Available Questions 556 found Page 6 of 28
Standalone Questions
#1507
Mathematics
Linear Programming
SA
APPLY
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically :
Minimize
$Z = 13x – 15y$
Subject to constraints
$x + y \le 7$,
$2x – 3y + 6 \le 0$,
$x \ge 0, y \ge 0$
Minimize
$Z = 13x – 15y$
Subject to constraints
$x + y \le 7$,
$2x – 3y + 6 \le 0$,
$x \ge 0, y \ge 0$
Key:
Sol:
Sol:
#1504
Mathematics
Definite Integrals
SA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $I_{1}=\int_{-\pi/4}^{\pi/4}\frac{dx}{1+\cos 2x}$ and $I_{2}=\int_{-1/2}^{1/2}|x|\,dx $, then show that $I_{1}-4I_{2}=0$.
Key:
Sol:
Sol:
#1503
Mathematics
Integrals
SA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
$\text{Find: }\int \frac{x^{2}}{(x^{2}+9)(x^{2}+16)}\,dx.$
Key:
Sol:
Sol:
#1502
Mathematics
Integrals
SA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
$\text{Find }\int \sqrt{\frac{x+2}{x-2}}\,dx.$
Key:
Sol:
Sol:
#1501
Mathematics
Definite Integrals
SA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
$\text{Evaluate: }\int_{0}^{1} x\,\tan^{-1}x\,dx.$
Key:
Sol:
Sol:
#1500
Mathematics
Inverse Trigonometric Functions
VSA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
$\text{Evaluate: }\tan\!\left(\sin^{-1}1-\cos^{-1}\!\left(-\frac{1}{2}\right)\right).$
Key:
Sol:
Sol:
#1499
Mathematics
Inverse Trigonometric Functions
VSA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
$\text{Simplify: }\tan^{-1}\!\left(\frac{\cos 2x-\sin 2x}{\cos 2x+\sin 2x}\right),\quad 0<x<\frac{\pi}{4}.$
Key:
Sol:
Sol:
#1498
Mathematics
Vector Algebra
VSA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Vectors \(\vec{a}=3\hat{i}-2\hat{j}+2\hat{k}\) and \(\vec{b}=\hat{i}+2\hat{k}\) represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence find their lengths.
Key:
Sol:
Sol:
#1497
Mathematics
Vector Algebra
VSA
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the vector of magnitude \(14\) in the direction of \(\overrightarrow{QP}\), where \(P=(1,3,2)\) and \(Q=(-1,0,8)\) respectively.
Key:
Sol:
Sol:
#1495
Mathematics
Derivatives
VSA
APPLY
2026
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $ \sqrt{3}\,(x^2+y^2)=4xy$, then find \(\dfrac{dy}{dx}\) at $\left(\frac{1}{2},\,\frac{\sqrt{3}}{2}\right).$
Key:
Sol:
Sol:
#1493
Mathematics
Differential Equations
MCQ_SINGLE
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The general solution for the differential equation $\frac{dy}{dx} = e^{3x-y}$ is
(A) $3e^y = e^{3x} + C$
(B) $\log (3x - y) = C$
(C) $e^{3x-y} = C$
(D) $-e^y + 3e^{3x} = C$
Key: A
Sol:
Sol:
#1492
Mathematics
Integrals
VSA
APPLY
KNOWLEDGE
1 Marks
Evaluate the following integral $\int x^2 dx$
Key:
Sol:
Sol:
$\frac{ x^3}{3}$
#1491
Mathematics
Matrices and Determinants
MCQ_SINGLE
REMEMBER
2026
AISSCE(Board Exam)65/1/1
KNOWLEDGE
1 Marks
Which of the following cannot be the order of a row-matrix ?
(A) $2 \times 1$
(B) $1 \times 2$
(C) $1 \times 1$
(D) $1 \times n$
Key: A
Sol:
Sol:
#1490
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
UNDERSTAND
2026
AISSCE(Board Exam)65/1/1
KNOWLEDGE
1 Marks
If $2 \cos^{-1} x = y$, then
(A) $0 \leq y \leq \pi$
(B) $-\pi \leq y \leq \pi$
(C) $0 \leq y \leq 2\pi$
(D) $-\pi \leq y \leq 0$
Key: C
Sol:
Sol:
#1489
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A matrix B = $[b_{ij}]_{m \times m}$ is said to be a diagonal matrix, if :
(A) $b_{ij} = 0$, when $i = j$
(B) $b_{ij} = 1$, when $i = j$
(C) $b_{ij} = 1$, when $i \neq j$
(D) $b_{ij} = 0$, when $i \neq j$
Key: D
Sol:
Sol:
#1488
Mathematics
Matrices and Determinants
MCQ_SINGLE
REMEMBER
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
For any square matrix A with real entries, if $A + A'$ is a symmetric matrix then :
(A) (A - A') cannot be a skew symmetric matrix
(B) (A - A') is a skew symmetric matrix
(C) A is always a symmetric matrix
(D) A is always a skew symmetric matrix
Key: B
Sol:
Sol:
#1487
Biology
Sexual Reproduction in Flowering Plants
#1485
Mathematics
Three Dimensional Geometry
LA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Find the point Q on the line $\frac{2x+4}{6}=\frac{y+1}{2}=\frac{-2z+6}{-4}$ at a distance of $3\sqrt{2}$ from the point $P(1,2,3)$.
Key:
Sol:
Sol:
#1484
Mathematics
Differential Equations
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Solve the differential equation $\frac{dy}{dx}=\cos x-2y$.
Key:
Sol:
Sol:
#1482
Mathematics
Definite Integrals
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\pi}\frac{x\tan x}{\sec x+\tan x}dx$
Key:
Sol:
Sol: