CBSE Class 8 Mathematics Algebraic Expressions and Identities Assignment Set 03

Question. Multiply 6x³ – y + 3x²y by x² + y².
(A) 6x⁵ – 3x⁴y – 6x³y² + 2x²y³ – y4
(B) 6x⁵ + 3x⁴y + 6x³y² – x2y + 3x²y³ – y³
(C) 6x⁵ – 3x⁴y + 6x³y² + 2x²y³ – y5
(D) 6x⁵ + 3x⁴y – 6x³y² + 2x²y³ – y⁵
Answer : B

Question. Find the missing term in the following problem.
(3x/4 - 4y/3)² = 9x²/16 + 16y²/9 + ?
(A) 2xy
(B) – 2xy
(C) 12xy
(D) – 12xy
Answer : B

Question. What should be added to 4p² + 5p + 7 to get 7p² + 2p + 9?
(A) 3p² – 3p + 2
(B) 3p² + 3p + 2
(C) –3p² + 3p – 2
(D) 3p² – 3p – 2
Answer : A

Question. If 3x – 7y = 10 and xy = – 1, then the value of 9x² + 49y² is ____.
(A) 58
(B) 142
(C) 104
(D) – 104
Answer : A

Question. The product of (x² + 3x + 5) and (x² – 1) is ____.
(A) x⁴ + 3x³ – 4x² – 3x – 5
(B) x⁴ + 3x³ + 4x² – 3x – 5
(C) x⁴ + 3x³ + 4x² +3x – 5
(D) x⁴ + x³ + x + 5
Answer : B

Question. Multiply : (4x + 3y/5) and (3x - 4y/5)
(A) 12x² + 7xy/5 - 12y²/25
(B) 12x² + 7xy/5 + 12y²/25
(C) 12x² - 7xy/5 - 12y²/25
(D) None of these
Answer : C

Question. Add : 5x² - (1/3) x + 5/2, (1/2)x + (1/2) x - 1/3 and x² + (1/5) x - 1/6
(A) (5/2)x² + (11/30) x + 2
(B) (3/2)x² + (30/11) x + 3
(C) (5/2)x² + (13/30) x + 1
(D) (3/4)x² + (12/11) x + 5
Answer : A

Question. What must be subtracted from x⁴ + 2x² – 3x + 7 to get x³ + x² + x – 1 ?
(A) x⁴ – x³ + x² – 4x + 8
(B) x³ + x² – 4x + 8
(C) x⁴ – x³ + x² + 4x – 8
(D) x⁴ – x³ – x² + 4x – 8
Answer : A

Question. If x + x/1 = 5, find the value of x⁴ + 1/x⁴ .
(A) 144
(B) 400
(C) 236
(D) 527
Answer : D

Question. If 3x + 4y = 18 and xy = 6, find the value of 9x² + 16y².
(A) 180
(B) 144
(C) 324
(D) 170
Answer : A

Question. Simplify :

(A) − (x²y²/40)
(B) − (x²y²/50)
(C) xy/50
(D) − (x²y²/5)
Answer : B

Question. Square of 9x – 7xy is
(A) 81x² + 49x²y²
(B) 81x² – 49x²y²
(C) 81x² + 49x²y² –126x²y
(D) 81x² + 49x²y² – 63x²y
Answer : C

Question. Fill in the blanks.
(i) The product of two monomials is always P .
(ii) An equation is true for Q values of the variable.
(iii) An identify is true for R values of the variable.
(iv) The numerical factor of a term is called S.
            P                  Q              R                   S
(A) Binomial          all             certain          variable
(B) Monomial        certain      all                 coefficient
(C) Binomial         certain       all                 variable
(D) Monomial       all              certain          coefficient
Answer : B

Question. Simplify : a² - 13a + 30 / (a-10) = a² + 4a + 4 / a+2
(A) a² – 8a – 20 = 0
(B) a² + 30a – 40 = 0
(C) a² – 80a – 30 = 0
(D) a² + 7a – 30 = 0
Answer : A

Question. If (x – 5) notebooks cost ₹ (x² – 13x + 40), what is the cost of one notebook?
(A) (x – 1)
(B) (x – 2)
(C) (x – 6)
(D) (x – 8)
Answer : D

Question. Simplify : 

Answer : C

Question. Which of the following options hold?
Statement-I : The value of the product (4a² + 3b) (4a² + 3b) at a = 1 and b = 2 is 100.
Statement-II : Value of (997 + 496) (997- 96)2/997 x 496 is 2.
(A) Both Statement-I and Statement-II are true.
(B) Statement-I is true but Statement-II is false.
(C) Statement-I is false but Statement-II is true.
(D) Both Statement-I and Statement-II are false.
Answer : B

Question. Ameesha and Prachi love gardening. They water their garden regularly. The length and breadth of Ameesha’s kitchen garden are x m and y m respectively. The length of Prachi’s kitchen garden is 5 m more than that of Ameesha’s garden and the breadth of Prachi’s garden is 3 m more than that of Ameesha’s garden. Find the difference between the area of Ameesha’s kitchen garden and Prachi’s kitchen garden.
(A) (5x + 8y + 10)m²
(B) (3x + 5y – 15)m²
(C) (3x + 5y + 15)m²
(D) (xy + 3x + 5y + 15)m²
Answer : C

Question. Amit want to buy a rectangular field whose area is (3a² + 5ab + 2b²) sq. units. One of its sides is (a + b) units. Find the length of the fence around the field.
(A) (10a + 20b) units
(B) (4a + 3b) units
(C) (2a + 2b) units
(D) (8a + 6b) units
Answer : D

Question. AT-shirt costs ₹(x² – xy – y²) and a sweater costs ₹(2x² + 8xy – 2y²) and a jeans cost ₹(x² – 3xy + 4y²). After buying these items Mohit paid ₹(2x + y)² to the cashier. How much amount Mohit receive from the cashier?
(A) ₹ 0
(B) ₹ 2x
(C) ₹ (x + y)
(D) ₹ 2y
Answer : A

Question. If x² + 1/x² = 53, find the value of x − 1/x
(A) 51
(B) 53
(C) 61
(D) 63
Answer : A

Question. Find the value of a if pqa = (3p + q)² – (3p – q)².
(A) 11
(B) 21
(C) 10
(D) 12
Answer : D

Question. The perimeter of a triangular field is 6p² – 4p + 9 and two of its sides are p² – 2p + 1 and 3p² – 5p + 3. Find the third side of the field.
(A) 8p² + 11p – 7
(B) 2p² + 3p + 5
(C) 3p² + 5p – 4
(D) 5p² – 5p + 9
Answer : B

Question. If x² + y² = 29 and xy = 2, find the value of
(i) x + y (ii) x – y (iii) x⁴ + y⁴
          (i)           (ii)        (iii)
(A) ± √35        ± 6        849
(B) ± √23        ± 5        833
(C) ± √33        ± 5        833
(D) ± √29        ± 3        849
Answer : C

Question. Match the following.

(A) P → (iii); Q → (iv); R → (i); S → (ii)
(B) P → (ii); Q → (i); R → (iv); S → (iii)
(C) P → (iv); Q → (iii); R → (i); S → (ii)
(D) P → (iii); Q → (ii); R → (iv); S → (i)
Answer : A