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#### Pre Half yearly

11th Standard

Reg.No. :
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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 100

Part A

15 x 1 = 15
1. There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

45

(b)

40

(c)

39

(d)

38

2. In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

(a)

110

(b)

10C3

(c)

120

(d)

116

3. If nC4,nC5,nC6 are in AP the value of n can be

(a)

14

(b)

11

(c)

9

(d)

5

4. The number of different signals which can be give from 6 flags of different colours taking one or more at a time is

(a)

1958

(b)

1956

(c)

16

(d)

64

5. The product of r consecutive positive integers is divisible by

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

6. If (a2-a)C2=(a2-a)C4, then a =

(a)

2

(b)

3

(c)

4

(d)

none of these

7. If p(n):49n + 16n$\lambda$ is divisible by 64 for n $\in$ N is true, then the least negative integral value of $\lambda$ is

(a)

-3

(b)

-2

(c)

-1

(d)

-4

8. How many words can be formed using all the letters of the word ANAND:

(a)

30

(b)

35

(c)

40

(d)

45

9. If nPr=k x n-1Pr-1 what is k:

(a)

r

(b)

n

(c)

n+1

(d)

r+1

10. A candidate is required to answer 7 question out of 12 questions, which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

(a)

779

(b)

781

(c)

780

(d)

782

11. The sum up to n terms of the series $\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +$....is

(a)

$\sqrt { 2n+1 }$

(b)

$\frac { \sqrt { 2n+1 } }{ 2 }$

(c)

$\sqrt { 2n+1 } -1$

(d)

$\frac { \sqrt { 2n+1 } -1 }{ 2 }$

12. The coefficient of x6 in (2 + 2x)10 is

(a)

10C6

(b)

26

(c)

10C626

(d)

10C6210

13. $\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+...$is:

(a)

$\frac{e^{-1}}{2}$

(b)

$\frac{e+e^{-1}}{2}$

(c)

$\frac{e-e^{-1}}{2}$

(d)

none of these

14. The slope of the line which makes an angle 45 with the line 3x- y = -5 are

(a)

1,-1

(b)

$\frac{1}{2},-2$

(c)

$1,\frac{1}{2}$

(d)

$2,-\frac{1}{2}$

15. If the equation of the base opposite to the vertex (2,3) of an equilateral triangle is x +y = 2, then the length of a side is

(a)

$\sqrt{\frac{3}{2}}$

(b)

6

(c)

$\sqrt{6}$

(d)

$3\sqrt{2}$

16. Part B

10 x 2 = 20
17. In how many ways 5 persons can be seated in a row?

18. Find the value of 4!+5!

19. Using the mathematical induction, show that for any natural number n > 2,
$\left(1-{1\over 2^2} \right)\left(1-{1\over 3^2} \right)\left(1-{1\over 4^2} \right)...\left(1-{1\over n^2} \right)={n+1\over 2n}$

20. By the principle of mathematical induction, prove that for n > 1,
$1^2+2^2+3^2+L+n^2>{n^3\over 3}$

21. A person wants to buy a car. There are two brands of car available in the market and each brand has 3 variant models and each model comes in five different colours as in figure. In how many ways she can choose a car to buy?

22. There are 10 bulbs in a room. Each one of them can be operated independently. Find the number of ways in which the room can be illuminated.

23. Part C

10 x 3 = 30
24. Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?

25. In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together.

26. If an electricity consumer has the consumer number say 238:110:29, then describe the linking and count the number of house connections upto the 29th consumer connection linked to the larger capacity transformer number 238 subject to the condition that each smaller capacity transformer can have a maximal consumer link of say 100.

27. Find the number of strings of 5 letters that can be formed with the letters of the word PROPOSITION.

28. Write the first 6 terms of the sequences whose nth term an given below
${ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}$

29. If a,b,c are in geometric progressions and if ${ a }^{ \frac { 1 }{ x } }={ b }^{ \frac { 1 }{ y } }={ c }^{ \frac { 1 }{ z } }$ , then prove that x, y, z are in arithmetic progression

30. If pth term of an AP is q and qth term is p, find (p + q)th term.

31. The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and
(iii) Find the value of F for 38°C.

32. Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12

33. Part D

7 x 5 = 35
34. In a parking lot one hundred, one year old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?

35. How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?

36. Find the total number of subsets of a set with [Hint: nC0+nC1+nC2+...+nCn=2n].
n elements.

37. How many different selections of 5 books can be made from 12 different books if,
(i) Two particular books are always selected?
(ii) Two particular books are never selected?

38. How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?

39. In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?