Available Questions 833 found Page 3 of 42
Standalone Questions
#1850
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
The value of p for which vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $2\hat{i} - p\hat{j} + \hat{k}$ are perpendicular to each other is
(A) $0$
(B) $1$
(C) $\frac{5}{2}$
(D) $-\frac{5}{2}$
Key: C
Sol:
Sol:
#1849
Mathematics
Differential Equations
MCQ_SINGLE
ANALYZE
2026
AISSCE(Board Exam)
Competency
1 Marks
The order and degree of the differential equation $\frac{d}{dx}(e^y) = 0$ respectively are
(A) 0, 1
(B) 1, 1
(C) 2, 1
(D) 1, not defined
Key: B
Sol:
Sol:
#1848
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The integrating factor of differential equation $R\frac{dx}{dy} + Px = Q$ where P, Q, R are functions of y is
(A) $e^{\int\frac{P}{Q}dy}$
(B) $e^{\int Pdy}$
(C) $e^{\int\frac{P}{R}dy}$
(D) $e^{\int\frac{P}{R}dx}$
Key: C
Sol:
Sol:
#1847
Mathematics
Applications of Integrals
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
The area bounded by the curve $y = x|x|$, x-axis and the ordinates $x = -1$ and $x = 1$ is given by
(A)
(B) $1/3$
(C) $2/3$
(D) $4/3$
Key: C
Sol:
Sol:
#1846
Mathematics
Definite Integrals
MCQ_SINGLE
EVALUATE
2026
AISSCE(Board Exam)
Competency
1 Marks
The value of $\int_{-1}^{1} \frac{x^3}{x^2 + 2|x| + 1} dx$ is
(A) 0
(B) log 2
(C) 2 log 2
(D) $\frac{1}{2}$ log 2
Key: A
Sol:
Sol:
#1845
Mathematics
Integrals
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
If $\int \frac{3ax}{b^2 + c^2x^2} dx = A \log |b^2 + c^2x^2| + K$, then the value of $A$ is
(A) $3a$
(B) $\frac{3a}{2b^2}$
(C) $\frac{3a}{b^2c^2}$
(D) $\frac{3a}{2c^2}$
Key: D
Sol:
Sol:
#1844
Mathematics
Applications of Derivatives
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
The least value of $f(x) = x^3 - 12x$, $x \in [0, 3]$ is
(A) $ -16$
(B) $ -9$
(C) $ 0$
(D) $ 16$
Key: A
Sol:
Sol:
#1843
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric ?
(A) $AB$
(B) $AB + BA$
(C) $(A + B)^2$
(D) $A - B$
Key: D
Sol:
Sol:
#1842
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
One of the values of $x$ for which $\begin{vmatrix} \cos x & \sin x \\ -\cos x & \sin x \end{vmatrix} = 1$ is
(A) $0$
(B) $\frac{\pi}{4}$
(C) $\frac{\pi}{3}$
(D) $\frac{\pi}{2}$
Key: B
Sol:
Sol:
#1841
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
If $\Delta_{1}=\begin{vmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{vmatrix}$ and $\Delta_{2}=\begin{vmatrix} 0 & 2 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 6 \end{vmatrix}$, then
(A) $\Delta_{1}=2 \Delta_{2}$
(B) $\Delta_{2}=-2 \Delta_{1}$
(C) $\Delta_{1}=\Delta_{2}$
(D) $\Delta_{2}=-\Delta_{1}$
Key: B
Sol:
Sol:
#1840
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The feasible region of a linear programming problem with objective function Z = 5x + 7y is shown below : The maximum value of Z - minimum value of Z is
(A) 8
(B) 29
(C) 35
(D) 43
Key:
Sol:
Sol:
#1839
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The degree of an objective function of a linear programming problem is
(A) 0
(B) 1
(C) 2
(D) Any natural number
Key: B
Sol:
Sol:
#1838
Mathematics
Probability
ASSERTION_REASON
EVALUATE
2026
AISSCE(Board Exam)
Competency
1 Marks
In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is $\frac{2}{3}$.
For any two events A and B, $P(A|B) = \frac{P(A \cup B)}{P(B)}$
Key: C
Sol:
Sol:
#1837
Mathematics
Vector Algebra
ASSERTION_REASON
APPLY
2026
AISSCE(Board Exam)
Competency
1 Marks
Lines given by $x = py + q, z = ry + s$ and $x = p'y + q', z = r'y + s'$ are perpendicular to each other when $pp' + rr' = 1$.
Two lines $\vec{r} = \vec{a_1} + \lambda \vec{b_1}$ and $\vec{r} = \vec{a_2} + \mu \vec{b_2}$ are perpendicular to each other if $\vec{b_1} \cdot \vec{b_2} = 0$.
Key: D
Sol:
Sol:
#1836
Mathematics
Linear Programming
SA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically :
Minimize $Z = 13x - 15y$
Subject to constraints
$$x + y \leq 7,$$
$$2x - 3y + 6 \geq 0,$$
$$x \geq 0, y \geq 0$$
Minimize $Z = 13x - 15y$
Subject to constraints
$$x + y \leq 7,$$
$$2x - 3y + 6 \geq 0,$$
$$x \geq 0, y \geq 0$$
Key:
Sol:
Sol:
#1835
Mathematics
Relations and Functions
LA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A function $f : \mathbb{R} - \left\{\frac{3}{5}\right\} \longrightarrow \mathbb{R} - \left\{\frac{3}{5}\right\}$ is defined as $f(x) = \frac{3x + 2}{5x - 3}$. Show that f is one-one and onto.
Key:
Sol:
Sol:
#1834
Mathematics
Relations and Functions
LA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A relation R is defined on Z, the set of integers, as $R = \{(x, y) : |x - y|\text{ is divisible by a prime number 'p', } x, y \in \mathbb{Z}\}$
check whether R is an equivalence relation or not.
check whether R is an equivalence relation or not.
Key:
Sol:
Sol:
#1833
Mathematics
Differential Equations
LA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $x = \cos t, y = \cos mt$, prove that $\left(1-x^2\right) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + m^2y = 0$.
Key:
Sol:
Sol:
#1832
Mathematics
Matrices and Determinants
LA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $\begin{bmatrix} 3 & -1 & \sin 3x \\ -7 & 4 & \cos 2x \\ -11 & 7 & 2 \end{bmatrix}$ is a singular matrix, then find all values of $x$
where $x \in \left[0, \frac{\pi}{2}\right]$.
where $x \in \left[0, \frac{\pi}{2}\right]$.
Key:
Sol:
Sol:
#1831
Mathematics
Matrices and Determinants
LA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix}$, find $A^{-1}$ and use it to solve the following system of equations :
$-2y + z = 7, 2x - y - z = 8, x - 2y = 10$
$-2y + z = 7, 2x - y - z = 8, x - 2y = 10$
Key:
Sol:
Sol: