Mathematics I - Unit Wise Questions

1. Circle(O) the correct answer.

i) If A ={ x : x is a triangle}, B = {x : x is an isosceles triangle} and C = {x : x is an equilateral triangle}then,

a) A ⊂ B ⊂ C      b) C ⊂ B ⊂ A     c) B ⊂ C ⊂ A       d) B ⊂ A ⊂ C

1.

ii) If and g(x) = x + 1 then, what is the value of gof( x)?

1.

i) If A = [-1,3) and B = [2,5], then A-B is equal to

a) [-1,2)    b) [-1,3)    c) (-1,2)    d) [-1,3]

1. In class of 100 students 40 students failed in Mathematics, 70 failed in English and 20 failed in both subjects. Find

a) How many students passed in both subjects?

b) How many students passed in Mathematics only?

c) How many students failed in mathematics only?

2. Find the domain and range of the function 

1 ii) If A, G, H are the Arithmetic mean, Geometric mean and Harmonic mean between two positive numbers then,

a) A < G < H   b)A > H > G    c) G < A < H     d) A > G > H

1.

iii) What is the reciprocal of the complex number (2,1)?

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

3. Find the Maclurin series of the function f(x) = sinx.

1 iii) Range of the function  is,

a)(-2 , 2)     b)[-2, 2)     c) [-2, 2]       d) (-2, 2] 

1.

iv) What type of function  y = f(x) = ax² + bx + c is?

a) Constant function    b) Linear function    c) Identity function    d) Quadratic function

4. Prove that  = (x - y) (y - z) (z - x).

1 iv) The sum of the series given by  is equal to

a) e - 2    b) e      c) e - 1      d) 

1.

v) Geometrical meaning of scalar triple product of three vectors  is the

a) Volume of parallelepiped formed by  as adjacent sides

b) x  Projection of  on and 

c) x  Projection of  on 

d)

1 v) If the order of matrix A is m x n and order of matrix B is n x m, then the order of the matrix AB is,

a) n x n       b) m x n       c) n x m          d) m x m

5. Find a unit vector perpendicular to the plane containing points P(1, -1, 0), Q(2, 1, -1) and R(-1, 1, 2).

1 vi) Length of the Latus rectum of the parabola 2y2 - 9x = 0 is,

a)  b)  c)  d)

1.

vi) If a, b, c is in H.P then, what is the value of b?

6. In how many ways can be letter of words “Sunday” be arranged? How many of these arrangement begin with S? How many begin with S and don’t end with y?

7. If  then show that x² + y² = 1.

1 vii) Which of the following statement is not true?

a) is a vector        b) is a vector

c) is a vector          c) is a vector

1.

vii) Which of the following is the rank of the Matrix  ?

a) 0    b) 1    c) 2    d) 3

1 viii) How many triangles can be formed by joining six non-collinear points.

a) 80               b) 40                    c)160              d)240

1.

viii) In how many ways 6 persons can seat in a round table?

a) 720      b) 360      c) 120      d) 60

1.

ix) Let , and a map  defined by T(x)=A(x) then what is the image of  under T?

1 ix) Real part of the complex number  is,

a)                       b)                      c) 2                          d) 

8. a) Define conic section. Find the coordinates of vertices, eccentricity and foci of the ellipse

    9x² + 4y² - 18x - 16y - 11 = 0. (1+5)

1.

x) If then, this is the equation of..

a) Parabola    b) Hyperbola    c) Ellipse    d) Circle

x) If S₁ is the sum of first n natural numbers and S₂ is the sum of cubes of first n numbers then,

a) S₁ =          b)  = S₂               c)S₁ = 3S₂            d) S₂ =

    b)  If   T(x₁, x₂) = (x₁ + x₂, x₂, x₁)defined by be the linear transformation, then find matrix associated with linear map T. (4)

9. a) Define irrational number. Prove that √2 is an irrational number. (1+4)

b) If functions  defined by f(x) = 2x + 1 and  defined by g(x) = x² - 2. Find the formulae for composite functions  and also verify that  (4+1)

10. a) If arithmetic mean, geometric mean and harmonic mean between two unequal positive numbers are A, G, H respectively. Then prove that A > G > H. (4)

    b) What is the relation between permutation and combination of n objects taken r at a time?  A committee of 5 is to be constituted from 6 boys and 5 girls. In how many ways can this be done so as to include at least a boy and a girl? (1+5)