Available Questions 783 found Page 8 of 40
Standalone Questions
#1689
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If A and B are skew-symmetric matrices of same order, then $AB^{\prime}+BA^{\prime}$ is a/an:
(A) symmetric matrix
(B) skew-symmetric matrix
(C) null matrix
(D) identity matrix
Key:
Sol:
Sol:
#1688
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If the area of $\Delta$ ABC with vertices $A(3,1)$, $B(-2,1)$ and $C(0,k)$ is 5 sq. units, then values of k are:
(A) 3, 1
(B) -1, 3
(C) -1, 2
(D) 0, 2
Key:
Sol:
Sol:
#1687
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If A is a square matrix such that $A^{2}=A$ then $(A-I)^{3}-A$ is equal to :
(A) I
(B) $-I$
(C) A
(D) $A^{2}$
Key:
Sol:
Sol:
#1686
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If A is a non-singular matrix, then which of the following is not true?
(A) adj A is singular
(B) $(adj~A)^{-1}=adj(A^{-1})$
(C) $|A|\ne 0$
(D) $A^{-1}$ exists
Key:
Sol:
Sol:
#1685
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$, then order of A must be:
(A) $3\times1$
(B) $1\times3$
(C) $1\times1$
(D) $3\times3$
Key:
Sol:
Sol:
#1684
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If matrix $A=\begin{bmatrix}-p&q\\r&p\end{bmatrix}$ is such that $A^{2}=I$ then :
(A) $1+p^{2}+qr=0$
(B) $1-p^{2}-qr=0$
(C) $1-p^{2}+qr=0$
(D) $1+p^{2}-qr=0$
Key:
Sol:
Sol:
#1683
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
For a square matrix A, $(3A)^{-1}=$
(A) $3A^{-1}$
(B) $9A^{-1}$
(C) $\frac{1}{3}A^{-1}$
(D) $\frac{1}{9}A^{-1}$
Key:
Sol:
Sol:
#1682
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}$ and $A+A^{\prime}=I$, then the value of $x \in [0,\frac{\pi}{2}]$ is
(A) $0$
(B) $\frac{\pi}{3}$
(C) $\frac{\pi}{4}$
(D) $\frac{\pi}{2}$
Key:
Sol:
Sol:
#1681
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let $A=\begin{bmatrix}0&-3&4\\1&0&2\end{bmatrix}$ and $B=\begin{bmatrix}-3&0&1\\2&4&0\end{bmatrix}$. If $A + B + C = O$, then matrix C is:
(A) $\begin{bmatrix}-3&-3&5\\3&4&2\end{bmatrix}$
(B) $\begin{bmatrix}3&3&-5\\-3&-4&-2\end{bmatrix}$
(C) $\begin{bmatrix}3&3&5\\-3&-4&-2\end{bmatrix}$
(D) $\begin{bmatrix}-3&-3&-5\\3&4&2\end{bmatrix}$
Key:
Sol:
Sol:
#1680
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $A=[a_{ij}]$ is a $2\times 2$ matrix whose elements are given by $a_{ij}=\frac{|i-3j|}{2}$, then $A^{\prime}$ is:
(A) $\begin{bmatrix}1&\frac{5}{2}\\\frac{1}{2}&2\end{bmatrix}$
(B) $\begin{bmatrix}1&\frac{1}{2}\\\frac{5}{2}&2\end{bmatrix}$
(C) $\begin{bmatrix}2&\frac{5}{2}\\\frac{1}{2}&1\end{bmatrix}$
(D) $\begin{bmatrix}2&\frac{1}{2}\\\frac{5}{2}&1\end{bmatrix}$
Key:
Sol:
Sol:
#1679
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $adj(B)=\begin{bmatrix}\frac{1}{3}&0&0\\0&\frac{1}{3}&0\\0&0&\frac{1}{3}\end{bmatrix}$, then the value of det $(B^{-1})=$
(A) $\frac{1}{3}$
(B) $\frac{1}{9}$
(C) 3
(D) 9
Key:
Sol:
Sol:
#1678
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $\begin{vmatrix}-1&-2&5\\-2&a&-1\\0&4&2a\end{vmatrix}=-86$, then the sum of all possible values of a is
(A) 4
(B) 5
(C) -4
(D) 9
Key:
Sol:
Sol:
#1677
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $A^{2}=4A+3I$ and $A^{-1}=xA+yI$, then the value of $(x+y)$ is :
(A) -1
(B) 1
(C) $\frac{5}{3}$
(D) 7
Key:
Sol:
Sol:
#1676
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $A=\begin{bmatrix}1&a&b\\-1&2&c\\0&5&3\end{bmatrix}$ is a symmetric matrix, then the value of $3a+b+c$ is
(A) 2
(B) 6
(C) 4
Key:
Sol:
Sol:
#1675
Mathematics
Matrices and Determinants
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If a square matrix A is such that $A^{2}=A$ and $(I-A)^{3}=xA+I$ then value of x must be:
(A) 7
(B) 5
(C) -7
(D) -1
Key:
Sol:
Sol:
#1674
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
The domain of $f(x)=\cos^{-1}(2x-5)$ is:
(A) [-1,1]
(B) [4, 6]
(C) $[-7,-3]$
(D) [2, 3]
Key:
Sol:
Sol:
#1673
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The following graph represents:
(A) $y=\cos^{-1}x$
(B) $y=\sec^{-1}x$
(C) $y=\tan^{-1}x$
(D) $y=\text{cosec}^{-1}x$
Key:
Sol:
Sol:
#1672
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined?
(A) $\tan^{-1}:R\rightarrow(-\frac{\pi}{2},\frac{\pi}{2})$
(B) $\sec^{-1}:R-(-1,1)\rightarrow[0,\pi]-\{\frac{\pi}{2}\}$
(C) $\cot^{-1}:R\rightarrow(0,\pi)$
(D) $\text{cosec}^{-1}:R-(-1,1)\rightarrow[-\frac{\pi}{2},\frac{\pi}{2}]$
Key:
Sol:
Sol:
#1671
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The principal value of $\sec^{-1}(\sqrt{2})+2\text{cosec}^{-1}(-\sqrt{2})$ is:
(A) $-\frac{\pi}{2}$
(B) $-\frac{\pi}{4}$
(C) $\frac{\pi}{4}$
(D) $\frac{\pi}{2}$
Key:
Sol:
Sol:
#1670
Mathematics
Relations and Functions
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A relation R on set $A=\{1,2,3\}$ defined as $R=\{(1,1), (2,2), (1,2)\}$ is
(A) Reflexive only
(B) Reflexive and Transitive
(C) Symmetric and Transitive
(D) Transitive only
Key:
Sol:
Sol: