MCQs for JSSC PGT Mathematics Exam

31

Mathematics • Number Systems

Express in decimal the value of the binary sum 100001 + 110111. Express in decimal the value of the binary sum 100001 + 110111.

A. 78 78 B. 87 87 C. 88 88 D. 80 80

सही उत्तर: C Correct Answer: C

Binary 100001 equals 33 and binary 110111 equals 55. Their sum is 88.

32

Mathematics • Mathematical Modelling

Single-species population model is given by the equation (where the symbols have their usual meaning): Single-species population model is given by the equation (where the symbols have their usual meaning):

A. dN/dt = B(t)D(t) + D(t)N(t) dN/dt = B(t)D(t) + D(t)N(t) B. dN/dt = B(t)N(t) + D(t)N(t) dN/dt = B(t)N(t) + D(t)N(t) C. dN/dt = B(t)/N(t) + N(t)/D(t) dN/dt = B(t)/N(t) + N(t)/D(t) D. dN/dt = B(t)N(t) - D(t)N(t) dN/dt = B(t)N(t) - D(t)N(t)

सही उत्तर: D Correct Answer: D

The rate of population change equals births minus deaths. With per-capita birth and death rates B(t) and D(t), dN/dt = B(t)N(t) - D(t)N(t).

33

Mathematics • Queueing Theory

In a take-away food joint with a single service counter, customers are served on a first-come-first-served basis. The arrival rate follows a Poisson distribution and service time follows an exponential distribution. If 2 customers arrive every 10 minutes and 18 customers are served per hour, what is the expected number of customers in the joint at any given time? In a take-away food joint with a single service counter, customers are served on a first-come-first-served basis. The arrival rate follows a Poisson distribution and service time follows an exponential distribution. If 2 customers arrive every 10 minutes and 18 customers are served per hour, what is the expected number of customers in the joint at any given time?

A. 2 2 B. 5 5 C. 9 9 D. 1 1

सही उत्तर: A Correct Answer: A

For the M/M/1 queue, lambda = 12 per hour and mu = 18 per hour. The expected number in the system is lambda/(mu - lambda) = 12/6 = 2.

34

Mathematics • Abstract Algebra

The set of units in Z_14, under the usual operations of addition and multiplication modulo 14, is: The set of units in Z_14, under the usual operations of addition and multiplication modulo 14, is:

A. Z_14 Z_14 B. {1} {1} C. {1, 13, 3, 5, 11, 9} {1, 13, 3, 5, 11, 9} D. {1, -1, 3, 5, 2, 7} {1, -1, 3, 5, 2, 7}

सही उत्तर: C Correct Answer: C

The units modulo 14 are exactly the residue classes relatively prime to 14: 1, 3, 5, 9, 11 and 13.

35

Mathematics • Limits

Calculate lim (x^2 - 4)/(x^2 + 5x - 14) as x approaches 2. Calculate lim (x^2 - 4)/(x^2 + 5x - 14) as x approaches 2.

A. Undefined Undefined B. 2/7 2/7 C. 4/5 4/5 D. 4/9 4/9

सही उत्तर: D Correct Answer: D

Factor and cancel x - 2: (x^2 - 4)/(x^2 + 5x - 14) = (x + 2)/(x + 7). At x = 2 this equals 4/9.

36

Mathematics • Digital Logic

Which logic gate has the following truth table? Inputs (A,B) and output C: (0,0)->0, (0,1)->1, (1,0)->1, (1,1)->1. Which logic gate has the following truth table? Inputs (A,B) and output C: (0,0)->0, (0,1)->1, (1,0)->1, (1,1)->1.

A. OR with 2 inputs OR with 2 inputs B. NAND NAND C. AND with 2 inputs AND with 2 inputs D. NOR NOR

सही उत्तर: A Correct Answer: A

The output is 1 whenever at least one input is 1, which is the truth table of a two-input OR gate.

37

Mathematics • Group Theory

Which one of the following is a group? Which one of the following is a group?

A. The set of all 2 by 2 matrices under multiplication. The set of all 2 by 2 matrices under multiplication. B. (R+, x), where a x b = sqrt(ab) for all a, b in R+. (R+, x), where a x b = sqrt(ab) for all a, b in R+. C. (C[0,1], x), where (f x g)(x) = f(x)g(x). (C[0,1], x), where (f x g)(x) = f(x)g(x). D. The set of odd integers under addition. The set of odd integers under addition.

सही उत्तर: C Correct Answer: C

Option C is the answer marked in the source paper. It represents the stated collection of continuous functions under pointwise multiplication.

38

Mathematics • Dynamics

The moment of inertia of a uniform thin rod of mass M and length L about a perpendicular axis of rotation at its end is: The moment of inertia of a uniform thin rod of mass M and length L about a perpendicular axis of rotation at its end is:

A. (1/8)ML^2 (1/8)ML^2 B. (1/2)ML^2 (1/2)ML^2 C. (1/3)ML^2 (1/3)ML^2 D. (1/4)ML^2 (1/4)ML^2

सही उत्तर: C Correct Answer: C

The moment of inertia of a uniform rod about its centre is ML^2/12. By the parallel-axis theorem, about an end it is ML^2/12 + M(L/2)^2 = ML^2/3.

39

Mathematics • Conic Sections

For what value of m is the line y = mx + 5 tangent to the ellipse represented by 4x^2/9 + y^2/16 = 1? For what value of m is the line y = mx + 5 tangent to the ellipse represented by 4x^2/9 + y^2/16 = 1?

A. 2 2 B. plus or minus 2 plus or minus 2 C. plus or minus 3 plus or minus 3 D. 3 3

सही उत्तर: B Correct Answer: B

For y = mx + c to be tangent to x^2/a^2 + y^2/b^2 = 1, c^2 = a^2m^2 + b^2. Here a^2 = 9/4, b^2 = 16 and c = 5, giving m^2 = 4, so m = plus or minus 2.

40

Mathematics • Number Systems

The binary equivalent of 57 is: The binary equivalent of 57 is:

A. 101111 101111 B. 111001 111001 C. 111000 111000 D. 101010 101010

सही उत्तर: B Correct Answer: B

57 = 32 + 16 + 8 + 1, so its binary representation is 111001.

MCQs for JSSC PGT Mathematics Exam

MCQs for JSSC PGT Mathematics Exam

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