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12th Standard English Medium Maths Subject Creative 1 Mark Questions with Solution Part - II

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    1 Marks

    25 x 1 = 25
  1. 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

  2. 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

  3. If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2 is inconsistent then k is ___________

    (a)

    -3, -\(\frac{1}{2}\)

    (b)

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

    (c)

    1

    (d)

    2

  4. 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

  5. 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

  6. If z = \(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) = ___________

    (a)

    0

    (b)

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

    (c)

    cot\(\frac { \theta }{ 2 } \)

    (d)

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

  7. The amplitude of \(\frac{1}{i}\) is equal to _______

    (a)

    0

    (b)

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

    (c)

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

    (d)

    \(\pi \)

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

    (a)

    cos 11θ - isin 11θ

    (b)

    cos 11θ + isin 11θ

    (c)

    cosθ + i sinθ

    (d)

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

  9. The conjugate of \(\frac { 1+2i }{ 1-(1-i)^{ 2 } } \) is _______

    (a)

    \(\frac { 1+2i }{ 1-(1-i)^{ 2 } } \)

    (b)

    \(\frac { 5 }{ 1-(1-i)^{ 2 } } \)

    (c)

    \(\frac { 1-2i }{ 1+(1+i)^{ 2 } } \)

    (d)

    \(\frac { 1+2i }{ 1+(1-i)^{ 2 } } \)

  10. The value of \(\frac { (cos{ 45 }^{ 0 }+isin{ 45 }^{ 0 })^{ 2 }(cos{ 30 }^{ 0 }-isin{ 30 }^{ 0 }) }{ cos{ 30 }^{ 0 }+isin{ 30 }^{ 0 } } \) is __________

    (a)

    \(\frac { 1 }{ 2 } +i\frac { \sqrt { 3 } }{ 2 } \)

    (b)

    \(\frac { 1 }{ 2 } -i\frac { \sqrt { 3 } }{ 2 } \)

    (c)

    \(-\frac { \sqrt { 3 } }{ 2 } +\frac { 1 }{ 2 } \)

    (d)

    \(\frac { \sqrt { 3 } }{ 2 } +\frac { 1 }{ 2 } \)

  11. If a, b, c ∈ Q and p +√q (p, q ∈ Q) is an irrational root of ax2+bx+c = 0 then the other root is ___________

    (a)

    -p+√q

    (b)

    p-iq

    (c)

    p-√q

    (d)

    -p-√q

  12. Let a > 0, b > 0, c >0. Theh n both the root of the equation ax2+bx+c = 0 are _________

    (a)

    real and negative

    (b)

    real and positive

    (c)

    rational numbers

    (d)

    none

  13. lf the root of the equation x3 + bx2+ cx - 1 = 0 form an lncreasing G.P, then ___________

    (a)

    one of the roots is 2

    (b)

    one of the roots is 1

    (c)

    one of the roots is -1

    (d)

    one of the roots is -2

  14. If \((2+\sqrt{3})^{x^{2}-2 x+1}+(2-\sqrt{3})^{x^{2}-2 x-1}=\frac{2}{2-\sqrt{3}}\) then x = _________

    (a)

    0, 2

    (b)

    0, 1

    (c)

    0, 3

    (d)

    0, √3

  15. If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

    (a)

    0

    (b)

    1

    (c)

    4

    (d)

    3

  16. If p(x) = ax2 + bx + c and Q(x) = -ax2 + dx + c where ac ≠ 0 then p(x). Q(x) = 0 has at least _______ real roots.

    (a)

    no

    (b)

    1

    (c)

    2

    (d)

    infinite

  17. If \(\alpha ={ tan }^{ -1 }\left( tan\frac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\frac { 2\pi }{ 3 } \right) \) then ___________

    (a)

    \(4\alpha =3\beta \quad \)

    (b)

    \(3\alpha =4\beta \)

    (c)

    \(\alpha -\beta =\frac { 7\pi }{ 12 } \)

    (d)

    none

  18. If \(\alpha ={ tan }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \frac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \) __________

    (a)

    \(\frac { \pi }{ 6 } \)

    (b)

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

    (c)

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

    (d)

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

  19. \(sin\left\{ 2{ cos }^{ -1 }\left( \frac { -3 }{ 5 } \right) \right\} =\) __________

    (a)

    \(\frac { 6 }{ 15 } \)

    (b)

    \(\frac { 24 }{ 25 } \)

    (c)

    \(\frac { 4 }{ 5 } \)

    (d)

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

  20. If tan-1(cot \(\theta\)) = 2\(\theta\), then\(\theta\) = _____________

    (a)

    \(\pm 3\)

    (b)

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

    (c)

    \(\pm \frac { \pi }{ 6 } \)

    (d)

    none

  21. The value of tan \(\left( { cos }^{ -1 }\frac { 3 }{ 5 } +{ tan }^{ -1 }\frac { 1 }{ 4 } \right) \) is ______

    (a)

    \(\frac { 19 }{ 8 } \)

    (b)

    \(\frac { 8 }{ 19 } \)

    (c)

    \(\frac { 19 }{ 12 } \)

    (d)

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

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

    (a)

    4 tan-1x

    (b)

    0

    (c)

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

    (d)

    \(\pi \)

  23. 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

  24. The distance between the foci of a hyperbola is 16 and e = \(\sqrt { 2 } \). Its equation is ____________

    (a)

    x2 - y2 = 32

    (b)

    y2 - x2 = 32

    (c)

    x2 - y2 = 16

    (d)

    y2 - x2 = 16

  25. When the eccentricity of a ellipse becomes zero, then it becomes a __________

    (a)

    straight line

    (b)

    circle

    (c)

    point

    (d)

    parabola

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