Available Questions 450 found Page 6 of 23
Standalone Questions
#1344
Mathematics
Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{2x+1}{(x+1)^{2}(x-1)}dx$
Key:
Sol:
Sol:
#1343
Mathematics
Definite Integrals
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate : $\int_{0}^{\pi}\frac{e^{cos~x}}{e^{cos~x}+e^{-cos~x}}d~x$
Key:
Sol:
Sol:
#1342
Mathematics
Derivatives
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $x=a~sin^{3}\theta$, $y=b~cos^{3}\theta$ then find $\frac{d^{2}y}{dx^{2}}$ at $\theta=\frac{\pi}{4}$
Key:
Sol:
Sol:
#1341
Mathematics
Derivatives
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $\sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y)$, prove that $\frac{dy}{dx}=\sqrt{\frac{1-y^{2}}{1-x^{2}}}$
Key:
Sol:
Sol:
#1340
Mathematics
Derivatives
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find $\frac{dy}{dx}$ , if $(cos~x)^{y}=(cos~y)^{x}.$
Key:
Sol:
Sol:
#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:
#1333
Mathematics
Inverse Trigonometric Functions
VSA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find value of k if $sin^{-1}[k~tan(2~cos^{-1}\frac{\sqrt{3}}{2})]=\frac{\pi}{3}.$
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: