CTET 2019 July Paper 2 with answer Keys (Mathematics)

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Q.31. If \(x = 2^3 \times 3^2 \times 5^3 \times 7^3\), \(y = 2^2 \times 3^3 \times 5^4 \times 7^3\), and \(z = 2^4 \times 3^4 \times 5^2 \times 7^5\), then H.C.F. of \(x, y\) and \(z\) is

1. \((30)^2 \times 7^3\)
2. \((15)^3 \times 7^4\)
3. \((30)^3 \times 7^3\)
4. \(30 \times 7^5\)

Correct Answer: (1)

Q.32. If \(52272 = p^2 \times q^3 \times r^4\), where \(p, q\) and \(r\) are prime numbers, then the value of \((2p + q - r)\) is

1. 21
2. 22
3. 23
4. 29

Correct Answer: (3)

Q.33. If the 7-digit number \(134x58y\) is divisible by 72, then the value of \((2x + y)\) is

1. 6
2. 7
3. 8
4. 9

Correct Answer: (3)

Q.34. Which of the following is not a Pythagorean triplet?

1. 7, 24, 25
2. 8, 15, 17
3. 11, 60, 63
4. 13, 84, 85

Correct Answer: (3)

Q.35. The measure of an angle for which the measure of the supplement is four times the measure of the complement is

1. 30°
2. 45°
3. 60°
4. 75°

Correct Answer: (3)

Q.36. If the angles, in degrees, of a triangle are \(x\), \(3x + 20\) and \(6x\), the triangle must be

1. Obtuse
2. Acute
3. Right
4. Isosceles

Correct Answer: (1)

Q.37. In triangles ABC and DEF, \(\angle C = \angle F\), \(AC = DF\), and \(BC = EF\). If \(AB = 2x - 1\) and \(DE = 5x - 4\), then the value of \(x\) is

1. 1
2. 2
3. 3
4. 4

Correct Answer: (1)

Q.38. One side of a triangle is 5 cm and the other side is 10 cm and its perimeter is \(P\) cm, where \(P\) is an integer. The least and the greatest possible values of \(P\) are respectively

1. 19 and 29
2. 20 and 28
3. 21 and 29
4. 22 and 27

Correct Answer: (3)

Q.39. Let \(x\) be the median of the data 13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14. If 8 is replaced by 18, then the median of the data is \(y\). What is the sum of the values of \(x\) and \(y\)?

1. 27
2. 28
3. 29
4. 30

Correct Answer: (3)

Q.40. A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

1. \(\frac{4}{5}\)
2. \(\frac{3}{10}\)
3. \(\frac{1}{5}\)
4. \(\frac{1}{2}\)

Correct Answer: (4)

Q.41. The total surface area of a cuboid is \(194\,\text{m}^2\). If its length is 8 m and breadth is 6 m, then what is its volume (in \(\text{m}^3\))?

1. 112
2. 126
3. 168
4. 224

Correct Answer: (3)

Q.42. The area of a trapezium is \(105\,\text{cm}^2\) and its height is 7 cm. If one of the parallel sides is longer than the other by 6 cm, then the length of the longer side, in cm, is

1. 18
2. 16
3. 15
4. 12

Correct Answer: (1)

Q.43. The curved surface area of a right circular cylinder of base radius 3 cm is \(94.2\,\text{cm}^2\). The volume (in \(\text{cm}^3\)) of the cylinder is (Take \(\pi = 3.14\))

1. 138.6
2. 141.3
3. 125.6
4. 113.04

Correct Answer: (2)

Q.44. If \(x\) is added to each of 14, 12, 34 and 30, the numbers so obtained, in this order, are in proportion. What is the value of \(\sqrt{12x + 9}\)?

1. 8
2. 9
3. 11
4. 13

Correct Answer: (2)

Q.45. Which one of the following statements is true?

1. A regular hexagon has only 4 lines of symmetry.
2. A regular polygon of 10 sides has 10 lines of symmetry.
3. A circle has no line of symmetry.
4. An angle has two lines of symmetry.

Correct Answer: (2)

Q.46. The value of \(x\) which satisfies \(10(x + 6) + 8(x - 3) = 5(5x - 4)\) also satisfies the equation

1. \(5(x - 3) = x + 5\)
2. \(3(3x - 5) = 2x + 1\)
3. \(2(x + 3) = 5(x - 5) + 4\)
4. \(5(x - 5) = 2(x - 3) + 5\)

Correct Answer: (4)

Q.47. What should be subtracted from \(5y - 13x - 8a\) to obtain \(11x - 16y + 7a\)?

1. \(6x + 21y + 15a\)
2. \(21y - 5x - a\)
3. \(21y - 24x - 15a\)
4. \(24x - 21y + a\)

Correct Answer: (3)

Q.48. Which of the following statements is correct regarding children coming to school from rural areas in the context of Mathematics?

1. They need not learn formal mathematics as it is of no use to them.
2. They may have rich oral mathematical traditions and knowledge.
3. They do not know any mathematics.
4. They have poor communication skills in mathematics.

Correct Answer: (2)

Q.49. Read the following statements: A. Axioms are propositions which are assumed. B. Axioms are special theorems. C. Axioms are definitions. D. Axioms, when proved becomes theorems. Which of the following statement(s) is correct?

1. A and C
2. A and D
3. Only B
4. Only A

Correct Answer: (4)

Q.50. Which of the following statements does not reflect contemporary view of students’ errors in mathematics?

1. They should be overlooked.
2. They are a part of learning.
3. They are a rich source of information.
4. They can guide the teacher in planning her classes.

Correct Answer: (1)

Q.51. Which of the following statement(s) regarding Mathematics is true? A. Mathematics is a tool. B. Mathematics is a form of art. C. Mathematics is a language.

1. A & B
2. B & C
3. Only A
4. A, B & C

Correct Answer: (4)

Q.52. To prove that 2 is an irrational number, a teacher begins by assuming that it is a rational number and then proceeds to show how this assumption is not feasible. This is an example of proof by

1. Induction
2. Deduction
3. Contradiction
4. Verification

Correct Answer: (3)

Q.53. Which of the following statements reflects a desirable assessment practice in the context of mathematics learning?

1. Only paper-pencil tasks are suited to assess students.
2. Holding conversations and one to one discussion with children can also be helpful in assessing them.
3. Assessment should be product oriented.
4. Incorrect answers of children should largely be ignored.

Correct Answer: (2)

Q.54. Which of the following statements is true of learning mathematics?

1. Everyone can learn and succeed in mathematics.
2. Girls need extra attention.
3. Mathematics is meant for a select few.
4. Informal algorithms are inferior.

Correct Answer: (1)

Q.55. The role of proportional reasoning in understanding the concept related to ratio and proportion was highlighted by

1. Van Hiele
2. Zoltan Dienes
3. Jean Piaget
4. Lev Vygotsky

Correct Answer: (3)

Q.56. A student is not able to solve word problems involving transposition in algebra. The best remedial strategy is to

1. Give more practice on transposition.
2. Give word problems in another language.
3. Explain word problems in simple language.
4. Explain the concept of equality using an alternate method.

Correct Answer: (4)

Q.57. Contemporary understanding of Mathematics Pedagogy encourages teachers to do all of the following, except

1. Encourage approximation.
2. Introduce computation before conceptual understanding.
3. Guess-and-verify solutions.
4. Develop systematic reasoning.

Correct Answer: (2)

Q.58. The value of \([(-4) \div 2] \times (-3) - (-3)[(-3) \times (-7) - 8]\)
\(+ (4)[(-48) \div 6]\) is

1. 9
2. −11
3. 13
4. −16

Correct Answer: (3)

Q.59. The fractions \(\frac{44}{49}, \frac{33}{38}, \frac{22}{25}\) and \(\frac{24}{29}\) are written in descending order as

1. \(\frac{24}{29}, \frac{33}{38}, \frac{22}{25}, \frac{44}{49}\)
2. \(\frac{22}{25}, \frac{24}{29}, \frac{33}{38}, \frac{44}{49}\)
3. \(\frac{44}{49}, \frac{22}{25}, \frac{33}{38}, \frac{24}{29}\)
4. \(\frac{44}{49}, \frac{33}{38}, \frac{24}{29}, \frac{22}{25}\)

Correct Answer: (3)

Q.60. Which one of the following statements is not true for integers?

1. Multiplication is associative.
2. Division is commutative.
3. 1 is the multiplicative identity.
4. Subtraction is not commutative.

Correct Answer: (2)