Bangalore University 2010-2nd Year M.C.A Entrance -Year -Maths-Practice -6 - Question Paper
TEST PAPER 6
Total Questions: 60
Time allotted 75 minutes
dx
11
Q.1)
is equal to
+ e
(a) 1 + ex + c (c) log (l + ex) + c
(b) I log (l + e) + c (d) 2log(l + ex) + c
n / 2
Q.2) J esinx cos x dx is equal to
(b) e - 1 (d) e
(a) e + 1 (c) e + 2
Q.3) The area bounded by the coordinate axes and the curve 4x +*Jy = 1 is equal to (a) 1
(b) 2
<d) 6
(O 33
Q.4) The value of J log (tan x~)dx is equal to
0
(b) 0
n
(d) -
8
(c)
4
dy
dy
Q.5) The degree of the differential equation- x = I y - x I is
dx I dx.
(a) 2
(c) 4
(b) 3
(d) 5
Q.6) y - A cos at + B sin a t is a solution of the differential equation
d2 y
(a)
2 -a y = 0 dt2
<o dL+a=0
Q.7) The differential equation3 + = 2 x4 y4 is not linear. The integrating factor to solve this equation
dx x
is
(a) \
x
(c)
1
(b)
x
(d) x4
The general solution of + y = sin x is
dx
(a) y = ce~2x + -sinx--cosx (b) y = ce~x + -sinx--cosx
4 2 2 2
(c) y = ce~3x + sin x (d) y = ce~x
The solution of = j 1 - x2 - y2 + x2y2 is
Q.9)
dx
(a) sin-1 y - sin-1 x + c (b) sin-1 y = -2/1 - x2 + 1sin-1 x + c
(c) sin-1 y =1W1 - x2 + -sin-1 x + c (d) sin-1 y =1W1 - x2 + -cos-1 x + c
2 2 2 4
Which one of the following pairs is not correctly matched?
Q.10)
Differential Equations Their Solutions
s.dy,, f Pdx
(a) + P (x) y = 0 ... y = ces
dx
2
(b) ---+ ax dx = 0 ... tan 1 1 + a = c
x2 + y2 x J 2
x dy - ydx , .
(c )-2 - 2 = 0 . log (x + y) + c
x y
(d) ydx + x dy = 0 ... xy = c
The differential of the system of circles touching the y-axis at the origin, is given by
Q. 11)
Q.12)
(a) x2 + y2 - 2xy = 0 (b) x2 + y2 + 2xy = 0
dx dx
(c) x2 -y2 + 2xy = 0 (d) x2 - y2 - 2xy = 0
dx dx
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) 4log2 hours (b) 5log2 hours
log3 V 7 log 3
(c) 2log2 hours (d) log2 hours
log3 V 7 log 3
If b is a unit vector in the xy-plane making an angle of with the x-axis, then b is equal to
Q.13)
Q.14)
(a) i + j (b) i - j
(c) (/ + j )/V2 (d) (/ - j)
Distance between two points whose position vectors are 3i + j - 2k and i - 3y + 5k is
(a) 69 units (b) V69 units
(c) 13 units (d) 29 units
Q.15) If A O and both the conditions
(i) A.B = A.C and (ii) A x B = A x C hold simultaneously, then
(a) B = C = O
(c) B * C
(b) B = C
(d) B * O, C * O
a, p,%,q are non-empty sets then
(a) (ax)u(xn) = (ax)n(xn)
(b) (ax)n(xn) = (ax)n(xn)
(c) (an) x (n n) = (ax) u(x)
(d) (an)x(nn) = (axn)u(x)
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
Q.17)
Q.18)
Q.19)
(a) 100 (b) 200
(c) 300 (d) 400
In a Euclidean plane, which 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
The modulus and principle amplitude of (1+/'V3) , respectively are
(a) 2-7
3n
(d) 4, -
4
(c) 5,tan-1 -
If 1, ra, ra2 are the cube roots of unity, then value of(x + y)2 to (xra + yw2) + (xra2 + yo) is equal to
Q.20)
(b) 3xy (d) 9xy
(a) xy (c) 6xy
|
is equal to |
(b) 3/2
The value of
(a) 3 (c) 0
Q.21)
(d) 2
The complex number z, satisfying the equation --= 1 lies on
Q22)
i + z
(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
The binary number 1101101 + 1011011 is written in decimal system as (a) 198 (b) 199
(c) 200 (d) 201
The binary equivalent to the decimal number 0.3125 (a) 0101 (b) .1010
(c) .0101 (d) .1101
The binary number 10110100001 in decimal system is (a) 441 (b) 1441
Q.25)
Q.26)
Q.27)
Q.28)
Q.29)
Q.30)
Q.31)
Q32)
(c) 1241 (d) 241
The the mth and the nth terms of an H.P. are n and m respectively, then the mnth term is (a) 0 (b) 1
(c) 2 (d) 2
If a, b, c are in G.P., then- + -1 is a2 -b2 b2 (a) (b)
(c) (d)
The value of 3-1+-- =... is equal to
3 9
20 9
(a) (b)
9 20
9 4
(c) - (d) -
49
If (x - 2) (x + 6) > 0, then the solution set is (a) (x: x > 2) (b) (x: x < 6)
(c) (x : x < -6) (d) (x : x > 2 or x < -6)
The value of 6 + 46+6 +... is equal to (a) 2 (b) 3
(c) 46 (d) 6
If the equations x2 - px + q = 0 and x2 + qx - p = 0 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
The number of words that can be formed from the letters of the word INDRAPRASTHA when the
vowels are never separated is
(a) 727560 (b) 725760
(c) 752760 (d) 757260
The number of 2-digit even numbers that can be formed from the digits 1, 2, 3, 4 and 5, repetition
being not allowed, is
(a) 25 (b) 5!
(c)16 (d) 8
The number of ways in which 6 people can be seated at a round table is (a) 6 (b) 60
(c) 120 (d) 720
The coefficient of the middle term in the expansion of (2 + 3x)4 is
(a) 6 (b) 5!
(c) 8! (d) 216
If in the binomial expansion of (1 + x)n when n is a natural number, the coefficients of the 5th, 6th and
7th 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
1 2
If log8 m + log = , then m is equal to
6 3
Q.35)
Q.36)
Q.37)
(b) 18 (d) 4
(a) 24 (c) 12
Q.38)
If ax = by = cz, and logb a = logc b , then which one of the following will hold true?
(b) x2 = yz (d) y = xz
(a) y = xz (c) z2 = xy
Q.39)
If | x +11 = 3, then | x6 + -11 is equal to
(b) 414 (d) 322
(a) 927 (c) 364
The rank of the matrix
Q.40)
is equal to
12 3 0
2 4 3 2
3 2 13 6 8 7 5
(b) 2 (d) 4
(a) 1 (c) 3
|
If A = |
| |||||||||
|
(a) A2 + AB + BA + B2 (c) A2 + AB + BA + B21 | ||||||||||
, the (A + B)2 is not equal to
(b) A2 + 2 AB + B2 (d) A21 + AB + BA + B2
Q41)
0 1 -1 0
= (1 + pA), then the value of a and p are given by
Q.42)
If A =
'a)a=Ti p=72 <c)=p= j?
<b)=T p=72 <d)=-p=;1
Q.43) If A be an n x n matrix and C any scalar, then | CA | (a) nC |A| (b) C |A|
|
(c) nC\A\ | |||||||||||||||
|
(d) C|A|
(a) symmetric (c) non-singular
(b) skew symmetric (d) orthogonal
Q.45) If x =
= 6 + 11i, then
(b) x = 3, y = 4 (d) x = -3, y = -4
x -3i 1
y 1 i 0 2i -i (a) x = -3, y = 4 (c) x = 3, y = -4
|
then A-1 is equal to | ||||||||||||||||||||||||
|
Q.46) If A =
y
5 y3
Q.47) The expansion of the determinant
(a) x - 3 (c) y - 3
Q.48) The value of the determinant
(a) gfkl (c) abdl
contains which one of the following as a factor?
x3 10 y5 27 (b) x - y
(d) (x - 3)(y -3)
h g f b c e
is
0 d k 0 0 l (b) abhg
(d) ablc
|
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 3x + y + 2 z = 3; 2 x - 3 y - z = -3 and x + 2y + z = 4 is
(a) x = 3, y = 2, z = -2 (b) x = 2, y = 1, z = 3
cos# sin# sin# cos#
The adjoint of (a)
is equal to (b) (d)
|
cos# |
sin# |
|
sin# |
cos# |
|
cos# |
-sin# |
|
sin# |
cos# |
cos# - sm<
- sin# cos#
cos# sin#
-sin# cos#
(c)
Q.52)
The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their angles is 90. 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.
The value of tan31.tan32.tan32.tan33...tan59 is equal to
(a) -1 (b) 0
(c) 1 (d) 2
, (-Hn'] (21n\ , (283n The number I-I ,tanl-I and cot I-| are in
I 6 J I 4 J 1 6
(a) A.P.
(c) H.P.
Q.53)
Q54)
(b) G.P.
(d) none of the above
The correct value of the parameter f of the identity 2(sin6 x + cos6 x) +t(sin4 x + cos4 x) = -1 is
Q55)
(b) -1
(d) -3
(a) 0 (c) -2
Q.56)
If w = x + y + z , thensinx + siny + sinz - sin is equal to
, . . . y + z . z + x . x + y
(a) 4 sin ---sin-sin-
2 2 2
- . . y + z z + x x + y
(c) 4tan-tan-tan-
2 2 2 2 2
To derive the tangent formula, the following steps are given:
sin A cos B cos A sin B
--1--
cos A cos B cos A cos B
cos A cos B sinA sin B
+ -
cos A cos B cos A cos B
1. tan (A + B) =
, . sin (A + B)
2. tan (A + B )=--f
v cos (A + B)
sin A cos B + cos A sin B cos A cos B - sin A sin B
Their correct and proper sequential form to derive the formula is (a) 2, 4, 3, 1 (b) 1, 2, 3, 4
/ . tan A + tan B
4. tan (A + B) =-
1 - tan A tan B
. . y + z z + x x + y
(b) 4 cos--cos-cos-
2 2 2
,. y + z z + x x + y (d) 4cot-cot-cot-
Q.57)
3. tan (A + B) =
Q.58) Consider the following:
1. If cot 0 - x, then x+1 = secdcosecd .
x
1 2 1 2
2. If x + = sin0 , thenx +- = sin 0-2
x x
3. If x = psec0 andy = qtan0, then x2q2 -y2p1 = p2q2.
4. The maximum value of cos0 - V3 sin0 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 x + = 2cos0 , thenx3 + --is equal to
x x
(a) -2cos0 (b) cos 0
(c) 2 cos30 (d) 3 cos 30
in4 (3-0'} + sin4 (n-a)} - 2{sin6 -a} + sin6 (
Q.60) The expression 3{sin4-aj + sin4 (3n-a)} - 2{sin6 \-a | + sin6 (
-a) is equal to
(a) sin 2a + sin 3a (b) 3
(c) 1 (d) 0
1. (c) 13. (c) 25. (b) 37. (a) 49. (c)
2. (b) 14. (b) 26. (b) 38. (a) 50. (c)
3. (d) 15. (b) 27. (b) 39. (d) 51. (a)
4. (b) 16. (d) 28. (c) 40. (c) 52. (c)
5. (d) 17. (a) 29. (a) 41. (b) 53. (c)
6. (d) 18. (d) 30. (b) 42. (c) 54. (b)
7. (b) 19. (b) 31. (d) 43. (d) 55. (d)
8. (b) 20. (c) 32. (b) 44. (b) 56. (a)
9. (c) 21. (d) 33. (d) 45. (a) 57. (d)
10. (c) 22. (b) 34. (c) 46. (a) 58. (d)
11. (d) 23. (c) 35. (d) 47. (a) 59. (c)
12. (c) 24. (c) 36. (b) 48. (c) 60. (c)
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Attachment: |
| Earning: Approval pending. |
