Mock Test-Maths/Reasoning/Quant

MOCK TEST-MATHS/REASONING/QUANT

INFOMATHS/MCA/TEST/MATHS/REASONING/QUANT

1.The value of log10 tan 1 + log10 tan 3 + ……… + log10 (tan 89) is given by

(a)45 (log 10 tan 1)

(b)45 log10 (tan 89)

(d)0

2.The value of tan 81 - tan 63 -tan 27 + tan 9 is

(a) 1(b) 2(c) 3(d) 4

3.Let n be an odd integer. If sin n  = , for every value of , then

(a) b0 = 1, b1 = 3 (b) b0 = 0, b1 = n

4.The maximum value of (cos 1) . (cos ) …. (cos n), under the restrictions 0 1, 2, n and (cot 1) . (cot 2) ….. (cot n) = 1 is

(a) (b) (c) (d) 1

5.If tan x = then

(a) (b)

6.If sin 2x = n sin 2y, then the value of is

(a) (b) (c) (d)

7.If the length of a chord of a circle is equal to that of the radius of the circle then the angle subtended, in radians, at the centre of the circle by chord is

(a) 1(b) (c) (d)

8.The values of  lying between 0 and /2 and satisfying the equation

= 0 are

(a) and (b) and

9.If then

(a) (b)

10.If cos A + cos B = m and sin A + sin B = n where m, n =  0, then sin (A + B) is equal to

(a) (b)

11.The value of is

(a) 0(b) 3(c) 9(d) N.O.T

12.If 0  x  and , then x is equal to

(a) (b) (c) (d)

13.tan5x tan 3x tan 2x =

(a)tan 5x – tan 3x – tan 2x

(b)

(d)none of these.

14.If p1, p2, p3 are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then p1 p2 p3 =

(a) (b)

15.The area of a regular polygon of n sides is

(a) (b)

16.In any ABC, a sin A = b sin B, then the triangle is

(a) isosceles (b) right angled

17.If in a  ABC, 8R2 = a2 + b2 + c2, then the triangle ABC is

(a) right angled (b) isosceles

18.In a triangle ABC, is equal to

(a) (b) (c) (d)

19.The set of values of x for which = 1 is

(a)

(b)

(c)

(d)

20.If 1 + sin  + sin2+ …. to  = 4 + 2 0 <  < , , then  =

(a) (b)

21.If tan ( cos ) = cot ( sin ), then the value (s) of cos is (are)

(a) (b)

22. The minimum value of 2sin x + 2cos x is

(a) 1(b) 2

23.The most general value of , satisfying the two equations, , tan  = 1 is

(a) (b)

24.If the complex numbers sin x + i cos 2x and cos x – i sin 2 x are conjugate to each other, then x is equal to

(a) n (b)

25.The solution of tan 2  tan  = 1 is

(a) (b)

26.The number of pairs (x, y) satisfying the equations sin x + sin y – sin (x + y) and | x | + | y | = 1 is

(a) 2(b) 4(c) 6(d) infinite

27.tan | x | = | tan x | if

(a)

(b)

(d)None of these

28.The number of all possible triplets (a1, a2, a3) such that

a1 + a2 cos 2x + a3 sin2 x = 0 for all x is

(a) 0(b) 1(c) 2(d) infinite

29.The number of real solution of tan-1 is

(a) zero (b) one (c) two(d) infinite

30.Let n be an odd integer. If sin n  = , for every value of , then

(a)b0 = 1, b1 = 3

(b)b0 = 0,b1 = 4

(c)b0 = - 1, b1 = n

(d)b0 = 0, b1 = n2 – n + 3

31.The solution of

is:

(a) (b)

32.If A = tan-1 and B = tan-1, then the value of A – B is

(a) 0(b) 45(c) 60(d) 30

33.The sum of first 50 terms of the series cot-1 3 + cot-1 7 + cot –1 21 + …. is

(a) (b)

34.

for 0 < | x | < then x equals.

(a) (b) 1(c) (d) -1

35.If 3 sin-1, then x is equal to

(a) (b) (c) (d)

36.If sin-1 a + sin-1 b + sin-1 c = , then the value of

(a) AP(b) GP(c) HP(d) none of these.

37.The value of

(a) (b) (c) (d) 0

38If cot-1 [(cos )1/2] – tan-1 [(cot )1/2] = x, then sin x =

(a) (b)

39.If  = sin-1 [sin (- 600)], then one of the possible values of  is

(a) (b) (c) (d)

40.The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45. If the elevation of the to at the same point is to be 60, the tower must be raised to a height.

(a) 120 () m (b) 120 ( m

41.If two of heights h1 and h2 subtend angles 60 and 30 respectively at the midpoint of the line joining their feet, then h1 : h2 =

(a) 1 : 2 (b) 1 : 3 (c) 2 : 1 (d) 3 : 1

42.The smallest positive root of the equation tan x – x = 0, lies in

(a) (b)

43.If the ex-radii r1, r2, r3 of  ABC are in HP, then its sides are in

(a) HP(b) GP(c) AP(d) none of these.

44.If in a triangle ABC, then cos A is equal to

(a) (b) (c) (d) N.O.T

45.If 2 cos then lies between, (n  Z)

(a) and

(b) and

(d)-  and + =

46.The value of cos

(a) (b) (c) (d) none of these.

47.If x1, x2, x3, ….., xn are in A.P. whose common difference is a, then the value of sin  (sec x1 sec x2 + sec x2 sec x3 + … x sec xn – 1 sec xn) is

(a) (b)

(d) sin n  cos x1 cos xn.

48.If in a triangle ABC, , then

(a) a, b, c are in AP (b) a2, b2, c2 are in AP

49.The real part of sinh ( + i ) is

(a) sinh  cos (b) sin  cosh 

50.sinh-1 (cot x) =

(a)log (tan x – sin x)

(b)log (tan x + sin x)

(c)log (cot x – cosec x)

(d)log (cot x + cosec x)

51.If cos-1 a + cos-1 b + cos-1 c = , then value of a2 + b2 + c2 + 2abc is

(a) 0(b) 1(c) 2(d) N.O.T

52.Let the function

f(x) = x2 + x + sin x – cos x + log (1 + | x |) be defined over the internal [0, 1]. The odd extension of f(x) to the interval [-1, 1] is :

(a)x2 + x + sin x + cos x – log (1 + | x |)

(b)-x2 + x + sin x + cos x – log (1 + | x |)

(c)-x2 + x + sin x - cos x + log (1 + | x |)

(d)None of these

53.In a triangle ABC, cosec A (sin B + cos C + cos B . sin C) equals :

(a) c/a (b) a/c(c) 1(d) none

54.If  = a2 – (b2 – c2), where  is the area of the ABC, then tan A is equal to:

(a) 15/16(b) 8/15(c) 8/17(d) 1/2

55.If  is the imaginary cube root of unity, then the value of sin is:

(a) (b)

REASONING AND QUANT

Directions [Questions 56 to 59]

A, B, C, D, E, F and G are seven girls having different amount of money from among Rs. 10, 20, 40, 80, 120 and 200 with them. They had 3 chocolates, 2toffees and 2 lollipops together, each one having one of these seven items.

B and F do not have chocolates and they have Rs.200 and Rs. 80 respectively.
C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
A has Rs. 10 and does not have a toffee.
The girl having Rs. 40 with her is the only one other than A to have the same type of item.
E and the girl having Rs. 20 with her have the same kind of item.

56. How much amount does G have with her?

A) Rs. 20 B) Rs. 10

C) Rs. 60 D) None of these

57. Which of the following girls have chocolates with them?

A) F, C, G B) C, G, E

C) C, G, D D) None of these

58. Which of the following combination is definitely correct?

A) C - chocolate – Rs. 60

B) G - toffee – Rs. 20

C) D - chocolate – Rs. 40

D) Noneof these

59. Which girl has Rs. 40 with her?

A) E B)A C) D D) None of these

60. P, Q, R, S, T, U and V are sitting in a row facing North. In order to determine, who is sitting exactly in the middle of the row, which of the following information is needed ?

i) T and U are sitting at extreme ends of the row

ii) S is third to the right of T

iii) Q is four places to the left of Rand P is two places to the left of V

A) i and ii only are sufficient

B) i and iii only are sufficient

C) i and either ii or iii are sufficient

D)i,ii and iii

Study the following information carefully and answer the questions given below:

Seven persons namely Paramjit, Tarun, Morya, Jeeva, Vaani, Ram and Waqar are goodfriends and are studying in M.Com, M.A. and M.Sc courses. Three are doing M.Com, two are in M.A.and another two are in M.Sc. Each of them has a very distinct and favorite color choice ranging fromblue, red, yellow, white, black, pink and brown but not necessarily in the same order. None doingM.Com like either red or black. Morya is doing M.A. and he likes blue. Ram is doing M.Sc and likesbrown. Jeeva is doing M.Com and likes yellow. Paramjit who does not like red is in the samediscipline of Ram. Tarun is in the same discipline of Morya. Vaani does not like pink.

61. Which among the following groups is doing M. Com?

a) Jeeva, Vaani and Waqar

b) Vaani, Waqar and Tarun

c) Jeeva, Vaani and Tarun

d) Jeeva, Paramjit and Ram

62. What is the color combination choice of those who are in M.Sc discipline?

a) Brown and Pinkb) Black and White

c) Black and Brownd) Yellow and Black

e) None of The Above

63. Which color does Vaani like?

a) Yellowb) Pink

c) Whited) Brown

64. What is the color combination choice of those who are in M.A. discipline?

a) Red and Black

b) Blue and Red

c) Blue and Black

d) None of The Above

65. Morya is related with which discipline?

a) M.Sc.

b) M.A.

c) M.Com

d) N.O.T

66.Sneha is engaged. Her Fiance is one amongst Abdul, John, King and Vimal. Sneha either speaks truth or lies. One of four men always speaks truth while others may or may not speak the truth. Now based on the below statements, can you find the Fiance?
1) Abdul says "Sneha always speaks truth".
2) King says "Sneha always lies".
3) Vimal says "Sneha always speaks truth but only to him".
4) John says "The only truth speaking person amongst Vimal and John is Sneha's Fiance"

a) Abdul b) King c) Vimal d) John.

67.A man escapes from jail with help from his girlfriend. Four girls are accused of being the man's girlfriend. His girlfriend is lying. Two girls are innocent and telling the truth. The other girl is the man's sister who is helping the girlfriend lie. Who is the man's sister?
Amanda: "Melinda is his girlfriend."
Vanessa: "Eva is lying."
Eva: "Amanda is lying."
Melinda: "Vanessa is not his sister."

(a) Melinda (b) Eva

Directions (Q. 68-72): Study the following information carefully to answer these questions.

P, Q, R, S, T, U, V and W are sitting around a circular table, facing the centre. P sits third to the right of W and third to the left of Q. S sits second to the right of T. V sits second to the left of R. T is not the neighbour of Q while U is neither a neighbour of T nor of W.

68. Who sits second to the left of V?

1) R2) P3) U4) T5) N.O.T

69. Who sits between U and P?

1) S2) R3) V4) Q5) N.O.T

70. Starting from P’s position, if all the eight are arranged in alphabetical order in clockwise direction, the seating position of how many members (excluding P) would not change?

1) None2) One3) Two4) Three5) Four

71. Which of the following pairs has only one person sitting between them, if the counting is done in the clockwise direction?

1) T,V2) V, Q3) W, P4) R, P5) N.O.T

72.Four of the following are alike in a certain way based on their positions in the seating arrangement and so form a group. Which is the one that does not belong to that group?

1) W, T2) P, U3) S, Q4) R, P5) P, Q

73.A sum of Rs 5000 was lent partly at 6% partly at 9% simple interest. If the totalannual interest be Rs 390, the ratio in whichthe money was lent at given rates is:

a) 1:1 b) 1:2 c) 2:3 d) 3:2

74. The difference between the simple interest the compound interest on Rs 5000 at10% p.a. for 3 years is:

a) Rs 145 b) Rs 150 c) Rs 165 d) None

75.A deposited Rs6000 in a bank at 5% perannum simple interest. B deposited Rs 5000at 8% p.a. compound interest. After 2 years,the difference between their interests will be

a) Rs 230 b) Rs 232 c) Rs 600 d) Rs 832

76. What will be the compound interest on Rs25000 after 3 years at 12% per annum?

a) Rs 9000.30 b) Rs 9720

c) Rs 10123.20 d) Rs 10483.20

77. How much would a sum of Rs 16000approximately amount to in 2 years at 10%p.a. compounded half-yearly?

a) Rs 17423 b) Rs 18973c) Rs 19448 d) Rs 19880

78.The compound interest on Rs 16000 for 9months at 20% p.a. compounded quarterly is

a) Rs2518 b) Rs 2520 c) Rs 2522 d) Rs 2524

79.If the interest is payable annually, then theprincipal on which the compound interestfor 3 years at 10% p.a. is Rs 331, is given by

a) Rs 900b) Rs 1000 c) Rs 1050 d) Rs 1100

80.In a certain year there were exactly four Fridays and four Mondays in January. On what day of the week did the 20th of January fall that year?

(a) Saturday (b) Sunday

81. In any year, if April 1 is a Wednesday then so is

(a) January 1(b) July 1

82.Which two months in a year have the same calendar?

(a) June - October(b) April – November

83.If second Saturday and all Sunday’s are holidays in a 30 day month beginning on Saturday, how many working days will be there in a month?

(a)22(b)20(c)24(d)21

84.A girl was born on September 6,1970, which happened to be a Sunday. Her birthday has again fall on Sunday in

85.If the first day of June is a Saturday, then the date on which the last Saturday of that month falls is.

(a) 22 (b) 28(c) 29(d) 30

86.If January 1st falls on Saturday in a year, then the number of Saturdays in that year is

(a) 52(b) 51(c) 54(d) 53

87.On July,2, 1985, it was Wednesday. The day of the B- week on July 2, 1984 was

(a) Monday (b) Tuesday

88.The calendar for 1990 is the same as for

89.If the 2nd of a month falls on Sunday what day will the 30th of that month be?

(a) Monday (b) Saturday

90.In a leap year, one of the months started with a Sunday. What is the shortest time gap between two such months? For example, if February and March both started on a Sunday, then the time gap is 1 month.

(a) 6 months (b) 3 months (c) 2 months

(d) 1 month (e) None of the above

Questions 91-94 are based on the following :

There is a family of six members A, B, C, D, E and F
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a colour amongst Green, Yellow, Black, Red, White and Pink
No lady member likes either Green or White.
C, who likes Black colour, is the daughter-in-law of E.
B is the brother of F and son of D and likes Pink.
A is the grandmother of F and F does not like Red.
Wife of the husband having a choice for Green colour, likes Yellow.

91. Which of the following is the colour preference of A?

A) Red B) Yellow

C) Either Red or Yellow D)Cannot be determined

92. Which of the following could be the colour combination of one of the couples?

A) Yellow-Red B) Green-Black

C) Red-Yellow D) Yellow-Green

93. Which of the following is one of the married couples?

A) CD B) AC

C) AD D) Cannot be determined

94.Which of the following is true about F?

A) Brother of B B) Sister of B

C) Daughter of C D)Cannot be determined

95.Three ladies X, Y and Z marry three men A, B and C. X is married to A, Y is not married to an engineer. Z is not married to a doctor, C is not a doctor and A is a lawyer. Then which of the following statements is correct?

(a) X is married to a doctor

(b) Y is married to C, who is a doctor

(d) N.O.T

96.There are five books A, B, C, D and E placed on a table. If A is placed below E, C is placed above D, B is placed below A and D is placed between A and E, then which of the following books can be on the top?

(a) D or E (b) C or E

97.Among five children A, B, C, D and E, B is taller than E but shorter than D. A is shorter than C but taller than D. If all the children stand in a line according to their heights, then who would be the fourth if counted from the tallest one?

(a) D(b) C(c) B(d) A

98.The interest on a certain loan is Rs.100 in the first year and Rs.205 in the first two years. What is the rate percentage?

(a) 5%(b) 4%(c) 10%(d) 6%

99.A man had Rs.2000. He lent a part of it at 5 % interest and the rest at 4 % interest.

The total interest he received in one year was Rs.92 The money he lent at 5% interest was

(a) Rs.1200(b) Rs.1250

100. The difference between compound interest & simple interest & simple interest at the same rate on Rs 5000 for 2 years is Rs 72. The rate of interest per annum is

a) 6% b) 8% c) 10% d) 12%

TEST-TRIGONOMETRY

DATE :- 5-5-2016

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
D / D / B / A / B / A / C / A / B / B
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
B / A,B / A / D / A,B / A / A / A / A / C
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
C / D / D / D / B / C / C / D / C / B
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
D / D / A / B / A / A / D / B / A / B
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
D / C / C / A / B / B / A / B / A / D
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
A / B / C / B / C / A / B / A / C / A
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
A / C / C / B / B / D / C / C / A / B
71 / 72 / 73 / 74 / 75 / 76 / 77 / 78 / 79 / 80
D / E / C / D / B / C / C / C / B / B
81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90
B / C / C / D / C / D / B / D / D / B
91 / 92 / 93 / 94 / 95 / 96 / 97 / 98 / 99 / 100
B / D / A / A / D / D / C / A / A / D

INFOMATHS/MCA/TEST/MATHS/REASONING/QUANT