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Dear Friends, here are the subjective questions paper of secondary level mathematics-2074 of internal competition.The full marks was given 60 and time 2 hours and 15 minutes.Please read the full questions below.

Attempt all the questions

1.a. Define a group and prove that fourth root of unity forms a multiplicative inverse. 2+3

1.b.Define odd and even vertices of network with examples. Prove that the number of odd vertices of a network is always even. 2+3

2.a.Define argument. Test the validity of the following argument ” if the polygon is square, then it has four sides. If the polygon has four sides, it has three angles. Therefore, if a polygon is is a square,then it has three angles. 1+4

2.b. Explain Babylonian and Egyptian numeration system. 2.5×2

3.a.What are the different measures of dispersion? Why is standard deviation known as the best measure of dispersion? 2+3

3.b. A bag contains 24 balls numbered from 1 to 24. One ball is drawn at random, what is the probability of: 2.5×2

- i) it is the multiple of 4 and 6
- ii) It is a multiple of 4 or 6.

4..How do you derive the formula for the area of circle? Prepare a lesson plan to teach the area of circle. 5+5

5.Define Saccheri quadrilateral and prove that, in elliptic geometry, the length of the summit of a Saccheri quadrilateral is less than the length of its base.Also show that the sum of two acute angles of is greater than 90 degree. 1+4+5

6.Define isometric transformation with suitable examples. prove that reflection is an isometric transformation. 3+7

Here is a subjective questions paper of secondary level mathematics-2075.. The full mark is 60 and time is 2 hours 15 minutes. Subjective questions paper.

1.a.Define prime number. Show that no other consecutive number is prime other than (2,3). 1+3

1.b.prepare a lesson plan to teach the concept of limit of lim x tends to zero sinx/x=1 using geometric relation at school level. 5

2.Define conditional statements and state different form as of conditional statements with suitable examples. prove that the conditional and its contrapositive of a statement are logically equivalent. 1+4+5

3.a.Distinguish between absolute and relative measure of dispersion. Calculate root mean square deviation from median from the following distribution. 1+4

Class interval | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |

Frequency | 7 | 18 | 25 | 31 | 15 | 4 |

b. Discuss different types of variables with examples. find the probability distribution of the number of heads obtained in 4 tosses of a balanced coin.2+3

4.Discuss the axiomatic construction of Euclidean geometry on the basis of consistence,completeness and independence. State and prove “betweenness relation for points in a straight line.(The verification of the axiom of order) 4+6

5.Define Saccheri Quadrilateral. prove that two Saccheri quadrilaterals in hyperbolic Geometry are congruent if their summit and summit angles are congruent.Also prove that the angle sum of every right triangle exceeds two right angles in Elliptic Geometry. 1+4+5

6.Define different isometric transformations. Find the image of triangle whose vertices are A=(-1,3),B=(4,7) and C=(0,6) under translation T=(-3,2) 4+6

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