1

What is the remainder when 4^96 is divided by 6?

4 3 2 1

2

If 37/13=2+ (1/(x+(1/(y+1/z)))) where x,y and z are natural numbers what is the value of z

1 2 3 Cannot be determined

3

For what value of k is (x-5) is a factor of x³-3x²+kx-10?

-8 4 2 1

4

What is 5+√10/(5√5-2√20-√32+√50)

5 5√2 5 √5 √5

5

The digits in the units place of the product 81*82*83*...*99 is

0 4 6 8

6

The square root of (0.75)³/(1-0.75)+[0.75 + (0.75)² +1] is

1 2 3 4

7

What is the reaminder obtained when 1421*1423*1425 is divided by 12

1 2 3 4

8

Consider the following equations:

1.The equation 1990x-173y=11 has no solution in integers for x and y

2.The equation 3x-12y=7 has no solution in integers for x and y

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

9

A student was asked to multiply a number by 25.He instead multiplied the number by 52 and got the answer 324 more than correct answer.The number to be multiplied was

12 15 25 32

10

What is the number of possible pairs of (P,Q) if the number 357P25Q is divisible by both 3 and 5?

7 6 5 none of the above

11

The difference between the squares of two consecutive odd integers is always divisible by

3 7 8 16

12

The expression x³q²- x³pt+4x²pt-4x²q²+3xq²-3xpt is divisible by

(x-1) only (x-3) only Both (x-1) and (x-3) Neither (x-1) nor (x-3)

13

The difference between Compound itnerest and simple interest at the same rate of interest R percent p.a on an amount of Rs 15000 for 2 years is Rs 96.What is ths value of R?

8 10 12 Cannot be determined

14

What is the maximum value of m if the number N=35*45*55*60*124*75 is divisible by 5^m?

4 5 6 7

15

A milkman claims to sell milk at cost price only,but he making a profit of 20% since he has mixed some amount of water in the milk.What is the percentage of milk in the mixture?

80 250/3 75 200/3

16

There is 60% increase in an amount in 6 years at SI.What will be the CI on Rs 12000 after 3 years at the same rate of interest?

2160 3120 3972 6240

17

16 litres of mixture contains milk and water in the ratio 5:3.If 4 litres of milk is added to the mixture,ratio of milk to water in the new mixture will be

2:1 7:3 4:3 8:3

18

A person could save 10% of his income.But 2 years later,when his income increased by 20%,he could save the same amount only as before.By how much percentage has his expenditure increased?

22 (2/9) 23(1/3) 24(2/9) 25(2/9)

19

In how much time the SI on a principal amount be 0.125 times principal amount at 10% p.a?

5/4 7/4 9/4 11/4

20

A man rows 32km downstream and 14km upstream and he takes 6 hours to cover each distance.What is the speed of current?

0.5km 1km 1.5km 2km

21

A car travels the first one-third of a distance with a speed of 10km/hr,the next one-third distancewith a speed of 20km/hr and the last one-third distance with a speed of 60km/hr.The average speed of the car for the whole journey is

18 24 30 36

22

Two persons A and B start walking simultanoeusly from two places c km apart and walk in the same direction.If A travels at the rate of p km/hr and B travels at the rate of q km/hr ,then A has travelled before he overtakes B at a distance of

qc/p+q pc/p-q qc/p-q pc/p+q

23

For which value of k does the pair of equations x²-y²=0 and (x-k)²+y²=1 yield a unique positive solution of x?√

2 0 1.414 -1.414

24

The efficiency of P is twice that of Q,whereas efficiency of P and Q together is three times that of R.If P,Q and R work together on a job,in what ratio should they share their earnings?

2:1:1 4:2:1 4:3:2 4:2:3

25

In a flight of 600km ,an aircraft was slowed down due to bad weather.Its average speed for the trip was reduced by 200km/hr and the time of flight increased by 30 minutes.The duration of the flight is

4 hours 3 hours 2 hours 1 hour

26

With uniform speed,a car covers a distance in 8 hours.Had the speed been increased by 4km/hr,the same distancec could have been covered in 7 hours 30 minutes.What is the distance covered?

420 480 520 640

27

A runs 5/3 times as fast as B.If A gives B a start of 80m,how far the winning post from the starting point be so that A and B might reach it at the same time?

200 300 270 160

28

A thief is noticed by a policeman from a distance of 200m.The thief starts running and the policeman chases him.The thief and the policeman run at the speed of 10km/hr and 11km/hr respectively.What is the distance between them after 6 minutes?

100 120 150 160

29

When a ball bounces,it rises to 2/3rd of the height from which it fell.If the ball is dropped from a height of 36m,how high will it rise at the third bounce?

10(1/3) 10(2/3) 12(1/3) 12(2/3)

30

A light was seen regularly at an interval of 13 seconds.It was seen for the first time at 1hour 54 minutes 50 seconds and the last time at 3 hours 17 minutes 49 seconds.How many times was the light seen?

375 378 383 384

31

An automobile financer claims to be leding money at S.I but he includes the interest every 6 months for calculating the principal.If he charging at the rate of 10%,effective rate of interest becomes

10.25% 10.5% 10.75% 11%

32

What are the possible solutions of the equation x^√x=√[(x^x)]^n,where x and n are positive integers?²

0,n 1,n n,n*n 1,n*n

33

Let A and B be finite non-empty sets with the number of elements in A=m and number of elements in B=n.Let m>n.If for some integer k>=1,the number of non-empty subsets of A=2^k+number of non-empty subsets of B,then which one of the following is correct?

m=n+2 m=n+1 m=n+p for some odd prime number p m=n+t for some composite number t

34

If n is a natural number and n=p1^x1*p2^x2*p3^x3,where p1,p2 and p3 are distinct prime factors,then number of prime factors of n is

x1+x2+x3 x1 x2 x3 (x1+1)(x2+1)(x3+1) None of the above

35

Consider the following statements for the sequence of numbers given below

11,111,1111,11111,...

1.Each number can be expressed in the form (4m+3),where m is a natural number

2.Some numbers are squares

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

36

The HCF and LCM of two polynomials are (x+y) and (3x^5+5x^4y+2x³y²-3x²y³-5xy^4-2y^5) respectively.If one of the polynomials is x²-y²,then the other polynomial is

3x^4+8x^3y-10x^2y^2+7xy^3+2y^4 3x^4+8x^3y+10x^2y^2+7xy^3+2y^4 3x^4-8x^3y-10x^2y^2+7xy^3+2y^4 3x^4-8x^3y+10x^2y^2+7xy^3-2y^4

37

Let p be a prime number other tha 2 or 5.One would like to express the vulgar fraction 1/p in the form of a recurring decimal.Then the decimal will be

A pure recurring decimal and its period will be necessarily (p-1) A mixed recurring decimal and its period will be necessarily (p-1) A pure recurring decimal and its period will be some factor of (p-1) A mixed recurring decimal and its period will be some factor of (p-1)

38

Consider the following statements:

1.There exists only one prime number p such that (17p+1) is a square.

2.If x is a product of 10 consecutive prime numbers staring from 2,then (x+1) is also a prime number

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

39

The sign of quadratic polynomial ax²+bx+c=0 is always positive if

a is positive and b*b-4ac<=0 a is positive and b*b-4ac>=0 a can be any real number and b*b-4ac<=0 a can be any real number and b*b-4ac>=0

40

If A,G and H are the arithmetic,geometric and harmonic means between a and b respectively,then which one of the following relations is correct?

G is the geometric mean between A and H A is the arithmetic mean between G and H H is the harmonic mean between A and G None of above

41

The geometric mean of 3 positive numbers a,b and c is 3 and the geometric mean of 3 other positive numbers d,e,f is 4.Also,atleast 3 elements in the set {a,b,c,d,e,f} are distinct.Which one of the following inequalities gives the best information about M,the arithmetic mean among 6 numbers?

M>2*1.732 M>3.5 M>=3.5 It is not possible to set any precise lower limit for m

42

There are 5 parties A,B C,D and E in an election.Out of total 100000 votes cast,36000 were cast to party A,24000 to party B,18000 to party C,7000 to party D and rest to party E.What angle will be allocated to party E in a pie chart?

15 54 60 72

43

Out of 532 savings account held in a post office,218 accounts have deposits over Rs 10000 each.Further in 302 accounts,the first or sole depositors are men,of which deposits exceed Rs 10000 in 102 accounts.In how many accounts the first or sole depositors are women and the deposits are upto Rs 10000 only?

116 114 100 Cannot be determined

44

If x+y+z=0 and x³+y³+z³+3xyz is equal to

0 6xyz 12xyz xyz

45

If three metalllic spheres of radii 6cm,8cm and 10cm are melted to form a single sphere,then the diameter of the new sphere will be

12 24 30 36

46

If each interior angle of a regular polygon is 135°,then the number of diagonals of polygon is equal to

54 48 20 18

47

The sides of a triangular field are 41m,40m and 9m.The number of rose beds that can be prepared in the field if each rose bed on an average,needs 900sq.m space is

2000 1800 900 800

48

The ratio of outer and inner perimeters of a circular path is 23:22.If the path is 5m wide,diameter of the inner circle is

55 110 220 230

49

A cylindrical vassel of radius 4m contains water.A solid sphere of radius 3m is lowered into water until it is completely immersed.Water level in the vessel will rise by

1.5 2 2.25 4.5

50

If the height of a right circular cone is increased by 200% and radius of the base is decreased by 50%,then the volume of the cone

remains unaltered decreases by 25% increases by 25% increases by 50%

51

The angles of a triangle are in the ratio 4:1:1.Then the ratio of largest side to the perimeter is

2/3 1/(2+1.732) 1.732(2+1.732) 2(1+1.732)

52

Let a,b ,c be the sides of a right triangle,where c is the hypotenuse.The radius of the circle which touches the sides of the triangle is

(a+b-c)/2 (a+b+c)/2 (a+2b+2c)/2 (2a+2b-c)/2

53

The area of the largest triangle that can be inscribed in a semi-circle of radius r is²

r*r 2r*r 3r*r 4r*r

54

AD is a diameter of a circle and AB is a chord.If AD=34cm,AB=30cm,distance of AB from the center of the circle is

17 15 13 8

55

If a star figure is formed by elongating the sides of a regular pentagon,then the measure of each angle at the angular points of the star figure is

36 35 32 30

56

Four equal sized maximum circular plates are cut off from a square paper sheet of area 784sq.cmThe circumference of each plate is

11 22 33 44

57

If tan(A+B)=√3 and tan A=1,then tan(A-B) is equal to

0 1 1/√3 2

58

If the radius of a aphere is increased by 10%,then its volume is increased by

33.1% 30% 50% 10%

59

ABCD is a parallelogram.where AB:AD=2:1.One of the angles of a parallelogram is 60.The two diagonals are in the ratio

7:3 √7:√3 7:5 None of the above

60

Consider the following statements

1.Let D be a point on the side BC of a triangle ABC.If area of a triangle ABD=area of a triangle ACD,then for all points O on AD,area of triangle ABO=area of triangle ACO

2.If G is a point of concurrence of medians of a triangle ABC,then the area of a triangle ABG=area of a triangle BCG=area of a triangle ACG

Which of the above statement are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

61

If cos A=tan B,cos B=tan C,cos C=tan A,then sin A is equal to

(√3-1)/2 (√3-1)/4 (√5-1)/2 (√5-1)/4

62

If (3-tan²A)/(1-3tan²A)=K whre K is a real number,then cosec A(3sin A-4sin³A) is equal to

2K/(K-1) 2K/(K-1) where 1/3<=K<=3 2K/(K-1) whereK<1/3 or K>3 2K/(K+1)

63

The angles of elevation of the top of a tower from two points P and Q at distances m² and n² respectively,from the base and in the same straight line with it are complementary.The height of the tower is

(mn)^1/2 mn^1/2 m^1/2 n mn

64

The angle of elevation of a cloud from a point 200m above the lake is 30° and angle of depression of its reflection in the lake is 60°.

The height of the cloud is

200 300 400 600

65

If tan A+cot A=4 then (tan²)²A+(cot ²)²A is equal to

110 191 80 194

66

If p=√(1-sin x)/(1+sin x) ,q=(1-sinx)/cos x,r=cos x/(1+sin x),then which of the following is correct?

1.p=q=r

2.p²=qr

Select the correct answer

1 only 2 only Both 1 and 2 Neither 1 nor 2

67

Consider the following

1.cos A/(1-tan A) + sin A/(1-cot A)=sin A +cos A

2.(1-sin A-cos A)²=2(1-sin A)(1+cos A)

Which of the above identities are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

68

ABC is a triangle right angled at B and AB:BC=3:4.What is sin A+ sin B+sin C equal to

2 11/5 12/5 3

69

The value of cosec²67+sec²57-cot²33-tan²23 is

2√2 2 √2 0

70

Consider the following statements

1.There exists atleat one value of x between 0 and ∏/2 which satisfies the equation sin^4x-2sin²x-1=0

2.sin 1.5 > cos 1.5

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

71

From the top of a tower,angles of depression of two objects P and Q seperated at a distance of 100(3-√3) are 45° and 60° respectively.The height of the tower is

200 250 300 None of the above

72

If sin x +cos x=c then (sin ^6)x+(cos^6)x=²

(1+6c^2-3c^4)/16 (1+6c^2-3c^4)/4 (1+6c^2+3c^4)/16 (1+6c^2+3c^4)/4

73

Consider the following statements

1.There exists no value of x such that 1/(1-sinx)=4+2√3,0<x<π/2

2. sin x=3^sin²x does not hold for any real x

1 only 2 only Both 1 and 2 Neither 1 nor 2

74

A triangle ABC is inscribed in a circle.If the sum of squares of sides of a triangle is equal to twice the square of diameter then sin²A+sin²B+sin²C is equal to

2 3 4 None of the above

75

The area of a rhombus with side 13cm and one diagonal 10cm will be

140 130 120 110

76

Two circles,each of radius r,with centres P and Q,are such that each circle passes through the centre of the other circle.Then the area common to the circles is less than one-third of sum of areas of the two circles by

√3r²/4 √3r²/3 √3r²/2 √3r²

77

A sphere and a cube have the same surface area.The ratio of square of their volumes is π

6:π 5:π 3:5 1:1

78

The radius of a sphere is equal to radius of the base of a right circular cone,and the volume of sphere is double the volume of cone.The ratio of height of cone to radius of the base is

2:1 1:2 2:3 3:2

79

Water flows through cylindrical pipe of internal diameter 7cm at the rate of 5m/s.The time,in minutes,the pipe would take to fill an empty rectangular tank 4m*3m*3.1m is

28 24 20 12

80

The total surface area of a right circular cone of height 24cm with a hemisphere of radius 7cm upon its base is π

327π 307π 293π 273π

81

The last digit in the expansion of 17^256

9 7 3 1

82

A rectangular block of wood having dimensions 3m*2m*1.75m has to be panted in all its faces.The layer of paint must be 0.1mm thick.Paint comes in cubical boxes having their edges equal to 10cm.The minimum number of boxes of paint to be purchased is

5 4 3 2

83

The sides of a triangle are 25cm,39cm and 56cm.The perpendicular from the opposite vertex on the side of 56cm is

10 12 15 16

84

The diagonals of a trapezium are at right angles,and the slant sides if produced,form an equilateral triangle with the greater of the two parallel sides.If the area of the trapezium is 16 sq.cm,then the distance between parallel sides is

2 4 8 Cannot be determined

85

Three equal circles each of diameter d are drawn on a plane in such a way that each circle touches the two other circles.A big circle is drawn in such a manner that it touches each of the small circles internally.The area of the big circle is πd² (√3+2)²

πd² πd²(2-√3)² πd²(√3+1)²/2 πd² (√3+2)²/12

86

If the angle between radii of a circle is 130°,then the angle between tangents at the ends of the radii is

90 70 50 40

87

Let OA,OB,OC and OD are rays in the anti-clockwise direction such that <AOB=<COD=100,<BOC=82 and <AOD=78.Consider the following statements.

1.AOC and BOD are lines

2.<BOC and <AOD are supplementary

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

88

At 8:30,the hour hand and minute hand of the clock form an angle of

80 85 70 60

89

The complement angle of 80 is

18/π 5π/9 π/18 9/5π

90

Consider the following questions

1.If the non-parallel sides of a trapezium are equal,then it is cyclic

2.If the chord of a circle is equal to its radius,then the angle subtended by this chord at a point in major segment is 30

Which of the above statements are correct?

1 only 2 only Both 1 and 2 Neither 1 nor 2

91

Out of the two concentric circles,the diameter of the outer circle is 26cm and the chord MN of length 24 cm is tangent to the inner circle.The radius of the inner circle is

5 6 8 10

92

What is the mean of the distribution?

37.2 38.1 39.2 40.1

93

What is the median class?

20-30 30-40 40-50 50-60

94

What is the median of the distribution?

37 38 39 40

95

From a circular piece of cardboard of radius 3 cm,two sectors of 40° each have been cut off.The area of the remaining portion is

44 22 33 11

96

The diagonals of three faces of a cuboid are 13,√281 and 20 linear units.Then the total surface area of the cuboid is

672 664 658 650

97

A rectangular paper of 44cm long and 6cm wide is rolled to from a cylinder of height equal to width of the paper.The radius of base of the cylinder so rolled is

5 7 14 3.5

98

If a-b=4 and a²+b²=40,where a and b are positive integers,then a³+(b³)² is

264 280 300 324

99

What is the mode of the distribtuion

43.33 42.66 38.33 40.66