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Child Development | Mathematics and Science | Social studies | Language-I(Eng) | Language-II(Hindi) |

Q41. A square sheet ABCD, when rotated on its diagonal AC at its axis of rotation, sweeps a

(a) cone

(b) spindle

(c) cylinder

(d) trapezium

Answer: (b) spindleSolution: When a square is rotated on it diagonal as its axis of rotation, the spindle shape is formed. |

Q42. The area of a triangle with base x units is equal to the area of a square with side x units. Then, the altitude of the triangle is

(a) x/2 units

(b) x units

(c) 2x units

(d) 3x units

Answer: (c) 2x unitsSolution: Let altitude of the triangle is h units. Now, ½ × base × altitude = (side) ⇒ x × h = 2x ⇒ h = 2x |

Q43. Which is greatest among $ 33\frac{1}{2}\%, \frac{4}{15} $ and 0.35?

(a) 33½%

(b) 4/15

(c) 0.35

(d) cannot be compared

Answer: (c) 0.35Solution: $ 33\frac{1}{2}\% =\,\,\frac{67}{200}=0.335, \frac{4}{15}=0.266667 $ So, greatest 0.35 |

Q44. The factorization of 25 – p^{2} – q^{2} – 2pq is

(a) (5 + p + q) (5 – p + q)

(b) (5 + p +q) (5 – p – q)

(c) (5 + p – g) (5 – p + q)

(d) (5+ p – q ) (5 – p – q)

Answer: (b) (5 + p +q) (5 – p – q)Solution: 25 – p |

Q45. A rectangle is divided horizontally into two equal parts. The upper part is further divided into three equal parts and the lower part is divided into four equal parts. Which fraction of the original rectangle is the shaded part?

(a) 3/5

(b) 2/7

(c) 4/7

(d) 7/12

Answer: (d) 7/12Solution: fraction of upper part = ½ and shaded area = 1/2 × 2/3 = 1/3 fraction of lower part = ½ and shaded area = 1/2 × 2/4 = 1/4 Total shaded area = 1/3 + 1/4 = 7/12 |

Q46. In the given figure, PS = SQ = SR and ∠SPQ= 54°. Find the measure of ∠x.

(a) 54°

(b) 72°

(c) 108°

(d) 36°

Answer: (d) 36°Solution: SP = SQ, ∴ ∠SQP = ∠SPQ = 54°, ∴ ∠PSQ = 180° – (54° + 54°)= 72° ∴ ∠QSR = 180° – 72° = 108° , now ∠SRQ + ∠SQR = 180° – 108° = 72° ∴ x° = 72°/2 = 36° ( ∠SRQ = ∠SQR) |

Q47. 2x – 13, 2x – 11, 2x – 9, 2x – 7 are consecutive

(a) prime numbers

(b) even numbers

(c) odd numbers

(d) natural numbers

Answer: (c) odd numbersSolution: let x is integer, then 2x is even number ∴ 2x – 13, 2x – 11, 2x – 9, 2x – 7 are consecutive odd numbers |

Q48. The fractional equivalent of 57.12% (approx.) is

(a) 349/625

(b) 359/625

(c) 357/625

(d) 347/625

Answer: (c) 357/625Solution: 57.12% = 57.12/100 = 5712/10000 = 357/625 |

Q49. The ratio of the side and height of an equilateral triangle is

(a) 2 : 1

(b) 1 : 1

(c) $ \text{2:}\sqrt{3} $

(d) $ \sqrt{3}:2 $

Answer: (c)$ \text{2:}\sqrt{3} $ Solution: height of an equilateral triangle (h) = $ \frac{\sqrt{3}}{2}\times \,\,side\,\,\Rightarrow \,\,side\,\,: (h)\,\,=\,\,\text{2 : }\sqrt{3} $ |

Q50. If two adjacent sides of a square paper are decreased by 20% and 40% respectively, by what percentage does the new area decrease?

(a) 48%

(b) 50%

(c) 52%

(d) 60%

Answer: (c) 52%Solution: let side of square = 100x Then area = 10000x New side are 80x and 60x and area = 4800x Area decrease = 10000x Percentage decrease = (5200x |