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Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants

Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants are part of Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 4 Determinants.

Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants

Plus Two Maths Determinants 3 Marks Important Questions

Question 1.
Prove that 1!2!3!2!3!4!3!4!5! (March – 2015)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 1

Question 2.
Using properties of determinants prove the following. (March – 2010; Christmas -2017)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 2
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 3
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 4

Plus Two Maths Determinants 4 Marks Important Questions

Question 1.
Consider the matrix A=[2532]

(i) Find adj (A)
(ii) Find A1
(iii) Using A-1 solve the system of linear equations 2x + 5y = 13x + 2y = 7 (March – 2010)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 5

Plus Two Maths Determinants 6 Marks Important Questions

Question 1.
Consider the matrix A=[abcbcacab]

(i) Using the column operat,on
C1 → C1 + C2 + C3,
show that |A|=(a+b+c)|1bc1ca1ab|
(ii) Show that |A| = – (a3 + b3 + e3 — 3abc)
(iii) Find A x adj(A) if a = 1,b = 10,c = 100 (May – 2010)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 6
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 7

Question 2.
(i) (a) If A=[115013012]

What is the value of |3A|?
(b) Find the equation of the line joining the points (1,2) and (-3,-2) using determinants.
(ii) Show that |1aa21bb21cc2|=(ab)(bc)(ca)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 8

(b) Let (x,y) be the coordinate of any point on The line, then (1,2), (-3, -2) and (x, y) are collinear.

Hence the area formed will be zero.
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 9

Question 3.
Consider the following system of linear equations; x + y + z = 6, x – y + z = 2, 2x + y + z = 1
(i) Express this system of equations in the Standard form AXB
(ii) Prove that A is non-singular.
(iii) Find the value of x, y and z satisfying the above equation. (May – 2011)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 10

Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 31

Question 4.
(i) lf |x352|=5, then x = ………..
(ii) Prove that
|y+kyyyy+kyyyy+k|=k2(3y+k)
(iii) Solve the following system of linear Equations, using matrix method; 5x + 2y = 3, 3x + 2y = 5 (March – 2012)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 32
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 11

Question 5.
(i) Let B is a square matrix of order 5, then |kB| is equal to ………..
(a) |B|
(b) k|B|
(c) k5|B|
(d) 5|B|

(ii) Prove that |1xx21yy21zz2|=(xy)(yz)(zx)
(iii) Check the consistency of the following equations; 2x + 3y + z = 6, x + 2y – z = 2, 7x + y + 2z =10 (May – 2012)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 12
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 13

Therefore the system is consistent and has unique solutions.

Question 6.
(i) Find the values of x in which |3xx1|=|3241|

(ii) Using the property of determinants, show that the points A(a,b + c), B(b,c + a), C(c,a + b) are collinear.
(iii) Examine the consistency of system of following equations: 5x – 6y + 4z = 15, 7x + y – 3z = 19, 2x + y + 6z = 46 (EDUMATE – 2017; March – 2013)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 14
Since, the system is consistent and has unique solutions.

Question 7.
Consider a system of linear equations which is given below;
2x+3y+10z=4;4x6y+5z=16x+9y20z=2

(i) Express the above equation in the matrix form AX = B.
(ii) Find A-1, the inverse of A.
(iii) Find x,y and z. (May – 2013)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 15

Question 8.
Consider the matrices A=[2345]

(i) Find A2 – 7A – 21 = 0
(ii) Hence find A-1
(iii) Solve the following system of equations using matrix method 2x + 3y = 4; 4x + 5y = 6 (March – 2014)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 16
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 17

(iii) The given system of equations can be converted into matrix form AX = B
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 18

Question 9.
(i) Let A be a square matrix of order 2 x 2 then |KA| is equal to
(a) K|A|
(b) K2|A|
(c) K3|A|
(d) 2K|A|

(ii) Prove that
|abc2a2a2 b bca2 b2c2ccab|=(a+b+c)3

(iii) Examine the consistency of the system of Equations. 5x + 3y = 5; 2x + 6y = 8 (May- 2014)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 19
(iii) The given system of equation can be written in matrix form as
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 20
solution exist and hence it is consistent.

Question 10.
(a) Choose the correct statement related to the matnces A=[1001],B=[0110]
 (i) A3=A,B3B (ii) A3A,B3=B (iii) A3=A,B3=B (iv) A3A,B3B

(b) lf M=[7523] then verity the equation M2 – 10M + 11 I2 = O

(c) Inverse of the matrix [012011102] (March – 2015)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 21
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 22

Question 11.
Solve the system of Linear equations x + 2y + z = 8; 2x + y – z = 1; x – y + z = 2 (March – 2015)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 23

Question 12.
(a) If |x11x|=15 then find the value of X.

(b)Solve the following system of equations 3x – 2y + 3z = ?, 2x + y – z = 1 4x – 3y + 2z = 4 (May – 2015)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 24
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 25

Question 13.
(i)The value of the determinant |111111111| is
(a) -4
(b) 0
(c) 1
(d) 4

(ii) Using matrix method, solve the system of linear equations x + y + 2z = 4; 2x – y + 3z = 9; 3x – y – z = 2 (May – 2016)
Answer:
(i) (d) 4
(ii) Express the given equation in the matrix form as AX = B
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 26

Question 14.
(i) If A=[a110] is such that A2 = I then a equals
(a) 1
(b) -1
(c) 0
(d) 2

(ii)Solve the system of equations x – y + z = 4; 2x + y – 3z = 0; x + y + z = 2 Using matrix method. (March – 2017)
Answer:
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 27
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 28

Question 15.
(i) IfA is a 2 x 2 matrix with |A| = 5, then |adjA| is
(a) 5
(b) 25
(c) 1/5
(d) 1/25

(ii) Solve the system of equations using matrix method.
x + y + z = 1; 2x + 3y – z = 6; x – y + z = -1 (May – 2017)
Answer:
(i) (a) 5
(ii) LetA X=B,
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 29
Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants 30

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