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Mathematical Solved Aptitude Paper For XAT, MAT, FMS Exam Preparation

1. If psin X = q and X is acute, then ?(p2—q2) tanX is equal to
(a) p
(b) q
(c) pq
(d)p+q

Ans.b

2- If tan?=3/4 and 0 is less than 6 is less than 90°, then sin ? . cos ? is equal to
(a) 12/25
(b) 3/5
(c) 18/25
(d) 4/5

Ans.a

3 If cos? = 5/13 0 is less than ? is less than 90º then the value of (cos? + 5cot?) / (cosec? – cos? )
(a) 169/109
(b) 155/109
(c) 185/109
(d) 395/109

Ans.c

4. The value of sin 0° + cos 30° — tan 45° + cosec 60° + cot 90° is equal to
(a) (7?3 – 6 )/ 66
(b) (6 + 7?3)/ 6
(c) 0
(d) 2

Ans.a

5. If sin ? = -1/2 then the possible values of ? between 0 and 2 ? are
(a) 2l0° and 300°
(b) 240° and 230°
(c) 240° and 300°
(4) 210º and 330º

Ans.d

6- The value of sin?/6+cos?/3-tan²45° is equal to `
(a) 1
(b) 0
(c) -1
(d) 2

Ans.b

7. The value of sin l5° is equal to
(a) (?3 + 1)/ ?2
(b) (?3 – 1)/ ?2
(c) (?3 + 1)/ 2?2
(d) (?3 – 1)/2?2

Ans.d

8. If sinx = 0.5040, then x is equal to
(a) 180° 5’
(b) 60°15’
(c) 30°16’
(d) 90°10’

Ans.c

9. If A. B and C are angles of a triangle, then sin 2A + sin 2B + sin 2C is equal to
(a) 8sinAsinBsinC
(b) 2 sinA sin B sin C
(c) sinA sinB sinC
(d) 4 sin A sinB sinC

Ans.d

10. The value of sin²? — sin² ? is
(a) sin (? + ?) sin (? – ?)
(b) cos (? + ?) cos (? – ?)
(c) cos (? + ?) sin (? – ?)
(d) sin (? + ?) cos (? – ?)

Ans.a

11. If the angle of elevation of sun is ? and the length of the shadow of a pole f length p is s. then
(a) p = scos?
(b) p = ssin?
(c) p=s/cot?
(d) p= ccot?

Ans.c

12. The foot of 2. ladder leaning against a wall of length 5 meters nests on a level ground 5?3 metres from the base of the wall, The angle of inclination of die ladder with the ground is
(a) 60°
(b) 50°
(c) 40º
(d) 30º

Ans.d

13. From the top of a 60 metre high tower, I the angle of depression of the top and bottom of a building are observed to be 30° and 60° respectively. The height of the building is
(a) 60?3 metres
(b) 40?3 metres
(c) 40 metres
(d) 20 metres

Ans.c

14. A and B are two points and C is any point collinear with A and B. If AB = l0, BC = 5, then AC is equal to
(a) either 15 or 5
(b) necessarily 5
(c) necessarily l5
(d) NONE OFTHE ABOVE

Ans.a

15. If A, B and C are non-collinear points then AB, BC and AC are respectively
(a) 20, 5 and 15
(b) 10, 5 and 15
(c) 10, 5 and 5.
(d) 5, 5 and 5

Ans.d

16. The sum of the interior angles of a l2 sided regular polygon is equal to
(a) 180°
(b) 360°
(c) 1800°
(d) 2160º

Ans.c

17. Three lines intersect at a point generat- ing six angles, If one of these angles is 90°, then the number of other distinct angles is
(a) 1 or 2
(b) 1 or 3
(c) 2 or 3
(d) 2 or 4

Ans.a

18. In the triangle ABC, if the base angles at B and C are bisected by BO and CO respectively, then ?BOC is equal to
(a) 90º — A/2
(b) 180 – A/2
(c) 90 +A/2
(d) b/2 + C/2

Ans.c

19. L. M and N are the mid-points of the sides XY, XZ and YZ respectively of ? XYZ, If the area of ?LMN is 6 cm², then the area cf ?XIM is
(a) 6cm²
(b) 8cm²
(c) 12cm²
(d)15 cm²

Ans.a

20. If ABC is a triangle and D, E and F are respectively the mid—p0ints of AB, BC and CA, then the triangle ABC is
(a) similar to ? DEF but not ?DBE
(b) similar to ? DEF but not ? ECF
(c) similar to the triangles DBE. ECF, ADF and DEF
(d) not similar to any ofthe triangles DBE, ECF, ADF and DEF

Ans.d

21. The diagonals of a rectangle ABCD cut at O. OAL is an equilateral triangle drawn so that B and L are on the same side of AC. If ?ACD = 30°, then the angles of ?ALB are
(a) 60°,60° and 60°
(b) 30°,30° and l20°
(c) 30º, 60º and 90°
(d) not determinable from the given data

Ans.d

22. ABCD is a trapezium where AB and CD are non-parallel sides. If the vertices A, B, C and D are concyclic then
(a) AB is also parallel to CD
(b) AB = 1/2CD
(c)1/2AB = CD
(d) AB = CD

Ans.d

23. ABCD is a cyclic quadrilateral. The tangents to the circle drawn at A and C meet at P. lf ?ABC = 100°, then LAPC is equal to
(a) 10°
(b) 20°
(c) 40º
(d) 60º

Ans.c

24. AB is a line segment and O is an ex- ternal point. X is any point on AB and Y is the mid•point of OX. Consider the fol- lowing statements in this regard :
Assertion (A):
The locus of Y as X moves on AB is a line segment joining the mid—points of OA and OB.
Reason (R) : A line segment joining the mid-point of two sides of a triangle is parallel to the third side. Of these statements
(a) both A and Rar•etrueai1dRisthec<>rrect explanation of A
(b) both A and R are true but R is NOT correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

Ans.d

25. If the perimeter of a right angled iso-sceles triangle is ?2+ 1, then the length of the hypotenuse will be
(a) 1
(b) 2?2
(c) ?2
(d) 3?2

Ans.a

26. A tile is of size 9″ by 9″. The number  of tiles needed to cover a l2 ft wide and ‘l8 ft long floor will be
(a) 32
(b) 384
(c) 216
(d) 24

Ans.b

27. If the area of the region bounded by the inscribed and the circumscribed circles of a square is 9?, then the area of the square will be
(a) 6?
(b) 5?
(c) 25
(d) 36

Ans.d

28. A wire is in the form of a circle of radius 42 cm. If it is bent into a square, then the side of the square will be
(a) 60 cm
(b) 62 cm
(c) 64 cm
(d) 66 cm

Ans.d

30. If the area of the trapezium, whose parallel sides are 6 cm and l0 cm is 32 sq cm, then the distance between the parallel sides is
(a) 2 cm
(b) 4 cm
(c) S cm
(d) 8 cm

Ans.b

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