# Mathematics Entrance Test 7

Mathematics Entrance Test

Mathematics Objective Type Questions
with Answers for the preparation of Engineering Entrance Test like AIEEE, IIT-JEE, CET etc. (Important For 10+1 & 10+2 Science Students)

Test 7

(1) Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

(a) 5/9
(b) 1/9
(c) 8/9
(d) 4/9

(2) A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after

(a) 19 s
(b) 1 s
(c) 21 s
(d) 25 s

(3) If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval

(a) (5, 6]
(b) (6, ∞)
(c) (-∞, 4)
(d) [4, 5]

(4) A plane passes through (1, − 2, 1) and is perpendicular to two planes 2x − 2y + z = 0 and x − y + 2z = 4. The distance of the plane from the point (1, 2, 2) is

(a) 0
(b) 2
(c) Square Root of 3
(d) 2 Square Root of 2

Answer (d) 2 Square Root of 2

(5) A tangent drawn to the curve y = f(x) at P(x, y) cuts the x-axis and y-axis at A and B respectively such that BP : AP = 3 : 1, given that f(1) = 1, then

(a) equation of curve is x dy/dx - 3y = 0
(b) normal at (1, 1) is x + 3y = 4
(c) curve passes through (2, 1/8)
(d) equation of curve is x dy/dx + 3y = 0

Answer (c) curve passes through (2, 1/8)

(6) Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is

(a) 1
(b) 9/4
(c) 4/9
(d) 2/3

(7) The number of values of x in the interval [0, 3π] satisfying the equation 2sin2x + 5sinx − 3 = 0 is

(a) 4
(b) 6
(c) 1
(d) 2

(8) Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

(a)
not reflexive, symmetric and transitive
(b) reflexive, symmetric and not transitive
(c) reflexive, symmetric and transitive
(d) reflexive, not symmetric and transitive

Answer (b) reflexive, symmetric and not transitive

(9) A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

(a) 90°
(b) 120°
(c) 45°
(d) 60°

(10) A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s2, then the height above the point P from where the body began to fall is

(a) 720 m
(b) 900 m
(c) 320 m
(d) 680 m