CTET 2024 (15 Dec) Paper 2 with answer Keys (Mathematics)

DET–24 : PART–II (Mathematics & Science)

Questions 31–60

Q.31. A metallic solid cuboidal box of dimensions \(200\,\text{cm} \times 50\,\text{cm} \times 100\,\text{cm}\) is melted and recast into a solid cube. The difference between the surface areas of the two solids is:

1. \(10000\text{ cm}^2\)
2. \(25000\text{ cm}^2\)
3. \(20000\text{ cm}^2\)
4. \(15000\text{ cm}^2\)

Correct Answer: (1)

Q.32. The mean of observations \(42, 48, x-15, x-17, x-20, 58, 60\) arranged in ascending order is \(53\). The median of the data is:

1. 56
2. 53
3. 54
4. 55

Correct Answer: (3)

Q.33. The time spent by a student during a day is shown in a pie chart with central angles: School \(90^\circ\), Homework \(60^\circ\), Play \(60^\circ\), Sleep \(120^\circ\), Others \(30^\circ\). What is the difference between the time spent on sleep and school?

1. 4 hours
2. \(1\frac12\) hours
3. 2 hours
4. 3 hours

Correct Answer: (3)

Q.34. A student was asked to find the value of \(x\) in \(x+4=3\). He subtracted \(4\) from \(3\). Which statement best describes this?

1. Such problems should be avoided
2. The student solved correctly
3. The student made an algorithm-based error
4. The student should memorize rules

Correct Answer: (3)

Q.35. Which of the following mathematical statements is not true?

1. Every multiple of a number is ≥ the number
2. The number of factors of a number is finite
3. Every factor is ≤ the number
4. Every factor is always greater than the number

Correct Answer: (4)

Q.36. The most appropriate way to introduce experimental probability to Class VIII is:

1. Defining it on the board
2. Tossing a fair coin repeatedly and noting outcomes
3. Solving numerical problems
4. Giving many theoretical examples

Correct Answer: (2)

Q.37. Appropriate reasons for assessment at upper primary stage are:

(A) Identifying individual learner needs (B) Checking achievement of curriculum objectives (C) Verifying memorization of procedures (D) Selecting students for competitions

1. (B) and (D)
2. (A) and (C)
3. (A), (C) and (D)
4. (A) and (B)

Correct Answer: (4)

Q.38. Which of the following is a closed-ended problem?

1. Write four equivalent fractions of \(\frac{5}{7}\)
2. List four rational numbers between \(\frac{5}{11}\) and \(\frac{10}{11}\)
3. List four natural numbers between 104 and 109
4. Write four integers less than 5

Correct Answer: (3)

Q.39. A characteristic of an effective mathematics classroom is:

1. Allowing multiple solution strategies
2. Solving only teacher-given problems
3. Emphasizing abstract nature only
4. Encouraging individual work only

Correct Answer: (1)

Q.40. While using questioning as an assessment tool, teachers should:

1. Answer questions themselves
2. Ask only low achievers
3. Assess misconceptions and errors
4. Ask many questions without pause

Correct Answer: (3)

Q.41. If \((x+5)+7y = 5+(x+7y)\), which property of addition is used?

1. Commutative & Associative
2. Commutative
3. Distributive
4. Associative & Distributive

Correct Answer: (1)

Q.42. The spiral approach recommended by NCF–2005 means:

1. Revisiting concepts with increasing complexity
2. Teaching new concepts each grade
3. Repeating same content every year
4. Teaching easy and hard topics together

Correct Answer: (1)

Q.43. In which statement is the number \(6\) used in cardinal sense?

1. 6 is successor of 5
2. 6 is predecessor of 7
3. She sat in the 6th row
4. There are 6 elements in a set

Correct Answer: (4)

Q.44. Evaluate: \[ \frac{0.125 \times 5^7 \times 8 \times 0.729}{0.017 \times 0.0081 \times 0.25} \]

1. 153000
2. 153
3. 1530
4. 15300

Correct Answer: (1)

Q.45. If LCM of two numbers is 392, which cannot be their HCF?

1. 196
2. 28
3. 42
4. 56

Correct Answer: (3)

Q.46. Smallest positive integer which is not a factor of \(264 \times 90 \times 1680\) is:

1. 15
2. 12
3. 13
4. 14

Correct Answer: (3)

Q.47. If \[ \begin{array}{c} ABA \\ \times 5 \\ \hline 44B0 \end{array} \] then which is correct?

1. A=8, B=9
2. A=4, B=2
3. A=9, B=8
4. A=2, B=4

Correct Answer: (1)

Q.48. If \(x\) is the smallest number subtracted from 7751 to make it a perfect square, find \(3x+5\).

1. 16
2. 7
3. 10
4. 13

Correct Answer: (1)

Q.49. In \((5x+3y)(6x-5y)-(3x+7y)(4x+5y)\), the coefficient of \(xy\) is:

1. 13
2. 6
3. 9
4. 11

Correct Answer: (2)

Q.50. One factor of \[ \frac{81x^2 - 126xy + 49y^2}{(5x-7y)^2} \] is:

1. \(5x-7y\)
2. \(7x-2y\)
3. \(2x-5y\)
4. \(7x+2y\)

Correct Answer: (4)

Q.51. If \(\frac{7}{x}+\frac{1}{4}=\frac{1}{7}+\frac{2}{x}+\frac{1}{4}\), find \(\frac{5}{x}-\frac{3}{x}\).

1. \(\frac{11}{8}\)
2. 1
3. \(\frac{3}{2}\)
4. \(\frac{7}{5}\)

Correct Answer: (3)

Q.52. Two articles sold at ₹348 each. Profit on A = 20%, loss on B = 13%. Overall profit (₹) is:

1. 12
2. 6
3. 7
4. 9

Correct Answer: (2)

Q.53. ₹16000 amounts to ₹\(x\) in \(2\frac13\) years at 15% p.a. compounded yearly. Find \(x\).

1. 22360
2. 21160
3. 21488
4. 22218

Correct Answer: (4)

Q.54. Difference of two complementary angles is \(40^\circ\). If smaller angle is \(y\), find \(2y+15^\circ\).

1. 65°
2. 45°
3. 50°
4. 55°

Correct Answer: (1)

Q.55. Which figures do not have equal number of lines of symmetry?

1. Kite & isosceles trapezium
2. Isosceles triangle & kite
3. Kite & parallelogram
4. Rectangle & rhombus

Correct Answer: (3)

Q.56. In triangle \(PQR\), point \(S\) lies on \(QR\) such that \(PS \perp QR\) and \(PS\) bisects \(\angle QPR\). Which is true?

1. \(\triangle PQS \cong \triangle PRS\) (RHS)
2. \(\triangle PQS \cong \triangle PSR\) (RHS)
3. \(\triangle PQS \cong \triangle PRS\) (ASA)
4. \(\triangle PQS \cong \triangle PSR\) (ASA)

Correct Answer: (3)

Q.57. Which can be the third side of a triangle with sides 19 cm and 15 cm?

1. 34 cm
2. 3 cm
3. 4 cm
4. 33 cm

Correct Answer: (4)

Q.58. In quadrilateral \(ABCD\): \(\angle A=(3x-10)^\circ,\ \angle B=(x+30)^\circ,\ \angle C=(2x+30)^\circ,\ \angle D=(2x-10)^\circ\). The quadrilateral is a:

1. Rectangle
2. Trapezium
3. Parallelogram
4. Kite

Correct Answer: (4)

Q.59. Area of a triangle with sides 24 cm, 45 cm, 51 cm equals area of a rectangle of length 45 cm. Perimeter of rectangle is:

1. 114 cm
2. 55 cm
3. 57 cm
4. 110 cm

Correct Answer: (1)

Q.60. From a circular sheet of diameter 16 cm, a circle of radius 6 cm is removed. Remaining area (use \(\pi=\frac{22}{7}\)) is:

1. 44
2. 176
3. 88
4. 66

Correct Answer: (3)