CTET 2024 July Paper 2 with answer keys (Mathematics)

Q.31. Perimeter of a quadrilateral ABCD is 120 cm. If \(BC=48\) cm, \(CD=17\) cm, \(AD=40\) cm and \(\angle A=\angle B=90^{\circ}\) then area of quadrilateral ABCD (in \(cm^{2}\)) is:

  1. 660
  2. 690
  3. 720
  4. 750
1

Q.32. Which of the following statement is least appropriate regarding the proofs in mathematics?

  1. It explains why a particular mathematical result must be true.
  2. It helps to reveal the connections and provide insights into the underlying structure of mathematics.
  3. It can help the students to validate their own reasoning.
  4. Proofs are built on intuitive knowledge and not reasoning.
4

Q.33. PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such that \(OP=(x+7)\) cm, \(OQ=(x+y)\) cm, \(OR=20\) cm and \(OS=16\) cm. Then, value of \(7y+5\) (in cm) is:

  1. 21
  2. 23
  3. 26
  4. 28
3

Q.34. The value of $52\times3\div4+\sqrt{441}\div7\times3+5-32\div8\times12$ is:

  1. 0
  2. 5
  3. 15
  4. 21
2

Q.35. Arun is three years older than Varun. Eight years ago, \(\frac{5}{6}\) of Arun's age exceeded \(\frac{3}{5}\) of Varun's age by 6 years. If the present age of Varun is x years, then the value of x can be determined by solving the equation:

  1. \(\frac{5}{6}(x-5)-\frac{3}{5}(x-8)=6\)
  2. \(\frac{5}{6}(x-8)-\frac{3}{5}(x-5)=6\)
  3. \(\frac{3}{5}(x+5)-\frac{5}{6}(x-8)=6\)
  4. \(\frac{3}{5}(x+3)-\frac{5}{6}(x-8)=6\)
1

Q.36. The domain of learning that deals with attitudes and values is known as:

  1. Knowledge domain
  2. Cognitive domain
  3. Affective domain
  4. Psychomotor domain
3

Q.37. The height and base radius of a right circular cylinder are 9 cm and 6 cm respectively. If the base radius becomes half and height increases by 3 cm, then which of the following describes the new volume of the cylinder?

  1. The new volume will be twice the original volume.
  2. The new volume will be half the original volume.
  3. The new volume will be thrice the original volume.
  4. The new volume will be one-third the original volume.
4

Q.38. Arrange the following statements according to ascending levels of geometrical thinking as per Van-Hiele's theory of geometrical learning.
(a) Identification of properties of geometrical shapes
(b) Classification of different shapes
(c) Finding relationship between the properties of geometrical shapes
(d) Identification of geometrical shapes as they are

  1. (a), (b), (c), (d)
  2. (d), (b), (a), (c)
  3. (d), (c), (b), (a)
  4. (a), (c), (b), (d)
2

Q.39. In a pie chart, the marks obtained by a student in Mathematics, Science, Social Science, Hindi and English are respectively represented by sectors of central angles \(90^{\circ}\), \(80^{\circ}\), \(65^{\circ}\), \(75^{\circ}\) and \(50^{\circ}\). If the total marks obtained by the students were 540, then what is the difference of the marks obtained by him/her in Mathematics and English?

  1. 60
  2. 50
  3. 40
  4. 30
1

Q.40. At upper primary stage, as per NCERT, which of the following topics have NOT been included under number system?

  1. Complex Numbers
  2. Fractions
  3. Exponents and Powers
  4. Square roots and cube roots
1

Q.41. Which of the following statement is NOT correct with respect to Rubrics as a tool of assessment?

  1. Rubrics has a fixed scale.
  2. Rubrics has a list of characteristics describing performance for each point on the scale.
  3. Rubrics consist of a clear performance target for students.
  4. Rubrics make evaluation more subjective.
4

Q.42. The number of faces (F), edges (E) and vertices (V) of a polyhedron are 7, 15 and x, respectively. Then, the value of $(2F+3E-4x)$ is:

  1. 20
  2. 19
  3. 18
  4. 17
2

Q.43. If \((2x+5y)^{2}-5(2x+5y)-14=(2x+5y+p)(2x+5y+q),\) then the value of \((p+q)\) is:

  1. 7
  2. -14
  3. 9
  4. -5
4

Q.44. Two parallel lines are intersected by a transversal and the two interior angles so formed on the same side of the transversal are \((2x+15^{\circ})\) and \((3x-20^{\circ})\). Then, the value of \((4x+6^{\circ})\)is:

  1. \(154^{\circ}\)
  2. \(150^{\circ}\)
  3. \(148^{\circ}\)
  4. \(146^{\circ}\)
1

Q.45. The sum of the largest and smallest fractions among \(2\frac{3}{5}, \frac{3}{8}, \frac{6}{7}\) and \(2\frac{8}{15}\) is:

  1. \(2\frac{9}{35}\)
  2. \(2\frac{37}{40}\)
  3. \(2\frac{7}{35}\)
  4. \(2\frac{39}{40}\)
4

Q.46. Which of the following does not imply the meaning of assessment?

  1. It is evaluation.
  2. It helps to label the students.
  3. It helps to diagnose individual differences.
  4. It is a procedure to gather information of student's performance.
2

Q.47. Which of the following is NOT an indicator of creativity in Mathematics?

  1. Students use convergent thinking in different contexts.
  2. Students are able to think flexibly.
  3. Students use multiple and alternate problem solving strategies.
  4. Students can pose questions.
1

Q.48. If x is the least number which must be added to 955 to make it a perfect square, then value of \(3x+2\) is equal to:

  1. 20
  2. 14
  3. 11
  4. 5
1

Q.49. How many natural numbers between 1 and 500 are divisible by each of the numbers 3, 5 and 7?

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

Q.50. According to National Curriculum Framework 2005 which of the following process is least important in mathematics?

  1. Solving day to day problems.
  2. Understanding when and how a mathematical technique is to be used.
  3. Finding short-cuts in mathematics.
  4. Generalizing a mathematical formula.
3

Q.51. M is a point on side AB of a triangle ABC such that \(AM=BM=CM\). If angles A and B are respectively x and \(70^{\circ}\) then the value of \((3x+25^{\circ})\) is equal to:

  1. \(70^{\circ}\)
  2. \(85^{\circ}\)
  3. \(100^{\circ}\)
  4. \(115^{\circ}\)
2

Q.52. A sum invested at 10% p.a. for 2 years becomes 3,267, when the interest is compounded annually. What will be the simple interest on the same sum at the same rate in \(2\frac{1}{2}\) years?

  1. 625
  2. 650
  3. 675
  4. 700
3

Q.53. D is a point on side AB of a \(\Delta ABC\) such that CD is the bisector of \(\angle ACB\). If \(\angle A=50^{\circ}\) and \(\angle B=70^{\circ},\) then \(\angle ADC\) is equal to:

  1. \(30^{\circ}\)
  2. \(50^{\circ}\)
  3. \(70^{\circ}\)
  4. \(100^{\circ}\)
4

Q.54. Marks obtained by some students of a class are 36, 37, 31, 42, 23, 38, 17, 18, 35, 25, 29 and 35. The difference of the mean and the range of the data is :

  1. 4.5
  2. 5.0
  3. 5.5
  4. 6.0
3

Q.55. A trader buys 12 fans for 24,000. He marks each fan at 25% above the cost price. If he sells all fans by giving 10% discount on the marked price, then his overall profit (in ₹) is :

  1. 2700
  2. 3000
  3. 3200
  4. 3500
2

Q.56. \(\frac{(a-b+c)^{2}-(a-b-c)^{2}}{b-a}\) is equal to :

  1. \(b-c\)
  2. \(c-a\)
  3. -4c
  4. 2c
3

Q.57. Area of a right triangle is \(240~cm^{2}\). If its one side other than the hypotenuse is 30 cm, then perimeter (in cm) of the triangle is :

  1. 80
  2. 84
  3. 92
  4. 100
1

Q.58. A teacher distributes different types of triangle shaped paper cuttings to the learners and tells them to measure and tabulate the angles in order to find the sum of angles. He tells them to note the result in each case. This method of teaching is an example of :

  1. Discovery method
  2. Teacher centered approach
  3. Deductive method
  4. Analytical approach
1

Q.59. Which of the following is NOT true?

  1. 3+4×5 is not a mathematical expression
  2. Operations of multiplication can be done on mathematical expressions
  3. The expression (\(x^2+10x+25\)) cannot be simplified further
  4. The value of the variable in an equation which satisfy the equation is called a solution of the equation
3

Q.60. The ratio of two numbers is 3 : 7 and their LCM is 630. Then, sum of the LCM and HCF of these numbers is :

  1. 30
  2. 300
  3. 600
  4. 660
4

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