Class 11th

42. Find the distance between parallel lines

(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l (x + y) + p = 0 and l (x + y) – r = 0.

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42.

(i) Given, equation of lines are

15x + 8y- 34 = 0

15x + 8y + 31 = 0

So, c₁ = 34 and c₂ = 31, A = 15 and B = 8

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19. Let R be the relation on Z defined by R = {(a,b): a, b $\in$ Z, a – b is an integer}. Find the domain and range of R.

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19. Given, R= { (a, b): a, b $\in$ z and a – b is an integer}

We know that, the difference of two integers is also an integer.

R= { (a, b): a – b $\in$ z & a, b $\in$ z}

Domain of R=Z.

Range of R= Z.

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18. Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

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18. Given, A={x, y, z}so, n(A)=3

B={1,2} so n(B)=2

? n(A * B)=n(A) *n(B)=3 * 2=6

Hence, no. of relation from A to B=Number of subsets of A * B

=2⁶

=64.

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41. Find the points on the x-axis, whose distances from the line $\frac{x}{3} + \frac{y}{4} = 1$ are 4 units.

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Kindly go through the solution

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17. Write the relation R = {(x,x³) : x is a prime number less than 10} in roster form.

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17. GivenR= { (x, x³) : x is a prime number less than 10}

R = { (x, x³) : x = 2,3,5,7}

= { (2,2³), (3,3³), (5,5³), (7,7³)}

= { (2,8), (3,27), (5,125), (7,343)}

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40. Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).

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40.

The given equation of the line is.

12 (x + 6) = 5 (y- 2)

⇒ 12x + 72 = 5y- 9

⇒ 12x- 5y + 72 + 9 = 0

⇒ 12x- 5y + 82 = 0

The perpendicular distance of point (-1, 1) from the line is given by

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16. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x $\in$ {0, 1, 2, 3, 4, 5}}.

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16. Given, R = { (x, x+5): x $\in$ {0,1,2,3,4,5}

= { (0,0+5), (1,1+5), (2,2+5), (3,3+5), (4,4+5), (5,5+5)}

= { (0,5), (1,6), (2,7), (3,8), (4,9), (5,10)}

So, domain of R= {0,1,2,3,4,5}

range of R= {5,6,7,8,9,10}

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15. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a , b $\in$ A, b is exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

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15. Given, A= {1,2,3,4,6}

R= { (a, b): a, b $\in$ A, b is exactly divisible by a}

(i) R= { (1,1), (1,2), (1,3), (1,4), (1,6), (2,2), (2,4), (2,6), (3,3), (3,6), (4,4), (6,6)}

(ii) Domain of R= {1,2,3,4,6}

(iii) Range of R= {1,2,3,4,6}

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39. Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

(i) x – √3y + 8 = 0, (ii) y – 2 = 0, (iii) x – y = 4.

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As w lies in IV^th quadrant

Cos w = cos 45° and sin w = - sin 45°

= cos (360°- 45°) = sin (360°- 45°)

= cos 315° &nbs

...more

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14. The Fig 2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?

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