Q.31. Let \( P = 12xy - 10y^2 - 18x^2 \), \( Q = 14x^2 + 12y^2 + 9xy \) and \( R = 5y^2 - x^2 + xy \). Then \( (P + Q) - R = \)

  1. \(22xy + 3x^2 - 3y^2\)
  2. \(20xy - 7x^2 - 3y^2\)
  3. \(20xy - 3x^2 - 3y^2\)
  4. \(22xy - 3x^2 + 3y^2\)
Correct Answer: (C)

Q.32. If \( x^4 + \frac{1}{x^4} = 322,\; x \neq 0 \), then one value of \( \left(x - \frac{1}{x}\right) \) is

  1. 4
  2. 6
  3. 8
  4. 2
Correct Answer: (B)

Q.33. If \( 15x^2 - 26x + 8 = (Ax + B)(Cx + D) \), where \( A \) and \( C \) are positive integers, find \( (2A + B - C - 2D) \).

  1. 1
  2. 2
  3. 3
  4. 0
Correct Answer: (A)

Q.34. In ΔABC and ΔDEF, if AB = EF, BC = DE and CA = FD, then

  1. ΔABC ≅ ΔFED
  2. ΔABC ≅ ΔEFD
  3. ΔABC ≅ ΔDFE
  4. ΔABC ≅ ΔDEF
Correct Answer: (2)

Q.35. Which of the following can be the sides of a right angled triangle?

  1. 35 cm, 77 cm and 88 cm
  2. 15 cm, 32 cm and 57 cm
  3. 65 cm, 72 cm and 97 cm
  4. 20 cm, 21 cm and 31 cm
Correct Answer: (3)

Q.36. The number of edges of a polyhedron which has 7 faces and 10 vertices is

  1. 14
  2. 15
  3. 17
  4. 13
Correct Answer: (1)

Q.37. In ΔABC, side AB is produced to E and side CA is produced to D. If ∠BAD = 125° and ∠EBC = 100°, then which of the following is true?

  1. AB > BC
  2. Difference between ∠ABC and ∠ACB is 35°
  3. Difference between ∠BAC and ∠ACB is 20°
  4. ΔABC is an isosceles triangle
Correct Answer: (2)

Q.38. In trapezium PQRS, PQ ∥ SR and the ratio of PQ to SR is 3 : 2. If the area of the trapezium is 480 cm² and the distance between PQ and SR is 12 cm, then the length of SR is

  1. 32 cm
  2. 36 cm
  3. 48 cm
  4. 24 cm
Correct Answer: (4)

Q.39. A rectangular sheet of paper 88 cm × 10 cm is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder? (Take π = 22/7)

  1. 6.16
  2. 7.392
  3. 8.624
  4. 5.54
Correct Answer: (2)

Q.40. The volume of a cube is 2197 cm³. What is its lateral surface area (in cm²)?

  1. 576
  2. 845
  3. 1014
  4. 676
Correct Answer: (1)

Q.41. What is the mean of the range, mode and median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4

  1. 9
  2. 10
  3. 12
  4. 8
Correct Answer: (4)

Q.42. Which of the following is most appropriate strategy for introducing the concept of multiplication of two decimal numbers in the middle school?

  1. The process should be visually represented.
  2. Multiplication as repeated addition should be emphasized.
  3. Multiplication as inverse of division should be emphasized.
  4. The algorithm should be used to introduce the concept.
Correct Answer: (1)

Q.43. Which of the following is a narrow aim of teaching mathematics?

  1. To develop students’ ability to argue the truth and falsity of statements.
  2. To make students proficient in handling numbers and number operations.
  3. To develop students’ generalization abilities.
  4. To encourage systematic reasoning among students.
Correct Answer: (2)

Q.44. Which of the following is most appropriate strategy for teaching students to solve mathematical problems?

  1. Provide a list of formulae at the beginning.
  2. Explain the steps required for solution.
  3. Encourage students to view problems from many perspectives.
  4. Discourage guess and verify approach.
Correct Answer: (3)

Q.45. Identify the incorrect statement from the following:

  1. The notion of argumentation is central to mathematics.
  2. Mathematical communication involves precise use of language.
  3. Conjectures do not have utility in constructing mathematical knowledge.
  4. Hypothesis have a role in construction of mathematical knowledge.
Correct Answer: (3)

Q.46. Which of the following is a desirable strategy for assessing students’ learning in mathematics?

  1. Students’ incorrect answers should be ignored.
  2. Students’ justification of their responses should be an important basis of assessment.
  3. Development of mathematical vocabulary should not be a basis of assessment.
  4. Same tasks should be given to all students for parity.
Correct Answer: (B)

Q.47. For a given figure to be a triangle, the condition that it is a union of three segments is

  1. a sufficient but not a necessary condition.
  2. both necessary and sufficient condition.
  3. neither necessary nor sufficient condition.
  4. a necessary but not a sufficient condition.
Correct Answer: (D)

Q.48. Consider the following statements:
A: If \(n\) is even, then \(n^2\) is even.
B: If \(n^2\) is not even, n is not even.
C: If \(n^2\) is even, then n is even.
D: If n is not even, then \(n^2\) is not even.
Which of the following statements is true?

  1. D is converse of A.
  2. B is inverse of A.
  3. D is contraposition of A.
  4. C is converse of A.
Correct Answer: (D)

Q.49. Which of the following teaching–learning resources in mathematics cannot be used for visually challenged students?

  1. Taylor’s abacus
  2. Tiles
  3. GeoBoard
  4. GeoGebra
Correct Answer: (D)

Q.50. Which of the following statements is true?

  1. A person good in arithmetical computation is also good in Mathematics and vice-versa.
  2. Intuition has no role in generating mathematical knowledge.
  3. Mathematical statements can be conditional.
  4. Mathematics consists of all the theorems proved in mathematics books.
Correct Answer: (C)

Q.51. Which of the following statements is NOT correct regarding differently abled children of dyslexia in mathematics learning in an inclusive classroom?

  1. Visual patterns in mathematics help in overcoming difficulties experienced by dyslexic children.
  2. Dyslexic children may have difficulty in writing down their ideas in a systematic and organized manner.
  3. Dyslexia impacts only language learning, not mathematics learning.
  4. Dyslexia has an impact on coordination of verbal and spatial aspects of numbers.
Correct Answer: (C)

Q.52. The number of distinct prime factors of the largest 6-digit number is

  1. 4
  2. 5
  3. 6
  4. 3
Correct Answer: (B)

Q.53. If the 8-digit number 179x091y is divisible by 88, then what is the value of (x − y)?

  1. 2
  2. 3
  3. 4
  4. 1
Correct Answer: (A)

Q.54. Let a = \(\frac{11}{13}\), b = \(\frac{13}{14}\) and c = \(\frac{15}{17}\) be three fractions. Which of the following is true?

  1. \(\frac{}{}\)15/17 < \(\frac{11}{13}\) < \(\frac{11}{13}\)
  2. \(\frac{11}{13}\) < \(\frac{15}{17}\) < \(\frac{13}{14}\)
  3. \(\frac{11}{13}\) < \(\frac{13}{14}\) < \(\frac{15}{17}\)
  4. \(\frac{13}{14}\) < \(\frac{11}{13}\) < \(\frac{15}{17}\)
Correct Answer: (B)

Q.55. If \(0.139 + 0.75 + 2.105 − (1.001 × 1.1) = 2 − k\), then the value of k is

  1. 0.982
  2. 0.1071
  3. 0.1075
  4. 0.8925
Correct Answer: (B)

Q.56. If \(a = \frac{−3}{4}\) and \(b = \frac{5}{6}\), then which of the following does not lie between a and b?

  1. \(\frac{-1}{2}\)
  2. \(\frac{-2}{5}\)
  3. \(\frac{-7}{9}\)
  4. 0
Correct Answer: (C)

Q.57. The product of \(1.7 \times 10^4\) and \(12.5 \times 10^{-6}\) is expressed in the standard form \(k \times 10^n\). The value of \((2k + n)\) is

  1. 1.125
  2. 2.25
  3. 3.25
  4. 2.125
Correct Answer: (C)

Q.58. Two numbers are in the ratio 3 : 5. If 12 is added to both the numbers, then the ratio becomes 5 : 7. The sum of the given two numbers is

  1. 40
  2. 48
  3. 56
  4. 32
Correct Answer: (B)

Q.59. The marked price of an article is ₹840. A shopkeeper gives a discount of 15% on the marked price and still makes a profit of 19%. What is the cost price of the article?

  1. ₹580
  2. ₹600
  3. ₹640
  4. ₹540
Correct Answer: (B)

Q.60. If \(\displaystyle \frac{(5x − 7)}{3} + 2 = \displaystyle\frac{(4x − 3)}{4} + 4x\), then the value of \((8x + 5)\) is

  1. 7
  2. 9
  3. 13
  4. 6
Correct Answer: (D)