। अर्जुन: प्रीत: भूत्वा ब्रह्मास्त्रम् ' अक्षिपत ।
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13.
17. Show that any number of the form 6 x , where n N can never end with the digit 0. ∈ [2]
18. Seema a home tutor used to teach maths in her locality of Paschim vihar. After teaching the
chapter Polynomials, she took a class test in which she wrote the following polynomials:
i. 5x2
- 8x - 4
ii. x
2
- 20x + 91
You have to find the zeros of the above quadratic polynomials by splitting the middle term.
[2]
19. Find the zeroes of the quadratic polynomial given as: x2
+ 7x + 10, and also verify the
relationship between the zeroes and the coefficients.
[2]
20. Check whether g(x) is a factor of p(x) by applying the division algorithm.
p(x) = 2x5
- 4x3
+ 2x2
+ 5x + 1, g(x) = x3
- 4x + 1
[2]
21. Find the zeroes of the polynomial 4x2
– 3x – 1 by factorisation method and verify the relation
between the zero and the coefficient of the polynomial.
[2]
22. A teacher after teaching the chapter polynomial in class 10th wrote the sum and product of
zeros respectively on the blackboard to test the skill grasped by his students. Find out the
Polynomials that the teacher have in his mind.
i. 0 and
ii. and
iii. and
iv. and
[2]
2
– √
2 + 3
– √ 2 − 3
– √
2 5
– √ − 5
– √
3
2 −
1
2
23. are zeroes of the polynomial x2
- 6x + a. Find the value of a, if = 20. α [2] , β 3α + 2β
24. If zeroes and of a polynomial x2
- 7x + k are such that , then find the value of k. α β α − β = 1 [2]
a) 2 b) 1
c) 0 d) 3
25. Number of zeroes of the polynomial p(x) shown in the Figure, are: [2]
26. 5 books and 7 pens together cost Rs.79 whereas 7 books and 5 pens together cost Rs.77. find
the total cost of 1 book and 2 pens.
[2]
27. The sum of two numbers is 8 and the sum of their reciprocals is . Find the numbers. [2] 8
15
28. Does the pair of the linear equation have no solution? Justify your answer.
2x + 4y = 3, 12y + 6x = 6
[2]
29. Write a pair of linear equations which has the unique solution x = -1, y =3. How many such
pairs can you write?
[2]
30. Taxi charges in a city consist of fixed charges and the remaining depending upon the distance
travelled in kilometres. If a man travels 80 km, he pays ₹1330, and travelling 90 km, he pays
[2]