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  • Question 1
    (a) Given A=2-62   0, B=-3240, C=4002
    Find the matrix X such that A + 2X = 2B + C.
    [3]
    (b) At what rate % p.a. will a sum of Rs 4000 yield Rs 1324 as compound interest in 3 years? [3]
    (c) The median of the following observations
    11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.
    Find the value of x and hence find the mean.
    [4]
    VIEW SOLUTION
  • Question 2
    (a) What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional? [3]
    (b) If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b. [3]
    (c) Draw a histogram from the following frequency distribution and find the mode from the graph:
    Class 0–5 5–10 10–15 15–20 20–25 25–30
    Frequency 2 5 18 14 8 5
    [4]
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  • Question 3
    (a) Without using tables evaluate:
    3 cos 80°. cosec 10° + 2 sin 59° sec 31°.
    [3]
    (b) In the given figure, ∠BAD = 65°, ∠ABD = 70°and ∠BDC = 45°.

    (i) Prove that AC is a diameter of the circle.
    (ii) Find ∠ACB
    [3]
    (c) AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7). Find
    (i) the length of radius AC
    (ii) the coordinates of B.
    [4]
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  • Question 4
    (a) Solve the following equation and calculate the answer correct to two decimal places:
    x2 – 5x – 10 = 0
    [3]
    (b) (b) In the given figure, AB and DE are perpendicular to BC.

    (i) Prove that ΔABC ~ ΔDEC
    (ii) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.
    (iii) Find the ratio of area of ΔABC: area of ΔDEC.
    [3]
    (c) Using a graph paper, plot the points A(6, 4) and B(0, 4).
    (i) Reflect A and B in the origin to get the images A' and B'.
    (ii) Write the co-ordinates of A' and B'.
    (iii) State the geometrical name for the figure ABA' B'.
    (iv) Find its perimeter.
    [4]
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  • Question 5
    (a) Solve the following inequation, write the solution set and represent it on the number line:
    -x3x2-113<16, x  R
    [3]
    (b) Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is 8% per annum and Mr. Britto gets Rs 8088 from the bank after 3 years, find the value of his monthly instalment. [3]
    (c) Salman buys 50 shares of face value Rs 100 available at Rs 132.
    (i) What is his investment?
    (ii) If the dividend is 7.5%, what will be his annual income?
    (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?
    [4]
    VIEW SOLUTION
  • Question 6
    (a) Show that 1-cos A1+cos A=sin A1+cos A. [3]
    (b) In the given circle with centre O, ∠ABC = 100°, ∠ACD = 40° and CT is a tangent to the circle at C. Find ∠ADC and ∠DCT.
    [3]
    (c) Given below are the entries in a Saving Bank A/c pass book.
    Date Particulars Withdrawls Deposit Balance
    Feb 8
    Feb 18
    April 12
    June 15
    July 8
    B/F
    To self
    By cash
    To self
    By cash
    -
    4000
    -
    5000
    -
    -
    -
    2230
    -
    6000
    8500



     
    Calculate the interest for six months from February to July at 6% p.a.
    [4]
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  • Question 7
    (a) In ΔABC, A(3, 5), B(7, 8) and C(1, –10). Find the equation of the median through A. [3]
    (b) A shopkeeper sells an article at the listed price of Rs 1500 and the rate of VAT is 12% at each stage of sale. If the shopkeeper pays a VAT of Rs 36 to the Government, what
    was the price, inclusive to TAX, at which the shopkeeper purchased the article from the wholesaler?
    [3]
    (c) In the figure given, from the top of a building AB = 60 m high, the angles of
    depression of the top and bottom of a vertical lamp post CD are observed to 30° and
    60° respectively. Find:

    (i) The horizontal distance between AB and CD.
    (ii) The height of the lamp post.
    [4]
    VIEW SOLUTION
  • Question 8
    (a) Find x and y if x3xy4y21=512. [3]
    (b) A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. [3]
    (c) Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots: x2 + (p – 3) x + p = 0. [4]
    VIEW SOLUTION
  • Question 9
    (a) In the figure alongside, OACB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion. Take π=227
    [3]
    (b) A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box. [3]
    (c) Find the mean of the following distribution by step deviation method:
    Class interval 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
    Frequency 10 6 8 12 5 9
    [4]
    VIEW SOLUTION
  • Question 10
    (a) Using a ruler and compasses only:
    (i) Construct a triangle ABC with the following data:
    AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°
    (ii) In the same diagram, draw a circle with BC as diameter.
    Find a point P on thecircumference of the circle which is equidistant from AB and BC.
    (iii) Measure ∠BCP.
    [4]
    (b) The marks obtained by 120 students in a test are given below:
    Marks 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 80–90 90–100
    No of students 5 9 16 22 26 18 11 6 4 3

    Draw an ogive for the given distribution on a graph sheet.
    Use suitable scale for ogive to estimate the following:
    (i) The median.
    (ii) The number of students who obtained more than 75% marks in the test.
    (iii) The number of students who did not pass the test if minimum marks required to pass is 40.
    [6]
    VIEW SOLUTION
  • Question 11
    (a) In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The
    point P(–3, 4) on AB divides it in the ratio 2: 3. Find the coordinates of A and B.
    [3]
    (b) Using the properties of proportion, solve for x, given x4+12x2=178. [3]
    (c) A shopkeeper purchases a certain number of books for 960. If the cost per book was 8 less, the number of books that could be purchased for 960 would be 4 more. Write an equation, taking the original cost of each book to be x, and solve it to find the original cost of the books. [4]
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