#### Algebra Important Questions

9th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:00:00 Hrs
Total Marks : 50
7 x 1 = 7
1. If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k= ?

(a)

-6

(b)

-7

(c)

-8

(d)

11

2. The type of the polynomial 4–3x3 is

(a)

constant polynomial

(b)

linear polynomial

(c)

(d)

cubic polynomial.

3. The sum of the polynomials p(x) = x3 – x2 – 2, q(x) = x2–3x+ 1

(a)

x3 – 3x – 1

(b)

x3 + 2x2 – 1

(c)

x3 – 2x2 – 3x

(d)

x3 – 2x2 + 3x –1

4. The product of the polynomials p(x) = 4x –3 q(x) = 4x + 3

(a)

1 – x – 8

(b)

16x2 – 9

(c)

18x3 + 12x2 – 12x – 8

(d)

18x3 – 12x2 + 12x + 8

5. The Auto fare is found as minimum rs 25 for 3 kilometer and thereafter rs12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

(a)

c = 25 + n

(b)

c = 25 + 12n

(c)

c = 25 + (n–3)12

(d)

c = (n–3)12

6. Which of the following is trinomial?

(a)

-7z

(b)

${ z }^{ 2 }-{ 4y }^{ 2 }$

(c)

${ x }^{ 2 }y-{ xy }^{ 2 }+y$

(d)

$12a=9ab+5b-3$

7. The roots of the polynominal equation ${ x }^{ 2 }+2x=0$are_______________

(a)

x=0, 2

(b)

x=1, 2

(c)

x=1, -2

(d)

x=0, -2

8. 3 x 1 = 3
9. The coefficient of -5x is ___________

()

-5

10. 7x - 5y + 3 has __________ terms

()

3

11. The degree of polynomial 5x2y + 3x3y2 + 3xy +7 is ____________

()

5

12. 6 x 2 = 12
13. Which of the following expressions are polynomials. If not give reason: $\frac { 1 }{ { x }^{ 2 } } +3x-4$

14. Which of the following expressions are polynomials. If not give reason: ${ m }^{ 2 }-\sqrt [ 3 ]{ m } +7m-10$

15. Write the coefficient of xand x in each of the following polynomials ${ \pi x }^{ 2 }-x+2$

16. Find the roots of the following polynomial equations: 5x – 3 = 0

17. Check whether p(x) is a multiple of g(x) or not
p(x) = 2x3-11x2-4x+3 ; g(x) = 2x + 3

18. Factorise the following : 25m-2-16n2

19. 6 x 3 = 18
20. Find the degree of each term for the following polynomial and also find the degree of the polynomial
6ab8+5a2b3c2-7ab+4b2c+2

21. Let p(x)=4x2-3x+2x3+5 and q(x)=x2+2x+4 find p(x)-q(x)

22. Find the degree of the following polynomials 3x4+9x2+27x6

23. Write the Variable, Coefficient and Constant in the given algebraic expression

 Expression Variable Coefficient Constant x +7 3y -2 5x2 2xy + 11 -1/2 p+7 - 8 + 3a x x,y 1 -1/2 -8 7
24. Identify monomials, binomials and trinomial from the following expression.
(i) -8 abc
(ii) 3a2bc+8-9a2
(iii) -9
(iv) a2+b2+c2-k2
(v) a+b
(vi) 7ab3
(vii) -z+$\sqrt{3}$z3

25. Show that (x-3) is a factor of x+ 9x- x - 105

26. 2 x 5 = 10
27. Find the product (4x – 5), (2x2 + 3x – 6).

28. The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.