Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.

Add : (i) `3mn -5mn, 8mn - 4mn` (ii) `t-8tz, 3tz - z, z-t`

Answer» (i) `3mn- 5mn+ 8mn- 4mn`
`= 11mn- 9mn= 2mn`
(ii) `t- 8tz+ 3tz - z + z -t`
`=- 8tz + 3tz = - 5tz `
answers
Discussion
2.

Collect like terms and simplify the expression : `12m^2-9m+5m-4m^2-7m+10`

Answer» `12m^2 - 9m + 5m- 4m^2 -7m + 10`
`= 12m^2 - 4m^2 - 9m+ 5m - 7m + 10`
`= m^2[12-4] + m[-9+5-7] + 10`
`= 8m^2-11m+ 10`
answer
Discussion
3.

Get the algebraic expressions in the following cases using variables, constants andarithmetic 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 numbers m and n.(vii) Product of numbers y and z subtracted from 10.(viii) Sum of numbers a and b subtracted from their product.

Answer» (i) `y-z`
(ii) `(x+y)/2`
(iii) `z xx z =z^2`
(iv) `p*q*1/4 = (pq)/4`
(v) `x^2+y^2`
(vi) `3mn+ 5`
(vii) `10-yz`
(viii) `ab-(a+b) = ab- a-b`
answers
Discussion
4.

Find the values of the following expressions for `x=2.` (i) `x+4` (ii) `4x-3` (iii) `19-5x^2` (iv) `100-10x^3`

Answer» (i) `x+ 4 = 2+4 = 6`
(ii) `4x-3 = 4(2)-3`
`= 8-3=5`
(iii) `19- 5x^2 = 19 5(2)^2`
`= 19-20 = -1`
(iv) `100-10x^3`
`= 100- 10(2^3)`
`= 100-80= 20`
answer
Discussion
5.

Simplify the expression and find its value when `a =5 and b=-3` then `2(a^2+ab)+3-ab`

Answer» `= 2(a^2 + ab) + 3 - ab`
`= 2a^2 + 2ab + 3 - ab`
`= 2a^2 + ab + 3 `
`= 2 (5)^2 + (5)(-3) + 3 `
`= 50-15 +3`
`= 38`
answer
Discussion
6.

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams. (a) `x-3` (b) `1+x+x^2` (c) `y-y^3` (d) `5xy^2 + 7x^2y`

Answer» (a) term : `x-3 `
factor: `x,-3`
(b)term: `1+x+x^2`
factor: `1,x,x^2: x,x`
(c) term: `y-y^3`
factor: `y,-y^3: -1,y,y,y`
(d) term: `5xy^2 + 7x^2y`
factor: `5x^2y: 5,x,x,y ; 7x^2y: 7,x,x,y`
(e) term : `-ab+ 2b^2-3a^2`
factor : `-ab : -1,a,b ; 2b^2 : 2,b,b ; -3a^2 : -1,3,a,a`
answers
Discussion
7.

State with reasons, which of the following pairs of terms are of like terms and which are of unlike terms : (i) `7x, 12y` (ii) `15x-21x` (iii) `4ab,7ba`

Answer» (i) `7x = 7 xx x`
`12y = 2 xx 2 xx 3 xx y` so, unlike
(ii) `-21x = -3 xx 7 xx x`
`15x = 3 xx 5 xx x` so, like
(iii) `-4ab = -2 xx 2 xx a xx b`
`7ba = 7 xx b xx a ` like
(iv) `3xy = 3 xx x xx y `
`3x = 3 xx x` unlike
(v) `6xy^2 = 2 xx 3 xx x xx y xx y`
`9 x^2y = 3 xx 3 xx x xx x xx y` unlike
(vi) `pq^2 = p xx q xx q`
`-4pq^2 = -2 xx 2 xx p xx q xx q`
(viii) `mn^2, 10mn`
`mn^2 = m xx n xx n`
`10mn = 5 xx 2 xx m xx n`
answers
Discussion
8.

Identify, in the following expressions, terms which are not constants. Give their numerical coefficients: `xy+4, 13-y^2, 13-y+5y^2, 4p^2 q-3pq^2+5`

Answer» expression ; term ; numerical
(i) `xy + 4 ; xy ; 4 `
(ii) `13-y^2 ; -y^2 ; 13`
(iii) `13-y + 5y^2 ; 5y^2 - y ; 13`
(iv) `4p^2q - 3pq^2 + 5 ; 4p^2 q , -3pq^2 ; 5`
answers
Discussion