CTET 2011 Question Paper-2 with Answer: Exam Portal

CTET 2011 Question Paper-2 with Answer
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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

(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

(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

(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%

(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

(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)²l₁

Now, ∏r²l = ∏ (r/4)²l₁

⇒ 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

(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

(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

(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

(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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CTET 2011 Question Paper-2 with Answer

Mathematics and Science

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