AP 9th Maths Mock Test 2021 For Chapter 2 : “Polynomials and Factorization” Online Practice Test

1. If x+\frac{1}{x} = \sqrt{3} then the value of x^{3}+\frac{1}{x^{3}} is
2. Factors of 6-x-x^{2} are
3. If (x+2) is a factor of 2x^{3}-kx^{2}+3x+10 then the value of k is
4. If (y-3) is a factor of y^{3}-2y^{2}-9y+18 then the other two factors are
5. The factors of x^{3}+2x^{2}+3x+6 is
6. The value of 'k' if 2x-3 is a factor of 2x^{3}-9x^{2}+x+k is
7. The value of 'a' and 'b' if x^{2}-5x+6 is a factor of 3x^{3}+ax^{2}+bx+12
8. When we divide a polynomial p(x) by (x-a) then the remainder is equal to
9. The remainder when a^{3} - 10 is divided by a-3 is
10. If p(x) = 2x^{3}+3x^{2}-29x-60 is divided by (x+2) then remainder is
11. The remainder when 2x^{2}-3x+5 is divided by x+1 is
12. The remainder when 5x^{2}+3x-7 is divided by x+9 is
13. If p(x) = x^{2}-9x+18 is divided by x+2 then the remainder is
14. Statement I : The remainder when x^{101}+101 is divided by x+1 is 100
Statement II: (x-1) is a factor of (x^{10}-1) and (x^{11}-1)
15. Which of the following is correct ?
i . Factorization of ax^{2}+bx+c(a\neq0)is existed
ii . 4x^{2}-5x+a and ax^{3}+3x^{2}-13 are divided by (x-2) leave the same remainder then the value of a is 1
iii . x^{3}+y^{3} = (x+y)(x^{2}+xy+y^{2})
iv . 4x^{3}+\sqrt{2}x^{2}+3 is a polynomial of degree 2
16. Find the correct statements
a. 2(a^{2}+b^{2}) = (a^{2}-b^{2}) then a=b
b. x+y+z = 0 then x^{3}+y^{3}+z^{3}-3xyz = 0
c. 30.5\times29.5 then the formula used here is
(a+b)(a-b)
d. 50\frac{1}{2}\times49\frac{1}{2} then the formula used here is (a+b)^{2}
17. The correct statements are
a. (x-2),(x+\frac{1}{2}) are factors of px^{2}+5x+r then p\neqr
b. (x+4),(x+3) are factors of x^{3}-6x^{2}-19x+84
c. (x+a),(x+b) = x^{2}+(a+b)x+ab
d. (x+4),(x+1) are factors of x^{2}+5x+4
18. The value of the polynomial p(x) = \frac{-11}{9}-\frac{17}{26}x at x = \frac{13}{9} is
19. The value of the polynomial p(x) = \frac{-11}{9} - \frac{17}{26}x at x = \frac{13}{9} is
20. a-b \div  \sqrt{a} +  \sqrt{b} then the quotient is
21. If x + 3 is a factor of x^{2} + 7x + k = 0 then the value of k is
22. If (x - 2) is a factor of x^{3} - 2ax^{2} + ax -1 then the value of a is
23. If a = 12 , b = -1 , c = -6 then the value of a + b -c is
24. If a^{2} + b^{2} = 100 , ab = 48 then (a + b)^{2} =
25. If x + \frac{1}{x} = 4 then x^{3} + \frac{1}{x^{3}} =
26. If x^{11} + 101 is divided by x + 1 then the remainder is
27. Assertion A : Polynomials are classified as monomials , binomials , trinomials
Reason R : The classification is based on degree of the polynomial
28. Assertion A : x^{2} + 5x + 4 = (x + 4)(x + 1)
Reason R : (x + a) (x + b) = x^{2} + (a + b)x + ab
29. Assertion A : (2y + 1) is a factor of 4y^{3} + 4y^{2} -y -1
Reason R : p(y) will be of (y + a) only , if (y + a) divides p(y) exactly
30. Assertion A : 3x^{3} - 2x^{2} + 5\sqrt{x} + x\sqrt{5} is a cubic polynomial
Reason R : The degree of polynomial is the highest degree of its variable term
31. Assertion A : x = \frac{-b}{a} is the only zero of the polynomial p(x) = ax + b
Reason R : A linear polynomial in one variable has only one zero
32. Assertion A : Polynomials are named as linear polynomial , quadratic polynomial and cubic polynomial
Reason R : If exponent is negative integer then it is not a polynomial
33. If (x - a ) is a factor of polynomial p(x) then p(a) =
34. (x + a)(x + b) =
35. 9x^{2} - 25 can be factorized by using which identity
36. Statement I : Every polynomial is a multinomial
Statement II : Every multinomial is a polynomial
37. A : 2x^{2} + \frac{3}{x} + 5 is a polynomial
B : An algebraic expression in which the variables involved only non - negative integral powers is called a polynomials
38. Which of the following is a factor of 2x^{3} + x^{2} - 21x + 18 ?
39. Which of the following are polynomials ?
40. Which of the following are true ?
a. (x + y)^{2} = x^{2} + 2x + 2y + y^{2}
b. (x - y)^{2} = x^{2} - 2xy + y^{2}
c. (x + y + z)^{2} = x^{2} +  y^{2} + z^{2} + 2xy + 2yz + 2zx
d. (x + y - z)^{2} = x^{2} +  y^{2} - z^{2} + 2xy + 2yz - 2zx
41. A : a^{3}b^{3} - 64(a + b)^{3} = (ab - 4a - 4b)[(a^{2}b^{2} + 4ab)(a + b) + 16(a + b)^{2}]
B : x^{3} - y^{3} = (x -y)(x^{2} + xy + y^{2})
42. Arrange the steps to evaluate the following products without actual multiplication of 50\frac{1}{2} \times 49\frac{1}{2}
1. (50)^{2} - (\frac{1}{2})^{2}
2. 2500 - \frac{1}{4}
3. [50 + \frac{1}{2}][50 - \frac{1}{2}]
4. 2499\frac{3}{4}
43. Arrange the steps without actually calculating the cubes , find the value of the following (-10)^{3} + 7^{3} + 3^{3}
1.(-7)^{3} + (-3)^{3} - 441 - 189
+ (7)^{3} + (3)^{3}
2. (-7 - 3)^{3} + (7)^{3} + (3)^{3}
3. (-7)^{3} + (-3)^{3} + 3(-7)^{2}(- 3) + 3(- 7)(-3)^{2} + (7)^{3} + (3)^{3}
4. - 630
44. Arrange the steps to divide 3y^{3} + 2y^{2} + y by 'y' and write division fact
1. \frac{3y^{3} }{y} + \frac{2y^{2} }{y} + \frac{y}{y}
2. 3y^{2} + 2y + 1
3. 3y^{3} + 2y^{2} + y \div y
4. \frac{3^{3} + 2^{2} + y}{y}
45. The value of 'a' in ax^{3} - 4x^{2} + x + 3 is
46. The remainder of 7x^{2} + 3x + 4 is
47. Which polynomial is suitable with factor x - 1 and remainder 0 ?
48. The solution for 201\times198
49. The expand form of (5x - 4y -2z)^{2}
50. The suitable answer with identities(x + y)^{3} and evaluation 1331000
51. Find the evolution for product (4x + 3y)^{2} + (4x - 3y)^{2} and identity (x + y)^{2} + (x - y)^{2}
52. Which identity is used to calculate 202\times198 ?
53. If ax^{2} + bx + c is exactly divisible by (4x - 3)(3x + 2) then the values of a , b , c are expectively
54. If \frac{x}{y} + \frac{y}{x} = -1 [ x , y , z  \neq 0] then the value of x^{3} - y^{3} is
55. If 2(a^{2} + b^{2}) = (a + b)^{2} then the result is
56. Which of the following is division rule ?
57. Match the following
58. Match the following

59. An expression containing only one term is called
60. An expression containing two terms is called
61. An expression containing three terms is called
62. An expression containing more than two terms is called
63. An algebraic expression containing one or more terms with positive integrals indices is called
64. Constant term is an expression
65. The sum of powers in each of its variable is called
66. The highest power of terms in a polynomial is called
67. Every non - zero number is considered as monomial with degree zero is known as
68. Quantities which have only one fixed value are called
69. If all the coefficients on a polynomial are zeros , then it is called
70. The combination of terms obtained by the operation like addition and subtraction is known as
71. Which of the following are not a monomial ?
72. Which of the following are polynomial ?
73. 4x - 3y + 5z + a it is a
74. In 3s + 6 , variable is
75. In ax + b , b is a
76. Which of the following are examples of constant ?
77. The zero of polynomial of 7t + 10 is
78. A polynomial having highest degree ....... is called linear polynomial
79. A polynomial having highest degree ....... is called cubic polynomial
80. A polynomial having highest degree '2' is called
81. Which of the following are not a polynomial ?
82. Which of the following having highest degree one ?
83. Degree of polynomial for 5 is
84. Degree of -8 x^{2} y is
85. In the expression 6x^{2} + 8y - 60 . coefficient of y is
86. 1 -  x^{2} , here coefficient of  x^{2} is
87. The zeroes of  x^{2} - 5x + 6
88. s(z) =  z^{3} - 1 at z = 1 is
89. If 2 is a zero of the polynomial p(x) = 2 x^{2} - 3x + 7a , find value of a
90. If 0 and 1 are the zeroes of the polynomial f(x) = 2x^{3} - 3x^{2} + ax + b , find value of a and b
91. If a + b + c = 9 and ab + bc + ca = 26 , find a^{2} + b^{2} + c^{2}=
92. If x + y + z = 0 then x^{3} + y^{3} + z^{3} =
93. The value of (-10)^{3} + 7^{3} + 3^{3}
94. (\frac{1}{2}) ^{3} + (\frac{1}{3}) ^{3} - (\frac{5}{6}) ^{3} =
95. How many terms a cubic polynomial with one variable can have ?
96. Find the value of 4x^{2} - 5x + 3 when x = \frac{1}{2}
97. Find the remainder when x^{3} - p x^{2} + 6x - p is divided by x - p
98. Find the remainder when 9 x^{3} -3 x^{2} + x - 5 is divided by x -  \frac{2}{3}
99. If the polynomials x^{3} + a x^{2} + 5 and x^{3} - 2 x^{2} + a are divided by (x + 2) leave the same remainder , find the value of a
100. Find the remainder when f(x) = x^{4} - 3x^{2} + 4 is divided by g(x) = x - 2

 

Leave a Comment