Alegebric NCERT Questions

NCERT TEXT BOOK EXERCISES

EXERCISE-12.1

  1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i)      Subtraction of z from y.

(ii)     One-half of the sum of numbers x and y.

(iii)    The number z multiplied by itself.

(iv)    One-fourth of the product of numbers p and q.

(v)     Numbers x and y both squared and added.

(vi)    Number 5 added to three times the product of number m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii)  Sum of numbers a and b subtracted from their product.

  1. (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams.

(a)     x − 3                      (b) 1 + x + x2                 (c) y − y3

(d)               (e) − ab + 2b2 − 3a2

(ii)     Identify terms and factors in the expressions given below:

(a)      − 4x + 5                 (b) − 4x + 5y (c) 5y + 3y2

(d)     xy + 2x2y2              (e)  pq + q

(f)      1.2 ab − 2.4 b + 3.6 a

          (g)                      (h) 0.1p2 + 0.2 q2

  1. Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 − 3t2                         (ii) 1 + t + t2 + t3

(iii) x + 2xy+ 3y               (iv) 100m + 1000n

(v) − p2q2 + 7pq               (vi) 1.2a + 0.8b

(vii) 3.14 r2                     (viii) 2 (l + b)

(ix) 0.1y + 0.01 y2

  1. (a) Identify terms which contain x and give the coefficient of x.

(i) y2x + y            (ii) 13y2− 8yx                (iii) x + y + 2

(iv) 5 + z + zx      (v) 1 + x+ xy                (vi) 12xy2 + 25              (vii) 7x + xy2

(b)     Identify terms which contain y2 and give the coefficient of y2.

(i) 8 − xy2            (ii) 5y2 + 7x                   (iii) 2x2y −15xy2 + 7y2

  1. Classify into monomials, binomials and trinomials.

(i) 4y − 7z            (ii) y2                            (iii) x + y − xy

(iv) 100               (v) ab − a − b                (vi) 5 − 3t

(vii) 4p2q − 4pq2 (viii) 7mn                      (ix) z2 − 3z + 8

(x) a2 + b2             (xi) z2 + z                     (xii) 1 + x + x2

  1. State whether a given pair of terms is of like or unlike terms.

(i) 1, 100             (ii)                  (iii) − 29x, − 29y

(iv) 14xy, 42yx     (v) 4m2p, 4mp2              (vi) 12xz, 12 x2z2

  1. Identify like terms in the following:

(a)      −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2, y, 2xy,3x

(b)     10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2

 

EXERCISE-12.2

  1. Simplify combining like terms:

(i)      21b − 32 + 7b − 20b

(ii)     − z2 + 13z2 − 5z + 7z3 − 15z

(iii)    p − (p − q) − q − (q − p)

(iv)    3a−2b−ab − (a − b + ab) + 3ab + b − a

(v) 5x2y − 5x2 + 3y x2 − 3y2 + x2 − y2 + 8xy2 −3y2

(vi)    (3 y2 + 5y − 4) − (8y − y2 − 4)

  1. Add:

(i)      3mn, − 5mn, 8mn, −4mn

(ii)     t − 8tz, 3tz − z, z − t

(iii)    − 7mn+5, 12mn+2, 9mn − 8, − 2mn − 3

(iv)    a + b − 3, b − a + 3, a − b + 3

(v)     14x + 10y − 12xy − 13, 18 − 7x − 10y + 8xy, 4xy

(vi)    5m − 7n, 3n − 4m + 2, 2m − 3mn − 5

(vii)   4x2y, − 3xy2, − 5xy2, 5x2y

(viii) 3p2q2 − 4pq + 5, − 10p2q2, 15 + 9pq + 7p2q2

(ix)    ab − 4a, 4b − ab, 4a − 4b

(x)     x2 − y2 − 1 , y2 − 1 − x2, 1− x2 − y2

  1. Subtract:

(i)      − 5y2 from y2

(ii)     6xy from − 12xy

(iii)    (a − b) from (a + b)

(iv)    a (b − 5) from b (5 − a)

(v)     − m2 + 5mn from 4m2 − 3mn + 8

(vi)    − x2 + 10x − 5 from 5x − 10

(vii)   5a2 − 7ab + 5b2 from 3ab − 2a2 −2b2

(viii) 4pq − 5q2 − 3p2 from 5p2 + 3q2 − pq

  1. (a) What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?

(b)     What should be subtracted from 2a + 8b + 10 to get − 3a + 7b + 16?

  1. What should be taken away from 3x2− 4y2 + 5xy + 20 to obtain

− x2 − y2 + 6xy + 20?

  1. (a) From the sum of 3x − y + 11 and − y − 11, subtract 3x − y − 11.

(b)     From the sum of 4 + 3x and 5 − 4x + 2x2, subtract the sum of 3x2 − 5x and − x2 + 2x + 5.

 

EXERCISE-12.3

  1. If m= 2, find the value of:

(i) m − 2 (ii) 3m − 5 (iii) 9 − 5m   (iv) 3m2 − 2m − 7 (v)

  1. If p= −2, find the value of:

(i)      4p + 7        (ii)       −3p2 + 4p + 7    (iii)      −2p3 − 3p2 + 4p + 7

  1. Find the value of the following expressions, when x= − 1:

(i) 2x − 7 (ii) − x + 2 (iii) x2 + 2x + 1 (iv) 2x2 − x − 2

  1. If a= 2, b = − 2, find the value of:

(i) a2 + b2 (ii) a2 + ab + b2 (iii) a2 − b2

  1. When a= 0, b = − 1, find the value of the given expressions:

(i) 2a + 2b (ii) 2a2 + b2 + 1 (iii) 2a2 b + 2ab2 + ab (iv) a2 + ab + 2

  1. Simplify the expressions and find the value if xis equal to 2

(i) x + 7 + 4 (x − 5)          (ii) 3 (x + 2) + 5x − 7

(iii) 6x + 5 (x − 2)            (iv) 4 (2x −1) + 3x + 11

  1. Simplify these expressions and find their values if x= 3, a = − 1, b = − 2.

(i) 3x − 5 − x + 9 (ii) 2 − 8x + 4x + 4         (iii) 3a + 5 − 8a + 1

(iv) 10 − 3b − 4 − 5b                                (v) 2a − 2b − 4 − 5 + a

  1. Simplify these expressions and find their values if x= 3, a = − 1, b = − 2.

(i) 3x − 5 − x + 9              (ii) 2 − 8x + 4x + 4        (iii) 3a + 5 − 8a + 1

(iv) 10 − 3b − 4 − 5b        (v) 2a − 2b − 4 − 5 + a

  1. What should be the value of aif the value of 2x2 + x − a equals to 5, when x = 0?
  2. Simplify the expression and find its value when a= 5 and b = −3.

2 (a2 + ab) + 3 − ab

 

EXERCISE-12.4

  1. Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

(a)

 

(b)

 

(c)

 

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are required to form 5, 10, 100 digits of the kind −

,   ,  .

  1. Use the given algebraic expression to complete the table of number patterns.
S. No Expression Terms
1st 2nd 3rd 4th 5th … 10th … 100th …
(i) 2n − 1 1 3 5 7 9 – 19 – – –
(ii) 3n + 2 2 5 8 11 – – – – – –
(iii) 4n + 1 5 9 13 17 – – – – – –
(iv) 7n + 20 27 34 41 48 – – – – – –
(v) n2 + 1 2 5 10 17 – – – – 10, 001 –

 

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