CTET June 2011 Paper II Solved Question

# Test1

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

Sol:
Let length of the rectangle = X and breadth = Y,
According to question,

Sol:

#### 3. If a, b and c are three natural numbers in ascending order, then chose the correct option c 2-a 2 = b 2 c 2-a 2 < b 2 c 2-a 2 > b c 2+b 2 = a 2

Sol:
Let a,b and c are the three natural numbers in ascending order, then $a{b}^{2}\phantom{\rule{0ex}{0ex}}⇒{c}^{2}-{a}^{2}>b$

#### 4. 'Buy three, get one free.' What is the percentage of discount being offered here ?

Sol:
Let the price of an item = x
price of actual items = price of 4 items = 4x
price offered to customer for the 4 items =3x
discount = 4x-43=x
% discount = $\frac{x×100}{4x}=25%$

#### 5. The Value of √2 + √3 + √2 - √3 is

Sol:
√2 + √3 + √2 - √3 = √2+√2=2√2

#### 6. When recast, the radius of an iron rod is made one-fourth. If its volume remains constant, then the new length will become

sol:
Let the radius of the iron rod = r, length = h
hence its volue = πr2h
A/Q,
radius after recasting = $\frac{r}{4}$
let the new length = H
Again from question, ${\mathrm{\pi r}}^{2}\mathrm{h}=\mathrm{\pi }\left(\frac{\mathrm{r}}{4}{\right)}^{2}\mathrm{H}$
=> 16h=H
Hence new lenght = 16 times of its original length

Sol:

#### 8. The smallest number by which 68600 must be multiplied to get a perfect cube

Sol:
$68600=2×2×2×5×5×7×7×7\phantom{\rule{0ex}{0ex}}=14\sqrt{5×5}$
Hence 5 is the required number for the given number to be perfect cube.

#### 9. 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 ? Sol: Given QA=4, CQ=2, CA=10
Let CP=X
∴ PQ=(X-2)
PB=(10-X)
According to question,
AP=PB
From ∆ AQP
AP 2 = QP 2+QA 2
(10-X) 2=(X-2)2+42 (10-X+X-2)(10-X-X+2)=16
8(12-2X)=16
12-2X=2
6-X=1
∴ X= 5

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