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Model 5 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 115

    Part A

    23 x 5 = 115
  1. Solve: \(\frac { 2 }{ x } +\frac { 3 }{ y } +\frac { 10 }{ z } =4,\frac { 4 }{ x } -\frac { 6 }{ y } +\frac { 5 }{ z } =1,\frac { 6 }{ x } +\frac { 9 }{ y } -\frac { 20 }{ z } \)=2

  2. Verify that arg(1+i) + arg(1-i) = arg[(1+i) (1-i)]

  3. If a, b, c, d and p are distinct non-zero real numbers such that (a2+b2+c2) p2-2 (ab+bc+cd) p+(b2+c2+d2)≤ 0 the n. Prove that a,b,c,d are in G.P and ad=bc

  4. If \({ tan }^{ -1 }\left( \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right) =a\) than prove that x2=sin2a

  5. A kho-kho player In a practice Ion while running realises that the sum of tne distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distance between the poles is 6m.

  6. ABCD is a quadrilateral with \(\overset { \rightarrow }{ AB } =\overset { \rightarrow }{ \alpha } \) and \(\overset { \rightarrow }{ AD } =\overset { \rightarrow }{ \beta } \) and \(\overset { \rightarrow }{ AC } =2\overset { \rightarrow }{ \alpha } +3\overset { \rightarrow }{ \beta } \). If. the area of the quadrilateral is λ times the area of the parallelogram with \(\overset { \rightarrow }{ AB } \) and \(\overset { \rightarrow }{ AD } \) as adjacent sides, then prove that \(\lambda =\frac { 5 }{ 2 } \)

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  7. Show that the curves 4x = y2 and 4xy = k cut at right angles if k2 = 512.

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

  9. Find the intervals for which the function f(x)=2x2-9x2-12x+1 is increasing or decfreasing and find the local extermems.

  10. Find the local maximum and local minimum values of f(x)=x4-3x+3x2-x.

  11. Using differential find the approximate value of cos 61; if it is given that sin 60° = 0.86603 and 10 = 0.01745 radians.

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

  13. Using integration, find the area of the triangle with sides y = 2x+1, y = 3x + 1 and x = 4.

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

  15. Find the area of the region bounded by a2y2=a2(a2-x2)

  16. Find the area bounded by the curve y2(2a-x)=x2 and the line x=2a.

  17. Solve: \(\frac { dy }{ dx } \) = (3x+2y+1)2

  18. Solve :(x2+xy)dy=(x2+y2)dx

  19. A thermometer reading 80°

  20. 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.

  21. Ten coins are tossed simultaneously. What is the probability of getting (a) exactly 6 heads (b) at least 6 heads (c) at most 6 heads?

  22. Verify (p ∧ -p) ∧ (~q ∧ p) is a tautlogy, contradiction or contingency.

  23. Prove without using the truth table \(\sim \left( pV\left( qVr \right) \right) \equiv \left( \sim pV\sim q \right) V\left( -r \right) \)

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