Quant Boosters  Kamal Lohia  Set 7

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Number of Questions: 30
Topic: Quant Mixed Bag
Answer key available?: Yes
Source: Quant Masters Forum

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q1) Find sum of all real x such that x² + x  2x√(x  2)  6 = 0.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q2) How many triplets of prime numbers (x, y, z) satisfy x(x + y) = z + 120?

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q3) Find pair of positive integers (m, n) such that the quadratic equation 4x²  2mx + n = 0 has two real roots both of which are between 0 and 1.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q4) Solve the equation {√(2 + √3)}ⁿ + {(2  √3)}ⁿ = 4 for real n.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q5) Let S be the sum of reciprocals of two real roots of the equation (a²  4)x² + (2a  1)x + 1 = 0 where a is a real number, find the range of S.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q6) Let a, b be two real number, a > 0 and the equation x  a  b = 5 has three distinct roots, find the value of b

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q7) Find f(x) such that 2f(1  x) + 1 = xf(x).

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q8) Find sum of all real x such that (x  1)^4 + (x + 3)^4 = 82.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q9) Let x₁, x₂ be the two real roots of the quadratic equation x² + x  3 = 0, find the value of x₁³  4x₂² + 19.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q10) If x₁, x₂ be the two real roots of the quadratic equation x² + ax + a  1/2 = 0, find the value of a such that (x₁  3x₂)(x₂  3x₁) reaches the maximum value.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q11) Find the number of positive integral solutions (x, y) such that:
x√(y) + y√(x) = √(2013x)  √(2013y) + √(2013xy) = 2013.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q12) Given f(1) = 1/5 and when n > 1, {f(n  1)}/f(n) = {2nf(n  1) + 1}/{1  2f(n)}, find f(n).

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q13) Given 2x + 6y ≤ 15, x ≥ 0, y ≥ 0, find the maximum value of 4x + 3y.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q14) Find the product of maximum and minimum possible value of real y such that y = (x²  x + 1)/(x² + x + 1) where x is a real number.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q15) Hexagon ABCDEF is inscribed in a circle. The sides AB, CD, and EF are each x units in length whereas the sides BC, DE, and FA are each y units in length. Then, the radius of the circle is
(a) rt[(x² + y² + xy)/3]
(b) rt[(x² + y² + xy)/2]
(c) rt[(x² + y² – xy)/3]
(d) rt[(x² + y² – xy)/2]

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q16) ABC is an isosceles triangle with AB= AC = 4. O is a point inside the triangle ABC.
Find the area of triangle OBC.
I. ∠BAC = 45˚.
II. ∠BOC = 90˚.(a) question can be answered by using one statement alone but not by other statement alone.
(b) question can be answered by using either statement alone.
(c) question can be answered by using both statements together but not by either alone.
(d) question cannot be answered even by using both statements together.

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q17) In figure, CD = BC, ∠BAD = 66˚, AB is the diameter and O the center of the semicircle.
Measure the angle ∠DEC
(a) 48˚
(b) 54˚
(c) 57˚
(d) 63˚

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q18) ABCDHFEG is a cuboid and EFHGJ is a right pyramid with base EFHG and J lying on plane ABCD. If volume inside cuboid but outside pyramid is 480cm³, find h.
(a) 8
(b) 10
(c) 12
(d) 16

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q19) ABCD is a square with side length 2 cm. It is divided into five rectangles of equal areas, as shown in the figure. The perimeter of the rectangle BEFG is
(a) 51/16
(b) 36/11
(c) 58/15
(d) 47/13