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Model 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 28

    Pat A

    28 x 1 = 28
  1. If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

    (a)

    sinx cosx

    (b)

    1

    (c)

    2

    (d)

    none

  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) ≠ \(\rho\)([AIB]), then the system is

    (a)

    consistent and has infinitely many solutions

    (b)

    consistent and has a unique solution

    (c)

    consistent

    (d)

    inconsistent

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

    (a)

    1

    (b)

    -1

    (c)

    i

    (d)

    0

  5. The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) =1 lies on

    (a)

    circle x2+y2 =1

    (b)

    x-axis

    (c)

    y-axis

    (d)

    the lines x+y=1

  6. If x =cosθ + i sinθ, then the value of xn+\(\frac { 1 }{ { x }^{ n } } \) is

    (a)

    2 cosθ

    (b)

    2i sin nθ

    (c)

    2i sin nθ

    (d)

    2i cos nθ

  7. If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

    (a)

    \(\frac{1}{3}\) ≤k≤

    (b)

    k≥5

    (c)

    k≤0

    (d)

    none

  8. 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 rots is 1

    (c)

    one of the rots is -1

    (d)

    one of the rots is -2

  9. 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

  10. ·If \(\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \)

    (a)

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

    (b)

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

    (c)

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

    (d)

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

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

    (a)

    5

    (b)

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

    (c)

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

    (d)

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

  12. 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)

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

  13. y2 - 2x - 2y + 5 = 0 is a

    (a)

    circle

    (b)

    parabola

    (c)

    ellipse

    (d)

    hyperbola

  14. 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

  15. The area of the circle (x - 2)2 + (y - k)2 = 25 is

    (a)

    25ㅠ

    (b)

    5ㅠ

    (c)

    10ㅠ

    (d)

    25

  16. If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then

    (a)

    \(\left| \overset { \rightarrow }{ d } \right| \)

    (b)

    \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)

    (c)

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

    (d)

    a, b, c are coplanar

  17. 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\(\sqrt { 3 } \)

  18. The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is

    (a)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (b)

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

    (c)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (d)

    \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

  19. Equation of the normal to the curve y=2x2+3 sin x at x=0 is

    (a)

    x + y = 0

    (b)

    3y = 0

    (c)

    x + 3y = 7

    (d)

    x + 3y = 0

  20. The curve y = ex is ________

    (a)

    convex

    (b)

    concave

    (c)

    convex upwards

    (d)

    concave upwards

  21. If f(x,y) = 2x2 - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is

    (a)

    7,11

    (b)

    11,7

    (c)

    0,7

    (d)

    1,0

  22. If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f= sin u then f is a homogeneous function of degree ..................

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    4

  23. \(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 7 }\) dx is

    (a)

    (b)

    (c)

    (d)

  24. \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

    (a)

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

    (b)

    0

    (c)

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

    (d)

    \( \pi\)

  25. 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

  26. The number of binary operations that can be defined on a set of 3 elements is

    (a)

    32

    (b)

    33

    (c)

    39

    (d)

    31

  27. 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

  28. 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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