# Mathematics Entrance Test 2

Mathematics Entrance Test

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

Test 2

(1) If the system of linear equations
x + 2ay + az = 0
x + 3by + bz = 0
x + 4cy + cz = 0

has a non-zero solution, then a, b, c

(a) are in A. P.
(b) are in G. P.
(c) are in H.P.
(d) satisfy a + 2b + 3c = 0

(2) If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, and c/b are in

(a) arithmetic progression
(b) geometric progression
(c) harmonic progression
(d) arithmetic-geometric-progression

(3) A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

(a) 140
(b) 196
(c) 280
(d) 346

(4) The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

(a) 6! * 5!
(b) 50
(c) 5! * 4!
(d) 7! * 5!

(5) Let f (x) be a polynomial function of second degree. If f (1) = f (- 1) and a, b, c are in A. P., then f' (a), f' (b) and f' (c) are in

(a)
A.P.
(b) G.P.
(c) H. P.
(d) arithmetic-geometric progression

(6) If x1, x2, x3 and y1, y2, y3 are both in G.P. with the same common ratio, then the points (x1, y1) (x2, y2) and (x3, y3)

(a) lie on a straight line
(b) lie on an ellipse
(c) lie on a circle
(d) are vertices of a triangle

Answer (a) lie on a straight line

(7) The real number x when added to its inverse gives the minimum value of the sum at x equal to

(a) 2
(b) 1
(c) - 1
(d) - 2

(8) The area of the region bounded by the curves y = |x - 1| and y = 3 - |x| is

(a) 2 sq units
(b) 3 sq units
(c) 4 sq units
(d) 6 sq units

(9) The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively

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

(10) Locus of centroid of the triangle whose vertices are (a cos t, a sin t), (b sin t, - b cos t) and (1, 0), where t is a parameter, is

(a) (3x - 1)2 + (3y)2 = a2 - b2
(b) (3x - 1)2 + (3y)2 = a2 + b2
(c) (3x + 1)2 + (3y)2 = a2 + b2
(d) (3x + 1)2 + (3y)2 = a2 - b2
Here 2 is read as Square

Answer (b) (3x - 1)2 + (3y)2 = a2 + b2

(11) The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' will be perpendicular, if and only if

(A) aa' + bb' + cc' + 1 = 0
(B) aa' + bb' + cc' = 0
(c) (a + a') (b + b') + (c + c') = 0
(d) aa' + cc' + 1 = 0

(12) The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

(a) is increased by 2
(b) is decreased by 2
(c) is two times the original median
(d) remains the same as that of the original set

(13) Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

(a) 4/5
(b) 3/5
(c) 1/5
(d) 2/5

(14) The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then P (X = 1) is

(a) 1/32
(b) 1/16
(c) 1/8
(d) 1/4

(15) Let R1 and R2 respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then R1, R, R2 are in

(a) arithmetic-geometric progression
(b) A.P.
(c) G.P.
(d) H.P.

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