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12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Five

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. 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

  2. If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| =

    (a)

    \(\frac { 1 }{ 13 } \)

    (b)

    \(\frac { 1 }{ 5} \)

    (c)

    \(\frac { 1 }{ 12 } \)

    (d)

    none of these

  3. 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

  4. \({ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right) \) =

    (a)

    0

    (b)

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

    (c)

    -1

    (d)

    none

  5. The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

    (a)

    \(\frac13\)

    (b)

    \(\frac23\)

    (c)

    \(\frac34\)

    (d)

    none of these

  6. If \(\overset { \rightarrow }{ a } \),\(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \) are any three vectors, then \(\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) \) if and only if 

    (a)

    \(\overset { \rightarrow }{ b } \)\(\overset { \rightarrow }{ c } \) are collinear

    (b)

    \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ c } \) are collinear

    (c)

    \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are collinear

    (d)

    none

  7. 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

  8. If u = log (x3 + y3 + z3 - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) =

    (a)

    \(\frac { 3 }{ x+y+z } \)

    (b)

    x+y+z

    (c)

    \(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

    (d)

    \(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

  9. The transformation y=vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \)

    (a)

    \(\frac { 3av }{ 4v+1 } =\frac { dx }{ x } \)

    (b)

    \(\frac { 3dv }{ v+1 } =\frac { dx }{ x } \)

    (c)

    \(2x\frac { dv }{ dx } =v\)

    (d)

    \(\frac { 3dv }{ 1-2v } ==\frac { dx }{ x } \)

  10. If a random variable X has the p.d.f.\(f(x)=\cfrac { k }{ { x }^{ 2 }+1 } ,0<x<\infty \) then k is

    (a)

    \(\pi \)

    (b)

    \(\cfrac { 1 }{ \pi } \)

    (c)

    1

    (d)

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

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