Math PAPER–CLASS-9th
Time: 2:30 Hr.
Name:
Roll. No:
PAPER OBJECTIVE
Q.1: Choose the correct option and fill up the bubbles.
Sr.
Statements
A
The logarithm of unity to any base is:
If 𝑎 𝑥 = 𝑛, then
𝑙𝑜𝑔 𝑒 = 𝑤ℎ𝑒𝑟𝑒 𝑒 ≅ 2.718
2 1
(iv) The determinant of matrix 𝐵 = [
] is:
4 7
(v) [√2 0 ] 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑎 𝑚𝑎𝑡𝑟𝑖𝑥
0 √2
(vi) 𝐼𝑚𝑎𝑔𝑖𝑛𝑎𝑟𝑦 𝑝𝑎𝑟𝑡 𝑜𝑓 (−1 + √−2)2 𝑖𝑠:
2 6
(vii) 𝐼𝑓 |
| = 0 , 𝑡ℎ𝑒𝑛 𝑥 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜:
3 𝑥
(viii) The vertical line represent in matrix is:
(i)
(ii)
(iii)
(ix)
(x)
(xi)
Date:
Section:
−1
2
25
( ) =
16
The determinant of [𝑎] is:
Formula of finding multiplicative inverse of “A”
When square matrix is said to be singular matrix
if |𝐴| =
Which matrix is an additive identity of
(xiii)
2 − 𝑏𝑦 − 2?
𝐴 𝑛𝑜𝑛 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑖𝑛𝑔, 𝑛𝑜𝑛 𝑟𝑒𝑐𝑢𝑟𝑖𝑛𝑔 𝑑𝑒𝑐𝑖𝑚𝑎𝑙
(xiv)
represents:
The scalar matrix and identity matrix are
(xv)
75
(12)
B
C
D
1
𝑎 = 𝑙𝑜𝑔𝑥 𝑛
10
𝑥 = 𝑙𝑜𝑔𝑛 𝑎
0
𝑎 = 𝑙𝑜𝑔𝑛 𝑥
0.4343
0
𝑒
𝑥 = 𝑙𝑜𝑔𝑎 𝑛
∞
7
10
8
−7
𝑈𝑛𝑖𝑡
𝑍𝑒𝑟𝑜
𝑆𝑐𝑎𝑙𝑎𝑟
𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙
1
−2√2
−1
2√2
6
−9
9
−6
Column
5
4
−𝑎
𝐴𝑑𝑗𝐴
𝐴
Row
4
5
1
|𝐴|
𝐴𝑑𝑗
Diagonal
−5
4
𝑎
𝐴𝑑𝑗𝐴
−
|𝐴|
None
−4
5
Zero
𝐴𝑑𝑗𝐴
|𝐴|
7
1
0
None
0 0
]
0 0
Natural
numbers
Additive
inverse
1 0
]
0 1
Rational
numbers
0 1
]
1 1
Irrational
numbers
0 1
[
]
1 0
Symmetric
Diagonal
(xii)
[
[
[
1
Prime numbers
Rectangular
*Subjective (Part I)*
2. Write Short Answers of any five parts.
(i)
Define abscissa and ordinate.
(ii)
Multiply: [8 5] [ 2
(iii)
(iv)
(v)
(vi)
(vii)
6
4 −4
(5×2=10)
−5
2]
4
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑖𝑑 𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑗𝑜𝑖𝑛𝑖𝑛𝑔 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡𝑠: 𝐴(0,0), 𝐵(0, −5)?
2 4
7 10
1 𝑏
If 2[
] + 3[
]=[
] then find a and b?
−3 𝑎
18 1
8 −4
1 −2
Find multiplicative inverse (if it exists) 𝐴 = [
]
3 4
−1 2 1 1
Multiply the matrices:[
][
]
1 3 2 0
Evaluate:
291.3×42.36
3. Write Short Answers of any five parts.
(i)
Define ordered pair.
(5×2=10)
(ii)
(iii)
𝑈𝑠𝑖𝑛𝑔 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑜𝑟𝑚𝑢𝑙𝑎, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡𝑠: 𝑈(0,2) 𝑎𝑛𝑑 𝑉(−3,0)?
(iv)
Find the multiplicative inverse of the following matrix: 𝐴 = [
(v)
(vi)
Evaluate:
log 512 𝑡𝑜 𝑡ℎ𝑒 𝑏𝑎𝑠𝑒 2√2 .
Simplify:
𝑥 2 ÷ (𝑥 2 )3
(vii)
Use laws of exponents to simplify: [ 𝑥 4 𝑦 −3 𝑧 0 ]
Evaluate:
(−𝑖)5
2 4
]
−2 1
3
𝑥 −2 𝑦 −1 𝑧 −4
−3
(5×2=10)
4. Write Short Answers of any five parts.
(i)
Find Multiplicative inverse of the matrix: [√2 0 ]
0 √2
(ii)
Express the following recurring decimal as the rational number 𝑞 :
(iii)
Simplify:
(iv)
(v)
(vi)
(vii)
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥: 𝑙𝑜𝑔625 5 = 4 𝑥
Define coordinate axes.
𝐼𝑓 𝑙𝑜𝑔2 = 0.3010, 𝑙𝑜𝑔3 = 0.4771, log 5 = 0.6990 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓:
Define isosceles triangle.
𝑝
̅̅̅̅
0.13
3
52 ÷ (52 )3
1
log 30
*Subjective (Part II)*
Attempt any three Questions. Each Question has 10 marks
3𝑥 − 2𝑦
5. (a) Solve the linear equations by Cramer’s rule:
5𝑥 − 2𝑦
3
(10×3=30)
= −6
= −10
0.07921 ×(19.99)2
(b) Use log tables to find the value of: √ (5.79)4 ×0.9474
2
6. (a) 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 ∶
1
(216) ⁄3 ×(25) ⁄2
√
−3⁄
2
(0.04)
5
7
Use log tables to find the value of: √2.709 × √1.239
4 0
−4 −2
7. (a) If 𝐴 = [
] 𝑎𝑛𝑑 𝐵 = [
] 𝑡ℎ𝑒𝑛 𝑣𝑒𝑟𝑖𝑓𝑦 𝑡ℎ𝑎𝑡: (𝐴𝐵)−𝟏 = 𝐵 −1 𝐴−𝟏
−1 2
1 −1
(b)
3 −1
(b) 𝐼𝑓 𝐵 = [
] then Prove: 𝐵𝐵 −1 = 𝐼 = 𝐵 −1 𝐵
2 −2
Theorem: The right bisectors of the sides of triangle are concurrent.
Best of Luck