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Class XII Math Test Paper

This document outlines a mathematics exam for class 12 with 4 sections - A, B, C and D. Section A has 7 questions of 1 mark each about matrices, determinants and properties. Section B has 3 questions of 2 marks each on properties of skew symmetric matrices and using determinants. Section C has 4 questions of 3 marks each on solving systems of equations using matrices and properties of determinants. Section D has 1 question of 5 marks involving matrix multiplication and solving a system of equations.

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Ansh Sehrawat
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87 views2 pages

Class XII Math Test Paper

This document outlines a mathematics exam for class 12 with 4 sections - A, B, C and D. Section A has 7 questions of 1 mark each about matrices, determinants and properties. Section B has 3 questions of 2 marks each on properties of skew symmetric matrices and using determinants. Section C has 4 questions of 3 marks each on solving systems of equations using matrices and properties of determinants. Section D has 1 question of 5 marks involving matrix multiplication and solving a system of equations.

Uploaded by

Ansh Sehrawat
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Vikas Bharati Public School

I Unit Test (session 2021-22)


Time : 1hr Mathematics Class XII M.M:30
General instruction :
This question paper consists of 4 sections .All questions are compulsory.
(i) Section A consist of 7 questions of 1mark each.
(ii) Section B consist of 3 questions of 2 marks each.
(iii) Section C consist of 4 questions of 3 marks each.
(iv) Section D consist of 1 question of 5marks.

SECTION A
𝑝, 𝑖 = 𝑗
Q1 If A = [aij] of order m x m where aij= then matrix A is
0, 𝑖 ≠ 𝑗
(a) Identity matrix (b) diagonal matrix (c) scalar matrix (d) Null matrix
Q2 State following statement is true or false .
If any two rows or columns of a determinant are proportional then the
value of the determinant is zero .
Q3 If A is a square matrix of order 3 x 3 and |3A| = k |A|. Find the value of k.
Q4 If A is a square matrix then (A+A’) is a
(a) Skew symmetric matrix (c) symmetric matrix
(b) Zero matrix (d) none of the these
cos 𝑎 sin 𝑎
Q5 If A = then find ‘a’where 0 < a < π/2 when A+A’=√2 I2
− sin 𝑎 cos 𝑎
43 1 6
Q6 Using properties of determinant find 35 7 4
17 3 2
Q7 Find the number of all possible matrices of order 2x3 with each entry 1,2
or 3.
SECTION B
Q8 Prove that each diagonal element of a skew symmetric matrix is zero.
Q9 Using determinant find the value of k when the three points A(5,1)
B(k,-1) and C(11,4) are collinear .
Q10 Examine the consistency of the given system of equations
x+3y = 5
2x +6y = 8
SECTION C
Q11 On her birthday Salma decided to donate some money to children of an
Orphanage home . If there were 8 children less everyone would have got
Rupees 10 more. However if there were 16 children more everyone
would have got rupees 10 less .Using matrix method find the number
Of children and the amount distributed by Salma.
Q12 using properties of determinant solve for ‘x’
3𝑥 − 8 3 3
3 3𝑥 − 8 3 =0
3 3 3𝑥 − 8
5 3
Q13 Show that A = satisfies the equation A2 -3A – 7I = 0 and
−1 −2
Hence find A-1.
Q14 Using properties of determinants prove
1 𝑥 𝑥+1
2𝑥 𝑥(𝑥 − 1) 𝑥(𝑥 + 1) = 6x2(1- x2)
3𝑥(1 − 𝑥) 𝑥(𝑥 − 1)(𝑥 − 2) 𝑥(𝑥 − 1)(𝑥 + 1)

SECTION D
2 2 −4 1 −1 0
Q15 Given A = −4 2 −4 and B = = 2 3 4 Find BA and using
2 −1 5 0 1 2
This solve the system of equation

y + 2z = 7

x-y = 3

2x + 3y + 4z = 17

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