CAREER POINT
PRE FOUNDATION DIVISON
IMO Stage-II Exam.-2016
CLASS-9
MATHEMATICS
Date : 14-02-2016Q.1 Fill in the blanks.
A non-terminating and non-recurring decimal expansion is a/an …… number.
The decimal expansion of 125
1 is in ….. form -
(A) Rational, terminating (B) Irrational, terminating
(C) Rational, non-terminating recurring (D) Rational, recurring
Q.2 A pair of dice is thrown. The probability of getting even number on first die & odd number on the second die is -
(A) 5 1 (B) 2 1 (C) 4 1 (D) 3 1
Q.3 A point whose abscissa and ordinate are 2 and 5 respectively, lies in -
(A) First quadrant (B) Second quadrant (C) Third quadrant (D) Fourth quadrant
Q.4 Which of the following statements is INCORRECT ?
(A) A solid has 3 dimension (B) A surface has 2 dimensions (C) A line has 0 dimension (D) None of these
Q.5 The dimensions of a rectangular piece of paper are 22 cm × 14 cm. It is rolled once across the breadth and once across the length to form right circular cylinders of biggest
possible surface areas. Find the difference in volumes of the two cylinders that will be formed -
(A) 196 cm3 (B) 308 cm3 (C) 49 cm3 (D) 105 cm3
Q.6 It is not possible to construct a triangle whose sides are -
(A) 3 cm, 3 cm and 6 cm (B) 5 cm, 12 cm and 13 cm (C) 15 cm, 8 cm and 17 cm (D) 3 cm, 4 cm and 5 cm
Q.7 The mean of the data x1, x2, ……., xn is 102,
then mean of the data 5x1, 5x2, …., 5xn is -
(A) 102 (B) 204
(C) 606 (D) 510
Q.8 A triangle and a parallelogram have same base and same area. If the sides of the triangle are 20 cm, 25 cm and 35 cm, and the base sides is 25 cm for the triangle as well as the parallelogram, find the vertical height of the parallelogram -
(A) 2 6 cm (B) 4 6 cm (C) 6 cm (D) None of these
Q.9 How many linear equations are satisfied by x = 2 and y = – 3 ?
(A) Only one
(B) Two
(C) Three
Q.10 In the figure given below, I || u and m || n. If ACB = 55º and AED = 30º, find x, y, z and respectively x D y y z u i m B C E A n (A) 95º, 125º, 150º, 55º (B) 150º, 95º, 125º, 55º (C) 125º, 150º, 95º, 55º (D) 55º, 95º, 150º, 125º
Q.11 How many statements are INCORRECT ?
(i) If a circle is divided into four equal arcs, each is a minor are.
(ii) A sector of a circle can have area more than the area of the whole circle
(iii) The area of each quadrant of a circle is one-third of the area of the whole circle (iv) One and only one chord of a circle can be
the diameter of the circle.
(A) 1 (B) 2
(C) 3 (D) 0
Q.12 In the given figure, || BC and D is mid-point
of BC.
If area (ABC) = x × area (EDC),find the value of x
(A) 2
1 (B) 1
(C) 4 (D) 2
Q.13 It is not possible to construct a triangle ABC
with BC = 5 cm, B = 75º and AB + AC equal to -
(A) 7.5 cm (B) 8 cm
(C) 9 cm (D) 4.5 cm
Q.14 Select the INCORRECT statement.
(A) The difference of a rational number and an irrational number is an irrational number.
(B) The product of a non-zero rational number with an irrational number is an irrational number.
(C) The quotient of an irrational number with a non-zero rational number is an irrational number.
(D) None of these
Q.15 If we multiply or divide both sides of a linear
equation in two variables with a non-zero n umber, then the solution of the linear equation -
(A) Changes
(B) Changes in case of multiplication only (C) Changes in case of division only (D) Remains unaltered
Q.16 If (2x + 1) is a factor of the polynomial p(x) =
kx3 + 23 x2 + 71 x = 30, then find the value of 8 ) 1 – k ( - (A) –2 (B) 8 5 (C) 8 1 (D) 2
Q.17 A field is 15 m long and 12 m broad. At one
corner of this field a rectangular well of dimensions 8 m × 2.5 m × 2 , is dug, and the dug-out soil is spread evenly over the rest of the field. Find the rise in the level of the rest of the field
-(A) 25 cm (B) 15 cm
(C) 125 cm (D) 200 cm
Q.18 The abscissa of a point is positive in the - (A) First and Second quadrant
(B) Second and Third quadrant (C) Third and Fourth quadrant
Q.19 Find the area of the quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12 cm. DA = 15 cm and AC = 9 cm. (Take 110 = 10.5 approx.) - (A) 57 cm2 (B) 45 cm2 (C) 75 cm2 (D) 72 cm2
Q.20 Let be the lower class limit of a class-interval in a frequency distribution and m be the mid-point of the class. Then, the upper class limit of the class is -
(A) m + 2 m (B) + 2 I m (C) 2m – (D) m – 2
Q.21 If (2k – 1, k) is a solution of the equation 10x – 9y = 12, then k =
(A) 1 (B) 2
(C) 3 (D) 4
Q.22 In the given figure, E and F are mid-points of
the sides AB and AC respectively of the ABC; G and H are mid-points of the sides AE and AF respectively of the AEF. If GH = 1.8 cm, find BC –
(A) 7.2 cm (B) 10 cm
(C) 15 cm (D) 72 cm
Q.23 In Fig. (i), X is the centre of the circle and in Fig. (ii), O is the centre of the circle. Find a and f respectively.
(A) 78º, 76º (B) 38º, 43º (C) 48º, 76º (D) 76º, 78º
Q.24 In ABC, AB = 7.2 cm, BC = 4.8 cm, AM
BC and CL AB. If CL = 4 cm, find AM –
(A) 4 cm (B) 10 cm
(C) 5 cm (D) 6 cm
Q.25 If ABC ~ PQR and ABC is not
congruent to RPQ, then which of the following is not true -
(A) BC = PQ (B) AC = PR
(C) QR = BC (D) AB = PQ
Q.26 Which of the following is not true for a
parallelogram ?
(A) Opposite sides are equal (B) Opposite angles are equal
(C) Opposite angles are bisected by the diagonals
(D) Diagonals bisect each other
Q.27 If bisectors of A and B of a parallelogram
ABCD intersect each other at P, bisectors of B and C at Q, bisectors of C and D at R and bisectors of D and A at S, then PQRS is a -
(A) Rectangle (B) Rhombus (C) Square (D) None of these
Q.28 The construction of a triangle ABC, given
that BC = 3cm, C = 60º, is possible when the difference of AB and AC is equal to - (A) 3.2 cm (B) 3.1 cm
(C) 3 cm (D) 2.8 cm
Q.29 Which of the following polynomials has
(x + 1) as a factor ? (i) x3 + x2 + x + 1
(ii) x4 + x3 + x2 + x + 1 (iii) x4 + 3x3 + 3x2 + x + 2 (iv) x3 – x2 – (2 + 2 ) x – 2 (A) (i), (ii) (B) (iii), (iv) (C) (ii), (iii) (D) (i), (iv)
Q.30 A die is thrown 300 times and the outcomes 1, 2, 3, 4, 5, 6 have frequencies as below :
Outcomes 1 2 3 4 5 6
Frequency 55 53 58 49 48 37
Find the probability of getting a prime number-
(A) 0.395 (B) 0.53
(C) 0.355 (D) 0.215
Q.31 In figure, ABCD is a parallelogram and E is mid-point of the side CD, then area (ABED) = k × area (BEC), then k =
A B C E D (A) 2 (B) 2 1 (C) 3 (D) 3 1 Q.32 If x = 60 8 4 ¸then 2 1 x 2 x = (A) 5 (B) 3 (C) 2 5 (D) 2 3
Q.33 In the given figure, ABCD is a rhombus. Find
y - A y C B D 20º E 73º (A) 56º (B) 107º (C) 33.5º (D) None of these Q.34 Factorise : y2 – 12 3 y + 105 - (A) (y + 7 3 ) (y + 5 3 ) (B) (y – 7 3 ) (y + 5 3 ) (C) (y – 7 3 ) (y – 5 3 ) (D) (y + 7 3 ) (y – 5 3 )
Q.35 In the given figure, AC = BC and ACY =
140º. X Y Z y x A B C
Find x and y respectively -
(A) 110º, 100º (B) 40º, 110º (C) 110º, 110º (D) 140º, 100º
Q.36 Eculid’s Postulate 1 is -
(A) A straight line may be drawn from any one point to any other point.
(B) A terminated line can be produced indefinitely
(C) All right angles are equal to one another (D) None of these
Q.37 The weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median -
(A) 41 kg, 35 kg (B) 35 kg, 41 kg (C) 35 kg, 35 kg (D) 37 kg, 36 kg Q.38 If = 1 + 2 + 3 and m = 1 + 2 – 3 , then 8 m 2 – 2 – m2 2 = (A) 1 (B) 0 (C) –1 (D) 5
Q.39 The distance of the point P(4, 3) from the origin is -
(A) 4 units (B) 3 units (C) 5 units (D) 7 units
Q.40 A circular piece of paper of radius 20 cm is trimmed into the shape of the biggest possible square. Find the area of the paper cut off. (Use = 7 22 ) - (A) 457 7 1 cm2 (B) 800 cm2 (C) 157 7 1 cm2 (D) 7 8800 cm2
Q.41 If E is an event associated with an experiment, then -
(A) P(E) 1 (B) –1 P(E) 1 (C) 0 P (E) 1 (D) None of these
Q.42 A triangle and a parallelogram have a
common side and are of equal areas The triangle having sides 26 cm, 28 cm and 30 cm stands on the parallelogram. The common side of the triangle and the parallelogram is 28 cm. Find the vertical height of the triangle and that of the parallelogram respectively – (A) 26 cm, 24 cm (B) 20 cm, 24 cm (C) 12 cm, 24 cm (D) 24 cm, 12 cm
Q.43 If and m be two positive real numbers, such
that > 3m, 2 + 9m2 = 369 and m = 60, then find the value of
12 m 3 – 1 - (A) 12 1 (B) 4 1 (C) 9 (D) 4 5
Q.44 The distance between the graph of the
equations x = –3 and x = 2 is - (A) 1 unit (B) 2 units (C) 3 units (D) 5 units
Q.45 Which of the following is not possible in case
of a triangle ABC ? (A) AB = 3 cm, BC = 4 cm and CA = 5 cm (B) AB = 5 cm, BC = 8 cm and CA = 7 cm (C) A = 50º, B = 60º and C = 70º (D) AB = 2 cm, BC = 4 cm and CA = 7 cm Q.46 If (x3 + ax2 + bx + 6) has (x – 2) as a factor
and leaves a remainder 3 when divided by (x – 3), find the value of 2a + 3b.
(A) –9 (B) 9
(C) –11 (D) 11
Q.47 If O is centre of circle as shown in figure, SOP = 102º and ROP = SOU = 72, then find OSU and RTU respectively –
Q R P O S U T (A) 54º, 93º (B) 45º, 110º (C) 54º, 96º (D) 45º, 94º
Q.48 If h, s, V be the height, curved surface area and volume of a cone respectively, then (3Vh3 + 9V2 – s2h2) is equal to - (A) 0 (B) (C) sh V (D) V 36
Q.49 The given bar-graph shows the percentage
distribution of the total production of a car manufacturing company into various models over two years. Study the graph carefully and answer the question.
Percentage of six different types of cars manufactured by a company over two years
Difference between total number of cares of models P, Q and T manufactured in 2000 and 2001 is -
(A) 2,45,000 (B) 2,27,500 (C) 2,10,000 (D) 98,000
Q.50 While constructing a triangle ABC, in which
BC = 3.8 cm, B = 45º and AB + AC = 6.8 cm we follow the following steps :
Step 1 : Draw the perpendicular bisector of CD meeting BD at A.
Step 2 : From ray BX, cut-off line segment BD equal to AB + AC i.e., 6.8 cm.
Step 3 : Join CA to obtain the required triangle ABC.
Step 4 : Draw BC = 3.8 cm.
Step 5 : Draw CBX = 45º
Step 6 : Join CD.
Arrange the above steps in correct order. Arrange the above steps in correct order. (A) 4, 5, 6, 1, 2, 3
(B) 5, 4, 6, 2, 3, 1 (C) 4, 5, 2, 6, 1, 3 (D) None of these
