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12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Two

12th Standard

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Maths

Time : 00:25:00 Hrs
Total Marks : 25

    Answer all the questions

    25 x 1 = 25
  1. If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

    (a)

    \(\frac { 1 }{ 3 } \)

    (b)

    \(\frac { 1 }{ 9 } \)

    (c)

    \(\frac { 1 }{ 4 } \)

    (d)

    1

  2. The rank of the matrix \(\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right] \) is

    (a)

    1

    (b)

    2

    (c)

    4

    (d)

    3

  3. The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinitely many

  4. In a homogeneous system if \(\rho\) (A) =\(\rho\)([A|0]) < the number of unknouns then the system has ________

    (a)

    trivial solution

    (b)

    only non - trivial solution

    (c)

    no solution

    (d)

    trivial solution and infinitely many non - trivial solutions

  5. If |z-2+i|≤2, then the greatest value of |z| is

    (a)

    \(\sqrt { 3 } -2\)

    (b)

    \(\sqrt { 3 } +2\)

    (c)

    \(\sqrt { 5 } -2\)

    (d)

    \(\sqrt { 5 } +2\)

  6. The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) =1 lies on

    (a)

    circle x2+y2 =1

    (b)

    x-axis

    (c)

    y-axis

    (d)

    the lines x+y=1

  7. \(\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } } \) = ________

    (a)

    cos 11θ - isin 11θ

    (b)

    cos 11θ + isin 11θ

    (c)

    cosθ + i sinθ

    (d)

    \(cos\frac { 6\theta }{ 5 } +isin\frac { 6\theta }{ 5 } \)

  8. The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

    (a)

    0

    (b)

    n

    (c)

    < n

    (d)

    r

  9. The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has

    (a)

    no solution

    (b)

    one solution

    (c)

    two solution

    (d)

    more than one solution

  10. \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

    (a)

    \(\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (b)

    \(\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (c)

    \(\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (d)

    \({ tan}^{ -1 }\left( \frac { 1}{ 2 } \right) \)

  11. The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinte

  12. If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is

    (a)

    \(\cfrac { 3 }{ 2 } \)

    (b)

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

    (c)

    \(\cfrac { \sqrt { 3 } }{ 2 } \)

    (d)

    \(\cfrac { 2 }{ \sqrt { 3 } } \)

  13. The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
    and x+2y=4 is

    (a)

    10

    (b)

    \( {2} \sqrt {5}\)

    (c)

    6

    (d)

    4

  14. Equation of tangent at (-4, -4) on x2 = -4y is

    (a)

    2x - y + 4 = 0

    (b)

    2x + y - 4 = 0

    (c)

    2x - y - 12 = 0

    (d)

    2x + y + 4 = 0

  15. \(\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0\) , then the value of \([\vec { a } ,\vec { b } ,\vec { c } ]\) is

    (a)

    \(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

    (b)

    \(\frac{1}{3}\)\(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

    (c)

    1

    (d)

    -1

  16. If  \(\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1\)such that \(\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b } \) and \(5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \) are perpendicular to each other, then the angle between \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) is

    (a)

    45o

    (b)

    60o

    (c)

    cos-1 \(\left( \frac { 1 }{ 3 } \right) \)

    (d)

    cos-1 \(\left( \frac { 2 }{ 7 } \right) \)

  17. The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =\overset { \wedge }{ 3i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k } \) is _______________

    (a)

    4

    (b)

    \(2\sqrt { 3 } \)

    (c)

    \(4\sqrt { 3 } \)

    (d)

    \(5\sqrt { 3 } \)

  18. \(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

    (a)

    1

    (b)

    -1

    (c)

    0

    (d)

  19. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

    (a)

    \(\frac{1}{31}\)

    (b)

    \(\frac15\)

    (c)

    5

    (d)

    31

  20. The cube root of 127 is ............

    (a)

    5.026

    (b)

    5.26

    (c)

    5.028

    (d)

    5.075

  21. The value of \(\frac { (n+2) }{ (n) } =90\) then n is 

    (a)

    10

    (b)

    5

    (c)

    8

    (d)

    9

  22. The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

    (a)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0\)

    (b)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0\)

    (c)

    \(\frac { { d }y }{ { dx } } +y=0\)

    (d)

    \(\frac { { d }y }{ { dx } } -y=0\)

  23. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2 , where k is the face that comes up k = {1, 2, 3, 4, 5}.
    The expected amount to win at this game in Rs. is

    (a)

    \(\cfrac { 19 }{ 6 } \)

    (b)

    \(-\cfrac { 19 }{ 6 } \)

    (c)

    \(\cfrac { 3 }{ 2 } \)

    (d)

    \(-\cfrac { 3 }{ 2 } \)

  24. If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

    (a)

    0.125

    (b)

    0.25

    (c)

    0.375

    (d)

    0.75

  25. The operation * defined by a*b =\(\frac{ab}{7}\) is not a binary operation on

    (a)

    Q+

    (b)

    Z

    (c)

    R

    (d)

    C

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