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Important 5 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 105

    Part A

    21 x 5 = 105
  1. For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 is consistent.

  2. Find all the roots \((2-2i)^{ \frac { 1 }{ 3 } }\) and also find the product of its roots.

  3. If c ≠ 0 and \(\frac { p }{ 2x } =\frac { a }{ x+x } +\frac { b }{ x-c } \) has two equal roots, then find p. 

  4. Simplify \({ sin }^{ -1 }\left( \cfrac { sinx+cosx }{ \sqrt { 2 } } \right) ,\cfrac { \pi }{ 4 } <x<\cfrac { \pi }{ 4 } \)
     

  5. The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.

  6. If \(\left| \overset { \rightarrow }{ A } \right| =\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \) and \(\overset { \wedge }{ i } =\overset { \wedge }{ j } -\overset { \wedge }{ k } \) are two given vector, then find a vector B satisfying the equations \(\overset { \rightarrow }{ A } \times \overset { \rightarrow }{ B } \)\(\overset { \rightarrow }{ C } \) and \(\overset { \rightarrow }{ A } \).\(\overset { \rightarrow }{ B } \)=3

  7. Find the angle of intersection of the curves 2y2 = x3 and y2 =32x.

  8. If the curves 4x=y2 and 4xy=k cut at right angles show that k2=512.

  9. Find the local maximum and local minimum values for f(x)=12x2-2x2-x4.

  10. Find \(\frac { \partial f }{ \partial x } ,\frac { \partial f }{ \partial y } ,\frac { { \partial }^{ 2 }f }{ \partial { x }^{ 2 } } ,\frac { { \partial }^{ 2 }f }{ { \partial y }^{ 2 } } \)  at x = 2, y = 3 if f(x,y) = 2x2 + 3y2 - 2xy

  11. Find \(\cfrac { \partial w }{ \partial u } ,\cfrac { \partial w }{ \partial v } \) if w=sin-1(x,y) where x=u+v,y=u-v

  12. Show that the area under the curve y = sin x and y = sin 2x between x = 0 and x = \(\frac { \pi }{ 3 } \) and x axis are as 2:3

  13. Find the area of the loop of the curve 3ay2=x(x-a)2

  14. Show that the ratio of the area under the curve y=sinx and y=sin2x between x=0 and \(x=\cfrac { \pi }{ 3 } \) and x- axis are as 2 : 3.

  15. The surface area of a balloon being inflated changes at a constant rate. If initially, its radius 3 units and after 2 seconds it is 5 units, find the radius after t seconds.

  16. Sovle : (x+y+1)2dy=dx,y(-1)=0

  17. A thermometer reading 80°

  18. From a lot of 10 items containing 3 defective items, 4 items are drawn at random. Find the mean and variance of the number of defective items drawn.

  19. The probability that an engineering college student will graduate is 0.3. Find the probability that out of 6 students (i) none (ii) one (iii) at least one will graduate.

  20. Construct the truth table for (p ∧ q) v r.

  21. Show that (2018)2017+(2020)2017≡0(mod2019).

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