Available Questions 601 found Page 10 of 31
Standalone Questions
#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:
#1301
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find the particular solution of the differential equation given by $x^{2}\frac{dy}{dx}-xy=x^{2}cos^{2}(\frac{y}{2x})$ given that when $x=1$, $y=\frac{\pi}{2}$
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:
#1294
Mathematics
Vector Algebra
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
2 Marks
In the given figure, ABCD is a parallelogram. If $\vec{AB}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{DB}=3\hat{i}-6\hat{j}+2\hat{k}$ , then find $\vec{AD}$ and hence find the area of parallelogram ABCD.
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: