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Algebraic Expressions Test - 7

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Algebraic Expressions Test - 7
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  • Question 1
    1 / -0
    The value ofis
    Solution


    =
  • Question 2
    1 / -0
    The addition of , andgives
    Solution
    + +gives



    =
  • Question 3
    1 / -0
    Simplify:
    Solution


    =

    =

    =

    =

    =
  • Question 4
    1 / -0
    Find the value of .
    Solution


    Using (a + b)(a - b) = a2 - b2

    = =
  • Question 5
    1 / -0
    The value of 16x2 + 81y2 - 72xy, when x = 20 and y = 4 is
    Solution
    When x = 20 and y = 4, then
    16(20)2 + 81(4)2 - 72(20)(4)
    = 6400 + 1296 - 5760
    = 7696 - 5760
    = 1936
  • Question 6
    1 / -0
    An expression is taken away fromto obtain. Find that expression from among the following.
    Solution
    Required expression = () - ()

    =-

    =
  • Question 7
    1 / -0
    Write the given algebraic expression in descending order of its exponent.

    Solution


    =

    =
  • Question 8
    1 / -0
    How many diagonals are there in a regular octagon?
    Solution
    Draw an octagon, select one vertex and construct each diagonal from this vertex. You will see there are 5 such diagonals.
    Thus, for each of the 8 vertices, one can draw 5 diagonals and hence, one has constructed 5 x 8 = 40 diagonals.
    But you have constructed each diagonal twice, once from each of its ends. Thus, there are 20 diagonals in a regular octagon.
  • Question 9
    1 / -0
    Simplify: -
    Solution
    -

    = -7p3 - p2q - 24pq2 - 6q3
  • Question 10
    1 / -0
    By what quantity is more than ?
    Solution
    - ()

    =
  • Question 11
    1 / -0
    If p = -2 and q = 1, then what is the value of ?
    Solution
    Putting the values:



    -48 + 8 - 4 + 12 = -32
  • Question 12
    1 / -0
    The order of an expression is
    Solution
    The order of an expression is the order of the highest variable, that is, 3.
  • Question 13
    1 / -0
    The degree of is
    Solution
    Degree corresponds to the highest value of a variable, that is, 3.
  • Question 14
    1 / -0
    If , then the value of is
    Solution


    =

    =

    =

    =

    =
  • Question 15
    1 / -0
    If x = 11c4 + 21c3 + 12c2 - 9c + 5, y = 26c3 - 10c2 - 9c + 7 and z = -10c2 + 7c + 9, then x - y + z is equal to
    Solution
    x - y + z

    = (11c4 + 21c3 + 12c2 - 9c + 5) - (26c3 - 10c2 - 9c + 7) + (-10c2 + 7c + 9)

    = 11c4 + 21c3 + 12c2 - 9c + 5 - 26c3 + 10c2 + 9c - 7 - 10c2 + 7c + 9

    = 11c4 - 5c3 + 12c2 + 7c + 7
  • Question 16
    1 / -0
    Which of the following equations is incorrect?
    Solution






    So, the equation given in option 3 is incorrect.
  • Question 17
    1 / -0
    Simplify:

    6x(12x - 8y) - 3y(3x + y) + 2(x + 6y - 3)(x + y - 2)
    Solution
    6x(12x - 8y) - 3y(3x + y)+ 2(x + 6y - 3)(x + y - 2)

    =

    =
  • Question 18
    1 / -0
    What will be obtained when (4a + 5b - 7c) is added to (2a - 11b + c) and then the answer is divided by (6a - 6b - 6c)?
    Solution
    (4a + 5b - 7c) + (2a - 11b + c) = (6a - 6b - 6c)

    = = 1
  • Question 19
    1 / -0
    If x = 4, y = -5 and z = 2, find the value of the expression.
    Solution
    = = 256 - 125 + 4 + 160 = 295
  • Question 20
    1 / -0
    How many monomials are there?

    (i)) 5m2n
    (ii) 3xy + 5x + 1
    (iii) 5x3 - 9y2
    (iv) a
    Solution
    Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.

    (i) 5m2n
    (ii) a
  • Question 21
    1 / -0
    In an apartment,people live. Out of them, the number of females is. How many males live there?
    Solution
    Total number of people living =
    Number of females =
    Number of males = Total number of people living - Number of females
    =-= 5x2 + 3x - 2
  • Question 22
    1 / -0
    Sham earns Rs. x everyday and spends Rs. y per week. What are his savings in 4 weeks?
    Solution
    Amount of money earned in one day = Rs. x
    So, amount of money earned in 7 days = Rs. 7x
    So, amount of money earned in 4 week = 4 × 7x = Rs. 28x
    Amount of money spend in 1 week = Rs. y
    So, amount of money spend in 4 weeks = Rs. 4y
    Total income = Rs. 28x
    Total expenses = 4y
    = Rs. (28x - 4y)
  • Question 23
    1 / -0
    Suhail's weekly salary was Rs. 4555r. He saved 40% of it. He gave of the remainder to his wife and purchased a piano for of the leftover amount. How much money would he be left with, if r = 4?
    Solution
    If the value of r is 4,
    Weekly salary = 4555 x 4 = Rs. 18,220

    Amount saved = 18220 x= Rs. 7288

    Remainder = (18220 - 7288) = Rs. 10,932
    Amount given to wife = 10932 x= Rs. 2733
    Again, remaining amount = 10932 - 2733 = Rs. 8199

    Amount spent on piano = 8199 x = Rs. 6832.50
    Amount left = 18220 - (7288 + 2733 + 6832.5) = Rs. 1366.5
  • Question 24
    1 / -0
    An air conditioner costs Rs. 165.50s. Additional stabiliser costs Rs. 25s. What is the total cost of 4 air conditioners and 6 additional stabilisers?
    Solution
    Cost of 1 air conditioner = Rs. 165.50s

    Therefore, cost of 4 air conditioners = (4 x 165.50s) = Rs. 662s

    Cost of 1 additional stabiliser = Rs. 25s

    Therefore,
    Cost of 6 additional stabilisers = 6 x 25s = Rs. 150s

    So, total cost = (Rs. 662s + Rs. 150s) = Rs. 812s
  • Question 25
    1 / -0
    From 2000 to 2003, the amount spent by Rahul on groceries (G) and bills (B) can be described by the following expressions, where x is the number of years since 2000.

    Amount spent by Rahul on groceries (G) =
    Amount spent by Rahul on bills (B) =

    What was the total amount spent by Rahul on groceries and bills from 2000 to 2003?
    Solution
    Amount spent on groceries =

    Amount spent on bills =

    Total amount spent =+

    =
  • Question 26
    1 / -0
    State T for true and F for false.

    (i) The value of, when x = 1, is 4.
    (ii)is a monomial.
    (iii) a + b - c is a trinomial.
    Solution
    (i)= 2 - 5 + 7 = 4 (Hence, true)

    (ii)is a trinomial. (Hence, false)

    (iii) a + b - c is a trinomial because it has 3 different terms. (Hence, true)
  • 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 for x = 9 and y = 2.
    Solution


    Putting x = 9 and y = 2

    =

    = 4158 - 648 + 46144 + 9072 = 58726
  • 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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