Mathematics SSC-I Class 9 Solution – 2nd Set Model Question Paper

Model Question Paper SSC-I
Mathematics(Science Group)
(2nd Set)SOLUTION
SECTION-A
1 D 2 A 3 D 4 A 5 D 6 A 7 A 8 A
9 A 10 B 11 A 12 B 13 D 14 B 15 D




SECTION-B
Question-2(i)
−5 −3 3 1 −18 −11
BC= [ ][ ]=[ ]
2 1 1 2 7 4
0 2 −18 −11 14 8
A (BC)= [ ][ ]=[ ]
3 −1 7 4 −61 −37
0 2 −5 −3 4 2
AB= [ ][ ]=[ ]
3 −1 2 1 −17 −10
4 2 3 1 14 8
(AB) C= [ ][ ]=[ ]
−17 −10 1 2 −61 −37
From above A (BC) = (AB) C

Question-2(ii)
3
√46.3(0.05)2
Let 𝑥 =
√8.54

Taking log of both sides
3
𝑙𝑜𝑔𝑥 = 𝑙𝑜𝑔 √46.3 + 𝑙𝑜𝑔(0.05)2 − 𝑙𝑜𝑔√8.54

𝑙𝑜𝑔𝑥 = 𝑙𝑜𝑔(46.3)1⁄3 + 𝑙𝑜𝑔(0.05)2 − 𝑙𝑜𝑔(8.54)1⁄2
1 1
𝑙𝑜𝑔𝑥 = 𝑙𝑜𝑔46.3 + 2𝑙𝑜𝑔0.05 − 𝑙𝑜𝑔8.54
3 2
1 1
𝑙𝑜𝑔𝑥 = (1.6660) + 2(2. 6990) − (0.9315)
3 2
𝑙𝑜𝑔𝑥 = 0.5553 + 2(−2 + 0.6990) − 0.4658
𝑙𝑜𝑔𝑥 = 0.5553 − 4 + 1.3980 − 0.4658

𝑙𝑜𝑔𝑥 = −2.5125 = 2. 5125

𝑥 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔2. 5125

, 𝑥 = 0.03256

Question-2(iii)
−3
15𝑚3 𝑛−2 𝑝−1
( )
25𝑚−2 𝑛−9
−3
3𝑚3+2 𝑛−2+9 𝑝−1
=( )
5
−3
3𝑚5 𝑛7 5𝑝 3
=( ) = ( 5 7)
5𝑝 3𝑚 𝑛

53 𝑝3
=( )
33 𝑚5×3 𝑛7×3

125𝑝3
=( )
27𝑚15 𝑛21

Question-2(iv)
(1 + 𝑖)3 (𝑥 + 𝑦𝑖) = (4 + 5𝑖)
(1 + 3𝑖 + 3𝑖 2 + 𝑖 3 )(𝑥 + 𝑦𝑖) = 4 + 5𝑖
(1 + 3𝑖 − 3 − 𝑖)(𝑥 + 𝑦𝑖) = 4 + 5𝑖
(2𝑖 − 2)(𝑥 + 𝑦𝑖) = 4 + 5𝑖
2𝑥𝑖 + 2𝑦𝑖 2 − 2𝑥 − 2𝑦𝑖 = 4 + 5𝑖
2𝑥𝑖 − 2𝑦 − 2𝑥 − 2𝑦𝑖 = 4 + 5𝑖
(−2𝑥 − 2𝑦) + (2𝑥 − 2𝑦)𝑖 = 4 + 5𝑖
Equating the real and imaginary parts
−2𝑥 − 2𝑦 = 4 ⟶ 𝑒𝑞𝑛 − 𝐼 2𝑥 − 2𝑦 = 5 ⟶ 𝑒𝑞𝑛 − 𝐼𝐼
Adding equations I and II
−2𝑥 − 2𝑦 + 2𝑥 − 2𝑦 = 4 + 5
9
−4𝑦 = 9 ⟹ 𝑦 = −4

Subtracting equations II from I
−2𝑥 − 2𝑦 − 2𝑥 + 2𝑦 = 4 − 5
1
−4𝑥 = −1 ⟹𝑥=4

Question-2(v)
1
𝑥− =7
𝑥
1 3
(𝑥 − ) = 73
𝑥