Answers posted by rvidyagovindarajan_1

0 votes

The ratio of the coefficient of $x^{10}$ in $(1-x^2)^{10}$ and the term independent of $x$ in $(x-\large\frac{2}{x}$$)^{10}$ is ?

answered Jan 23, 2014

General term in $(-1)^r.(1-x^2)^{10}$ is $^{10}C_rx^{2r}$For coefficient of $x^{10}$, $2r=10$ ...

0 votes

$ \displaystyle\sum_ {i=o} ^{{m} ^{10}} C_i ^{20}C_{m-i}$ is maximum when $m=?$

answered Jan 23, 2014

Toolbox: $^mC_i$ is coefficient of $x^i$ in the expansion of $(1+x)^m$ $^mC_r$ is ma...

0 votes

If $A,B,C$ are three points on $x\:axis,\:y\:axis\:and\:z\:axis$ respectively which are at the distances $a,b,c$ from origin respectively and $P$ is a point which is equidistant from $A,B,C,O$ then the coordinates of $P$ is?

answered Jan 23, 2014

Given: $A(a,0,0),\:B(0,b,0)\:and\:C(0,0,c)$Let $P(x,y,z)$ be equidistant from $O,A,B\:and \:C$$\R...

0 votes

) UrnAcontain1white,2black,3redballs.UrnBcontain2white,1black,1redballs.UrnC contains4white,5black,3redballs.TwoballsaredrawnfromoneoftheUrnandfoundtobeone whiteandonered.FindtheprobabilitiesthattheycomefromUrns A,Bor C.

answered Jan 16, 2014

Toolbox: Baye's Theorem :$P(E_i/E)=\large\frac{P(E_i).P(E/E_i)}{P(E_1).P(E/E_1)+P(E_2).P(E...

0 votes

A die is thrown120 times and getting 1 or 5 is considered success. Find the mean,varianceof numberofsuccesses.

answered Jan 16, 2014

Toolbox:$P(X=r)=^nC_r.p^r.q^{n-r}$This question is from Binomial distribution.Let $X$=Distribution...

0 votes

The volume of a parallelopiped formed by $\hat i+a\hat j+\hat k,\:\hat j+a\hat k\:and\:\:a\hat i+\hat k$ is minimum if $a=?$

answered Jan 13, 2014

Toolbox:Volume of a parallelopiped formed by $\overrightarrow a,\:\overrightarrow b\:and\:\overrigh...

0 votes

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:and\:\overrightarrow w=\hat i+2\hat j+3\hat k$ and $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$

answered Jan 13, 2014

Let $\overrightarrow n=x\hat i+y\hat j+z\hat k$Given: $ |\overrightarrow n|=1$ $\Rightarrow\: x^2+...

0 votes

If $\overrightarrow v=2\hat i+\hat j-\hat k\:\:and\:\;\overrightarrow w=\hat i+3\hat k$ and $\overrightarrow u$ is a unit vector,then the maximum value of $ [\overrightarrow u\:\overrightarrow v\:\overrightarrow w]$ is ?

answered Jan 13, 2014

Given: $\overrightarrow v=2\hat i+\hat j-\hat k,\:\:\overrightarrow w=\hat i+3\hat k,\:\:and \:\: |...

0 votes

If $A(4,7,8),\:B(2,3,4),\:C(2,5,7)$ are vertices of a triangle then the length of internal bisector of angle $A$ is ?

answered Jan 12, 2014

Toolbox:The internal angular bisector of angle $A$ divides the side $BC$ in the ratio $AB:AC$Give...

0 votes

Find the angle between any two diagonals of a cube.

answered Jan 12, 2014

Let the base of the cube be $O,A,B,C$ and the top face be $ D,E,F,G$so that $O$ is origin, $...

0 votes

The cosine of angle between the medians drawn from vertices of isosceles rt. angled triangle is?

answered Jan 12, 2014

Toolbox: The Angle between $\overrightarrow {AC}$ and $\overrightarrow {BD}$ is given by $...

0 votes

If from a point $P(a,b,c)$ perpendiculars $PA,\:PB,\:$ are drawn on $yz\:\:and\:\:zx$ planes. then the equation of the plane $OAB$ is ?

answered Jan 11, 2014

Given that $A$ is foot of $\perp$ of $P(a,b,c)$ on $yz$ plane and $B$ is foot of $\perp$ dr...

0 votes

If the vertices of a triangle are $A(1,4,2),\:B(-2,1,2)\:C(2,-3,4)$ then the angle $B$ = ?

answered Jan 11, 2014

Angle $B$ is angle between $\overrightarrow {BA}$ and $\overrightarrow {BC}$Given: $A(1,4,2),\:...

0 votes

The projection of a line segment on $x,y,z$ axes are $12,\:4,\:3$ respectively, then the length of the line segment is ?

answered Jan 11, 2014

Toolbox:Projection of $\overrightarrow a$ on $\overrightarrow b$ is given by $\large\frac{\overr...

0 votes

The locus of a point $(x,y,z)$ for which $z=k$ is a ?

answered Jan 11, 2014

Given that the point on the locus is such that its $z$ coordinate is constant $k$.$\therefore$ th...

0 votes

The points $(5,0,2),\:(2,-6,0),\:(4,-9,6)\:and\:(7,-3,8)$ represent vertices of a ?

answered Jan 11, 2014

Let the points be $A(5,0,2),\:B(2,-6,0),\:C(4,-9,6),\:D(7,-3,8)$$AB=\sqrt {9+36+4}=7$$BC=\sqrt{4+...

0 votes

A line segment of length $21$ has $d.r.=(2,-3,6)$ and makes obtuse angle with $x\:axis$, then the components of the line segment (vector) are?

answered Jan 10, 2014

Let the components of the line segment (vector) be $(x,y,z)$Given the length of the vector =21.$...

0 votes

If $P(2,3,4)\;and\:Q(1,b,1)$ are two points and $O$ is origin such that $OP$ is $\perp$ to $OQ$, then $b=?$

answered Jan 10, 2014

Given points are $P(2,3,4)\:\:and\:\:Q(1,b,1)$$\Rightarrow\:\overrightarrow {OP}=(2,3,4)$ and $...

0 votes

The point which divides the line joining the points $(2,4,5)\:\:and\:\:(3,5,-4)$ in the ratio $2:3$ externaly lies on the plane?

answered Jan 10, 2014

Toolbox:Section formula: The coordinates of the point, that divides $P(x_1,y_1,z_1)\:and\:Q(x_2,y...

0 votes

If the plane $x-2y+3z=0$ is rotated through a right angle about its line of intersection with the plane $2x+3y-4z-5=0$, then the eqn. of the plane in its new position is ?

answered Jan 10, 2014

Given equations of the given plane are $x-2y+3z=0$..........(i) and$2x+3y-4z-5=0$.........(ii...

0 votes

The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?

answered Jan 9, 2014

The eqn. of the lines are $x=1,\:\:y=2$.....(i) and $y=-1,\:\:z=0$.....(ii)The equations can ...

0 votes

The angle between the line formed by $3x-7y-5z=1$ and $8x-11y+2z=0$ and the line formed by $5x-13y+3z+2=0$ and $8x-11y+2z=0$

answered Jan 9, 2014

Given equations of the planes be$3x-7y-5z-1=0..........(i)$$8x-11y+2z=0........(ii)$$5x-13y+3z+2=0.....

0 votes

The equation of projection of the line $\large\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{3}$ on the plane $x+y+z=1$ is given by ?

answered Jan 9, 2014

Toolbox:Projection of a line on a plane is the line of intersection of the given plane and the plane...

0 votes

Equation of the line through the point $(2,-1,-1)$, which is parallel to the plane $4x+y+z+2=0$ ans is $\perp$ to the line $x=\large\frac{y}{-2}=$$z-5$ is ?

answered Jan 8, 2014

Given: Eqn. of the plane $4x+y+z+2=0$ ......(i)Eqn. of the line is $\large\frac{x}{1}=\frac{y}{...

0 votes

The direction cosine of a line which is $\perp$ to two perpendicular lines whose direction cosines are $(l_1,m_1,n_1)\:\:and\:\:(l_2,m_2,n_2)$ is ?

answered Jan 8, 2014

Any line $\perp$ to given two lines will be along $\overrightarrow b_1\times\overrightarrow b_2$ ...

0 votes

The equation of the plane that meets the coordinate axes at the points $A,B,C$ respectively and the centroid of the $\Delta\:ABC$ is $(2,1,5)$ is ?

answered Jan 7, 2014

Let the points on the coordinate axes, at which the plane meets be $A(a,0,0),\:\:B(0,b,0)\:\:and\:...

0 votes

The equation of the plane which makes double the intercepts of the plane $3x+6y-z+12=0$ is ?

answered Jan 7, 2014

The given plane is $3x+6y-z+12=0$Converting the eqn. into intercept form $\large\frac{x}{-4}+\frac...

0 votes

If $ \overrightarrow r\times\overrightarrow b=\overrightarrow c\times\overrightarrow b$ and $\overrightarrow r.\overrightarrow a=0$, where $\overrightarrow a=2\hat i+3\hat j-\hat k,\:\overrightarrow b=3\hat i-\hat i+\hat k\:and\:\:\overrightarrow c=\hat i+\hat j+3\hat k$, then $\overrightarrow r=?$

answered Jan 7, 2014

Let $\overrightarrow r=x\hat i+y\hat j+z\hat k$Given: $ \overrightarrow r.\overrightarrow a=0$ $\R...

0 votes

If $\overrightarrow a=(-1,1,1)\:\:\overrightarrow b=(2,0,1)\:and\:\overrightarrow x$ is vector such that $\overrightarrow x.\overrightarrow a=7,\:\overrightarrow x.\overrightarrow b=0$ and $\overrightarrow a,\overrightarrow b,\overrightarrow x$ are coplanar, then $\overrightarrow x=?$

answered Jan 7, 2014

Let the vector $\overrightarrow x=x_1\hat i+x_2\hat j+x_3\hat k$Given $\overrightarrow x,\:\overri...

0 votes

In a rt. angled triangle $ABC$ if hypotenuse, $AB=p$, then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}$= ?

answered Jan 7, 2014

Toolbox:$\overrightarrow a.\overrightarrow a=|\overrightarrow a|^2$Since $ABC$ is rt. angled $\Del...

0 votes

A vector $a\hat i+b\hat j+c\hat k$ is such that its magnitude is $ |a|+|b|+|c|$. This is possible only if

answered Jan 7, 2014

Given $ |\overrightarrow a\hat i+b\hat j+c\hat k|=|a|+|b|+|c|$$\Rightarrow\:a^2+b^2+c^2=a^2+b^...

0 votes

If $P$ is point whose position vector is $\overrightarrow r=x\hat i+y\hat j+z\hat k$ where $x,y,z \in N$ and $\overrightarrow a=\hat i+\hat j+\hat k$, then the number of possible points $P$ for which $\overrightarrow r.\overrightarrow a=10$ is ?

answered Jan 7, 2014

Since given that $\overrightarrow r.\overrightarrow a= 10,$$x+y+z=10$That is sum of three natural n...

0 votes

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

answered Jan 7, 2014

Let $\overrightarrow b=x\hat i+y\hat j+z\hat k$,Given: $\overrightarrow a.\overrightarrow b=3$$\Ri...

0 votes

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\;and\:\:\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c$ is such that $\overrightarrow c.\overrightarrow a=|\overrightarrow c|$, $|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and the angle between $\overrightarrow a\times\overrightarrow b$ and $\overrightarrow c$ is $30^{\circ}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

answered Jan 7, 2014

Given: $\overrightarrow a=2\hat i+ \hat j-2\hat k,\:\overrightarrow b=\hat i+\hat j,\:\overrightarr...

0 votes

If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

answered Jan 6, 2014

Given that $\overrightarrow a\:and\:\overrightarrow b$ are mutually $\perp$ unit vectors. $\Righta...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma $ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

answered Jan 6, 2014

Toolbox:$\overrightarrow a.\overrightarrow b=|\overrightarrow a||\overrightarrow b|cos\theta$Given: ...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are any three vectors such that $\overrightarrow a=\overrightarrow b+\overrightarrow c$ and $\overrightarrow b$ is $\perp$ to $\overrightarrow c$, then ?

answered Jan 6, 2014

Given : $\overrightarrow a=\overrightarrow b+\overrightarrow c$$\Rightarrow\:|\overrightarrow a|^2...

0 votes

A line makes angle $\theta$ with both $x\:axis$ and $z\:axis$. If it makes angle $\alpha$ with $y\:axis$ and $\sin^2\alpha=2 \sin^2\theta$ then $\cot^2\theta=?$

answered Jan 6, 2014

Since the line makes angle $\theta,\alpha\:and\:\theta$ with the coordinate axes,$cos^2\theta+cos...

0 votes

A tetrahedron has vertices $O(0,0,0),\:A(1,2,1)\:B(2,1,3)\:C(-1,1,2)$. The angle between the faces $OAB$ and $ABC$ is ?

answered Jan 6, 2014

Let $\overrightarrow n_1$ and $\overrightarrow n_2$ be the normals to the face $OAB$ and $ABC...

0 votes

The value of $k$ for which the line $\overrightarrow r=(4\hat i+2\hat j-\hat k)+\lambda(\hat i-k\hat j+2\hat k)$ lies on the plane $2x-4y+z=3$ is ?

answered Jan 6, 2014

For any line to lie on a plane, two conditions are to be satisfied.1. Every point on the line ($\ov...

0 votes

The value of $k$ for which the line $\large\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ to lie on the plane $2x-4y+3z=6$ is ?

answered Jan 6, 2014

For any line to lie on a plane, two conditions are to be satisfied.1. The line should be $\perp$ ...

0 votes

A line with direction ratio $(2,1,2)$ meets the lines $x=y+a=z\:\;and\:\:x+a=2y=2z$. The coordinates of the points of intersections are ?

answered Jan 6, 2014

Out of the four options, option $ (b) \: (3a,2a,3a)\:and\:(a,a,a)$ is the correct answer. Becau...

0 votes

A variable plane is at a distance $k$ from origin and meets the coordinate axes at the points $A,B,C$ respectively. then the locus of centroid of the $\Delta\:ABC$ is ?

answered Jan 6, 2014

Toolbox:Centroid of triangle with vertices $A(x_1,y_1,z_1),\:B(x_2,y_2,z_2)\:\:and\:\:C(x_3,y_3,z_3)...

0 votes

The equation of the plane passing through the point $(1,1,1)$ and having direction ratios $b,c,a$ $(a < b < c)$, where $a,b,c$ are prime factors of $2001$ is ?

answered Jan 6, 2014

The prime factors of $2001$ are $3,23\:and\:29$ Equation ofa plane passing through the poin...

0 votes

If $P(0,1,0)\:and\:Q(0,0,1)$ are two points in space, then the projection of $PQ$ on the plane $x+y+z=3$ is ?

answered Jan 6, 2014

Toolbox:Projection of a line segment $PQ$ on any plane is $PQ\:cos\theta$ where $\theta$ is ang...

0 votes

Distance of a point $P(\overrightarrow c)$ from the the line $\overrightarrow r=\overrightarrow a+\lambda \overrightarrow b$ is ?

answered Jan 6, 2014

Toolbox:$|\overrightarrow a\times\overrightarrow b|^2=|\overrightarrow a|^2 |\overrightarrow b|^2-(\...

0 votes

If the vectors $\overrightarrow a+\lambda \overrightarrow b+3\overrightarrow c,\:-2\overrightarrow a+3\overrightarrow b-4\overrightarrow c\:and\:\overrightarrow a-3\overrightarrow b+5\overrightarrow c$ are coplanar and $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non coplanar, then $\lambda=?$

answered Jan 6, 2014

Given that $\overrightarrow x=\overrightarrow a+\lambda \overrightarrow b+3\overrightarrow c,\:\ove...

0 votes

A vector $\overrightarrow a$ is parallel to the line of intersection of planes $P_1$ containing vectors $\hat i,\:\hat i+\hat j$ and $P_2$ conataining vectors $\hat i-\hat j,\:\hat i+\hat k$. Then the angle between $\overrightarrow a$ and $\hat i-2\hat j+2\hat k$ is?

answered Jan 5, 2014

Since it is given that plane $P_1$ contains $\hat i\:\:and\:\:\hat i+\hat j$,normal to this plan...

0 votes

The vectors $\overrightarrow a,\overrightarrow b,\overrightarrow c\:\overrightarrow d$ be are such that $(\overrightarrow a\times\overrightarrow b)\times (\overrightarrow c\times\overrightarrow d)=0$ and $P_1,\:P_2$ are two planes containing the pair of vectors $\overrightarrow a,\overrightarrow b$ and $\overrightarrow c,\overrightarrow d$ respectively, then the angle between the planes is ?

answered Jan 5, 2014

Toolbox:Normal to a plane is $\perp$ all the vectors on the plane.Since it is given that $\overrigh...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are the sides $BC,CA\:and \:AB$ respectively of the $\Delta \:ABC$, then

answered Jan 5, 2014

Toolbox:In any $\Delta\:ABC$, $\overrightarrow {BC}+\overrightarrow {CA}+\overrightarrow {AB}=0$In...

Ask Questions, Get Answers