Question Bank  Algebra  Hemant Malhotra

Number of Questions : 100
Topic : Algebra
Answer key available ? : No
Source : Elite's Grid forum.

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.

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)

Q 3) Find minimum value of x + y + z when xyz = 45, where x, y, z are different positive integers

Q 4) Find number of real roots of x^3 + 5x^2 + 6x + 3 = 0

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

Q 6) Find the minimum value of x + 3 + x  3 + x  4 + x  5 + x + 5

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

Q 8 ) Find total number of integer solutions of x^2  y^2 = 1002

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

Q 10) Number of roots of x^12  x^6 + 1 = 0
a) 2
b) 4
c) 6
d) None of the above

Q 11) How many Integral Solution for the equation x7 + y < =10 , y >= 0

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

Q 13) Find all positive integers x and y such that x^2  3xy  y = 0

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

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?

Q 16) what is the area enclosed by 3x + 4y = 12

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

