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Recent questions tagged easy

$\tan^{-1}x+\tan^{-1}y=c$ is the general solution of the differential equation:

asked Jan 18, 2013 by sreemathi.v

1 answer

Which of the following is a second order differential equation\begin{array}{1 1}(A)\;(y')^2+x=y^2 & (B)\;y' y''+y=\sin x\\(C)\;y'''+(y'')^2+y=0 & (D)\;y'=y^2\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of $x\Large \frac{dx}{dy}\normalsize-y=x^4-3x$ is \[(A)\;x\quad(B)\;log x\quad(C)\;\frac{1}{x}\quad(D)\;-x\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Family $y=Ax+A^3$ of curves is represented by the differential equation of degree\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solution of differential equation $x dy-y dx=0$ represents:

asked Jan 18, 2013 by sreemathi.v

1 answer

The differential equation for $y=A\cos\alpha x+B\sin\alpha x,$where A and B are arbitrary constants is\begin{array}{1 1}(A)\;\frac{d^2y}{dx^2}+x^2y=0 & (B)\;\frac{d^2y}{dx^2}+\alpha^2y=0\\(C)\;\frac{d^2y}{dx^2}+y=0 & (D)\;\frac{d^2y}{dx^2}-y=0\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

The order and degree of the differential equation $\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx}\bigg)^{\frac{1}{4}}+x^{\frac{1}{5}}=0$,respectively,are\[(A)\;2\;and\;not\;defined\quad(B)\;2\;and\;2\quad(C)\;2\;and\;3\quad(D)\;3\;and\;3\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The degree of the differential equation $1+\bigg[\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^{\large\frac{3}{2}}=\frac{d^2y}{dx^2}$ is:\[(A)\;4\quad(B)\;\frac{3}{2}\quad(C)\;not\;defined\quad(D)\;2\]

asked Jan 18, 2013 by sreemathi.v

1 answer

The degree of the differential equation $\large\bigg(\frac{d^2y}{dx^2}\bigg)^2+\bigg(\frac{dy}{dx}\bigg)^2$$=x\sin \bigg(\large\frac{dy}{dx}\bigg)$ is:\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;not\;defined\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the differential equation of system of concentric circles with centre(1,2).

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of $(x+2y^3)\Large \frac{dy}{dx}\normalsize =y \;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $\Large \frac{dy}{dx}\normalsize=1+x+y^2+xy^2,$when y=0,x=0.

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve:$y\;dx-x\;dy=x^2y\;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $\Large\frac{dy}{dx}\normalsize+1=e^{x+y}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation$\Large \frac{dy}{dx}\normalsize =2xy-y$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the differential equation of all non vertical lines in a plane.

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the solution of $\Large \frac{dy}{dx}\normalsize =2^{y-x}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-false: If $\overrightarrow{a}$ and $\overrightarrow{b}$ are adjacent sides of a rhombus,then $\overrightarrow{a}.\overrightarrow{b}=0$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: The formula $(\overrightarrow{a}+\overrightarrow{b})^2=\mid{\overrightarrow{a}\mid}^2+\mid{\overrightarrow{b}\mid}^2\;+2\mid\overrightarrow{a}\mid.\mid\overrightarrow{b}\mid$ is valid for non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: If $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid \overrightarrow{a}-\overrightarrow{b}\mid$,then the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are orthogonal.

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: Position vector of a point P is a vector whose initial point is origin.

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: If $\mid\overrightarrow{ a}\mid=\mid\overrightarrow {b}\mid$,then necessarily it implies $\overrightarrow{ a}=\overrightarrow {b}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow a$ is any non-zero vector ,then $(\overrightarrow a.\hat i)\hat i\;+(\overrightarrow a.\hat j)\hat j\;+(\overrightarrow a.\hat k)\hat k$ equals__________.

asked Jan 17, 2013 by sreemathi.v

1 answer

The value of the expression ${\mid \overrightarrow{a}\times \overrightarrow{b}\mid}^2+(\overrightarrow{a}.\overrightarrow{b})^2$ is _________.

asked Jan 17, 2013 by sreemathi.v

1 answer

The number of vectors of unit length perpendicular to the vectors $\overrightarrow{a}=2\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=\hat j+\hat k$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\mid\overrightarrow{a}\mid=4$ and $-3\leq\:\lambda\leq 2$,then the range of $\mid\lambda\overrightarrow{a}\mid$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$ and $\mid\overrightarrow{a}\mid=.2, \mid\overrightarrow{b}\mid=3,\mid\overrightarrow{c}\mid=5$,then value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

Projection vector of $\overrightarrow{a}$ on $\overrightarrow{b}$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are unit vectors such that$\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$,then the value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector $\hat i+\lambda\hat j+\hat k,\hat i+\hat j-\hat k$ and $3\hat i+6\hat j-5\hat k$ are coplanar if

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

For any vector $\overrightarrow{a}$,the value of $(\overrightarrow{a}.\hat i)^2+ (\overrightarrow{a}.\hat j)^2+ (\overrightarrow{a}.\hat k)^2 $ is equal to

asked Jan 17, 2013 by sreemathi.v

1 answer

The value of $\lambda$ for which the vectors $3\hat i+6\hat j+\hat k $ and $ 2\hat i+4\hat j+\lambda\hat k$ are parallel is

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the value of $\lambda$ such that the vectors $\overrightarrow{a}=2\hat i+\lambda\hat j+\hat k$ and $\overrightarrow{b}=\hat i+2\hat j+3\hat k$ are orthogonal

asked Jan 17, 2013 by sreemathi.v

1 answer

The angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with magnitudes $\sqrt 3$ and 4,respectively,and $\overrightarrow{a}.\overrightarrow{b}=2\sqrt 3$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is

asked Jan 17, 2013 by sreemathi.v

1 answer

The position vector of the point which divides the join of points $2\overrightarrow{a}-3\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ in the ratio 3:1 is

asked Jan 17, 2013 by sreemathi.v

1 answer

If \( \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} \), then find x?

asked Jan 17, 2013 by thanvigandhi_1

1 answer

The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the angle between the vectors $2\hat i\;-\hat j\;-\hat k$ and $3\hat i\;+4\hat j\;+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ is inclined at equal angles to the three axes.If the magnitude of $\overrightarrow{r}$ is $2\sqrt 3$ units,find $\overrightarrow{r}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find a unit vector in the direction of $\overrightarrow{PQ},$where $P$ and $Q$ have co-ordinates $(5,0,8)$ and $(3,3,2)$,respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}=\hat i-\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i-\hat j-2\hat k,$then find the unit vector in the direction of $ 6 \overrightarrow{b} $

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the unit vector in the direction of sum of vectors $\overrightarrow{a}=2\hat i+\hat j+\hat k\;and\;\overrightarrow{b}=2\hat j-\hat k$

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $x=2y+3$ and the y-lines $y=1$ and $y=-1$ is \[(A)\;4 sq.units\quad(B)\;\frac{3}{2} sq. units\quad(C)\;6 sq.units\quad(D)8 sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

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