Important One Mark Question Paper

11th Standard

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Mathematics

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

    Answer ALL Questions

    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)=\(\frac { \left( { x }^{ 2 }-cosx \right) \left( 1+{ x }^{ 2 } \right) }{ \left( x-sinx \right) \left( 2x-{ x }^{ 3 } \right) } +{ e }^{ -\left| x \right| }\) 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. 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 Sn-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)

    2n-n-1

    (b)

    1-2n

    (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. Thye 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+3y=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)

    \(\frac{x}{a}-\frac{y}{b}=1\)

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