Algebraic Expressions and Identities

17. The expression abc + 2bca + 3cab is an example of

(A) monomial
(B) binomial
(C) trinomial
(D) polynomial

16. Which of the following expressions represent a monomial?

(A) 6x + 10x – 3x – 5x
(B) –6x² + 3y³ – x² + y³
(C) –6x + 3x² + 5x³ – 2y⁴
(D) –6y² – 2y⁴

15. Which of the following expressions represent a binomial?

(A) 6x + 10x – 3 – 5x
(B) –6x² + 3y³ – 1 + y³
(C) –6x + 3x² + 5x³ – 2y⁴
(D) –6y² – 2y⁴ + 1

14. What is the value of 3x × (5y + 2)?

(A) 15xy + 2
(B) 15xy + 6x
(C) 5y + 6x
(D) 15xy + 2xy

13. What is the value of (–3x) × (–5y + 2)?

(A) –15xy – 6x
(B) –15xy + 6x
(C) 15x – 6xy
(D) 15xy – 6x

12. What is the value of x(x – 3) + 2 for x = 1?

(A) 0
(B) 2
(C) –3
(D) 4

11. What is the value of 3y(2y – 7) – 3 (y – 4) – 63 for y = –2?

(A) 11
(B) 21
(C) –21
(D) 12

10. Simplified value of –pqr(p² + q² + r²) is

(A) –p³qr – pq³r – pqr³
(B) –p³qr + pq³r – pqr³
(C) –p³qr – pq³r + pqr³
(D) –p³qr + pq³r + pqr³

9. Simplified value of (px + qy) (ax – by) is

(A) apx² + pbxy + aqxy – qby²
(B) apx² – pbxy + aqxy + qby²
(C) apx² – pbxy + aqxy – qby²
(D) apx² – pbxy – aqxy – qby²

8. Sum of a – b + ab, b + c – bc and c – a – ac is

(A) 2c + ab – ac – bc
(B) 2c – ab – ac – bc
(C) 2c + ab + ac + bc
(D) 2c – ab + ac + bc

7. If we add p(p – q), q(q – r) and r(r – p), the result is

(A) p² + q² + r² – pq – qr – rp
(B) 2p² + 2q² + 2r² – pq – qr – rp
(C) p² + q² + r² – 2pq – 2qr – 2rp
(D) 0

6. If we add 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy, the result is

(A) 5xy + 3zx + 5x – 4y
(B) 5xy + 9yz + 3zx + 5x – 4y
(C) 5xy + 9yz + 5x – 4y
(D) 5xy + 9yz + 3zx – 4y

5. If we subtract 5x² – 4y² + 6y – 3 from 7x² – 4xy + 8y² + 5x – 3y, the result is

(A) 2x² – 4xy – 9y + 3
(B) 2x² + 5x – 9y + 3
(C) 2x² – 4xy + 12y² + 5x – 9y + 3
(D) 12y² + 5x – 9y + 3

4. The expression (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) is equal to

(A) ab + bc + ca
(B) 0
(C) abc
(D) a² + b² + c²

3. Let the length and breadth of a rectangle is l and b respectively. If the length of the rectangle is increased by 5 units and breadth is decreased by 3 units, the area of the new rectangle will be

(A) (l + 5) × (b + 3)
(B) (l + 5) × (b – 3)
(C) (l – 3) × (b + 5)
(D) (l – 5) × (b + 3)

2. Let the price of bananas per dozen be ₹p and for the school picnic bananas needed is z dozens. If the price per dozen was less by ₹2 and the bananas needed were less by 4 dozens, the payment amount was

(A) ₹(p + 2) × (z – 4)
(B) ₹(p – 2) × (z + 4)
(C) ₹(p + 2) × (z + 4)
(D) ₹(p – 2) × (z – 4)

1. Let the price of bananas per dozen be ₹p and for the school picnic bananas needed is z dozens. If the price per dozen was less by ₹2 and the bananas needed were less by 4 dozens, then we need to pay a lesser amount of