Available Questions 450 found Page 18 of 23
Standalone Questions
#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 \((15, 20)\).
#684
Mathematics
Linear Programming
MCQ_SINGLE
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If the feasible region of a linear programming problem with objective function \(Z = ax + by\), is bounded, then which of the following is correct?
(A) It will only have a maximum value.
(B) It will only have a minimum value.
(C) It will have both maximum and minimum values.
(D) It will have neither maximum nor minimum value.
Key: C
Sol:
Sol:
#683
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \(Z=5x+7y,\) where x and y are the number of units of X and Y respectively sold. Which of the following statement is correct?
(A) The objective function maximizes the difference of the profit earned from products X and Y.
(B) The objective function measures the total production of products X and Y.
(C) The objective function maximizes the combined profit earned from selling X and Y.
(D) The objective function ensures the company produces more of product X than product Y.
Key: C
Sol:
Sol:
The objective function maximizes the combined profit earned from selling products X and Y.
#678
Mathematics
Linear Programming
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A linear programming problem deals with the optimization of a/an:
(A) logarithmic function
(B) linear function
(C) quadratic function
(D) exponential function
Key: B
Sol:
Sol:
#677
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The number of corner points of the feasible region determined by constraints \(x\ge0, y\ge0, x+y\ge4\) is:
(A) 0
(B) 1
(C) 2
(D) 3
Key: C
Sol:
Sol:
#676
Mathematics
Linear Programming
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The common region determined by all the constraints of a linear programming problem is called :
(A) an unbounded region
(B) an optimal region
(C) a bounded region
(D) a feasible region
Key: D
Sol:
Sol:
#675
Mathematics
Linear Programming
MCQ_SINGLE
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called :
(A) feasible solutions
(B) constraints
(C) optimal solutions
(D) infeasible solutions
Key: B
Sol:
Sol:
#672
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The line \(x=1+5\mu\), \(y=-5+\mu\), \(z=-6-3\mu\) passes through which of the following point ?
(A) \((1, -5, 6)\)
(B) \((1, 5, 6)\)
(C) \((1, -5, -6)\)
(D) \((-1, -5, 6)\)
Key: C
Sol:
Sol:
\((1, -5, -6)\)
#671
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If P is a point on the line segment joining (3, 6, -1) and (6, 2, -2) and y-coordinate of P is 4, then its z-coordinate is:
(A) \(-\frac{3}{2}\)
(B) 0
(C) 1
(D) \(\frac{3}{2}\)
Key: A
Sol:
Sol:
We are given two points, \(A = (3, 6, -1)\) and \(B = (6, 2, -2)\). The point \(P\) lies on the line segment \(AB\), and its \(y\)-coordinate is \(4\). We need to find its \(z\)-coordinate.
Let \(P\) divide the line segment \(AB\) in the ratio \(\lambda:1\).
Step 1: Find the Ratio (\(\lambda\))
We use the section formula for the \(y\)-coordinate, where \(y=4\), \(y_1=6\), and \(y_2=2\):
\[y = \frac{\lambda y_2 + y_1}{\lambda + 1}\]
\[4 = \frac{\lambda(2) + 6}{\lambda + 1}\]
\[4(\lambda + 1) = 2\lambda + 6\]
\[4\lambda + 4 = 2\lambda + 6\]
\[2\lambda = 2\]
\[\mathbf{\lambda = 1}\]
The point \(P\) is the **midpoint** of the segment \(AB\) since \(\lambda = 1\).
Step 2: Find the \(z\)-coordinate (\(z\))
Now, we use the section formula for the \(z\)-coordinate with \(\lambda=1\), \(z_1=-1\), and \(z_2=-2\):
\[z = \frac{\lambda z_2 + z_1}{\lambda + 1}\]
\[z = \frac{(1)(-2) + (-1)}{1 + 1}\]
\[z = \frac{-2 - 1}{2}\]
\[\mathbf{z = -\frac{3}{2}}\]
#670
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If the direction cosines of a line are \(\sqrt{3}k, \sqrt{3}k\), \(\sqrt{3}k,\) then the value of k is:
(A) \(\pm1\)
(B) \(\pm\sqrt{3}\)
(C) \(\pm3\)
(D) \(\pm\frac{1}{3}\)
Key: D
Sol:
Sol: