JECA Exam Solved Paper

I am going to participate in West Bengal MCA Joint Entrance Exam, so need previous question paper, will you please provide here?

This is the West Bengal MCA Joint Entrance Exam questions:

1 (95.6x 910.3) ÷ 92.56256 = 9?
(A) 13.14
(B) 12.96
(C) 12.43
(D) 13.34
(E) None of these

2. (4 86%of 6500) ÷ 36 =?
(A) 867.8
(B) 792.31
(C) 877.5
(D) 799.83
(E) None of these

3. (12.11)2 + (?)2 = 732.2921
(A)20.2
(B) 24.2
(C)23.1
(D) 19.2
(E) None of these

4.576÷ ? x114=8208
(A)8
(B)7
(C)6
(D)9
(E) None of these

5. (1024—263—233)÷(986—764— 156) =?
(A)9
(B)6
(C)7
(D)8
(E) None of these

6. ?125÷5x ?=6265
(A)1253
(B) 1250
(C)1245
(D) 1550
(E) None of these

7.(42)2÷6.3 x 26 =?
(A)7182
(B) 7269
(C)7260
(D) 7240
(E) None of these

8.384×12×2=?
(A)9024
(B) 9216
(C)6676
(D) 6814
(E) None of these

9.6534÷40÷33=?
(A)3.06
(B) 5.25
(C)4.82
(D) 6.12
(E) None of these

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Answered By StudyChaCha Member

As you want to get JECA exam question paper so here I am giving you some questions of that paper:
JECA Question Paper
Q.1)
1
x
dx
e
−
+
∫
is equal to
(a)
1
x
ec
++
(b)
()
1
log 1
2
x
ec
+
+
(c)
()
log 1
x
ec
++
(d)
(
)
2log 1
x
ec
+
+
Q.2)
/2
sin
0
cos
x
exdx
π
∫
is equal to
(a)
e
+ 1 (b)
e
– 1
(c)
e
+ 2 (d)
e
Q.3)
The area bounded by the coordinate axes and the curve
1
xy
+
=
is equal to
(a) 1 (b)
1
2
(c)
1
3
(d)
1
6
Q.4)
The value of
()
/2
0
log tan
x
dx
π
∫
is equal to
(a)
2
π
(b) 0
(c)
4
π
(d)
8
π
Q.5)
The degree of the differential equation
4
dy dy
xyx
dx dx
−
⎛⎞
−= −
⎜⎟
⎝⎠
is
(a) 2 (b) 3
(c) 4 (d) 5
Q.6)
y
– A cos
ω
t
+ B sin
ω
t
is a solution of the differential equation
(a)
2
2
2
0
dy
y
dt
ω
−=
(b)
2
2
0
dy
y
dt
ω
−
=
(c)
2
2
0
dy
y
dt
ω
+=
(d)
2
2
2
0
dy
y
dt
ω
+
=
Q.7)
The differential equation
44
3
32
dy y
x
y
dx x
+=
is not linear. The integrating factor to solve this equation
is
(a)
2
1
x
(b)
3
1
x
(c)
4
1
x
(d)
4
x
Q.8)
The general solution of
sin
dy
yx
dx
+=
is
(a)
2
11
sin cos
42
x
yce x x
−
=+ −
(b)
11
sin cos
22
x
yce x x
−
=+ −
(c)
3
sin
x
yce x
−
=+
(d)
x
yce
−
=
Q.9)
The solution of
2222
1
dy
x
yxy
dx
=−−+
is
(a)
11
sin sin
yxc
−−
−+
(b)
121
11
sin 1 sin
22
yx xc
−−
=
−+ +
(c)
121
11
sin 1 sin
22
yxx xc
−−
=−+ +
(d)
121
11
sin 1 cos
24
yxx xc
−−
=
−+ +
Q.10)
Which one of the following pair
s is not correctly matched?
Differential Equations Their Solutions
(a)
()
0
dy
Pxy
dx
+=
...
P
dx
yce
∫
=
(b)
22
0
xdy ydx
ax dx
xy
−
+=
+
...
2
1
tan
2
yx
ac
x
−
⎛⎞
+
=
⎜⎟
⎝⎠
(c)
22
0
xdy ydx
xy
−
=
−
...
(
)
log
x
yc
+
+
(d)
0
ydx x dy
+=
...
x
yc
=
Q.11)
The differential of the system of circles touc
hing the y-axis at th
e origin, is given by
(a)
22
20
dy
xy xy
dx
+− =
(b)
22
20
dy
xy xy
dx
+
+=
(c)
22
20
dy
xy xy
dx
−+ =
(d)
22
20
dy
xy xy
dx
−
−=
Q.12)
The rate at which bacteria multiply
is proportional to the instantaneous
number present.
If the original
number doubles in 2 hours,
then they will triple in
(a)
log 2
4
log 3
hours
(b)
log 2
5
log 3
hours
(c)
log 2
2
log 3
hours
(d)
log 2
log 3
hours
Q.13)
If
b
r
is a unit vector in the
xy
-plane making an angle of
4
π
with the
x
-axis, then
b
r
is equal to
(a)
ˆˆ
ij
+
(b)
ˆˆ
ij
−
(c)
()
ˆˆ
/2
ij
+
(d)
(
)
ˆˆ
/2
ij
−
Q.14)
Distance between two points
whose position vectors are
ˆ
ˆˆ
32
ij k
+
−
and
ˆ
ˆˆ
35
ijk
−
+
is
(a) 69 units (b)
69
units
(c) 13 units (d) 29 units
Q.15)
If
A
O
≠
ur ur
and both the conditions
(i)
..
A
BAC
=
uu
rur uu
rur
and (ii)
A
BAC
×=×
ur ur ur ur
hold simultaneously, then
(a)
BCO
==
ur ur ur
(b)
BC
=
u
rur
(c)
BC
≠
ur ur
(d)
,
BOCO
≠
≠
u
rururur
Q.16)
,,,
α
βξη
are non-empty sets then
(a)
()()()
(
)
α
βξηαβξη
×∪×=×∩×
(b)
()()()
(
)
α
βξηαξβη
×∩×=×∩×
(c)
()()()
(
)
α
βξηαξ βη
∩×∩=×∪×
(d)
()()()
(
)
α
βξηαη βξ
∩×∩=×∪×
Q.17)
There are 600 students in a school, If 400 of them
can speak Telugu, 300 can
speak Hindi, then the
number of students who can speak both Telugu and Hindi are
(a) 100 (b) 200
(c) 300 (d) 400
Q.18)
In a Euclidean plane, whic
h one of the following is
not
an equivalence relation?
(a) Parallelism of lines (a line being deemed parallel to itself)
(b) Congruence of triangles
(c) Similarity of triangles
(d) Orthogonality of lines
Q.19)
The modulus and principle amplitude of
(
)
2
13
i
+
, respectively are
(a)
2,
2
π
−
(b)
2
4,
3
π
(c)
1
54
,tan
83
−
⎛⎞
−
⎜⎟
⎝⎠
(d)
3
4,
4
π
−
Q.20)
If 1,
ω
,
ω
2
are the cube roots of unity, then value of
()
2
x
y
+
to
(
)( )
22
22
xy x y
ω
ωωω
+++
is equal to
(a)
xy
(b) 3
xy
(c) 6
xy
(d) 9
xy
Q.21)
The value of
33
13 13
22
nn
ii
⎡⎤⎡⎤
−+ −−
+
⎢⎥⎢⎥
⎣⎦⎣⎦
is equal to
(a) 3 (b) 3/2
(c) 0 (d) 2
Q.22)
The complex number z, satisfying the equation
1
iz
iz
−
=
+
lies on
(a) a circle with the centre (0, 0) and radius 1
(b) the
x
-axis
(c) the
y
-axis
(d) the line
y
=
x
+ 1
Q.23)
The binary number 1101101
+ 1011011 is written in
decimal system as
(a) 198 (b) 199
(c) 200 (d) 201
Q.24)
The binary equivalent to the decimal number 0.3125
(a) 0101 (b) .1010
(c) .0101 (d) .1101
Q.25)
The binary number 10110100001 in decimal system is
(a) 441 (b) 1441
(c) 1241 (d) 241
Q.26)
The the
m
th and the
n
th terms of an H.P. are
n
and
m
respectively, then the
mn
th term is
(a) 0 (b) 1
(c) 2 (d)
1
2
Q.27)
If
a, b, c
are in G.P., then
22 2
11
ab b
+
−
is
(a)
22
1
cb
−
(b)
22
1
bc
−
(c)
22
1
ca
−
(d)
22
1
ba
−
Q.28)
The value of
11
31 ...
39
−+ − =
is equal to
(a)
20
9
(b)
9
20
(c)
9
4
(d)
4
9
Q.29)
If
()()
260
xx
−+≥
, then the solu
tion set is
(a)
()
:2
xx
≥
(b)
(
)
:6
xx
≤
(c)
()
:6
xx
≤−
(d)
(
)
:2 6
xx orx
≥≤−
Q.30)
The value of
666...
+++
is equal to
(a) 2 (b) 3
(c)
6
(d) 6
Q.31)
If the equations
2
0
xpxq
−+=
and
2
0
xqxp
+
−=
have a common root, then which one of the
following will hold true?
(a)
p
=
q
(b)
p
+
q
= 2
(c)
p
+
q
= 1 (d)
p
–
q
= 1
Q.32)
The number of words that can be
formed from the letters of th
e word INDRAPRASTHA when the
vowels are never separated is
(a) 727560 (b) 725760
(c) 752760 (d) 757260
Q.33)
The number of 2-digit even
numbers that can be formed from th
e digits 1, 2, 3, 4 and 5, repetition
being not allowed, is
(a) 2
5
(b) 5!
(c)16 (d) 8
Q.34)
The number of ways in which 6 people can be seated at a round table is
(a) 6 (b) 60
(c) 120 (d) 720
Q.35)
The coefficient of the middle term in the expansion of
()
4
23
x
+
is
(a) 6 (b) 5!
(c) 8! (d) 216
Q.36)
If in the binomial expansion of (1 +
x
)
n
when
n
is a natural number, the coefficients of the 5
th
, 6
th
and
7
th
terms are in A.P., then
n
is equal to
(a) 7 or 13 (b) 7 or 14
(c) 7 or 15 (d) 7 or 17
Q.37)
If
8
12
log log
63
g
m
+=
, then
m
is equal to
(a) 24 (b) 18
(c) 12 (d) 4
Q.38)
If
x
yz
abc
==
, and
log log
bc
ab
=
, then which one of the
following will hold true?
(a)
2
yxz
=
(b)
2
x
yz
=
(c)
2
zxy
=
(d)
yxz
=
Q.39)
If
1
3
x
x
⎛⎞
+=
⎜⎟
⎝⎠
, then
6
6
1
x
x
⎛⎞
+
⎜⎟
⎝⎠
is equal to
(a) 927 (b) 414
(c) 364 (d) 322
Q.40)
The rank of the matrix
1230
2432
3213
6875
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
is equal to
(a) 1 (b) 2
(c) 3 (d) 4
Q.41)
If
21
01
A
−
⎡⎤
=
⎢⎥
⎣⎦
and
10
11
B
⎡⎤
=
⎢⎥
−−
⎣⎦
, the
()
2
A
B
+
is
not
equal to
(a)
22
A
AB BA B
+++
(b)
22
2
A
AB B
+
+
(c)
22
A
AB BA B I
+++
(d)
22
A
IABBAB
+
++
Q.42)
If
()
2
01
1
10
A
A
αβ
⎡⎤
==+
⎢⎥
−
⎣⎦
, then the value of
α
and
β
are given by
(a)
11
,
22
αβ
==
(b)
11
,
22
αβ
−
==
(c)
1
2
αβ
==±
(d)
1
2
αβ
=− =±
Q.43)
If A be an
n
×
n
matrix and C any scalar, then | CA |
(a)
C
nA
(b)
n
CA
(c)
nC A
(d)
CA
Q.44)
The matrix
074
70 5
45 0
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
−
⎣⎦
is
(a) symmetric (b) skew symmetric
(c) non-singular (d) orthogonal
Q.45)
If
31
1611
02
xi
x
yi i
ii
−
⎡⎤
⎢⎥
==+
⎢⎥
⎢⎥
−
⎣⎦
, then
(a)
3, 4
xy
=− =
(b)
3, 4
xy
=
=
(c)
3, 4
xy
==−
(d)
3, 4
xy
=
−=−
Q.46)
If
12
34
A
⎡⎤
=
⎢⎥
⎣⎦
, then A
-1
is equal to
(a)
21
31
22
−
⎡⎤
⎢⎥
⎢⎥
−
⎣⎦
(b)
21
31
22
⎡
⎤
⎢
⎥
⎢
⎥
−
⎣
⎦
(c)
21
31
22
−−
⎡⎤
⎢⎥
⎢⎥
⎣⎦
(d)
21
31
22
−
⎡
⎤
⎢
⎥
⎢
⎥
⎣
⎦
Q.47)
The expansion of the determinant
23
35
3
59
10 27
xy
xy
xy
contains which one of the following as a factor?
(a)
3
x
−
(b)
x
y
−
(c)
3
y
−
(d)
(
)
(
)
33
xy
−
−
Q.48)
The value of the determinant
0
00
000
ahg f
bc e
dk
l
is
(a)
gfkl
(b)
abhg
(c)
abdl
(d)
ablc
Q.49)
If
12
23
34
A
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
and
12
21
B
⎡⎤
=
⎢⎥
⎣⎦
, then
(a) both AB and BA exist
(b) neither AB nor BA exists
(c) AB exists but BA
does not exists
(d) AB does not exist but BA exist
Q.50)
The solution of equations
323;23 3
xy z x yz
+
+= −−=−
and
24
xyz
+
+=
is
(a)
3, 2, 2
xyz
===−
(b)
2, 1, 3
xyz
=
==
(c)
1, 2, 1
xy z
===−
(d)
1, 2, 1
x
yz
=
==
Q.51)
The adjoint of
cos sin
sin cos
θ
θ
θ
θ
⎡⎤
⎢⎥
⎣⎦
is equal to
(a)
cos sin
sin cos
θ
θ
θ
θ
−
⎡⎤
⎢⎥
−
⎣⎦
(b)
cos sin
sin cos
θ
θ
θ
θ
⎡
⎤
⎢
⎥
⎣
⎦
(c)
cos sin
sin cos
θ
θ
θ
θ
⎡⎤
⎢⎥
−
⎣⎦
(d)
cos sin
sin cos
θ
θ
θ
θ
−
⎡
⎤
⎢
⎥
⎣
⎦
Q.52)
The number of sides of two regular polygons are in the
ratio 5 : 4. The difference between their angles
is 9
0
. Which one of the following is correct?
(a) One of them is a pentagon and the other is a rectangle.
(b) One of them must be a hexagon.
(c) One of them is an octagon.
(d) One of the has 20 sides and the other has 16 sides.
Q.53)
The value of
tan31 .tan32 .tan32 .tan33 ...tan59
oooo o
is equal to
(a) -1 (b) 0
(c) 1 (d) 2
Q.54)
The number
11 21
,tan
64
π
π
−
⎛⎞⎛⎞
⎜⎟⎜⎟
⎝⎠⎝⎠
and
283
cot
6
π
⎛⎞
⎜⎟
⎝⎠
are in
(a) A.P. (b) G.P.
(c) H.P. (d) none of the above
Q.55)
The correct value of the parameter ‘
t
’ of the identity
(
)
(
)
66 44
2 sin cos sin cos 1
xxtxx
+
++=−
is
(a) 0 (b) -1
(c) -2 (d) -3
Q.56)
If
wxyz
=++
, then
sin sin sin sin
xyz
ω
++−
is equal to
(a)
4 sin sin sin
222
yz zx xy
+++
(b)
4 cos cos cos
222
yz zx xy
+
++
(c)
4tan tan tan
222
yz zx xy
+++
(d)
4cot cot cot
222
yz zx xy
+
++
Q.57)
To derive the tangent formula, the following steps are given:
1.
()
sin cos cos sin
cos cos cos cos
tan
cos cos sin sin
cos cos cos cos
A
BAB
A
BAB
AB
A
BAB
A
BAB
+
+=
+
2.
()
()
()
sin
tan
cos
A
B
AB
A
B
+
+=
+
3.
()
sin cos cos sin
tan
cos cos sin sin
A
BAB
AB
A
BAB
+
+=
−
4.
()
tan tan
tan
1tan tan
A
B
AB
A
B
+
+=
−
Their correct and proper sequential form to derive the formula is
(a) 2, 4, 3, 1 (b) 1, 2, 3, 4
(c) 1, 4, 2, 3 (d) 2, 3, 1, 4
Q.58)
Consider the following:
1. If
cot
x
θ
−
, then
1
sec cosec
x
x
θ
θ
+=
.
2. If
1
sin
x
x
θ
+=
, then
22
2
1
sin 2
x
x
θ
+= −
3. If
sec
xp
θ
=
and
tan
yq
θ
=
, then
22 2 2 22
x
qyp pq
−=
.
4. The maximum value of
cos 3 sin
θ
θ
−
is 3.
Which of these are correct?
(a) 1 and 2 (b) 2 and 3
(c) 3 and 4 (d) 1, 2 and 3
Q.59)
If
1
2cos
x
x
θ
+=
, then
3
3
1
x
x
+
is equal to
(a)
1
cos
2
θ
(b) cos
θ
(c) 2 cos3
θ
(d) 3 cos 3
θ
Q.60)
The expression
()
()
44 66
3
3{sin sin 3 } 2{sin sin 5
22
ππ
α
πα α πα
⎛⎞ ⎛⎞
−+ − − −+ −
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
is equal to
(a)
sin 2 sin 3
α
α
+
(b) 3
(c) 1 (d) 0

__________________
Answered By StudyChaCha Member