At Saralstudy, we are providing you with the solution of Class 10 Mathematics Some Applications of Trigonometry according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 10th mathematics Some Applications of Trigonometry so that you can prepare for the exam according to your own pace and your speed.

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- 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:-
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 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:-
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.

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

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

- 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:-
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:-
On dividing x

^{3 }– 3x^{2 }+ x + 2 by a polynomial g(x), the quotient and remainder were x – 2 nd –2x + 4, respectively. Find g(x). - Q:-
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy?

(ii) a lemon flavoured candy? - Q:-
Prove that 3 + 2√5 is irrational.

- Q:-
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(A) 7 cm (B) 12 cm

(C) 15 cm (D) 24.5 cm - Q:-
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.

- Q:-
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

- Q:-
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to

(A) 50° (B) 60°

(C) 70° (D) 80° - Q:-
Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

- Q:-
A die is thrown twice. What is the probability that

(i) 5 will not come up either time? (ii) 5 will come up at least once?

[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

- NCERT Chapter