# (Paper) Maths Objective Type Questions with Answers for the preparatin of Engineering Entrance Test : AIEEE, IIT-JEE, CET : 4

**Mathematics Objective Type Questions****
with Answers for the preparation of Engineering Entrance Test** :
**AIEEE, IIT-JEE, CET**

**(Important For 10+1 & 10+2 Science
Students)**

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

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

(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

Answer (c) 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)

(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

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

(c) 7/20

(d) 4/5

Answer (c) 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

(c) 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

(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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