Available Questions 833 found Page 21 of 42
Standalone Questions
#1325
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.
Key:
Sol:
Sol:
#1324
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
A card from a well shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.
Key:
Sol:
Sol:
#1323
Mathematics
Linear Programming
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically: Maximise $Z=2x+3y$ subject to the constraints: $x+y\le6$, $x\ge2$, $y\le3$, $x,y\ge0$
Key:
Sol:
Sol:
#1322
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find the particular solution of the differential equation $(xe^{\frac{y}{x}}+y)dx=x~dy$, given that $y=1$ when $x=1$
Key:
Sol:
Sol:
#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:
#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: