# Mathematics Entrance Test 4

Mathematics Entrance Test

Free Mathematics Online Questions with Answers for the preparation of Engineering Entrance Test like AIEEE, IIT-JEE, CET etc.

Test 4

(1) The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is

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

(2) Let A (2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

(a) 2x + 3y = 9
(b) 2x – 3y = 7
(c) 3x + 2y = 5
(d) 3x – 2y = 3

Answer (a) 2x + 3y = 9

(3) The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is –1 is

(a) x/2 + y/3 = -1 and x/-2 + y/1 = -1
(b) x/2 - y/3 = -1 and x/-2 + y/1 = -1
(c) x/2 + y/3 = 1 and x/2 + y/1 = 1
(d) x/2 - y/3 = 1 and x/-2 + y/1 = 1

Answer (d) x/2 - y/3 = 1 and x/-2 + y/1 = 1

(4) Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

(a) 3/2
(b) 5/2
(c) 7/2
(d) 9/2

(5) A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

(a) (3a, 3a, 3a), (a, a, a)
(b) (3a, 2a, 3a), (a, a, a)
(c) (3a, 2a, 3a), (a, a, 2a)
(d) (2a, 3a, 3a), (2a, a, a)

Answer (b) (3a, 2a, 3a), (a, a, a)

(6) Consider the following statements:
(1) Mode can be computed from histogram
(2) Median is not independent of change of scale
(3) Variance is independent of change of origin and scale. Which of these is/are correct?

(a) only (1)
(b) only (2)
(c) only (1) and (2)
(d) (1), (2) and (3)

Answer (c) only (1) and (2)

(7) If the straight lines x = 1 + s, y = –3 – Ks, z = 1 + ls and x = , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then K equals

(a) –2
(b) –1
(c) – 1/2
(d) 0

(8) The probability that A speaks truth is , while this probability for B is . The probability that they contradict each other when asked to speak on a fact is

(a) 3/20
(b) 1/5
(c) 7/20
(d) 4/5

(9) The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

(a) 37/256
(b) 219/256
(c) 128/256
(d) 28/256

(10) A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

(a) 17/4 km/h and 13/4 km/h
(b) 13/4 km/h and 17/4 km/h
(c) 17/9 km/h and 13/9 km/h
(d) 13/9 km/h and 17/9 km/h

Answer (a) 17/4 km/h and 13/4 km/h

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