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11th Standard English Medium Maths Subject Creative 2 Mark Questions with Solution Part - II

11th Standard

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Maths

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

    2 Marks

    25 x 2 = 50
  1. Check whether the following sets are disjoint where p = {x : x is a prime < 15} and Q = {x : x is a multiple of 2 and x < 16}

  2. If A⊂B then find A⋂B and A\B (using venn diagram)

  3. Show that the relation R on the set A = {1, 2, 3} given by R = {(1, 1) (2, 2) (3, 3) (1, 2) (2, 3)} is reflexive but neither symmetric nor transitive.

  4. Show that the function f : N➝N given by f(x) = 2x is one-one but not onto.

  5. Let S = {1, 2, 3,....,10}. Define 'm is related to n' if m divides n.

  6. Let P denote the set of all straight lines in a plane. Let R be the relation defined on P as lR m if I is parallel to m

  7. If  \(f(x)=\frac { x-1 }{ x+1 } \), then show that \(f\left( \frac { 1 }{ x } \right) =-f(x)\)

  8. Find the domain and range of the function f(x) = \(\frac { { x }^{ 2 }-9 }{ x-3 } \).

  9. Solve |3x - 4| = |x-2|

  10. Solve \(\frac{1}{|3x-2|}<2\) and express using interval notching.

  11. Find the domain and range of the real valued function f(x) = \(\frac{5-x}{x-5}\).

  12. Solve: (x - 2)(x + 3)2< 0

  13. Prove that 2\(cos\left( \frac { \pi }{ 13 } \right) cos\left( \frac { 9\pi }{ 13 } \right) +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } \) = 0

  14. Prove that \(\frac { 1+sinx-cosx }{ 1+sinx+cosx } =tan\frac { x }{ 2 } \) .

  15. Let p(n) be the statement "7 divides 23n-1" What is p(n+1) =?

  16. If 5Pr = 7Pr-1 find r.

  17. Find the greatest term in (1 + 2x)8 when x = 2.

  18. Write down the series whose rth  term is \(\frac{1}{3}r\). Is it an arithmetic series?

  19. Transform the equation 3x + 4y + 12 = 0 in to normal form.

  20. Solve\(\left[ \begin{matrix} { x }^{ 2 } \\ { y }^{ 2 } \end{matrix} \right] -3\left[ \begin{matrix} x \\ 2y \end{matrix} \right] =\left[ \begin{matrix} -2 \\ 9 \end{matrix} \right] \)

  21. Prove that \(\left| \begin{matrix} 1 & 1+p & 1+p+q \\ 2 & 3+2p & 4+4p+2q \\ 3 & 6+3p & 10+6p+3q \end{matrix} \right| =1\)

  22. Prove that \(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{matrix} \right| =xy\)

  23. Evaluate\(\lim _{ x\rightarrow 0 }{ \frac { { x }^{ \frac { 2 }{ 3 } }-9 }{ x-27 } } \)

  24. \(If\lim _{ x\rightarrow 2 }{ \frac { { x }^{ n }-{ 2 }^{ n } }{ x-2 } } =80\quad and\quad n\in N,\quad find\quad n.\)

  25. Show that the function is \(f\left( x \right) =\begin{cases} \frac { \sin { x } }{ x } +\cos { x,\quad x\neq 0 } \\ 2,\quad \quad \quad x=0 \end{cases}\) continuous at x =0.

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