Email

Chat with tutors

Login

Ask Questions, Get Answers

Menu X

home ask tuition questions practice papers mobile tutors pricing

X

Recent questions tagged exemplar

Distance of the point $(\alpha,\beta,\gamma)$ from y-axis is

asked Jan 4, 2013 by sreemathi.v

1 answer

If $l_1,m_1,n_1,l_2,m_2,n_2,l_3,m_3,n_3$ are direction cosines of three mutually perpendicular lines,prove that the line whose direction cosines are proportional to $l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3$ make equal angles with them.

asked Jan 4, 2013 by sreemathi.v

1 answer

Show that the straight lines whose direction cosines are given by $2l+2m-n=0\;and\;mn+nl+lm=0$ are at right angles.

asked Jan 4, 2013 by sreemathi.v

1 answer

$\overrightarrow{AB}=3 \hat i-\hat j+\hat k \;and\; \overrightarrow{CD}=-3\hat i+2 \hat j+4\hat k$ are two vectors. The position vectors of the points $A$ and $C$ are $6\hat i+7\hat j+4\hat k\;and\;-9\hat j+2\hat k,$ respectively.Find the position vector of a point $P$ on the line $AB$ and a point $Q$ on the line $CD$ such that $\overrightarrow{PQ}$ is perpendicular to $\overrightarrow{AB}\;and\;\overrightarrow{CD}$ both.

asked Jan 4, 2013 by sreemathi.v

1 answer

Show that the points $ (\hat i-\hat j+3 \hat k)\; and\;3(\hat i+\hat j+\hat k)$ are equidistant from the plane $ \overrightarrow{r}.(5 \hat i+2 \hat j-7 \hat k)+9=0$ and lies on opposite side of it.

asked Jan 4, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the intersection of the planes $ \overrightarrow{r}.\quad(\hat i+3 \hat j)-6=0\; and\;\overrightarrow{r}.(3\hat i-\hat j-4 \hat k)=0,$ whose perpendicular distance from origin is unity.

asked Jan 4, 2013 by sreemathi.v

1 answer

The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle $\alpha$.Prove that the equation of the plane in its new position is $ax+by\pm \bigg(\sqrt {a^2+b^2}\tan \alpha\bigg)z=0$.

asked Jan 4, 2013 by sreemathi.v

1 answer

Find the equation of the plane which is perpendicular to the plane $5x+3y+6z+8=0$ and which contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the shortest distance between the lines given by $\overrightarrow{r}=(8+3\lambda)\hat i-(9+16\lambda)\hat j+(10+7\lambda)\hat k\; and\; \overrightarrow{r}=15\hat i+29\hat j+5\hat k+\mu(3\hat i+8\hat j-5\hat k)$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the points $(2,1,-1)$ and $(-1,3,4)$ and perpendicular to the plane $x-2y+4z=10.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equations of the line passing through the point $(3,0,1)$ and parallel to the planes $x+2y=0$ and $3y-z=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the length and the foot of perpendicular from the point$\bigg(1,\large\frac{3}{2}$$,2\bigg)$ to the plane 2x-2y+4z+5=0

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the distance of a point(2,4,-1) from the line $\large \frac{x-5}{1}\;=\frac{y-3}{4}\;=\frac{z-6}{-9}$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the foot of perpendicular from the point(2,3,-8)to the line $\Large \frac{4-x}{2}\;=\frac{y}{6}\;=\frac{1-z}{3}$.Also,find the perpendicular distance from the given point to the line.

asked Jan 3, 2013 by sreemathi.v

1 answer

Two systems of rectangular axis have the same origin.If a plane cuts them at distances a,b,c and a',b',c',respectively,from the origin,prove that\[\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{{a'}^2}+\frac{1}{{b'}^2}+\frac{1}{{c'}^2}\]

asked Jan 3, 2013 by sreemathi.v

1 answer

O is the origin and A is (a,b,c).Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

asked Jan 3, 2013 by sreemathi.v

1 answer

If a variable line in two adjacent positions has direction cosines l,m,n and $l+\delta l,m+\delta m,n+\delta n$,show that the small angle $\delta\theta$ between the two positions is given by \[\delta\theta^2=\delta l^2+\delta m^2+\delta n^2\]

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the angle between the lines whose direction cosines are given by the equations $l+m+n=0,l^2+m^2-n^2=0$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equations of the two lines through the origin which intersect the line $\;\large\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at angles of $\large \frac{\pi}{3}$ each.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the points (2,1,0),(3,-2,-2) and (3,1,7).

asked Jan 3, 2013 by sreemathi.v

1 answer

If the line drawn from the point $(-2,-1,-3)$ meets a plane at right angle at the point $(1,-3,3)$ find the equation of the plane.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which is at a distance $3\sqrt 3$ units from origin and the normal to which is equally inclined to coordinate axis.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

asked Jan 3, 2013 by sreemathi.v

1 answer

Prove that the lines $x=py+q;z=ry+s$ and $x=p'y+q';z=r'y+s'$ are perpendicular if $pp'+rr'+1=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Prove that the line through $A(0,-1,-1)$ and $B(4,5,1)$ intersects the line through $C(3,9,4)$ and $D(-4,4,4)$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the angle between the lines $r=(3\hat i+2\hat j+6\hat k) +\lambda(2\hat i+\hat j+2\hat k) \;and\; r=(2\hat i-5\hat k)+\mu(6\hat i+3\hat j+2\hat k)$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the vector equation of the line which is parallel to the vector $3\hat i+2\hat j+6\hat k$ and which passes through the point $(1,-2,3).$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the position vector of a point A in space such that $\overrightarrow{OA}$ is inclined at $60^{\circ}$ to OX and at $45^{\circ}$ to OY and $\mid \overrightarrow{OA}\mid$=10 units.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f.g is continuous at $x=a$,then f and g are separately continuous at $x=a.$

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: The composition of two continuous functions is a continuous function.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f is continuous on its domain D ,then | f | is also continuous on D.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Rolle's theorem is applicable for the function $f(x)=|x-1|$ in [0,2].

asked Jan 3, 2013 by sreemathi.v

1 answer

If $f(x)=\mid \cos x-\sin x\mid,then\;f'(\frac{\pi}{3})$=__________.

asked Jan 3, 2013 by sreemathi.v

1 answer

If $f(x)=\mid \cos x\mid$,then $f'(\frac{\pi}{4})$=____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

Derivative of $x^2$ w.r.t $x^3$ is _____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

An example of a function which is continuous everywhere but fails to be differentiable exactly at two point is ____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

For the function $f(x)=x+\large \frac{1}{x},\normalsize x\in[1,3]$,the value of c for mean value theorem is

asked Jan 3, 2013 by sreemathi.v

1 answer

The value of c in Rolle's theorem for the function $f(x)=x^3-3x$ in the interval $[0,\sqrt 3]$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

If $x=t^2$,$y=t^3,then\;\large \frac{d^2y}{dx^2}$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

The derivative of $\cos^{-1}(2x^2-1)$ w.r.t $\cos^{-1}x$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=\sqrt{sin x+y}$, then $\Large \frac{dy}{dx}$ is equal to

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=log\bigg(\large \frac{1-x^2}{1+x^2}\normalsize \bigg),then\;\large \frac{dy}{dx}$ is equal to

asked Jan 2, 2013 by sreemathi.v

1 answer

Let $f(x)=|sin x|$,then

asked Jan 2, 2013 by sreemathi.v

1 answer

If $f(x)=\left \{\begin{array}{1 1}mx+1, & if\;x\leq\large\frac{\pi}{2}\\\sin x+n, & if\;x>\large\frac{\pi}{2}\end{array}\right.$,is continuous at $x=\large\frac{\pi}{2}$,then

asked Jan 2, 2013 by sreemathi.v

1 answer

If $f(x)=x^2\sin \frac{1}{x}$,when $x\neq0$,then the value of the function f at $x=0$,so that the function is continuous at $x=0$,is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=e^{|x|}$ is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=\cot x$ is discontinuous on the set

asked Jan 2, 2013 by sreemathi.v

1 answer

The set of points where the functions f given by $f(x)=|2x-1|\sin x$ is differentiable is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=\Large \frac{4-x^2}{4x-x^3}$ is

asked Jan 2, 2013 by sreemathi.v

1 answer

Page:

« prev
1
...
31
32
33
34
35
36
37
...
42
next »

Feedback Terms Facebook Twitter About Us

Your payment for is successful.

...