# Social Harmony

**Topics:**Quadratic equation, Orders of magnitude, Mathematics in medieval Islam

**Pages:**10 (1564 words)

**Published:**June 21, 2013

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Common Instructions to Candidates: 1) This is a question cum answer paper booklet. 2) Space is provided to write answers below each question. Answer should be written within the space provided. 3) This question paper has 58 questions including the matching type question. 4) Candidate should not write the answer with pencil. Answer written with pencil will not be evaluated (Except graphs, diagrams & maps). 5) In case of multiple choice, fill in the blanks and matching questions, scratching, rewriting & marking is not allowed. Answers with such errors will not be evaluated.

I.

Four alternatives are given to each of the following incomplete statements. Select the most appropriate one and write its serial letter and also the correct answer in the space provided. [20 x 1 = 20] 1. If Tn = (–1)n, then the correct relation between the sum of terms is a) c) 2. S1 = S2 S3 = S4 b) d) S2 = S3 S2 = S4

HCF of ab, bc and ac is a) c) abc 1 b) d) a2 b2 c2 ab + bc + ac.

3.

The corresponding sides of two similar triangles are in the ratio 4 : 9. The ratio between their areas is a) c) 2:3 81 : 16 b) d) 16 : 81 14 : 19

4.

If 9 x = 12 + 147 , the value of x is a) 12 b) 9 c) 3 d)

3

5.

The incorrect statement among the following is a) c)

n n

Pn = nCn P0 = nC0

b) d)

-2-

n n

P1 = n C 1 Pn = nPn–1

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6. An example for HP among the following is a) c) 7. 1, 1,

1 2 3 , , 2 3 4 2 1 2 , , 3 2 5

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b) d)

1 1, 1 , 1 , 3 6 9

1,

1 1 1 , , 4 7 9

A non - traversable network among the following is

a)

b)

c)

d)

8.

The fourth term of the sequence a) c) 9 27 3

3 , 3, 3 3 is b) 21

d)

9 3

9.

The LCM of (x + y)2, (x – y)2 and (x2 – y2) is a) c) (x2 + y2)2 (x2 - y2)2 b) d) x4 – y4 (x + y) (x – y)3

10. The sum and the product of three numbers are 0 and 30 respectively. The sum of their cubes is a) c) 0 160 b) d) 90 900

11. If v2 = u2 + 2as, then the value of ‘u’ is a) c) v2 - 2as b) d) -3-

± v 2 + 2as

± v 2 − 2as

2as – v2

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12. The quadratic equation whose roots are 1 and –1 is a) c) 13. If a) c) ax2 – x – 1 = 0 x2 = 1 b) d) then ax2 – 1 = 0 x2 + 1 = 0

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∑ a = 0,

abc

∑a

abc

3

is b) d) 1 3abc

0 –3abc

14. The value of 1! × 3! × 0! is a) c) 6 3 b) d) 0 1

15. In the given figure if ∠PAO = 30º, the measure of ∠POQ is P

O

A b) d) 120º 30º

a) c)

60˚ 90º

Q

16. The pure quadratic equation in the following is a) c)

81 x (x + 2)2 = 3x 4x =

b) d)

1 =5 x 5 – x2 = x x+

17. The diagonal of a square is 10 2 cm, then the length of its side is a) c) 2 cm 8 cm b) d) 10 cm 20 cm

-4-

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18. The Harmonic Mean between 1 and 2 is a) c)

1 1 2

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b) d)

1

1 4

1

1 3

1

2 3

19. The matrix of the given network is P a) 2 0 0 2 2 1 2 1 n n

Q b) 2 1 1 2 1 1 1 1

c)

d)

20. The value of a) n(n –1)

∑ n + ∑ ( n − 1) is

n=1 n=1

b)

n2 2

c)

2n2

d)

n2 [10 x 1 = 10]

II. Complete the following statements by filling the blanks.

21. If the order of matrix A is m × n and the order of matrix B is n × p, then the order of matrix AB is ________. 22. A regular polyhedron enclosed by pentagonal faces is ___________. 23. If P and Q are non - empty sets and P – Q = P, then P ∩ Q is _________. 24. The mathematician who proposed Basic Proportionality Theorem is ____________. 25. The angle in a semi circle is _____________. -5-

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26. The formula used to find the coefficient of variation is ___________. 27. The conjugate of a x + b y is ______________.

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28. A solid described by the revolution of a semi circle about a fixed diameter is ______. 29. The formula used to find the curved surface area of a cylinder is __________. 30. The reciprocals of the terms of an AP form _____________. III. Solve the following problems in the space provided. 31. In a group of 25 persons 8 drink tea only, 7 drink coffee only...

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