Narayana IIT Academy 23-09-23_SR.

IIT_*CO-SC(MODEL-A&B)_JEE-MAIN_PTM-8_Q’P
60. Find the total number of alkyl bromides (excluding stereoisomers) which on reaction
with magnesium in dry ether followed by reaction with water gives 3  Ethylpentane .

MATHEMATICS MAX.MARKS: 100

SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer,
out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

x3 x 2
61. Let f : R  R , f  x     x  10 then f(x) is
3 2
A) one –one and onto B) many one and onto
C) one-one and into D) many one and into
62. Let f :  2, 2   3, 2 and graph of function is as shown in the figure. Then
(2,2)

-2 (1,0) 2

(0,-1)
(-2,-3)

A) f  x  is one one function B) f  x  is many one function

C) f(x) is one-one & into function D) f(x) is many one & into function

63. Range of
x 2
 3 x  1
where x  R is
x 2
 4 x  1

 5   1   5 1   6 
A)  ,     ,   B)  ,  C)  2, 1 D)  2, 
 2  6   2 6   5

 cos2 x  4cos x  10 
64. Range of y  sgn  2  is (where sgn (x) represents signum function)
 cos x  2 cos x  9 
A){0} B){1} C){0,1} D){-1,0,1}

1  p x  1  q  x 1  r  x
2 2 2

65. Let f : R  R and p 2  q 2  r 2  2 such that f  x   1  p  x 1  q x  1  r  x , then f(x) is

2 2 2

1  p  x 1  q  x 1  r x 
2 2 2

A) one one and onto B) many one and onto

C) one-one and into D) many one and into

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1 x
66. Solution set of  0 is
2 x

A)  , 1  1,   B)  , 2    2,  

C)  , 2    1,1   2,   D)  ,  

 4x  9x 
67. The value of x satisfying the equation log 6    x is
 2 
A) positive B) negative
C) neither positive nor negative D) irrational
68. Sum of values of x satisfying the equation 3 x  x  5 is

5 2 5
A)0 B)  C) D) 
4 5 2
69. Range of the values of the expression y  sinx. tanx.cot x , is
A) (-1,1)-{0} B) (-1,1) C) [-1,1] D) [-1,1]-{0}
70. Let f : R  R be a function such that f  x   x3  x 2  3 x  sin x then

A) f is one-one and onto B) f is one-one and into

C) f is many one and into D) f is many one and onto
x
71. Let f :  2, 4   1, 3 be a function defined by f  x   x    ( where [.] denotes the greatest integer
2
function), then f 1  x  is equal to :

A) 2x B) x C) x+1 D) x-1
2x
   
72. If lim  1   2   e 2 then
x 
 x x 
A)   1,   2 B)   2,   1 C)   1,   any real constant D)   1,   1

f  x  x 2  x, 0  x  2
73. Let . If the definition of f is extended over the set R   0, 2 by

f  x  2  f  x 
then f is a
A) Periodic function of period 1 B) Non periodic function
1
C) Periodic function of period 2 D) Periodic function of period
2
74. If f(x) is a polynomial function of the second degree such that f(-3)=6, f(0)=6 and f(2)=11 then the
graph of the function f(x) cuts of ordinate x=1 at the point
A) (1, 8) B) (1, 4) C) (1, -2) D) (1,-8)

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a/ x
75. lim  cos x  a sin bx  is equal to (a and b are non zero real numbers)
x 0

2 2 2 2
A) e  a b B) e ab C) e a b D) e b a

 {x}  {2 x}  {3 x}  ....  {nx} 

76. Lt    (where {…} is Fractional Part )
n 
 n2 
A) 1 B) –1 C) 0 D) None
x  6  sin  x  3   3
77. lim =
x 3  x  3 cos  x  3
1 3 5
A) B)5 C) D)
5 4 6
 
78. lim  log  x 1  x  log  x   x  1 log x1  x  2  ....  log xk 1  x k    is equal to
   
x      
1
A) 1 B) -k C) D) k
k

79. lim x 3  x 2  1  x 4  x 2  is equal to

x   

1 2 1 3
A) B) C) D)
4 2 4 2 2
x tan 2 x  2 x tan x
80. lim 2
is equal to
x 0
1  cos 2 x 
1 1
A) 2 B) -2 C) D) 
2 2
SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
This section contains 10 questions. The answer to each question is a Numerical value. If the Answer in the
decimals , Mark nearest Integer only. Have to Answer any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, -1 in all other cases.
81. If f " 0   4 and f '  0  exist finitely and equals to zero then the value of
2 f  x  3 f 2x   f  4x 
lim
x0 x2 is
x sec x
82. The value of lim  sin x  is
x 0

83. Let f  x   5  sin x, g  t   2  cos3 t and h  x1    3sin x1  4 cos x1   2 , then maximum possible

value of f  x   g  t   h  x1  is (where x, x1 and t are independent variables)

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84. If f  x   2 x2  2 x  20 , then the number of integer(s) in the range of f(x) for x   1,1 in

(are)
85. If minimum value of f  x   x  x  1  x  2  x  3  x  4 is k at x   , then   k  is

86. Let f  x    x3  x and x   , 1  1,   then the number of solutions of f  x   f 1  x  is

87. The number of real solutions of e x  x  1 is

88. Let f(x) =[x] and g(x) =x+[x]. The number of solutions of the equation 4(x- f(x)) =g(x)
is (where [.] is G.I.F)
sin  ax 2  bx  c 
89. If  is a repeated root of ax 2  bx  c  0 then Lt is
x 
 x  2

90. If f(x+y,x-y) = xy then the arithmetic mean of f(x,y) and f(y,x) is

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SPACE FOR ROUGH WORK

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SPACE FOR ROUGH WORK

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