Available Questions 559 found Page 23 of 28
Standalone Questions
#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:
#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:
#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:
#690
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack is :
(A) \(\frac{2}{13}\)
(B) \(\frac{3}{26}\)
(C) \(\frac{19}{26}\)
(D) \(\frac{3}{13}\)
Key: B
Sol:
Sol:
#689
Mathematics
Probability
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(P(A|B)=P(A^{\prime}|B)\), then which of the following statements is true?
(A) \(P(A)=P(A^{\prime})\)
(B) \(P(A)=2~P(B)\)
(C) \(P(A\cap B)=\frac{1}{2}P(B)\)
(D) \(P(A\cap B)=2~P(B)\)
Key: C
Sol:
Sol:
#688
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let E be an event of a sample space S of an experiment, then \(P(S|E)=\)
(A) \(P(S\cap E)\)
(B) \(P(E)\)
(C) 1
(D) 0
Key: C
Sol:
Sol:
#687
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let E and F be two events such that \(P(E)=0\cdot1\), \(P(F)=0\cdot3,\) \(P(E\cup F)=0\cdot4\) then \(P(F|E)\) is:
(A) 0.6
(B) 0.4
(C) 0.5
(D) 0
Key: D
Sol:
Sol:
#686
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If A and B are events such that \(P(A/B)=P(B/A)\ne0,\) then :
(A) \(A\subset B\), but \(A\ne B\)
(B) \(A=B\)
(C) \(A\cap B=\phi\)
(D) \(P(A)=P(B)\)
Key: D
Sol:
Sol:
#685
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The corner points of the feasible region in graphical representation of a L.P.P. are \((2, 72)\), \((15, 20)\) and \((40, 15)\). If \(Z = 18x + 9y\) be the objective function, then
(A) \(Z\) is maximum at \((2, 72)\), minimum at \((15, 20)\)
(B) \(Z\) is maximum at \((15, 20)\), minimum at \((40, 15)\)
(C) \(Z\) is maximum at \((40, 15)\), minimum at \((15, 20)\)
(D) \(Z\) is maximum at \((40, 15)\), minimum at \((2, 72)\)
Key: C
Sol:
Sol:
To find the maximum and minimum values of the objective function \(Z = 18x + 9y\), we must evaluate \(Z\) at each of the given corner points of the feasible region.The corner points \((x, y)\) are: \((2, 72)\), \((15, 20)\), and \((40, 15)\).
At \(\mathbf{(2, 72)}\):\[Z = 18(2) + 9(72)\]\[Z = 36 + 648 = \mathbf{684}\]At \(\mathbf{(15, 20)}\):\[Z = 18(15) + 9(20)\]\[Z = 270 + 180 = \mathbf{450}\]At \(\mathbf{(40, 15)}\):\[Z = 18(40) + 9(15)\]\[Z = 720 + 135 = \mathbf{855}\]Maximum Value: \(855\), which occurs at the point \(\mathbf{(40, 15)}\).Minimum Value: \(450\), which occurs at the point \(\mathbf{(15, 20)}\).
The correct conclusion is: \(Z\) is maximum at \((40, 15)\), minimum at \((15, 20)\).