1. The problem involves finding the values of m and c for a line equation given information about two other lines and their point of intersection. 2. Find the equation of a line parallel to another line and passing through a point that divides the line between two other points in a specific ratio. 3. Find the equation of the altitude of a triangle drawn from a given vertex to the opposite side.

1. Co-ordinate Geometry, sequence
and series and trigonometry

2. 1. If the line y = mx + c, passes through the
point of intersection of the lines x + 2y = 7
and 4x – 3y = 6 and parallel to the line
y = 2x + 3, find the values of m and c.
2. Find the equation of the line parallel to line
2x + 3y = 5 and passing through the point
which divides the line joining the points (1,-2)
and (4,7) in the ratio 1:2.

3. 3. Find the equation of altitude of triangle ABC with
vertices A(2,3), B(-4,1) and C (2,0) drawn from the
vertex A (2,3).
4. If(2,3) and (-6,5) are the end points of one of the
diagonal of a rhombus, find the equation of other
diagonal.
5. A straight line K is perpendicular to the line
3x – 4y + 18 = 0 and the area of triangle bounded
by the line K with coordinate axis is 6 square
units. Find the equation of line K.

4. 6. Raju borrowed Rs. 4368 from Nepal bank and
promised to pay in 6 installments. If each
installment being treble of the preceding one,
what are the first and last installment?
7. Three numbers are in A.P and their sum is 15.
If first two terms are each decreased by 1 and
third term is increased by 1,then resulting
numbers are in G.P then find the numbers.

5. 8. Find the number of geometric means inserted
between 4 and 128 in which the ratio of first
mean to the last mean is 1:8.
9. n GMs are inserted between 16/27 and 243/16
such that the ratio of (n-1)th mean to 4th mean is
9:4. Find the value of n?
10. In a GP, whose common ratio is positive, the
sum of first two terms is 4/3 and sum of next two
terms is 12, find the first term and common ratio.

6. 11) A class consists of number of boys whose age
are in AP. The common difference is 4 months. If
the youngest boy be only 8 yrs and sum of
their ages is 168 yrs, find the no. of boys and
age of oldest boy.
12) The sum of three numbers in GP is 14 and
their product is 64. Find the numbers.
13) Three numbers are in the ratio 1:4:12. If 1 is
added to the first number, the resulting
numbers together with other two numbers
form a GP. Find the original three numbers.

7. 14) Find the equation of circle which passes
through the point (4, 3) with radius 5 units
and the centre lies on the line 2x+y-1= 0.
15) Find the equation of circle having the centre
at (4, 2) tangent being 3x+4y = 10.
16) Prove that the points (2, -4), (3, -1), (3, -3)
and (0, 0) are concyclic.
17) Find the equation of circle whose centre is at
the point of intersection of 2x+y = 4 and
2y-x = 3 and passing through (4, 6).

8. Trigonometry:
18) Prove that:
a) sinθ. sin( 60-θ). Sin(60+θ) = 1/4sin 3θ.
b) Tanθ. Tan(60+θ). Tan (60-θ) = Tan3θ.
c) cos2π/7 + cos4π/7 + cos6π/7 = -1/2
d) cos2 A + sin2 A cos2B = cos2B + sin2B cos2A
19) If cosec A+ sec A = cosec B + sec B then
prove that tanA .tanB = cot (A+B/2)
20) If A+B+C = π, prove that
a) cos(B+C-A) + cos(C+A-B) + cos(A+B-C) =
1+4cosA cosB cosC
b) sin A/2 + sinB/2 + sinC/2 = 1+ 4sin(A+B/4) sin(B+C/4)
sin(C+A/4)

9. 21) Solve: (0≤θ≤360)
a) Sinx + cosx = 1
b) cosx + cos2x + cos3x = o
22) The pillar is coloured in the ratio 1:9 from the bottom. If these two parts
make an equal angle 20m far from the foot of pillar, find the height of pillar.
23) A ladder 8m long reaches a point 8m below from the top of vertical flagstaff.
From the foot of ladder, the angle of elevation of flagstaff is 60. Find the
height of flagstaff.
24) The angle of elevation of an aeroplane from a point A on the ground is 45.
after 20 sec flight, the angle of elevation changes to 30. If the aeroplane is
flying at a height of 2km , find the speed of aeroplane.
25) The shadow of a tower on the ground is found to be 45m longer when sun’s
altitude is 45 than it is 60. What will be the height of tower.
26) Two poles are such that one is double the height of the other and are at a
distance of 40m. If the angle of elevation of the top of the poles from a point
midway between them are complementary, find the height of the pole.

10. 27) From the top of the cliff, a man observes a
boat at an angle of depression of 30, which is
approaching a shore to the point
immediately beneath the observer with a
uniform speed. Four minutes later, the angle
of depression of the boat is found to be 60.
Find the time taken by the boat to reach the
shore. Ans 2min.