CAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :

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1 CAREER POINT PRE FOUNDATION DIVISON IMO Stage-II Exam.-07 CLASS-9 MATHEMATICS Date : Q. In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and PRUV is a square on PR, then PS =. A) PT C) QU B) RU D) PV Q. Find the value of a ab b if the polynomial x 0x ax b) is exactly divisible by x ) and x ). A) 8 B) 44 C) 55 D) 69 Q.5 The taxi fare in a city is such that 50 is the fixed amount, 6 per km is charged. Taking the distance covered as x km and total fare as y, write a linear equation in x and y. What is the total fare for 0 km? A) x = 50 6y, 70 B) y = 50 6x, 0 C) x = 50 6y, 0 D) y = 50 6x, 70 Q.6 The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. If AB = cm, DE = 4 cm, PB = 8 cm, find RS. Q. If =.44 and =.7, then find the value of ) ) ). ) A).46 B).78 C) 4.7 D). Q.4 Select the incorrect statement. A) A straight line can be drawn from one point to any other point. B) A terminated line can be produced indefinitely. C) A circle can be drawn with any radius and any centre. D) For every line L and for every point P not lying on L, there exists two lines passing through P and parallel to L. A) 6 cm B) 8 cm C) 0 cm D) Can't be determined Q.7 In the given figure, AFD = 5º and DBCF is a parallelogram. Find EFC FDB FCB. A) 85º B) 75º C) 00º D) 60º CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

2 Q.8. dm of lead is to be drawn into a cylindrical wire of diameter 0.50 cm. The length of the wire is A) 0 m B) m C) 98 m D) 4 m Q.9 Find the mode of the following data. Marks Number of students A) 5 B) 0 C) 0 D) 5 Q.0 A coin is tossed 000 times, if the probability of getting a tail is 8, how many times head is obtained? A) 55 B) 75 C) 65 D) 75 Q. A cone, a hemisphere and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. Their total surfaces area in the ratio A) ) : : 4 B) ) : : 4 C) : : 4 D) : 7 : 8 Q. With the vertices of PQR as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 6 cm, 0 cm and 4 cm. Find the radii of the circles. Q. In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle. If area of 78 the quadrant is cm and DA = 0 cm, 7 find the area of the rectangle. A) 0 cm B) 00 cm C) 40 cm D) 80 cm Q.4 Simplify : x y) x y) 6yx y ) A) 6 y x B) 8 x y C) 8 y D) xy Q.5 What must be subtracted from x 6x 5x 80, so that the result is exactly divisible by x x. A) x 6 B) x C) 4x 4 D) 4x 5 Q.6 ABCD is quadrilateral. If AC and BD are its diagonals, then the - A) Sum of the squares of the sides of the quadrilateral is equal to the sum of the squares of its diagonals. B) Perimeter of the quadrilateral is equal to the sum of the diagonals C) Perimeter of the quadrilateral is less than the sum of the diagonals. D) Perimeter of the quadrilateral is greater than the sum of the diagonals. Q.7 It is given that XYZ = 64º and XY is produced to point P. If ray YQ bisects ZYP, find XYQ and reflex QYP. A) 0º, 64º B) º, 0º C) 4º, 4º D) 60º, 0º A) 4 cm, 6 cm, 0 cm B) 5 cm, 4 cm, cm C) cm, 5 cm, 6 cm Q.8 The perimeter of a triangle is - A) Greater than the sum of its altitudes B) Less than the sum of its altitudes. C) Equal to twice the sum of its altitudes. D) Equal to the sum of its altitudes. CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

3 Q.9 Which of the following statements is incorrect? A) If the mean of 4, 6, x, 8, 0, is 8, then x = 7. B) If the median of 59, 6, 65, x, x, 7, 85, 99 is 67, then x = 66. C) If the mode of,, 5, 7, 5,, 7, 5, 9,, p, is 5, then the value of p is 7. D) If the mean of 0 observations is 5 and that of other 5 observations is 8, then the mean of all the 5 observations is 6.8. Q.0 In the given figure, O is centre of the circle and BCO = 0º. Find x and y respectively. A) 0º, 5º B) 5º, 0º C) 0º, 60º D) 45º, 0º Q.4 If x y) 7 = A 0 x 7 A x 6.y A x 5.y A x 4.y A 4 x.y 4 A 5 x.y 5 A 6 x.y 6 A 7 y 7, find the value of A 0 A A A A 4 A 5 A 6 A 7. A) 5 B) 8 C) 56 D) Q.5 Difference between 'postulate' and 'axiom' is - A) There is no difference. B) Axioms are taken for granted without proof whereas postulates are to be proved. C) 'Postulates' are the assumptions used specially for geometry and 'axioms' are the assumptions used throughout mathematics. Q.6 x and y are exterior angles of a ABC, at the points B and C respectively. Also B > C, then relation between x and y is - A) x > y B) x = y C) x < y a Q. If x = a A) x x C) x x a a, then a =. B) x D) x Q.7 In triangles ABC and PQR, AB = AC, C = P and B = Q. The two triangles are A) Isosceles but not congruent. B) Isosceles and congruent. C) Congruent but not isosceles. D) Neither congruent nor isosceles. Q. If x and x 4 are factors of ax 6 bx 5 cx 4 dx ex fx g, then find the value of i) a 5c e ii) a c e g i) ii) A) 0 0 B) 0 C) 0 D) Q. If x is divisible by x, then remainder is. A) 00 B) 0 C) 99 D) 98 Q.8 If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has. A) x coordinate = 5 B) y coordinate = 5 only C) y coordinate = 5 only D) y coordinate = 5 or 5 Q.9 A rhombus shaped field has green grass for 6 cows to graze. If each side of the field is 0 m and longer diagonal is 48 m, then how much area of grass each cow will get, if 6 m of area is not to be grazed. A) 6 m B) m C) 8 m D) 9 m CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

4 Q.0 Any solution of the linear equation x 0y = 9 in two variables, is of the form. A) B) C) D),0,n, n is a real number n,, n is a real number 0, Q. In the given figure, ABCD is a parallelogram. If AP, BP, CR, DR are the angle bisectors of A, B, C, D respectively, then the quadrilateral PQRS is exactly a. A) Square C) Rectangle B) Parallelogram D) Rhombus Q. O is any point in the interior of ABC, then OA OB OC) is AB BC CA). A) Equal to C) Greater than B) Less than Q.4 The diameter of a sphere is decreased by 5%. By what percentage its volume decreases? A) 5% B) 4.75% C) 4.50% D) 57.8% Q.5 Find the value of p, if the mean of the following distribution is 7.5. Number of students Frequency p 8 4 A) 4 B) C) 5 D) Q.6 While working out a questions on probability it was formed that there were 86 letters of English alphabet. The following was observation of occurrence of each letter. a = 70, b = 4, e = 6, r = 40, i = 6 others not including vowels) = 00 Then probability of a vowel is 70 6 A) B) C) 86 D) 86 Q.7 In the given figure, chord AB and CD are equidistant chords from centre of the circle. If AB is 8 cm, then length of the chord CD is equal to. Q. In the given figure, find a, b and c respectively. A) 4 cm C) 6 cm B) 8 cm D) 5 cm Q.8 Find two rational numbers between 0. and A) 0., 0.5 B) 0., 0.55 C) 0.5, 0.55 D) 0.5, 0.55 A) 05º, 5º, 60º B) 05º, º, 6º C) 5º, º, 6º D) 05º, º, 60º Q.9 In twelve hours beginning from past midnight, the minute hand and hour hand will overlap. A) 0 times B) times C) 4 times CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

5 Q.40 Following are the steps of construction of a triangle ABC, in which BC =.8 cm, B = 45º and AB AC = 6.8 cm. Select the correct order of arrangement of steps. Step- : Draw the perpendicular bisector of CD meeting BD at A. Step- : Draw BC =.8 cm Step- : Join CD Step-4 : From ray BX, cut-off line segment BD equal to AB AC i.e., 6.8 cm. Step-5 : Draw CBX = 45º Step-6 : Join CA to obtain the required triangle ABC. A), 4, 5,,, 6 B), 5,,, 4, 6 C), 5, 4,,, 6 D), 5, 4,,, 6 Q.4 The triangular side walls of a flyover have been used for advertisements. The sides of the walls are m, m and 0 m. The advertisements yield an earning of 5000 per m per year. A company hired one of its walls for months. How much rent did it pay? A) B) C) D) Q.4 In a middle school out of 5 students make honor roll. What percent of students does not make honor roll? A) 65% B) 40% C) 60% Q.4 Which of the following statements is incorrect? A) Product of two irrational numbers is always irrational. B) Sum of two irrational numbers can never be irrational. C) Sum of an integer and a rational number can never be an integer. D) All of these Q.44 If 9 n n / m ) 7) n =, then find 7 the value of m n. A) B) C) D) 0 a b ) b c ) c a ) Q.45 Simplify: a b) b c) c a) A) a b)b c)c a) B) a b c C) a b)b c)c a) D) abc ACHIEVERS SECTION Q.46 Read the statements carefully and select the correct option. Statement-I : In a quadrilateral ABCD, AB BC CD DA) > AC Statement-II : The sum of any two sides of a triangle is greater than the third side. A) Statement-I is true and Statement-II is false. B) Both Statement-I and Statement-II are false. C) Both Statement-I and Statement-II are true. D) Statement-I is false and Statement-II is true. Q.47 Read the statements carefully and state 'T' for true and 'F' for false. The internal and external diameters of a hollow hemispherical vessel are 0 cm and 8 cm respectively. Then, i) Its inner curved surface area is cm. ii) Its outer curved surface area is cm. 547 iii) Its volume is cm. i) ii) iii) A) T T F B) T T T C) F F F D) F T F CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

6 Q.48 If x 4 4 = 94, find the value of x x x x and x. x x x x x x x A) B) C) D) 5 4 8, x Q.50 Two steel sheets each of length a and breadth a are used to prepare the surfaces of two right circular cylinders one having volume v and height a and other having volume v and height a. Then, A) v = v B) a v = a v v v C) a v = a v D) = a a Q.49 If two sides AB and BC and the median AD of ABC are equal respectively to the two sides PQ and QR and the median PM of the other triangle PQR, then i) ABD ii) ABC i) A) PQM B) PMR C) PQR D) PQR ii) PQR PQM PQM PMR CAREER POINT : 8, Shakti Nagar, Kota Raj.), Ph:

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