Available Questions 450 found Page 8 of 23
Standalone Questions
#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:
#1276
Mathematics
Integrals
SA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find: $\int\frac{1}{x[(log~x)^{2}-3~log~x-4]}dx$
Key:
Sol:
Sol:
#1275
Mathematics
Definite Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate : $\int_{-2}^{2}\sqrt{\frac{2-x}{2+x}}dx$
Key:
Sol:
Sol:
#1274
Mathematics
Derivatives
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Show that: $\frac{d}{dx}(|x|)=\frac{x}{|x|},x\ne0$
Key:
Sol:
Sol:
#1273
Mathematics
Derivatives
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $x=e^{cos~3t}$ and $y=e^{sin~3t}$ , prove that $\frac{dy}{dx}=-\frac{y~log~x}{x~log~y}$
Key:
Sol:
Sol:
#1272
Mathematics
Applications of Derivatives
VSA
ANALYZE
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Show that $f(x)=e^{x}-e^{-x}+x-tan^{-1}x$ is strictly increasing in its domain.
Key:
Sol:
Sol:
#1271
Mathematics
Integrals
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find: $\int\frac{e^{4x}-1}{e^{4x}+1}dx$
Key:
Sol:
Sol:
#1270
Mathematics
Applications of Derivatives
VSA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If M and m denote the local maximum and local minimum values of the function $f(x)=x+\frac{1}{x}(x\ne0)$ respectively, find the value of $(M-m)$
Key:
Sol:
Sol:
#1269
Mathematics
Derivatives
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $y=cosec(cot^{-1}x)$, then prove that $\sqrt{1+x^{2}}\frac{dy}{dx}-x=0$ .
Key:
Sol:
Sol:
#1267
Mathematics
Inverse Trigonometric Functions
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the domain of the function $f(x)=sin^{-1}(x^{2}-4).$ Also, find its range.
Key:
Sol:
Sol:
#1266
Mathematics
Inverse Trigonometric Functions
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find the value of $tan^{-1}(-\frac{1}{\sqrt{3}})+cot^{-1}(\frac{1}{\sqrt{3}})+tan^{-1}[sin(-\frac{\pi}{2})]$
Key:
Sol:
Sol:
#1263
Mathematics
Applications of Integrals
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Using integration, find the area of the region enclosed between the circle $x^{2}+y^{2}=16$ and the lines $x=-2$ and $x=2.$
Key:
Sol:
Sol:
#1260
Mathematics
Relations and Functions
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A relation R on set $A=\{-4,-3,-2,-1,0,1,2,3,4\}$ be defined as $R=\{(x,y):x+y$ is an integer divisible by 2). Show that R is an equivalence relation. Also, write the equivalence class [2].
Key:
Sol:
Sol: