Match the items of Column-I with those in Column II.
\begin{tabular}{|l|l|l|l|}
\hline \multicol....
Match the items of Column-I with those in Column II.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & \begin{tabular}{l}
The solution of \\
\( \cos (x+y) d y=d x \) is
\end{tabular} & (p) & \( y=\tan \left(\frac{x+y}{2}\right)+c \) \\
\hline (B) & \begin{tabular}{l}
The general solution of \\
the differential equation \\
\( (x+y) d x+x d y=0 \) is
\end{tabular} & (q) & \( y\left(1+x^{3}\right)=\frac{x}{2}-\frac{1}{4} \sin 2 x+c \) \\
\hline (C) & \begin{tabular}{l}
The solution of the equation \\
\( \frac{d y}{d x}=\frac{y}{x}\left(\log \frac{y}{x}+1\right) \) is
\end{tabular} & (r) & \( \log \left(\frac{y}{x}\right)=c x \) \\
\hline (D) & \begin{tabular}{l}
The solution of the \\
differential equation \\
\( \frac{d y}{d x}+\frac{3 x^{2}}{1+x^{3}} y=\frac{\sin ^{2} x}{1+x^{3}} \) is
\end{tabular} & (s) & \( x^{2}+2 x y=c \) \\
\hline
\end{tabular}
(1) (A) \( \rightarrow(\mathrm{r}),(\mathrm{B}) \rightarrow(\mathrm{s}),(\mathrm{C}) \rightarrow(\mathrm{q}),(\mathrm{D}) \rightarrow(\mathrm{p}) \)
(2) (A) \( \rightarrow \) (p), (B) \( \rightarrow \) (s), (C) \( \rightarrow \) (r), (D) \( \rightarrow \) (q)
(3) (A) \( \rightarrow \) (s), (B) \( \rightarrow \) (p), (C) \( \rightarrow \) (r), (D) \( \rightarrow \) (q)
(4) (A) \( \rightarrow \) (p), (B) \( \rightarrow \) (q), (C) \( \rightarrow \) (s), (D) \( \rightarrow \) (r)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2024-01-22 | If a vector \( \vec{r} \) satisfies the equation \( \vec{r} \times(\hat{i}+2 \hat{j}+\hat{k})=\h.... |
| 2024-01-22 | What is the distance between the planes \( x-2 y+z-1=0 \) and \( -3 x+6 y-3 z+2=0 \) ?.... |
| 2024-01-22 | If a line makes angles \( \alpha, \beta \) and \( \gamma \) with the coordinate axes, then \( \c.... |
| 2024-01-22 | \( \vec{a} \) and \( \vec{c} \) are unit vectors and \( |\vec{b}|=4 \) with \( \vec{a} \times \v.... |
| 2024-01-22 | Let the unit vectors \( a \) and \( b \) be perpendicular and the unit vector \( c \) be incline.... |
| 2024-01-22 | The vectors \( a, b \) and \( c \) are equal in length and taken pairwise, make equal angles. If.... |
| 2024-01-22 | The volume of the tetrahedron whose vertices are the points with position vectors \( i-6 j+10 k,.... |
| 2024-01-22 | The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mat.... |
| 2024-01-22 | The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mat.... |
| 2024-01-22 | If the vector \( 2 i-3 j+7 k \) is inclined at angles \( \alpha, \beta, \gamma \) with the coord.... |
| 2024-01-22 | Match the items of Column-I with those in Column II.
\begin{tabular}{|l|l|l|l|}
\hline \multicol.... |
| 2024-01-22 | The points \( (0,7,10),(-1,6,6) \) and \( (-4,9,6) \) are the vertices of.... |
| 2024-01-22 | For non-coplanar vectors \( a, b \) and \( c,|(a \times b) . \mathrm{c}|=|a| \)
\( |b||c| \) hol.... |
| 2024-01-22 | \( P(1,1,1) \) and \( Q(\lambda, \lambda, \lambda) \) are two points in the space such that \( P.... |
| 2024-01-22 | \( P(0,5,6), Q(1,4,7) . R(2,3,7) \) and \( S(3,4,6) \) are four points in the space. The point f.... |
| 2024-01-22 | Match the entries of Column-I with those of
Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multic.... |
| 2024-01-22 | If \( r \) satisfies the equation \( r \times(i+2 j+k)=i-k \), then for any scalar \( t, r \) is.... |
| 2024-01-22 | The vectors \( A B=3 i-2 j+2 k \) and \( B C=-i-2 k \) are the adjacent sides of a parallelogram.... |
| 2024-01-22 | \( \left(x^{2}+y^{2}\right) d y=x y d x \). If \( y\left(x_{0}\right)=e, y(1)=1 \), then value o.... |
| 2024-01-22 | The area of a parallelogram having diagonals \( a=3 i \) \( +j-2 k \) and \( b=i-3 j+4 k \) is.... |
| 2024-01-22 | If \( y \cos x+x \cos y=\pi \), then \( y^{\prime \prime}(0) / \pi \) is
\( P \).... |
0