# (Model Test Paper) Engineering Entrance Examination Model Paper For (Mathematics)

**Test Paper : Engineering Entrance Examination Model Paper For (Mathematics)**

**Question
1:** If 300 jellybeans cost you x dollars. How many jellybeans can you
purchase for 50 cents at the same rate?

If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for
50 cents at the same rate?

1. 150/x

2. 150x

3. 6x

4. 1500/x

5. 600x

**Question 2:**How many different necklaces can be formed with 6 white and 5 red beads?

1. 12

2. 21

3. 30

4. 32

5. 51

**Question 3:**For what values of 'm' is y = 0, if y = x2 + (2m + 1)x + m2 - 1? x is a real number.

1. m -2

2. m < 0

3. m = 0

4. m -1.25

5.

**Question 4:**In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?

Ans. .

1. BC = 4 cm

2. BC = 4.1 cm

3. BC = 4.2 cm

4. BC = 3.9 cm

5.

**Question 5:**In case of induction motor the torque is

1. Directly proportional to slip

2. Inversely proportional to slip

3. Directly proportional to square of the slip

4. Inversely proportional to square of the slip

5.

**Question 6:**If the sum of n terms of two series of A.P are in the ratio 5n+4:9n+6 .find the ratio of their 13th terms

If the sum of n terms of two series of A.P are in the ratio 5n+4:9n+6 .find the ratio of their 13th terms

1. 129/231

2. 1/2

3. 23/15

4. None of the above

5.

**Question 7:**What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

1. 3

2. 4

3. 5

4. 6

5.

**Question 8:**there is one no which is formed by writing one digit 6 times such a no is always divisible by

1. 7 only

2. 11 only

3. 13 only

4. all of them

5.

**Question 9:**The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

1. 1650

2. 1700

3. 1750

4. 1800

5. 1850

**Question 10:**80.40/20+(-4.02)=?

1. -0.82

2. 0

3. 8.22

4. 8.4

5. None

**Question 11:**Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

1. 2 hours

2. 4.5 hours

3. 5.75 hours

4. 6 hours

5. 7.5 hours

**Question 12:**If we write all the whole no from 200 and 400,then how many of these contain the digit 7 once and only once

1. 32

2. 34

3. 35

4. 36

5.

**Question 13:**(8.2% OF 365) - (1.75% OF108) = ?

1. 16.02

2. 28.04

3. 42.34

4. 53.76

5. NONE

**Question 14:**what will be the resultant of 1/loga abc +1/logb abc+1/logc abc?

1. log a*logb*logc

2. log a+log b+log c

3. logabc abc =1

4. log 1

5.

**Question 15:**The some of exterior angles of a hexagon is

1. 360

2. 540

3. 720

4. none of these

5.

**Question 16:**The angel which exeeds it's complement by 20 degree is

1. 45

2. 55

3. 70

4. 110

5.

**Question 17:**A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

1. (0, 2)

2. (1, 0)

3. (0, 1)

4. (2, 0)

5.

**Question 18:**The sum of 2 numbers is 84, if one of them exceeds the other by 12.Find the numbers?

1. 40,52

2. 1,13

3. 36,48

4. 72,84

5. 71,80

**Question 19:**Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.

1. 99840

2. 99900

3. 99960

4. 99990

5.

**Question 20:**How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

1. 16C7 * 7!

2. 12C4 * 4C3 * 7!

3. 12C3 * 4C4

4. 12C4 * 4C3

5.

**Question 21:**In an examination paper there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

1. 24

2. 48

3. 96

4. None of these

5.

**Question 22:**Intersections

C is a circle and P is a point exterior to it. Several lines are drawn through P such that Each line has nonempty intersection with C. If 2005 points of intersection are formed, then among the lines

1. There need not be een one tangent

2. There may be two tangents

3. There may be three tangents

4. There has to be precisely one tangent

5. None of these

**Question 23:**A basket contains 3 blue, 5 black and 3 red balls. If 3 balls are drawn at random what is the probability that all are black?

1. 2/33

2. 1/11

3. 3/11

4. 8/33

5.

**Question 24:**Find the number of different chains can be prepared using 7 different coloured beads.

1. 360

2. 720

3. 240

4. 680

5.

**Question 25:**Which of the following is equivalent to (x)(x)(x)(x), for all x ?

1. 4x

2. x ^ 4

3. x + 4

4. 4 ^ x

5. 2 x ^ 2

**Question 26:**An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down

1. 0.084

2. 0.916

3. 0.036

4. 0.964

5.

**Question 27:**Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

1. (x-z)2 y is even

2. (x-z)y2 is odd

3. (x-z)y is odd

4. (x-y)2z is even

5.

**Question 28:**how many solutions are there for consistent dependent lines?

1. Unique

2. Infinite many solutions

3. No solutions

4. none of the above

5.

**Question 29:**The average of (54,820)2 and (54,822)2 =

1. (54,821)2

2. (54,821.5)2

3. (54,820.5)2

4. (54,821)2 + 1

5.

**Question 30:**6,30,260,3130.....? ?

1. 5782

2. 56442

3. 107662

4. 46662

5.

**Question 31:**If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

1. 2 minutes and 44 seconds

2. 2 minutes and 58 seconds

3. 3 minutes and 10 seconds

4. 3 minutes and 26 seconds

5. 4 minutes and 15 seconds

**Question 32:**If both x and y are prime numbers, which of the following CANNOT be the difference of x and y?

1. 1

2. 3

3. 9

4. 15

5. 23

**Question 33:**Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

1. 1050

2. 540

3. 1440

4. 1590

5.

**Question 34:**What largest number of five digit is divisible by 99?

1. 99909

2. 99981

3. 99990

4. 99999

5.

**Question 35:**(1/10)18 - (1/10)20 = ?

1. 99/(10)20

2. 99/10

3. 0.9

4. none of these

5.

**Question 36:**Two unbiased dice are thrown together. What is the probability that total of the numbers on the dice is greater than 10.

1. a. 1/12

2. b. 5/12

3. c. 5/6

4. d. 1/18

5.

**Question 37:**If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?

1. -22.5

2. 16

3. -10.5

4. -17.5

5.

**Question 38:**What is the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream (2 pt.=1 qt. and 4 qt.=1 gal)

1. 16

2. 24

3. 30

4. 64

5. 13

**Question 39:**In a single throw of two dice, what is the probability of getting at least one ace?

1. a. 1/12

2. b. 1/36

3. c. 5/36

4. d. 11/36

5.

**Question 40:**12345679 * 72 is equal to :

1. 88888888

2. 888888888

3. 898989898

4. 999999998

5.

**Question 41:**514789 – 317463 – 87695 – 11207 = ?

1. 96584

2. 98242

3. 96845

4. 98424

5.

**Question 42:**0.005 x 0.5 x 0.05 =

1. 0.00125

2. 0.000125

3. 0.0000125

4. 0.125

5. 0.0125

**Question 43:**trignometry

if sin46=2;thencos44=?

1. 0

2. 1

3. 2

4. 3

5. none of these

**Question 44:**Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?

1. 256

2. 260

3. 316

4. 320

5. It cannot be determined from the given information.

**Question 45:**If the function f(x) = 2x3 – 9ax2 + 12 a2 x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p2 = q, then a

1. 2

2. 1

3. 6

4. 4

5. 5

**Question 46:**If w is 10% less than x, and y is 30% less than z, they wy is what percent less than xz?

1. 10

2. 20

3. 37

4. 40

5. 100

**Question 47:**The value of variate that occur most often is called

1. median

2. mean

3. mode

4. none

5.

**Question 48:**A carton contains 10 boxes,each box containing one dozen cubes.How many cartons are needed to fill 960 cubes?

1. 7

2. 8

3. 9

4. 12

5. 10

**Question 49:**If y = 3, then y3(y3-y)= ?

If y = 3, then y3(y3-y)= ?

1. 300

2. 459

3. 648

4. 999

5. 1099

**Question 50:**Find the number of ways of arranging 4 boys and 3 girls so that the row begins with aboy and ends with a girl

1. 1440

2. 1340

3. 1240

4. 1150

5.

**Question 51:**A boy was asked to multiply a certain number by 53. He multiplied it by 35 and got his answer less than the correct one by 1206. Find the number to be multiplied.

1. 37

2. 67

3. 87

4. 97

5.

**Question 52:**Free International CallsSMS & Call Friends for Free across the World. Call Now! Safe Feed Of My BabyFor Safe Feeding And Healthy Baby, visit.Your Ad HereA conical tent of radius 12m and height 16m is to be made. Find its cost if canvas is Rs. 10 per m2

1. (a) Rs 7543

2. (b) Rs 7445

3. (c) Rs 7342

4. (d) 7600

5.

**Question 53:**Number of ways of selecting 4 letters from the word EXAMINATION:

1. 136

2. 163

3. 170

4. 63

5. 172

**Question 54:**The angle between the two tangents to the parabola y 2 = 4x drawn from the point (1, 4) is

1. n/4

2. n/6

3. n/2

4. n/3

5.

**Question 55:**What is the sine of the angle whose tangent is the square root of 7?

What is the sine of the angle whose tangent is the square root of 7?

1. .93

2. 1.0

3. .85

4. .60

5.

**Question 56:**If the mean of 5 observations x,x+2,x+4,x+6,x+8, is 11 then the mean of first 3 observations is :

1. 9

2. 14

3. 18

4. None

5.

**Question 57:**If 8x + 5x + 2x + 4x = 114, the 5x + 3 = ?

If 8x + 5x + 2x + 4x = 114, the 5x + 3 = ?

1. 12

2. 25

3. 33

4. 47

5. 86

**Question 58:**What is the value of ‘C’ in the system of Roman numerals?

1. 50

2. 100

3. 1000

4. 1200

5.

**Question 59:**-----------is the most stable of all the measures of cetral tendency.

1. G.M

2. H.M

3. A.M

4. None

5.

**Question 60:**How many equal sides are there in a heptagon?

1. 5

2. 7

3. 6

4. 8

5.

**Question 61:**What is the name of device used to survey the petroleum?

1. Flowmeter

2. Resistivity meter

3. Magnetometer

4. Galvanometer

5.

**Question 62:**Turn odd man out: 1,4,9,16,25,35,49

1. 49

2. 35

3. 25

4. 16

5.

**Question 63:**For the values of a variable 3,1,5,2,6,8,4 the mean is

1. 3

2. 5

3. 4

4. none

5.

**Question 64:**In a drawer of shirts, 8 r blue, 6 r green, and 4 r magenta. If Mason draws 2 shirts at random, what is the probability that at least one of the shirts he draws will be blue?

1. 25/153

2. 28/153

3. 5/17

4. 4/9

5. 12/17

**Question 65:**A ball is drawn from an urn containing one red ball and one black ball. If the ball drawn is red, a coin is tossed; if it is black, a die is thrown. What is the probability of getting a head?

1. a. 1/2

2. b. 1/12

3. c. 1/4

4. d. 1/3

5.

**Question 66:**polynomials

Divide the polynomial x^3-27x^2+8x+18 by x-1 by long division method?

1. x^2+26x+18

2. x^2-18x+26

3. x^2-26x-18

4. x^2 -26x+18

5.

**Question 67:**Which of the following is incorrect?

1. An incentre is a point where the angle bisectors meet.

2. The median of any side of a triangle bisects the side at right angle.

3. The point at which the three altitudes of a triangle meet is the orthocentre

4. The point at which the three perpendicular bisectors meet is the centre of the circumcircle.

5.

**Question 68:**Write down the sum of first eight even natural numbers:

1. 56

2. 48

3. 62

4. 72

5. 88

**Question 69:**The distance between Athens and Carthage is 120 miles. A car travels from Athens to Carthage at 60 miles per hour and returns from Carthage to Athens along the same route at 40 miles per hour. What is the average speed for the round trip?

1. 48

2. 50

3. 52

4. 56

5. 70

**Question 70:**If chocolate, nuts and caramel are to be mixed in the ratio 3:5:7 respectively, and 5 tons of chocolate are available, how many tons of the mixture can be made? (Assume there is enough nuts and caramel to use all the chocolate.)

1. 15

2. 20

3. 25

4. 30

5. 75

**Question 71:**An ice-cream company makes a popular brand of ice-cream in a rectangular-shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company has decided to reduce the volume of the bar by 20%. The thickness will remain the same, but the length and width will be decreased by the same percentage amount. The new length L will satisfy ?

1. 5.5 < L < 6

2. 5 < L < 5.5

3. 4 < L < 4.5

4. 4.5 < L < 5

5.

**Question 72:**Frances can complete a job in 12 hours, and Joan can complete the same job in 8 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?

1. 6 p.m.

2. 7 p.m.

3. 8 p.m.

4. 10 p.m.

5. 12 p.m.

**Question 73:**If the length of rectangle A is one-half the length of rectangle B, and the width of rectangle A is one-half the width of rectangle B, what is the ratio of the area of rectangle A to the area of rectangle B?

1. 1/4

2. 1/2

3. 1/1

4. 2/1

5.

**Question 74:**If the difference between 5 times and 9 times of a number is 24 ,the number is:

1. 4

2. 3

3. 6

4. 8

5. 5

**Question 75:**What is the value of 1*1! + 2*2! + 3!*3! + ............ n*n!, where n! means n factorial or n(n-1)(n-2)...1

1. n(n-1)(n-1)!

2. (n+1)!/(n(n-1))

3. (n+1)! - n!

4. (n + 1)! - 1!

5.

**Question 76:**Two unbiased dice are thrown together. What is the probability that getting a sum of 10 or more if 5 appears on the first die ?

1. a. 1/12

2. b. 5/12

3. c. 5/6

4. d. 1/18

5.

**Question 77:**A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum (in percentage) is

1. 2 1/2

2. 4

3. 5

4. 6 2/3

5.

**Question 78:**The two lines x = ay + b, z – cy + d and x = a’ y + b’, z = c’y + d’ will be perpendicular, if and only if

1. aa’ + bb’ + cc’ = 0

2. (a + a’) (b + b’) + (c + c’) = 0

3. aa’ + cc’ + 1 = 0

4. aa’ + bb’ + cc’ + 1 = 0

5.

**Question 79:**A lattice point is a point (x, y) in the plane

A lattice point is a point (x, y) in the plane such that x and y are integers. The number of rectangles with corners at lattice points, sides parallel to the axes, and center at the origin which have precisely 2004 lattice points on all of its sides put together is

1. 0

2. 501

3. 499

4. 500

5. 2004

**Question 80:**The speed of a car is 30km first hour and 32 km in the second hour .Its average speed is:

1. 30 km

2. 31 km

3. 2 km

4. 32 km

5. 33 km

**Question 81:**Two cards are drawn simultaneously from a pack of 52 cards. Find the probability of getting both red cards ?

1. a. 25/102

2. b. 12/102

3. c. 12/51

4. d. 25/51

5.

**Question 82:**The surface area of the three coterminous faces of a cuboid are 6, 15, 10 sq.cm respectively. Find the volume of the cuboid.

1. 30

2. 20

3. 40

4. 35

5.

**Question 83:**A number when divided by 899 gives a remainder is 29.When the same number is divided by 16,what will be remainder?

1. 11

2. 13

3. 15

4. data inadequate

5.

**Question 84:**An integer is chosen at random from the first 200 positive integers. What is the probability that the integer is divisible by 6 or 8 ?

1. a. 1/2

2. b. 1/3

3. c. 1/4

4. d. 2/5

5.

**Question 85:**LCM of 2/3 and 4/9 =?

1. 2/9

2. 2/3

3. 4/9

4. 4/3

5. none

**Question 86:**A and B throw a dice. The probabilty that A's throw is not greater than B's is

1. 5/12

2. 7/12

3. 11/12

4. 5/36

5.

**Question 87:**In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC = ?

1. 6

2. 4

3. 3

4. 2

5. 1

**Question 88:**(24x3-18x3)/(8x7-23.5x2)=?

1. 2

2. 1

3. 1/2

4. 6

5.

**Question 89:**The ratio compunded of 2:3, 9:4, 5:6, and 8:10 is

1. 1:1

2. 1:5

3. 3:8

4. none of these

5.

**Question 90:**One number is chosen at random from the numbers 1 to 21. Find the probability that it may be a prime number.

1. a. 1/13

2. b. 4/21

3. c. 8/21

4. d. 1/7

5.

**Question 91:**3,12,27,48,75,108,?

1. 147

2. 162

3. 183

4. 192

5. 197

**Question 92:**Who is the Indian mathematician who invented Calculus long before Newton and Leibniz?

1. Aryabhatta

2. Brahmagupta

3. Bhaskaracharya

4. Bhaskaracharya II

5.

**Question 93:**Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).

1. 36

2. 18

3. 15

4. 30

5.

**Question 94:**sin 45 = _________.

1. 1

2. cos 45

3. 0

4. undefined

5.

**Question 95:**You get a wage increase of 4% plus an extra £5 per week. Your present wages are £250 per week. What will your new wage be?

1. £260

2. £265

3. £270

4. £275

5. £280

**Question 96:**Arabic Numerals weren’t developed by Arabs. Which nation contributed this concept of numeral system?

1. India

2. Greece

3. Rome

4. Persia

5.

**Question 97:**11.12% 650 + ? % of 400 = 110

1. 25

2. 18

3. 8

4. 80%

5.

**Question 98:**Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary to the original level is

Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary to the original level is

1. 20%

2. 25%

3. 33 1/3%

4. 30%

5.

**Question 99:**The letters of the word VARIETY are placed at random in a row. What is the probability that three vowels come together ?

1. a. 2/7

2. b. 3/7

3. c. 4/7

4. d. 1/7

5.

**Question 100:**If a=2/3b , b=2/3c, and c=2/3d what part of d is b/

1. 8/27

2. 4/9

3. 2/3

4. 75%

5. 4/3