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Question (21)

QN009358

Using Śhrīdharāchārya’s method, 65 2 equals

(A) 4125
(B) 4225
(C) 4325
(D) 4355

Correct Answer: B

Explanation:

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Question (22)

QN009359

If (x+3)(x+4)=x 2 +7x+12, then the coefficient of x is obtained by

(A) Multiplying 3 and 4
(B) Subtracting 3 and 4
(C) Adding 3 and 4
(D) Squaring 3 and 4

Correct Answer: C

Explanation:

The coefficient is 3+4=7.

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Question (23)

QN009360

Factorise x 2 +9x+20.

(A) (x+4)(x+5)
(B) (x+10)(x+2)
(C) (x+15)(x+2)
(D) (x−4)(x−5)

Correct Answer: A

Explanation:

Numbers whose sum is 9 and product is 20 are 4 and 5.

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Question (24)

QN009361

Factorise x 2 −8x+15.

(A) (x−3)(x−5)
(B) (x+3)(x+5)
(C) (x−15)(x+1)
(D) (x−8)(x+15)

Correct Answer: A

Explanation:

Numbers whose sum is −8 and product is 15 are −3 and −5.

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Question (25)

QN009362

Expand (a+b) 3 .

(A) a 3 +b 3
(B) a 3 +3a 2 b+3ab 2 +b 3
(C) a 3 +ab+b 3
(D) a 3 +2a 2 b+2ab 2 +b 3

Correct Answer: B

Explanation:

This is the cube expansion identity.

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Question (26)

QN009363

Expand (2x+1) 3 .

(A) 8x 3 +12x 2 +6x+1
(B) 8x 3 +6x 2 +6x+1
(C) 8x 3 +12x 2 +3x+1
(D) 4x 3 +12x 2 +6x+1

Correct Answer: A

Explanation:

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Question (27)

QN009364

Which identity gives the factorisation of x 3 −y 3 ?

(A) (x−y)(x 2 +xy+y 2 )
(B) (x+y)(x 2 −xy+y 2 )
(C) (x−y) 3
(D) x 2 −y 2

Correct Answer: A

Explanation:

This is the difference of cubes identity.

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Question (28)

QN009365

Factorise 8a 3 −27b 3 .

(A) (2a−3b)(4a 2 +6ab+9b 2 )
(B) (2a+3b)(4a 2 −6ab+9b 2 )
(C) (2a−3b)(4a 2 −6ab+9b 2 )
(D) (a−3b)(8a 2 +9b 2 )

Correct Answer: C

Explanation:

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Question (29)

QN009366

The expression (x+y)(x 2 −xy+y 2 ) simplifies to

(A) x 3 −y 3
(B) x 3 +y 3
(C) x 2 +y 2
(D) (x+y) 3

Correct Answer: B

Explanation:

This is the sum of cubes identity.

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Question (30)

QN009367

If x+y+z=6, x 2 +y 2 +z 2 =18, and xy+yz+zx=9, then x 3 +y 3 +z 3 −3xyz equals

(A) 36
(B) 48
(C) 54
(D) 60

Correct Answer: C

Explanation:

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Question (21)

Using Śhrīdharāchārya’s method, 65 2 equals

Explanation:

Link:

Question (22)

If (x+3)(x+4)=x 2 +7x+12, then the coefficient of x is obtained by

Explanation:

Link:

Question (23)

Factorise x 2 +9x+20.

Explanation:

Link:

Question (24)

Factorise x 2 −8x+15.

Explanation:

Link:

Question (25)

Expand (a+b) 3 .

Explanation:

Link:

Question (26)

Expand (2x+1) 3 .

Explanation:

Link:

Question (27)

Which identity gives the factorisation of x 3 −y 3 ?

Explanation:

Link:

Question (28)

Factorise 8a 3 −27b 3 .

Explanation:

Link:

Question (29)

The expression (x+y)(x 2 −xy+y 2 ) simplifies to

Explanation:

Link:

Question (30)

If x+y+z=6, x 2 +y 2 +z 2 =18, and xy+yz+zx=9, then x 3 +y 3 +z 3 −3xyz equals

Explanation:

Link:

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