Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3. Q.No. 1 to 8 are of objective type questions, carrying 1 mark each. 4. Q.No.9 to 14 are of short answer type questions, carrying 2 marks each. 5. Q. No. 15 to 24 carry 3 marks each. Q. No. 25 to 34 carry 4 marks each.

1.

Point (–3, 5) lies in the (A) first quadrant (C) third quadrant

(B) second quadrant (D) fourth quadrant

2.

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 ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to: (A) 80º (B) 50º (C) 40º (D) 30º The linear equation 3x – y = x – 1 has : (A) A unique solution (B) Two solutions (C) Infinitely many solutions (D) No solution The width of each of five continuous classes in a frequency distribution is 5 and the lower class-limit of the lowest class is 10. The upper class-limit of the highest class is: (A) 15 (B) 25 (C) 35 (D) 40 In a cylinder, if radius is halved and height is doubled, the volume will be (A) Same (B) doubled (C) halved (D) four times Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks

3.

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7.

In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is : (A) 0.5 (B) 0.6 (C) 0.7 (D) 0.8 The total surface area of a cube is 96 cm2. The volume of the cube is: (A) 8 cm3 (B) 512 cm3 (C) 64 cm3 (D) 27 cm3 AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.

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10.

Find the capacity in litres of a conical vessel with (i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 12 cm

11.

The relative humidity (in %) of a certain city for a month of 30 days was as follows: 98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89 (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88 (ii) Which month or season do you think this data is about? (iii) What is the range of this data? Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg): 4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00 Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

12.

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13.

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.

14.

The value of π up to50 decimal places is given below: 3.14159265358979323846264338327950288419716939937510 (i) Make a frequency distribution of the digits from 0 to 9 after the decimal point. (ii) What are the most and the least frequently occurring digits? Draw the graph of each of the following linear equations in two variables: (i) (ii)

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Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find (i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given...