#### Important One Mark Question Paper

11th Standard

Reg.No. :
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Mathematics

Time : 01:00:00 Hrs
Total Marks : 50

50 x 1 = 50
1. The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

2. The function f:R➝R is defined by f(x)=$\frac { \left( { x }^{ 2 }+cosx \right) \left( 1+{ x }^{ 4 } \right) }{ \left( x-sinx \right) \left( 2x-{ x }^{ 3 } \right) } +{ e }^{ -\left| x \right| }$ is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function.

3. Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

(a)

(2,4)∈R

(b)

(3,8)∈R

(c)

(6,8)∈R

(d)

(8,7)∈R

4. Let f: R➝R be given by f(x)=x+$\sqrt { { x }^{ 2 } }$ is

(a)

injective

(b)

Surjective

(c)

bijective

(d)

none of these

5. Let R be the universal relation on a set X with more than one element. Then R is

(a)

not reflexive

(b)

not symmetric

(c)

transitive

(d)

none of the above

6. If $f(x)={1-x\over 1+x},(x\neq0)$ then f-1(x) =

(a)

f(x)

(b)

$1\over f(x)$

(c)

-f(x)

(d)

-$1\over f(x)$

7. Which one of the following is not a singleton set?

(a)

A = {x : 3x - 5 = 0, x ∈ Q}

(b)

B = {| x | = 1 / x ∈ Z}

(c)

{x : x3 - 1 = 0, x ∈ R}

(d)

{x : 30x = 60, x ∈ N}

8. If |x+2| $\le$ 9, then x belongs to

(a)

$(-\infty ,-7)$

(b)

[-11, 7]

(c)

$(-\infty ,-7)\cup (11,\infty)$

(d)

(-11, 7)

9. The number of solution of x2+|x-1|=1 is

(a)

1

(b)

0

(c)

2

(d)

3

10. $(\sqrt { 5 } -2)(\sqrt { 5 } +2)$ is equal to

(a)

1

(b)

3

(c)

23

(d)

21

11. (x2-2x+2)(x2+2x+2) are the factors of the polynomial

(a)

(x2-2x)2

(b)

x4-4

(c)

x4+4

(d)

(x2-2x+2)2

12. Find the other root of x2-4x+1=0 given that 2+$\sqrt{3}$ is a root:

(a)

$\sqrt{3}$+2

(b)

-$\sqrt{3}$-$\sqrt{2}$

(c)

2-$\sqrt{3}$

(d)

$\sqrt{3}$-2

13. $\sqrt [ 4 ]{ { \left( -2 \right) }^{ 4 } } \times { \left( -1000 \right) }^{ \frac { 1 }{ 3 } }$is

(a)

20

(b)

-20

(c)

2-10

(d)

100

14. The number of real solutions of the equation |x2| - 3|x| + 2 = 0 is

(a)

1

(b)

2

(c)

3

(d)

4

15. The maximum value of 4sin2x+3cos2x+$sin\frac { x }{ 2 } +cos\frac { x }{ 2 }$ is

(a)

$\frac { 1 }{ 8 }$

(b)

$\frac { 1 }{ 2 }$

(c)

$\frac { 1 }{ \sqrt { 3 } }$

(d)

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

16. If cospፀ + cosqፀ = 0 and if p ≠ q, then ፀ is equal to (n is any integer)

(a)

$\frac { \pi (3n+1) }{ p-q }$

(b)

$\frac { \pi (2n+1) }{ p+q }$

(c)

$\frac { \pi (n\pm 1) }{ p\pm q }$

(d)

$\frac { \pi (n+2) }{ p+q }$

17. A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

(a)

10$\pi$ seconds

(b)

20$\pi$ seconds

(c)

5$\pi$ seconds

(d)

15$\pi$ seconds

18. The value of sin2$\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 }$ is

(a)

$\frac { 1 }{ 2 }$

(b)

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

(c)

1

(d)

0

19. If cos x=$\frac { -1 }{ 2 }$ $0 < x < 2\pi$and , then the solutions are

(a)

x=$\frac { \pi }{ 3 } ,\frac { 4\pi }{ 3 }$

(b)

x=$\frac { 2\pi }{ 3 } ,\frac { 4\pi }{ 3 }$

(c)

x=$\frac { 2\pi }{ 3 } ,\frac { 7\pi }{ 6 }$

(d)

x=$\frac { 2\pi }{ 3 } ,\frac { 5\pi }{ 3 }$

20. The quadratic equation whose roots are tan75° and cot75° is:

(a)

x2+4x+ 1 =0

(b)

4x2-x+ 1 =0

(c)

4x2+ 4x - 1 = 0

(d)

x2 - 4x + 1 = 0

21. In $\triangle$ABC, $\hat{C}$ = 90° then a cosA + b cosB is:

(a)

2R sinB

(b)

2 sinB

(c)

0

(d)

2a sinB

22. Number of solutions of the equation tan x+sec x=2 cos x lying in the interval [0,2π] is

(a)

0

(b)

1

(c)

2

(d)

3

23. In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is

(a)

125

(b)

124

(c)

64

(d)

63

24. The number of 5 digit numbers all digits of which are odd is

(a)

25

(b)

55

(c)

56

(d)

625

25. The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

(a)

$\times$ 11 C7+10C8

(b)

11C7+10C8

(c)

12C8-10C6

(d)

10C6+2!

26. The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

(a)

52C5

(b)

48C5

(c)

52C5 + 48C5

(d)

52C5 - 48C5

27. If Pr stands for r Pr then the sum of the series 1+ P1 + 2P2 + 3P3 +...+ nPn is

(a)

Pn+1

(b)

Pn+1-1

(c)

Pn-1+1

(d)

(n+1)P(n-1)

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

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

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

(a)

r

(b)

n

(c)

n+1

(d)

r+1

30. The number of squares which can form on a chess a board is

(a)

64

(b)

160

(c)

224

(d)

204

31. If nPt = 720 nCr, then the value of r =

(a)

6

(b)

5

(c)

4

(d)

7

32. If Sn denotes the sum of n terms of an AP whose common difference is d, the value of S- 2Sn-1 + Sn-2 is

(a)

0

(b)

2d

(c)

4d

(d)

d2

33. The nth term of the sequence $\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 }$......is

(a)

2- n - 1

(b)

1 - 2-n

(c)

2-n + n - 1

(d)

2n-1

34. If $\Sigma n=210$ then $\Sigma { n }^{ 2 }$=

(a)

2870

(b)

2160

(c)

2970

(d)

none of these

35. The coefficient of x8y12 in the expansion of (2x + 3y)20 is

(a)

0

(b)

28312

(c)

28312 + 21238

(d)

20C8 28 312

36. With usual notation C0 + C2 +C4 + ... is:

(a)

2n-1

(b)

2n

(c)

2n+1

(d)

2n+2

37. The value of $1-\frac{1}{2}(\frac{3}{4})+\frac{1}{3}(\frac{3}{4})^2-\frac{1}{4}(\frac{3}{4})^3+...$is:

(a)

$\frac{3}{4}log(\frac{7}{4})$

(b)

$\frac{4}{3}log(\frac{7}{4})$

(c)

$\frac{1}{3}log(\frac{7}{4})$

(d)

$\frac{4}{3}log(\frac{4}{7})$

38. The value of n for which $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the arithmetic mean of a and b is

(a)

1

(b)

2

(c)

4

(d)

0

39. The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x2+3y2=0

(b)

x2-3y2=0

(c)

3x2+y2=0

(d)

3x2-y2=0

40. Which of the following point lie on the locus of 3x2+3y2-8x-12y+17 = 0

(a)

(0,0)

(b)

(-2,3)

(c)

(1,2)

(d)

(0,-1)

41. The image of the point (2, 3) in the line y = -x is

(a)

(-3, -2)

(b)

(-3,2)

(c)

(-2, -3)

(d)

(3,2)

42. If the two straight lines x + (2k -7)y + 3 = 0 and 3kx + 9y - 5 = 0 are perpendicular then the value of k is

(a)

k=3

(b)

$k=\frac13$

(c)

$k=\frac23$

(d)

$k=\frac32$

43. Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is

(a)

$\frac{35}{\sqrt{34}}$

(b)

$\frac{1}{3\sqrt{34}}$

(c)

$\frac{35}{2\sqrt{34}}$

(d)

$\frac{35}{3\sqrt{34}}$

44. If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be

(a)

2

(b)

2

(c)

3

(d)

5

45. The slope of the line joining A and B where A is (-1, 2) and B is the point of intersection of the lines 2x + 3y = 5 and 3x + 4y = 7 is:

(a)

-2

(b)

2

(c)

$\frac{1}{2}$

(d)

-$\frac{1}{2}$

46. The equation of a line which makes an angle of 135° with positive direction of x-axis and passes through the point (1,1) is

(a)

x+y=2

(b)

x-y=0

(c)

$2\sqrt {2x}-\sqrt {2y}=0$

(d)

x-3y=0

47. Pair of lines perpendicular to the lines represented by ax2+2hxy+by2=0 and through origin is

(a)

ax2+2hxy+by2=0

(b)

bx2+2hxy+ay2=0

(c)

bx2-2hxy+ay2=0

(d)

bx2-2hxy+ay2=0

48. The value $\lambda$ for which the equation 12x2-10xy+2y2+11x-5y+$\lambda$ =0 represent a pair of straight lines is

(a)

$\lambda$=1

(b)

$\lambda$=2

(c)

$\lambda$=3

(d)

$\lambda$=0

49. The distance between the parallel lines 3x-4y+9=0 and 6x-8y-15=0 is

(a)

$\frac{-33}{10}$

(b)

$\frac{10}{33}$

(c)

$\frac{33}{10}$

(d)

$\frac{33}{20}$

50. The locus of a point which is collinear with the points (a,0) and (0,b) is

(a)

x+y=1

(b)

$\frac{x}{a}+\frac{y}{b}=1$

(c)

x+y=ab

(d)

$\frac{x}{a}-\frac{y}{b}=1$