Question Bank - Algebra - Hemant Malhotra
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Number of Questions : 100
Topic : Algebra
Answer key available ? : No
Source : Elite's Grid forum.
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Q 1) Let m be the minimum value of f(x) = |x - 1| + |2x - 1| + |3x - 1| + ... + |20x - 1|.
Let c be the minimum value of x for which f(x) = m. Determine c.
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Q 2) If a, b, c are roots of 3x^3 + 2x^2 + x + 3 = 0 find (1/a^2) + (1/b^2) + (1/c^2)
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Q 3) Find minimum value of x + y + z when xyz = 45, where x, y, z are different positive integers
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Q 4) Find number of real roots of x^3 + 5x^2 + 6x + 3 = 0
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Q 5) x, y and z are positive real numbers such that xyz = 32. Find the minimum value of x^2 + 4xy + 4y^2 + 2z^2
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Q 6) Find the minimum value of |x + 3| + |x - 3| + |x - 4| + |x - 5| + |x + 5|
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Q7) 2x^3 y^2 = 15^3 where y > 0 and 2x + 5y has its minimum value. Find value of x
a) 2/15
b) 15
c) 2
d) 15/2
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Q 8 ) Find total number of integer solutions of x^2 - y^2 = 1002
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Q 9) If a, b are integers then how many ordered pairs (a,b) satisfies the equation a^2 + ab + b^2 = 1
a) 6
b) 4
c) 2
d) 8
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Q 10) Number of roots of x^12 - x^6 + 1 = 0
a) 2
b) 4
c) 6
d) None of the above
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Q 11) How many Integral Solution for the equation |x-7| + |y| < =10 , y >= 0
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Q12) If the real numbers x and y satisfy x^3 - 3x^2 + 5x - 17 = 0 and y^3 - 3y^2 + 5y + 11 = 0, then the numerical value of x+y is
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Q 13) Find all positive integers x and y such that x^2 - 3xy - y = 0
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Q 14) How many ordered triples (a, b, c) satisfy the equation (a^2 − 1)^2 + (b^2 −4)^2 + (c^2 − 9)^2 = 0
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Q 15) In the expression m× (n)^p - q , the values of m,n,p, q are 0, 1, 2, and 3 although not necessarily in that order. What is the maximum possible value of the result?
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Q 16) what is the area enclosed by |3x| + |4y| = 12
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Q 17) a,b,c be nonnegative integers such that a+b+c=12. what is the maximum value of a × b × c + a × b + b × c + a × c
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