Available Questions 833 found Page 6 of 42
Standalone Questions
#1790
Mathematics
Differential Equations
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the general solution of the differential equation $2x^{2}\frac{dy}{dx}=y^{2}+2xy.$
Key:
Sol:
Sol:
#1789
Mathematics
Differential Equations
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the general solution of the differential equation: $y\log y\frac{dx}{dy}+x=\frac{2}{y}$
Key:
Sol:
Sol:
#1788
Mathematics
Differential Equations
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following differential equation: $x\frac{dy}{dx}=y-x\sin^{2}(\frac{y}{x})$ given that $y(1)=\frac{\pi}{6}$
Key:
Sol:
Sol:
#1787
Mathematics
Definite Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{0}^{2}\frac{1}{\sqrt{x^{2}+2x+3}}dx$
Key:
Sol:
Sol:
#1786
Mathematics
Definite Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{0}^{\pi}\frac{\sin^{2026}x}{\sin^{2026}x+\cos^{2026}x}dx$
Key:
Sol:
Sol:
#1785
Mathematics
Definite Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{-\frac{\pi}{6}}^{\frac{\pi}{2}}(\sin|x|+\cos|x|)dx$
Key:
Sol:
Sol:
#1784
Mathematics
Definite Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{\frac{\pi}{12}}\frac{dx}{1+\sqrt{\cot x}}$
Key:
Sol:
Sol:
#1783
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{x-\sin x}{1-\cos x}dx$
Key:
Sol:
Sol:
#1782
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{x+3}{x^{2}+4x+5}dx$
Key:
Sol:
Sol:
#1781
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{\cos x}{(2+\sin x)(4+\sin x)}dx$
Key:
Sol:
Sol:
#1780
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\tan^{-1}(\frac{1-x}{1+x})dx$
Key:
Sol:
Sol:
#1779
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{dx}{x^{1/2}+x^{1/3}}$
Key:
Sol:
Sol:
#1778
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $\frac{d}{dx}(F(x))=\frac{1}{e^{x}+1}$ then find $F(x)$ given that $F(0)=\log\frac{1}{2}$
Key:
Sol:
Sol:
#1777
Mathematics
Integrals
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{x+2}{\sqrt{9x-x^{2}}}dx$
Key:
Sol:
Sol:
#1776
Mathematics
Applications of Derivatives
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A spherical balloon loses its volume due to escape of air from it in such a way that decrease of volume at any instant is proportional to its surface area. Show that the radius is decreasing at a constant rate.
Key:
Sol:
Sol:
#1775
Mathematics
Derivatives
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Differentiate $\tan^{-1}(\frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}})$ with respect to $\cos^{-1}x^{2}$.
Key:
Sol:
Sol:
#1774
Mathematics
Derivatives
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $xy=e^{x-y}$, then find $\frac{dy}{dx}$.
Key:
Sol:
Sol:
#1773
Mathematics
Derivatives
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $(\sin x)^{y}=y^{\cos x}$ then find $\frac{dy}{dx}$.
Key:
Sol:
Sol:
#1772
Mathematics
Matrices and Determinants
SA
2026
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $A=\begin{bmatrix}3&2&0\\1&4&0\\0&0&5\end{bmatrix}$, then compute $A^{2}-7A+10~I$.
Key:
Sol:
Sol:
#1771
Mathematics
Relations and Functions
SA
APPLY
2026
AISSCE(Board Exam)
Competency
3 Marks
Let n be a fixed positive integer. A relation R is defined in set Z such that $R=\{(x,y):(x-y) \text{ is divisible by } n, x, y\in Z\}$. Determine if R is an equivalence relation.
Key:
Sol:
Sol: