mock test-1 - shikhar classes · mock test-1 part ² i : maths this section contains 15 single...

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SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 1 MOCK TEST-1 PART I : MATHS This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted. 1. The unit digit in the expression (36 234 ) (33 512 ) (39 180 ) (54 29 ) (25 123 ) (31 512 ) will be (A) 8 (B) 0 (C) 6 (D) 5 2. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions? (A) 23 (B) 24 (C) 25 (D) 26 3. If x + y = 4, then the value of 3 3 x y 12xy 64 will be (A) 0 (B) 128 (C) 64 (D) 64 4. ABCD is a trapezium in which AB ||CD. If ADC = 2 ABC, AD = a cm and CD = b cm, then the length (in cm) of AB is (A) a 2b 2 (B) a + b (C) 2 a b 3 (D) 2 a b 3 5. Let x Q, y Q C ,. Which of the following statement is always WRONG? (A) XY Q C (B) Y/X Q, whenever defined (C) 2x y Q (D) x/y Q c , whenever defined 6. If the area of the triangle given below is 20 sq. units, then what are the co-ordinates of point C? (A) 40 0, a (B) 2 2 (a b , 0) + (C) 20 ,0 b (D) 40 ,0 b 7. In the given figure, BD is the diameter of the circle with centre O, COD = 92° and ABD = 65°. Then y equals…… (A) 65 0 (B) 46 0 (C) 44 0 (D) 21 0 8. The value of the digit d for which the number 5456d is divisible by 18, is (a) 3 (b) 4 (c) 6 (d) None

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  • SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 1

    MOCK TEST-1

    PART – I : MATHS

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    1. The unit digit in the expression (36234

    ) (33512

    ) (39180

    ) – (5429) (25123) (31512) will be (A) 8 (B) 0 (C) 6 (D) 5 2. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the

    smaller wheel make when the larger one makes 15 revolutions? (A) 23 (B) 24 (C) 25 (D) 26

    3. If x + y = –4, then the value of 3 3x y 12xy 64 will be (A) 0 (B) 128 (C) 64 (D) –64

    4. ABCD is a trapezium in which AB ||CD. If ADC = 2 ABC, AD = a cm and CD = b cm, then the length (in cm) of AB is

    (A) a

    2b2

    (B) a + b (C) 2

    a b3

    (D) 2

    a b3

    5. Let x Q, y QC,. Which of the following statement is always WRONG? (A) XY QC (B) Y/X Q, whenever defined (C) 2x y Q (D) x/y Qc, whenever defined 6. If the area of the triangle given below is 20 sq. units, then what are the co-ordinates of point C?

    (A) 40

    0,a

    (B) 2 2(a b , 0)+ (C) 20

    ,0b

    (D) 40

    ,0b

    7. In the given figure, BD is the diameter of the circle with centre O, COD = 92° and ABD = 65°. Then y equals……

    (A) 65

    0 (B) 46

    0 (C) 44

    0 (D) 21

    0

    8. The value of the digit d for which the number 5456d is divisible by 18, is (a) 3 (b) 4 (c) 6 (d) None

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 2

    9. A farmer divides his herd of x cows among his 4 son’s such that first son gets one-half of the herd, the second son gets one fourth, the third son gets one-fifth and the fourth son gets 7 cows, then the value of x is

    (a) 100 (b) 140 (c) 160 (d) 180

    10. If , are the zero’s of polynomial 2( ) ( 1)f x x p x c then ( 1)( 1) is equal (a) 1c (b) 1 c (c) c (d) 1 c

    11. What is the remainder when the polynomial 200 199 50 49 2( ) 2 2 1p x x x x x x x is divided by ( 1)( 2)?x x (a) 1 (b) 7 (c) 2 1x (d) 6 5x 12. 450 litres of a mixture of milk and water contain the milk and water in the ratio 9 : 1. How much water should be

    added to get a new mixture containing milk and water in the ratio 3 : 1? (a) 54 (b) 90 (c) 45 (d) 63 13. The area of the quadrilaterals, the coordinates of whose vertices are (1, 2), (6, 2), (5, 3) and (3, 4) are (a) 9/2 (b) 5 (c) 11/2 (d) 11 14. If x

    2 + px + q = 0 and x

    2 + qx + p = 0 have a common root, then…….

    (A) p = q (B) 1 + p + q = 0 (C) p + q = 0 (D) Both A and B 15. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume

    of the volume of the reduced cylinder to that of the original one? (a) 1 : 4 (b) 1 : 8 (c) 1 : 2 (d) 8 : 1

    PART – II : APTITUDE

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    Direction (16): Count the number of cubes in the given figure and choose the correct answer out of given alternatives. 16.

    (A) 15 (B) 12 (C) 18 (D) 16 Directions (17): The following question shows a sheet of paper when folded and then cut like the figure. X, Y, Z. On unfolding the sheet, the sheet will appear like which alternative. 17.

    Direction (18): Choose the Venn diagram which best describe the relationship among the three given classes (the size of circle does not indicate relative sizes of classes)

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 3

    18. Protons – Electrons – Atom

    (A) (B) (C) (D) Direction : (19 to 20 ) Read the following information carefully and answer the questions given below it. In a car exhibition, seven cars of seven different brands, viz Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo were displayed in a row, facing east direction such that : I. Cadillac was to the immediate right of Fargo. II. Fargo was fourth to the right of Fiat. III. Maruti was between the Ambassador and Bedford. IV. Fiat, which was third to the left of Ambassador, was at one of the extreme ends. 19. Which cars are neighbours of Cadillac? (A) Ambassador and Maruti (B) Maruti and Fiat (C) Fiat and Mercedes (D) Mercedes and Fargo 20. Which of the following is definitely true? (A) Maruti is to the immediate left of Ambassador (B) Bedford is to the immediate left of Fiat. (C) Bedford is at one of the ends (D) Fiat is second to the right of Maruti Direction : (21 to 22 ) There are six places P, Q, R, S, T and U. There are exactly two district parks, two shopping malls and two amusement parks not a district park. Q and T are not shopping malls. S is not an amusement park. P and S are not shopping malls. P and Q are not alike.

    21. Which two places are district parks? (a) P and Q (b) R and P (c) Q and S (d) P and U

    22. Which two places are neither shopping malls nor district parks? (a) P and Q (b) P and T (c) U and R (d) Q and S

    Directions : (23 to 25) A cube of 4 cm has been painted on its surfaces in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. Two remaining surfaces have been left unpainted. Now the cube is cut into smaller cubes of side 1 cm each. 23. How many cubes will have no side painted? (A) 18 (B) 16 (C) 22 (D) 8 24. How many cubes will have at least blue colour on its surfaces? (A) 20 (B) 8 (C) 24 (D) 32 25. Pointing towards a person in a photograph, Mukesh said, “She is the only daughter of the mother of my brother’s

    sister.” How is that person related to Mukesh? (A) Mother (B) Cousin (C) sister (D) Aunt Directions (26 to 28): In the following diagram three classes of population are represented by three figures. The triangle represents the school teachers, the square represents the married persons and the circle represents the persons living in joint families.

    26. Persons who live in joint families, are unmarried and who do not work as school teachers are represented by (A) C (B) B (C) E (D) D 27. Married teachers living in joint families are represented by (A) C (B) B (C) D (D) A

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 4

    28. If KEDGY is coded as EKDYG then how will LIGHT be coded? (A) ILHTG (B) ILGHT (C) ILGTH (D) THGIL Direction : (29 to 30) Read the following information carefully and answer the questions given below : There are five men A, B, C,D and E and six women P, Q, R, S, T and U, A, B and R are advocates ; C, D, P, Q and S are doctors and the rest are teachers. Some teams are to be selected from amongst these eleven persons subjected to the following conditions: A, P and U have to be together B cannot go with D or R. E and Q have to be together. C and T have to be together D and P cannot go together C cannot go with Q. 29. If the team is to consist of one male advocate, one male doctor, one lady doctor and two teachers , the members of

    the team are (A) ACPTU (B) ADEPT (C) ADEPU (D) BCEQU 30. If the team is to consist of one advocate, three doctors and one male teacher, the members of the team are (A) ADPSU (B) CDRST (C) DEQRS (D) DEQRT

    PART – III : MATHS [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    31. An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 12 dm

    2, then the

    difference of their areas (in dm2) is

    32. If 2 3 is a root of the quadratic equation 2x 2( 3 1)x 3 2 3 0 , then the second root is 33. If the angles of depression and elevation of the top of a tower of height h from the top and bottom of a second tower

    are x and y respectively, then the height of the second tower is 34. In the figure, ABCD is a parallelogram and PBQR is a rectangle.

    A B

    CD

    P

    QR

    If AP : PB = 1 : 2 = PD : DR, what is the ratio of the area of ABCD to the area of PBQR? 35. Number of two digit numbers having the property that they are perfectly divided by the sum of their digits with

    quotient equal to 7, is 36. The mean age of a group of persons is 40. Another group has mean age 48. If the ratio of number of persons in two

    groups is 5 : 3, then mean age of all the persons in two group is

    37. Two circles touch externally. The sum of their areas is 130 sq cm and the distance between their centres is 14 cm. The radii of the circles are

    38. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket

    drawn bears a number which is a multiple of 3 ? 39. F(x) is a polynomial in x. When F(x) is divided by (x – 2), the remainder obtained is 3, when the same polynomial is

    divided by (x – 3), the remainder obtained is 2. What is the remainder when F(x) is divided by (x – 3) (x – 2)

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 5

    PART – IV : SCIENCE [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided.

    Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    40. An object placed in front of a convex lens produces two times magnified real image. If the focal length of the lens is

    20 cm. Find the distance of image from lens. 41. A truck starts from rest and moves with constant acceleration. If it covers 200 m in first 10 seconds. Find the distance

    (in metres) it will cover in next 5 seconds. 42. In the given circuit, considering the battery to be ideal

    3 W 12 W

    6 W 24 W

    30 V

    Find current flowing through 6 W resistor.

    43. Suppose two elements X and Y combine to form two compounds XY2 and X3Y2. 0.1 mole XY2 has weight 10 gram

    while 0.05 mole of X3Y2 has weight 9g . Find the atomic masses of X and Y. 44. Write the name of all the element in second group of periodic table. 45. Write the IUPAC name of given compound

    .

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 6

    MOCK TEST-2

    PART – I : MATHS

    This Section contains 15 Single Choice Questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    1. H. C. F. of x

    2 + 5x + 6 and x

    3 + 27 is

    (A) x + 2 (B) x – 2 (C) x – 3 (D) x + 3 2. The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breath and height are halved while the length

    is doubled, then the total area of the four walls of the room will (A) Remain the same (B) Decrease by 30% (C) Decrease by 15% (D) Decrease by 18.75% 3. A is a right circular cylinder on which a cone B is placed. The entire structure is melted and spheres are formed each

    having radius 1 cm. How many spheres can be formed nearly?

    3 cm

    6.25 cm

    A

    B

    4 cm

    (A) 18 (B) 20 (C) 21 (D) 23 4. Four watches are ringing alarm bells in the interval of 6, 12, 15 and 18 seconds. If they start at same time, how many

    times they will ring together in 4 hrs. (A) 80 times (B) 81 times (C) 20 times (D) 21 times 5. After covering distance of 30 km with a uniform speed there is some defect in a train engine and therefore, its speed

    is reduced to 4/5 of its original speed. Consequently, the train reaches its destination late by 45 minutes. Had it happened after covering 18 kilometers more, the train would have reached 9 minutes earlier. Find the speed of the train and the distance of journey.

    (A) Speed = 40 km/hr, Distance = 160 km (B) Speed = 20 km/hr, Distance = 100 km (C) Speed = 30 km/hr, Distance = 120 km (D) Speed = 35 km/ hr, Distance = 140 km

    6. If x + 1 50

    x 7 , then which is always true?

    (A) x700

    > 700 (B) x700

    < 700 (C) 700x 700 or 700x 700

    (D) 700x 700 and 700x 700 7. Vijay has been invited for dinner in a club. While walking through the garden path towards the building, he observes

    that there is an electric rod on the top of the building. From the point where he is standing, the angles of elevation of the top of the electric rod and the top of the building are and respectively. IF the heights of the electric rod and the building are p and q respectively, mark all the correct statements.

    (A) The height of the tower is ptan tan

    tan tan

    q f

    f q (B) The height of the electric rod is

    qtan

    (tan tan )

    q

    f q

    (C) The height of the tower is p tan

    tan tan

    q

    q q (D) The height of the electric rod is

    q(tan tan )

    tan

    f q

    q

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 7

    8. In the figure AD = BD, BE = 1

    EC2

    and 1

    CF AF3

    . IF the area of ABC= 120 cm2, the area (in cm2) of DEF is

    A

    B

    D

    C

    E

    F

    (A) 21 (B) 35 (C) 40 (D) 45

    9. The sum of digits of the number 2 24n 810 1 where ‘n’ is a positive integer, is (A) 4 (B) 8 (C) 9 (D) 11 10. The greatest angle of a quadrilateral is double the least. If the angle are in arithmetic series [a, a + d, a + 2d, a + 3d],

    the other two angles are

    (A) 2

    ,3 3

    p p (B)

    5 6,

    9 9

    p p (C)

    4 5,

    9 9

    p p (D)

    3,

    4 4

    p p

    11. Diagonal DB of a rhombus ABCD is equal to one of sides.

    The values of A is (A) 30

    0 (B) 60

    0 (C) 120

    0 (D) 90

    0

    12. In a data, 10 numbers are arranged in increasing order. If the 7

    th entry is increased by 4, then the median increases

    by (A) zero (B) 4 (C) 6 (D) 5 13. A circle is inscribed in trapezoid PQRS. If PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm, what is the length of the

    diameter of the circle?

    (A) 14 cm (B) 25 cm (C) 24 cm (D) 674 cm

    14. Which among 1/ 2 1/ 3 1/ 4 1/ 62 ,3 ,4 ,6 and 1/1212 is the largest?

    (A) 1/ 22 (B) 1/33 (C) 1/ 44 (D) 1/ 66

    15. If D is any point on the side BC of a ABC, then (A) AB + BC + CA > 2AD (B) AB + BC + CA < 2AD (C) AB + BC + CA > 3AD (D) None

    PART – II : APTITUDE

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    16. Amit said, “This girl is the wife of the grandson of my mother.” How is Amit related to the girl? (A) Father (B) Father-in-law (C) Grandfather (D) Husband

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 8

    17. If KEDGY is coded as EKDYG then how will LIGHT be coded? (A) ILHTG (B) ILGHT (C) ILGTH (D) THGIL 18. Three positions of the same dice are given below. Observe the figures carefully and tell which number will come in

    place of ‘?’

    (i) (ii) (iii) (A) 1 (B) 6 (C) 3 (D) 5 Directions: (17 to 18) Study the following information to answer the given questions : (i) In a class of boys and girls, Amar’s rank is 12th and Meeta’s rank is 8th. (ii) Amar’s rank among the boys is 6th and Meeta’s rank among girls is 3rd. (iii) In the class Meeta’s rank is 52th from the other end. (iv) From the other end, Amar’s rank among the boys is 26th. 19. How many boys are there in the class? (A) 31 (B) 28 (C) 29 (D) Can’t be determined 20. Which of the following is Meeta’s rank among the girls from the other end ? (A) 23

    rd (B) 28

    th (C) 26

    th (D) Can’t be determined

    Directions: (19 to 20) Read the following information carefully and answer the questions given below. I. There is a family of six persons- L, M, N, O, P and Q. They are professor, businessman, chartered account, bank

    manager, engineer and medical representative, not necessarily in that order. II. There are two married couples in the family. III. O, the bank manager is married to the law professor. IV. Q, the medical representative, is the son of M and brother of P. V. N, the chartered accountant, is the daughter - in law of L. VI. The businessman is married to the chartered accountant. VII. P is an unmarried engineer. VIII. L is the grandmother of Q.

    21. How is O related to Q? (A) Father (B) Grandfather (C) Uncle (D) Brother 22. How is P related to Q (A) Brother (B) Sister (C) Cousin (D) Either brother or sister

    Directions: (21 to 22) Stud the following information to answer the given question. (i) Eight friends A, B, C, D, E, F, G and H are seated in a circle facing centre. (ii) D is between B and G and F is between A and H. (iii) E is second to the right of A.

    23. If B is sitting opposite to C then F is sitting opposite to? (A) B (B) G (C) A (D) D 24. Which of the following is C’s position? (A) Between E and A (B) Between G and E (C) Second to the left of B (D) Can’t be determined Directions : (25 to 26) In the following diagram, the square represents girls, the circle tall persons, the triangle is for tennis players and the rectangle stands for the swimmers. On the basis of the given diagram, answer the following questions

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 9

    25. Which letter represents tall girls who are swimmers but don’t play tennis? (A) C (B) D (C) G (D) H 26. Which letter represents girls who are swimmers, play tennis but are not tall? (A) B (B) E (C) F (D) None Directions: (25 to 26) The second figure in the first part of the problem figures bears a certain relationship to the first figure. Similarly one of the figures in answers figures bears the same relationship to the first figures in the second part. You have to select the figure from the set of answer figures which would replace the sign of questions mark(?). 27. Problem figure

    Directions: (28) The outer border of width 1 cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. this cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are now separated. 28. How many cubes have one face coloured pink and an adjacent face yellow? (A) 0 (B) 1 (C) 2 (D) 4 29. How many cubes have two face coloured yellow? (A) 0 (B) 44 (C) 40 (D) None of these Directions: (30) Answer the questions on the basis of the information given below. If ‘$’ represents ‘+’, ‘ * ’ represents ‘ –‘, ‘#’ represents ‘x’ and ‘@’ represents ‘/’ then answer the following questions based on the above given representation.

    30. What is the value of 4#3$10@5$8#2 *18 ?

    (A) 10 (B) 12 (C) 6.8 (D) 11.2

    PART – III : MATHS [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and Zero in all other cases. There is no step marking.

    31. The mean weight of a class of 34 students is 46.5 kg. If weight of the teacher is include, the mean rises by 500 gm.

    Then weight of the teacher is

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 10

    32. In the figure shown, the bigger circle has radius 1 unit. Therefore, the radius of smaller circle must be

    33. Find the unit digit of the number 2

    2006 + 5

    2007 is equal to

    34. If 1

    x 3x

    , then the value of 66

    1x

    x is

    35. What is the probability of getting a king or a queen in a single drawn from a pack of 52 cards? 36. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is 37. Circles with centres O, O’ and P each tangent of the line L and also mutually tangent. If the radii of circle O and circle

    O’ are equal and the radius of the circle P the smaller one is 6, then the radius of the larger circle is

    38. Three unbiased coins are tossed. What is the probability of getting at most 2 heads? 39. In the following figure, if O is the centre of the circle and radius OA = 14 cm, if the area of the shaded portion is k

    then find the value of k.

    PART – IV : SCIENCE [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    40. M1 and M2 are two mirrors as shown in figure. The focal length of mirror M2 is 30 cm. A point object O is kept on the principal axis of M2 at exactly midpoint between the mirrors. The distance between mirrors is 40 cm. Considering two successive reflections, first on M1 and then on M2.find the distance of final image from the object.

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 11

    41. In the above circuit, find VE – VG. Assume the battery to be ideal.(Resistance between C and D is 2 ohm)

    42. A ball projected vertically upwards with initial speed v0 achieves maximum height h0. If the ball is now projected

    vertically with initial speed 2v0, find the new maximum height up to which the ball reaches in terms of h0.

    43. Write the name of all the elements of 14

    th group in the periodic table?

    44. Write the structure and molecular formula of 2,3- dimethylbutane 45. Balance the following chemical reaction

    (i) 6 8 2 2 2C H O CO H O (ii) 3 4 3 4 2H PO NaOH Na PO H O

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 12

    MOCK TEST-3

    PART – I : MATHS

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    1. Find the sum of all odd natural numbers less than 200 (a) 1000 (b) 10100 (c) 9900 (d) 10000

    2. H.C.F. of 3( 3 2)x x and 2( 4 3)x x is (a) (x – 1) (b) (x – 1)2 (c) (x – 1) (x + 2) (d) (x – 1) (x – 3)

    3. If

    21

    9,xx

    then the value of 33

    1x

    x is

    (a) 18 (b) 12 (c) 24 (d) 6 4. The difference between two number is 2. Their product is 84 greater than the square of the smaller number. The sum

    of the number is (a) 164 (b) 86 (c) 84 (d) 42 5. ABCDE is a regular pentagon, A star of five points ACEBDA is formed to join their alternate vertices. The sum of all

    five vertex angles of this star is

    (a) Two right angle (b) Three right angle (c) Four right angle (d) Five right angle

    6. The sides of an 8 8 square are cut by certain points into pieces of length 1 and 7, 2 and 6, 3 and 5 and 4 and 4 as shown in figure. The area of the quadrilateral determined by these four points are

    (a) 28 (b) 36 (c) 48 (d) 8

    7. Both roots of the quadratic equation 2 63 0x x k are prime numbers. The number of possible value of k is

    (a) 0 (b) 1 (c) 2 (d) 3

    8. In the diagram O is the centre of a circle. AE + EB = CE + ED. OP AB and OQ CD then true relation between OP and OQ is

    (a) OP > OQ (b) OP < OQ (c) 1

    2OP OQ (d) OP = OQ

  • Entrance Test : SAMPLE PAPER XENON

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    9. The average age of two brothers is 13. It is increased by 11 years when their mother’s age is also included. The age of the mother is

    (a) 45 years (b) 46 years (c) 47 years (d) 48 years 10. A coin is successively tossed to times. Find the probability of getting :

    (1) Exactly one head (2) At least one head

    (a) 1 3

    ,2 4

    (b) 2 1

    ,3 4

    (c) 1 4

    ,4 5

    (d) 1 2

    ,2 3

    11. n

    2 –1 is divisible by 8, if n is

    (a) A non integer (b) A natural number (c) An odd integer (d) An even integer 12. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is (a) 10 : 17 (b) 20 : 27 (c) 17 : 27 (d) None of these 13. A solid metallic sphere of radius r is converted into a solid right circular cylinder of radius R. If the height of the

    cylinder is twice the radius of the sphere then

    (a) R = r (b) r 2

    R3

    (c) 2r

    R3

    (d) 3r

    R2

    14. Three squares have the dimensions indicated in the diagram. The area of the quadrilateral ABCD, is

    (a) 21/4 (b) 15/4 (c) 42/4 (d) Data not sufficient 15. Two numbers are respectively 25% and 40% less than a third number. What percent is the second of the first? (a) 90 % (b) 80 % (c) 70 % (d) 60 %

    PART – II : APTITUDE

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    16. A clock which gains 6 minutes every three hours is set at 1.00 P.M. on a certain day. Find the time shown by the

    watch on next day at 13:50 hours. (a) 15 hrs 21 min 40 sec (b) 14 hrs 39 min 40 sec

    (c) 13 hrs 0 min 20 sec (d) None of these

    Direction: (17 to 18) the following question are based on the following information: Five men A, B, C, D and E read a newspaper. The one who reads first gives it to C. The one who reads last had taken from A. E was not the first or last to read. There were two readers between B and A.? 17. B passed the newspaper to whom? (a) A (b) C (c) D (d) E 18. Who read the newspaper last? (a) A (b) B (c) C (d) D

    Directions (Questions 19-20): Read the following information carefully and answer the questions below: A family consists of six members P, Q, R, S, T and U. There are two married couples. Q is a doctor and the father of T. U is the grandfather of R and is a contractor. S is grandmother of T and is a housewife. There is one doctor, one contractor, one nurse, one housewife and two students in the family. 19. Who is the husband of P?

    (a) R (b) U (c) Q (d) S

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    20. Who is the sister of T? (a) R (b) U (c) T (d) Information insufficient

    Directions (Questions 21-22): Read the following information carefully and answer the

    In a class, 70 students passed in Mathematics, 50% of the students passed in English, 25% of the students passed in both and 5% of the students passed in neither Mathematics nor English. 21. How many students are there in the class? (a) 93 (b) 145 (c) 100 (d) 140 22. How many students failed in atleast one subject? (a) 5 (b) 25 (c) 50 (d) 75 Directions (Questions 23-24): Read the following information carefully and answer the A solid cube each side 8 cm has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical block of each side 2 cm.

    23. How many cubes have no face painted? (a) 0 (b) 4 (c) 8 (d) 12 24. How many cubes have two faces painted black? (a) 2 (b) 4 (c) 8 (d) None Directions (Questions 25-26): Read the following information carefully and answer the In a certain code language “ in jee loo” means “you did it”, “joo ip an” means “how are things”, “loo sam” means “you sing” and “an pee joo” means “things are sweet”. 25. Which of the following is the code for ‘how’?

    (a) joo (b) ip (c) am (d) joo 26. What is the code for “you sing sweet”

    (a) loo sam an (b) loo pee joo (c) pee sam loo (d) loo ip pee Directions (Questions 27-28): Read the following information carefully and answer the questions given below: Six boys A, B, C, D, E and F are marching in a line. They are arranged according to their height, the tallest are being at the back and the shortest in front. F is between B and A E is shorter than D but taller than C who is taller than A E and F have two boys between them A is not the shortest among them all 27. Where is E?

    (a) Between A & B (b) Between C & A (c) Between D & C (d) In front of C

    28. Who is the tallest? (a) B (b) D (c) F (d) A

    Directions (Questions 29-30): Read the following information carefully and answer the

    Answer the questions on the basis of the information given below. If ‘$’ represents ‘+’, ‘ * ’ represents ‘ –‘, ‘#’ represents ‘x’ and ‘@’ represents ‘/’ then answer the following questions based on the above given representation.

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    29. What is the value of 4#3$10@5$8#2 *18 ?

    (a) 10 (b) 12 (c) 6.8 (d) 11.2 30. Which of the following has the value equivalent of 5$ 6# 2$ 8@4 ?

    (a) 4 # 7 * 12 $ 2 # 1 (c) 8 # 3 * 9 $ 6 @ 3

    (c) 8 @ 2 * 3 $ 6 # 3 (d) 4 $ 7 * 12 $ 2 # 1

    PART – III : MATHS [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    31. Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2 : 3,

    and Q divides AB in the ratio 3 : 4. If PQ = 2, then the length of side AB is 14xk . find k 32. If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, than the ratio of their volume

    is 12

    k find k

    33. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then the number of such

    triangles that exists are 2xk find k

    34. Given x y 12 8 and y x 99 3 ; then the value of one third of (x + y). is 35. There is a common chord of 2 circles with radius 15 and 20. The distance between the two centres is 25. Then

    length of the chord is 6xk find k. 36. A rectangular sheet of paper, when halved by folding it at the mid-point of its longer side, results in a rectangle,

    whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle.

    If the shorter side of the original rectangle is 2, the area of the smaller rectangle is 2 k find k 37. The difference between two numbers is 1450. When larger number is divided by the smaller one, the quotient is 3

    and the remainder is 10. The smaller number has how many digits ? 38. In given figure, OA = 3, OB = 4 and AB.AD = 2, then find AB

    2.

    O

    B A D

    39. A right circular cone of diameter k cm and height 12 cm rests on the base of a right circular cylinder of radius k cm

    (their bases lie in the same plane, as shown). The cylinder is filled with water to a height of 12 cm. If the cone is then removed, the height to which the water will fall, is

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    PART – IV : SCIENCE [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided.

    Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    40. The displacement versus time for a certain particle moving along the x axis is shown in Figure. Find the average

    speed of the particle in the time interval 0 to 5 sec.

    41. In a portion of some large electrical network, current in certain branches are known. Find the value of VD – VC 42. M1 and M2 are two concave mirror of same focal length 10 cm. OX is their common principal axis with O as the pole

    for mirror M1. A point object O’ is kept on the principal axis at distance 15 cm from O. The distance between the mirrors is 20 cm. Considering two successive reflections, first on M1 and then on M2.find the distance of final image from point O. (take OX to be positive direction).

    M1 M2

    ·O XO’

    43. In an atom of an element the sum of neutrons and protons is 14. The number of neutrons is two more than number

    of protons. Write the name of element 44. Complete the following chemical reactions

    (a) 2 4Zn H SO ......... ......... (b) 4 2CH 2O ............. ......... 45. Calculate the total number of mole of atoms in 980gm of 2 4H SO

    A

    7A

    9V

    4V 2A B

    3A

    W2 5V W4

    W10

    W63V

    W8

    DC

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    MOCK TEST-4

    PART – I : MATHS

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    1. If PQRS is a square, AB||SQ, A is mid point of SR and AC = CB, which one is true?

    (a) SA = BQ (b) PC is the bisector of SPQ (c) PC if produced will pass through R (d) All of these 2. The mean of the value of 1, 2, 3 ….. n with respective frequency x, 2x, 3x ….. nx is

    (a) 1

    2

    n (b)

    2 1

    3

    n (c)

    2

    n (d)

    2 1

    6

    n

    3. 1, –2, 3, –4, 5, –6, …. n(–1)n+1 consider the sequence. What is the average of the first 300 terms of the sequence (a) –1 (b) 0.5 (c) 0 (d) –0.5 4. Which of the following number is the largest?

    (a) 1/2 2(1 2 ) (b) 1

    1 12

    6 3

    (c) 0.5(24) (d) 10 9 8

    7 6 5

    5.

    4 43 66 39 9a a

    (a) 12 8a a (b) 16 12a a (c) 4a (d) All of these

    6. If a, b are coprime, then 2 2,a b are

    (a) Co-prime (b) Not coprime (c) Odd numbers (d) Even numbers 7. A clock has its second’s hand 2 cm long. The average speed of the tip of second’s hand in 15 sec is

    (a) ( / )2

    cm s

    (b) ( / )15

    cm s

    (c) ( / )20

    cm s

    (d) cm/s

    8. 1 1

    1 1 1 1

    x x

    x y x y

    is equal to

    (a) 2

    2 2

    2y

    y x (b)

    2

    2 2

    2x

    y x (c)

    2

    2 2

    2y

    y x (d) None

    9. From a lighthouse 100 m high, it is observed that two ships are approaching it from west and south. If angles of

    depression of the two ships are 300 and 45

    0 respectively the distance between the ships, in meters, is

    (a) 100 3 1 (b) 2100 3 1 (c) 2003

    (d) None

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    10. The ratio of the areas of two similar triangles is equal to (a) The ratio of corresponding medians (b) The ratio of corresponding sides (c) The ratio of the squares of corresponding sides (d) None of these 11. In the figure, the radius of the larger circle is 2 cm and the radius of the smaller circle is 1 cm and the larger circle

    passes through the centre of the smaller circle. The length (in cm) of the chord AB is

    (a) 15

    2 (b) 2 (c)

    3

    2 (d) None

    12. If a right circular cone, with slant height l , and a right circular cylinder have the same radius r, same total surface

    area and heights h and h’ respectively, then l rl r

    =

    (a) h/h’ (b) 2h/h’ (c) h/2h’ (d) 2h’/h

    13. If x y z2 4 8= = and xyz = 288, then the value of 1 1 1

    2x 4y 8z+ + is

    (a) 7

    96 (b)

    11

    96 (c)

    13

    96 (d)

    15

    96

    14. E is the midpoint of diagonal BD of a parallelogram ABCD. If the point E is joined to a point F on DA such that

    1,

    3DF DA then the ratio of the area of DEF to the area of quadrilateral ABEF is

    (a) 1 : 7 (b) 1 : 4 (c) 1 : 5 (d) 2 : 5 15. In the figure given below, equilateral triangle EDC surmounts square ABCD. Find the angle DEB represented by x

    A

    X

    E

    B

    CD

    (a) 60

    0 (b) 15

    0 (c) 30

    0 (d) 45

    0

    PART – II : APTITUDE

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    16. How many squares does the figure have? (a) 6 (b) 7 (c) 9 (d) 10

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    17. In the following question, there are two terms to the left of the sign :: which are related in some way. Obtain the same relationship between the term to the right of the sign :: from one of the four alternatives gives under it.

    EF : JK :: NO : ? (a) DC (b) GI (c) ML (d) TU 18. Nivedita stops after going 10 km towards west from her office. Then she goes 8 km turning to her left. After this she

    goes 4 km turning to her left. How far is she from her office? (a) 18 km (b) 8 km (c) 16 km (d) None of these 19. If x means –, – means x, + means ÷ and ÷ means + then—

    13 – 12 ÷ 400 + 20 x 100 = ? (a) 1/1760 (b) 76 (c) 176 (d) 186 20. Introducing Priyanka, Saroj says that her mother is the only daughter of my mother. How is Saroj related to

    Priyanka? (a) Mother (b) Sister (c) Daughter (d) None of these 21. A wrist watch which is running 12 minutes late on a Sunday noon is 16 minutes ahead of the correct time at 12 noon

    on the next Sunday. When is the clock 8 minutes ahead of time? (a) Thursday 10 am (b) Friday noon (c) Friday 8 pm (d) Tuesday noon Directions (22): In the following each question there are two statements and two conclusions I and II there-after are given. Accept the given statements as true even if they are inconsistent with known facts and ignoring the universally known facts find out which conclusion follows logically from the given statements. Give answer (A) if only the conclusion I follows. Give answer (B) if only the conclusion II follows. Give answer (C) if either the conclusion I or the II follows. Give answer (D) if neither the conclusion I nor the II follows. Give answer (E) if the conclusions I and II both follow. 22. Statements: Some elephants are horses.

    All horses are crocodiles. Conclusions: I. No crocodile is elephant. II. Some elephants are crocodiles.

    Direction: (23 to 24) Read the following paragraph carefully Four workmen A, B, C and D and three men E, F and G play bridge, a game four players. (i) The group consists of three married couples and a widow. (ii) Spouses are never partners in game. (iii) No more than one married couple ever plays in the same game. (iv) One day they played four games as follows. A and E versus B and F. A and G versus D and F. B and C versus F and G. C and E versus D and G. 23. Whom is E married to? (a) A (b) B (c) C (d) D 24. Whose is G married to? (a) A (b) B (c) C (d) D Directions (25 to 26) : There are four trees – tamarind, coconut, mango, and neem – each at a different corner of a rectangular plot. A well is located at one corner and a cabin at another adjacent corner. Tamarind and coconut trees are on either side of the gate which is located at the centre of the side opposite to the side at whose extremes, the well and the cabin are located. The mango tree is not at corner where the cabin is located. 25. If the tamarind tree is diagonally opposite to the well, then which is diagonally opposite to the coconut tree? (a) Mango (b) Gate (c) Well (d) Cabin 26. Which of the following pairs can be diagonally opposite to each other in the plot? (a) Neem and tamarind (b) Cabin and neem (c) Mango and well (d) Coconut and tamarind

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    Direction : (27 to 28) A cube is coloured orange on one face, pink of the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. it is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements. 27. How many cubes have at least one face coloured pink ? (a) 1 (b) 9 (c) 16 (d) 25 28. How many cubes have all the faces uncoloured? (a) 24 (b) 36 (c) 48 (d) 64 Directions : (29 to 30) Study the figure below and answer the following questions.

    29. Find out the number of families which have all the four things mentioned in the diagram. (a) 40 (b) 30 (c) 35 (d) 20 30. Find out the number of families which have scooters.

    (a) 145 (b) 100 (c) 188 (d) 240

    PART – III : MATHS [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme:

    You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    31. If 3 3 3 3 3/21

    (1 2 3 4 ) ,x

    then x is 2000

    k find k

    32. In this figure, AOB is a quarter circle of radius 10 cm and PQRO is a rectangle of perimeter 28 cm. The perimeter of

    the shaded region is a + b . Find a – 2b =

    33. An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 12 dm

    2, then the

    difference of their areas (in dm2) is

    34. A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3

    cm. The number of such cones is 7xk . find k

    35. In given figure PQR = 100°, where P, Q and R are points on a circle with centre O. Then, OPR is 2xk .find k

    36. The expression

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    1 1 1 1 1 1 1 1 1 1 1 1

    .......... 1 ............ 1 ........ ...........2 3 2008 2 3 2007 2 3 2008 2 3 2007

    Simplifies to 2008

    k . find k

    37. Three unbiased coins are tossed. What is probability of getting exactly two heads is 3

    k. Find k

    38. In the figure given below PS is the diameter, points P, Q, R and T, S, R are collinear. QTS is 6xk find k

    T S

    Q

    O

    P

    R 250

    350

    39. In Figure, AB = 12 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle

    with centre C touches all the three circles. If the area of the shaded region is k cm2 then what is the value of k?

    PART – IV : SCIENCE [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    40. An ISRO astronaut projects a ball vertically upwards with same velocity from the surface of Earth and the surface of

    Moon. It takes time t1 to reach maximum height on the Earth while t2 time to reach maximum height on the Moon. If gravity on Moon is one-sixth to that on Earth, find the ratio of t2/t1. (Neglect air friction)

    41. An object of length 5mm is placed at a distance 30cm from a concave mirror. If radius of curvature of mirror is 40 cm.

    What will be the size of image (write your answer in millimetres)? 42. If equivalent resistance between point C and D in the combination of resistance shown is R. Then find the value of

    10R.

    2W 4WC

    D

    2W6W1W

    43. Find the numbers of neutrons, protons and electrons in 5525Mn

    44. Complete the following chemical reaction

    2 4

    4

    a. Cu H SO ......... .........

    b. Zn CuSO ............. .........

    45. Calculate the total number of mole of atoms in 980gm of 3 4H PO

    P Q

    R S

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    MOCK TEST-5

    PART – I : MATHS

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    1. How many pairs of positive integers (n, m), with n m satisfy the equation 1 1 1

    ?5 n m

    (a) 1 (b) 2 (c) 3 (d) 4 2. The number of positive fraction m/n such that 1/3< m/n < 1 and having the property that the fraction remains the

    same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is

    (a) 1 (b) 3 (c) 6 (d) Infinite 3. Among the numbers 2

    250, 3

    200, 4

    150 and 5

    100 the greatest is

    (a) 2250

    (b) 3200

    (c) 4150

    (d) 5100

    4. When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder

    is 4. The remainder is z when x + y is divided by 5. The value of 2 5

    3

    z is

    (a) –1 (b) 1 (c) –2 (d) 2 5. The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15

    years join the group on the spot, due to which their average becomes 15.5 years. The number of persons initially going for the picnic is

    (a) 5 (b) 10 (c) 20 (d) 30 6. PQRS is a parallelogram and M, N are the mid-points of PQ and RS respectively. Which of the following is not true?

    (a) RM trisects QS (b) PN trisects QS (c) PSN RQM (d) MS is not parallel to QN

    7. ABCD is a quadrilateral whose diagonals intersect each other at the point O such that OA = OB = OD. If OAB = 30°, then the measure of ODA is

    (a) 30° (b) 45° (c) 60° (d) 90°

    8. In the figure, PQ is a chord of a circle with centre O and PT is the tangent at P such that QPT = 70°. Then the measure of PRQ is equal to

    (a) 135° (b) 150° (c) 120° (d) 110°

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    9. A circle with area A cm2 is contained in the interior of a larger circle with area (A + B) cm

    2 and the radius of the larger

    circle is 4cm. If A, B, A + B are in arithmetic progression, then the diameter (in cm) of the smaller circle is

    (a) 3

    2 (b)

    4 3

    3 (c)

    8 3

    3 (d) 2 3

    10. A right circular cone is cut off at the middle of its height and parallel to the base. Call the smaller cone so formed as

    A and the remaining part as B, then

    (a) 4Vol. A < Vol. B (b) Vol. A = Vol. B (c) Vol. A > Vol. B (d) Vol. 1

    8A (Vol. B)

    11. A cylinder, a Hemi-sphere and a cone stand on the same base and have the same heights. The ratio of the areas of

    their curved surface is

    (a) 2 : 2 : 1 (b) 2 : 2 : 1 (c) 2 : 3 :1 (d) None of the above 12. Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

    (a) 2xyz is odd (b) 2(x y) z is even

    (c) 2(x y z) (x y) is even (d) (x y)(y z)(x y z) is odd 13. The greatest angle of a quadrilateral is double the least. If the angle are in arithmetic series [a, a + d, a + 2d, a + 3d],

    the other two angles are

    (a) 2

    ,3 3

    p p (b)

    5 6,

    9 9

    p p (c)

    4 5,

    9 9

    p p (d)

    3,

    4 4

    p p

    14. If x y z

    a b c= = , then

    3 / 22 2 2 2 2 2

    3 3 3

    a x b y c z

    a x b y c z

    =………….

    (a) xyz

    abc (b)

    xyz

    abc (c)

    2

    xyz

    (abc) (d)

    2(xyz)

    abc

    15. Which of the following statements is correct? (a) If x

    6 + 1 is divided by x+ 1, then the remainder is –2.

    (b) If x6 + 1 is divided by x – 1, then the remainder is 2

    (c) If 6x 1+ is divided by x + 1, then the remainder is 1 (d) If x

    6 + 1 is divided by x – 1, then the remainder is –1.

    PART – II : APTITUDE

    This Section contains 15 Single choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking Scheme: You will be awarded 3 marks for correct answer, -1 for wrong answer and zero if Question is left un-attempted.

    16. David sets his watch at 6:10 am on Sunday, which gains 12 minutes in a day. On Wednesday if this watch is

    showing 2:50 pm. What is the correct time? (a) 1: 50 pm (b) 2:10 pm (c) 2 : 30 pm (d) 3 : 30 pm 17. Pointing towards a man is the photograph, lady said “the father of his brother is the only son of my mother”. How is

    the man related to lady? (a) Bother (b) Son (c) Cousin (d) Nephew 18. Two buses start from the opposite points of a main road, 150 kms apart. The first bus runs for 25 kms and takes a

    turn right and runs for 15 kms. It then turns left and runs for another 25 kms and takes the direction back to reach the main road, In the meantime, due to a minor breakdown, the other bus has run only 35 kms along the main road, What would be the distance between the two buses at this point ?

    (a) 75 kms (b) 80 kms (c) 65 kms (d) 85 kms

    19. If ÷ means +, - means ÷, × means - and + means ×, then (32 8) 8 2

    ?4 18 8 9 1

    (a) 0 (b) 1 (c) 12 (d) None of these

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    20. Find the missing number in the following series: 2, 3, 6, 18, ?, 1944 (a) 154 (b) 180 (c) 108 (d) 452

    Directions : (21 to 22) A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. Now the cube is cut into sixty four smaller cubes of equal size. 21. How many smaller cubes have only one surface painted? (a) 8 (b) 16 (c) 24 (d) 32 22. How many smaller cubes will have no surface painted? (a) 0 (b) 4 (c) 8 (d) 16 Directions : (23 to 24) Read the following information carefully and answer the questions given below it. I. Five professors (Dr. Joshi, Dr. Davar, Dr. Natrajan, Dr. Choudhary and Dr. Zia) teach five different subjects

    (zoology, physics, botany, geology and history) in four universities (Delhi, Gujarat, Mumbai, and Osmania). Do not assume and specific order.

    II. Dr. Choudhary teaches zoology in Mumbai University. III. Dr. Natranjan is neither in Osmania University nor in Delhi University and he teaches neither geology nor

    history. IV. Dr. Zia teaches physics but neither in Mumbai University nor in Osmania University. V. Dr. Joshi teaches history in Delhi University. VI. Two professors are from Gujarat University. VII. One professor teaches only one subject and in one University only. 23. Who teaches geology ? (a) Dr Natrajan (b) Dr. Zia (c) Dr. Davar (d) Dr. Joshi 24. Who teaches botany ? (a) Dr. Zia (b) Dr. Davar (c) Dr. Joshi (d) Dr. Natrajan Directions : (25 to 26) Read the following information carefully and answer the questions given below it. I. Eight persons, E, F, G, H, I, J, K and L are seated around a square table - two on each side. II. There are three lady members and they are not seated next to each other. III. J is between L and F. IV. G is between I and F. V. H, a lady member, is second to the left of J. VI. L, a male number, is seated opposite of E, a lady member. VII. There is lady member between F and I. 25. Who among the following is seated between E and H? (a) F (b) I (c) J (d) None of these 26. How many persons are seated between K and F? (a) One (b) Two (c) Three (d) Cannot to determined Directions: (27 to 28) A + B mans ‘A is father of B’ A - B means ‘A is wife of B’ A × B means ‘A is brother of B’ A ÷ B means ‘A is daughter of B’ 27. P ÷ R + S + Q, which of the following is true? (a) P is daughter of Q (b) Q is aunt of P (c) P is aunt of Q (d) P is mother of Q 28. If P - R + Q, which of the following is true (a) P is mother of Q (b) Q is daughter of P (c) P is aunt of Q (d) P is sister of Q Directions L (14 to 53): In each question of the following two statements are given and four conclusions I, II, III and IV are given under them. The given statements may be contrary to the universal opinion, even then you have to assume them as true. Then decide which conclusion on the basis of given statements is logically valid.

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 25

    29. Statements: All boxes are benches. All boxes are chairs.

    Conclusions: I. All benches are chairs. II. All benches are boxes

    III. Some benches are chairs. IV. Some chairs are boxes. (a) All (b) Only I and III (c) Only II and IV (d) Only III and IV 30. Statements: All labourers are wrestlers. All grocers are labourers.

    Conclusions: I. All grocers are wrestlers. II. Some wrestlers are grocers.

    III. Some wrestlers are labourers. IV. Some labourers are grocers. (a) All (b) Only I and IV (c) Only IV (d) Only II and III

    PART – III : MATHS [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme:

    You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    31. If , are the zeroes of 2 6 0x x k . What is the value of k if 3 2 20 32. In a 120 litre mixture of milk and water, the ratio of milk to water is 2 : 1. How many litre of water is to be added to

    this, to make this ratio 1 : 2 in the new mixture? 33. If the elevation of the sun changed from 30° to 60°, then the difference between the length of shadows of a pole 15

    m high, made at these two positions, is 34. If the centroid and circumcentre of a triangle are (3, 3) and (6, 2) respectively, then the orthocenter is 35. In the figure C is a right angle, DE AB, AE = 6, EB = 7 and BC = 5. The area of the quadrilateral EBCD is

    36. A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of

    drawing a red ball is 11/20 and that of blue ball is 1/5, then the number of black balls is 37. In the figure, assume that the circle are mutually tangent and that the circle with centre at A has radius 1. The lines

    AB and AC are tangent to the circle at O in the points B and C respectively. If the area of the shaded region is /4, the radius of the circle centered at O, is

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 26

    38. Number of two digit numbers having the property that they are perfectly divided by the sum of their digits with quotient equal to 7, is

    39. Kunal arranged some metal blocks at the bottom of a tank as seen in the figure below. Then he filled the 30 cm by

    25 cm by 25 cm tank with water. If each block is 4 cm long 3 cm wide and 5 cm tall, then how much water is needed to fill the tank to 80% of the tank’s height?

    PART – IV : SCIENCE [SUBJECTIVE]

    This Section contains 9 Subjective Type Questions. Write solution for each question along with final answer within the space provided. Marking Scheme: You will be awarded 5 marks for correct solution with correct answer and zero in all other cases. There is no step marking.

    40. A concave mirror has a radius of curvature of 20 cm. The image of a object formed in mirror is 2.50 times the size of

    the object. How for is the mirror from the object?

    41. A battery of e.m.f. 10 V is connected to resistance as shown in figure. Find the potential difference BA VV between

    the points A and B is

    42. The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. The

    distance covered by the body in the 5th

    second of its motion is

    43. How many electron’s are present in 13756 Ba

    44. How many moles of O atom are present in 132 gm of CO2 45. Number of element which are more reactive then Fe in K, Na, Al, Cu, Hg, H, Pb, Ag, Ca

    10V

    1W A 3W

    3W 1W B

    3W

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 27

    ANSWER KEY

    Mock test -1

    1 2 3 4 5 6 7 8 9 10 C C A B B D D D B B 11 12 13 14 15 16 17 18 19 20 D B C B A A C B D A 21 22 23 24 25 26 27 28 29 30 C B A D C C B C A C 31 32 33 34 35 36 37 38 39 40 6 3 h (1 + tan

    x cot y)

    1 : 2 4 43 11 cm and 3 cm

    3

    10

    5x 60 cm

    41 42 43 44 45 250m 1A x = 40,

    y = 30

    Be, Mg, Ca, Sr, Ba, Ra

    3-ethyle -2, 5 dimethyl hexane

    Mock test -2

    1 2 3 4 5 6 7 8 9 10 D B C A C C D B A C 11 12 13 14 15 16 17 18 19 20 B A C B A B C A A C 21 22 23 24 25 26 27 28 29 30 B D B A C D C A C B 31 32 33 34 35 36 37 38 39 40 64 kg

    1

    2 1

    7 322 2

    13

    35 24

    . 7/8 98 cm2 40 cm

    41 42 43 44 45 8V 4h0 C,Si,Ge,Sn,Pb

    6 8 2 2 2C H 8O 6CO 4H O

    3 4 3 4 2H PO 3NaOH Na PO 3H O

    Mock test -3

    1 2 3 4 5 6 7 8 9 10 D A A B A B B D B A 11 12 13 14 15 16 17 18 19 20 C B B A B B B D C A 21 22 23 24 25 26 27 28 29 30 C D B D B C C B B C 31 32 33 34 35 36 37 38 39 40 5 7 5 9 4 2 3 3 1 3 m/s

    41 42 43 44 45 52 V

    15 CM

    14

    6C (a) 2 4 4 2Zn H SO ..ZnSO H (b) 4 2 2 2CH 2O CO 2H O

    70

  • Entrance Test : SAMPLE PAPER XENON

    SHIKHAR : Indra Complex, Vijaya Nagar, Chetakpuri, Gwalior (0751) 2446970 28

    Mock test -4

    1 2 3 4 5 6 7 8 9 10 D B D A D A B A C C 11 12 13 14 15 16 17 18 19 20 A D B C B C D D B C 21 22 23 24 25 26 27 28 29 30 B B D B D A D C D C 31 32 33 34 35 36 37 38 39 40 2 7 6 9 5 1 8 5 5 6

    41 42 43 44 45 10 mm 15 W

    30,25,23

    2 4

    4 4 2

    a. Cu H SO noreaction

    b. Zn CuSO ZnSO H

    80

    Mock test -5

    1 2 3 4 5 6 7 8 9 10 B B B A C D C D C A 11 12 13 14 15 16 17 18 19 20 D D C B B B D C B C 21 22 23 24 25 26 27 28 29 30 C C C D D C C A D A 31 32 33 34 35 36 37 38 39 40 –16 120 10 3 (–3, 5) 22.5

    10

    r 1 2 4 12720

    cm3

    6 cm

    41 42 43 44 45

    V2 25 m 55

    6 4