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) 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)
13) 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)
14) 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)
15)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)
16) 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)
17) 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)
18) AB is a fixed line. Write about the locus of the point P so that AB²= AP²+ BP². (2)
19) Find the equation of a line that passes through (1,3) and is parallel to the line y= -3x +2. (3)
20) In the given figure, calculate:
a) angle APB
b) angle AOB. (3)
21) 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)
22) 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
23) 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:
b) How many students obtained 40% marks ?
c) How many students obtained 90% and above ?
d) What is the medium marks ? (4)
24) Prove that √{(1+ cosx)/(1- cosx)= cosecx + cotx. (3)
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