Paper Generator

#1735 Mathematics Linear Programming

MCQ_SINGLE 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

For the feasible region shown below, the non-trivial constraints of the linear programming problem are

(A) $x+y \le 5$, $x+3y \le 9$

(B) $x+y \le 5$, $x+3y \ge 9$

(C) $x+y \ge 5$, $x+3y \le 9$

(D) $x+y \ge 5$, $3x+y \le 9$

Detail View Add

#1734 Mathematics Linear Programming

MCQ_SINGLE 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

In the graph, the feasible region representing the Linear Programming Problem for maximising objective function $Z=px+qy$, $p, q>0$ is shaded. If all points on segment AB give max (Z), then which of the following is true? [Graph shows A at (0, 5) and B at (3, 4)]

(A) $p=2q$

(B) $p=3q$

(C) $q=3p$

(D) $q=2p$

Detail View Add

#1730 Mathematics Three Dimensional Geometry

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If $l_{1}$, $m_{1}$, $n_{1}$ and $l_{2}$, $m_{2}$, $n_{2}$ are direction cosines of lines $L_{1}$ and $L_{2}$ respectively and $\theta$ is the acute angle between them, then :

(A) $\cos\theta=l_{1}l_{2}+m_{1}m_{2}+n_{1}n_{2}$

(B) $\sin\theta=l_{1}l_{2}+m_{1}m_{2}+n_{1}n_{2}$

(C) $\tan\theta=\frac{l_{1}}{l_{2}}+\frac{m_{1}}{m_{2}}+\frac{n_{1}}{n_{2}}$

(D) $\cos\theta=|l_{1}l_{2}+m_{1}m_{2}+n_{1}n_{2}|$

Detail View Add

#1726 Mathematics Vector Algebra

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?

(A) $\vec{a}.\vec{b}\le|\vec{a}||\vec{b}|$

(B) $|\vec{a}+\vec{b}|\ge|\vec{a}|+|\vec{b}|$

(C) $|\vec{a}-\vec{b}|=|\vec{a}|-|\vec{b}|$

(D) $|\vec{a}\times\vec{b}|\ge|\vec{a}||\vec{b}|$

Detail View Add

#1720 Mathematics Differential Equations

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

The order and degree of the differential equation $1+(\frac{d^{3}y}{dx^{3}})^{3}=\lambda\frac{d^{2}y}{dx^{2}}$ is:

(A) Order = 3, Degree = 3

(B) Order = 2, Degree = 2

(C) Order = 3, Degree = 1

(D) Order = 2, Degree = 1

Detail View Add

#1717 Mathematics Differential Equations

MCQ_SINGLE APPLY 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) $-e^{y}+3e^{3x}=C$

Detail View Add

#1712 Mathematics Applications of Integrals

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

The area of the region bounded by the curve $y=x$ and x-axis, between $x=0$ and $x=2$ is:

(A) 2 sq. units

(B) $\frac{1}{2}$ sq. unit

(C) 1 sq. unit

(D) 4 sq. units

Detail View Add

#1709 Mathematics Definite Integrals

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

The value of $\int_{-5}^{-1}\frac{1}{x}dx$ is equal to:

(A) $-\log 5$

(B) $x^{6}$

(C) $\log(-5)$

(D) $x^{-6}$

Detail View Add

#1705 Mathematics Integrals

MCQ_SINGLE REMEMBER 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

$\int\frac{1}{\sqrt{1+\cos 2x}}dx$ is equal to:

(A) $\log|\cos x|+C$

(B) $\frac{1}{\sqrt{2}}\log|\sec x-\tan x|+C$

(C) $\frac{1}{\sqrt{2}}\log|\sec x+\tan x|+C$

(D) $\log|\sin 2x|+C$

Detail View Add

#1704 Mathematics Integrals

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

$\int\frac{dx}{\sqrt{25-16x^{2}}}$ is equal to:

(A) $\frac{1}{5}\sin^{-1}4x+C$

(B) $\frac{1}{25}\sin^{-1}16x+C$

(C) $\frac{1}{4}\sin^{-1}\frac{4x}{5}+C$

(D) $\frac{1}{16}\sin^{-1}\frac{4x}{5}+C$

Detail View Add

#1697 Mathematics Derivatives

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If $\sin^{-1}x=y$ then $\frac{dy}{dx}$ is:

(A) $\cos^{-1}x$

(B) $\cos y$

(C) $\frac{1}{1-x^{2}}$

(D) $\sec y$

Detail View Add

#1695 Mathematics Derivatives

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

Differential of $e^{e^{x}}$ with respect to x is:

(A) $\log x$

(B) $e^{e^{x}}$

(C) $e^{x}e^{e^{x}}$

(D) $(e^{x})^{2}$

Detail View Add

#1672 Mathematics Inverse Trigonometric Functions

MCQ_SINGLE APPLY 2026 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined?

(A) $\tan^{-1}:R\rightarrow(-\frac{\pi}{2},\frac{\pi}{2})$

(B) $\sec^{-1}:R-(-1,1)\rightarrow[0,\pi]-\{\frac{\pi}{2}\}$

(C) $\cot^{-1}:R\rightarrow(0,\pi)$

(D) $\text{cosec}^{-1}:R-(-1,1)\rightarrow[-\frac{\pi}{2},\frac{\pi}{2}]$

Detail View Add

#1507 Mathematics Linear Programming

SA APPLY

KNOWLEDGE 3 Marks

Solve the following linear programming problem graphically :
Minimize
$Z = 13x – 15y$
Subject to constraints
$x + y \le 7$,
$2x – 3y + 6 \le 0$,
$x \ge 0, y \ge 0$

Detail View Add

#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 $I_{1}-4I_{2}=0$.

Detail View Add

#1503 Mathematics Integrals

SA REMEMBER 2026 AISSCE(Board Exam)

KNOWLEDGE 3 Marks

$\text{Find: }\int \frac{x^{2}}{(x^{2}+9)(x^{2}+16)}\,dx.$

Detail View Add

#1502 Mathematics Integrals