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Algebraic Expressions Test - 8

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Algebraic Expressions Test - 8
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  • Question 1
    1 / -0
    The value of -6x2y × xyz × xy2z2 × 5y2 is
    Solution
    -6x2y × xyz × xy2z2 × 5y2

    = -6 × × × 5 × () × () × ()

    =

    =
  • Question 2
    1 / -0
    Simplify the following expression and mark the correct option.

     + + ()
    Solution
    ++ ()

    = + + ( )

    =

    =




  • Question 3
    1 / -0
    Simplify the following expression and mark the correct option.

    Solution
    Let be A and be B.
    Now, we have
    A2 - B2
    = (A + B)(A - B)
    By putting the values of A and B be in above equation, we get





    = [6x][]

  • Question 4
    1 / -0
    The product of and is
    Solution









  • Question 5
    1 / -0
    What is the value of 3x3 - 9y2 + 4xy when x = 5 and y = 7?
    Solution
    3x3 - 9y2 + 4xy
    When x = 5 and y = 7, then
    3 × (5)3 - 9 × (7)2 + 4 × (5) × (7)
    = 3 × 125 - 9 × 49 + 4 × 35
    = 375 - 441 + 140
    = 74
  • Question 6
    1 / -0
    An expression is added to 2a2 + b3 + 10b + 13ab to obtain a3 + 6a2 + 7b3 + 19b + 13ab. The added expression is:
    Solution
    a3 + 6a2 + 7b3 + 13ab + 19b - (2a2 + b3 + 13ab + 10b)
    = a3 + 6a2 + 7b3 + 13ab + 19b - 2a2 - b3 - 13ab - 10b
    = 4a2 + a3 + 6b3 + 9b
  • Question 7
    1 / -0
    Simplify the given expression and mark the correct option.

    5x + 6x5 - 17x - x4 + x17 + 9x + 4x4
    Solution
    5x + 6x5 - 17x - x4 + x17 + 9x + 4x4
    = (5x -17x + 9x) + 6x5 + (4x4 - x4) + x17
    = -3x + 6x5 + 3x4 + x17
    = x17 + 6x5 + 3x4 - 3x
  • Question 8
    1 / -0
    What should be the value of y, if the value of 2x2 + x - y is 5 when x = 1?
    Solution
    2x2 + x - y = 5 when x = 1.
    Putting x = 1 in the given equation,
    2 × (1)2 + 1 - y = 5
    2 + 1 - y = 5
    3 - y = 5
    y = 3 - 5
    y = -2
  • Question 9
    1 / -0
    Simplify the following expression and mark the correct option.

    x4 + 16x + 19x + x2 + 3x3 - (16x - 3x + 2x2 - 3x3 + 6x3)
    Solution
    x4 + 16x + 19x + x2 + 3x3 - (16x - 3x + 2x2 - 3x3 + 6x3)

    => x4 + 16x + 19x + x2 + 3x3 - 16x + 3x - 2x2 + 3x3 - 6x3

    => x4 + 16x + 19x - 16x + 3x + x2 + 3x3 - 2x2 + 3x3 - 6x3

    => x4 + 22x - x2
  • Question 10
    1 / -0
    x5 + 16x + 2x2 + 17x4 + 19 is more than 16x + 18 + x2 + x5 + 17x4 by
    Solution
    x5 + 16x + 2x2 + 17x4 + 19 - (16x + 18 + x2 + x5 + 17x4)

    = x5 + 16x + 2x2 + 17x4 + 19 - 16x - 18 - x2 - x5 - 17x4

    = x2 + 1
  • Question 11
    1 / -0
    What will you get on subtracting the sum of x2 + y2 + 2xy and x2 + 2y2 - 2xy from the sum of -x2 - y2 and -x2 - 3y2?
    Solution
    Sum of the former given terms, S1 = 2x2 + 3y2
    Sum of the latter given terms, S2 = -2x2 - 4y2
    Now, S2 - S1 = -2x2 - 4y2 - 2x2 - 3y2 = -4x2 - 7y2
  • Question 12
    1 / -0
    Which of the following expressions is a binomial?
    Solution
    An algebraic expression that has two terms is called a binomial.
    3x + 4y and bx + c are examples of binomials.
    So, among the given expressions, 6 + a3 is a binomial.
  • Question 13
    1 / -0
    What is the degree of the given expression?

    5b9 + 7b4 + 4b2 - 6b + 0
    Solution
    5b9 + 7b4 + 4b2 - 6b + 0
    The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
    The largest degree of b is 9.
    So, the degree of the given expression is 9.
  • Question 14
    1 / -0
    If =, then what is the value of++ 2?
    Solution
    =
    Solving the expression,
    ++ 2
    = ++ 2 (Multiplying and Dividing 1st term by n)
    = ++ 2
    Now, put =
    = + + 2
    = + + 2
    = -9 ++ 2
    = - 7
    =
  • Question 15
    1 / -0
    If P = 45a3 - 21a2 + 12a + 10, Q = -60a2 + 35a + 8 and R = 9a3 - 64a2 - 5, then what is the value of P + Q - R?
    Solution
    Given:
    P = 45a3 - 21a2 + 12a + 10
    Q = -60a2 + 35a + 8
    R = 9a3 - 64a2 - 5
    Now, P + Q - R = 45a3 - 21a2 + 12a + 10 + (-60a2 + 35a + 8) - (9a3 - 64a2 - 5)
    = 45a3 - 21a2 + 12a + 10 - 60a2 + 35a + 8 - 9a3 + 64a2 + 5
    = 45a3 - 9a3 - 21a2 - 60a2 + 64a2 + 12a + 35a + 10 + 8 + 5
    = 36a3 - 17a2 + 47a + 23
  • Question 16
    1 / -0
    Which of the following equations is incorrect?
    Solution
    (1) 5x - 7y2 - 7y = 2y - 7x2 (It is incorrect.)

    (2) 7xy - (-8xy) = 15xy (It is correct.)

    (3) -3x2 - x2 = -4x2 (It is correct.)

    (4) 5x + 7x + (-6x) = 6x (It is correct.)
  • Question 17
    1 / -0
    Simplify the following expression:

    (4y - 5 + 2x)(3x + 5y - 7) + {(7x - 5xy + 12) - (8x - 3y + 9)}
    Solution
    Given:

    (4y - 5 + 2x)(3x + 5y - 7) + {(7x - 5xy + 12) - (8x - 3y + 9)}

    On solving the expression, we get

    (12xy + 20y2 - 28y - 15x - 25y + 35 + 6x2 + 10xy - 14x) + (7x - 5xy + 12 - 8x + 3y - 9)

    = (6x2 + 20y2 + 22xy - 29x - 53y + 35) + (-x + 3y - 5xy + 3)

    = 6x2 + 20y2 + 22xy - 29x - 53y + 35 - x + 3y - 5xy + 3

    = 6x2 + 20y2 + 17xy - 30x - 50y + 38
  • Question 18
    1 / -0
    What must be subtracted from 6m + 2n2 + 3n to get 4m + 1 - 3n2?
    Solution
    Let x is a number which is subtracted from 6m + 2n2 + 3n
    Then,
    6m + 2n2 + 3n - x = 4m + 1 - 3n2
    x = 6m + 2n2 + 3n - 4m - 1 + 3n2
    x = 2m + 5n2 + 3n - 1
  • Question 19
    1 / -0
    Which of the following statements is true?
    Solution
    An expression with two terms is called a binomial.
  • Question 20
    1 / -0
    Which of the following expressions is a trinomial?
    Solution
    An expression with three unlike terms is called a trinomial, where unlike terms are the terms having different algebraic factors.
    So, 4x + 4y + 7 is a trinomial expression.
  • Question 21
    1 / -0
    In a college, 5y2 + 6y + 9 peons and 6y2 + 3y + 8 managers work. What is the total number of peons and managers working in the college?
    Solution
    Number of peons working = 5y2 + 6y + 9
    Number of managers working = 6y2 + 3y + 8
    Total number of managers and peons = 5y2 + 6y + 9 + 6y2 + 3y + 8 = 11y2 + 9y + 17
  • Question 22
    1 / -0
    A company P buys x number of products in a month and sells y number of the same products over 3 months. What will be the number of products in the company's stock after 3 years?
    Solution
    Number of products that company P buys monthly = x
    Number of products that company P buys yearly = 12x
    Number of products that company P sells quarterly = y
    Number of products that company P sells yearly = 4y
    Number of products left with company P after 1 year = 12x - 4y
    So, number of products left with the company after 3 years = 3(12x - 4y) = 36x - 12y
  • Question 23
    1 / -0
    Rohit's monthly salary is Rs. 7220a. He spends half of the salary on his day-to-day expenses and saves of the remainder. What amount out of total salary is left with him after covering his expenses and putting the savings aside, if the value of a is 4?
    Solution
    Monthly salary of Rohit = Rs. 7220 × 4 = Rs. 28,880

    Half of Rohit's salary = = Rs. 14,440
    Savings = = Rs. 9626.67

    Amount left with Rohit after covering all expenses and putting savings aside = 14,440 - 9626.67 = Rs. 4813.33
  • Question 24
    1 / -0
    If the cost of a set of chairs is Rs. 456.10 and that of a table is Rs. 320.90, then what will be the total cost of 5 sets of chairs and 4 tables?
    Solution
    Cost of one set of chairs = Rs. 456.10
    Cost of one table = Rs. 320.90
    Total cost of 5 sets of chairs and 4 tables = (5 × 456.10) + (4 × 320.90)
    = 2280.5 + 1283.6 = Rs. 3564.1
  • Question 25
    1 / -0
    If A = 5x2 + 6y + 9 and B = 6y2 + 3x + 8, then what is the sum of A and B?
    Solution
    A = 5x2 + 6y + 9
    B = 6y2 + 3x + 8
    A + B = (5x2 + 6y + 9) + (6y2 + 3x + 8) = 5x2 + 6y2 + 6y + 3x + 17
  • Question 26
    1 / -0
    Write 'T' for True and 'F' for False and choose the correct option:

    (1) The terms which have the same algebraic factors are called unlike terms, and the terms which have different algebraic factors are called like terms.
    (2) The degree of the expression 5a2 - 6a + 10 is 1.
    (3) The factors of expression 4pq + 9 are 4, p, q and 9.
    Solution
    Statement (1) is false because the terms which have the same algebraic factors are called like terms, and the terms which have different algebraic factors are called unlike terms.)
    Statement (2) is false because the degree of a polynomial is the largest exponent. In case of 5a2 - 6a + 10, the degree is 2.
    Statement (3) The factors of expression 4pq + 9 are 4, p, q and 9. (False: the factors of expression cannot be determined.)
  • Question 27
    1 / -0
    Match the following:

    Solution
    a.

    (11x2 - 8x + 4) + (6x2 + 7x + 10)
    Adding the like terms first,

    = 11x2 + 6x2 - 8x + 7x + 4 + 10

    = 17x2 - x +14

    b.
    xy2 × zxy

    Multiplying all the terms,

    (x × x × y2 × y × z)

    = x2y3z

    c.
    2

    By expanding the terms,



    = 2 + (2y)2 - 2 × × 2y

    = 3x2 + 4y2 - 4xy

    d.

    (4x + 2y)(16x - 8y)

    = (4x + 2y)4(4x - 2y)

    = 4{(4x)2 - (2y)2}

    = 64x2 - 16y2
  • Question 28
    1 / -0
    Find the value of 5(x + 2y) + 7(x2 - y2) - 2xyz + (x + y + z) + 3x + 5y - 2z, if x = -2, y = 3 and z = -4.
    Solution
    5(x + 2y) + 7(x2 - y2) - 2xyz + (x + y + z) + 3x + 5y - 2z

    Now, put the values as x = -2, y = 3 and z = -4:

    5(-2 + 2(3)) + 7((-2)2 - (3)2) - 2(-2)(3)(-4) + (-2 + 3 - 4) + 3(-2) + 5(3) - 2(-4)

    = 5(4) + 7(4 - 9) - 2(24) + (-3) - 6 + 15 + 8

    = 20 - 35 - 48 - - 6 + 15 + 8

    = -46 -

    =
  • Question 29
    1 / -0
    Fill in the blanks:

    1. Terms which have the same algebraic factors are ______ terms.
    2. An algebraic expression of more than three terms is called a _______.
    3. m × m has two factors, so to express it we can write: m × m = _______.
    4. The ________ of two like terms is a like term with coefficient equal to the sum (or difference) of the coefficients of the two like terms.
    Solution
    1. Terms which have the same algebraic factors are like terms..
    2. An algebraic expression of more than three terms is called a polynomial.
    3. m × m has two factors, so to express it we can write: m × m = m2.
    4. The sum or difference of two like terms is a like term with coefficient equal to the sum (or difference) of the coefficients of the two like terms
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