CAT2003L Related Question Answers
76. There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters) of the triangle ABC would be
77. Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m, which one of the following is necessarily true?
78. Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centers at P and R respectively, and S is the center of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi-circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to
79. In the figure below, ABCDEF is a regular hexagon and $$\angle{AOF}$$ = 90° . FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?
80. How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that x < y, z < y and x $$\neq$$ 0 ?
81. A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose $$\angle{APB}$$ = 60° then the relationship between h and b can be expressed as
82. In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to
83. In the diagram given below, $$\angle{ABD}$$ = $$\angle{CDB}$$ = $$\angle{PQD}$$ = 90° . If AB:CD = 3:1, the ratio of CD: PQ is
84. There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is
86. If $$log_3 2, log_3 (2^x - 5), log_3 (2^x - 7/2)$$ are in arithmetic progression, then the value of x is equal to
87. In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If $$\angle{ACD}$$ = y degrees and $$\angle{AOD}$$ = x degrees such that x = ky, then the value of k is
88. In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?
89. Given that $$-1 \leq v \leq 1, -2 \leq u \leq -0.5$$ and $$-2 \leq z \leq -0.5$$ and $$w = vz /u$$ , then which of the following is necessarily true?
90. There are 6 boxes numbered 1,2,… 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
91. Consider the following two curves in the x-y plane:$$y = x^3 + x^2 + 5$$$$y = x^2 + x + 5$$Which of following statements is true for $$-2 \leq x \leq 2$$ ?
92. In a certain examination paper, there are n questions. For j = 1,2 …n, there are $$2^{n-j}$$ students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is
93. If x, y, z are distinct positive real numbers the $$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ would be
94. A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition
95. The number of positive integers n in the range $$12 \leq n \leq 40$$ such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n is
96. Let T be the set of integers {3,11,19,27,…451,459,467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is
97. Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 - E1 on OR, and then on the chord road E1 - N2. What is the radius of the outer ring road in kms?
98. Amit wants to reach E2 from N1 using first the chord N1 - W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question?
99. The tone that the author uses while asking “what French winemaker will ever admit that?” is best described as
100. What according to the author should the French do to avoid becoming a producer of merely old fashioned wines?
Powered By:Omega Web Solutions© 2002-2017 Omega Education PVT LTD...Privacy | Terms And Conditions