All India Sainik School Entrance Model paper for 2018

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Defence Academy Coimbatore A leading coaching academy for Sainik, Military and RIMC Schools, NDA, IMA, AFCAT SSB, FSB Interview http://www.ssbcoaching.com call 094437 20076



Maths

Dear aspirant,
From the year 2018, the admission to All India Sainik School will be based on Multiple choice questions instead of subjective types answers.

Defence Academy has come out with a model guess paper, hope this will be helpful to students. Like earlier, you will have to work out and find the answers given as options and mark the same in the OMR (OMR, Optical Mark Recognition. Sheet)   



The sheet would look like the picture given below:
Class IX Entrance Exam Math’s Quiz 2018 Set -01 Compiled by www.sainikrimc.com

 1. 80 Percent may be expressed as a ratio
          a) 1 : 2                   b) 2 : 3                  c) 4 : 5                   d) 1 : 5

 2. The Coefficient of x in -8xy2 is
          a) 8                       b) -8                      c) -8y²                             d) y²

 3. Which is the following is not a factor of 6x2
          a) x                       b) 2                       c) x²                      d) 4

 4. Which of the following is divisible by 3 but not by 6
          a) 123                    b) 216                    c) 552                    d) 312

 5. Area of a square is 2.5 sq m. It is equivalent to
          a) 25000cm2           b) 2500cm2               c) 250 sq cm            d) 25 sq cm

 6. (6- ¹ X 2¯¹) ÷3¯¹ equal
          a) 1/ 6                             b) 1 / 4                             c) 1 / 3                  d) 1 /12

 7. Weight of 5 books is 7.5 kg, find the weight of 3 books
          a) 2 kg                            b) 15 kg                     c) 5 kg                 d) None of these

 8. The surface area of a cube is 1734 cm2. Its volume is
          a) 2197cm3            b) 4913cm3                c) 2744cm3            d) 4096 cm3

 9. A mixture of milk and water is in the ratio of 3:2. Find the percentage of milk in the mixture.
          a) 20 %                 b) 30%                      c) 40 %                  d) 60%

 10. Subtract: - 3pq (p-q) from 2pq (p+q).
          a) -p2q+5 pq2        b) P2q+5 pq2             c) p2q-5 pq2          d) None of these

 11. Factors: - x power4 -(x-z) 4
          a) x (2x-z)(2x2-2xz+z2)                           b) 2z(2x-z)(2x2-2xz+z2)
          c) z (2x-z)(2x2-2xz+z2)                           d) None of these

 12. The area of a rhombus is 240 Sq cm and one of the diagonal is 16 cm. Find the other diagonal.
          a) 30 cm                 b) 25 cm                 c) 32 cm                 d) 15 cm

 13. Find the value of m for which 5 power m ÷ 5 power -3 = 5 power 5
          a) 0                       b) 1                       c) 2                        d) 3

 14. If the three digit number 24x is divisible by 9, what is the value of x?
          a) 1                       b) 2                       c) 3                        d) 4

 15. The cost of an article was Rs 15,500 & Rs.450 were spent on its repairs. If it is sold for a profit of 15% find the selling price of the article.
          a) Rs.18342.50       b) Rs.18442.50          c) Rs.18542.00        d) Rs.14342.50

 16. If 3x + 5y=11 and XY=2, find the value of 9x2+25y2
          a) 32                      b) 46                      c) 51                     d) 61

 17. Divide 44(x4-5x3-24x2) by 11x(x-8)
          a) 4x (x-3)              b) 4x (x+3)              c) -x (x+3)                d) -4x (x+3)

 18. The area of a trapezium is 34 cm2 and the length of one of the parallel side is 10 cm and its height is 4cm. Find the length of the other parallel side.
          a) 6 cm                  b) 7.5 cm                  c) 7 cm                    d) 8 cm

 19. If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weight 2.5 Kilograms?
          a) 750                   b) 770                      c) 800                    d) 850

 20. Find CI paid when a sum of Rs.10, 000 is invested for 1 year and 3 months at 8½% per annum compounded annually
          a) Rs.1080.50           b) Rs.1080.00           c) Rs.1080.56           d) Rs.1085.56

 21. The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet
          a) 322 cm               b) 342 CM               c) 443 CM               d) 232 CM

 22. A Factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
          a) 48                      b) 49                      c) 51                      d) 42

 23. The product of two rational number is (- 5/6). If one rational number is (-7/12), then the second rational number will be
          a) 35/12                 b) 10 / 7                 c) (- 10/7)               d) (7/10)

 24. Factors of the expression xy +5x +5y+25 are___________
          a) (x+5) (y+5)          b) (y +5) (x+5)     c) (5 +y) (2 - x)       d) (y+2) (x - 5)

 25. Two numbers are in the ratio 5: 6 and least common multiple (LCM) is 660. Greater number will be_____
          a) 1320                   b) 110                    c) 165                    d) 225

 26. Total surface area of a cube is150 sq cm, then its volume will be ____
          a) 125 cubic c          b) 100 cubic c          c) 150 cubic cm          d) 120 cubic cm

 27. Value of (√24 + √216) / (√96) will be___
          a) 2√6                             b) 2                       c) 2 by 50               d) 1/√2

 28. The difference of two supplementary angels is 40 degrees then angles will be___
          a) 60 degrees and 40 degrees                 b) 76 degrees and 116 degrees
          c) 60 degrees and 120 degrees                d) 70 degrees and 110 degrees

 29. Each angle of a regular polygon is 156 degrees, then the number of sides will be
          a) 10                      b) 12                      c) 14                      d) 15

 30. If x - Minus 2, y = minus 3 and z = 5, then the value of x³ + y³ + z³ is equal to___
          a) 0                       b) 90                      c) 120                    d) 3


 31. The Arithmetic mean of 0, 2, 3, 4 and 6 will be_____
          a) 3                       b) 15                      c) 4                        d) 5

 32. IfA ={1,3,5} and B = { 3, 5,7, 9}, then A set B will be___
          a) {1,3,5,9}            b) {3,5}                  c) {1,3,4}               d) None of these

 33. If 2 power x = 8, then x+ y² + x ³ will be ____
          a) 39                      b) 14                      c) 12                      d) 19

 34. Opposite angles of a cyclic quadrilateral are ____
          a) Equal                  b) 90 degree each    c) Supplementary      d) none of these

 35. 1/5th of a pole is black, 1/4th is white and remaining 3 m is yellow, then the length of the pole is___
          a) 8 m                    b) 5 and 4/ 11          c) 5 and 5/11           d) 3 m

 36. If the diagonal of a square is 4 √ 2 cm long, what is the length of the side?

          a) 3cm                             b) 1/2 cm                c) 2 cm                   d) 4 cm

 37. Diagonal of a parallelogram ______
          a) Are perpendicular bisectors of one and another?                  b) Bisect each other
          c) Are parallel and do not intersect                                        d) None of the above

 38. The base of an Isosceles triangle is 48 cm and its perimeter is 108 cm. Its area is equal to ___
          a) 433 sq cm           b) 423 sq cm           c) 432 sq cm           d) 416 sq  cm

 39. If the circumference of circle is 44 cm, then its area is___
          a) 154 sq cm           b) 77 sq  cm            c) 100 sq cm           d) 160 sq cm

 40. The greatest Chord of a circle is___
          a) Tangent              b) Radius                c) Diameter             d) Circumference

 41. The product of additive inverse and multiplicative inverse of -1/3 is
          a) 1                       b) 0                       c) -1                      d) 1/3

 42. Half a herd of deer are grazing in the field and three fourth of the remaining are playing nearby. The rest 9 are drinking water from the pond.  Find the number of the deer in the herd.
          a) 72                      b) 48                      c) 96                      d) 84

 43. The factors of 3 +23y - 8 y² are
          a) (1-8y) (3+y)        b) (1+8y) (3-y)        c) (1 -8y) (y-3)          d) (8y-1) (y+3)

 44. In Triangle ABC, AD bisects angle BAC and AD = DC.  If angle BDA = 70 degree, then the measurement of angle ABD is___
          a) 75°                    b) 80°                    c) 85°                     d) 90 °

 45. The base of a Right Triangle is 8 cm and its hypotenuse is 10 cm. Its area is___
          a) 24 cm²               b) 40 cm²               c) 48 cm²                d) 80 cm²


 46. The circumference of a circle disc is 88 cm. Then its area will be
          a) 616 sq cm           b) 88 sq cm             c) 154 sq cm          d) None of these

 47. The diagonal of a quadrilateral shaped field is 24 meter and the Perpendiculars dropped on it from the remaining opposite vertices is 8 m and 13 m.  The area of field is___ Sq cm
          a) 616 sq cm           b) 525 sq cm           c) 175 sq cm           d) 252 sq cm

 48. A circle having a diameter 30 cm has a chord of 24 cm, then the distance of the chord from its center is__
          a) 9 cm                  b) 15 cm                 c) 12 cm                 d) 13 cm

 49. The sum of heights of a certain number of players is 745cms, and the mean height is 149 cm. The number of players are  
          a) 8                       b) 6                       c) 7                        d) 5

 50. A polyhedron is having 20 vertices and 30 edges. Its number of faces are___
          a) 12                      b) 13                      c) 15                      d) 14


Answers to the above problems
Q.No
Answer
Q.No
Answer
Q.No
Answer
Q.No
Answer
1
C
14
C
27
B
40
C
2
C
15
A
28
D
41
C
3
C
16
D
29
D
42
A
4
A
17
B
30
B
43
B
5
A
18
C
31
A
44
B
6
B
19
A
32
B
45
A
7
D
20
C
33
A
46
A
8
B
21
A
34
C
47
A
9
D
22
B
35
C
48
A
10
A
23
B
36
D
49
D
11
B
24
B
37
B
50
A
12
A
25
A
38
C


13
C
26
A
39
A


                                     




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please call 094437 20076
www.ssbcoaching.com

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