Assertion (A) & Reason (B) MCQ - Maths STD 12 Science Questions - Vidyadip

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Assertion (A) & Reason (B) MCQ

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17 questions · timed · auto-graded

Question 11 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: For a matrix $\begin{bmatrix}2&-1\\-3&4\end{bmatrix},$ A. adj $\text{A}=\begin{bmatrix}4&0\\0&4\end{bmatrix}.$
Reason: For a square matrix A, $\text{A}(\text{adj}\text{A})=(\text{adj}\text{A})\text{A}=\mid\text{A}\mid.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 21 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If $\text{A}=\begin{bmatrix}1&0&1\\0&1&2\\0&0&4\end{bmatrix}$ then $\mid3\text{A}\mid=9\mid\text{A}\mid.$
Reason: If A is a square matrix of order n then $\mid\text{k}\text{A}\mid=\text{k}^{\text{n}}\mid\text{A}\mid.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 31 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The value of x for which $\begin{vmatrix}\text{x}&2\\18&\text{x}\end{vmatrix}=\begin{vmatrix}6&2\\18&6\end{vmatrix}$ is $\pm\ 6.$
Reason: The determinant of a matrix A order 2x2, $\text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is = ab - dc.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is true but R is false.

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Question 41 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: For two matrices A and B of order 3, $\mid\text{A}\mid=2\mid\text{B}\mid=-3$ then if $\mid2\text{AB}\mid$ is -48.
Reason: For a square matrix A, $\text{A}(\text{adj}\ \text{A})=(\text{adj}\ \text{A})\text{A}=\mid\text{A}\mid.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are true but R is not the correct explanation of A.

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Question 51 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The value of x for which $\begin{vmatrix}3&\text{x}\\\text{x}&1\end{vmatrix}=\begin{vmatrix}3&2\\4&1\end{vmatrix}$ is $\pm2\sqrt{2}.$
Reason: The determinant of a matrix A order 2x2, $\text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is = ad - bc.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are true and R is the correct explanation of A.

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Question 61 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Inverse of the matrix $\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}$ is the matrix $\begin{bmatrix}-2&0&1\\9&2&-3\\6&1&-2\end{bmatrix}.$
Reason: Inverse of a square matrix A, if it exits is given by $\text{A}^{-1}=\frac{1}{\text{IAI}}$ adj A.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are true and R is the correct explanation of A.

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Question 71 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The points A(a, b + c), B(b, c +a ) and C(c, a + b) are collinear.
Reason: Three points A (x₁, y₁) , B(x₂, y₂) and C(x3, y3) are collinear if area of a triangle ABC is zero.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are true and R is the correct explanation of A.

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Question 81 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Value of x for which the matrix $\begin{bmatrix}1&2&0\\0&1&2\\-1&2&\text{x}\end{bmatrix}$ is singular is 5.
Reason: A square matrix is singular if $\mid\text{A}\mid=0.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 91 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Values of k for which area of the triangle with vertices (2, -6), (5, 4) and (k, 4) is 35 sq units are 12, 2.
Reason: Area of a triangle with vertices A (x₁, y₁), B(x₂, y₂) and C(x3, y3) is $\frac{1}{2}\begin{vmatrix}\text{x}1&\text{y}1&1\\\text{x}2&\text{y}2&1\\\text{x}3&\text{y}3&1\end{vmatrix}.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 101 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The equation of the line joining (1, 2) and (3, 6) using determinants is y = 3x.
Reason: The area of $\triangle\text{PAB}$ is zero if P(x, y) is a point on the line joining a A and B.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 111 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The minor of the element 3 in the matrix $\begin{bmatrix}2&3&1\\0&-2&4\\2&1&5\end{bmatrix}$ is 8.
Reason: Minor of an element aij of a matrix is the determinant obtained by deleting its j^th row and i^th column.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are false.

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Question 121 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Value of x for which the matrix $\begin{bmatrix}1&2&0\\0&1&2\\-1&2&\text{x}\end{bmatrix}$ is singular is 5.
Reason: A square matrix is singular if $\mid\text{A}\mid=0.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 131 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: In a square matrix of order 3 the minor of an element a₂₂ is 6 then cofactor of a₂₂ is -6.
Reason: Cofactor an element aij = A_IJ = (-1)^i+j M_ij.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Question 141 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If A is an invertible matrix of order 2, and det A = 3 then det( A ^-1) is equal to $\frac{1}{3}.$
Reason: If A is an invertible matrix of order 2 then det (A ^-1) = det A.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is true but R is false.

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Question 151 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Inverse of a matrix $\text{A}=\begin{bmatrix}2&3\\1&2\end{bmatrix}$is the matrix $\text{A}^{-1}=\begin{bmatrix}2&-3\\-1&2\end{bmatrix}.$
Reason: Inverse of a square matrix $\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ is $\begin{pmatrix}\text{d}&-\text{b}\\-\text{c}&\text{a}\end{pmatrix}.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is true but R is false.

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Question 161 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Let $\text{A}^{-1}=\begin{bmatrix}5&-7\\-2&3\end{bmatrix}$ and $\text{B}^{-1}=\begin{bmatrix}7&6\\8&7\end{bmatrix}$ then $(\text{AB})^{-1}=\begin{bmatrix}23&31\\26&35\end{bmatrix}.$
Reason: $(\text{AB})^{-1}=\text{A}^{-1}\text{B}^{-1}.$

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

Both A and R are false.

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Question 171 Mark

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If A is a non singular square matrix of order 3x3 and $\mid\text{A}\mid=5$ then $\mid\text{adj}\text{A}\mid$ is equal to 125.
Reason: $\mid\text{adj}\text{A}\mid=(\mid\text{A}\mid)^{\text{n}-1}$ where n is order of A.

Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Answer

A is false but R is true.

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Assertion (A) & Reason (B) MCQ - Maths STD 12 Science Questions - Vidyadip