CTET June 2011 Paper II Solved Question

OC Study

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,
X2X+Y=13=> 3X=2X+2Y=> X=2Y=> XY=21=> X:Y=2:1

2. If a * b = a2 + b2 and a . b = a2 - b2, the value of (5 * 2) . 25 is?

Sol:
5*2=52+22=25+4=29Therefore, 5*2.25=(52+22)2-252=(25+4)2-252=292-252=841-625=216

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

Sol:
Let a,b and c are the three natural numbers in ascending order, then a<b<ca2<b2<c2b2<c2-a2c2-a2>b2c2-a2>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 = x×1004x=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 = r4
let the new length = H
Again from question, πr2h=π(r4)2H
=> 16h=H
Hence new lenght = 16 times of its original length

7. Find the value of 547.5270.082 if x=547.5270.0082

Sol:
Given,x=547.5270.0082Dividing both side by 10,x10=547.5270.082x10=54752782Hence 54752782=x10

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=145×53
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 ?
math9.jpg

Sol:
solution image
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

10. A square sheet ABCD when rotated on its diagonal AC as its axis of rotation sweeps a
solution image
  1. Circle
  2. Spindle
  3. Cylinder
  4. trapezium

Sol:
Spindle

11. 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

Sol:

12. Which is greatest among 33 and half %; 4/15 and 0.35 ?

Sol:

13. The factorization of 25 - p2 - q2 - 2pq is

Sol:

14. Unit's digit in 132003 is?

Sol:

15. 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 the shaded part?

Sol:

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

Sol:

17. 2x - 13, 2x - 11, 2x - 9, 2x - 7 are consecutive
  1. Natural Number
  2. Even Number
  3. Odd Number
  4. Prime Number

Sol:

19. The fractional equivalent of 57.12% (approx.) is
  1. 349/625
  2. 359/625
  3. 357/625
  4. 347/625

Sol:

20. The ratio of the side and height of an equilateral triangle is
  1. 2:1
  2. 1:1
  3. 2:√3
  4. √3:2

Sol:

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

Sol:

22.
4/16 - 1/8 = 3/8
6/7 - 2/9 = 4/2
The above represents the work of a student. If this error pattern continues, the student's answer to 5/11 - 2/7 will be?

Sol:

23. A teacher in grade-VI provided each child with a centimeter grid paper and a pair of scissors. She wanted them to explore how two-dimensional shapes can be folded into three-dimensional objects. Which of the following concepts are the students exploring?
  1. Rotation
  2. Reflections
  3. Nets
  4. Decimals

Sol:

24. When doing exponents, the work observed in a learner's notebook was as follows :
4 3X42=45
6 4X64=68
7 3X37=2110
  1. add exponents
  2. add exponents and multiply
  3. multiply numbers with same base
  4. multiply numbers with different bases

Sol:

25. Given linear equations I, II and III, a learner is not able to solve III algebraically. The most likely area of difficulty is that the learner has not understood
  1. The two equations can be added or subtracted to solve them
  2. That equations can be solved by method of substitutions
  3. The method of solving equations graph
  4. That both the equations in 3 can be altered by multiplying with suitable numbers

Sol: