Available Questions 695 found Page 14 of 35
Standalone Questions
#1321
Mathematics
Differential Equations
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation $\frac{dy}{dx}=y~cot~2x,$ given that $y(\frac{\pi}{4})=2.$
Key:
Sol:
Sol:
#1320
Mathematics
Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{3x+5}{\sqrt{x^{2}+2x+4}}dx$
Key:
Sol:
Sol:
#1319
Mathematics
Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int e^{x}[\frac{1}{(1+x^{2})^{\frac{3}{2}}}+\frac{x}{\sqrt{1+x^{2}}}]dx$
Key:
Sol:
Sol:
#1318
Mathematics
Definite Integrals
SA
APPLY
2024
AISSCE(Board Exam)
Competency
3 Marks
Evaluate $\int_{0}^{\frac{\pi}{4}}\frac{x~dx}{1+cos~2x+sin~2x}$
Key:
Sol:
Sol:
#1317
Mathematics
Derivatives
SA
2024
AISSCE(Board Exam)
3 Marks
Given that $y=(sin~x)^{x}\cdot x^{sin~x}+a^{x},$ find $\frac{dy}{dx}$
Key:
Sol:
Sol:
#1316
Mathematics
Integrals
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int\frac{1}{x(x^{2}-1)}dx.$
Key:
Sol:
Sol:
#1315
Mathematics
Applications of Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
2 Marks
The volume of a cube is increasing at the rate of $6~cm^{3}/s.$ How fast is the surface area of cube increasing, when the length of an edge is 8 cm?
Key:
Sol:
Sol:
#1314
Mathematics
Applications of Derivatives
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the interval in which the function $f(x)=x^{4}-4x^{3}+10$ is strictly decreasing.
Key:
Sol:
Sol:
#1313
Mathematics
Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $x^{y}=e^{x-y},$ prove that $\frac{dy}{dx}=\frac{log~x}{(1+log~x)^{2}}.$
Key:
Sol:
Sol:
#1312
Mathematics
Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $y=cos^{3}(sec^{2}2t)$, find $\frac{dy}{dt}$ .
Key:
Sol:
Sol:
#1311
Mathematics
Inverse Trigonometric Functions
VSA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the principal value of $tan^{-1}(1)+cos^{-1}(-\frac{1}{2})+sin^{-1}(-\frac{1}{\sqrt{2}})$
Key:
Sol:
Sol:
#1310
Mathematics
Inverse Trigonometric Functions
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Express $tan^{-1}(\frac{cos~x}{1-sin~x})$ where $\frac{-\pi}{2}<x<\frac{\pi}{2}$ in the simplest form.
Key:
Sol:
Sol:
#1309
Mathematics
Three Dimensional Geometry
LA
REMEMBER
2024
AISSCE(Board Exam)
Competency
5 Marks
The image of point $P(x,y,z)$ with respect to line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is $P^{\prime}(1,0,7)$ Find the coordinates of point P.
Key:
Sol:
Sol:
#1308
Mathematics
Applications of Integrals
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Using integration, find the area of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1,$ included between the lines $x=-2$ and $x=2$.
Key:
Sol:
Sol:
#1307
Mathematics
Definite Integrals
LA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\frac{\pi}{2}}sin~2x~tan^{-1}(sin~x)dx$
Key:
Sol:
Sol:
#1306
Mathematics
Definite Integrals
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\frac{\pi}{4}}\frac{sin~x+cos~x}{9+16~sin~2x}dx$
Key:
Sol:
Sol:
#1305
Mathematics
Matrices and Determinants
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $A=[\begin{bmatrix}-1&a&2\\ 1&2&x\\ 3&1&1\end{bmatrix}]$ and $A^{-1}=[\begin{bmatrix}1&-1&1\\ -8&7&-5\\ b&y&3\end{bmatrix}],$ find the value of $(a+x)-(b+y)$.
Key:
Sol:
Sol:
#1304
Mathematics
Matrices and Determinants
LA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
5 Marks
If $A=[\begin{bmatrix}1&-2&0\\ 2&-1&-1\\ 0&-2&1\end{bmatrix}],$ find $A^{-1}$ and use it to solve the following system of equations: $x-2y=10$, $2x-y-z=8$, $-2y+z=7$
Key:
Sol:
Sol:
#1303
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
E and F are two independent events such that $P(\overline{E})=0\cdot6$ and $P(E\cup F)=0\cdot6$ Find $P(F)$ and $P(\overline{E}\cup\overline{F})$
Key:
Sol:
Sol:
#1302
Mathematics
Linear Programming
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Solve the following linear programming problem graphically: Maximise $z=500x+300y,$ subject to constraints $x+2y\le12$, $2x+y\le12$, $4x+5y\ge20$, $x\ge0$, $y\ge0$
Key:
Sol:
Sol: