Available Questions 559 found Page 12 of 28
Standalone Questions
#1339
Mathematics
Three Dimensional Geometry
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the vector equation of the line passing through the point (2, 3, -5) and making equal angles with the co-ordinate axes.
Key:
Sol:
Sol:
#1338
Mathematics
Integrals
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int\frac{1}{5+4x-x^{2}}dx$
Key:
Sol:
Sol:
#1337
Mathematics
Integrals
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int cos^{3}x~e^{log~sin~x}dx$
Key:
Sol:
Sol:
#1335
Mathematics
Continuity and Differentiability
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Check for differentiability of the function f defined by $f(x)=|x-5|$, at the point $x=5$.
Key:
Sol:
Sol:
#1334
Mathematics
Continuity and Differentiability
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Verify whether the function f defined by $f(x)=\begin{cases}x~sin(\frac{1}{x}),x\ne0\\ 0&,x=0\end{cases}$ is continuous at $x=0$ or not.
Key:
Sol:
Sol:
#1329
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.
Key:
Sol:
Sol:
#1328
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Let $A=R-\{5\}$ and $B=R-\{1\}$. Consider the function $f:A\rightarrow B$, defined by $f(x)=\frac{x-3}{x-5}$ Show that f is one-one and onto.
Key:
Sol:
Sol:
#1327
Mathematics
Applications of Integrals
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Using integration, find the area bounded by the ellipse $9x^{2}+25y^{2}=225$, the lines $x=-2,$ $x=2$, and the X-axis.
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:
#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:
#1316
Mathematics
Integrals
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int\frac{1}{x(x^{2}-1)}dx.$
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:
#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: