PAPER CODE :219
(11TH CLASS- 12013)
MATHEMATICS
TIME: 30 MINUTES, MARKS: 20
GROUP FIRST
OBJECTIVE
NOTE: YOU HAVE FOUR CHOICES OF EACH OBJECTIVE TYPE QUESTION AS A,B,C and D.THE CHOICE WHICH YOU THINK IS CORRECT , FILL THAT CIECLE 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.NO.1

• The additive inverse of 2 is

(a) 0
(b) 1   
(c) -2  
(d) 1/2

• If A ≤B then AUB =
  

(a) A                                              
(b) B                                      
(c) Φ                      
(d) X

• is a
  
  (a) zero matrix                          
  (b) identity                         
  (c) diagonal         
  (d) scalar
  

• If     then the order of At is

(a) 3x2                                          
(b) 2x3                                  
(c) 2x2                   
(d) 3x3

• The polynomial ax³ +bx² +8 has degree =
  

(a) 8                                                               
(b) 3                                       
(c) a+b                  
(d) 4

• The solution of equation x² +5x -6=0 is
  

(a) {-1,6}                                      
(b) {1,-6}                              
(c) {1}                    
(d) {6}

• x³ +1/(x-1)(x+2) is
  

(a) proper fraction                   
(b) improper fraction     
(c) identity          
(d) mixed fraction

• 2,4,6,8,10,12,……….. is
  

(a) G.P                                          
(b) A.P                                  
(c) geometric series
(d) None

• The nth term of sequence 1/3, 2/5,3/7    ………… is
  

(a) n/2n-1                                    
(b) n/2n+1                          
(c) n/3n-1            
(d) n/3n+1

• 0! =
  

(a) 0                                                               
(b) 1                                       
(c) -1                      
(d) 2

• 6.5.4 =
  

(a) 6!/3!                                       
(b) 3!/6!                                               
(c) 1/6!                 
(d) 6!

• The co-efficient of last term is expansion of  (a-b)⁵ is
  

(a) 1
(b) -1
(c) 0
(d) 2

• In the expansion of (a+t)⁷  the 2nd term is
  

(a) a⁷                                             
(b) 7a⁶b                                
(c) 7ab⁶                
(d) 8

• ¼  (rotation) anti clock wise=
  

(a) 45°                                           
(b) 90°                                   
(c) 180°                 
(d) 360°

• sin 196° =
  

(a) sin16°                                     
(b) cos 33°                            
(c) cos 16°             
(d) -sin 16°

• The domain of sin  x is
  

(a) [-1,1]                                      
(b) -π/2                                
(c) R                       
(d) Q

• If a,b,c are sides of triangle then a²+c²-b²/2ac   =
  

(a) cos a                                       
(b) cos β                                               
(c) cos y                
(d) sin β

• Law of cosine  a² = b² + c²  -2bc  cos a Pythagoras theorem if
  

(a) a = 90°                                        
(b) a = 0°                                  
(c) a = 180°            
(d) a = 360°

• The value of sin (cos-1  ) is
  

(a) 1/2                                           
(b) 1/                          
(c)                   
(d) 2/

• Solution of 1+cos x = () is
  

(a) π/2
(b) π
(c) 2π
(d) 4π

(11th CLASS 12013)
MATHEMATICS
TIME: 2.30 HOURS
GROUP FIRST
SUBJECTIVE
MARKS:80
SECTION-I

• Express the complex number 1+I    in polar form
• State de moivre theorem
• Define function
• Prove that P~P  is an absurdity
• Show that     
• Define transpose of a matrix
• If       find        4A – 3B
• Without expansion show that  
• Evaluate (-1+  )5  +  (-1   5
• State factor theorem
• If a, β are the roots of 3x2 -2x+4=0  find sum and product of the roots
• Define radical equation

3. ATTEMPT ANY EIGHT SHORT QUESTIONS (16)

• Which term of A.P 5,2,-1 …….. is  -85
• Find 13th term of sequence x, 1,2,-x…….
• What is an A.P whose nth term is 2n -1
• Find the geometric mean between a,b
• Resolve 1/x2-1   into partial fractions
• What are partial fractions?
• Find the value of n when C₂ = 21
• Evaluate ¹²C₃sub>
• Evaluate 5!
• Write 9.8.7.6 in factorial form
• Show that ⁿC_r = ⁿC_n-r
• State the principle of mathematical induction

4. ATTEMPT ANY NINE SHORT QUESTIONS:  (18)

• CONVERT 37°, 25’,28”  into radians
• Find r when 1= 56cm θ =45°
• Show that sin(360-θ) =-sinθ
• If cos a = 3/5 find value of cot a
• Show that  cos(a+β) +cos(a-β)= 2 cos a cos β
• Without calculator find value of sin (105°)
• What is domain od sin x?
• State the law of sine
• In right triangle ABC a = 62°,40’  b= 796, y = 90° find a
• State the law of tangents
• What is an oblique triangle?
• Find solution of equation sin 2x = cos x in [0,2π]
• Solve sin x= ½

SECTION-II

ATTEMPT ANY THREE QUESTIONS FROM THIS SECTION

5.(a) Prove that ~q (p→q) →~ p is a tautology
(b) If A =      SHOW THAT A+(A)t  hermition

6.(a) Show that the roots of x2 +(m x + c)2 =a2  will be equal if c2 =a2 (1+m2)
(b) Resolve into partial fractions   2x3 +x2 –x-3/x(2x+3)(x-1)

7.(a) Find n so that  an +bn/an-1 + bn-1   may be A.M between a and b
(b) Expand the following up to 1st 4 terms (1-x)1/2

8.(a) If cot θ= 5/2 and terminal arm of angle is in 1st quadrant , find the value of 3sinθ+4cosθ/cosθ-sinθ
(b) Reduce sin⁴ θ to an expression involving only function multiples of θ raised to 1st power

9.(a) Prove that in an equilateral triangle R: = 1:2:3
(b) Prove that tan^-1 ¼ + tan -1 1/5 = tan^-1  9/19