) (D)
f and g have the same domain dom f and dom g
Let f x
6.
7.
d a
(C)
a b c d 1 (D)
(B)
a b 1 8.
9.
(A) (C) (D)
(B)
(C)
x
(D)
The domain of definition of
10.
(B)
2,
{2, 3} [2, 3]
(B) (D)
(2, 3) None of these
(A)
0 x 1
(B)
0 x 1
(C)
x 1
(D)
x 0
Let f : R R be a function defined by
x
3
x
then graph of f (x) lies is :
1 x2 Only III quadrant Only IV quadrant I, II quadrant III and IV quadrant
Period of the function f x sin 4 3x cos 4 3x is : (A)
2
(B)
3
(C)
6
(D)
None of these
f x x f x x are :
, 1
1 x x
Domain of the function a x a y a a 1 is :
(A) (B) (C) (D)
Let f x x 1 and x x 2 . Then the value of x satisfying
1 x
f x
f x is an even function
x x x 2 cos tan The function f x sin is 2 3 4 periodic with period : (A) 6 (B) 3 (C) 4 (D) 12
(A)
(A) (C)
d=a
0, x0 , x 1 then f (x) is : Let f x x 2 sin 2 x x 1 x x , (A) Even function (B) Odd function (C) Neither even nor odd function
1 If 3 f x f log x 4 then f e x equals : x
f x log 1 log x 2 5 x 16
ax b . Then fof x x provided that : cx d
(A)
(D) 4.
, g x
, 2 , 1 2 ,
VMC/Functions
68
HWT/Mathematics
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : FNC [9]
ROLL NO.
START TIME :
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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.
The domain of definition of 3x 1 f x log0.5 log2 is : 3x 2 (B)
1 3 ,
(A)
(C)
1 3 ,
(D)
1 3 ,
(C)
If f x sin log x , then the value of
7.
x f xy f 2 f x cos log y is : y 1 (B) 0 1 (D) None of these
If f is even function defined on the interval 5, 5 then 9.
1
If f x x 2 x then if
(B) (D)
f
x
1
VMC/Functions
(B)
1 , x 0 , then f x 2 equals : x
f x f x
f x
f x
(B)
f x f x
(D)
None of these
Number of solutions of log x 3 2 x 3 is : (A) 3 (B) 1 (C) 2 (D) 0 Domain of the function f x 2 x 1 x (A)
[2, 6]
(B)
2 , 6
(C)
[8, 12]
(D)
None of these
If f x and g x be periodic and non-periodic
2 None of these 10.
k then for what
(A)
always periodic
(B)
never periodic
(C)
can’t say
(D)
periodic it g(x) is linear function of x
Number of solutions of x 2 2 2 x 0 (where [.] denotes greatest integer function) (A) 1 (B) (C) 0 (D)
value of k equation has exactly 4 roots : (A)
3 4
(D)
functions respectively, then f g x is :
Period of f x sin 2 x cos 2 x is : (A) (C)
5.
8.
1 4
If f x x
1 , 3
number of real values of x satisfying the equation x 1 f x f are : x2 (A) 1 (B) 2 (C) 3 (D) 4 4.
6.
(A)
(A) (C) 3.
(C)
1 2
69
2 infinite
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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, question marked with ‘*’ may have More than One correct option. 1.
Let f x
4x x
4 2
(C)
. Then the value of
1 2 3 1996 is : f f f . . . . f 1997 1997 1997 1997
(A) (C) 2.
*3.
4.
6.
(B) (D)
999 None of these
*7.
Range of the function f x 3 sin x 2 cos x is : (A)
2 , 13
(B)
3, 13
(C)
13 , 13
(D)
2 , 3
If
(A) (C) 8.
10 x f x e , x 10, 10 10 x
200 x 1 f x kf , then is : 2 k 100 x a prime (B) a composite even (D) odd
If h x 2 max f ( x ) g ( x ) , 0 , then h(x) is equal to :
If f x 27 tan 3 x cot 3 x and , are two values
(A)
f x g x g x f x
of x for which 3 tan x cot x 2 , then :
(B)
f x g x g x f x
(C)
f x g x g x f x
(D)
f x g x g x f x
(A)
f f
(C)
f 2
Domain of f x (A) (C)
5.
998 997
(D)
,nI 2 None of the above x : x 2n 1
R+ R
(B)
f 26
(D)
f f
1 x12 x 9 x 4 x 1 (B) (D)
2
is :
9.
1 x 1 f x log0.4 is : 2 x 5 x 36
R can’t be easily specified
(A)
Range of f x sin x cos x is : (A)
{0, 1}
(B)
1, 0, 1
(C)
{1, 2}
(D)
{1}
Domain of the function
(C) *10.
, 0 6 1, 6
f x x3
and g x sec 2 x tan 2 x . The two functions are
(B)
f x e x e x
equal over the set : (A)
(C)
f x sin x
(D)
e x e x
VMC/Functions
x x cos 2 2 2
(B)
R
70
(D)
0, 1, 6 1, 6
Function(s) whose graph is symmetrical about origin is(are) : (A)
Let f x sin 2
(B)
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