Mathematics BS Mathematics/Intermediate 1 Semester/Term

Intermediate Part-I

MATHEMATICS (Subjective)

Time: 02:30 Hours

Marks: 80

SECTION - I

Roll No..

2. Attempt any EIGHT parts:

Write the name of property used as I = - 1 =x - 3 > - 5

(ii)

Define complex number.

(ii)

V x€ C, prove that x x- i x??

(iv) Define complement of a set.

(V)

Construct the truth table for a = a

(vi) If a', b are elements of a group G, then solve as - b

(VI) Find A' if A = 5 3

(vi) Find x if 3X-2A = B and A = [-3 3 -3] and B =[3 =4 -1]

(ix) If A is a square metrix of order 3, show that A + A' is symmetric.

(ix) Solve 2x2 - 32 = 0

(xi) Distuse nature of roofs of 2x' - 7x + 3 = 0

(xii) Find two consecutive numbers, whose problen is 152.

3. Attempt any EIGHT parts:

(i) Define a rational fraction.

(il) Convert the improper fraction

2x*

(x - 3)x + 2y as sum of a polynomial and a proper rational fraction

（m）If

（x-2）（x-1）2=

(iv)

（x-1）2+

x-2 then find C

(v)

Write the first four terms of arithmetic sequence if m = 17 and m = 37

Find three arithmetic means between 2 and 3/2

and

4 are in G.P, then show that common ratio is a V 6

(vii) Find two geometric means between 1 and 8

(VIII) I y= i+3

+

then find the interval for which the series is convergent.

(ix) Define mutually exclusive events with one example.

（x） 1f2+6+18+.

+ 2 - 3° - 3^ - 1 then check the statement for n = 2, 3 either true in false.

(x) Find the Sith term in the expansion of (at at

(xii) Using binomial theorem find the value of V65 to two places of decimals.

4. Attempt any NINE parts:

(i) Define radian.

(i¡)

What is the circular curcular of the angle between the bands of a watch at 4 Q clock?

(iii)

Prove the identity

Soso - sine =

cot 8 - 1

cot 0 - 1

(iv)

If a, B, y are angles of a triangle ABC, then prove that tan (a +

B) + tan y = 0

(v)

Prove that

c0s = tan 2

sin o.

sin 8x + sin 2x

(vi) Prove that

= tan 5x

cos 8x + cos 2x

(vii) Find the period of cosec 4

(viii) Define circum-circlu.

(ix)

Find the area of the triangle ABC, given rate side and two angles: c = 32, a = 47°24', B = 70°16'