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11th Standard English Medium Maths Subject Creative 5 Mark Questions with Solution Part - II

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 125

    5 Marks

    25 x 5 = 125
  1. For A = {0,1,2,3, 4}, B = {1, -2, 3, 4, 5, 6} and C = {2, 4, 6, 7} verify A\(B ∩ C) = (A\B) U(A\C) Using venn diagram.

  2. The cartesian product A \(\times\) A has 9 elements among which are found (-1, 0) and (0, 1).Find the set A and the remaining elements of A \(\times\)A.

  3. Show that the relation R on the set R of all real numbers defined as R = {(a, b): a < b2} is neither reflexive, nor symmetric nor transitive.

  4. Consider the function \(f:[0,{\pi\over 2}]⟶R\) given by f(x) = sin x and \(g:[0,{\pi\over 2}]⟶R\)given by g(x) = cos x. Show that f and g are one-one but (f + g) is not one-one.

  5. A relation R is defined on the set z of integers as follows:
    (x, Y) ∈ R ⇔ x2 + y2 = 25. Express R and R-1 as the set of ordered pairs and hence find their respective domains.

  6. Solve: \(\sqrt{x+5}+\sqrt{x+21}=\sqrt{6x+40}\)

  7. If \({{{log}_{e}^{x}}\over{b-c}}={{{log}_{e}^{y}}\over{c-a}}={{{log}_{e}^{z}}\over{a-b}},\) show that xyz = 1

  8. Evaluate \(\sqrt [ 3 ]{ {{{(45.4)}^{2}}\over{{(3.2)}^{2}}\times{(6.5)}^{2}} } \)

  9. Show that \({{1}\over{3-\sqrt{8}}}-{{1}\over{\sqrt{8}-\sqrt{7}}}+{{1}\over{\sqrt{7}-\sqrt{6}}}-{{1}\over{\sqrt{6}-\sqrt{5}}}+{{1}\over{\sqrt{5}-2}}=5\)

  10. Prove that \(\sqrt { 5 } \) is an irrational number

  11. \(\frac { |x-2|-1 }{ |x-2|-2 } \le 0\)

  12. Find the pairs of ceonsecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11

  13. Forensic Scientists use h = 61.4+2.3F to predict the height h in centimeters for a female whose thigh bone (femur) measures F cm. If the height of the female lies between 160 to 170 cm find the range of values for the length of the thigh bone?

  14. Determine the region in the Plane determined by the inequalities x+y≤9,y>x,x≥0

  15. Solve \((x+1)^{ \frac { 1 }{ 3 } }=\sqrt { x-3 } \)

  16. Solve \(\sin { 2x } +\sin { 4x } +\sin { 6x } =0\)

  17. Show that \(\sin ^{ -1 }{ \left( \frac { 12 }{ 13 } \right) } +\cos ^{ -1 }{ \left( \frac { 4 }{ 5 } \right) } +\tan ^{ -1 }{ \left( \frac { 63 }{ 16 } \right) } =\pi \)

  18. Prove that tan 70° - tan 20° - 2 tan 40° = 4 tan 10°.

  19. Solve : 2 tan θ - cot θ = - 1

  20. Solve: tan-1 (x + 1) + tan-1 (x - 1) = tan-1\(\frac{4}{7}\).0

  21. How many numbers are there between 100 and 1000 such that atleast one of the their digits in 7?

  22. In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.

  23. If nPr = nPr+1 and nCr = nCr-1 find the values of n and r.

  24. Find r if 5Pr = 2 6Pr-1

  25. 2n < (n + 2)! for all natural number n.

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