Available Questions 601 found Page 24 of 31
Standalone Questions
#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.
#682
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
The corner points of the feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). If \(Z=ax+by;\) (a, \(b>0)\) be the objective function, and maximum value of Z is obtained at (0, 2) and (3, 0), then the relation between a and b is:
(A) \(a=b\)
(B) \(a=3b\)
(C) \(b=6a\)
(D) \(3a=2b\)
Key: D
Sol:
Sol:
#681
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
For a Linear Programming Problem (LPP), the given objective function \(Z=3x+2y\) is subject to constraints: \(x+2y\le10\), \(3x+y\le15\), \(x, y\ge0\). The correct feasible region is: (A) ABC
(B) AOEC
(C) CED
(D) Open unbounded region BCD
Key: B
Sol:
Sol:
#680
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
For a Linear Programming Problem (LPP), the given objective function is \(Z=x+2y\). The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph. \(P\equiv(\frac{3}{13},\frac{24}{13})\) \(Q\equiv(\frac{3}{2},\frac{15}{4})\) \(R\equiv(\frac{7}{2},\frac{3}{4})\) \(S\equiv(\frac{18}{7},\frac{2}{7})\). Which of the following statements is correct? (A) Z is minimum at \(S(\frac{18}{7},\frac{2}{7})\)
(B) Z is maximum at \(R(\frac{7}{2},\frac{3}{4})\)
(C) (Value of Z at P) > (Value of Z at Q)
(D) (Value of Z at Q) < (Value of Z at R)
Key: B
Sol:
Sol:
#679
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
In a Linear Programming Problem (LPP), the objective function \(Z=2x+5y\) is to be maximised under the following constraints: \(x+y\le4\), \(3x+3y\ge18\), \(x, y\ge0\). Study the graph and select the correct option. The solution of the given LPP: <div class="image-placeholder"></div>
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(A) lies in the shaded unbounded region.
(B) lies in \(\Delta AOB\).
(C) does not exist.
(D) lies in the combined region of \(\Delta AOB\) and unbounded shaded region.
Key: C
Sol:
Sol:
#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:
#674
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
Competency
1 Marks
Of the following, which group of constraints represents the feasible region given below ?
(A) \(x+2y\le76\), \(2x+y\ge104\), \(x, y\ge0\)
(B) \(x+2y\le76\), \(2x+y\le104,\) \(x, y\ge0\)
(C) \(x+2y\ge76\), \(2x+y\le104\), \(x, y\ge0\)
(D) \(x+2y\ge76\), \(2x+y\ge104,\) \(x, y\ge0\)
Key: B
Sol:
Sol:
#673
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
The equation of a line parallel to the vector \(3\hat{i}+\hat{j}+2\hat{k}\) and passing through the point \((4, -3, 7)\) is:
(A) \(x=4t+3, y=-3t+1, z=7t+2\)
(B) \(x=3t+4, y=t+3, z=2t+7\)
(C) \(x=3t+4, y=t-3, z=2t+7\)
(D) \(x=3t+4, y=-t+3, z=2t+7\)
Key: C
Sol:
Sol:
The vector equation of a line passing through point $\vec{a}$ and parallel to vector $\vec{b}$ is $\vec{r} = \vec{a} + t\vec{b}$.
Here, $\vec{a} = (4, -3, 7)$ and $\vec{b} = (3, 1, 2)$.
So, $(x, y, z) = (4, -3, 7) + t(3, 1, 2) = (4+3t, -3+t, 7+2t)$.
Thus, $x = 3t+4, y = t-3, z = 2t+7$.
This matches Option C.
#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 \(z_2=-2\):
\[z = \frac{\lambda z_2 + z_1}{\lambda + 1}\]
\[z = \frac{(1)(-2) + (-1)}{1 + 1}\]
\[z = \frac{-2 - 1}{2}\]
\[\mathbf{z = -\frac{3}{2}}\]