MATHEMATICS (New)
Inter Part-I
(F resh/Reappear)
Note: Time allowed for Section - B and Section - C is 2 Hours and 40 minutes.
Section - B
Marks: 50
Q-ll) Answer any TEN parts. Each part carries FIVE marks.
1- If Zl = 2a -3bi, = -a +2bi then verify
2- If A is a square matrix of order 3, then show that A + At is symmetric.
3- Show that 2i - 5j- 3k is perpendicular to both 2i -j + 3K and i- 2j +4k
4- Insert three arithmetic means between ½ and 9.
5- Sum 1.4.7 +4.7.10+7.10.13+ ------------ To n terms.
6- How many diagonals can be drawn in a plane figure of 11 sides?
7- Find the coefficient of X 9
8- Find the domain and range of
9- Find the maximum and minimum values of the function f(x,y) = 7x + 21y subject to the constraints 2x +Y ≥ 2, 2x +3y ≤ 6, x +2y ≤ 8, x ≥ 0, y ≥ 0
10- Prove that
11- Two cars leave a station at the same time. One runs 300 east of north at 250 km/h, the other 450 east of south at 300 km/h. How far apart are they at the end of 2 hours.
12- Draw the graph of y = Cos 2x 0 ≥ x ≥2 π
13- Show that
Section - C
Marks: 30
Note : Attempt any THREE questions. Each question carries equal marks.
Q. Ill) (a)Use Crammers rule to solve the system of equation
2x-Y+3z = 10, 2X+Y -2z= -4, 3x + y + z = 7
(b)Find the value of t so that the vectors
ti +j+k, i+tj+k, i + j +tk are coplanar.
Q-IV) (a) lf a10 -x, an -y, a16 = z show that xz =y
(b) Given P(A) = 0.5 and P(B) = O. 10. Find P (A U B) if A and B are mutually exclusive.
Q – V) (a) Prove that Sin 3∅ + Sin ∅ + 2 Sin 2∅ = 4 Sin 2∅ cos2 ∅/2
(b) Find the area of the inscribed circle of the triangle whose sides measures 11,12 and 13 unit.
Q-VI) (a) Solve the equation 2 Sin2x- 3 Sin x +1 = 0
(b) The angle of elevation of a building is 460 from A and 630 from B. If AB is 25 m then find the height of the building.
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