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

12th Standard

    Reg.No. :
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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

    (a)

    0

    (b)

    -2

    (c)

    -3

    (d)

    -1

  2. If A is a matrix of order m \(\times\) n, then \(\rho\) (A) is _________

    (a)

    m

    (b)

    n

    (c)

    ≤ min (m,n)

    (d)

    ≥ min (m,n)

  3. If z = x + iy is a complex number such that |z+2| = |z−2|, then the locus of z is

    (a)

    real axis

    (b)

    imaginary axis

    (c)

    ellipse

    (d)

    circle

  4. The number of real numbers in [0, 2π] satisfying sin4x - 2sin2x + 1 is

    (a)

    2

    (b)

    4

    (c)

    1

    (d)

  5. Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 4 } =1\) parallel to the straight line 2x − y = 1. One of the points of contact of tangents on the hyperbola is

    (a)

    \(\left(\frac{9}{2 \sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)

    (b)

    \(\left(\frac{-9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)

    (c)

    \(\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)

    (d)

    \((3 \sqrt{3},-2 \sqrt{2})\)

  6. If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between \(\vec { a } \ and \ \vec { b } \) is

    (a)

    \(\frac { \pi }{ 2 } \)

    (b)

    \(\frac { 3\pi }{ 4 } \)

    (c)

    \(\frac { \pi }{ 4 } \)

    (d)

    \( { \pi }\)

  7. The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

    (a)

    -8

    (b)

    -4

    (c)

    -2

    (d)

    0

  8. The value of \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

    (a)

    \(\frac{1}{11000}\)

    (b)

    \(\frac{1}{10100}\)

    (c)

    \(\frac{1}{10010}\)

    (d)

    \(\frac{1}{10001}\)

  9. If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\) When

    (a)

    p < q

    (b)

    p = q

    (c)

    p > q

    (d)

    p exists and q does not exist

  10. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

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