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) 2:1 Sol: 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} $
$ \Rightarrow \,\,3a\,\,=\,\,2a\,\,+\,\,2b $
$ \Rightarrow a\,\,=\,\,2b $
$ \Rightarrow \frac{a}{b}=\text{2:}1 $ |
Q32. If a x b = a2 + b2 and a. b= a2 – b2, the value of (5 x 2).25 is
(a) 215
(b) 225
(c) 226
(d) 216
| Answer: (d) 216 Solution: 5 x 2 = 25 + 4 = 29 Now (5 x 2).25 = 29.25 = 292 – 252 = (29 + 25)(29 – 25)=216 |
Q33. If a, b and c are three natural numbers in ascending order, then
(a) c2 – a2 > b
(b) c2 – a2 = b2
(c) c2 – a2 < b2
(d) c2 + a2 = a2
| Answer: (a) c2 – a2 > b Solution: we have a < b < c Now, c2 – a2 = (c – a) (c + a), as c > b then c + a > b and a, b, c natural number then c – a will minimum be 2. Hence c2 – a2 > b |
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 original Solution: let radius and length are r and l Now volume V = ∏r2l After change radius and length are r1=r/4 and l1 volume V1 = ∏ (r/4)2 l1 Now, ∏r2l = ∏ (r/4)2 l1 ⇒ l = l1/16 ⇒ l1 = 16l ∴ 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/10 Solution: $ \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) 5 Solution: 68600 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 = ( 2 × 7)3 × 5 × 5 ∴ 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 km Solution: 
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, AQ2 + PQ2 = AP2 = PB2 ⇒ 16 + (x–2)2 = (10 – x)2 ⇒ 16 + x2 – 4x + 4 = 100 –20x + x2 ⇒ 16x = 80 ⇒ x = 5 |
Q40. Unit’s digit in 132003 is
(a) 1
(b) 3
(c) 7
(d) 9
| Answer: (c) 7 Solution: Remainder of 2003/4 = 3, now 33 = 27 Then unit digit in 132003 is 7 |
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