Available Questions 145 found Page 4 of 8
Standalone Questions
#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:
#977
Mathematics
Relations and Functions
ASSERTION_REASON
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Assertion (A): Let $f(x) = e^{x}$ and $g(x) = \log x$. Then $(f + g)x = e^{x} + \log x$ where domain of $(f + g)$ is $\mathbb{R}$.
Reason (R): $\text{Dom}(f + g) = \text{Dom}(f) \cap \text{Dom}(g)$.
Key: D
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:
#959
Mathematics
Relations and Functions
MCQ_SINGLE
APPLY
2025
JEE Main 2025
Competency
0 Marks
Let A = { (α, β) ∈ R x R : |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = { (α, β) ∈ R × R: 16(α-2)²+9(β-6)² ≤ 144}. Then
(A) A ⊂ B
(B) B ⊂ A
(C) neither A ⊂ B nor B ⊂ A
(D) A ∪ B = {(x, y) : -4 ≤ x ≤ 4, -1 ≤ y ≤ 11}
Key: B
Sol:
Sol:
#940
Mathematics
Inverse Trigonometric Functions
VSA
APPLY
2024
Competency
2 Marks
Find value of k if \(\sin^{-1}[k~\tan(2~\cos^{-1}\frac{\sqrt{3}}{2})]=\frac{\pi}{3}.\)
Key:
Sol:
Sol:
#935
Mathematics
Differential Equations
SA
APPLY
2023
Competency
3 Marks
Solve the differential equation given by:$$x \, dy - y \, dx - \sqrt{x^{2} + y^{2}} \, dx = 0$$
Key:
Sol:
Sol:
#934
Mathematics
Linear Programming
SA
APPLY
2023
Competency
3 Marks
Solve graphically the following linear programming problem : Maximise \(z = 6x + 3y\), subject to the constraints\begin{align}
4x + y &\ge 80 \\
3x + 2y &\le 150 \\
x + 5y &\ge 115 \\
x, y &\ge 0
\end{align}
4x + y &\ge 80 \\
3x + 2y &\le 150 \\
x + 5y &\ge 115 \\
x, y &\ge 0
\end{align}
Key:
Sol:
Sol:
#933
Mathematics
Linear Programming
LA
APPLY
2023
Competency
5 Marks
Solve the following Linear Programming Problem graphically: Maximize: \(P = 70x + 40y\) subject to: \(3x + 2y ≤ 9, 3x + y ≤ 9, x ≥ 0, y ≥ 0\)
Key:
Sol:
Sol:
#930
Mathematics
Applications of Integrals
LA
APPLY
2023
Competency
5 Marks
The area of the region bounded by the line \(y=mx (m>0)\), the curve \(x^{2}+y^{2}=4\) and the \(x\)-axis in the first quadrant is \(\frac{\pi}{2}\) units. Using integration, find the value of m.
Key:
Sol:
Sol:
#929
Mathematics
Applications of Integrals
LA
APPLY
2023
Competency
5 Marks
33. Using integration, find the area of the region bounded by the parabola $y^{2}=4ax$ and its latus rectum.
Key:
Sol:
Sol:
#928
Mathematics
Linear Programming
SA
APPLY
2023
Competency
3 Marks
Determine graphically the minimum value of the following objective function : $z=500x+400y$ subject to constraints $x+y\le200, x\ge20, y\ge4x, y\ge0$
Key:
Sol:
Sol:
#923
Mathematics
Relations and Functions
LA
APPLY
2023
Competency
5 Marks
Show that a function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined as $f(x)=\frac{5x-3}{4}$ is both one-one and onto.
Key:
Sol:
Sol:
#922
Mathematics
Relations and Functions
LA
APPLY
2023
Competency
5 Marks
Let $f : \mathbb{R} - \left\{ \frac{4}{3} \right\} \to \mathbb{R}$ be a function defined as:$$f(x) = \frac{4x}{3x+4}$$Show that $f$ is a one-one function. Also, check whether $f$ is an onto function or not.
Key:
Sol:
Sol: