# Mathematics I - Unit Wise Questions

Unit 1: Set theory and Real & Complex Number
32 Questions

1.

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

1 marks | Asked in 2019-Objective |

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 marks | Asked in 2019-Objective |

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?

5 marks | Asked in 2019 |

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 marks | Asked in 2020-objective

2. Find the domain and range of the function

5 marks | Asked in 2019 |

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 marks | Asked in 2020-objective

1 iii) Range of the function  is,

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

1 marks | Asked in 2020-objective

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

5 marks | Asked in 2019 |

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)

1 marks | Asked in 2019-Objective |

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

5 marks | Asked in 2019 |

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 marks | Asked in 2019-Objective |

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

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

1 marks | Asked in 2020-objective

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 marks | Asked in 2019-Objective |

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

1 marks | Asked in 2020-objective

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

5 marks | Asked in 2019 |

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?

5 marks | Asked in 2019 |

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

a)  b)  c)  d)

1 marks | Asked in 2020-objective

1.

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

1 marks | Asked in 2019-Objective |

7. If  then show that x2 + y2 = 1.

5 marks | Asked in 2019 |

1.

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

a) 0    b) 1    c) 2    d) 3

1 marks | Asked in 2019-Objective |

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 marks | Asked in 2020-objective

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

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

1 marks | Asked in 2020-objective

1.

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

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

1 marks | Asked in 2019-Objective |

1 ix) Real part of the complex number  is,

a)                       b)                      c) 2                          d)

1 marks | Asked in 2020-objective

1.

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

1 marks | Asked in 2019-Objective |

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

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

10 marks | Asked in 2019 |

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 marks | Asked in 2020-objective

1.

x) If then, this is the equation of..

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

1 marks | Asked in 2019-Objective |

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

4 marks | Asked in 2019 |

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

5 marks | Asked in 2019 |

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)

5 marks | Asked in 2019 |

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)

6 marks | Asked in 2019 |

Unit 2: Relation, Functions and Graphs
0 Questions
Unit 3: Sequence and Series
0 Questions
Unit 4: Matrices and Determinants
0 Questions
Unit 5: Analytical Geometry
0 Questions
Unit 6: Permutation and Combination
1 Questions

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)

6 marks | Asked in 2019 |