" /> -->

Full Portion Two Marks Question Paper

12th Standard EM

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 50
    25 x 2 = 50
  1. If A is a non-singular matrix of odd order, prove that |adj A| is positive

  2. Find the rank of the matrix \(\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{matrix} \right] \) by reducing it to a row-echelon form.

  3. Solve the following system of homogenous equations.
    2x + 3y − z = 0, x − y − 2z = 0, 3x + y + 3z = 0

  4. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  5. Find z−1, if z=(2+3i)(1− i).

  6. Simplify the following
    \({ i }^{ 59 }+\cfrac { 1 }{ { i }^{ 59 } } \)

  7. If z=\(\left( \frac { \sqrt { 3 } }{ 2 } +\frac { i }{ 2 } \right) ^{ 107 }+\left( \frac { \sqrt { 3 } }{ 2 } -\frac { i }{ 2 } \right) ^{ 107 }\) , then show that Im (z) =0

  8. Determine the number of positive and negative roots of the equation x9-5x4-14x2=0.

  9. If sin ∝, cos ∝ are the roots of the equation ax2 + bx + c-0 (c ≠ 0), then prove that (n + c)2 - b2 + c2

  10. Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  11. Find the principal value of
    \({ Sin }^{ -1 }\left( sin\left( \frac { 5\pi }{ 6 } \right) \right) \)

  12. Ecalute \(sin\left( { cos }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) \right) \)
     

  13. Find centre and radius of the following circles.
    x2+y2−x+2y−3= 0

  14. For the ellipse x2 + 3y2 = a2, find the length of major and minor axis.

  15. Find the volume of the parallelepiped whose coterminous edges are represented by the vectors \(-6\hat { i } +14\hat { j } +10\hat { k } ,14\hat { i } -10\hat { j } -6\hat { k } \) and \(2\hat { i } +4\hat { j } -2\hat { k } \)

  16. Find the parametric form of vector equation of a line passing through a point (2, -1, 3) and parallel to line \({ \overset { \rightarrow }{ r } }=\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) +t\left( 2\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \right) \)

    ()

    p=-1

  17. A manufacturer wants to design an open box having a square base and a surface area of I 108 sq. em. Determine the dimensions of the box for the maximum volume.

  18. Find the maximum and minimum values of f(x) = |x+3| ∀ \(x\in R\).

  19. Evaluate: \(\int ^{log 2}_{-log 2} e ^{-|x|}\) dx.

  20. Evaluate \(\int _{ 1 }^{ 2 }{ \frac { 3x }{ { 9x }^{ 2 }-1 } dx } \)

  21. Show that y = a cos bx is a solution of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ b }^{ 2 }y=0\).

  22. Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values ofthe random variable X and number of points in its inverse images.

  23. Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
    \(a*b=\left( \frac { a-1 }{ b-1 } \right) ,\forall a,b\in Q\)

  24. Let \(A=\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \end{matrix}\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix} \right) ,B=\left( \begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 0 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix} \right) ,C=\left( \begin{matrix} 1 & 1 \\ 0 & 1 \\ 1 & 1 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 1 \end{matrix} \right) \)be any three boolean matrices of the same type.
    Find (A∨B)∧C 

  25. In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.

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

TN 12th Standard EM Maths free Online practice tests

Reviews & Comments about 12th Maths - Full Portion Two Marks Question Paper

Write your Comment