INTERMEDITE
PART-I (11 CLASS)
MATHEMATICS
TIME ALLOWED: 30 Minutes
OBJECTIVE
MAXIMUM MARKS: 2
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. Attempt all many question as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not solve question on this sheet of OBJECTIVE PAPER

Q.NO.1          

• ⁿP_n equals
  

A. n!
B. (n + 1) !
C. !
D. n

• General term of the expansion (a+b)ⁿ is:
  

A. (n_r) a^n-r, b^n-r
B. (n_r) a^n-r, b^r
C. (n_r) aⁿ, b^n-r
D. (n_r) aⁿ, bⁿ

• If n is integer then n² > n – 3 is ture for:
  

A. n ≥ 3
B. n ≥ 2
C. n ≥ 1
D. n < 3

• Area of a sector of circular region of radius r equals:
  

A. r²ɵ
B. ½ r²ɵ
C. 2 r²ɵ
D. 1/3 r²ɵ

• The sum of all the angles of the triangle is
  

A. 360°
B. 270°
C. 180°
D. 90°

• The Period of 3 sin x/3 is
  

A. π
B. 2 π
C. 3 π
D. 6 π

• The circum radius R is equal to
  

A.
B.
C.
D.

• For a triangle ABC with usual notations equals:
  

A. tan α
B. tan α/2
C. cot α
D. cot α/2

• The domain of the principal sine function is :
  

A.
B.
C.
D. [0, 2π]

• If cosx = -1/2 then the reference angle is:
  

A. π/3
B. -π/3
C. π/6
D. -π/6

• Every Recurring Decirnal or Terminating Decimal is:
  

A. Rational number
B. Irrational number
C. Integer
D. None of these

• Which of the following is Unary Operation?
  

A. Addition   
B. Multiplication
C. Square root
D. Division

• Transpose of a diagonal matrix is:-
  

A. Scalar matrix         
B. Diagonal matrix
C. Row matrix
D. Null matrix

• If the matrix  is singular then ƛ equals:
  

A. 2
B. 4
C. 6
D. 8

• If ω is cube root of unity than ω²⁹ + ω²⁸ + 1 equals:
  

A. 0
B. 1
C. 2
D. 3

• The graph of quadratic function is:
  

A. Triangle
B. Parabola
C. Square
D. None of these

•  is a

A. Proper fraction
B. Improper fraction
C. Equation
D. Both A and B

• Sum of terms of an A.P is called:-
  

A. Geometric Series
B. Arithmetic Series
C. Arithmetic Progression
D. Harmonic Progression

• is convergent if
  

A. |r| < 1
B. |r| > 1
C. r = 1
D. r = -1

• When a dice is ro11ed the probability of even number is:-
  

A. 3    
B. ½
C. 2
D. 5

INTERMEDIATE
PART-I (11 CLASS-2013)
MATHEMATICS
TIME ALLOWED: 2.30 Hours
SUBJECTIVE
MAX MARKS: 80
NOTE: Write same question number and its part number on answer book, as given in the question paper.

SECTION-I

2. Attempt any eight parts.  (8 x 2=16.)

• Prove that a/b=c/d if' ad=bc.
  
• Simplify (2, 6) (3, 7),
  
• Write two proper sub sets of the set (a. b, c)
  
• Write the converse and the inverse of the conditionals ~p→q                                                             
  
• Define Singular and Non-Singular Matrices.
  
• Find x and y if
  
• Find the inverse of
  
• Define symmetric matrix.                                                                                       
  
• Solve the equation 9x² - 12x - 5 = 0
  
• Evaluate (1 + ω - ω²)4
  
• Discuss the nature of the roots of the equation 4x2 + 6x + I = 0.
  
• Use the Remainder Theorem to find the remainder when first polynomial is divided by the second polynomial x² + 3x + 7, x + 1

3. Attempt any right parts. (8 x 2 = 16)

• Resolve into partial fractions (7x + 25) / (x + 3)(x+ 4).
  
• What is an Identity?
  
• If the 5th term of an A.P is 16 and 20th term is 46. What is its 12th term?
  
• Sum the series: (x - a)+(x + a)+ ( x + 3a )+----------------- to n terms.
  
• Define G.M. between two numbers a and b.
  
• If A, G, H are Arithmetic, Geometric and Harmonic Means between a and b then show that A x H = G².
  
• Find the values of n and r when “Cr = 35 and “Pr = 210
  
• How many signals can be given by 6 flags of different colours when all numbers of flags can be used?
  
• Determine the probability of getting two heads in two successive tosses of a balanced coin
  
• There are 5 green and 3 red balls in a box, one ball is taken out, Find the probability that the ball is green
  
• Using Binomial expansion, expand (2a – x/a)³
  
• Using Binomial expansion, find the value of √99 upto 3 places of decimals

4. Attempt any nine parts. (9 x 2=18)

• Find r when ℓ = 56cm, ɵ = 45°.
  
• Prove the identity, cos² ɵ  sin²ɵ =              
  
• Write formulas for cos²α and tan²α in terms of α
  
• Prove that = tan 56°
  
• Express sin (x + 30°)+ sin( x - 30°)as product.
  
• Prove that cos (α + 45°)=1/√2(cosα - sinα).
  
• Find the period of the function 3cosx/5
  
• What do you mean by solution of a triangle?
  
• Write Law of Tangents for sides b and c
  
• Find the measure of the greatest angle, if sides of the triangle are 16, 20, 33.
  
• Sides of a triangle ABC are a= 13, b =14, c = 15, Find R and r₁
  
• Solve the equation sec²ɵ=4/3
  
• Solve the equation sin²x = cos x.

SECTION-II

Attempt any three questions. (3 x 10 = 30)

5.(a) Show that the set {1, ω, ω² }, when ω³ = 1 , is an Abelian group w.r.t ordinary multiplication.
(b) Solve the system of linear equations by Cramer's rule.

6.(a) Use Synthetic division to find the values of p and q if (x+ 1) and (x - 2) are the factors of the polynomial x3 + px2 + qx + 6.
(b) Resolve  into partial fraction.

7.(a) The ratio of the sums of n terns of two series in A.P. is 3n+2:n+1. Find the ratio of their 8th terms.
(b) If x is so small, its square and higher powers can be neglected, then show that

8.(a) Find the values of the trigonometric functions of the angle - 675°

(b) Prove that Sin10° Sin30° Sin50° Sin70° = 1/16

9.(a) Solve the triangle ABC if a = 53 , B=88°36', y = 31°54'
(b) Prove that Sin^-1 3/5 + Sin^-1 8/17 = Sin^-1 77/85