10th Standard English Medium Maths Subject Relations and Functions Book Back 5 Mark Questions with Solution Part - II

10th Standard

    Reg.No. :
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Maths

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

    5 Marks

    10 x 5 = 50
  1. Given A = {1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D) is true?

  2. Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
    A x (B U C) = (A x B) U (A x C)

  3. Given the function f:x ⟶ x2- 5x + 6, evaluate
    i) f( -1)
    ii) f (2a)
    iii) f (2)
    iv) f (x - 1)

  4. If the function f: R⟶ R defined by 
    \(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
    (i) f( 4)
    (ii) f( -2)
    (iii) f(4) + 2f(1)
    (iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

  5. Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, Verify whether A x C is a subset of B x D?

  6. If f(x) = \(\frac { x-1 }{ x+1 } \), x ≠ 1 show that f(f(x)) = -\(\frac{1}{x}\), provided x ≠ 0.

  7. The functions f and g are defined by f(x) = 6x + 8; g(x) = \(\frac { x-2 }{ 3 } \)
    i. Calculate the value of gg\(\left( \frac { 1 }{ 2 } \right) \)
    ii. Write an expression for gf(x) in its simplest form.

  8. Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
    (A U B) x  C = (A x C) U (B x C)

  9. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that
    A x ( B - C) = (A x B) - (A x C)

  10. Find f o g and g and g o f when f(x) = 2x + 1 and g(x) = x- 2

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