Important 1mark

11th Standard

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Maths

Time : 00:20:00 Hrs
Total Marks : 20
    19 x 1 = 19
  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:[0,2π]➝[-1,1] defined by f(x)=sin x is

    (a)

    one-to-one

    (b)

    on to

    (c)

    bijection

    (d)

    cannot be defined

  3. Let X={1,2,3,4}, Y={a,b,c,d} and f={f(1,a),(4,b),(2,c),(3,d),(2,d)}. Then f is

    (a)

    an one-to-one function

    (b)

    an onto function

    (c)

    a function which is not one-to-one

    (d)

    not a function

  4. For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

    (a)

    reflexive

    (b)

    symmetric

    (c)

    transitive

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

    (a)

    9

    (b)

    81

    (c)

    512

    (d)

    1024

  7. If \(f:R\rightarrow R\) is defined by \(f(x)=2x-3:\)

    (a)

    \({1\over 2x-3}\)

    (b)

    \({1\over 2x+3}\)

    (c)

    \({x+3\over 2}\)

    (d)

    \({x-3\over 2}\)

  8. \(n(A\cap B)=4\) and \((A\cup B)=11\) then \(n(p(A\triangle B))\) is:

    (a)

    44

    (b)

    256

    (c)

    64

    (d)

    128

  9. Let f and g be two odd functions then the function of f o g is

    (a)

    an even function

    (b)

    an odd function

    (c)

    neither even nor odd

    (d)

    a periodic function

  10. For any four sets A, B, C and D, which of the following is not true?

    (a)

    A x C   B x D

    (b)

    (A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

    (c)

    A x (B U,C) = (A x B) U (A x C)

    (d)

    A x (B ∩ C) = (A x B) ∩ (A x C)

  11. 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

  12. The domain and range of the function \(f(x)={|x-4|\over x-4}\)

    (a)

    R, [-1, 1]

    (b)

    R \ {4};{-1,1}

    (c)

    R \ {4};{-1,l}

    (d)

    R, (-1,1)

  13. The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and\(\hat{i}-2\hat{j}+\hat{k}\) is

    (a)

    \({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (b)

    \({2\hat{i}+\hat{j}\over\sqrt{5}}\)

    (c)

    \({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (d)

    \({2\hat{i}-\hat{j}\over\sqrt{5}}\)

  14. A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between \(\overrightarrow{OP}\)and the z-axis is

    (a)

    45°

    (b)

    60°

    (c)

    90°

    (d)

    30°

  15. Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and\(2\hat{i}+3\hat{j}+4\hat{k}\)If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\) ,then the position vector of the third vertex is

    (a)

    \(-2\hat{i}-\hat{j}+9\hat{k}\)

    (b)

    \(-2\hat{i}-\hat{j}-6\hat{k}\)

    (c)

    \(2\hat{i}-\hat{j}+6\hat{k}\)

    (d)

    \(-2\hat{i}+\hat{j}+6\hat{k}\)

  16. If \(|\overrightarrow{a}+\overrightarrow{b}|=60,\)\(|\overrightarrow{a}+\overrightarrow{b}|=40\)  and \(|\overrightarrow{b}|=46\)then \(|\overrightarrow{a}|\) is

    (a)

    42

    (b)

    12

    (c)

    22

    (d)

    32

  17. If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is

    (a)

    \(7\over4\)

    (b)

    \(15\over4\)

    (c)

    \(3\over4\)

    (d)

    \(17\over4\)

  18. \(\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx\) is

    (a)

    x2+c

    (b)

    2x2+c

    (c)

    \({x^2\over2}+c\)

    (d)

    \(-{x^2\over2}+c\)

  19. \(\int sin \sqrt{xdx}\) is

    (a)

    \(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)

    (b)

    \(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)

    (c)

    \(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)

    (d)

    \(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

  20. The condition that the equation ax2 + bx + c = 0 may have one root is the double the other is:

    (a)

    2b2 = 9ac

    (b)

    b2= ac

    (c)

    b2 = 4ac

    (d)

    9b2 = 2ac

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