Page 4 - DEHRADUN PUBLIC SCHOOL

Q.5 Find the amount of an annuity of Rs. 500 payable at the end of each year for 14 years if money is
worth 5% compounded annually.
Q.6 A manufacturer sells a refrigerator to a dealer for Rs. 45,000. The dealer sells it to a customer at
a profit of Rs. 4600. If the sales are intra - state and the rate of GST is 12%, find the amount
(i) of GST paid by the dealer to the state and central governments.
(ii) of total GST received by the state and central governments
(iii) paid by the customer to the dealer
Q.7 A shopkeeper has marked Rs. 7840 as the price o an article including 12% GST on the listed price.
A buyer asks for a discount on the listed price so that after charging GST, the selling price
becomes equal to the listed price. Find the amount discount the shopkeeper has to offer for the
deal.
Case- based questions
A project requires an initial investment of Rs. 250000 and is expected to generate the following
net cash inflows year-1 : Rs. 98000, year-2 : Rs. 120000, year-3: Rs. 150000. The discount rate is
12% per annum.
Based of the above information, answer the following questions-
(i) Find the present value of cash inflow expected to generate at the end of year-1, year-2 and
year-3
(ii) What is the net present value of the investment?
(iii) What is the difference between the net present value and the present value of cash outflow?

COORDINATE GEOMETRY
Q.1 If A(–2, 1), B(2, 3) and C(–2, –4) are three points, find the angle between BA and BC.
Q.2 Find the equation of a straight line which cuts off an intercept of 5 units on negative direction of
y - axis and makes an angle of 120 with the positive direction of x - axis.
0
Q.3 Find the equation of a line which divides the join of (1, 0) and (3, 0) in the ratio 2:1 and
perpendicular to it.
Q.4 Find the equations of the altitudes of the triangle whose vertices are A (7, –1), B (–2, 8) and C (1,
2).

Q.5 A straight line passes through the pint (  , ) and this point bisects the portion of the line
x y
intercepted between the axes. Show that the equation of the straight line is + = 1.
2 2
Q.6 Find the equation of the straight line upon which the length of perpendicular from origin is
0
3 2 units and this perpendicular makes an angle of 75 with the positive direction of x - axis.
Q.7 Find the value of m for which the lines m x + (2m +3) y + m + 6 = 0 and (2m + 1) x + (m – 1) y +
m – 9 = 0 intersect at a point on y - axis.
Q.8 Find the tangent of the angle between the lines whose intercepts on the axes are respectively a,
–b and b, –a.
Q.9 Two sides of a square lie on the lines x + y = 1 and x + y + 2 = 0. What is its area?
Q.10 Find the equation of the circle which passes through the origin and cuts off intercepts 3 an 4
from the positive parts of the axes respectively.
Q.11 Find the equation of the circle concentric with the circle 2x + 2y + 8x+ 10y–39 = 0 and having
2
2
its area equal to 16 square units.
Q.12 Find the equation of the parabola whose focus is the point (0, 0) and whose directrix is the
straight line 3x – 4y + 2 = 0
Q.13 At what point of the parabola x = 9y is the abscissa three times that of ordinate?
2
9
Q.14 Find the centre and radius of the circle given by the equation 2x 2 + 2y 2 + 3 + 4 + = 0
x
y
8
Q.15 Find the equation of the circle which passes through the points (5, –8), (2, –9) and (2, 1). Find
also the coordinates of its centre and radius.
Case-based question
Three girls, Rani , Mansi, Sneha are talking to each other and maintaining a social distance for
due to covid-19 . They are stand on a vertices of triangle whose coordinates are Rani (2, -2),
Mansi(1, 1) and Sneha(-1, 0).
Based on the above information answer the following

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