Mathematics · JEE

Matrices and Determinants Mock Test for JEE

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Q1MathsUnit 3: Matrices and Determinants

STATEMENT 1: In a

\Delta A B C, a, b, c

denotes lengths of the sides and

\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|=\mathbf{0}

then the triangle is equilateral triangle. STATEMENT 2: Sum of three non- negative numbers

=0 \Rightarrow

each number is zero.

Q2MathsUnit 3: Matrices and Determinants

\boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right]

for

\boldsymbol{x} \neq

\mathbf{0}, \boldsymbol{y} \neq \mathbf{0},

then

\boldsymbol{D}

is:

Q3MathsUnit 3: Matrices and Determinants

2 a=b,

the pair of equations

a x+

b y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b

possess

Q4MathsUnit 3: Matrices and Determinants

The addition of two numbers is

-72 .

If one number is thrice the another number. Find the greater number

Q5MathsUnit 3: Matrices and Determinants

Solve the following equations by substitution method.

\boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{7}

Q6MathsUnit 3: Matrices and Determinants

\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]

is an example of

Q7MathsUnit 3: Matrices and Determinants

Dashrath and Naresh are friends ,Naresh is 2 years younger than Dashrath.If the sum of their age is 56 years, find their present age.

Q8MathsUnit 3: Matrices and Determinants

Consider the following statements: 1. Determinant is a square matrix. 2. Determinant is a number associated with a square matrix. Which of the above statements is/are correct?

Q9MathsUnit 3: Matrices and Determinants

Find the area of triangle having vertices

\operatorname{are} \boldsymbol{A}(\mathbf{3}, \mathbf{1}), \boldsymbol{B}(\mathbf{1} \mathbf{2}, \mathbf{2})

and

\boldsymbol{C}(\mathbf{0}, \mathbf{2})

Q10MathsUnit 3: Matrices and Determinants

For any square matrix

\boldsymbol{A}, \boldsymbol{A}+\boldsymbol{A}^{T}

Q11MathsUnit 3: Matrices and Determinants

Assertion

\mathbf{f}[\boldsymbol{x} \mathbf{1}]\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathbf{3}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ -\mathbf{5}\end{array}\right]=\mathbf{0},

then value of

x

is either- 3 or 5 Reason Two matrices

\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right]

\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right]

are equal if

\&

only if their corresponding entries are equal \& only if their corresponding entries are equal

Q12MathsUnit 3: Matrices and Determinants

The ratio of income of two persons is 9: 7 and the ratio of their expenditure is

4: 3 .

If each of them manages to save Rs. 2000 per month, find their monthly income.

Q13MathsUnit 3: Matrices and Determinants

The matrix

\boldsymbol{B}

Q14MathsUnit 3: Matrices and Determinants

A

and

B

are square matrices of order 3 such that

|\boldsymbol{A}|=-\mathbf{1},|\boldsymbol{B}|=\mathbf{3},

then the determinant of

3 A B

is equal to

Q15MathsUnit 3: Matrices and Determinants

\operatorname{tet} f(\theta)=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & 1 & 1 \\ 1 & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & 1 & -1\end{array}\right|

f(\pi)+f(-\pi)

is equal to

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