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#793 Mathematics Continuity and Differentiability

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If x=A cos 4t + B sin 4t, then d²x/dt² is equal to

(A) x

(B) -x

(C) 16x

(D) -16x

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#792 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

The function f(x)=[x], where [x] denotes the greatest integer less than or equal to x, is continuous at

(A) x=1

(B) x=1.5

(C) x=-2

(D) x=4

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#791 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

The derivative of x²ⁿ w.r.t. x is

(A) x²ⁿ⁻¹

(B) 2x²ⁿ log x

(C) 2x²ⁿ(1+log x)

(D) 2x²ⁿ(1-log x)

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#790 Mathematics Inverse Trigonometric Functions

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

sin[ π/3 + sin⁻¹(1/2) ] is equal to

(A) 1

(B) 1/2

(C) 1/3

(D) 1/4

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#789 Mathematics Relations and Functions

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

Let A={3,5}. Then number of reflexive relations on A is

(A) 2

(B) 4

(C) 0

(D) 8

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#788 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If
\[
A =
\begin{bmatrix}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix},
\]
then $A^{-1}$ is

(A) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}

(B) \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}

(C) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

(D) \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

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#787 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

A is a square matrix of order 2 such that det(A)=4 , then det(4adjA) is

(A) 16

(B) 64

(C) 256

(D) 512

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#770 Mathematics Matrices and Determinants

MCQ_SINGLE REMEMBER 2025

KNOWLEDGE 1 Marks

The matrix $A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}$ is a/an:

(A) scalar matrix

(B) identity matrix

(C) null matrix

(D) symmetric matrix

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#767 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},$ then the value of $(x-y)$ is :

(A) 2 or 10

(B) 2 or 10

(C) 2 or - 10

(D) -2 or - 10

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#766 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

Let
\[
A = \begin{pmatrix}
1 & -2 & -1 \\
0 & 4 & -1 \\
-3 & 2 & 1
\end{pmatrix}, \quad
B = \begin{pmatrix}
-2 \\
-5 \\
-7
\end{pmatrix}, \quad
C = \begin{pmatrix}
9 & 8 & 7
\end{pmatrix},
\]
which of the following is defined?

(A) Only AB

(B) Only AC

(C) Only BA

(D) All AB, AC and BA

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Key: A
Sol:

The problem is to determine which matrix multiplication is defined. A product of two matrices $P \times Q$ is defined if and only if the number of columns of $P$ equals the number of rows of $Q$.

The order of Matrix A is 3×3

The order of Matrix B is 3×1 and

The order of Matrix C is 1×3

Checking Products

AB: $A_{3 \times 3} \times B_{3 \times 1}$ $\to 3 = 3$ . Defined.
AC: $A_{3 \times 3} \times C_{1 \times 3}$ $\to 3 \neq 1$ . Not Defined.
BA: $B_{3 \times 1} \times A_{3 \times 3}$ $\to 1 \neq 3$ . Not Defined.

Hence The correct option is Only AB.

#765 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If
\[
A = \begin{pmatrix}
7 & 0 & x \\
0 & 7 & 0 \\
0 & 0 & y
\end{pmatrix}
\]
is a scalar matrix, then $y^x$ is equal to

(A) $0$

(B) $1$

(C) $7$

(D) $\pm 7$

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#764 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $A$ and $B$ are invertible matrices, then which of the following is \underline{not correct}?

(A) $(A + B)^{-1} = B^{-1} + A^{-1}$

(B) $(AB)^{-1} = B^{-1} A^{-1}$

(C) $\text{adj}(A) = |A| A^{-1}$

(D) $|A^{-1}| = |A|^{-1}$

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#763 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $A=\begin{bmatrix}1&12&4y\\ 6x&5&2x\\ 8x&4&6\end{bmatrix}$ is a symmetric matrix, then $(2x+y)$ is

(A) $-8$

(B) 0

(C) 6

(D) 8

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#762 Mathematics Matrices and Determinants

MCQ_SINGLE UNDERSTAND 2025

KNOWLEDGE 1 Marks

Which of the following can be both a symmetric and skew-symmetric matrix ?

(A) Unit Matrix

(B) Diagonal Matrix

(C) Null Matrix

(D) Row Matrix

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#760 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If A and B are square matrices of order m such that $A^{2}-B^{2}=(A-B)(A+B),$ then which of the following is always correct?

(A) $A=B$

(B) $AB=BA$

(C) $A=0$ or $B=0$

(D) $A=I$ or $B=I$

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#759 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If M and N are square matrices of order 3 such that det $(M)=m$ and $MN=mI,$ then det (N) is equal to:

(A) -1

(B) 1

(C) $-m^{2}$

(D) $m^{2}$

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#758 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $A=\begin{bmatrix}1&2&3\\ -4&3&7\end{bmatrix}$ and $B=\begin{bmatrix}4&3\\ -1&2\\ 0&5\end{bmatrix},$ then the correct statement is:

(A) Only AB is defined.

(B) Only BA is defined.

(C) AB and BA, both are defined.

(D) AB and BA, both are not defined.

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#757 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $\begin{vmatrix}2x&5\\ 12&x\end{vmatrix}=\begin{vmatrix}6&-5\\ 4&3\end{vmatrix}$ then the value of x is:

(A) 3

(B) 7

(C) $\pm7$

(D) $\pm3$

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#756 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $A=[a_{ij}]$ is a $3\times3$ diagonal matrix such that $a_{11}=1$, $a_{22}=5$ and $a_{33}=-2$, then $|A|$ is:

(A) 0

(B) -10

(C) 10

(D) 1

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#755 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}$ is a singular matrix, then the value of x is:

(A) 0

(B) 1

(C) -2

(D) 4

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