# Mathematics Online Questions with Answers - 7

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

© 3

(d) 4

Answer (a) 1

(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

© 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

© 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}

© ^{7}⁄_{2}

(d) ^{9}⁄_{2}

Answer © ^{7}⁄_{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)

© (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)

© only (1) and (2)

(d) (1), (2) and (3)

Answer © 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

© – ^{1}⁄_{2}

(d) 0

Answer (a) –2

(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}

© ^{7}⁄_{20}

(d) ^{4}⁄_{5}

Answer © ^{7}⁄_{20}

(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}

© ^{128}⁄_{256}

(d) ^{28}⁄_{256}

Answer (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

© ^{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