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Important 1 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 24

    Part A

    24 x 1 = 24
  1. Which of the following is not an elementary transformation?

    (a)

    Ri ↔️ Rj

    (b)

    Ri ⟶ 2Ri + Rj

    (c)

    Cj ⟶ Cj + Ci

    (d)

    Ri ⟶ Ri + Cj

  2. If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

    (a)

    1

    (b)

    -1

    (c)

    i

    (d)

    0

  3. If z = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if

    (a)

    a > b > 0

    (b)

    a < b < 0

    (c)

    b < a < 0

    (d)

    b > a > 0

  4. 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

  5. If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ is __________

    (a)

    \(\frac{-7}{9}\)

    (b)

    \(\frac{7}{9}\)

    (c)

    0

    (d)

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

  6. 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

  7. In a \(\Delta ABC\)  if C is a right angle, then  \({ tan }^{ -1 }\left( \cfrac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \cfrac { b }{ c+a } \right) =\) 

    (a)

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

    (b)

    \(\cfrac { \pi }{ 4 } \)

    (c)

    \(\cfrac { 5\pi }{ 2 } \)

    (d)

    \(\cfrac { \pi }{ 6 } \)

  8. 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

  9. Th point of curve y = 2x2 - 6x - 4 at which the targent is parallel to x - axis is

    (a)

    \(\left( \frac { 5 }{ 2 } ,\frac { -7 }{ 12 } \right) \)

    (b)

    \(\left( \frac { -5 }{ 2 } ,\frac { -7 }{ 2 } \right) \)

    (c)

    \(\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 12 } \right) \)

    (d)

    \(\left( \frac { 3 }{ 2 } ,\frac { -7 }{ 2 } \right) \)

  10. If θ is the angle between the vectors \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \), then sinθ is

    (a)

    \(\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| } \)

    (b)

    \(\frac { \left| \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right| }{ \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } } \)

    (c)

    \(\sqrt { 1-{ \left( \frac { \overset { \rightarrow }{ a. } \overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| } \right) }^{ 2 } } \)

    (d)

    0

  11. For what value of \(\left( \overset { \rightarrow }{ a } \right) \) will the straight lines \(\frac { x+2 }{ a } =\frac { y }{ 3 } =\frac { z-1 }{ 4 } \)and \(\frac { x-3 }{ a } =\frac { y-1 }{ 4 } =\frac { z-7 }{ a } \)be perpendicular?

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    -3

  12. Let \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\) and \(\overset { \rightarrow }{ c } \) be three vectors having magnitudes 1, 1, 2 respectively.
    If \(\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } =0\) then the acute angle between \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ c } \) is ____________________

    (a)

    0

    (b)

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

    (c)

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

    (d)

    \(\frac { 2\pi }{ 3 } \)

  13. If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

    (a)

    2 < t < 5

    (b)

    2 ≤ t ≤ 5

    (c)

    t ≥ 2

    (d)

    t ≤ 2

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

    (a)

    1

    (b)

    -1

    (c)

    0

    (d)

  15. 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

  16. If u = yx then \(\frac { \partial u }{ \partial y } \) = ............

    (a)

    xyx-1

    (b)

    yxy-1

    (c)

    0

    (d)

    1

  17. The ratio of the volumes generated by revolving the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 about major and minor axes is

    (a)

    4:9

    (b)

    9:4

    (c)

    2:3

    (d)

    3:2

  18. \(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ 2a }{ f(x) } dx\)

    (a)

    f(2a -x) =f(x)

    (b)

    f(a -x) =f(x)

    (c)

    f(x) = - f(-x)

    (d)

    f(-x) =f(x)

  19. \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ { cos }^{ 3 }2x \ dx= } \)

    (a)

    \(\frac { 2 }{ 3 } \)

    (b)

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

    (c)

    0

    (d)

    \(\frac { 2\pi }{ 3 } \)

  20. The solution of \(\frac{dy}{dx}+y\) cot x=sin 2x is

    (a)

    y sin x=\(\frac{2}{3}\)sin3x+c

    (b)

    y sec x=\(\frac{x^2}{2}+c\)

    (c)

    y sin x =c+x

    (d)

    2y sin x=sin x-\(\frac{sin\ 3x}{3}+c\)

  21. The I.F of \(\frac{dy}{dx}-y\) tan x=cos x is

    (a)

    sec x

    (b)

    cos x

    (c)

    etan x

    (d)

    cot x

  22. The differential equation associated with the family of concentric circles having their centres at the origin is _________.

    (a)

    \(\frac { dy }{ dx } =\frac { -x }{ y } \)

    (b)

    \(\frac { dy }{ dx } =\frac { -y }{ x } \)

    (c)

    \(\frac { dy }{ dx } =\frac { x }{ y } \)

    (d)

    \(\frac { dy }{ dx } =\frac { y }{ x } \)

  23. Define * on Z by a*b = a+b+1 ∀ a,b \(\in \) Z. Then the identity element of z is

    (a)

    1

    (b)

    0

    (c)

    1

    (d)

    -1

  24. 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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