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11th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

    (a)

    T is an equivalence relation but S is not an equivalence relation

    (b)

    Neither S nor T is an equivalence relation

    (c)

    Both S and T are equivalence relation

    (d)

    S is an equivalence relation but T is not an equivalence relation.

  2. Let f:Z➝Z be given by f(x)=\(\begin{cases} \frac { x }{ 2 } \quad if\quad x\quad is\quad even \\ 0\quad if\quad x\quad is\quad odd \end{cases}\) . Then f is

    (a)

    one-one but not onto

    (b)

    onto but not one-one

    (c)

    one-one and onto

    (d)

    neither one-one nor onto

  3. If \({ log }_{ \sqrt { x } }\) 0.25 =4 ,then the value of x is

    (a)

    0.5

    (b)

    2.5

    (c)

    1.5

    (d)

    1.25

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

    (a)

    1

    (b)

    3

    (c)

    23

    (d)

    21

  5. 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)

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

  6. 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

  7. The equation of the line with slope 2 and the length of the perpendicular from the origin equal to \(\sqrt5\) is

    (a)

    x+2y=\(\sqrt5\)

    (b)

    2x+y=\(\sqrt5\)

    (c)

    2x+y=5

    (d)

    x+2y-5=0

  8. If A and B are symmetric matrices of order n, where (A \(\neq\) B), then

    (a)

    A + B is skew-symmetric

    (b)

    A + B is symmetric

    (c)

    A + B is a diagonal matrix

    (d)

    A + B is a zero matrix

  9. If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is

    (a)

    an identity matrix of order n

    (b)

    an identity matrix of order 1

    (c)

    a zero matrix of order 1

    (d)

    an identity matrix of order 2

  10. \(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is

    (a)

    \(\sqrt{2}\)

    (b)

    \(1\over \sqrt{2}\)

    (c)

    1

    (d)

    2

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