Available Questions 450 found Page 7 of 23
Standalone Questions
#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:
#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:
#1300
Mathematics
Definite Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{1}^{3}(|x-1|+|x-2|+|x-3|)dx$
Key:
Sol:
Sol:
#1299
Mathematics
Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{x^{2}}{(x^{2}+4)(x^{2}+9)}dx$
Key:
Sol:
Sol:
#1298
Mathematics
Derivatives
SA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $y=(tan~x)^{x}$, then find $\frac{dy}{dx}$ .
Key:
Sol:
Sol:
#1297
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:
#1296
Mathematics
Relations and Functions
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A function f is defined from $R\rightarrow R$ as $f(x)=ax+b$, such that $f(1)=1$ and $f(2)=3$ Find function $f(x)$. Hence, check whether function $f(x)$ is one-one and onto or not.
Key:
Sol:
Sol:
#1295
Mathematics
Relations and Functions
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A relation R on set $A=\{1,2,3,4,5\}$ is defined as $R=\{(x,y):|x^{2}-y^{2}|<8\}$. Check whether the relation R is reflexive, symmetric and transitive.
Key:
Sol:
Sol:
#1293
Mathematics
Vector Algebra
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $(\vec{a}+\vec{b})\perp\vec{a}$ and $(2\vec{a}+\vec{b})\perp\vec{b}$ , then prove that $|\vec{b}|=\sqrt{2}|\vec{a}|$.
Key:
Sol:
Sol:
#1292
Mathematics
Definite Integrals
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Evaluate: $\int_{0}^{\frac{\pi^{2}}{4}}\frac{sin\sqrt{x}}{\sqrt{x}}dx$
Key:
Sol:
Sol:
#1291
Mathematics
Integrals
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int x\sqrt{1+2x}dx$
Key:
Sol:
Sol:
#1290
Mathematics
Applications of Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Show that the function $f(x)=4x^{3}-18x^{2}+27x-7$ has neither maxima nor minima.
Key:
Sol:
Sol:
#1289
Mathematics
Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $y=\sqrt{tan\sqrt{x}}$ , prove that $\sqrt{x}\frac{dy}{dx}=\frac{1+y^{4}}{4y}$
Key:
Sol:
Sol:
#1288
Mathematics
Continuity and Differentiability
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Check whether the function $f(x)=x^{2}|x|$ is differentiable at $x=0$ or not.
Key:
Sol:
Sol: