Available Questions 601 found Page 23 of 31
Standalone Questions
#740
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(A=[a_{ij}]\) be a \(3\times3\) matrix, where \(a_{ij}=i-3j\), then which of the following is false ?
(A) \(a_{11}\lt0\)
(B) \(a_{12}+a_{21}=-6\)
(C) \(a_{13}\gt a_{31}\)
(D) \(a_{31}=0\)
Key:
Sol:
Sol:
#739
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(F(x)=\begin{bmatrix}\cos~x&-\sin~x&0\\ \sin~x&\cos~x&0\\ 0&0&1\end{bmatrix}\) and \([F(x)]^{2}=F(kx)\), then the value of k is :
(A) 1
(B) 2
(C) 0
(D) -2
Key: B
Sol:
Sol:
#738
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2024
KNOWLEDGE
1 Marks
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
(A) \(a_{ij}=\begin{cases}0,&if~i=j\\ 1,&if~i\ne j\end{cases}\)
(B) \(a_{ij}=1,\forall i,j\)
(C) \(a_{ij}=0,\forall i,j\)
(D) \(a_{ij}=\begin{cases}0,&if~i\ne j\\ 1,&if~i=j\end{cases}\)
Key:
Sol:
Sol:
#737
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
Let \(A=\begin{bmatrix}a&b\\ c&d\end{bmatrix}\) be a square matrix such that adj \(A=A\) Then, \((a+b+c+d)\) is equal to :
(A) 2a
(B) 2b
(C) 2c
(D) 0
Key:
Sol:
Sol:
#736
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If A and B are two skew symmetric matrices, then \((AB+BA)\) is :
(A) a skew symmetric matrix
(B) a symmetric matrix
(C) a null matrix
(D) an identity matrix
Key:
Sol:
Sol:
#735
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then \(A^{-1}\) is:
(A) \([\begin{matrix}\frac{1}{2}&0&0\\ 0&3&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(B) \(30[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(C) \(\frac{1}{30}[\begin{matrix}2&0&0\\ 0&3&0\\ 0&0&5\end{matrix}]\)
(D) \(\frac{1}{30}[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
Key:
Sol:
Sol:
#734
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
\(If\begin{bmatrix}a&c&0\\ b&d&0\\ 0&0&5\end{bmatrix}\) is a scalar matrix, then the value of \(a+2b+3c+4d\) is:
(A) 0
(B) 5
(C) 10
(D) 25
Key:
Sol:
Sol:
#733
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2024
KNOWLEDGE
1 Marks
Given that \(A^{-1}=\frac{1}{7}\begin{bmatrix}2&1\\ -3&2\end{bmatrix}\) matrix A is
(A) \(7[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(B) \([\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(C) \(\frac{1}{7}[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(D) \(\frac{1}{49}[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
Key:
Sol:
Sol:
#732
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
Competency
1 Marks
\(If~A=[\begin{matrix}2&1\\ -4&-2\end{matrix}].\) then the value of \(I-A+A^{2}-A^{3}+...is\):
(A) \([\begin{matrix}-1&-1\\ 4&3\end{matrix}]\)
(B) \([\begin{matrix}3&1\\ -4&-1\end{matrix}]\)
(C) \([\begin{matrix}0&0\\ 0&0\end{matrix}]\)
(D) \([\begin{matrix}1&0\\ 0&1\end{matrix}]\)
Key:
Sol:
Sol:
#731
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
\(If~A=\begin{bmatrix}-2&0&0\\ 1&2&3\\ 5&1&-1\end{bmatrix},\) then the value of | A (adj. A) | is:
(A) 100 I
(B) 10 I
(C) 10
(D) 1000
Key:
Sol:
Sol:
#730
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
Given that \([\begin{matrix}1&x\end{matrix}]\begin{bmatrix}4&0\\ -2&0\end{bmatrix}=0,\) the value of x is:
(A) -4
(B) -2
(C) 2
(D) 4
Key:
Sol:
Sol:
#729
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If A is a square matrix of order 3 such that the value of \(|adj\cdot A|=8,\) then the value of \(|A^{T}|\) is:
(A) \(\sqrt{2}\)
(B) \(-\sqrt{2}\)
(C) 8
(D) \(2\sqrt{2}\)
Key:
Sol:
Sol:
#728
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\ -1\\ x\end{bmatrix}=\begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\ x\end{bmatrix},\) then value of x is:
(A) -1
(B) 0
(C) 1
(D) 2
Key:
Sol:
Sol:
#727
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
Competency
1 Marks
Find the matrix \(A^{2}\), where \(A=[a_{ij}]\) is a \(2\times2\) matrix whose elements are given by \(a_{ij}=\) maximum (i, j) - minimum (i, j):
(A) \([\begin{matrix}0&0\\ 0&0\end{matrix}]\)
(B) \([\begin{matrix}1&0\\ 0&1\end{matrix}]\)
(C) \([\begin{matrix}0&1\\ 1&0\end{matrix}]\)
(D) \([\begin{matrix}1&1\\ 1&1\end{matrix}]\)
Key:
Sol:
Sol:
#706
Physics
Electrostatics
#695
Mathematics
Probability
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If E and F are two independent events such that \( P(E) = \frac{2}{3} \), \( P(F) = \frac{3}{7} \), then \(\mathbf{P(E \mid \overline{F})}\) is equal to:
(A) \( \frac{1}{6} \)
(B) \( \frac{1}{2} \)
(C) \( \frac{2}{3} \)
(D) \( \frac{7}{9} \)
Key: C
Sol:
Sol:
If events $E$ and $F$ are independent, then $$\mathbf{P(E \mid F) = P(E)}$$And similarly, if $E$ and $F$ are independent, then $E$ and $\overline{F}$ are also independent:$$\mathbf{P(E \mid \overline{F}) = P(E)}$$ Substitute the Given ValueSince $E$ and $F$ are independent events, we can directly state the result:$$P(E \mid \overline{F}) = P(E)$$Given that $P(E) = \frac{2}{3}$, we have:$$P(E \mid \overline{F}) = \frac{2}{3}$$
#694
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If E and F are two events such that \(P(E)>0\) and \(P(F)\ne1,\) then \(P(\overline{E}/\overline{F})\) is
(A) \(\frac{P(\overline{E})}{P(\overline{F})}\)
(B) \(1-P(\overline{E}/F)\)
(C) \(1-P(E/F)\)
(D) \(\frac{1-P(E\cup F)}{P(\overline{F})}\)
Key: D
Sol:
Sol:
#693
Mathematics
Probability
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(P(A\cup B)=0.9\) and \(P(A\cap B)=0\cdot4,\) then \(P(\overline{A})+P(\overline{B})\) is:
(A) 0.3
(B) 1
(C) 1.3
(D) 0.7
Key: D
Sol:
Sol:
#692
Mathematics
Probability
MCQ_SINGLE
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3 times. The probability that at least one pen picked was red is:
(A) \(\frac{124}{125}\)
(B) \(\frac{1}{125}\)
(C) \(\frac{61}{125}\)
(D) \(\frac{64}{125}\)
Key: C
Sol:
Sol:
#691
Mathematics
Probability
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
If \(P(A)=\frac{1}{7}\), \(P(B)=\frac{5}{7}\) and \(P(A\cap B)=\frac{4}{7},\) then \(P(\overline{A}|B)\) is:
(A) \(\frac{6}{7}\)
(B) \(\frac{3}{4}\)
(C) \(\frac{4}{5}\)
(D) \(\frac{1}{5}\)
Key: D
Sol:
Sol:
ok