CTET September 2015 Paper 2 mathematics solved

31.  If a = 3¹²⁹ x 5¹²⁸ x 7²²

           b =  3¹²⁸ x 5¹²⁹ x 7²¹

                c = 3¹²⁷ x 5¹²⁹ x 7²³ and

          d =3¹²⁷ x 5¹²⁸ x 7²⁴ then

H.C.F. of a , b, c and d is

(1). 3127x 5¹²⁸x7²²

(2). 3¹²⁸ x5¹²⁸ x 7²¹

(3).  3¹²⁸x 5¹²⁹x 7²¹

(4).  3¹²⁷ x 5¹²⁸ x   7²¹

 ^Answer: 
(4).  3¹²⁷ x 5¹²⁸ x   7²¹

Solution:

HCF is obtained by taking the terms with the lowest power that is common to all the numbers we are taking HCF of. Lowest terms in this question are 127, 128 and 21 respectively. Therefore option 4 is the correct answer. 

For more on HCF and LCM read How to Find HCF

 

32. The value of  ∛-2300 x ∛5290    is:

1. -230

2. -529

3. -270

4. 230

Answer:   1. -230

Solution: 

We can find the cube root of -2300 and the cube root  529. But if we rearrange them and bring them under one sign we get

  
∛-2300 x ∛5290 =  ∛-23x23x23x10x10x10 = -230

33. The value of (2^a)^bc/(5^b)^ac  , where a=2, b=3 and c=0, is :

1. 1

2. 0

3. -1

4. 2/5

Answer: 1. 1

Solution:

 
(2^a)^bc/(5^b)^ac   = ((2²)⁰/(5³)⁰ 

= 1 x 1 = 1

34. The value of

    4 + 44/10 +404/100 +444/1000 + 4/10000 is :

    1.       12.8224

    2.       12.8944

    3.       12.8844

    4.       12.8804

   

    Answer:   3.       12.8844

    

    Solution:

    Rewriting the above question in decimal to get

       4 + 4.4 + 4.04 + 0.444 + 0.0004

      = 12. 8844

35.  The smallest value of ‘y’ in the number 9y8071 so that it is divisible by 11 is :

1. 1

2.  0

3. 2

4. 3

Answer:  1. 1

Solution:

We will apply the divisibility rule of 11. We add the numbers at the odd places and the even places and subtract them. 

Sum of digits at odd places = y+0+1 = 1+y

sum of digits at even places = 7+8+9=24

and their difference = 24 - 1-y = 23-y

Now, either 23-y = 0 or a number divisible by 11. From our options only option 1 (1) can make this happen. 23-1 =22 which is divisible by 11.

Read more divisibility rules.

36. (14.96x10¹⁰ )  - (3.84x10⁸ ) is expressed in standard form as:

1.  14921.6 x 10⁹

2.  14.9216 x 10¹⁰

3. 14922.6 x 10⁸

4. 1.49216 x 10¹¹

 

Answer:4. 1.49216 x 10¹¹

Solution:

14.96x10¹⁰ can be written as 149.6 x10⁹

 3.84x10⁸can be written as 0.384 x10⁹)

 and their difference is    149.216 x 10⁹)

which in standard form is written as 1.49216 x 10¹¹)

 

37. The sum of mean , mode and median of the data

        6,3,9,5,1,2,3,6,5,1,3 is:

    1.       10

    2.        11

    3.       12

    4.       13

   

     Answer :  1.       10

     

     Solution: Mean = (6+3+9+1+2+3+6+5+1+3)/11 = 44/11 = 4

                       Mode = 3 (Most repeated number)

                       Median = middle value of  (1,1,2,3,3,3,5,5,6,6,9) = 3

     And therefore their sum is 10.

38. Natural numbers 4 to 15 are written on different slips (one number on one slip)         , kept in a box and mixed well. Renu picks up one slip from the box without looking into it. What is the probability that this slip bears a prime number?

1. 2/5

2. 3/11

3. 1/3

4. 5/12

Answer: 3. 1/3

Solution:

Total number of slips = 15-4 + 1 = 11+1 = 12

Number of prime numbers from 4 to 15 are 5,7,11,13. Total 4 in numbers.

Hence the probability of getting a prime number = 4/12 = 1/3 

 

39. A sum of money amounts to 4818 after 3 years and 7227 after 6 years on compound interest. The sum is :

1. 2409

2. 2490

3. 3122

4. 3212

Answer:4. 3212

Solution:

Applying the formula for compound interest, P = A(1+r/100)^t

7227 = 4818(1+r/100)^3  ----------------- i

4818 = A(1+r/100)^3 ----------------- ii

Dividing i and ii to get

7227/4818 = 4818/A
A = (4818 x 4818)/7227 = 3212

40. If the weight of 18 sheets of paper is 50 grams , how many sheets of the same paper will weigh 3(3/4) kg?

1. 1350

2. 1314

3. 1386

4. 1836

Answer:  1. 1350

Solution:

 Using Unitary method,

 3(3/4) KG has (18/50) x 3750 =  1350 sheets

To learn Unitary method read : Unitary Method

41. If (3x-2)/3 + (2x+3)/2 = x + 7/6 then the value of (5x-2)/4 is :

1. 1/12

2. (-1/3)

3. ¼

4. (-1/12)

Answer: 4. (-1/12)

Solution:

Given 
 (3x-2)/3 + (2x+3)/2 = x + 7/6

  [2(3x-2) + 3(2x+3)]/6 = (6x+7)/6

   6x - 4 + 6x +9 = 6x +7

  12x + 5 = 6x +7

   6x =2

     x = 1/3

And (5x-2)/4 = [5/3 - 2]/4 = -1/12

42.  If 4x ² + 12xy -8x +9y ²  -12y = (ax+by)(ax+by-4)

Then the value of a² + b² is:

      1.       5

      2.       10

      3.       13

      4.       25

     

       Answer:   3.       13

      

      Solution:   

       
4x ² + 12xy -8x +9y ²  -12y =   (ax)² + abxy + 4ax + abxy + (by)² -4by

     Comparing them to get a² =4, b² =9 and
a² + b^{2 = 13}

 

43. In the product of (5x+2) and (2x² – 3x +5), the sum of the coefficients of x² and x is :

1. -9

2. 8

3. 9

4. -8

Answer:2. 8

Solution 

Coefficient of  x²  will be obtained by multiplying 5x to (-3x) to get -15x² and 2 to (2x²) to get 4x²

and net coefficient of x² = -11

And the x is obtained by multiplying 5x by 5 to get 25x and 2  by -3x to get -6x.

And net coefficient of x is 19 .

  sum of the coefficients of x² and x is  -11 + 19 = 8

 

44. the internal base of a rectangular box is 15 cm long and 12(1/2) cm wide and its height is 7(1/2) cm. the box is filled with cubes of each of sides 2(1/2) cm. the number of cubes will be :

1. 45

2. 60

3. 90

4. 120

Answer:  3. 90

Solution:

Total volume to rectangular box = 15 x 12.5 x 7.5

volume of 1 box = 2.5 x 2.5 x2.5 = 

Number of cubes that can fit = (15 x 12.5 x 7.5) /2.5x2.5x2.5 = 90

45.  The perimeter of a trapezium is 58cm  and the sum of its non parallel sides is 20 cm. If its area is 152 cm² , then the distance between the parallel and sides, in cms, is :

1. 6

2. 8

3. 9.8

4. 15.2

Answer: 2. 8

Solution

Area of trapezium= 1/2 (Sum of parallel side)(height)

                              152   = 1/2(58-20) (height)

                              304 = 38(height)

                              height = 8

                         

46. The measure of each interior angle of a regular convex polygon is 156,. The number of sides of the polygon is :

1. 15

2. 12.

3. 10

4. 8

Answer: 1.   15

Solution:

Exterior angle = 180 - interior angle = 180 - 156 = 24 

Therefore using the formula that relates the exterior angles and the number of sides

         number of sides = 360/exterior angle = 360/24 = 15

 

47. If the number of sides of a regular polygon is ‘n’, then the number of lines of symmetry is equal to :

1. n/2

2. n²

3. 2n

4. n

Answer: 4.  n

Solution:

 There are n lines of symmetry for a regular polygon with 'n' sides.

 

48. The sides of a triangle are 6.5 cm, 10 cm and x cm , where x is a positive number . what is the smallest possible value of x among the following?

1. 4.5

2. 2.8

3. 3.5

4. 4

Answer:4.    4

Solution:

For a triangle the sum of any two sides should be greater than the third side. using this rule,

1. 4.5

if third side is 4.5 cm, then 6.5 + 4.5 > 10   correct. But is 4.5 the smallest possible value. lets check more.

2.   2.8

  2.8 + 6.5 = 9.3    < 10 . Not a triangle

3.  3.5

 6.5 + 3.5 = 10 = 10. Not possible

4.  4

      4+6.5 = 10.5 >10 . Correct and since 4 <4.5 this is the smallest possible number among the options and hence the right answer.

49. Chhaya simplified the  given rational number (-25)/(-30) =-5/6

This error can be considered as:

      1.       Careless error

      2.       Conceptual error

      3.       Procedural error

     4.       Error due to wrong interpretation of problem

Answer:   2.       Conceptual error

 

50. ‘Data Handling ‘ at upper primary focuses on :

1. data collection, organization and interpretation

2. data interpretation only

3. data organization only

4. techniques of data collection only

 

Answer:
1. data collection, organization and interpretation

 

51. which one of the following is not a Problem solving strategy in mathematics:

1. Trial and error

2. Drawing

3. Solving backwards

4. Rote learning

Answer: 4. Rote learning

 

52. According to piaget, when the child is at formal operational stage, it is appropriate to introduce:

1. Ratio and proportion

2. Data handling

3. Numbers

4. Geometry

Answer:1. Ratio and proportion

 

53. Read the following problem given in a textbook for class VII:

“A map is given with a scale of 2cm =1000km. What is the actual distance between two places , in kms, if the distance on the map is 2.5 cm?” the problem is :

      1.       Interdisciplinary in nature

      2.       Investigatory in nature

      3.       Based on higher order thinking skills

      4.       To enhance problem solving skills

Answer:      1.       Interdisciplinary in nature

 

54. Which one of the following is not a mathematical process?

1. Visualization

2. Estimation

3. memorization

4. Measurement

Answer: 3.   memorization

 

55. According to NCF 2005 , school mathematics takes place in a situation where :

1. mathematics is a part of children’s life experiences

2. children are forced to learn all concepts by daily practice

3. children are listeners and the teacher is an active narrator

4. children are involved drill of   formulae and pressure of performance in examination.

Answer: 1. mathematics is a part of children’s life experiences

 

56.In class VI, teacher gave a topic for debate as Formative Assessment(FA) task.

“Hindu –Arabic numerals are more powerful than Roman numerals”

Objective of this FA activity is to assess :

      1.       Knowledge

      2.       Analysis

      3.       Creativity

      4.       Understanding

Answer:       2.       Analysis

 

57. In a mathematics classroom emphasis is placed on :

1. mathematical content

2. mathematical content , process and reasoning

3. problem solving strategies

4. mathematical algorithms and processes

Answer:  2. mathematical content , process and reasoning

 

58.  A teacher gave the following problem related to ‘discount’ to the students for solving.

“ The marked price (M.P.) of a shirt and sweater are 200 and 300 respectively, and the discount on the marked prices of shirt and sweater are 20% and 12% respectively. While preparing the bill , the shopkeeper interchanged the discounts on these items by mistake.on getting the bill , Hamida noticed the mistake and paid the actual amount to the shop keeper . How much money did Hamida pay to shopkeeper.”

What value does the teacher try to promote through this problem.

      1.       Compassion

      2.       Honesty

      3.       Co-operation

      4.       Sympathy

Answer:  2.       Honesty

 

59. The difference between the greatest and the smallest fraction amongst

6/7, 8/9 ,9/10, 7/8

Is:

    1.       3/70

    2.       1/56

    3.       1/72

    4.       2/63

Answer:  1.       3/70

Solution:

The greater fraction is 9/10 and the smallest fraction is 6/7

And how. If we add same number to the numerator and denominator of an improper fraction  then value of the fraction increases.

Now the difference between the fractions is   (9/10 - 6/7) = (63- 60)/70 = 3/70

60. The additive inverse of S, where S= 1-2+3-4+5-6+7-8+…+49-50

1. 0

2. 25

3. -25

4. 1

Answer: 2.     25

Solution:

Rearranging the series to get

   S = (1+3+5+7+9 ....+49) + (-2-4-6-8-10...-50)

Now we get two Arithmetic progression with common difference of 2.

Using the formula for some of A.P. to get

S =  25(1+49)/2  -[25(2+50)/2]

    = 25(50)/2 - 25(52)/2

    = 25x25 - 25x26 = 25(-1) = -25

 Now the additive inverse (same number with an opposite sign )is -(-25) =25