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

**Candidate has to do questions number 31 to 90 either from Part-II ( Mathematics and Science ) of from Part-III ( Social Studies/ Social Science).**

**Mathematics and Science**

Directions: (Q. 31-90) Answer the following questions by selecting the most appropriate option.

Q31. The ratio between the length and perimeter of a rectangular plot is 1:3. What is the ratio between the length and breadth of the plot?

(a) 1 : 2

(b) 2:1

(c) 3:2

(d) Data inadequate

Answer: (b) 2:1Sol: Let length and breadth of rectangular are x and y ∴ perimeter = 2(x + y) According to question, $ \frac{a}{2\left( a+b \right)}=\frac{1}{3} $ |

Q32. If a x b = a^{2} + b^{2} and a. b= a^{2} – b^{2}, the value of (5 x 2).25 is

(a) 215

(b) 225

(c) 226

(d) 216

Answer: (d) 216
Now (5 x 2).25 = 29.25 = 29 |

Q33. If a, b and c are three natural numbers in ascending order, then

(a) c^{2} – a^{2} > b

(b) c^{2} – a^{2} = b^{2}

(c) c^{2} – a^{2} < b^{2}

(d) c^{2} + a^{2} = a^{2}

Answer: (a) c^{2} – a^{2} > bSolution: we have a < b < c Now, c Hence c |

Q34. Buy three, get one free.’ What is the percentage of discount being offered here?

(a) 33.33%

(b) 25%

(c) 20%

(d) 28.56%

Answer: (b) 25%Solution: Buy three, get one free means discount one out of 4 items, ∴ discount = 1/4 × 100 = 25% |

Q35. The value is $ \sqrt{2}\,\,+\,\,\sqrt{3}\,\,+\,\,\sqrt{2}\,\,-\,\,\sqrt{3} $

$ \left( a \right) \sqrt{6} $

$ \left( b \right) \,\,6 $

$ \left( c \right) 2\sqrt{2} $

$ \left( c \right) 2\sqrt{3} $

Answer: $ \left( c \right) 2\sqrt{2} $ Solution: $ \sqrt{2}\,\,+\,\,\sqrt{3}\,\,+\,\,\sqrt{2}\,\,-\,\,\sqrt{3}=2\sqrt{2} $ |

Q36. On recast, the radius of an iron rod is made one fourth. If its volume remains constant, then the new length will become

(a) 1/4 times of the original

(b) 1/16 times of the original

(c) 16 times of the original

(d) 4 times of the original

Answer: (c) 16 times of the originalSolution: let radius and length are r and l Now volume V = ∏r After change radius and length are r volume V Now, ∏r ⇒ l = l ⇒ l ∴ 16 times of the original |

Q37. Find the value of 547527/82 if 547.527/0.0082 = x.

(a) x/10

(b) 10

(c) 100x

(d) x/100

Answer: (a) x/10Solution: $ \frac{547.527}{0.0082}=x\,\,\Rightarrow \,\,\frac{547.527\times 10000}{0.0082\times 10000}=x\,\,\Rightarrow \frac{547527\times 10}{82}=x\,\,\Rightarrow \frac{547527}{82}=\frac{x}{10} $ |

Q38. The smallest number by which 68600 must be multiplied to get a perfect cube is

(a) 5

(b) 10

(c) 8

(d) 12

Answer: (a) 5Solution: 68600 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 = ( 2 × 7) ∴ it should be multiplied by 5 to make perfect cube. |

Q39. A cyclist at ‘C’ is cycling towards B. How far will he have to cycle from C before he is equidistant from both A and B?

(b) 3 km

(c) 6 km

(d) 5 km

Answer: (d) 5 kmSolution:
Let the cyclist x km from point C towards B at P point where he is equidistant from both A and B. CP = x km, PQ =( x – 2) km, PB = (10 – x) km Now, AQ ⇒ 16 + (x–2) ⇒ 16 + x ⇒ 16x = 80 ⇒ x = 5 |

Q40. Unit’s digit in 13^{2003} is

(a) 1

(b) 3

(c) 7

(d) 9

Answer: (c) 7Solution: Remainder of 2003/4 = 3, now 3 Then unit digit in 13 |