Inter (Part-I) Gujrawala Board 2015
Mathematics
Part I (Objective Type)
Time Allowed: 30 Minutes 
Max. 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.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• An equation containing at least one trigonometric function is called:

(a) Algebraic equation        
(b) Equation
(c) Linear equation            
(d) Trigonometric equation                                                                                                                                                                                                               

• tan-1(-√3 )

(a) 2π/3                 
(b) -2π/3     
(c) -π/6      
(d) + π/3

• In a right triangle, no angle is greater than:

(a) 90°                 
(b) 80°       
(c) 60°
(d) 45°

• The period of sin 2x is:

(a) π/3                  
(b) π/2       
(x)2π/3         
(d) π

• sin (θ + 270°) = ______.

(a) cot θ                
(b) tan θ                
(c) sin θ      
(d) -cosθ

• If cot θ >θ and sin θ < θ, then terminal arm of angle lies quadrant _______.                                                                                  

(a) I                          
(b) II                  
(c) III               
(d) IV

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

(a) a⁷                           
(b)7a⁶b              
(c) 7ab⁶       
(d) 0                                                                                                       

• The coefficient of last term in expansion of (a - b)5 is:

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

• The value of 6P1 is:

(a) 18                          
(b) 12              
(c) 6             
(d) 0

• 5! =___________.

(a) 140                       
(b) 120          
(c) 5                  
(d) 0

• Common difference of arithmetic sequence 3, 5 , 7, ... is:

(a) -2/15       
(b) 2/15         
(c) 5      
(d) 1/2

• The G.M. between 1 and 16 is

(a) -4        
(b) 4         
(c)+4       
(d) 1/4                                    

• x3+1/(x - 1)(x1+ 1) is a:

(a) Proper fraction       
(b) Improper fraction       
(c) Relation   
(d) Equation

• Product of all cube roots of unity is:

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

• If one root of x2- 3x + a= 0 is 2, then a =

(a)-2           
(b) 2                  
(c) 0            
(d)-3

• [0] is a_______matrix.                                                                                                                                                                      

(a) spare        
(b) unit           
(c) rectangular         
(d) scalar

• If A=  and |A|  = 1, then x=.      

(a) 0              
(b) 1              
(c) 2           
(d) 3

• If A ={ }, then P(A) = _____

(a) empty set         
(b) {0}             
(c) {ϕ}   
(d) 0                                                                                                                              

• If  ACB, then A∪B is.

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

• If n is prime, then √n  is:

(a) Rational number      
(b) Whole number
(c) Natural number       
(d) Irrational number

Inter (Part-I) Gujrawala Board 2015
Mathematics
Part I (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

Q2. Write short answer to any eight questions:                                         (2x8=16)

• Simplify (-i) 19
• Find multiplicative inverse of (2, 4).                    
• Find power set of {a,{b, c }}.
• Prove that A-B = AUBc.
• Write converse and contra positive of p--->q.
• Write the inverse of {(1, 2),(2, 5),(3, 7),(4, 9),(5, 11)}.
• Find x and y if  =
• Solve for matrix A if  A- =
• Prove without expansion = 0
• Reduce x-2-10 = 3x-1 to quadratic form.
• Show that x3 — y3 = (x — y)(x ɷy)(x — ɷ2y).
• If n is an odd integer, is x + a factor of xn+ an?

Q3. Write short answers to any EIGHT questions:                                            (2x8=16)

• Define proper and improper fraction.
• Find 13th term of the sequence x, 1, 2, —x, 3 —x,...
• Find A.M between x-3 and x+5.
• If 1/a ,1/b and 1/c are in G.P, show that r =+
• With usual notation show that AH = G2.
• How many signals can be given by 5 flags of different colours using 3 flags at a time?
• Find n when ⁿC₁₂ = ⁿC₆.
• How many triangles can be formed by joining the vertices of 5 sided figure?
• Evaluate ⁿC₁₇ without calculator.
• Using binomial theorem, expand 4
• Find the.6th term in the expansion of 10
• Expand (8-2x)-1 up 2 terms.                                                                                          s

Q4. Write short answer to any NINE questions:                                                    (2x9=18)

• Convert 150° into radians.
• Find value of cos θ without using table if θ  = 36°.
• Prove that tan (270°- θ) = cot θ.
• Find the value of sin 150° without using table.
• Prove that cos 330° sin 600° + cos 120° sin 150° = -1.
• Find the period of sin 4x.
• Find the value of tan α/2 in terms of s.                                        i
• Show that r1= S tan α/2- .
• Solve ΔABC, if b =125, y = 53°, α = 47°,
• Defined an escribed circle.
• Find the value of cos-1(-1/2)                                                                 
• Solve cosec2θ =4/3 in [θ, 2π].
• Solve sin x =1/2 in [θ,2π].

                                                               (Section-II)

Question #5
(a) Show that = l2 (3a + =l).       5
(b) If the roots of px2 + qx + q = 0 are α,β, then prove that  + + = 0              5

Question #6
(a) Resolve 1/(x + 1)(x + 1) into partial fractions.                                              5
(b) Find n, so that   may be A.M between a and b.

Question #7
(a) How many 6-digit numbers can be formed from the digits 2, 2, 3, 3, 4, 4? How many of them with lie between 400,000 and 430,000?                                                                                                          5
(b) Use binomial theorem to show that 1 + 1/4 + 1.3/4.8 + 1.3.5/4.8.12…..     5

Question #8
(a) Find the values of the remaining trigonometric functions of 0, if cos = 12/13 the terminal side of the angle is not in the I Quadrant.                                                                                                        5
(b) Prove that (without calculator) sin 10° sin 30° sin 50° sin 70° = 1/16                                                                                                               5

Question #9
(a)With usual notations, prove that r1 + r2 + r3- r = 4R.                              5
(b) Prove that 2 tan-11/3 + tan-11/7=π/4                                                             5