Available Questions 559 found Page 13 of 28
Standalone Questions
#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:
#1287
Mathematics
Applications of Integrals
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $A_{1}$ denotes the area of region bounded by $y^{2}=4x,$ $x=1$ and x-axis in the first quadrant and $A_{2}$ denotes the area of region bounded by $y^{2}=4x,$ $x=4$, find $A_{1}:A_{2}$.
Key:
Sol:
Sol:
#1286
Mathematics
Matrices and Determinants
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
If $A=\begin{bmatrix}1&cot~x\\ -cot~x&1\end{bmatrix}$ show that $A^{\prime}A^{-1}=\begin{bmatrix}-cos~2x&-sin~2x\\ sin~2x&-cos~2x\end{bmatrix}$
Key:
Sol:
Sol:
#1283
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A relation R is defined on $N\times N$ (where N is the set of natural numbers) as: $(a, b)~R~(c,d)\Leftrightarrow a-c=b-d$ Show that R is an equivalence relation.
Key:
Sol:
Sol:
#1282
Mathematics
Relations and Functions
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Show that a function $f:R\rightarrow R$ defined by $f(x)=\frac{2x}{1+x^{2}}$ is neither one-one nor onto. Further, find set A so that the given function $f:R\rightarrow A$ becomes an onto function.
Key:
Sol:
Sol:
#1281
Mathematics
Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int x^{2}\cdot sin^{-1}(x^{3/2})dx$
Key:
Sol:
Sol:
#1280
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A pair of dice is thrown simultaneously. If X denotes the absolute difference of the numbers appearing on top of the dice, then find the probability distribution of X.
Key:
Sol:
Sol:
#1278
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the general solution of the differential equation : $y~dx=(x+2y^{2})~dy$
Key:
Sol:
Sol:
#1277
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation given by $2xy+y^{2}-2x^{2}\frac{dy}{dx}=0$ $y=2$, when $x=1.$
Key:
Sol:
Sol: