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Sequences and S...

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  • Question 1
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    6,10,18,34,666, 10, 18, 34, 66
    The first number in the list above is 66. Determine a rule for finding each successive number in the list.

  • Question 2
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    m,2m,4m,...m, 2m, 4m, . . .
    The first term in the sequence above is mm, and each term thereafter is equal to twice the previous term. If mm is an integer, which of the following could NOT be the sum of the first four terms of this sequence?

  • Question 3
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    For all numbers a and b, let ab\displaystyle a\bigodot b be defined by ab=ab+a+b\displaystyle a\bigodot b=ab+a+b. Then for the numbers xx, yy and zz, which of the following is/are true?
    I. xy=yx\displaystyle x\bigodot y=y\bigodot x
    II. (x1)(x+1)=(xx)1\displaystyle \left( x-1 \right) \bigodot \left( x+1 \right) =\left( x\bigodot x \right) -1
    III. x(y+z)=(xy)+(xz) \displaystyle x\bigodot \left( y+z \right) =\left( x\bigodot y \right) +\left( x\bigodot z \right) 

  • Question 4
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    In the xyxy-plane, the vertices of a triangle are (1,3),(6,3)(-1,3), (6,3) and (1,4)(-1,-4). The area of the triangle is ___ square units.

  • Question 5
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    If mn=m+(m1)+(m2)+......+(mn)m * n = m+(m-1)+(m-2)+ ...... +(m-n), evaluate 757 * 5.

  • Question 6
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    Let n\boxed { n } be defined as (n+2)!(n1)!\frac{(n+2)!}{(n-1)!}, what is the value of 73\frac{\boxed{7}}{\boxed {3}} ?

  • Question 7
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    If ab=6×a3×ba\odot b = 6\times a - 3\times b, evaluate (53)20(5\odot 3) \odot 20

  • Question 8
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    In fig., the area of triangle ABC (in sq. units) is:

  • Question 9
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    Area of the triangle formed by the points (0,0),(2,0)\left( 0,0 \right) ,\left( 2,0 \right) and (0,2)\left( 0,2 \right) is 

  • Question 10
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    Consider an incomplete pyramid of balls on a square base having 1818 layers; and having 1313 balls on each side of the top layer. Then the total number NN of balls in that pyramid satisfies

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