Full Portion - Important One Mark Question Paper

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

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 \({ log }_{ 10 }^{ 8 }+{ log }_{ 10 }^{ 5 }-{ log }_{ 10 }^{ 4 }\)=

    (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

*****************************************

Reviews & Comments about 11th Maths Important One Mark Question Paper 1

Write your Comment