+1 Public March 2019 Important One Mark Questions

11th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 100
100 x 1 = 100
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. Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

(a)

R

(b)

(1,∞)

(c)

(-1,∞)

(d)

(-∞,1]

3. The function f:R➝R be defined by f(x)=sinx+cosx 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

4. Given A={5,6,7,8}. Which one of the following is incorrect?

(a)

Ø⊆A

(b)

A⊆A

(c)

{7,8,9}⊆A

(d)

{5}⊆A

5. If A = {(x,y) : y = ex, x∈R} and B = {(x,y) : y=e-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

6. If A = {(x,y) : y = sin x, x ∈ R} and B = {(x,y) : y = cos x, X ∈ R} then A∩B contains

(a)

no element

(b)

infinitely many elements

(c)

only one element

(d)

cannot be determined

7. Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

(a)

A

(b)

A'

(c)

B

(d)

N

8. The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

(a)

1120

(b)

1130

(c)

1100

(d)

insufficient data

9. If f(x)=2x-3 and g(x)=x2+x-2 then gof(x) is

(a)

2(2x2-5x+2)

(b)

(2x2-5x-2)

(c)

2(2x2+5x+2)

(d)

2x2+5x-2

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

(a)

injective

(b)

Surjective

(c)

bijective

(d)

none of these

11. For non-empty sets A and B, if A ⊂ B then (A x B) ⋂ (B x A) is equal to

(a)

A ⋂ B

(b)

A x A

(c)

B x B

(d)

none of these.

12. $n(p(A))=512,n(p(B))=32,n(A\cup B)=16,$ find $n(A\cap B):$

(a)

2

(b)

9

(c)

4

(d)

5

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

(a)

[5, )

(b)

(- , 6)

(c)

[5, 6]

(d)

(-5, ≠6)

14. The function f(x) = log (x + $\sqrt{x^2+1}$) is

(a)

an even function

(b)

an odd function

(c)

a periodic function

(d)

neither an even nor an odd function

15. 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)

-$1\over f(x)$

16. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

(a)

2m

(b)

2n

(c)

mn

(d)

2mn

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

(a)

$(-\infty ,-7)$

(b)

[-11, 7]

(c)

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

(d)

(-11, 7)

18.  Give that x;y and b are real numbers x<y;b>0, then

(a)

xb < yb

(b)

xb > yb

(c)

xb ≤ yb

(d)

$\frac { x }{ b } \ge \frac { y }{ b }$

19. If 3 is the logarithm of 343 then the base is

(a)

5

(b)

7

(c)

6

(d)

9

20. 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

21. The equation whose roots are numerically equal but opposite in sign to the roots 3x2-5x-7 =0 is

(a)

3x2-5x-7 =0

(b)

3x2+5x-7 =0

(c)

3x2-5x+7 =0

(d)

3x2+x-7

22. If 8 and 2 are the roots of x2+ax+c=0 and 3,3 are the roots of x2+dx+b=0;then the roots of the equation x2+ax+b = 0 are

(a)

1,2

(b)

-1,1

(c)

9,1

(d)

-1,2

23. If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

(a)

$\sqrt { { 4k }^{ 2 }-c }$

(b)

$\sqrt { { k }^{ 2 }-4c }$

(c)

$\sqrt { 4c-{ k }^{ 2 } }$

(d)

$\sqrt { k-8c }$

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

(a)

4

(b)

2

(c)

3

(d)

0

25. The value of log3 11.log11 13.log13 15log15 27.log27 81 is

(a)

1

(b)

2

(c)

3

(d)

4

26. If -3x+17 < -13 then

(a)

x ∈ (10,∞)

(b)

x ∈ [10,∞)

(c)

x ∈ (-∞,10]

(d)

x ∈ [10,10)

27. If |x+3| ≥10 then

(a)

x ∊ (-13,7]

(b)

x ∊ [-13,7)

(c)

x ∊ (-∞,-13] ᴗ [7,∞)

(d)

x ∊ (-∞,-13] ᴗ [7,∞)

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

(a)

1

(b)

3

(c)

23

(d)

21

29. Solve $\sqrt{7+6x-x^2}=x+1$

(a)

(1, -3)

(b)

(3, -1)

(c)

(1, -1)

(d)

(3, -3)

30. The value of 2 log10 3 + log10 16 - 2 log10 $6\over 5$ is

(a)

1

(b)

0

(c)

2

(d)

3

31. 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

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

(a)

1

(b)

2

(c)

3

(d)

4

33. If a and b are roots of x2 + x + 1 = 0 then the value of a2 + b2 =

(a)

1

(b)

-1

(c)

cannot be determined

(d)

0

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 cos280+sin280=k3, then cos 170 is equal to

(a)

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

(b)

-$\frac { { k }^{ 3 } }{ \sqrt { 2 } }$

(c)

±$\frac { { k }^{ 3 } }{ \sqrt { 2 } }$

(d)

-$\frac { { k }^{ 3 } }{ \sqrt { 3 } }$

37. If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

(a)

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

(b)

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

(c)

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

(d)

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

38. 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)

$\frac { 1 }{ 3 }$

39. cos2ፀ cos2ф+sin2(ፀ-ф)-sin2(ፀ+ф) is equal to

(a)

sin2(ፀ-$\phi$)

(b)

cos2(ፀ+$\phi$)

(c)

sin2(ፀ-$\phi$)

(d)

cos2(ፀ-$\phi$)

40. If f(ፀ)=|sinፀ|+|cosፀ|, ፀ$\in$R, then f(ፀ) is in the interval

(a)

[0,2]

(b)

[1,$\sqrt { 2 }$]

(c)

[1,2]

(d)

[0,1]

41. If the angles of a triangle are in A.P., then the measure of one of the angles in radians is

(a)

$\frac { \pi }{ 6 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 2 }$

(d)

$\frac { 2\pi }{ 3 }$

42. If tanx=$\frac { -1 }{ \sqrt { 5 } }$ and x lies in the IV quadrant, then the value of cosx is

(a)

$\sqrt { \frac { 5 }{ 6 } }$

(b)

$\frac { 2 }{ \sqrt { 6 } }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 1 }{ \sqrt { 6 } }$

43. $\frac { cos3x }{ 2cos2x-1 }$ is

(a)

cos x

(b)

sin x

(c)

tan x

(d)

cot x

44. If tanx =${1\over 7}$ ,tan y = ${1\over 3}$ then x + y is:

(a)

${\pi\over 4}$

(b)

${\pi\over 3}$

(c)

${\pi\over 2}$

(d)

${\pi}$

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

(a)

2R sinB

(b)

2 sinB

(c)

0

(d)

2a sinB

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

(a)

0

(b)

1

(c)

2

(d)

2 tan A

47. If sinθ=sin$\alpha$, then the angles θ and $\alpha$ are related by

(a)

$\theta=n\pi\pm\alpha$

(b)

$\theta=2n\pi+(-1)^n\alpha$

(c)

$\alpha=n\pi\pm(-1)^n\theta$

(d)

$\theta=(2n+1)\pi+\alpha$

48. The value of tan-1 (1)+cos-1($\frac{-1}{2}$)+sin-1($\frac{-1}{2}$)

(a)

$\frac{\pi}{4}$

(b)

$\frac{5\pi}{4}$

(c)

$\frac{3\pi}{4}$

(d)

$\frac{\pi}{2}$

49. 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

50. Area of triangle ABC is

(a)

$\frac{1}{2}$ab cos C

(b)

$\frac{1}{2}$ab sin C

(c)

$\frac{1}{2}$ab cos B

(d)

$\frac{1}{2}$bc sin B

51. The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

52. 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

53. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

(a)

6

(b)

9

(c)

12

(d)

18

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

(a)

4

(b)

4!

(c)

11

(d)

22

55. If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

210

56. 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

57. In 2nC3 : nC3 = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7

58. The number of 10 digit number that can be written by using the digits 2 and 3 is

(a)

10C2+9C2

(b)

210

(c)

210-2

(d)

10!

59. 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)

60. The number of ways to average the letters of the word CHEESE are

(a)

120

(b)

240

(c)

720

(d)

6

61. 5c1+5c2+5c3+5c4+5c5 is equal to

(a)

30

(b)

31

(c)

32

(d)

33

62. Among the players 5 are bowlers. In how many ways a team of 11 may be formed with atleast 4 bowlers?

(a)

265

(b)

263

(c)

264

(d)

275

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

(a)

19

(b)

17

(c)

23

(d)

25

64. The number of diagonals of a decagon:

(a)

10

(b)

20

(c)

35

(d)

40

65. The number of ways of selecting of 3 poets and 4 scientists such that poets are in even places:

(a)

12

(b)

36

(c)

72

(d)

144

66. If nCr-1 = 36, nCr = 84 and nCr+1 = 126 then r =

(a)

2

(b)

2

(c)

3

(d)

4

67. If nC10 = nC6, then nC2

(a)

16

(b)

4

(c)

120

(d)

240

68. The remainder when 3815 is divided by 13 is

(a)

12

(b)

1

(c)

11

(d)

5

69. The nth term of the sequence 1, 2, 4, 7, 11,... is

(a)

n3+3n2+2n

(b)

n3-3n2+3n

(c)

$\frac { n(n+1)(n+2) }{ 3 }$

(d)

$\frac { { n }^{ 2 }-n+2 }{ 2 }$

70. The value of the series$\quad \frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 6 } +$.....is

(a)

14

(b)

7

(c)

4

(d)

6

71. The coefficient of x5 in the series e-2x is

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { -4 }{ 15 }$

(d)

$\frac { 4 }{ 15 }$

72. 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)

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

73. The Co-efficient of x-17 in ${ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \right) }^{ 15 }$is

(a)

1365

(b)

-1365

(c)

3003

(d)

-3003

74. The first and last term of an A.P.are 1 and 11.If the sum of its terms is 36, then the number of terms will be

(a)

5

(b)

6

(c)

7

(d)

8

75. The series 1+4x+8x2+$\frac { 32 }{ 3 } { x }^{ 3 }+.....+\infty \quad is$

(a)

ex

(b)

e4x

(c)

e2x

(d)

e8x

76. The value of 2 + 4 + 6 + + 2n is

(a)

$\frac { n\left( n-1 \right) }{ 2 }$

(b)

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

(c)

$\frac { 2n\left( 2n-1 \right) }{ 2 }$

(d)

n(n + 1)

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

(a)

2n-1

(b)

2n

(c)

2n+1

(d)

2n+2

78. In the expansion of (2x + 3)5 the coefficient of x2 is:

(a)

720

(b)

1080

(c)

810

(d)

5

79. $\sqrt \frac{1-2x}{1+2x}$ is approximately equal to:

(a)

1- 2x-x2

(b)

1 + 2x+ x2

(c)

1+ 2x

(d)

1-2x+x2

80. The coefficient of a5 in the expansion of (3a + 5b)5 is

(a)

1

(b)

243

(c)

6750

(d)

9375

81. $\frac{2}{1!}+\frac{4}{3!}+\frac{6}{5!}+. . .\infty =$

(a)

e

(b)

2e

(c)

$\frac{1}{e}$

(d)

e2

82. 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

83. 21/4 41/8 81/16 161/32 . . . =

(a)

1

(b)

2

(c)

$\frac{3}{2}$

(d)

$\frac{5}{2}$

84. 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)

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

85. If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

(a)

20 sq. units

(b)

16 sq. units

(c)

25 sq. units

(d)

4 sq.units

86. The value of x so that 2 is the slope of the line through (2, 5) and (x, 3) is

(a)

-1

(b)

1

(c)

0

(d)

2

87. If the points (a, 0) (0, b) and (x,y) are collinear, then

(a)

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

(b)

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

(c)

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

(d)

$\frac{x}{a}+\frac{y}{b}=0$

88. 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)

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

89. 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

90. The equating straight line with y-intercept -2 and inclination with x-axis is 135° is:

(a)

x+y-2=0

(b)

y-x+2=0

(c)

y+x+2=0

(d)

none

91. If(1, 3) (2,1) (9, 4) are collinear then a is:

(a)

$\frac{1}{2}$

(b)

2

(c)

0

(d)

-$\frac{1}{2}$

92. The lines x + 2y - 3 = 0 and 3x - y + 7 = 0 are:

(a)

parallel

(b)

neither parallel nor perpendicular

(c)

perpendicular

(d)

parallel as wellas perpendicular

93. The length of perpendicular from the origin to a line is 12 and the line makes an angle of 120° with the positive direction of y-axis. then the equation of line is

(a)

$x+y\sqrt 3=24$

(b)

$x+y=12\sqrt 2$

(c)

x+y=24

(d)

$x+y=12\sqrt 3$

94. 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

95. The points (k+1,1),(2k+1,3) and (2k+2,2k) are collinear if

(a)

k=-1

(b)

$k=\frac{1}{2}$

(c)

k=3

(d)

k=2

96. 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

97. The equation x2+kxy+y2-5x-7y+6=0 represents a pair of straight lines then k=

(a)

$\frac{5}{3}$

(b)

$\frac{10}{3}$

(c)

$\frac{3}{2}$

(d)

$\frac{3}{10}$

98. 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)

$\frac{33}{20}$

99. The point (2,1) and (-3,5) are on

(a)

Same side of the line 3x-2y+1=0

(b)

Opposite sides of the line 3x-2y+1=0

(c)

On the line 3x-2y+1=0

(d)

On the line x+y=3

100. The co-ordinates of a point on x+y+3=0 whose distance from x+2y+2=0 is $\sqrt 5$, is

(a)

(9,6)

(b)

(-9,6)

(c)

(6,-9)

(d)

(-9,-6)