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#### Algebra - Important Question Paper

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k= ?

(a)

-6

(b)

-7

(c)

-8

(d)

11

2. The root of the polynomial equation 2x + 3 = 0 is

(a)

$\frac{1}{3}$

(b)

$-\frac{1}{3}$

(c)

$-\frac{3}{2}$

(d)

$-\frac{2}{3}$

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

(a)

constant polynomial

(b)

linear polynomial

(c)

(d)

cubic polynomial.

4. x3 – x2 is a …………..

(a)

monomial

(b)

binomial

(c)

trinomial

(d)

constant polynomial

5. If x51 + 51 is divided by x + 1, then the remainder is

(a)

0

(b)

1

(c)

49

(d)

50

6. Degree of the polynomial (y3–2)(y3 + 1) is

(a)

9

(b)

2

(c)

3

(d)

6

7. Let the polynomials be (A)–13q5 + 4q2 + 12q (B)(x2 +4 )(x2 + 9) (C)4q8 – q6 + 2 (D)-$\frac {5}{7}$y12+y3+y5
Then ascending order of their degree is

(a)

A,B,D,C

(b)

A,B,C,D

(c)

B,C,D,A

(d)

B,A,C,D

8. Which of the following is a monomial?

(a)

${ 4x }^{ 2 }$

(b)

$a+b$

(c)

$a+b+c$

(d)

$a+b+c+d$

9. Which of the following is trinomial?

(a)

-7z

(b)

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

(c)

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

(d)

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

10. The area of a rectangle with length $2l^{ 2 }m$ and breadth $3l^{ 2 }m$ is_______________________

(a)

$6l^{ 3 }m^{ 3 }$

(b)

$l^{ 3 }m^{ 3 }$

(c)

$2l^{ 3 }m$

(d)

$4l^{ 3 }m^{ 3 }$

11. Part B

6 x 2 = 12
12. Which of the following expressions are polynomials. If not give reason: ${ m }^{ 2 }-\sqrt [ 3 ]{ m } +7m-10$

13. Write the coefficient of xand x in each of the following polynomials ${ 4+\frac { 2 }{ 5 } x^{ 2 }-3x }$

14. Write the coefficient of xand x in each of the following polynomials $6-{ 2x }^{ 2 }+3x^{ 3 }-\sqrt { 7 } x$

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

16. Check whether –3 and 3 are zeros of the polynomial x2 – 9

17. Find the value of the polynomial f (y) =  6y - 3y2 + 3 at y = 1

18. Part C

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

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

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

22. Rewrite the following polynomial in standard form.
$7{ x }^{ 3 }-\frac { 6 }{ 5 } { x }^{ 2 }+4x-1$

23. Rewrite the following polynomial in standard form.
${ y }^{ 2 }+\sqrt { 5 } { y }^{ 3 }-11-\frac { 7 }{ 3 } y+{ 9y }^{ 4 }$

24. Add the following polynomials and find the degree of the resultant polynomial.
p(x)=6x2-7x+2 q(x)=6x3-7x+15

25. Part D

2 x 5 = 10
26. The area of a rectangle is x2 + 7x + 12. If its breadth is (x+3), then find its length.

27. The base of a parallelogram is (5x+4). Find its height, if the area is 25x2–16.