Mathematics:A
Paper Code No.6191
Paper I (Objective Type)
(Inter-A-2015)
Time: 30 Minutes
Inter (Part I)
 Marks: 20
Session (2011 - 2013 1(2012 - 2014) (2013. 13) (2014 - 16)
Note: Four possible choices A, B, C, and D to each question are given. Which choice is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Q.1

• (0,1)2 :

(A) ( 1 , 0 )
(B) (-1 , 0 )
(C) ( 0 , 1)
(D) ( 0 ,-1)

• Set containing elements A or B is denoted by:

(A) A B
(B) A  B
(C) A B
(D) BA

• If A = {a,{a,b}} then n (p(A))=

(A) 2
(B) 3
(C) 4
(D) 6

• If A =[aij] 3 x 3 ,then |KA| =

(A) | A |
(B) K|A|
(C) K2 |A|
(D) K3|A|

• The additive inverse of A is  :

(A) A-1
(B) A
(C) 
(D) - A

• A Quadratic Equation has degree:

(A) 0
(B) 1
(C) 2
(D) 3

• If α , β are the roots of x²–px-p-c=0 then α.β =

(A) p +c
(B) -p + c
(C) p - c
(D) - (p + c)

• Arithmetic Mean between  and  is =-

(A)
(B)
(C)
(D)

• Sum of Infinite Geometric Series is valid if

(A) r<1
(B) |r|<1
(C) |r|=1
(D) |r|>1

• For an event A, the range of P (A) is

(A) 0 < p (A)≤ 1
(B) 0 ≤P (A) ≤I
(C) 0 ≤P (A) < 1
(D) 0<P (A) < I

• If A and B are disjoint, then P(A B ) =

(A) P(A) +P(B)
(B) P (A) - P (B)
(C) P (A) • P (B)
(D) P (A) + P (B)-P (AB)

• Number of terms in die expansion of ( 1 + x )2n+ 1 is =

(A) 2n + 1
(B) 2n
(C) 2n + 2
(D) 3n + 1

• Middle term is the expansion of (x + y )21 is :

(A) 10th, 11th
(B) 9th, 10th
(C) 11th, 12th
(D) 12th, 13th

• Partial Fraction of 3

(A) +
(B)  +
(C)  +
(D)  ++ +

• In One hour, the angle in radian through by minute hand of clock is

(A) 2
(B) π
(C)
(D) 2π

•  =

(A) Cos2α
(B) Sin2α
(C) Cos²2α
(D) Sin²2α

• Range of Sin2x is :

(A) [-1,1]
(B) [- 2, 2]
(C) (-1, 1)
(D) (- 2, 2)

• R =

(A)
(B)
(C)
(D)

• tan-1  +tan -1

 (A)
(B)
(C)
(D)

• The Trigonometric Equation has solution :

(A) 0
(B) 1
(C) 2
(D) Infinite

Time : 2 : 30 Hrs Marks : 80
Inter Part I
Mathematics
(Subjective)
Inter-A-2015
Session (2011-13)(2012.14)(2013-15)(2014-16)
Note: It is compulsory to attempt (8. 8 ) parts each from Q.No.2 and 3 While attempt any (9) parts from Q. No.4 and attempt any |(03) questions from Part II Write same Question No. and its Part No. as given in the question paper.(25x 2 = 50)

Q.2

• Find the Multiplicative Inverse of (, +).
• Express the Complex Number 1+ in Polar Form.
• Write the Inverse and Contra positive of ̴  ̴→ ̴ q
• Let A = {1, 2, 3}. Determine the relation " r " such that x < y.
• Find x and y if
• Find the value of if A is singular, when A=
• Discuss the nature of the roots of 25x2.30x + 9 = 0
• Solve the equation   -    - 6 = 0
• Find the inverse of
• Evaluate :( 1 + w - w2)( 1- w + w2 )
• Define Proper Subset.
• Define Binary Operations.

Q.3

• Resolve  into Partial Fractions.
• Which term of the A.P.5, 2, -1, — is -85
• Find A.M. between 1 - x + x2 and 1 + x + x2
• if  ,  and  are in A.P show that b=  
• Calculate (0.97)3 by means of Binomial Theorem.
• Find the number of Diagonals of 5 sided figure.
• A die is rolled what is the probability that the dots on the top greater than 4
• Find the term involving x4 in the expansion of (3 - 2x)7.
• Find the value of n when 11p11 11.10.9
• If nc8  = nc12 Find n.
• Expand ( 4 - 3x )1/2 up to 2 terms
• Insert two G.Ms between 1 and 16.

Q.4

• Express Sin319° as a trigonometric function of an angle of positive degree measure less than 45°.
• A vertical pole is 8 m high and length of its shadow is 6 m. What is the angle of elevation of the sun at that moment?
• Write any two laws of tangents for a triangle ABC.
• Solve the trigonometric equation Cosec2 θ =  which lies in [ 0 , 2π ]
• Find the value of Cos2 α when Sin α =  where 0 ˂ α ˂
• Without using table/ calculator show that 2 Cos   = Sin   
• Find the value of θ; satisfying the equation 2Sine θ +Cos2θ -1 = 0
• Prove that Sin2 + Sin2tan2 : = 2
• Prove that tan ( 45o + A ) tan ( 45° - A) = 1
• Express Sin5 Cos 2 as sum or difference.
• Define Period of a Trigonometric Function.
• Find " r " when a = 13 , b = 14 , c = 15
• Prove that     =

Part - II

5.(a) Prove that 05

|b+caa²|
|c+abb²| = (a+b+c)(a-b)(b-c)(c-a)
|a+bcc²|
(b) Show that Roots of x² + ( mx + c )² = a² will be equal if C² = a² (1+m2): (5)

6.(a) Resolve     into Partial Fractions.
(b) If y =  x + x2 + x3 +------- and if 0 < x <   then show that x =

7.(a) Find values of n and r when ncr = 35 and npr = 210
(b) Determine Middle Terms in the expansion ( x -)

8.(a) Prove that Cosθ + Sinθ    +  =
(b) Show that Cot (α + β) =

9.(a) P and Q are two points in line with a tree. If the distance between P and Q is 30 m and the angles of elevation of the top of the tree at P and Q be 12° and 15° respectively, find the height of the tree. (5)
(b) Prove that Sin -1  + Sin -1  = Cos -1