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General Instructions:
1. All questions are compulsory.
2. The question paper consists of 30 questions divided into four sections – A, B, C and D. Section A comprises of ten questions of 1 mark each, Section B comprises of five questions of 2marks each, Section C comprises of ten questions of 3 marks each and Section D comprises of five questions of 6marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
There is no overall choice. However, an internal choice has been provided in one question of 2 marks each, three questions of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions.
4. In question on construction, the drawing should be neat and as per the given measurements.
5. Use of calculators is not permitted.
Question 1
  • Q1

    Find the discriminant of the quadratic equation

     

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  • Q2

    If, a, and 2 are three consecutive terms of an A.P., then find the value of a.

     

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  • Q3

    If the areas of two similar triangles are in the ratio 25:64, write the ratio of their corresponding sides.

     

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  • Q4

    In figure 1, ΔABC is circumscribing a circle. Find the length of BC.

     

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  • Q5

    Two coins are tossed simultaneously. Find the probability of getting exactly one head.

     

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  • Q6

    Find the [HCF × LCM] for the numbers 100 and 190.

     

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  • Q7

    If 1 is a zero of the polynomial p(x) = ax2 − 3(a − 1) x − 1, then find the value of a.

     

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  • Q8

    If sec2θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

     

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  • Q9

    If the diameter of a semicircular protractor is 14 cm, then find its perimeter.

     

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  • Q10

    Find the number of solutions of the following pair of linear equations:

    x + 2y − 8 = 0

    2x + 4y = 16

     

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  • Q11

    If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.

     

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  • Q12

    Which term of the A.P. 4, 12, 20, 28, … will be 120 more than its 21st term?

     

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  • Q13

    If , then evaluate

    OR

    Find the value of tan 60°, geometrically.

     

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  • Q14

    Find all the zeroes of the polynomial x3 + 3x2 − 2x − 6, if two of its zeroes are and.

     

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  • Q15

    In Figure 2, ΔABD is a right triangle, right-angled at A and AC BD. Prove that AB2 = BC . BD.

     

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  • Q16

    Prove that is an irrational number.

     

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  • Q17

    Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are times the corresponding sides of the first triangle.

     

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  • Q18

    Two dice are thrown simultaneously. What is the probability that

    (i) 5 will not come up on either of them?

    (ii) 5 will come up on at least one?

    (iii) 5 will come up at both dice?

     

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  • Q19

    In Figure, 3, AD ⊥ BC and BD CD. Prove that 2CA2 = 2AB2 + BC2.

    OR

    In Figure 4, M is mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL = 2 BL.

     

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  • Q20

    The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth term of the A.P.

     

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  • Q21

    The area of an equilateral triangle is cm2. Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take= 1.73]

    OR

    Figure 5 shows a decorative block which is made of two solids − a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere, fixed on the top, has a diameter of 4.2 cm. Find the total surface area of the block. [Take π =]

     

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  • Q22

    Find the ratio in which the point (x, −1) divides the line segment joining the points (−3, 5) and (2, −5). Also find the value of x.

     

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  • Q23

    Find the area of the quadrilateral ABCD whose vertices are A (1, 0), B (5, 3), C (2, 7) and D (­−2, 4)

     

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  • Q24

    Evaluate:

     

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  • Q25

    Solve for x and y:

    axby = 2ab

    OR

    The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is

     

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  • Q26

    A juice seller serves his customers using a glass as shown in Figure 6. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14)

    OR

    A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of

    (i) water displaced out of the cylindrical vessel.

    (ii) water left in the cylindrical vessel.

    [Take π ]

     

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  • Q27

    Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

    Using the above, do the following:

    In Figure 7, O is the centre of the two concentric circles. AB is a chord of the larger circle touching the smaller circle at C. Prove that AC = BC.

     

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  • Q28

    A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at that instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

     

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  • Q29

    Solve the following equation for x:

    9x2 − 9(a + b)x + (2a2 + 5ab + 2b2) = 0

    OR

    If (−5) is a root of the quadratic equation 2x2 + px − 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then find the values of p and k.

     

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  • Q30

    During the medical check-up of 35 students of a class their weights were recorded as follows:

    Weight (in kg)

    Number of students

    38 − 40

    3

    40 − 42

    2

    42 − 44

    4

    44 − 46

    5

    46 − 48

    14

    48 − 50

    4

    50 − 52

    3

    Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph.

     

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