CTET 2024 Dec Paper 2 with answer Keys (Mathematics)

CTET – Part II (Mathematics & Science)

Questions 31–60

Q.31. Which of the following numbers is written in the standard form?

1. \(83.7\times10^{-9}\)
2. \(45\times10^{3}\)
3. \(8.5\times10^{-12}\)
4. \(0.6\times10^{15}\)

Correct Answer: (C)

Q.32. In a pentagon \(ABCDE\), \(\angle A=(2x+98)^\circ,\ \angle B=(2x+18)^\circ,\ \)
\(\angle C=(2x-18)^\circ,\ \angle D=(2x+58)^\circ,\ \angle E=(2x-48)^\circ\). Find \((2x+108)\).

1. 124
2. 114
3. 116
4. 118

Correct Answer: (C)

Q.33. Which one of the following is the most appropriate feature of mathematics textbooks at elementary level?

1. Concepts should be presented from concrete to abstract
2. Language must be highly technical
3. Only repetitive practice questions
4. Concepts from complex to simple

Correct Answer: (A)

Q.34. A sum of ₹8000 becomes ₹9500 at \(7.5\%\) p.a. in \(x\) years at simple interest. What will be the amount at \(20\%\) p.a., compounded yearly, for the same time?

1. ₹13824
2. ₹11616
3. ₹12144
4. ₹12672

Correct Answer: (D)

Q.35. Two corresponding angles are \((3x-20)^\circ\) and \((5x-60)^\circ\). Find \((4x+30)^\circ\).

1. \(150^\circ\)
2. \(90^\circ\)
3. \(110^\circ\)
4. \(130^\circ\)

Correct Answer: (C)

Q.36. Which record is used to note problem-solving, measurement and experimentation abilities?

1. Teacher diary
2. Cumulative record
3. Report card
4. Anecdotal record

Correct Answer: (D)

Q.37. Distance between parallel sides of trapezium \(ABCD\) is \(12\) cm. If \(CD=24\) cm, \(AD=BC=13\) cm, find the area.

1. 228
2. 123.5
3. 114
4. 247

Correct Answer: (A)

Q.38. Data: \(1,0,2,4,0,3,1,1,2,4,1\). Find (Mean − Mode).

1. \(\frac{8}{9}\)
2. \(\frac{7}{11}\)
3. \(\frac{8}{11}\)
4. \(\frac{10}{9}\)

Correct Answer: (C)

Q.39. If \(565x9274y\) is divisible by \(88\), find \((2x+3y)\).

1. 22
2. 26
3. 25
4. 24

Correct Answer: (B)

Q.40. Mathematics required in banking, tailoring, shop-keeping shows its __________ value.

1. Professional
2. Disciplinary
3. Cultural
4. Utilitarian

Correct Answer: (D)

Q.41. \(OC\perp OD\), \(\angle AOC=x\), \(\angle BOD=3x\). Find \(\angle BOD\).

1. \(67\frac{1}{2}^\circ\)
2. \(22\frac{1}{2}^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

Correct Answer: (A)

Q.42. Least useful aid for teaching addition of integers?

1. Chart paper
2. Stairs
3. Lift
4. Number line

Correct Answer: (A)

Q.43. If \(x=k\) solves \(\frac{4}{x}-\frac{5}{x-1}=\frac{7}{3}\), find \(\frac{11k+18}{11k-12}\).

1. \(\frac49\)
2. \(\frac12\)
3. \(\frac34\)
4. \(\frac58\)

Correct Answer: (D)

Q.44. Numbers \(2<7 are="" by="" frac12="" happens="" multiplied="" p="" what="">

1. Terms change
2. Order remains same
3. Mean same
4. Order reverses

Correct Answer: (D)

Q.45. Important abilities to be assessed in mathematics are:

(a) Abstraction & relationships (b) Memorisation (c) Application in daily life (d) Full marks

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

Correct Answer: (B)

Q.46. CP = ₹750. SP = ₹608 after \(24\%\) discount. Profit % at marked price?

1. \(6\frac23\%\)
2. \(5\%\)
3. \(6\%\)
4. \(5\frac13\%\)

Correct Answer: (A)

Q.47. \(31096\div(2704\div2)+0.6738+0.63+0.059-0.79\) equals:

1. 24.5728
2. 23.6728
3. 23.5728
4. 24.6728

Correct Answer: (C)

Q.48. Cards numbered \(12\) to \(71\). Probability of non-prime?

1. \(\frac{45}{59}\)
2. \(\frac14\)
3. \(\frac{15}{59}\)
4. \(\frac34\)

Correct Answer: (D)

Q.49. Teacher-centred method?

1. Group discussion
2. Problem solving
3. Lecture
4. Heuristic

Correct Answer: (C)

Q.50. Wheel radius \(25\) cm, \(350\) rounds. Distance (m)?

1. 1100
2. 275
3. 550
4. 825

Correct Answer: (C)

Q.51. One factor of \(20pq^2+4pq+45pr^2-60pqr-6rp\) is:

1. \(15p-10r+2\)
2. \(2r-3q\)
3. \(2q-3r\)
4. \(10p-15r+2\)

Correct Answer: (B)

Q.52. Correct statement about assessment:

1. Formative after course
2. Assessment as learning supports self & peer assessment
3. Summative during teaching
4. No feedback in assessment for learning

Correct Answer: (B)

Q.53. Mensuration errors by Anamika. Correct actions?

1. I & II
2. Only I
3. Only II
4. Neither

Correct Answer: (A)

Q.54. In parallelogram, \(PQ=4x+1,\ QR=26,\ RS=25,\ PS=3y-1\). Find \(3x+2y\).

1. 39
2. 35
3. 36
4. 38

Correct Answer: (C)

Q.55. Rational numbers between \(-\frac{7}{10}\) and \(-\frac14\):

1. \(-\frac58,-\frac23,-\frac35\)
2. \(-\frac35,-\frac15,0\)
3. \(-\frac23,-\frac35,-\frac34\)
4. \(-\frac58,-\frac23,-\frac35\)

Correct Answer: (A)

Q.56. Smallest \(x\) such that \(2605-x\) is a perfect square. Find \(4x+7\).

1. 31
2. 11
3. 23
4. 27

Correct Answer: (C)

Q.57. \(A=3x^2-8x+11,\ B=-2x^2+12x,\ C=-4x^2+7,\ D=x^2-x-11\). If \((A+B+C)-D=px^2+qx+r\), find \(p+q+r\).

1. 31
2. 27
3. 28
4. 30

Correct Answer: (D)

Q.58. Reflection, Rotation, Translation, Enlargement mean:

1. Flip, Slide, Turn, Bigger
2. Turn, Slide, Flip, Bigger
3. Flip, Turn, Slide, Bigger
4. Slide, Flip, Turn, Bigger

Correct Answer: (C)

Q.59. Triangle construction possible for:

1. \(AB=5,BC=6,\angle ABC=130^\circ,\angle BAC=25^\circ\)
2. \(AB=3,BC=4,AC=7\)
3. \(AB=8,BC=4,\angle BCA=90^\circ,\angle ABC=60^\circ\)
4. \(\angle ACB=120^\circ,\angle ABC=25^\circ,AC=BC=4\)

Correct Answer: (C)

Q.60. Cube of side \(12\) cm cut into cubes of side \(4\) cm. Relation of surface areas?

1. New is three times
2. New is half
3. New is twice
4. New is one-third

Correct Answer: (A)