#### Full Portion - Important One Mark Question Paper

11th Standard

Reg.No. :
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Mathematics

Time : 01:30:00 Hrs
Total Marks : 100

Multiple Choice Questions

100 x 1 = 100
1. If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

(a)

[-9,9]

(b)

R

(c)

[-3,3]

(d)

[0,9]

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

(a)

B

(b)

A

(c)

Ø

(d)

$\frac{B}{A}$

4. If A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

(a)

{1,4,6,9}

(b)

{4,6,9}

(c)

{1}

(d)

None of these

5. Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then  R is

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

6. If n(A) = 2 and n(B ∪ C) = 3, then n[(A x B) ∪ (A x C)] is

(a)

23

(b)

32

(c)

6

(d)

5

7. The number of relations on a set containing 3 elements is

(a)

9

(b)

81

(c)

512

(d)

1024

8. 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

9. Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

(a)

reflexive

(b)

symmetric

(c)

transitive

(d)

equivalence

10. The range of the function ${1\over 1-2sinx}$ is

(a)

$(-∞,-1)\cup\left( {1\over 3},\infty\right)$

(b)

$\left( -1,{1\over 3}\right)$

(c)

$\left[ -1,{1\over 3}\right]$

(d)

$(-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)$

11. If $f:[-2,2]\rightarrow A$ is given by f(x)=33 then f is onto, if A is:

(a)

[3, 3]

(b)

(3, 3)

(c)

[-24,24]

(d)

(-24, 24)

12. The domain of the function $f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}$is

(a)

[5, )

(b)

(- , 6)

(c)

[5, 6]

(d)

(-5, ≠6)

13. The domain of the function $f(x)=\sqrt{log_{10}{3-x\over x}}$is

(a)

$(0,{3\over2})$

(b)

(0, 3)

(c)

$(-\infty, {3\over2}]$

(d)

$(0, {3\over2}]$

14. If $f(x)={1-x\over 1+x}, x≠0$ then $f[f(x)]+f\left[f\left(1\over x\right)\right]$

(a)

<2

(b)

> 2

(c)

> 2

(d)

None

15. n[P[P[p(Ø)]]] =

(a)

2

(b)

1

(c)

4

(d)

8

16. If A, B and C are three sets and if A ∈ B and B ⊂ C then

(a)

A ⊂ C

(b)

A need not be a subset of C

(c)

A = B

(d)

C ⊂ A

17. The solution 5x-1<24 and 5x+1 > -24 is

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

18. If a and b are the roots of the equation x2-kx+16=0 and a2+b2=32 then the value of k is

(a)

10

(b)

-8

(c)

-8,8

(d)

6

19. If  $\frac { 1-2x }{ 3+2x-{ x }^{ 2 } } =\frac { A }{ 3-x } +\frac { B }{ x+1 }$ ,then the value of A+B is

(a)

$\frac { -1 }{ 2 }$

(b)

$\frac { -2 }{ 3 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 2 }{ 3 }$

20. The number of roots of (x+3)4+(x+5)4=16 is

(a)

4

(b)

2

(c)

3

(d)

0

21. If x < 7,then

(a)

-x < -7

(b)

- x ≤ -7

(c)

-x > -7

(d)

-x ≥ -7

22. The rationalising factor of $\frac { 5 }{ \sqrt [ 3 ]{ 3 } }$ is

(a)

$\sqrt [ 3 ]{ 6 }$

(b)

$\sqrt [ 3 ]{ 3 }$

(c)

$\sqrt [ 3 ]{ 9 }$

(d)

$\sqrt [ 3 ]{ 27 }$

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

(a)

1

(b)

3

(c)

23

(d)

21

24. If the roots of x2-bx+c =0 are two consecutive integer,then b2-4c is

(a)

0

(b)

1

(c)

2

(d)

none of these

25. The value of log108+log105-log10=

(a)

${ log }_{ 10 }^{ 9 }$

(b)

${ log }_{ 10 }^{ 36 }$

(c)

1

(d)

-1

26. The factors of the polynomial $6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 }$ are

(a)

$(2x-5\sqrt { 3 } )(3\sqrt { 3 } x-1)$

(b)

$(2x-5\sqrt { 3 } )(3\sqrt { 3 } x+1)$

(c)

$(2x+5\sqrt { 3 } )(3\sqrt { 3 } x+1)$

(d)

$(2x+5\sqrt { 3 } )(3\sqrt { 3 } x-1)$

27. If $\alpha$ and $\beta$ are the roots of 2x2+4x+5=0 the equation where roots are 2$\alpha$ and 2$\beta$ is:

(a)

4x2+ 4x + 5 = 0

(b)

2x2 + 4x + 50 = 0

(c)

x2+4x+5=0

(d)

x2+4x+10=0

28. Solve 3x2 + 5x - 2≤0

(a)

(2,$\frac{1}{3}$)

(b)

[2,$\frac{1}{3}$]

(c)

(-2,$\frac{1}{3}$)

(d)

(-2,$\frac{-1}{3}$)

29. The zero of the polynomial function f(x)=9x2-16 are:

(a)

(9,16)

(b)

(3,4)

(c)

$(\frac{4}{3},-\frac{4}{3})$

(d)

$(\frac{3}{4},-\frac{3}{4})$

30. The value of a when x3-2x2+3x+a is divided by (x - 1), the remainder is 1, is:

(a)

-1

(b)

1

(c)

2

(d)

-2

31. If $\frac{x}{x^2-5x+6}=\frac{A}{x-2}+\frac{B}{x-3}$ then value of A is:

(a)

2

(b)

0

(c)

3

(d)

-2

32. The value of ${3^{-3}\times6^4\times 12^{-3}\over 9^{-4}\times 2^{-2}}$ is

(a)

35

(b)

36

(c)

34

(d)

3

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

(a)

1

(b)

2

(c)

3

(d)

4

34. Zero of the polynomial p(x) = x2 - 4x + 4

(a)

1

(b)

2

(c)

-2

(d)

-1

35. $\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

(a)

$\sqrt{2}$

(b)

$\sqrt{3}$

(c)

2

(d)

4

36. If $\pi <2\theta <\frac { 3\pi }{ 2 }$, then $\sqrt { 2+\sqrt { 2+2\quad cos4\theta } }$ equals to

(a)

-2 cosፀ

(b)

-2 sinፀ

(c)

2 cosፀ

(d)

2 sinፀ

37. Let fk(x)=$\frac { 1 }{ k }$[sinkx+coskx] where x$\in$R and k≥1. Then f4(x)-f6(x)=

(a)

$\frac { 1 }{ 4 }$

(b)

$\frac { 1 }{ 12 }$

(c)

$\frac { 1 }{ 6 }$

(d)

$\frac { 1 }{ 3 }$

38. 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)

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

39. $\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx }$ equal to

(a)

cos2x

(b)

cosx

(c)

cos3x

(d)

2cosx

40. If sinα+cosα=b, then sin2α is equal to

(a)

b2-1, if b≤$\sqrt { 2 }$

(b)

b2-1, if b>$\sqrt { 2 }$

(c)

b2-1, if b≥$\sqrt { 2 }$

(d)

b2-1, if b≥$\sqrt { 2 }$

41. The angle between the minute and hour hands of a clock at 8.30 is

(a)

800

(b)

750

(c)

600

(d)

1050

42. If tanA=$\frac { a }{ a+1 }$ and B=$\frac { 1 }{ 2a+1 }$ then the value of A+B is

(a)

0

(b)

$\frac { \pi }{ 2 }$

(c)

$\frac { \pi }{ 3 }$

(d)

$\frac { \pi }{ 4 }$

43. 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=$\frac { 2\pi }{ 3 } ,\frac { 5\pi }{ 3 }$

44. If the arcs of same lengths in two circles sustend central angles 30° and 40° find the ratio of their radii

(a)

3:4

(b)

4:3

(c)

7:12

(d)

none of these

45. The general solution of cosec$\theta$ = -2 is

(a)

$2n\pi +(-1)^n({\pi\over 6})$

(b)

$n\pi +(-1)^n({-\pi\over 6})$

(c)

$2n\pi \pm({\pi\over 6})$

(d)

$-{\pi\over 6}+n\pi$

46. (secA+tanA-1)(secA-tanA+1)-2tanA=

(a)

0

(b)

1

(c)

2

(d)

2 tan A

47. The value of cos 20°-sin 20° is

(a)

positive

(b)

negative

(c)

0

(d)

1

48. If cos $\alpha$=$\frac{3}{5}$ and cos $\beta=\frac{5}{13}$, then

(a)

cos$(\alpha+\beta)=\frac{33}{65}$

(b)

$sin(\alpha+\beta)=\frac{56}{65}$

(c)

$sin^2\frac{(\alpha-\beta)}{2}=\frac{4}{65}$

(d)

$cos(\alpha-\beta)=\frac{66}{65}$

49. If in a triangle a=5, b=4 and cos(A-B)=$\frac{31}{32}$ then the third side C is equal to

(a)

5

(b)

6

(c)

3

(d)

12

50. $\frac{1}{360}$ of a complete rotation clockwise is

(a)

-1°

(b)

-360°

(c)

-90°

(d)

51. The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

(a)

304$\times$ 292

(b)

303$\times$ 293

(c)

302$\times$ 294

(d)

30$\times$295

52. Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

53. 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

54. In 2nC3 : nC3 = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7

55. 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

56. 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

57. For all n $\in$ N, 3$\times$ 52n+1+23n+1 is divisible by

(a)

19

(b)

17

(c)

23

(d)

25

58. 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

59. is:

(a)

$\lfloor{n}(n+2)$

(b)

(c)

(d)

none of these

60. If nPr = 720, nCr =120 then r is:

(a)

2

(b)

4

(c)

3

(d)

5

61. The number of parallelogram formed if 5 parallel lines intersect with 4 other paralle llines is:

(a)

10

(b)

45

(c)

30

(d)

60

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

(a)

30

(b)

35

(c)

40

(d)

45

63. The number of ways of disturbing 7 identical balls in 3 distinct boxes, so that no box is empty is

(a)

7

(b)

6

(c)

35

(d)

15

64. Each of five questions is a multiple-choice test has 4 possible answers. The number of different sets of possible answers is

(a)

45-4

(b)

54-5

(c)

1024

(d)

1023

65. The number of positive integral solution of $x\times y\times z=30$ is

(a)

3

(b)

1

(c)

9

(d)

27

66. The number of 4 digit numbers, that can be formed by the digits 3, 4, 5, 6, 7, 8, 0 and no digit is being repeated is

(a)

720

(b)

840

(c)

280

(d)

560

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

(a)

6

(b)

5

(c)

4

(d)

7

68. The sequence$\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } }$...from an

(a)

AP

(b)

GP

(c)

HP

(d)

AGP

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

(a)

0

(b)

2d

(c)

4d

(d)

d2

70. The sum up to n terms of the series $\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +$.....is

(a)

$\frac { n(n+1) }{ 2 }$

(b)

2n(n+)

(c)

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

(d)

1

71. The value of $\frac { 1 }{ 2! } +\frac { 1 }{ 4! } +\frac { 1 }{ 6! } +....is$

(a)

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

(b)

$\frac { { (e+1) }^{ 2 } }{ 2e }$

(c)

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

(d)

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

72. The term without x in ${ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }$ is

(a)

495

(b)

-495

(c)

-7920

(d)

7920

73. The nth term of a G. Pis 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is

(a)

1

(b)

3

(c)

8

(d)

none of these

74. The Co-efficient of x3 in $\sqrt { \frac { 1-x }{ 1+x } } ,\left| x \right| <1\quad is\quad$

(a)

$\frac { 1 }{ 2 }$

(b)

$\frac { 3 }{ 8 }$

(c)

$\frac { -3 }{ 8 }$

(d)

$\frac {- 1 }{ 2 }$

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

(a)

10C6

(b)

26

(c)

10C626

(d)

10C6210

76. If nC10 > nCr for all possible F, then a value of n is

(a)

10

(b)

21

(c)

19

(d)

20

77. If a is the arithmetic mean and g is the geometric mean of two numbers, then

(a)

$\le$ g

(b)

$\ge$ g

(c)

a = g

(d)

a > g

78. AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic mean respectively the relationship between this is:

(a)

AM < GM < HM

(b)

AM ≤ GM ≤ HM

(c)

AM>GM>HM

(d)

AM≥GM≥HM

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

(a)

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

(b)

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

(c)

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

(d)

none of these

80. Sum of the binomial coefficients is

(a)

2n

(b)

n2

(c)

2n

(d)

n+17

81. If a,b, c are in A.P, as well as in G.P then

(a)

a = b ≠ c

(b)

a ≠ b = c

(c)

a ≠b ≠ c

(d)

a = b = c

82. 21/4 41/8 81/16 161/32 . . . =

(a)

1

(b)

2

(c)

$\frac{3}{2}$

(d)

$\frac{5}{2}$

83. If x, 2x + 2, 3x + 3 . . . are in G.P, then the 4th term is

(a)

27

(b)

-27

(c)

13.5

(d)

-13.5

84. If the point (8,-5) lies on the locus $\frac{x^2}{16}-\frac{y^2}{25}=k$, then the value of k is

(a)

0

(b)

1

(c)

2

(d)

3

85. 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)

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

86. The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with coordinate axes are

(a)

5,-5

(b)

5,5

(c)

5,3

(d)

5,-4

87. 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)

88. The area of the triangle formed by the lines x2 - 4y2 = 0 and x = a is

(a)

2a2

(b)

$\frac{\sqrt3}{2}a^2$

(c)

$\frac12a^2$

(d)

$\frac{2}{\sqrt3}a^2$

89. Slope of X-axis or a line parallel to X-axis is

(a)

0

(b)

positive

(c)

negative

(d)

infinity

90. The figure formed by the lines ax ± by ± c = 0 is a

(a)

rectangle

(b)

square

(c)

rhombus

(d)

none of these

91. If 7x2 - 8xy +A = 0 represents a pair of perpendicular lines, the A is

(a)

7

(b)

-7

(c)

-8

(d)

8

92. The locus of a moving point P(a cos3θ, a sin3θ) is

(a)

${ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }={ a }^{ \frac { 2 }{ 3 } }$

(b)

x2+y2=a2

(c)

x + y = a

(d)

${ x }^{ \frac { 3 }{ 2 } }+{ y }^{ \frac { 3 }{ 2 } }={ a }^{ \frac { 3 }{ 2 } }$

93. If the straight line y=mx+c passes through the point (1,2) and (-2,4) then the value of m and c are

(a)

$\frac{8}{3},\frac{-2}{3}$

(b)

$\frac{-2}{3},\frac{8}{3}$

(c)

$\frac{2}{3},\frac{-8}{3}$

(d)

$\frac{-2}{3},\frac{-8}{3}$

94. The equation of the straight line bisecting the line segment joining the points (2,4) and (4,2) and making an angle of 450 with positive direction of x-axis is

(a)

x+y=6

(b)

x-y=0

(c)

x-y=6

(d)

x+y=0

95. The equation of the straight line which passes through the point (2,4) and have intercept on the axes equal in magnitude but opposite in sign is

(a)

x-y=2

(b)

x-y+2=0

(c)

x-y+1=0

(d)

x-y-1=0

96. The lines ax+y+1=0,x+by+1=0 and x+y+c=0(a≠b≠c≠1) are concurrent, then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

(a)

-1

(b)

1

(c)

0

(d)

abc

97. 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

98. The points (a,0),(0,b) and (1,1) will be collinear if

(a)

a+b=1

(b)

a+b=2

(c)

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

(d)

a+b=0

99. Separate equation of lines for a pair of lines whose equation is x2+xy-12y2=0 are

(a)

x+4y=0 and x+3y=0

(b)

2x-3y=0 and x-4y=0

(c)

x-6y=0 and x-3y=0

(d)

x+4y=0 and x-3y=0

100. The locus of a point which is equidistant from (-1,1) and (4,2) is

(a)

5x+3y+9=0

(b)

5x+3y-9=0

(c)

3x-5y=0

(d)

3x+5y-9=0