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Sample 1 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 23

    Part A

    23 x 1 = 23
  1. 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

  2. In the non - homogeneous system of equations with 3 unknowns if \(\rho\)(A) = \(\rho\)([AIB]) = 2, then the system has _______

    (a)

    unique solution

    (b)

    one parameter family of solution

    (c)

    two parameter family of solutions

    (d)

    in consistent

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

  4. The modular of \(\frac { (-1+i)(1-i) }{ 1+i\sqrt { 3 } } \) is ______

    (a)

    \(\sqrt{2}\)

    (b)

    2

    (c)

    1

    (d)

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

  5. If (2+√3)x2-2x+1+(2-√3)x2-2x-1=\(\frac { 2 }{ 2-\sqrt { 3 } } \) then x=

    (a)

    0,2

    (b)

    0,1

    (c)

    0,3

    (d)

    0, √3

  6. The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    none

  7. If tan-1(3)+tan-1(x)=tan-1(8)then x= 

    (a)

    5

    (b)

    \(\cfrac { 1 }{ 5 } \)

    (c)

    \(\cfrac { 5 }{ 14 } \)

    (d)

    \(\cfrac { 14 }{ 5 } \)

  8. 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)

    \(\pi \)

  9. The length of the latus rectum of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 } \) = 1 is

    (a)

    \(\frac { 98 }{ 6 } \)

    (b)

    \(\frac { 72 }{ 7 } \)

    (c)

    \(\frac { 72 }{ 14 } \)

    (d)

    \(\frac { 98 }{ 12 } \)

  10. 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)

    \(\sqrt{19}\)

  11. The tangent at any point P on the ellipse \(\frac { { x }^{ 2 } }{ 6 } +\frac { { y }^{ 2 } }{ 3 } \) = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis; The CN CT = ______________

    (a)

    \(\sqrt6\)

    (b)

    3

    (c)

    \(\sqrt3\)

    (d)

    6

  12. If \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are two unit vectors, then the vectors \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) \) is parallel to the vector

    (a)

    \(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

    (b)

    \(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

    (c)

    2\(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

    (d)

    2\(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

  13. If \(\overset { \rightarrow }{ p } \times \overset { \rightarrow }{ q } =2\overset { \wedge }{ i } +3\overset { \wedge }{ j } \)\(\overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } =3\overset { \wedge }{ i } +2\overset { \wedge }{ k } \) then \(\overset { \rightarrow }{ p } .\left( \overset { \rightarrow }{ q } \left( \overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } \right) \right) \) is

    (a)

    9

    (b)

    6

    (c)

    2

    (d)

    5

  14. If the rate of increase of s =x3-5x2+5x+8 is twice the rate of increase of x, then one value of x is

    (a)

    \(\frac{3}{5}\)

    (b)

    \(\frac{10}{3}\)

    (c)

    \(\frac{3}{10}\)

    (d)

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

  15. The curve y = ex is ________

    (a)

    convex

    (b)

    concave

    (c)

    convex upwards

    (d)

    concave upwards

  16. If u = xy + yx then ux + uy at x = y = 1 is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

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

    (a)

    xyx-1

    (b)

    yxy-1

    (c)

    0

    (d)

    1

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

    (a)

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

    (b)

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

    (c)

    f(x) is odd

    (d)

    f(x) is even

  19. \(\int _{ a }^{ b }{ f(x) } dx=\) ..............

    (a)

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

    (b)

    \(\int _{ a }^{ b }{ f(a-x) } dx\)

    (c)

    \(\int _{ b }^{ a }{ f(b-x) } dx\)

    (d)

    \(\int _{ a }^{ b }{ f(a+b-x) } dx\)

  20. The I.F of y log y\(\frac{dx}{dy}+x-log\ y=0\) is

    (a)

    log(log y)

    (b)

    log y

    (c)

    \(\frac{1}{log\ y}\)

    (d)

    \(\frac{1}{log(log\ y)}\)

  21. The I.F. of (1+y2)dx=(tan-1-t-x)dy is ________.

    (a)

    etan-1 y

    (b)

    etan-1 x

    (c)

    tan-1 y

    (d)

    tan-1x

  22. The Identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x\(\in \)R, x≠0} under matrix multiplication is

    (a)

    \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \)

    (b)

    \(\left( \begin{matrix} \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \\ \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \end{matrix} \right) \)

    (c)

    \(\left( \begin{matrix} \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \\ \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \end{matrix} \right) \)

    (d)

    \(\left( \begin{matrix} \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \\ \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \end{matrix} \right) \)

  23. If p is true and q is unknown, then _________

    (a)

    ~ p is true

    (b)

    p v (~p) is false

    (c)

    p ∧ (~p) is true

    (d)

    p v q is true

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