JEE 2024 (JANUARY ATTEMPT)
MOCK TEST – 2
MATHEMATICS
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THERE ARE 30 QUESTIONS IN THIS TEST FORM.
ALL QUESTIONS ARE COMPUSORY.
EACH TEST ITEM CONTAINS EQUAL MARKS.
SECTION A CONTAINS 20 MULTIPLE CHOICE QUESTIONS. EACH QUESTION HAS 4 CHOICES (A), (B), (C)
AND (D), OUT OF WHICH ONLY ONE CHOICE IS CORRECT.
SECTION B CONTAINS 10 NUMERICAL VALUE TYPE QUESTIONS. ATTEMPT ANY 5. THE ANSWER TO
EACH QUESTION IS AN INTEGER RANGING FROM 0 TO 99.
SECTION – A
1
3
+log
(
x
 x)
10
2
16  x
1
and D2 be the Domain of g ( x) 
[ x]2  [ x]  2
1. Let D1 be the Domain of f ( x) 
(where [ x] denotes the greatest integer less than or equal to x)
If ( D1  D2 )  [ a, b)  (c, ), then a  b  c 
(a) 10
(b) 11
(c) 12
(d ) 13
 (tan 230 ) x  log e (456) 
2. If f ( x)  
, x  0 then the least value of
0 
 (log e (4567)) x  tan 23 

f  f  x  f 

(a) 4
 16  
f    is
 x 
( b) 2
( c) 8
1 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)
( d ) 16
3. Let the complex number z  x  iy be such that
2 z  3i
is purely
2z  i
imaginary. If x  y 2  0 then the value of 4 y 4  4 y 2  4 y  1 is
(a) 0
(b) 1
(c) 2
(d ) 3
4. Let p & q be the maximum & minimum values of the determinant
1  sin 2 2023 x
cos 2 2023 x
sin 2 2023 x
1  cos 2 2023 x
sin 2 2023 x
cos 2 2023 x
sin 2024 x
sin 2024 x .
1  sin 2024 x
then number of terms in the expansion of ( a  b  c ) 4 p  q is
(a) 91
(b) 105
(c) 120
( d ) 136
5. The shortest distance between the lines
x 1 y 1 z  2


&
2
2
1
x3 y5 z7


lies in the interval
1
8
4
(a ) (0,1]
(b) (1,2]
(c) (2,3]
( d ) (3,4]
6. Let f ( p )  sin 1 p.cos 1 p.tan 1 p.cot 1 p.sec 1 p.cos ec 1 p
m
If maximum value of f ( p) is k m , then  | x  128k | dx 
0
(a) 6
(b ) 9
(c) 18
2 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)
( d ) 36
cos 2  cos 2 

cos(   )
(c )  1
(d ) 1
7. If cos   cos   sin   sin  , then
(a )  2
(b ) 2
8. If x1 & x2 are two values of x satisfying the equation ,
x  1  2 log 2 (3  2 x )  2 log 4 (10  2  x )  0, then 2 ( x1  x2 ) 
( a ) 11
(b) 12
(c) 13
( d ) 14
9. Given the family of lines, a( x  y  2)  b(2 x  3 y  4)  0 .The line
of the family situated at the greatest distance from the point P (2, 3)
has equation
(a) x  y  2  0
(b ) 4 x  3 y  2  0
( c ) 4x  3 y  2  0
( d ) 4x  3 y  8  0
10. The mean and variance of 7 observations are 8 and 16 respectively.
If two observations are 6 and 8, then the variance of the remaining
5 observations is :
(a ) 21
(b ) 21.34
(c) 21.44
( d ) 21.64
11. Radius of the largest circle which passes through the focus of
the parabola y 2  4 x and contained in it is
(a) 1
(b ) 2
(c) 4
(d ) 8
12. If f ( x )  2 x 3  3( a  1) x 2  6 ax  2024 has maxima and minima
at p and q respectively if p  2 q , then a 
(a) 1
(b ) 2
(c ) 0.5
3 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)
( d ) 2024
 1  x2  
13. The number of solutions of the equation sin 
  sec( x  1)
 2x  2
is / are
1
(a) 0
(b ) 1
(c) 2
( d ) Infinite
14. Which of the following are not differentiable at x  0
(b ) cos | x |  | x |
(a) | x |
( d ) sin | x |  | x |
(c) cos | x |
15. If f ( x )  0 be a quadratic equation such that f (  )  f ( )  0 &

3 2
f ( x)
f( ) 
, then lim

x


2
4
sin(sin x)
(b ) 
(a) 0
2
16.If f ( x )  x  sin x, then

(c) 2
( d ) 4
f 1 ( x ) dx 

(b) 3  2
(a) 0
1  x 2  1  y 2  a ( x  y ), then
17.If
(a)
1  x2
1 y
2
(b )
1 y2
1 x
2
3
(c)
+2
2
3 2
(d )
+2
2
dy

dx
(c)
 1 y2
1 x
2
4 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)
(d )
 1  x2
1 y2
18.If C be the centroid of the triangle having vertices  3, 1 , 1, 3 
and  2, 4  . Let P be the point of intersection of the lines x  3 y  1  0
and 3 x  y  1  0, then the line passing through the points C and P
also passes through the point :
( a )  9, 7 
(b)  9, 6 
(c )  7, 6 
( d )  9, 7 
3  isin
,   [0, 2 ], is a real number , then an argument of sin  icos is
4  icos
4
3
4
3
( a ) tan 1
(b) tan 1
(c )   tan 1
( d )   tan 1
3
4
3
4
19.If
20.If the sum of two unit vectors is a unit vector , then magnitude of their
difference is
(a) 3
(b )
3
(c)
2
(d )
6
SECTION – B (ATTEMPT ANY 5)
21.If 
dx
1

log
2
( x  4) x 4 2
x 2
1

f ( x )  c, where c is the
x 2 2 2
cons tan t of int egration, such that f (2) 

4
, then find the value of
50
2
[ f (6)  f ( )].

3
22.Find the max imum value of 6sin x cos x  4 cos 2 x.
23. f ( x ), g ( x) are two differentiable function on [0, 2] such that
f ( x )  g ( x )  0 and f (1)  4  2 g (1) and f (2)  3 g ( 2)  9
then find the value of [ f ( x )  g ( x )] at x 
3
.
2
5 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)

24.If
dx

2

then
find
the
value
of
(6
k
 200).
0 ( x 2  4)( x 2  9) (k 2  11)
25. In an ellipse,if the lines joining a focus to the extremities of the minor
axis make an equilateral triangle with minor axis, the eccentricity of the
ellipse is
k
, then find the numerical value of k.
k 1
26.If a  2 sin 1 x  cos 1 x  b, then find the value of 2a 
3b

.
27.Let f : N  N for which f ( m  n )  f ( m )  f ( n ) m, n  N .If f (6)  18,
find f (2). f (3).
28.If a1 , a2 , a3 ......, a9 are in Arithmetic Pr ogression and a4  5, a5  4,
a1
then find the value of a4
a2
a5
a3
a6 .
a7
a8
a9
29.If 3 
3  d 3  2d

 .....    8, then Find the value of d .
2
4
4
3
1
1

30.Find the number of real roots of  x   + x   0.
x
x

6 | PREPARED BY: SHASHANK VOHRA (LECTURER MATHS, DOE DELHI)