CTET 2019 Dec Paper 2 with answer keys (Mathematics)

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Q.31. How many pairs of twin primes are there between the integers 1 to 100?

1. 5
2. 6
3. 7
4. 8

4

Q.32. If \(21168 = 2^a \times 3^b \times 7^c\), where \(a,b,c\) are natural numbers, then what is the value of \((4a-5b+c)\)?

1. 0
2. 1
3. 2
4. 3

4

Q.33. Let \(x\) be the least number which when divided by 8, 12, 20, 28, 35 leaves a remainder 5 in each case. What is the sum of digits of \(x\)?

1. 11
2. 14
3. 15
4. 17

4

Q.34. What number should be subtracted from each of 50, 61, 92, 117 so that the numbers, so obtained in this order, are in proportion?

1. 14
2. 17
3. 19
4. 23

2

Q.35. A sum of ₹1710 is divided in \(A,B,C\) such that \(4A, 6B, 9C\) are equal. What is the difference between \(A\) and \(C\)?

1. ₹360
2. ₹450
3. ₹480
4. ₹540

2

Q.36. The number of fruits in baskets \(A\) and \(B\) are in the ratio \(7:9\). If six fruits are taken out from \(A\) and put in \(B\), then this ratio becomes \(1:3\). The total number of fruits in \(A\) and \(B\) is

1. 28
2. 32
3. 36
4. 40

2

Q.37. \(\triangle ABC\) and \(\triangle ADB\) are on the common base \(AB\) and on the same side of \(AB\). \(DA \perp AB,\; CB \perp AB\) and \(AC = BD\). Which of the following is true?

1. \(\triangle ABC \cong \triangle ABD\)
2. \(\triangle ABC \cong \triangle ADB\)
3. \(\triangle ABC \cong \triangle BAD\)
4. \(\triangle ABC \cong \triangle BDA\)

3

Q.38. The sides of four triangles are given below:
(i) 20 cm, 22 cm, 24 cm
(ii) 15 cm, 32 cm, 37 cm
(iii) 11 cm, 60 cm, 61 cm
(iv) 19 cm, 40 cm, 41 cm
Which of them forms a right triangle?

1. (i)
2. (ii)
3. (iii)
4. (iv)

3

Q.39. The angles of a quadrilateral are in the ratio \(3:5:7:9\). What is the difference between the least and the greatest angles?

1. 50°
2. 60°
3. 72°
4. 90°

4

Q.40. The perimeter of a triangle is 12 cm. If all the three sides have integer lengths (in cm), then how many such different triangles are possible?

1. 2
2. 3
3. 4
4. 5

2

Q.41. A godown is in the shape of a cuboid whose length, breadth and height are 56 m, 42 m and 10 m respectively. How many (maximum) cuboidal boxes each measuring \(2.8\,\text{m} \times 2.5\,\text{m} \times 70\,\text{cm}\) can be stored into the godown?

1. 2400
2. 3600
3. 4800
4. 5400

3

Q.42. The circumference of the base of a right circular cylinder is 528 cm and its height is 2 m. What is the volume of the cylinder? Take \( \pi=\frac{22}{7} \).

1. 2.2176 m³
2. 3.3264 m³
3. 4.4352 m³
4. 6.6528 m³

3

Q.43. The area of a quadrilateral is 227.2 cm² and the lengths of the perpendiculars from the opposite vertices to a diagonal are 7.2 cm and 8.8 cm. What is the length of the diagonal?

1. 26.8 cm
2. 28.4 cm
3. 30.2 cm
4. 32.6 cm

2

Q.44. If \(5(3x+4)-8(6x+7)=9x-8\), then the value of \((x^2-2x+1)\) is

1. \(\frac{2}{3}\)
2. \(\frac{4}{9}\)
3. \(\frac{5}{3}\)
4. \(\frac{25}{9}\)

4

Q.45. What is the value of \(a(a+b^2+c)+b^2(a^2+b^2+c^2)-c(a+b^2)\), when \(a=1, b=-3, c=-2\)?

1. 138
2. 154
3. 162
4. 176

2

Q.46. The expression

\( (x - y)(x^2 + xy + y^2) \)
\(+ (x + y)(x^2 - xy + y^2) - (x + y)(x^2 - y^2) \)

is equal to

1. \(x^3 - y^3 + xy(x + y)\)
2. \(y^3 - x^3 + xy(x + y)\)
3. \(x^3 + y^3 + xy(y - x)\)
4. \(x^3 + y^3 + xy(x - y)\)

Correct Answer: (3)

Q.47. What is the mean of the median, mode and range of the data:
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11, 9, 24, 25, 29?

1. 31
2. 32
3. 33
4. 34

3

Q.48. A mathematical theorem is

1. a statement that has been proved logically from axioms.
2. a statement which is always true without proof.
3. a statement whose truth is unknown.
4. a statement without sufficient evidence.

1

Q.49. “Things which are equal to the same thing are equal to one another.” This axiom was given by

1. Euclid
2. Pythagoras
3. Descartes
4. Euler

1

Q.50. Which of the following can be used as assessment strategy to encourage interdisciplinary learning in Mathematics?

1. Projects and Field trips
2. Projects and Anecdotal records
3. Field trips and Anecdotal records
4. Anecdotal records and Olympiad

1

Q.51. Which method can be used to prove that the sum of two even integers is always even?

1. Mathematical induction
2. Direct proof
3. Contradiction
4. Contrapositive

2

Q.52. Which skills are promoted by Mathematics at upper primary stage?

1. Visualisation, Transposition, Generalisation, Estimation
2. Visualisation, Memorisation, Transposition, Generalisation
3. Memorisation, Estimation, Generalisation
4. Visualisation, Memorisation, Estimation

1

Q.53. Which task is least likely to develop critical thinking?

1. Evaluating \(72\times73\) in different ways
2. Formulating equations from situations
3. Identifying error in a solution
4. Routine calculation of volume

4

Q.54. Which aligns with “Mathematics for All” (NCF 2005)?

1. Mathematics for selected students
2. Uniform difficulty level problems
3. Highlighting contributions from diverse cultures
4. Separating talented students

3

Q.55. An effective mathematics classroom encourages

1. Teacher-dominated instruction
2. Single solution approach
3. Multiple solution strategies
4. Memorisation only

3

Q.56. A desirable practice in teaching volume is to

1. Begin with formula
2. Stress computation first
3. Relate volume to real objects
4. Avoid exploration

4

Q.57. According to Piaget, which is NOT true about spatial understanding?

1. Ideas develop in stages
2. Development follows historical order
3. Learning starts from sensory experience
4. Coordination of senses is needed

2

Q.58. If \(-12(-3)+[20/(-4)-(-24)/8]-[16/(-2)]\)
\(=(-28/7)+x\), then \(x=\)

1. 29
2. 39
3. 46
4. 47

3

Q.59. If \(30x0867y\) is divisible by 88, then \((3x+y)=\)

1. 4
2. 5
3. 6
4. 7

2

Q.60. The value of

\[ 6\frac{2}{3} + 2\frac{1}{2} \times 3\frac{3}{4} - 5\frac{1}{2} \times 4\frac{1}{4} + 1\frac{2}{3}\left(\frac{7}{8} + \frac{3}{4} \times \frac{2}{3}\right) \]

1. \(-11\frac{1}{12}\)
2. \(11\frac{1}{12}\)
3. \(6\frac{1}{2}\)
4. \(-6\frac{1}{2}\)

Correct Answer: (1)