Quant Boosters  Kamal Lohia  Set 7

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

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q20) Three circles are in a row touching each other such that all three of them have two common tangents. The radii of the largest and the smallest circle are 9 and 4 respectively. Line segment AB passes through the centres of the circles and lies on the two outer circles. What is the length of AB?
(a) 38
(b) 26 + 3rt(32)
(c) 26 + 2rt(38)
(d) 19

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q21) A regular hexagon with a perimeter of 12rt(2) units lies in the Cartesian plane in such a way that its center is on the origin, two of the vertices lie on the xaxis, and the midpoints of two of its sides lie on the yaxis. If the portion of the hexagon that lies in Quadrant I is completely revolved around the xaxis, a solid whose volume is X cubic units results. If the same portion is completely revolved around the yaxis, a solid with a volume of Y cubic units results. Evaluate (X/Y)² .
(a) 48/49
(b) 1
(c) 4/3
(d) 16/9

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q22) One angle of a regular polygon measures 179˚. How many sides does it have?
(a) 179
(b) 180
(c) 280
(d) 360

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q23) In two equilateral triangles ABC and BMN, ∠ABM = 120˚. AN & CM intersects at O. Find ∠MON.
(a) 120˚
(b) 90˚
(c) 60˚
(d) 30˚

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q24) In a parallelogram ABCD, let M be the midpoint of the side AB and N the midpoint of BC. Let P be the intersection point of the lines MC and ND. Find the ratio of area of ▲s APB : BPC : CPD : DPA.
(a) 3:1:2:4
(b) 3:2:1:4
(c) 2:1:3:4
(d) 1:2:3:4

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q25) In a quadrilateral ABCD, sides AD and BC are parallel but not equal and sides AB = DC = x. The area of the quadrilateral is 676 cm². A circle with centre O and radius 13 cm is inscribed in the quadrilateral such that it is tangent to each of the four sides of the quadrilateral. Determine the length of x.
(a) 13
(b) 24
(c) 26
(d) 12

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q26) C and D are two points on a semicircle with AB as diameter such that AC – BC = 7 and AD – BD = 13. AD and BC intersect at P. Find the difference in area of triangles ACP and BDP.
(a) 24
(b) 26
(c) 28
(d) 30

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q27) Points A, D and C lie on the circumference of a circle. The tangents to the circle at points A and C meet at the point B. If ∠DAC = 83˚ and ∠DCA = 54˚. Find ∠ABC.
(a) 88˚
(b) 94˚
(c) 100˚
(d) 104˚

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q28) The sum of all interior angles of eight polygons is 3240˚. What is the total number of sides of polygons?
(a) 16
(b) 18
(c) 32
(d) 34

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q29) Circles with centers P and Q have radii 20 and 15 cm respectively and intersect at two points A, B such that ∠PAQ = 90°. What is the difference in the area of two shaded regions?
(a) 175 Pi
(b) 150 Pi
(c) 125 Pi
(d) 90 Pi

Q30) Given f(x) = x  1/x, solve the equation f(f(x)) = x.