Mathematics I - Unit Wise Questions

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?

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

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) Range of the function  is,

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

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

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)

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

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

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).

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?

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?

7. If  then show that x² + y² = 1.

1.

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

a) 0    b) 1    c) 2    d) 3

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 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) Real part of the complex number  is,

a)                       b)                      c) 2                          d) 

1.

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

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

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

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 =

1.

x) If then, this is the equation of..

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

    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)