RAW- 1 (X)

1) Find the rate of sales tax levied on a car that was sold at a price three times its marked price.         (3)

2) When 7x² - 3 x + 8 is divided by (x-4), find the remainder (using remainder theorem).  (2)

3)If  2 cos x= 2/5, without using table, find sinx.      (2)

4) Calculate the length of the tangent drawn to a circle of diameter 8 cm from a point 5 cm away from the centre of the circle.     (2)

5) If x², 4 and 9 are in continued proportion, find the value of x.    (2)

6) If x ∈ Z, find the solution set for the inequation 5 < 2x -3≤ 14 and graph the solution on a number line.       (3)

7) Find p and q if g(x)= x +2 is a factor of f(x)= x³ - px + x+ q and f(2)= 4.     (3)

8) Given X= 1    -2 & Y= 0
                     -3    4          1
a) Find a matrix Z such that X + Z is a zero matrix.
b) Find the matrix M such that X + M = X.
c) Find XY.                 (3)


9) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.
b) If each observation is decreased in value by 1 unit, what would be the new mean be ?    (3)

10) In the figure below, AB is a chord of the circle with centre O and BT is standing to the circle at B.
If angle AOB= 32°, find the value of x and y.    (3)

11)  Construct a rectangular Pentagon of side 3cm. Draw the lines of symmetry.   (3)

12) a) A discount of 15% is allowed in the marked price of an article and sold for Rs.2975. Calculate its marked price.
b)  Given that the marked price is 40% above the cost price of the article, find its cost price and the profit made by the sale of the article in rupees.     (4)

13) The volume of a cylinder 14cm long is equal to that of a cube having an age 11 cm. Calculate the radius of the cylinder.     (4)

14) A piece of butter 3 cm by 5cm by 12cm is placed in a hemispherical bowl of radius 3.25cm. Will the butter overflow when it melts completely ?      (4)


15) Construct a ∆ABC in which AB= 5cm,  BC= 8cm and CA= 7cm. Construct the circle which passes through and B and has BC as tangent.     (5)

16) A company with 10000 shares of Rs50 each, declares an annual dividend of 5%. 
i) What is the total amount of dividend paid by the company ?
ii) What would be the annual income of a man who has 72 shares in the company ?
iii) If he receives only 4% on his investment, find the price he paid for each share.    (5)

17)i) State the equation of the mirror line, if point A(5,0) on reflection is mapped as A'(-5,0).
ii) State the equation of the mirror line, if point B(4,-3) on reflection is mapped as B'(4,3).
iii) Point C(-3,5) on reflection in y= 2 is mapped as C'. Find the co-ordinates of C.  (3)

18) Solve graphically 2x + 3 y= - 5;  2y + 3x = 0.      (5)

19) In a ∆ABC, angle A is obtuse, PB perpendicular to AC and QC perpendicular to AB. Prove that: AQ x AB = AP x AC.      (4)

20) Taniya standing on a vertical cliff in a jungle observes two rest houses in line with her on opposite sides deep in the jungle below. If their angles of depression are 30° and 45° and the distance between them is 222m, find the height of the cliff.    (5)

21) AB is a fixed line. Write about the locus of the point P so that AB²= AP²+ BP².   (2)

22) Calculate the value of:  2/(√5 - 3) to 3 significant figures by rationalising the denominator.       (3)

23) The base of a triangle is 2cm greater than twice its altitude. If the area is 12cm², calculate the base and the altitude.     (4)

24) Find the equation of a line that passes through (1,3) and is parallel to the line y= -3x +2.    (3)

25) In the given figure, calculate:
a) angle APB
b) angle AOB.        (3)

26) The midpoint of the line joining A(2, p) and B(q, 4) is (3, 5). Find the numerical values of p and q.     (3)

27) From the following table, find:
a) average wage of a worker. Give your answer, to the nearest paise.
b) model class.     (4)
Wages inRs.      No of Workers 
Less than 10         15 
Less than 20         35 
Less than 30         60 
Less than 40         80
Less than 50         90
Less than 60         127 
Less than 70         190
Less than 80         200
 
28) The relation f(x)= 2x is defined from set X to set Y where X={0,1,2,3} and Y= {1,2,6}. The Venn diagrams for sets X and Y are given in the figure. Copy the same and draw arrows to show the pairs that satisfy the relation. Is the relation a function? Give reasons?     (3)

29) Examine the ogive given below which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:
a) How many students are there in the set ?
b) How many students obtained 40% marks ?
c) How many students obtained 90% and above ?
d) What is the medium marks ?     (4)

30) Prove that √{(1+ cosx)/(1- cosx)= cosecx + cotx.       (3)

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