Available Questions 255 found Page 9 of 13
Standalone Questions
#1309
Mathematics
Three Dimensional Geometry
LA
REMEMBER
2024
AISSCE(Board Exam)
Competency
5 Marks
The image of point $P(x,y,z)$ with respect to line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is $P^{\prime}(1,0,7)$ Find the coordinates of point P.
Key:
Sol:
Sol:
#1304
Mathematics
Matrices and Determinants
LA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
5 Marks
If $A=[\begin{bmatrix}1&-2&0\\ 2&-1&-1\\ 0&-2&1\end{bmatrix}],$ find $A^{-1}$ and use it to solve the following system of equations: $x-2y=10$, $2x-y-z=8$, $-2y+z=7$
Key:
Sol:
Sol:
#1303
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
E and F are two independent events such that $P(\overline{E})=0\cdot6$ and $P(E\cup F)=0\cdot6$ Find $P(F)$ and $P(\overline{E}\cup\overline{F})$
Key:
Sol:
Sol:
#1302
Mathematics
Linear Programming
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Solve the following linear programming problem graphically: Maximise $z=500x+300y,$ subject to constraints $x+2y\le12$, $2x+y\le12$, $4x+5y\ge20$, $x\ge0$, $y\ge0$
Key:
Sol:
Sol:
#1301
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find the particular solution of the differential equation given by $x^{2}\frac{dy}{dx}-xy=x^{2}cos^{2}(\frac{y}{2x})$ given that when $x=1$, $y=\frac{\pi}{2}$
Key:
Sol:
Sol:
#1294
Mathematics
Vector Algebra
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
2 Marks
In the given figure, ABCD is a parallelogram. If $\vec{AB}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{DB}=3\hat{i}-6\hat{j}+2\hat{k}$ , then find $\vec{AD}$ and hence find the area of parallelogram ABCD.
Key:
Sol:
Sol:
#1285
Mathematics
Matrices and Determinants
LA
APPLY
2024
AISSCE(Board Exam)
Competency
5 Marks
Solve the following system of equations, using matrices: $\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4$ $\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$ , $\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$ where x, y, $z\ne0$
Key:
Sol:
Sol:
#1284
Mathematics
Three Dimensional Geometry
LA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
5 Marks
Find the equation of the line which bisects the line segment joining points $A(2,3,4)$ and $B(4,5,8)$ and is perpendicular to the lines $\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}$
Key:
Sol:
Sol:
#1279
Mathematics
Vector Algebra
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
The position vectors of vertices of $\Delta$ ABC are $A(2\hat{i}-\hat{j}+\hat{k}),$ $B(\hat{i}-3\hat{j}-5\hat{k})$ and $C(3\hat{i}-4\hat{j}-4\hat{k})$ Find all the angles of $\Delta$ Aะะก.
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Sol:
Sol:
#1268
Mathematics
Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
2 Marks
If $f(x)=|tan~2x|$, then find the value of $f^{\prime}(x)$ at $x=\frac{\pi}{3}$
Key:
Sol:
Sol:
#1265
Mathematics
Three Dimensional Geometry
LA
REMEMBER
2024
AISSCE(Board Exam)
Competency
5 Marks
Two vertices of the parallelogram ABCD are given as $A(-1,2,1)$ and $B(1,-2,5)$. If the equation of the line passing through C and D is $\frac{x-4}{1}=\frac{y+7}{-2}=\frac{z-8}{2}$ then find the distance between sides AB and CD. Hence, find the area of parallelogram ABCD.
Key:
Sol:
Sol:
#1264
Mathematics
Three Dimensional Geometry
LA
REMEMBER
2024
AISSCE(Board Exam)
Competency
5 Marks
Find the equation of the line passing through the point of intersection of the lines $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and $\frac{x-1}{0}=\frac{y}{-3}=\frac{z-7}{2}$ and perpendicular to these given lines.
Key:
Sol:
Sol:
#1262
Mathematics
Applications of Derivatives
LA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
5 Marks
The perimeter of a rectangular metallic sheet is 300 cm. It is rolled along one of its sides to form a cylinder. Find the dimensions of the rectangular sheet so that volume of cylinder so formed is maximum.
Key:
Sol:
Sol:
#1261
Mathematics
Applications of Derivatives
LA
REMEMBER
2024
AISSCE(Board Exam)
Competency
5 Marks
It is given that function $f(x)=x^{4}-62x^{2}+ax+9$ attains local maximum value at $x=1$ Find the value of 'a', hence obtain all other points where the given function f(x) attains local maximum or local minimum values.
Key:
Sol:
Sol:
#1259
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
The chances of P, Q and R getting selected as CEO of a company are in the ratio 4: 1: 2 respectively. The probabilities for the company to increase its profits from the previous year under the new CEO, P, Q or R are 0-3, 0-8 and 0.5 respectively. If the company increased the profits from the previous year, find the probability that it is due to the appointment of R as CEO.
Key:
Sol:
Sol:
#976
Mathematics
Vector Algebra
ASSERTION_REASON
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Assertion (A) : If $|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=256$ and $|\vec{b}|=8$, then $|\vec{a}|=2$.
Reason (R) : $\sin ^{2} \theta+\cos ^{2} \theta=1$ and $|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta$ and $\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta$.
Key: A
Sol:
Sol:
#975
Mathematics
Inverse Trigonometric Functions
ASSERTION_REASON
REMEMBER
2025
AISSCE(Board Exam)
Competency
1 Marks
Assertion (A) : Set of values of $\sec^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is a null set.
Reason (R) : $\sec^{-1}$ x is defined for $x \in \mathbb{R}-(-1, 1)$.
Key: A
Sol:
Sol:
#971
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 :$x + y \leq 4$, $3x + 3y \geq 18$, $x, y \geq 0$
Study the graph and select the correct option.
(A) lies in the shaded unbounded region.
(B) lies in $\triangle AOB$.
(C) does not exist.
(D) lies in the combined region of $\triangle AOB$ and unbounded shaded region.
Key: C
Sol:
Sol:
The feasible region of a Linear Programming Problem is the set of points that satisfy all the given constraints simultaneously.Constraint 1 requires the points to be in the region where the sum of $x$ and $y$ is less than or equal to 4.Constraint 2 requires the points to be in the region where the sum of $x$ and $y$ is greater than or equal to 6.Mathematically, a number cannot be both $\le 4$ and $\ge 6$ at the same time. Visually, looking at the graph, there is a clear gap between the shaded region $\Delta AOB$ and the shaded unbounded region above $PQ$. The two regions do not overlap.3. ConclusionSince there is no common region that satisfies all constraints, the feasible region is an empty set.Without a feasible region, there are no valid values for $x$ and $y$ to substitute into the objective function $Z$. Therefore, an optimal solution (maximum value) cannot be found.Answer:The correct option is (C) does not exist.
#970
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.Which of the following statements is correct ?
(A) Z is minimum at $(\frac{18}{7}, \frac{2}{7})$
(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:
Sol:
Sol:
#968
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
ANALYZE
2025
AISSCE(Board Exam)
Competency
1 Marks
The given graph illustrates : (A) $y = \tan^{-1}x$
(B) $y = \csc^{-1}x$
(C) $y = \cot^{-1}x$
(D) $y = \sec^{-1}x$
Key: A
Sol:
Sol: