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12th Standard English Medium Maths Reduced Syllabus Creative one Mark Questions with Answer key - 2021(Public Exam )

12th Standard

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Maths

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

    Multiple Choice Questions

    50 x 1 = 50
  1. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

    (a)

    k ≠ 0

    (b)

    -1 < k < 1

    (c)

    -2 < k < 2

    (d)

    k=0

  2. If \(\rho\)(A) = \(\rho\)([A/B]) = number of unknowns, then the system is

    (a)

    consistent and has infinitely many solutions

    (b)

    consistent

    (c)

    inconsistent

    (d)

    consistent and has unique solution

  3. If \(\rho\)(A) = r then which of the following is correct?

    (a)

    all the minors of order n which do not vanish

    (b)

    'A' has at least one minor "of order r which does not vanish and all higher order minors vanish

    (c)

    'A' has at least one (r + 1) order minor which vanish

    (d)

    all (r + 1) and higher order minors should not vanish

  4. If \(\rho\)(A) ≠ \(\rho\)([AIB]), then the system is

    (a)

    consistent and has infinitely many solutions

    (b)

    consistent and has a unique solution

    (c)

    consistent

    (d)

    inconsistent

  5. If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

    (a)

    |z| =1, arg(z) =\(\frac { \pi }{ 4 } \)

    (b)

    |z| =1, arg(z) =\(\frac { \pi }{ 6 } \)

    (c)

    |z|=\(\frac { \sqrt { 3 } }{ 2 } \), arg(z)=\(\frac { 5\pi }{ 24 } \)

    (d)

    |z| =\(\frac { \sqrt { 3 } }{ 2 } \), arg (z) =tan-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  6. The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

    (a)

    16

    (b)

    8

    (c)

    4

    (d)

    2

  7. The value of (1+i)4 + (1-i)4 is

    (a)

    8

    (b)

    4

    (c)

    -8

    (d)

    -4

  8. If zn =\(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z1, z2 ..... z6 is

    (a)

    1

    (b)

    -1

    (c)

    i

    (d)

    -i

  9. The points represented by 3 - 3i, 4 - 2i, 3 - i and 2 - 2i form _____ in the argand plane.

    (a)

    collinear points

    (b)

    Vertices of a parallelogram

    (c)

    Vertices of a rectangle

    (d)

    Vertices of a square

  10. If a =cosα + i sinα, b= -cosβ + i sinβ then \(\left( ab-\frac { 1 }{ ab } \right) \) is _________

    (a)

    -2i sin(α - β)

    (b)

    2i sin(α - β)

    (c)

    2 cos(α - β)

    (d)

    -2 cos(α - β)

  11. If x=cosθ + i sinθ, then xn+\(\frac { 1 }{ { x }^{ n } } \) is ______

    (a)

    2 cos nθ

    (b)

    2 i sin nθ

    (c)

    2n cosθ

    (d)

    2n i sinθ

  12. If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

    (a)

    b2-4ac=0

    (b)

    b2 - 4ac <0

    (c)

    b2 - 4ac >0

    (d)

    b2 - 4ac≥0

  13. If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

    (a)

    c>0

    (b)

    c<0

    (c)

    c=0

    (d)

    c≥0

  14. The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is 

    (a)

    \(\cfrac { \pi }{ 2 } \)

    (b)

    \(\cfrac { 5\pi }{ 3 } \)

    (c)

    \(\cfrac { 10\pi }{ 3 } \)

    (d)

    0

  15. \(sin\left\{ 2{ cos }^{ -1 }\left( \cfrac { -3 }{ 5 } \right) \right\} =\)

    (a)

    \(\cfrac { 6 }{ 15 } \)

    (b)

    \(\cfrac { 24 }{ 25 } \)

    (c)

    \(\cfrac { 4 }{ 5 } \)

    (d)

    \(\cfrac { -24 }{ 25 } \)

  16. 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)

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

  17. \(cot\left( \cfrac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

    (a)

    7

    (b)

    6

    (c)

    5

    (d)

    none

  18. If x>1,then \(2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \cfrac { 2x }{ 1+{ x }^{ 2 } } \right) \) ________

    (a)

    4 tan-1x

    (b)

    0

    (c)

    \(\cfrac { \pi }{ 2 } \)

    (d)

    \(\pi \)

  19. The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

    (a)

    x = -1

    (b)

    x = 1

    (c)

    x = \(\frac{-3}{2}\)

    (d)

    x = \(\frac{3}{2}\)

  20. If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is

    (a)

    6x2 + 10y2 = 5

    (b)

    6x2 + 10y2 = 15

    (c)

    x2 + 3y2 = 10

    (d)

    none

  21. The equation 7x2- 6\(\sqrt { 3 } \) xy + 13y2 - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents

    (a)

    parabola

    (b)

    ellipse

    (c)

    hyperbola

    (d)

    rectangular hyperbola

  22. The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is

    (a)

    x2 + y2 = 4

    (b)

    x2 +y2 = 9

    (c)

    x2 +y2 = 45

    (d)

    x2 +y2 = 14

  23. The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is

    (a)

    5

    (b)

    \(\sqrt{45}\)

    (c)

    10

    (d)

    \(\sqrt{50}\)

  24. If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

    (a)

    \(\sqrt{10}\)

    (b)

    1

    (c)

    5

    (d)

    \(\sqrt{19}\)

  25. If e1,e2 are eccentricities of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 and the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 then 

    (a)

    \({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\) = 1

    (b)

    \({ e }_{ 1 }^{ 2 }\)  + \({ e }_{ 2 }^{ 2 }\) = 1

    (c)

    \({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\) = 2

    (d)

    \({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\)=2

  26. If B, B1 are the ends of minor axis, F1 ,F2 are foci of the ellipse \(\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 then area of F1BF2B1 is

    (a)

    16

    (b)

    8

    (c)

    16\(\sqrt2\)

    (d)

    32\(\sqrt2\)

  27. The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

    (a)

    4, 2\(\sqrt3\)

    (b)

    2, \(\sqrt3\)

    (c)

    2\(\sqrt3\), 4

    (d)

    \(\sqrt3\), 2

  28. The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

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

    (a)

    4

    (b)

    2\(\sqrt { 3 } \)

    (c)

    4\(\sqrt { 3 } \)

    (d)

    5\(\sqrt { 3 } \)

  30. If \(\overset { \rightarrow }{ a } =\left| \overset { \rightarrow }{ a } \right| \overset { \rightarrow }{ e } \) then \(\overset { \rightarrow }{ e } .\overset { \rightarrow }{ e } \)

    (a)

    0

    (b)

    e

    (c)

    1

    (d)

    \(\overset { \rightarrow }{ 0 } \)

  31. The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are 

    (a)

    mutually perpendicular

    (b)

    parallel

    (c)

    inclined at 45o

    (d)

    inclined at 30

  32. If \(\lambda \overset { \wedge }{ i } +2\lambda \overset { \wedge }{ j } +2\lambda \overset { \wedge }{ k } \) is a unit vector, then the value of λ is 

    (a)

    土 \(\frac { 1 }{ 3 } \)

    (b)

    土 \(\frac { 1 }{ 4 } \)

    (c)

    土 \(\frac { 1 }{ 9 } \)

    (d)

    \(\frac { 1 }{ 2 } \)

  33. If the vectors \(a\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \)\(\overset { \wedge }{ i } +b\overset { \wedge }{ j } +\overset { \wedge }{ k } \) and \(\overset { \wedge }{ i } +\overset { \wedge }{ j } +c\overset { \wedge }{ k } \) (a ≠ b ≠ c ≠ 1) are coplaner, then \(\frac { 1 }{ 1-a } +\frac { 1 }{ 1-b } +\frac { 1 }{ 1-c } =\)

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    \(\frac { abc }{ (1-a)(1-b)(1-c) } \)

  34. If \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are three non - coplanar vectors, then \(\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } } +\frac { \overset { \rightarrow }{ b } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } } \)=_____________

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    \(\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } .\overset { \rightarrow }{ c } } \)

  35. The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are

    (a)

    -1, 2

    (b)

    1, \(\frac { 1 }{ 2 } \)

    (c)

    1, 2

    (d)

    none

  36. In LMV theorem, we have f'(x1) =\(\frac { f(b)-f(a) }{ b-a } \) then a < x1 _________

    (a)

    <b

    (b)

    ≤b

    (c)

    =b

    (d)

    ≠b

  37. If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is

    (a)

    \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \)

    (b)

    0

    (c)

    u

    (d)

    2u

  38. lf u = (x-y)4+(y-z)4 +(z-x)4 then \(\sum { \frac { \partial u }{ \partial x } } \) = 

    (a)

    4

    (b)

    1

    (c)

    0

    (d)

    -4

  39. The approximate value of (627)\(\frac14\) is ................

    (a)

    5.002

    (b)

    5.003

    (c)

    5.005

    (d)

    5.004

  40. The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    2

    (c)

    0

    (d)

    1

  41. The area enclosed by the curve y2 = 4x, the x-axis and its latus rectum is ............ sq.units.

    (a)

    \(\frac23\)

    (b)

    \(\frac43\)

    (c)

    \(\frac83\)

    (d)

    \(\frac{16}{3}\)

  42. The area of the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\)

    (a)

    (b)

    36π

    (c)

    2

    (d)

    36π2

  43. The volume generated by the curve y2 = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

    (a)

    72π

    (b)

    \(\frac { 256\times 19 }{ 3 } \)

    (c)

    40ㅠ

    (d)

    80ㅠ

     

  44. The solution of sec2x tan y dx+sec2y tan x dy=0 is

    (a)

    tan x+tan y =c

    (b)

    sec x+sec y=c

    (c)

    tan x tan y=c

    (d)

    sec x-sec y =c

  45. The general solution of \(4\frac{d^2 y}{dx^2}\)+y=0 is

    (a)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right] \)

    (b)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right] \)

    (c)

    \(y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 } \)

    (d)

    \(t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }\)

  46. If \(f(x)=\cfrac { 1 }{ 2 } \) ,\(E\left( { x }^{ 2 } \right) =\cfrac { 1 }{ 4 } \) then var(x) is 

    (a)

    0

    (b)

    \(\cfrac { 1 }{ 4 } \)

    (c)

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

    (d)

    1

  47. Var (2x ± 5) is =________

    (a)

    5

    (b)

    var (2x) ± 5

    (c)

    4 var (X)

    (d)

    0

  48. The sum of the mean and variance of a binomial distribution for 6 total is 2.16. Then the probability of success p=__________

    (a)

    0.4

    (b)

    0.6

    (c)

    0.8

    (d)

    0.2

  49. If * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is

    (a)

    20

    (b)

    40

    (c)

    400

    (d)

    445

  50. In (N, *), x * y = max(x, y), x, y \(\in \) N then 7 * (-7)

    (a)

    7

    (b)

    -7

    (c)

    0

    (d)

    -49

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