Maths 1 Qualifier important questions

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1. Q4Below is a list of real numbers: 3,, 2.5,, e49,, 7/12.22,, ,, -35,, 6,, 1729,, -2000 How m
2. Q5Below is a list of real numbers: 3,, 2.5,, e49,, 7/12.22,, ,, -35,, 6,, 1729,, -2000 How m
3. Q6Which of the following sets are the same? (i) Ankhita, Keerthana, Raju, Suresh (ii) Raju,
4. Q7Which of the following statement(s) is(are) false?
5. Q8Let M be the set of all days in a week whose starting letter is either 'S' or 'T', and N b
6. Q9Which of the following is a correct representation of set comprehension?
7. Q10Which of the following set comprehensions define squares of the first 100 natural numbers?
8. Q11Which of the following statement(s) is (are) true?
9. Q12Which of the following intervals are subsets of [2,3]?
10. Q13Two finite sets A and B are such that the total number of subsets of A is 56 more than the
11. Q14Let A=1,4 and B=2,4,6,8. Which of the following is the Cartesian product of A and B?
12. Q15Let B=Anil, Ramu, Suraj and G=Neha, Keerthi be the sets of boys and girls respectively. Ra
13. Q16Let f(x)=|x|+5 and Dom(f)=xR f(x)R. Which of the following is(are) true?
14. Q17Suppose f:ZZ is a function defined by f(x)=ax+b. For which of the following integer values
15. Q18If Dom(f)=xR f(x)R and f(x)=x+12/4x-8, then the domain for the function f is:
16. Q19The product of the minimum value of function f(x)=9|x|-8 and the maximum value of the func
17. Q20Let us define a function f:NN as follows: Which of the following is true?
18. Q21If f(x)=14-(3x+35-5x/4), then the domain for the function f is:
19. Q22Given below is a Venn diagram for sets of students who take Maths, Physics, and Statistics
20. Q23Let A be the set of all even natural numbers (including zero), B be the set of all odd nat
21. Q24Which of the following are irrational numbers?
22. Q25Suppose f:DR is a function defined by f(x)=x2-9x+3, where D is the domain. Let A be the se
23. Q26In a Zoo, there are 6 Bengal white tigers and 7 Bengal royal tigers. Out of these tigers,
24. Q27Consider the relation R=(x,y) x-y=0RR on the set R. Which of the following is/are true?
25. Q28Which of the following is/are true?
26. Q29Consider the following sets: A=xN x 2=0 and 1<= x<= 10 B=xN x 5=0 and 6<…
27. Q30Consider the set A=3k kN. Define a function f:N A, such that f(n)=6n. Which of the followi
28. Q31Which of the following gives the area A of a triangle whose vertices are P(x_1,y_1), Q(x_2
29. Q32Which of the following is/are correct with respect to the slope of a line?
30. Q33If l_1 and l_2 are lines parallel to each other with slopes m_1 and m_2 and with inclinati
31. Q34If lines are perpendicular to each other with slopes m_1 and m_2 and with inclinations and
32. Q35If the relation between x and y is as shown in the table below, then which among the follo
33. Q36The table shows the different types of energies consumed (approximate values, in TWh) in y
34. Q37The table shows the different types of energies consumed (approximate values, in TWh) in y
35. Q38A plane begins to land when it is at a height of 1500 metres above the ground. It follows
36. Q39We plot the displacement (S) versus time (t) for different velocities as it follows the eq
37. Q40A woman is reported missing in a locality. The police department finds a human femur bone
38. Q41A new detective agency came up with a relationship H=mf+70, where H is the height of a mal
39. Q42A rock is thrown in a pond and creates circular ripples whose radius increases at a rate o
40. Q43State Government wants to connect the state road to the national highway from a town. Ther
41. Q44Find out the perimeter of the triangle formed by the intersections of following 3 lines: L
42. Q45Suppose that P_1 and P_2 are points in a Cartesian coordinate system, with P_1 located at
43. Q46Suppose that P_1 and P_2 are points in a Cartesian coordinate system, with P_1 located at
44. Q47Mr. Mehta has two sons. Both sons send money to their father each month separately as M_1(
45. Q48A civil engineer found that the durability d of the road she is laying depends on two func
46. Q49A company's profits are known to be dependent on the months of a year. The profit pattern
47. Q50Raghav sells 2000 packets of bread for Rs. 20 each day and makes a profit of Rs. 4,000 per
48. Q51A farmer has a wire of length 576 metres. He uses it to fence his rectangular field to pro
49. Q52Find out the points where the curve y=4x2+x and the straight line y=2x-3 intersect with ea
50. Q53Let a and b be two consecutive positive odd natural numbers such that a2+b2=394. Then find
51. Q54Based on the figure, which of the following is/are correct?
52. Q55Find the quadratic polynomial which when divided by (x-2), (2x-1) and (x+1) gives the rema
53. Q56Box A has length z unit, breadth (z+1) unit, and height (z+2) unit. Box B has length (z+1)
54. Q57The population of a bacteria culture in laboratory conditions is known to be a function of
55. Q58Let r(x) be a polynomial function which is obtained as the remainder after dividing the po
56. Q59Given that P(x) and Q(x) are two non-zero polynomials of degrees m and n respectively. Let
57. Q60Let f:RR and g:RR be two functions, defined as f(x)=x4-8x2+7 and g(x)=-2f(x) respectively.
58. Q61Which among the following functions first increases and then decreases in all the interval
59. Q62An ant named B wants to climb an uneven cliff and reach its anthill. On its way home, B ma
60. Q63Consider a polynomial function f(x)=-1/300(x-2)2(x-3)(x+1)2(x+4)(x-5). Choose the correct
61. Q64Consider the following polynomial p(x) whose graph is given below: Which of the following
62. Q65Consider two polynomials p(x)=-x5+5x4-7x-2 and q(x)=-x5+5x4-x2-2. Which of the following o
63. Q66Mahesh has four sons (Shubh, Rabi, Mahendra, and Rajat). Shubh has two sons (Yashubh and N
64. Q67Consider the functions f:N0N0 and g:N0N0 given by: Wh…
65. Q68Consider the relations R_1 and R_2 on N i.e., R_1NN and R_2NN, d…
66. Q69A mobile company wants to launch its new model in collaboration with a network provider na
67. Q70Find the y-coordinate of the point of intersection of straight lines represented by: Given
68. Q71In a survey of 400 students, 220 students like Mathematics, 180 students like Physics, and
69. Q72In a survey among 250 students in Bandipur House of IITM BS degree, the following data wer
70. Q73You are monitoring your mobile data usage over time. Whenever the data usage reaches a fix
71. Q74A small cafe records, over five days, the number of hours (x) a barista works and the corr
72. Q75Mrs. Riya is a researcher, she does research on the decay of the quality of mango. She pro
73. Q76Suppose the line y=2x+k is the best fit line using SSE for the data set given in Table 1 f
74. Q77Consider a polynomial p(x)=0.3x3(x2-1)(x-2)2(x-3) and the following figures. Which of the
75. Q78Consider the polynomial p(x)=-(x+4)7(x-4)3(x+12)6. What is the degree of p(x)?
76. Q79Consider the polynomial p(x)=-(x+4)7(x-4)3(x+12)6. Calculate the number of turning points
77. Q80Consider a relation R defined on the set A=4,6,8,10,12 as R=(x,y):y=x+2. Which among the f
78. Q81Consider the following relations defined on the set of integers: - R_1=(x,y): x,yZ and |x-
79. Q82Suppose A is the set of odd positive integers less than or equal to 20, and B is the set o
80. Q83Consider a set S=a aN, a<= 10. Let R_1 and R_2 be relations on S S defined as R_1=(x,y) x,
81. Q84Consider the following relations defined on the set of integers: Choose the correct option
82. Q85If the slope of the parabola y=ax2+bx+c, where a,b,cZ, at x=3 and x=2 is 16 and 12 respect
83. Q86Consider a quadratic function q(x)=ax2+bx+c, where a,b,cR and a0 with the following inform
84. Q87Consider a quadratic function f(x)=2x2+4x+d. The y-intercept of f(x) is 5. Suppose the str
85. Q88Let l be the equation of line which passes through the point (1,6) and parallel to y=7x+6.
86. Q89Consider two polynomials p(x)=x4+3x3-9x+8 and q(x)=(x2+x)(x+3). Let r(x) be the remainder
87. Q90If x+a is one of the factors of find the value of a.
88. Q91Consider the following three straight lines: Which of the following options is true?
89. Q92If and are the roots of the equation x2+4x+1=0, then the equation whose roots are 2 and 2
90. Q93The Cartesian product B B has 16 elements. Two of the elements of the Cartesian product ar
91. Q94find the cardinality of
92. Q95A quadratic equation of the form ax2+bx+c=0 has its vertex at (3,-2) and its y-intercept a
93. Q96One root of the quadratic equation is three times the other root. If both roots are positi
94. Q97A quadratic equation has roots and . It is given that and Which of the following is the qu
95. Q98Consider the points Suppose the point B divides the line segment AC internally in the rati
96. Q99The distance between the parallel lines 3x+4y+c_1=0 and 3x+4y+c_2=0 is 4, where c_2>c_1>0.
97. Q100Aman and Prakash want to solve a quadratic equation. Aman made a mistake in writing down t
98. Q101Consider the polynomial p(x)=3(x-2)4(x+1)7(x-5)2. At how many of its real zeros does the g