11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
Published on: 11/11/2020
11th Standard Maths Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021
Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is _____________
3
1
2
\(\frac{1}{2}\)
2.
On using elementary row operation R1⟶R1-3R2 in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)________.
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
3.
If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is _________ .
5
6
4
3
4.
Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?
A + B is a symmetric matrix
AB is a symmetric matrix
AB = (BA)T
AT B = ABT
5.
If \(\left\lfloor . \right\rfloor \) denotes the greatest integer less than or equal to the real number under consideration and −1\(\le\) x < 0, 0 \(\le\) y < 1, 1 \(\le\) z < 2, then the value of the determinant \(\begin{vmatrix} \left\lfloor x \right\rfloor +1& \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor +1& \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor +1\end{vmatrix}\) is
\(\left\lfloor z \right\rfloor \)
\(\left\lfloor y \right\rfloor \)
\(\left\lfloor x \right\rfloor \)
\(\left\lfloor x \right\rfloor \)+1
6.
If a \(\neq\) b, b, c satisfy \(\begin{vmatrix} a&2b &2c \\3 & b & c \\ 4 & a & b \end{vmatrix}=0,\) then abc =
a + b + c
0
b3
ab + bc
7.
If \(\triangle\) = \(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\), then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\) is
\(\triangle\)
k\(\triangle\)
3k\(\triangle\)
k3\(\triangle\)
8.
The value of x, for which the matrix A = \(\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}\) is singular
9
8
7
6
9.
If A = \(\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}\), then for what value of \(\lambda\), A2 = O?
0
\(\pm 1\)
-1
1
10.
If aij = \({1\over2}(3i-2j)\) and A = [aij]2x2 is
\(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)
\(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)
\(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)
\(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)
1.
(d)
\(\frac{1}{2}\)
2.
(a)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
3.
(d)
3
4.
\(A \& B \text { are symmetric }\)
\(A^{T}=A \text {, and } B^{T}=B\)
\(\text { 1) }(A+B)^{T}=B^{T}+A^{T}=B+A=A+B \Rightarrow A+B\text { is symmetric }\)
\(\text { 2) }(A B)^{T}=B^{T} A^{T}=B A \neq A B\)
\(\therefore A B \text { is not symmetric }\)
\(\text { 3) } A B=A^{T} B^{T}=(B A)^{T}\)
\(\text { 4) } A^{T} B=A B=A B^{T}\)
5.
\(-1 \leq x<0 \Rightarrow\lfloor x\rfloor=-1 ;\)
\(0 \leq y<1 \Rightarrow\lfloor y\rfloor=0 ; 1 \leq z<2 \Rightarrow\lfloor z\rfloor=1 \)
\(\therefore|\cdot A|=\left|\begin{array}{ccc} -1+1 & 0 & 1 \\ -1 & 0+1 & 1 \\ -1 & 0 & 1+1 \end{array}\right|=\left|\begin{array}{ccc} 0 & 0 & 1 \\ -1 & 1 & 1 \\ -1 & 0 & 2 \end{array}\right|=1(0+1)=1 \)
\(|A|=1=\lfloor z\rfloor \)
6.
\(\left|\begin{array}{ccc} a & 2 b & 2 c \\ 3 & b & c \\ 4 & a & b \end{array}\right| =0 \)
\(\Rightarrow \frac{1}{2}\left|\begin{array}{lll} a & 2 b & 2 c \\ 6 & 2 b & 2 c \\ 4 & a & b \end{array}\right| =0 \quad R_{2} \rightarrow 2 R_{2} \)
\(\frac{1}{2}\left|\begin{array}{ccc} a-6 & 0 & 0 \\ 6 & 2 b & 2 c \\ 4 & a & b \end{array}\right| =0 \quad R_{1} \rightarrow R_{1}-R_{2} \)
\(\Rightarrow \frac{1}{2}\left[(a-6)\left(2 b^{2}-2 a c\right)\right] =0 \)
\((a-6)\left(2 b^{2}-2 a c\right) =0 \)
\(a=6,2 b^{2} =2 a c \)
\(b^{2} =a c \quad \therefore b^{3}=a b c \)
7.
\(\left|\begin{array}{lll} k a & k b & k c \\ k x & k y & k z \\ k p & k q & k r \end{array}\right|=k^{3}\left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=k^{3} \Delta\)
\(\text { Take } k \text { from } R_{1}, R_{2}, R_{3}\)
8.
\(|A|=0 \quad \text { [since } A \text { is singular] }\)
\(\left|\begin{array}{ll} e^{x-2} & e^{7+x} \\ e^{2+x} & e^{2 x+3} \end{array}\right| =0 \)
\(e^{x-2+2 x+3}-e^{2+x+7+x} =0 \)
\(e^{3 x+1} =e^{9+2 x} \)
\(3 x+1 =9+2 x \)
\(x =8 \)
9.
\(A^{2}=A \times A=\left[\begin{array}{cc} \lambda & 1 \\ -1 & -\lambda \end{array}\right]\left[\begin{array}{cc} \lambda & 1 \\ -1 & -\lambda \end{array}\right]\)
\(=\left[\begin{array}{cc} \lambda^{2}-1 & \lambda-\lambda \\ -\lambda+\lambda & -1+\lambda^{2} \end{array}\right]=0\)
\(\therefore \lambda^{2} =1 \)
\(\lambda =\pm 1\)
10.
\(A=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \)
\(a_{11}=\frac{1}{2}(3-2)=\frac{1}{2} ; a_{12}=\frac{1}{2}(3-4)=\frac{-1}{2} \)
\(a_{21}=\frac{1}{2}(3(2)-2)=\frac{4}{2}=2 ; a_{22}=\frac{1}{2}(6-4)=\frac{2}{2}=1 \)
\(\therefore A=\left[\begin{array}{ll} \frac{1}{2} & -\frac{1}{2} \\ 2 & 1 \end{array}\right] \)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - துணைப்பாடம் - யானை டாக்டர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
French
Tamilnadu Stateboard Standards
