Inter (Part-I) Gujrawala Board 2016
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.

• The reference angle of tan θ = -1 equals:

(A)
(B)-
(C) –π
(D) π

• cot  is equal to:

(A)           
(B)
(C)
(D)

• The period of 2 cos x is:

(A) 4π 
(B) 2π
(C) π   
(D) 3π

• Cot2 θ- cos ec2 θ equal to:

(A) 2   
(B) 0
(C) 1   
(D) -1

• Sum of odd co-efficients in the expansion (1 + x)n is:

(A) n2 
(B) 2n-2
(C) 2n-1
(D) 2n

• The polynomial 3x2 + 2x + 1 has degree:

(A) 0
(B) 3
(C) 2
(D) 4

• ⁿC_r r! equals to:

(A) n+1Pr
(B) nPr+1
(C) n-1Pr
(D) nPr

• G.M. between I and    is:

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

• If a, p are the roots of equation x2 - 4x + 5 = 0 then α β equals to:

(A) 5   
(B) -4
(C) 2   
(D) 4

• If A = {0} then power of A is

(A) { 0 }         
(B) {0,ᶲ}
(C) {ᶲ,{0}}     
(D) { {0},ᶲ}

• tan-1[] equals to:

(A) tan-1 A + tan-1 B 
(B) cot-1 A + cot-1 B
(C) tan-1 A - tan-1 B   
(D) cot-1 A - cot-1 B

• Radius of the inscribed circle is:

(A) r=
(B) r=
(C) r=
(D) r=

• Sin 3α equals to:

(A) 3 sin α - 4sin3 α
(B) 3 sin α + 4 sin3 α
(C) 4 sin3 α-3 sin α
(D) 4 sin3 α + 3 sin α

• H.M between 3 and 7 is:

(A)
(B)
(C) 5
(D) 21

• If each element of a matrix is zero, then it is called:

(A) null matrix           
(B) identity matrix
(C) scalar matric        
(D) diagonal matric

• (r + 1) th term in the expansion of (a + b)n is:
  

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

• sin3a equals to:

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

•  is:

(A) proper fraction    
(B) improper fraction
(C) identity    
(D) decimal

• If A is non-singular matri then (At)t equals:

(A) At 
(B) A
(C) -At
(D) -A

• The property  aR , a= a is called:

(A) reflexive   
(B) symmetric
(C) transitive  
(D) commutative

Inter (Part-I) Gujrawala Board 2016
Mathematics
Part I (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

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

• Name the property used in the inequality -3< -2 = > 0 < 1
• Find the multiplicative inverse of -3 -5i.
• Factorize: a2 + 4b2.
• Write down power set of {9, 11}.
• Write converse and inverse of conditional P  q
• Define semi-group.
• Find x and y if
• Find inverse of the matrix
• Without expansion verify that
• Solve the equation x(x+7)=(2x-1)(x+4)
• Evaluate  )(1+,where w is cube root of unity.
• If α, β are the roots of 3x2 _2x+4 = 0, find the value of +

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

• Resolve  into partial fractions.
• Which term of the A.P. -1, 4, 10, …is 148?
• Find the geometric mean of -2i and 8i.
• If y = 1 + x/2 + x²/4 + .......... show that x = 2(y-1)/y
• If 1/k , 1/(2k-1) and 1/(4k-1) are in H.P, find k 
• Write (n + 2)(n + 1)(n) in factorial form.
• Evaluate ²⁰P₃ without calculator.
• If ⁿC₈ = ⁿC₁₂, then find n.
• Define mutually exclusive events.
• Calculate (9.98)4 by means of binomial theorem.
• Prove the formula r +r2+r3+….r3= for n = 1 and 2.
• If 'x' is so small that its square and higher powers can be neglected, then show show that    

4. Write short answers to any NINE questions:                  (2x9=18)

• Define radian.
• Evaluate
• Prove that (sec θ- tan θ)2 =
• Prove that  
• Prove that 1+ tan α tan 2 α= sec 2 α
• Prove that sin(α + β)-sin(α -β) = 2 cos α sin β
• Write the domain and range of a cosine function.
• Define angle of elevation.
• The area of triangle is 121.34. If α = 32° 15' , β = 65° 37'. Find c.
• Prove that R = .
• Show that cos(sin-lx) =
• Solve sin x cos x = ,xϵ[0,2π]
• Solve tan2 0=,θϵ[0,π]

SECTION-II

NOTE: - Attempt any three questions. 10 x3=30

Question #5.        
(a) Use Cramer's rule to solve the system  (5)

Question #6.            
(a) Resolve into partial fractions:     (5)
(b) Insert four harmonic means between the given numbers 4 and 20.     (5)

Question #7.        
(a) Find the numbers greater than 23000 that can be formed from the digits 1, 2, 3, 5, 6, without repeating any digit.    (5)
(b) If …….., then prove that y2+2y-4=0             (5)
Question #8.        
(a) If cosec θ  and m > 0(0<θ< ), find the values of remaining trigonometric ratios.    (5)
(b) Prove that sin 10° sin 30° sin 50° sin 70° =
Question #9.        
(a) Prove that ∆ = r2 cot cot cot       (5)
(b) Prove that 2 tan-1 + tan-1=       (5)