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 5

(1) If A2 – A + I = 0, then the inverse of A is

(a) A + I

(b) A

(c) A – I

(d) I – A

Answer (d) I – A

(2) Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

(a) reflexive and transitive only

(b) reflexive only

(c) an equivalence relation

(d) reflexive and symmetric only

Answer (a) reflexive and transitive only

(3) If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

(a) 22.0

(b) 20.5

(c) 25.5

(d) 24.0

Answer (d) 24.0

(4) Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is

(a) y2 – 4x + 2 = 0

(b) y2 + 4x + 2 = 0

(c) x2 + 4y + 2 = 0

(d) x2 – 4y + 2 = 0

Here 2 is read as square

Answer (a) y2 – 4x + 2 = 0

(5) The system of equations

αx + y + z = α - 1,

x + αy + z = α - 1,

x + y + αz = α - 1

has no solution, if α is

(a) -2

(b) either – 2 or 1

(c) not -2

(d) 1

Answer (a) -2

(6) The value of α for which the sum of the squares of the roots of the equation

x2 – (a – 2)x – a – 1 = 0 assume the least value is

(a) 1

(b) 0

(c) 3

(d) 2

Answer (a) 1

(7) If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals

(a) – 2

(b) 3

(c) 2

(d) 1

Answer (d) 1

(8) If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

(a) 601

(b) 600

(c) 603

(d) 602

Answer (a) 601

(9) Let f be differentiable for all x. If f(1) = - 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then

(a) f(6) ≥ 8

(b) f(6) < size="2">

Answer (a) f(6) ≥ 8

(10) If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

(a) G.P.

(b) A.P.

(c) Arithmetic − Geometric Progression

(d) H.P.

Answer (b) A.P.

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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 5

(1) If A2 – A + I = 0, then the inverse of A is

(a) A + I

(b) A

(c) A – I

(d) I – A

Answer (d) I – A

(2) Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

(a) reflexive and transitive only

(b) reflexive only

(c) an equivalence relation

(d) reflexive and symmetric only

Answer (a) reflexive and transitive only

(3) If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

(a) 22.0

(b) 20.5

(c) 25.5

(d) 24.0

Answer (d) 24.0

(4) Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is

(a) y2 – 4x + 2 = 0

(b) y2 + 4x + 2 = 0

(c) x2 + 4y + 2 = 0

(d) x2 – 4y + 2 = 0

Here 2 is read as square

Answer (a) y2 – 4x + 2 = 0

(5) The system of equations

αx + y + z = α - 1,

x + αy + z = α - 1,

x + y + αz = α - 1

has no solution, if α is

(a) -2

(b) either – 2 or 1

(c) not -2

(d) 1

Answer (a) -2

(6) The value of α for which the sum of the squares of the roots of the equation

x2 – (a – 2)x – a – 1 = 0 assume the least value is

(a) 1

(b) 0

(c) 3

(d) 2

Answer (a) 1

(7) If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals

(a) – 2

(b) 3

(c) 2

(d) 1

Answer (d) 1

(8) If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

(a) 601

(b) 600

(c) 603

(d) 602

Answer (a) 601

(9) Let f be differentiable for all x. If f(1) = - 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then

(a) f(6) ≥ 8

(b) f(6) < size="2">

Answer (a) f(6) ≥ 8

(10) If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

(a) G.P.

(b) A.P.

(c) Arithmetic − Geometric Progression

(d) H.P.

Answer (b) A.P.

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