Mathematics
(Objective)
Group-I
(Common for Old & New Scheme)
Paper (I)
Time Allowed:-30 minutes
PAPER CODE 2193
Maximum Marks: 20
Note : You have four choices for each objective type question as A, B, C and D. The choice which you think 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. Write PAPER CODE, which is printed on this question paper, on the both sides of the Answer Sheet and fill bubbles accordingly, otherwise the student will be responsible for the situation. Use of link Remover or white correction fluid is not allowed.

• Solution of the equation Cos2x=0 1st  quadrant is

(A) 300           
(B) 450           
(C) 600
(D) 150

• (ι)¹⁰¹ is equal

(A) 1         
(B) -1 
(C) ι    
(D) -ι

• (A∪B) equals

(A) A∪B     
(B) A'∩B'      
(C) A'∪B'     
(D) A∩B

• A monoid is always a

(A) Semi-group   
(B) Commutative group       
(C) Symmetric group           
(D) Group

• If A is a matrix of order 3x2 then order of At A is

(A) 3x2     
(B) 2x3          
(C) 2x2          
(D) 3x3

• If the matrix   is singular the λ is

(A) 2         
(B) 4   
(C) 6    
(D) 8

• The graph of the quadratic function is

(A) line    
(B) Parabola
(C) Triangle  
(D) Rectangle

• If α,βare the roots of ax²+bx+c=0 where a≠ 0 then αβequals
  

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

•  is a
  

(A) proper fraction  
(B) improper fraction          
(C) Equation 
(D) Identity   

• The A.P whose nth term is 2n-1 is
  

(A) 1,3,6…….  
(B) 2,3,5…..    
(C) 1,3,5…...   
(D) 5,3,1…..

• An infinite sequence has no
  

(A) Ist term    
(B) Middle term         
(C) Tenth term         
(D) Last term

• The sample space for tossing a coin once is
  

(A) {H}                
(B) {T,T}            
(C) {H,H}            
(D) {H,T}

• If a coin is tossed the probability of Head is
  

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

• If n is even then middle term of (a +b )n is
  

(A) ^th
(B) ^th 
(C)^th
(D) )^th

• If n is an integer then n² > n+3 true when
  

(A) n ≥ 3     
(B) n ≥ 2       
(C) n ≥1              
(D) n < 3        

• 2 sin 45°+   cos 45° is equal
  

(A)            
(B)             
(C)                                
(D) 1

• Cos 2α is equal
  

(A) 2Cos2α+1   
(B) 2Cos2α-1    
(C) 2Sin2α+1    
(D) 2Sin2α-1

• Period of Sec 3x is
  

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

• Cos α/2   Equals
  

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

•  – tan-1 x equals
  

(A) Cot^-1x           
(B) (Cot x)^-1      
(C) Tan x            
(D) (Cot x)

Mathematics
(Subject)
(Common for Old & New Scheme)
( Session:- 2010-12 to 2013-15)
Paper: (I)
Time Allowed: 2.30 hours
(Inter Part – I)
Maximum Marks: 80

2. Answer briefly any Eight parts from the followings:

• How many elements are in the power set of the set {1,2,3,4,5,6,7}
  
• For set A={1,2,34} find the relations in A. State Domain and Range of the relation {(x,y)} y+x=5
  
• Simplify (-a i) 4 a R
  
• Find x and y if =
  
• With out expansion show that
  
• Evaluate ω²⁸+ω²⁹+1           (vii) Disscuss the nature of the roots x2-5x +6=0
  
• If U={1,2,3,4,……20}  , A={2,4,6…..20} B={1,3,5,7…….19} the verify that (A∩B)′= A'∪B'
  
• If a, b are elements of a group then solve the equation ax= b
  
• Define square matrix and give one example
  
• Show that the product of all three cube roots of unity is one
  
• Define equal matrix and give one example.
  

3. Answer briefly any Eight parts from the following:-

• Resolve  into Partial fractions.
  
• Write the first four terms of the sequence if an=(-1)n n2
  
• If the first 5th term of an A.P is 16 and 20th term is 46. What is its 12th term.
  
• Insert three G.Ms between 2 and 32.
  
• Find the 12th term of harmonic sequence,,,…….
  
• Find the value of n when 11P = 11.10.9
  
• How many diagonals can be formed by joining the vertices of the polygon having 5 sides
  
• A box contains 10 red, 30 white and 20 black marbles.  A marble is drawn t random. Find the Probability that it is either red or white.
  
• Determine that probability of getting 2 heads in two successive tosses of a balanced coin.
  
• If x is so small that its and higher powers can be neglected then show that
  
• Calculate (0.97)3 by means of binomial theorem.
  
• Use mathematical induction to prove for every positive integer n 1+5+9+…. +(4n-3) =n(2n-1)

4. Answer briefly any Eight parts from the followings:-

• Convert the angle 3 radians in degrees.
  
• Write formulas for fundamental identities.
  
• State the distance formula
  
• Prove that Cos (α+45°) =  (Cos α-Sin α)
  
• Find the value of Sin 2α when Sin α = , where 0<
  
• Express 2 Sin 7θ Cos 3θ as a sum or difference
  
• Find the period of 3Cos
  
• State the laws of cosine (any two)
  
• Find the smallest angle of the triangle ABC, when a=37.34 ,b=3.24 , c=35.06
  
• Find the area of triangle ABC, in which b=37, c=45 , α = 300 50’
  
• Find the value of Sin-1
  
• Find the solution of Cosecθ=2 which lie in [0, 2π]
  
• Find the values of θ from 2 sin θ+cos2θ-1=0 θ[0, 2π]

Section-II

Attempt any three questions.   

5. (a) Solve the system of linear equations by Crammer’s. Rule
2x+2y+z=3
3x-2y-2z=1
5x+y-3z=2
(b) Solve the system of equations 3x+2y=7  ; 3x2=25+2y2

6. (a) Resolve  3x+2y=7      ;3x2­=25+2y2
(b) If the (positive) G.M. and H.M. between two numbers are 4 and , find the numbers

7. (a) Find the values of n and r when n-1C r-1: nCr:n+1Cr+1 =3:6:11
(b) If x is very nearly equal 1, then prove that Px^p-qx^q=(p-q)x^p+q

8. (a) Prove that  = 
(b) Find the values of the trigonometric functions of “-10350”

9. (a) Prove that r₁+r₂+r₃-r = 4R
(b) Prove that tan-1+ tan-1- tan-1=