Question 22

Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

Do you agree with this argument? Justify your answer.

Answer

**(i) Total no. Of outcomes = 36**

** • (**1, 2) and (2, 1) are events for getting a sum as 3

P (E) = 2/36 = 1/18

• (1, 3), (2, 2) and (3, 1) are the events of getting the Sum 4

P(E) = 3/36 = 1/12

• (1, 4), (2, 3), (3, 2) and (4, 1) are the events of getting the sum 5

P(E) = 4/36 = 1/9

• (1, 5), (2, 4), (3, 3), (4, 2) and (5, 1) are the events of Getting a sum 6

P(E) = 5/36

• (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1) are the event of getting a sum 7

P(E) = 6/36 = 1/6

• (3, 6), (4, 5), (5, 4) and (6, 3) are the events of getting a sum 9

P(E) = 4/36 = 1/9

• (4, 6), (5, 5) and (6, 4) are the events of getting a sum 10

P(E) = 3/36 = 1/12

• (5, 6), (6, 5) are the events of getting a sum 11

P(E) = 2/36 =1/18

**(ii)** No, the eleven sum is not equally likely.

- Q:-
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

- Q:-
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x

^{2}– 2x – 8 (ii) 4s^{2}– 4s + 1 (iii) 6x^{2}– 3 – 7x (iv) 4u^{2}+ 8u (v) t^{2 }– 15 (vi) 3x^{2 }– x – 4 - Q:-
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

- Q:-
Find two consecutive positive integers, sum of whose squares is 365.

- Q:-
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

- Q:-
Prove that 3 + 2√5 is irrational.

- Q:-
Find two numbers whose sum is 27 and product is 182.

- Q:-
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54 - Q:-
Is the following situation possible? If so, determine their present ages.

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. - Q:-
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i) t^{2}– 3, 2t^{4}+ 3t^{3}– 2t^{2}– 9t – 12(ii) x

^{2}+ 3x + 1, 3x^{4}+ 5x^{3}– 7x^{2}+ 2x + 2(iii) x

^{3}– 3x + 1, x^{5}– 4x^{3}+ x^{2}+ 3x + 1

- Q:-
Is it possible to design a rectangular park of perimeter 80 m and area 400 m

^{2}? If so, find its length and breadth. - Q:-
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

- Q:-
If P(E) = 0.05, what is the probability of ‘not E’?

- Q:-
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11).

- Q:-
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

- Q:-
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x

^{2}– 2x – 8 (ii) 4s^{2}– 4s + 1 (iii) 6x^{2}– 3 – 7x (iv) 4u^{2}+ 8u (v) t^{2 }– 15 (vi) 3x^{2 }– x – 4 - Q:-
Check whether the following are quadratic equations :

(i) (x + 1)^{2}= 2(x – 3) (ii) x^{2}– 2x = (–2) (3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x +1) = x(x + 5)(v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x

^{2}+ 3x + 1 = (x – 2)^{2}(vii) (x + 2)^{3}= 2x (x2 – 1) (viii) x^{3}– 4x^{2}– x + 1 = (x – 2)^{3} - Q:-
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

- Q:-
A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x. - Q:-
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m

^{2}? If so, find its length and breadth.

- NCERT Chapter