New ! Maths MCQ Practise Tests

12th Standard English Medium Maths Reduced syllabus One Mark Important Questions -2021(Public Exam )

12th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Multiple Choice Questions


    50 x 1 = 50
  1. If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

    (a)

    -40

    (b)

    -80

    (c)

    -60

    (d)

    -20

  2. If A = \(\left[ \begin{matrix} \cos { \theta } & \sin { \theta } \\ -\sin { \theta } & \cos { \theta } \end{matrix} \right] \) and A(adj A) =  \(\left[ \begin{matrix} k & 0 \\ 0 & k \end{matrix} \right] \) then adj (AB) is

    (a)

    0

    (b)

    sin θ

    (c)

    cos θ

    (d)

    1

  3. Which of the following is/are correct?
    (i) Adjoint of a symmetric matrix is also a symmetric matrix.
    (ii) Adjoint of a diagonal matrix is also a diagonal matrix.
    (iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).
    (iv) A(adjA) = (adjA)A = |A| I

    (a)

    Only (i)

    (b)

    (ii) and (iii)

    (c)

    (iii) and (iv)

    (d)

    (i), (ii) and (iv)

  4. The principal argument of (sin 40°+i cos40°)5 is

    (a)

    −110°

    (b)

    −70°

    (c)

    70°

    (d)

    110°

  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. (1+i)3 = ______

    (a)

    3 + 3i

    (b)

    1 + 3i

    (c)

    3 - 3i

    (d)

    2i - 2

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

    (a)

    cos 11θ - isin 11θ

    (b)

    cos 11θ + isin 11θ

    (c)

    cosθ + i sinθ

    (d)

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

  8. If xr=\(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x1, x2 ... x is

    (a)

    -∞

    (b)

    -2

    (c)

    -1

    (d)

    0

  9. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

    (a)

    -1

    (b)

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

    (c)

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

    (d)

    5

  10. For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has

    (a)

    one solution

    (b)

    two solution

    (c)

    at least two solution

    (d)

    no solution

  11. 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

  12. 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

  13. \(cot\left( \cfrac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

    (a)

    7

    (b)

    6

    (c)

    5

    (d)

    none

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

    (a)

    \(\pm 3\)

    (b)

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

    (c)

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

    (d)

    none

  15. The value of \({ sin }^{ -1 }\left( cos\cfrac { 33\pi }{ 5 } \right) \) is________

    (a)

    \(\cfrac { 3\pi }{ 5 } \)

    (b)

    \(\cfrac { -\pi }{ 10 } \)

    (c)

    \(\cfrac { \pi }{ 10 } \)

    (d)

    \(\cfrac { 7\pi }{ 5 } \)

  16. The circle x2+y2=4x+8y+5intersects the line3x−4y=m at two distinct points if

    (a)

    15< m < 65

    (b)

    35< m <85

    (c)

    −85<m < −35

    (d)

    −35<m <15

  17. The equation of the circle passing through the foci of the ellipse  \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) 1having centre at
    (0,3) is

    (a)

    x2+y2−6y−7=0

    (b)

    x2+y2−6y+7=0

    (c)

    x2+y2−6y−5=0

    (d)

    x2+y2−6y+5=0

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

    (a)

    circle

    (b)

    parabola

    (c)

    ellipse

    (d)

    hyperbola

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

    (a)

    straight line

    (b)

    circle

    (c)

    point

    (d)

    parabola

  20. If y = 2x + c is a tangent to the circle x2 + y2 = 5, then c is

    (a)

    土5

    (b)

    \(\sqrt5\)

    (c)

    土5\(\sqrt2\)

    (d)

    ±2\(\sqrt5\)

  21. The point of contact of y2 = 4ax and the tangent y = mx + c is

    (a)

    \(\left( \frac { 2a }{ { m }^{ 2 } } ,\frac { a }{ m } \right) \)

    (b)

    \(\left( \frac { a }{ { m }^{ 2 } } ,\frac { 2a }{ m } \right) \)

    (c)

    \(\left( \frac { a }{ m} ,\frac { 2a }{ { m }^{ 2 } } \right) \)

    (d)

    \(\left( \frac {-a }{ { m }^{ 2 }} ,\frac {- 2a }{ m } \right) \)

  22. 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)

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

  23. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

    (a)

    \(\frac { \sqrt { 7 } }{ 2\sqrt { 2 } } \)

    (b)

    \(\frac{7}{2}\)

    (c)

    \(\frac { \sqrt { 7 } }{ 2 } \)

    (d)

    \(\frac { 7 }{ 2\sqrt { 2 } } \)

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

  25. The p.v, OP of a point P make angles 60o and 45with X and Y axis respectively. The angle of inclination of  \(\overset { \rightarrow }{ OP } \)with z-axis is

    (a)

    75o

    (b)

    60o

    (c)

    45o

    (d)

    3

  26. If the work done by a force \(\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +m\overset { \wedge }{ j } -\overset { \wedge }{ k } \) in moving the point of application from(1, 1, 1) to (3, 3, 3) along a straight line is 12 units, then m is

    (a)

    5

    (b)

    2

    (c)

    3

    (d)

    6

  27. For any three vectors \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \)\(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) \times \left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) \) is

    (a)

    0

    (b)

    \(\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] \)

    (c)

    2\(\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] \)

    (d)

    \({ \left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] }^{ 2 }\)

  28. The distance from the origin to the plane \(\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +5\overset { \wedge }{ k } \right) =7\) is ______________ 

    (a)

    \(\frac { 7 }{ \sqrt { 30 } } \)

    (b)

    \(\frac { \sqrt { 30 } }{ 7 } \)

    (c)

    \(\frac { 30 }{ 7 } \)

    (d)

    \(\frac { 7 }{ 30 } \)

  29. If \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are mutually 丄r unit vectors, then \(\left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right| \) is _______________ 

    (a)

    3

    (b)

    9

    (c)

    \(\sqrt { 3 } \)

    (d)

    \(\sqrt { 3 } \)

  30. The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =\overset { \wedge }{ 3i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k } \) is _______________

    (a)

    4

    (b)

    \(2\sqrt { 3 } \)

    (c)

    \(4\sqrt { 3 } \)

    (d)

    \(5\sqrt { 3 } \)

  31. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

    (a)

    -2

    (b)

    2

    (c)

    1

    (d)

    -1

  32. The function/(x) = x9 + 3x7 + 64 is increasing on ________

    (a)

    R

    (b)

    (-∞, 0)

    (c)

    (0, ∞)

    (d)

    None of these

  33. 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

  34. lf u = (x-y)4+(y-z)4 +(z-x)4 then \(\sum { \frac { \partial u }{ \partial x } } \) = 

    (a)

    4

    (b)

    1

    (c)

    0

    (d)

    -4

  35. If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

    (a)

    -y sin (xy) + z2 cos (xz)

    (b)

    y sin (xy) - z2 cos (xz)

    (c)

    y sin (xy) + z2 cos (xz)

    (d)

    -y sin (xy) - z2 cos (xz)

  36. The cube root of 127 is ............

    (a)

    5.026

    (b)

    5.26

    (c)

    5.028

    (d)

    5.075

  37. If is a homogeneous function of x and y of degree n, then \(x\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +y\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = .............. \(\frac { { \partial }u }{ \partial { x } } \)

    (a)

    n

    (b)

    0

    (c)

    1

    (d)

    n - 1

  38. The volume generated by the curve y2 = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

    (a)

    72π

    (b)

    \(\frac { 256\times 19 }{ 3 } \)

    (c)

    40ㅠ

    (d)

    80ㅠ

     

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

    (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)

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

  40. \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { sinx }{ 2+cosx } dx= } \)

    (a)

    0

    (b)

    2

    (c)

    log 2

    (d)

    log 4

  41. 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

  42. The general solution of x \(\frac{dy}{dx}\)=y is _________.

    (a)

    y=cx

    (b)

    x2+y2=c

    (c)

    x2-y2=c

    (d)

    y=cx

  43. Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

    (a)

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

    (b)

    x(1-\(\sqrt{v}\))dv=v\(\sqrt{v}\)dx

    (c)

    x(1+\(\sqrt{v}\))dv=-v\(\sqrt{v}\)dx

    (d)

    v(1+\(\sqrt{v}\))dx-v\(\sqrt{v}\)dv=0

  44. If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0<x<2\) is the p.d.f, of x then c is

    (a)

    \(\cfrac { 1 }{ 3 } \)

    (b)

    \(\cfrac { 4 }{ 3 } \)

    (c)

    \(\cfrac { 8 }{ 3 } \)

    (d)

    \(\cfrac { 3 }{ 8 } \)

  45. Var (2x ± 5) is =________

    (a)

    5

    (b)

    var (2x) ± 5

    (c)

    4 var (X)

    (d)

    0

  46. If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to__________.

    (a)

    \(\cfrac { 5 }{ 16 } \)

    (b)

    \(\cfrac { 11 }{ 16 } \)

    (c)

    \(\cfrac { 10 }{ 16 } \)

    (d)

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

  47. A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is _________

    (a)

    2.5

    (b)

    1.56

    (c)

    5

    (d)

    25

  48. A random variable X has the following probapality mass function?

    X -2 3 1
    P(X=x) \(\cfrac { \lambda }{ 6 } \) \(\cfrac { \lambda }{ 4 } \) \(\cfrac { \lambda }{ 12 } \)
    (a)

    \(\cfrac { \lambda }{ 6 } +\cfrac { \lambda }{ 4 } +\cfrac { \lambda }{ 12 } =1\)

    (b)

    \(\lambda =2\)

    (c)

    \(P(X=3)=\cfrac { 1 }{ 8 } \)

    (d)

    \(P(1\le X\le 3)=\cfrac { 2 }{ 3 } \)

  49. If a * b = a2b2 - ab then 3 * (1 * 1)

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    4

  50. In (N, *), x * y = max(x, y), x, y \(\in \) N then 7 * (-7)

    (a)

    7

    (b)

    -7

    (c)

    0

    (d)

    -49

*****************************************

TN 12th Standard Maths free Online practice tests

Reviews & Comments about 12th Standard English Medium Maths Reduced syllabus One Mark Important Questions -2021(Public Exam )

Write your Comment