Math 8th 1st Term 1j2d5q

Roots Millennium School Khyber Campus Peshawar 1st Term Exam Dec. 2016 Class: 8th Time: 3 hrs

Paper: Maths Total Mark:75

Name:_______________________ Class__________

Section._____________

Section - A Marks:15

Time Allowed: 20 minutes Q.1. Write the correct option i.e. A,B,C or D in the boxes given in the front of each question. i.

If a matrix A is such that 𝐴 = −𝐴𝑡 then A is ___________ matrix. A. Skew Symmetric

B. Diagonal

C. Symmetric

2 3 ii. If 𝐴 = [ ] then AdjA equals to _____ 3 4 4 −3 −2 3 4 A. [ ] B. [ ] C. [ 3 2 3 −4 −3

−3 ] 2

1 3 ] then 𝐴−1 equals to _____ 2 −2 1 −2 −3 1 −1 −2 −3 [ ] B. − [ ] C. − [ 8 8 2 −2 1 −2 1

D. None of these

D. None of These

iii. If 𝐴 = [ A.

1 8

3 ] 2

D. None of These

1 0 iv. If 𝐴 = [ ] then A is called _____ matrix? 0 1 A. Singular B. Scalar C. Diagonal

x  2  3 then solution set is_______.

v. If A. vi

D. Identity

{-1,-5}

B.

{-1,5}

C

{1,5}

D. {1,-5}

x  2  6 then solution set is _________.

If A.

{38}

B. {34}

C. { }

D. {-4}

vii. (ab)-1/n =_______ A. (ab)n

B. 1/(ab)n

C. 1/(ab)1/n

D. (ab)-n

C.

D. -4ab

viii. (a+b)2+(a-b)2=___________ A. 2ab

B. -2ab

4ab

ix. If A  2 3 then order of A is________.   1 4 

A. 1 by 2 x.

B. 2 by 2

C. 2 by 1

D. 1 by 1

C.

D. -45

If a=2 then 5a-10=_______ A. 0

B. -5

5

xi. A+B=B+A is called _________law. A.

Distributive

B.

Commutative

C. Associative

xii. If A  7 8 then determinant of A is __________.    3 2

A. 10

B. 38

C. -10

D. 24

D. Transitive

xiii.

If A   3 1 then At =________.   9 2   A.

B.  3  9 1 2  

 3 1   1 2  

C.  3 1   9 2  

D.  2 1   9 3  

2 xiv. 12a b  ______ 4ab

A. 3a

B. 3ab

C.

ab

D.

-3ab

xv. If in a matrix number of rows and number of columns are equal then it is called __________ matrix. A. 𝑠𝑞𝑢𝑎𝑟𝑒

B. 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟

C. 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦

D. 𝑑𝑖𝑎𝑔𝑜𝑛al

Section – B

Marks: 36

Note: Time allowed for section B and C is 2hrs and 45 minutes. Q.2.

Attempt any 9 question of the following, each question carry 04 marks.   4  6 1 7 and B A    8 2  3 4

(i). Find the product of

x6 5

(ii). Solve

1   13  2  C 3  3   5 

(iii). Find the determinant of

x3 4 x 4

3

(iv). Simplify

4 𝐶=[ −1

(v). Find the multiplicative inverse of (vi). If 𝐶 = [

a 𝑐

(vii). If 𝐴 = [

−3 ]. 2

𝑏 ] show that (𝐶 𝑡 )𝑡 = 𝐶. 𝑑

−1 ] 1

𝐵 = [2

−2] 𝑎𝑛𝑑 𝐶 = [

3 −1

1 ] then prove that 2

(AB)C=A(BC).

x  12 6

(viii). Find the solution set of 1

(ix). Simplify  36  2  49 

x 1

(x). Show on number line (xi). Let 𝐴 = [3 (xii). If 𝐴 = [

7 2

2

1],

1 1 ], 𝐵 = [ 4 2

𝐵[−3

4

2], prove that (𝐴 + 𝐵)𝑡 = 𝐴𝑡 + 𝐵𝑡

1 ] Show that commutative law holds. 2

Section – “C” Note: Attempt any 3 questions of the following, each question carry 08 marks. Q.3. Solve the following using Cramer’s rule; 𝑥 − 2𝑦 = 5 , 2𝑥 − 𝑦 = 6 Q.4. Solve the following using Inversion method 𝑥 − 2𝑦 − 1 = 0 , 2𝑥 + 𝑦 + 3 = 0 2 Q.5. If 𝐴 = [ −3

0 1 ] and𝐵 = [ 1 −1

Q.6. Solve the radical equation.

−1 ] 𝑡ℎ𝑒𝑛 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 (𝐴𝐵)−1 = 𝐵 −1 𝐴−1 . 3

2(5x  1)  2x  14

Marks: 24