Available Questions 832 found Page 36 of 42
Standalone Questions
#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>
[Image Missing]
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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 \(z_2=-2\):
\[z = \frac{\lambda z_2 + z_1}{\lambda + 1}\]
\[z = \frac{(1)(-2) + (-1)}{1 + 1}\]
\[z = \frac{-2 - 1}{2}\]
\[\mathbf{z = -\frac{3}{2}}\]
#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:
#669
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The distance of point \(P(a,b,c)\) from y-axis is :
(A) b
(B) \(b^{2}\)
(C) \(\sqrt{a^{2}+c^{2}}\)
(D) \(a^{2}+c^{2}\)
Key: C
Sol:
Sol:
#668
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The coordinates of the foot of the perpendicular drawn from the point \((0, 1, 2)\) on the x-axis are given by:
(A) \((1,0,0)\)
(B) \((2,0,0)\)
(C) \((\sqrt{5},0,0)\)
(D) \((0,0,0)\)
Key: D
Sol:
Sol:
#667
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Direction ratios of a vector parallel to line \(\frac{x-1}{2}=-y=\frac{2z+1}{6}\) are:
(A) \(2,-1,6\)
(B) \(2, 1, 6\)
(C) \(2, 1, 3\)
(D) \(2,-1, 3\)
Key: D
Sol:
Sol:
#666
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If a line makes an angle of \(30^{\circ}\) with the positive direction of x-axis, \(120^{\circ}\) with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is:
(A) \(90^{\circ}\)
(B) \(120^{\circ}\)
(C) \(60^{\circ}\)
(D) \(0^{\circ}\)
Key: A
Sol:
Sol:
#665
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(\alpha\), \(\beta\) and \(\gamma\) are the angles which a line makes with positive directions of x, y and z axes respectively, then which of the following is not true?
(A) \(cos^{2}\alpha+cos^{2}\beta+cos^{2}\gamma=1\)
(B) \(sin^{2}\alpha+sin^{2}\beta+sin^{2}\gamma=2\)
(C) \(cos~2\alpha+cos~2\beta+cos~2\gamma=-1\)
(D) \(cos~\alpha+cos~\beta+cos~\gamma=1\)
Key: D
Sol:
Sol:
#664
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If a line makes an angle of \(\frac{\pi}{4}\) with the positive directions of both x-axis and z-axis, then the angle which it makes with the positive direction of y-axis is:
(A) 0
(B) \(\frac{\pi}{4}\)
(C) \(\frac{\pi}{2}\)
(D) \(\pi\)
Key: C
Sol:
Sol:
#663
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The vector equation of a line passing through the point (1, -1, 0) and parallel to Y-axis is :
(A) \(\vec{r}=\hat{i}-\hat{j}+\lambda(\hat{i}-\hat{j})\)
(B) \(\vec{r}=\hat{i}-\hat{j}+\lambda\hat{j}\)
(C) \(\vec{r}=\hat{i}-\hat{j}+\lambda\hat{k}\)
(D) \(\vec{r}=\lambda\hat{j}\)
Key: B
Sol:
Sol:
#662
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The lines \(\frac{1-x}{2}=\frac{y-1}{3}=\frac{z}{1}\) and \(\frac{2x-3}{2p}=\frac{y}{-1}=\frac{z-4}{7}\) are perpendicular to each other for p equal to:
(A) \(-\frac{1}{2}\)
(B) \(\frac{1}{2}\)
(C) 2
(D) 3
Key: C
Sol:
Sol: