CAT2017Shift-2Questions Related Question Answers
76. A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B7
77. Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is
78. Consider three mixtures — the first having water and liquid A in the ratio 1:2, the second having water and liquid B in the ratio 1:3, and the third having water and liquid C in the ratio 1:4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4: 3: 2. Then the resulting mixture has
79. Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
80. The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is
81. The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y =3x+c,then c is
82. ABCD is a quadrilateral inscribed in a circle with centre O. If $$\angle COD = 120$$ degrees and $$\angle BAC = 30$$ degrees, then the value of $$\angle BCD$$ (in degrees) is
83. If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
84. Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB,BC,and CA is $$4(\sqrt{2}-1)$$ cm,then the area, in sq cm, of the triangle ABC is
85. If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is
86. If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?
87. Let $$f(x) = x^{2}$$ and $$g(x) = 2^{x}$$, for all real x. Then the value of f[f(g(x)) + g(f(x))] at x = 1 is
88. The minimum possible value of the sum of the squares of the roots of the equation $$x^2+(a+3)x-(a+5)=0 $$ is
90. If $$log(2^{a}\times3^{b}\times5^{c} )$$is the arithmetic mean of $$log ( 2^{2}\times3^{3}\times5)$$, $$log(2^{6}\times3\times5^{7} )$$, and $$log(2 \times3^{2}\times5^{4} )$$, then a equals
91. Let $$a_{1},a_{2},a_{3},a_{4},a_{5}$$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $$2a_{3}$$ If the sum of the numbers in the new sequence is 450, then $$a_{5}$$ is
92. How man Y different pairs(a,b) of positive integers are there such that $$a\geq b$$ and $$\frac{1}{a}+\frac{1}{b}=\frac{1}{9}$$?
93. In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
94. How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
95. If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
97. An infinite geometric progression $$a_1,a_2,...$$ has the property that $$a_n= 3(a_{n+1}+ a_{n+2} + ...)$$ for every n $$\geq$$ 1. If the sum $$a_1+a_2+a_2...+=32$$, then $$a_5$$ is
98. If $$a_{1}=\frac{1}{2\times5},a_{2}=\frac{1}{5\times8},a_{3}=\frac{1}{8\times11},...,$$ then $$a_{1}+a_{2}+a_{3}+...+a_{100}$$ is
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