TEST
Question 1
8x2y3−x5
Sol :
=8x2y3−x5=x2(8y3−x3)=x2[(2y)3−(x)3]=x2(2y−3)(yy2+2xy+x2)
Question 2
x2+1x2+2−2x−2x
Sol :
Question 3
2x² – x – 6
Sol :
Question 4
a³ – 0.216
Sol :
=a3−0.226=(a)3−(0.6)3=(a−0.6)(a2+a×0.6+(0.6)2]=(a−0.6)(a2+0.6a+0.36)
Question 5
6x²y – xy – 2y
Sol :
Question 6
(x² – 3x)² – 8(x² – 3x) – 20
Sol :
Question 7
One of the factors of (x – 1) – (x² – 1) is
(a) x² – 1
(b) x + 1
(c) x – 1
(d) x + 4
Sol :
=(x−1)−(x2−1)
=(x-1)-(x+1)(x-1)
=(x-1)[1-x+1]
So, x-1 is its factor
option (C) is correct
Question 8
If xy+yx=−1 (x, y ≠ 0), then the value of x³ – y³ is
(a) 1
(b) – 1
(c) 12
(d) 0
Sol :
=xy+yx=−1
=x2+y2xy=−1
=x2+y2=−xy
=x3−y3=(x−y)(x2+xy+y2)....(formula)
=(x-y)×0=0
Option (d) is correct
Question 9
The product of =(x−1x)(x+1x)(x2+1x2)
(a) x4+1x4
(b) x3+1x3−2
(c) x4−1x4
(d) x2+1x2+2
Sol :
=(x2−1x2)(x2+1x2)
=(x2)2−(1x2)2=x4−1x4
Option (C) is correct
Question 10
If x – 2y= 11 and xy = 8, then the value of x³ – 8y³ is
(a) 1860
(b) 1600
(c) 1859
(d) 2000
Sol :
⇒x3−8y3−3xx×(2y)(x−2y)=1331
⇒x3−8y3−6xy(x−2y)=1331
⇒x3−8y3−6×8×11=1331
⇒x3−8y3−528=1331
⇒x3−8y3=1331+528
⇒x3−8y3=1859
So, option (C) is correct
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