The document contains a series of mathematics questions and answers from the Bitsat 2018 examination, covering topics such as set theory, complex numbers, and binomial expansion. Each question is presented with multiple-choice options, and the correct answer is provided for each. The questions test various mathematical concepts and problem-solving skills.

1. BITSAT 2018 MATHEMATICS QUESTION BANK
Ques. If A and B are any two sets, then )BA(A  is equal to
(a) A (b) B (c)
c
A (d)
c
B
Ans. (a)
Ques. If y
x
x
xxx
x











 1
1
)1(
1
4
1
)1()1( 222
then y =
(a) 22
)1(2
)1(


x
x
(b)
)1(3
)1(
2


x
x
(c) 22
)1(2
1


x
x
(d) None of these
Ans. (a)
Ques. The value of
805402010
15

is
(a) )25(5  (b) )22(5  (c) )21(5  (d) )23(5 
Ans. (c)
Ques. If A and B are two given sets, then
c
)BA(A  is equal to
(a) A (b) B (c)  (d)
c
BA 
Ans. (d)
Ques. If )log(log
2
1
2
log ba
ba
eee 




 
, then relation between a and b will be
(a) ba  (b) a = b/2 (c) ba 2 (d) a = b/3
Ans. (a)
Ques. The partial fractions of
)2()1(
13
2
xxx
x


are
(a)
)1( 2
 xx
x
+
2
1
x
(b)
21
1
2


 x
x
xx
(c)
2
1
12


 xxx
x
(d)
21
1
2




x
x
xx
Ans. (c)
Ques. If 22
)1()1()1()1()1(
43








x
C
x
B
x
A
xx
x
, then A
(a) –1/2 (b) 15/4(c) 7/4 (d) –1/4
Ans. (c)
Ques. Which is the correct order for a given number  in increasing order
(a)  1032 log,log,log,log e (b)  2310 log,log,log,log e
(c)  3210 log,log,log,log e (d)  1023 log,log,log,log e
Ans. (b)
Ques. The complex numbers 21 , zz and 3z satisfying 


32
31
zz
zz
2
31 i
are the vertices of a triangle which is
(a) Of area = 0 (b) Right angled isosceles (c) Equilateral (d) Obtuse angled isosceles
Ans. (c)
Ques. A complex number z is such that 







2
2
z
z
arg
3

 . The points representing this complex number will lie on
(a) An ellipse (b) A parabola (c) A circle (d) A straight line
Ans. (c)

2. https://www.examsegg.com/practice-papers/ Page 2 of 6
Ques. Let iba
ix
ix



1
1
and 122
ba , where a and b are real, then x
(a) 22
)1(
2
ba
a

(b) 22
)1(
2
ba
b

(c) 22
)1(
2
ab
a

(d) 22
)1(
2
ab
b

Ans. (b)
Ques. If ,
3
sin
3
cos 











 nnn ix

then xxxx ...... 321 is equal to
(a) 1 (b) – 1 (c) i (d) – i
Ans. (c)
Ques. Let na be the th
n term of the G.P. of positive numbers. Let 
100
1
2
n
na and 

100
1
12
n
na , such that   ,then the
common ratio is
(a)


(b)


(c)


(d)


Ans. (a)
Ques. If dcba ,,, and p are different real numbers such that 0)()(2)( 2222222
 dcbpcdbcabpcba , then dcba ,,,
are in
(a) A.P. (b) G.P. (c) H.P. (d) cdab 
Ans. (b)
Ques. If the roots of the equation 02
 qpxx are  and  and roots of the equation 02
 sxrx are 44
,  , then the
roots of the equation 024 22
 rqqxx will be
(a) Both negative (b) Both positive
(c) Both real (d) One negative and one positive
Ans. (c)
Ques. If , are the roots of the equation 02
 qpxx then the quadratic equation whose roots are ))(( 3322
  and
3223
  is
(a) 02
 PSxx (b) 02
 PSxx (c) 02
 PSxx (d) None of these
(where 22224
],55[ qpPqqpppS  )45( 224
qqpp 
Ans. (a)
Ques. The coefficient of the middle term in the binomial expansion in powers of x of 4
)1( x and of 6
)1( x is the same if 
equals
(a)
5
3
(b)
3
10
(c)
10
3
(d)
10
3
Ans. (c)
Ques. The smallest positive integer n, for which
n
n
n 




 

2
1
! hold is
(a) 1 (b) 2 (c) 3 (d) 4
Ans. (b)
Ques. If 



 

1
23
0
3
!)23(
,
!)3( n
n
n
n
n
x
b
n
x
a and 





1
13
!)13(n
n
n
x
c then the value of  abccba 3333
(a) 1 (b) 0 (c) – 1 (d) – 2
Ans. (a)

3. https://www.examsegg.com/practice-papers/ Page 3 of 6
Ques. If , are the roots of the equation 02
 qpxx , then  )1(log 2
qxpxe
(a) 



 ......
32
)( 3
33
2
22
xxx

 (b) 



 ......
3
)(
2
)(
)( 3
3
2
2
xxx


(c) 



 ......
32
)( 3
33
2
22
xxx

 (d) None of these
Ans. (a)
Ques.  ....
!4
)(log
!2
)(log
1
42
nn ee
(a) n (b) n/1 (c) )(
2
1 1
 nn (d) )(
2
1 nn
ee 

Ans. (c)
Ques. If
xaa
bxa
bbx
1 and
xa
bx
2 are the given determinants, then
(a) 2
21 )(3  (b) 21 3)( 
dx
d
(c) 2
21 )(2)( 
dx
d
(d) 2/3
21 3
Ans. (b)
Ques. If









 

100
0cossin
0sincos
)( 

F and















cos0sin
010
sin0cos
)(G , then 1
)]()([  GF
(a) )()(  GF  (b) )()(  GF  (c) 11
)]([)]([ 
 GF (d) 11
)]([)]([ 
 FG
Ans. (d)
Ques. If ,
3
2
)(sec,1)(tan  BABA then the smallest positive value of B is
(a) 
24
25
(b) 
24
19
(c) 
24
13
(d) 
24
11
Ans. (b)
Ques. For ,
2
0

  if 



0
2
,cos
n
n
x  



0
2
,sin
n
n
y  



0
22
,sincos
n
nn
z  then
(a) yxzxyz  (b) zxyxyz  (c) zyxxyz  (d) xyzxyz 
Ans. (b, c)
Ques. If ,
2
3
tan  the sum of the infinite series  ....)cos1(4)cos1(3)cos1(21 32
 is
(a)
3
2
(b)
4
3
(c)
22
5
(d)
2
5
Ans. (d)
Ques. In a ABC , 21sinsinsin  CBA and  CBA coscoscos 2 if the triangle is
(a) Equilateral (b) Isosceles (c) Right angled (d) Right angled isosceles
Ans. (d)
Ques. Which of the following pieces of data does not uniquely determine an acute angled ABC (R = circum-radius)
(a) BAa sin,sin, (b) cba ,, (c) RBa ,sin, (d) RAa ,sin,
Ans. (d)
Ques. There exists a triangle ABC satisfying the conditions

4. https://www.examsegg.com/practice-papers/ Page 4 of 6
(a)
2
,sin

 AaAb (b)
2
,sin

 AaAb (c)
2
,sin

 AaAb (d) None of these
Ans. (a)
Ques. If a, b, c be positive real numbers and the value of
ab
cbac
ca
cbab
bc
cbaa )(
tan
)(
tan
)(
tan 111 




 
 ,
then tan is equal to
(a) 0 (b) 1 (c)
abc
cba 
(d) None of these
Ans. (a)
Ques. If
2
...
42
cos....
42
sin
62
21
32
1 
















  xx
x
xx
x for ,2||0  x then x equals
(a) 1/2 (b) 1 (c) –1/2 (d) – 1
Ans. (b)
Ques.
5
tanh1
tanh1










is equal to
(a) 10
e (b) 5
e (c) 1 (d) – 1
Ans. (a)
Ques. tanh–1
(1/2) + tanh–1
(1/3) is equal to
(a) tanh–1
(5/7) (b) tanh–1
(7/5) (c) tanh–1
(1/6) 





6
1
tanh 1
(d) 





6
5
tanh 1
Ans. (a)
Ques. The equation of bisectors of the angles between the lines |||| yx  are
(a) xy  and 0x (b)
2
1
x and
2
1
y (c) 0y and 0x (d) None of these
Ans. (c)
Ques. A square of side a lies above the x–axis and has one vertex at the origin. The side passing through the origin makes an
angle )
4
0(,

  with the positive direction of x-axis. The equation of its diagonal not passing through the origin is
(a) axy  )cos(sin)sin(cos  (b) axy  )cos(sin)sin(cos 
(c) axy  )cos(sin)sin(cos  (d) axy  )cos(sin)sin(cos 
Ans. (b)
Ques. The angle between lines joining the origin to the points of intersection of the line 23  yx and the curve 422
 xy is
(a) 6/ (b) 4/ (c) 3/ (d) 2/
Ans. (c)
Ques. If the straight line 0,;2  babyax touches the circle 3222
 xyx and is normal to the circle 6422
 yyx , then
the values of a and b are respectively
(a) 1, –1 (b) 1, 2 (c) 1,
3
4
 (d) 2, 1
Ans. (c)
Ques. The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 523 22
 yx is
(a) )5/12(tan 1
(b) )5/6(tan 1
(c) )5/12(tan 1
(d) )5/6(tan 1
Ans. (c)

5. https://www.examsegg.com/practice-papers/ Page 5 of 6
Ques. Eccentricity of the rectangular hyperbola dx
xx
e x
 






1
0
3
11
is
(a) 2 (b) 2 (c) 1 (d)
2
1
Ans. (b)
Ques. jia 53  and jib 36  are two vectors and c is a vector such that bac  , then ||:||:|| cba is
(a) 39:45:34 (b) 39:45:34 (c) 34 : 39 : 45 (d) 39 : 35 : 34
Ans. (b)
Ques. The direction ratios of the lines OA and OB are 1, –2, –1 and 3, –2, 3. Then the direction cosines of the normal of plane
AOB where O is the origin, are
(a) 






 
29
2
,
29
3
,
29
4
(b) 








29
4
,
29
3
,
29
2
(c) 








29
3
,
29
2
,
29
4
(d) 






 
29
3
,
29
2
,
29
4
Ans. (a)
Ques. The equation of line of intersection of the planes 3213128,12544  zyxzyx can be written as
(a)
4
2
3
1
2




zyx
(b)
4
2
32


zyx
(c)
43
2
2
1 zyx




(d)
43
2
2
1 zyx





Ans. (c)
Ques. The function ),(|,|||)(  xxrqpxxf , where 0,0,0  rqp assumes its minimum value only at one point, if
(a) qp  (b) rq  (c) pr  (d) rqp 
Ans. (d)
Ques. k
nn
n
n












 4
sin
4
coslim

, then k is equal to
(a)
4

(b)
3

(c)  (d) None of these
Ans. (a)
Ques. The line 262  yx is a tangent to the curve 42 22
 yx . The point of contact is
(a) )6,4(  (b) )62,7(  (c) )3,2( (d) )1,6(
Ans. (a)
Ques. If f(x) = x5
– 20x3
+ 240x, then f(x) satisfies which of the following
(a) It is monotonically decreasing everywhere (b) It is monotonically decreasing only in ),0( 
(c) It is monotonically increasing everywhere (d) It is monotonically increasing only in )0,(
Ans. (c)
Ques.  


dx
xa
xa
(a) cxaaxa  221
/cos (b) cxaaxa  221
/cos
(c) cxaaxa   221
/cos (d) cxaaxa   221
/cos
Ans. (d)
Ques. dx
x
xxx


4
22
]log2)1[log(1
is equal to
(a) c
xx



















3
21
1log
1
1
3
1
2
2/1
2
(b) c
xx



















3
21
1log
1
1
3
1
2
2/3
2

6. https://www.examsegg.com/practice-papers/ Page 6 of 6
(c) c
xx



















3
21
1log
1
1
3
2
2
2/3
2
(d) None of these
Ans. (b)
Ques.  


dx
xx
xx
22
88
cossin21
cossin
(a) cx 2sin (b) cx  2sin
2
1
(c) cx 2sin
2
1
(d) cx  2sin
Ans. (b)
Ques. If  
1
0
,)()(
x
x
dttftxdttf then the value of )1(f is
(a) ½ (b) 0 (c) 1 (d) –1/2
Ans. (b)
Ques. If 

x
dttxf
1
,||)( ,1x then
(a) f and f are continous for 01 x (b) f is continous but f is not continous for 01 x
(c) f and f are not continous at 0x (d) f is continous at 0x but f is not so
Ans. (b)
Ques. The differential equation
3
2/12
2
2
y
dx
dy
dx
yd












has the degree
(a) ½ (b) 2 (c) 3 (d) 4
Ans. (d)
Ques. The solution of the equation 






x
y
tanxy
dx
dy
x is
(a) 0c
y
x
sinx 





(b) 0cysinx  (c) c
x
y
sinx 





(d) None of these
Ans. (c)
Ques. A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6m and weighs 3 Newton. Its
centre of gravity G is at a distance 0.4m from A. Then the tension of the string at A is
(a) 0.2 N (b) 1.4 N (c) 0.8 N (d) 1 N
Ans. (d)
Ques. A heavy rod ACDB, where AC = a and bDB  rests horizontally upon two smooth pegs C and D. If a load P were applied at
A, it would just disturb the equilibrium. Similar would do the load Q applied to B. If cCD  , then the weight of the rod is
(a)
c
QbPa 
(b)
c
QbPa 
(c)
c
QbPa
2

(d) None of these
Ans. (a)
Ques. A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins. If a coin is
drawn out of any purse, then the probability that it is a copper coin is
(a) 4/7 (b) ¾ (c) 37/56 (d) None of these
Ans. (c)
Ques. The coefficient of correlation between the observations (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) is
(a) 1 (b) – 1 (c) 0 (d) 2
Ans. (b)