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Questions asked by rvidyagovindarajan_1
Questions
870
questions
0
answers selected
$|\overrightarrow a\times\overrightarrow b|^2= ?$ (which one of the following )
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q75
asked
Dec 3, 2013
1
answer
If vector $\overrightarrow a$ is unit vector and it makes angle $\large\frac{\pi}{4}$ with $\hat k$ and $\overrightarrow a+\hat i+\hat j$ is also a unit vector, then $\overrightarrow a=?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q74
asked
Dec 3, 2013
1
answer
If $D\:\:and\:\:E$ are mid points of the side $\overline {AB}\:\:and\:\:\overline {AC}$ of a $\Delta \:ABC$, then $\overrightarrow {BE}+\overrightarrow {DC}=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q73
asked
Dec 3, 2013
1
answer
If sum of two unit vectors is also a unit vector then the magnitude of their difference is ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q72
asked
Dec 3, 2013
1
answer
If $\overrightarrow {AB}=3\hat i+\hat j-2\hat k,\:and \:\overrightarrow {AC}=-\hat i+3\hat j+4\hat k$ are two sides af the $\Delta ABC$, then the length of the median through $A$ is ?
jeemain
math
class12
ch13
vector-algebra
medium
q71
asked
Dec 1, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j+\hat k,\:\overrightarrow b=\hat i\:\:and\:\:\overrightarrow c=x\hat i-\hat j+\hat k$, then the value of $x$ for which $\overrightarrow a\:\overrightarrow b\:and\:\overrightarrow c$ are coplanar is ?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q70
asked
Dec 1, 2013
1
answer
The term independent of $x$ in the expansion $\bigg(\large\frac{x+1}{x^{\large\frac{2}{3}}-x^{\large\frac{1}{3}}+1}-\frac{x-1}{x-\sqrt x}\bigg)^{10}$ is ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
asked
Dec 1, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are three vectors of magnitude $3,4,5$ respectively. If each vector is $\perp$ to sum of the other two vectors then $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q69
asked
Nov 30, 2013
1
answer
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q68
asked
Nov 30, 2013
1
answer
If $ |\overrightarrow a+\overrightarrow b|=|\overrightarrow a|$, then the angle between $2\overrightarrow a+\overrightarrow b$ and $\overrightarrow b$ is ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q67
asked
Nov 29, 2013
1
answer
If $\overrightarrow a= x^2\hat i+2\hat j-2\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k\;and\:\overrightarrow c=x^2\hat i+5\hat j-4\hat k$ are three vectors, then the values of $x$ for which the angle between $\overrightarrow a\:and\:\overrightarrow b$ is acute and that between $\overrightarrow b\:and\:\overrightarrow c$ is obtuse is ?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q66
asked
Nov 29, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are non coplanar vectors and if $\overrightarrow a'=\large\frac{\overrightarrow b\times \overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\overrightarrow b'=\large\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:and \:\overrightarrow c'=\large\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow a.\overrightarrow a'+\overrightarrow b.\overrightarrow b'+\overrightarrow c.\overrightarrow c'=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q65
asked
Nov 29, 2013
1
answer
For any vector $\overrightarrow a\:\:and\:\:\overrightarrow b$ the angle between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ and $|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a$ is ?
jeemain
math
class12
vector-algebra
ch10
easy
vector-product
q64
asked
Nov 29, 2013
1
answer
If the vectors $p\hat i+\hat j+\hat k,\:\hat i+q\hat j+\hat k,\: \:and\:\:\hat i+\hat j+r\hat k$ $(p\neq q\neq r\neq 1)$ are three coplanar vectors then the value of $pqr-(p+q+r)=?$
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q63
asked
Nov 29, 2013
1
answer
The value of $a$ for which the volume of the parallelopiped formed by the vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k,\:\:a\hat i+\hat k$ is minimum is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q62
asked
Nov 28, 2013
1
answer
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 if $\hat n$ is a unit vector such that $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$, then $|\overrightarrow w.\hat n|=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q61
asked
Nov 28, 2013
1
answer
If in the expansion of $(x+a)^{15},$ the $11^{th}$ term is $G.M.$ of $8^{th} $ & $12^{th}$ terms, then which term is the greatest term?
jeemain
math
class11
ch8
binomial-theorem
properties-and-application
medium
asked
Nov 24, 2013
1
answer
If the sum of $5^{th}\:and\:6^{th}$ terms in the expansion of $(a-b)^n$, $n\geq5$, is 0, then $\large\frac{a}{b}$ = ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
asked
Nov 24, 2013
1
answer
If the sum of the coefficients of $(1+x)^n=4096$, then the largest coefficient is ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
asked
Nov 24, 2013
1
answer
The value of $^nC_0.^{2n}C_r$ - $^nC_1^{2-2}C_r$ + $^nC_2.^{2n-4}C_r$ - ...., if $r \lt n$ is
jeemain
math
class11
ch8
binomial-theorem
properties-and-application
difficult
asked
Nov 24, 2013
1
answer
Coeff. of $x^{50}$ in $(1+x)^{1000}$ + $x(1+x)^{999}$ + $x^2(1+x)^{998}$ + .... + $x^{1000}$ is
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
asked
Nov 23, 2013
1
answer
In how many ways can a mixed doubles game in tennis can be arranged from 5 couples, if no husband and wife play in the same game?
jeemain
math
class11
ch7
permutations-and-combinations
combinations
medium
mock
asked
Nov 23, 2013
1
answer
If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are non coplanar vectors and $p,q$ are real numbers so that $[3\overrightarrow u\:p\overrightarrow v\:p\overrightarrow w]-[p\overrightarrow v\:p\overrightarrow w\:q\overrightarrow u]-[2\overrightarrow w\:q\overrightarrow v\:q\overrightarrow u]=0$ then number of values of $p,q$ is
jeemain
math
class12
ch13
vector-algebra
medium
q60
asked
Nov 22, 2013
1
answer
$53^{53} - 33^{33}$ is divisible by
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
asked
Nov 22, 2013
1
answer
If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q59
asked
Nov 21, 2013
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
vector-product
q58
asked
Nov 21, 2013
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q57
asked
Nov 21, 2013
1
answer
If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q56
asked
Nov 20, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j,\:\:\overrightarrow b=2\hat j-\hat k$ and $\overrightarrow r\times \overrightarrow a=\overrightarrow b\times\overrightarrow a,\:\:\overrightarrow r\times\overrightarrow b=\overrightarrow a\times\overrightarrow b$ then a unit vector in the direction of $\overrightarrow r$ is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q55
asked
Nov 20, 2013
1
answer
If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit non collinear vectors and if $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b$ and $\overrightarrow v=\overrightarrow a\times\overrightarrow b$ then $ |\overrightarrow v|= ?$
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q54
asked
Nov 20, 2013
1
answer
If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2 $ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q53
asked
Nov 20, 2013
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non zero, non collinear vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow b\times\overrightarrow c=\overrightarrow c\times\overrightarrow a$, then $\overrightarrow a+\overrightarrow b+\overrightarrow c=?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q52
asked
Nov 19, 2013
1
answer
If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$, then $a,b,c$ should be ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q51
asked
Nov 19, 2013
1
answer
If $\overrightarrow a\:and\:\overrightarrow c$ are unit and collinear vectors and $|\overrightarrow b|=6$, then $\overrightarrow b-3\overrightarrow c=\lambda \overrightarrow a,$ if $\lambda=?$
jeemain
math
class12
ch10
vector-algebra
difficult
scalar-product
q50
asked
Nov 19, 2013
1
answer
If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$, then $\overrightarrow c.\overrightarrow b=?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q49
asked
Nov 19, 2013
1
answer
If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q48
asked
Nov 18, 2013
1
answer
If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are three vectors such that $|\overrightarrow u|=1,\:|\overrightarrow v|=2,\:|\overrightarrow w|=3$ and if the projection of $\overrightarrow v$ along $\overrightarrow u$ is equal to that of $\overrightarrow w$ along $\overrightarrow u$ and also if $\overrightarrow u$ and $\overrightarrow v$ are $\perp$ to each other, then $ |\overrightarrow u-\overrightarrow v+\overrightarrow w|= ?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q47
asked
Nov 18, 2013
1
answer
The value of $[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]$ where $|\overrightarrow a|=1,\:\:|\overrightarrow b|=5\:\:|\overrightarrow c|=3$ is ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q46
asked
Nov 18, 2013
1
answer
The greatest value of $|\overrightarrow a+\overrightarrow b|+|\overrightarrow a-\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors is ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q45
asked
Nov 18, 2013
1
answer
If $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$, then the value of $\lambda$ for which $\overrightarrow c=\lambda\hat i+\hat j+(2\lambda+1)\hat k$ is parallel to the plane containing $\overrightarrow a\:\:and\:\:\overrightarrow b$ is
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q44
asked
Nov 15, 2013
1
answer
If $\overrightarrow a,\overrightarrow b\:\overrightarrow c$ are three vectors of equal magnitude and angle between $\overrightarrow a\:and\:\overrightarrow b$ is $\alpha$, that between $\overrightarrow b\:\overrightarrow c$ is $\beta$, and that between $\overrightarrow a\:and\:\overrightarrow c$ is $\gamma$ then the minimum value of $cos\alpha+cos\beta+cos\gamma$ is ?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q43
asked
Nov 15, 2013
1
answer
If $\overrightarrow {OA}=\hat i+3\hat j-2\hat k\:\:and\:\:\overrightarrow {OB}=3\hat i+\hat j-2\hat k$ and $\overrightarrow {OC} $ is angular bisector of angle $AOB$ with $C$ being the point on the line $AB$, then $\overrightarrow {OC}=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q42
asked
Nov 13, 2013
1
answer
If $a,b,c$ are lengths of sides of a $\Delta\:ABC$ and for any non collinear vectors $\overrightarrow u\:\:and\:\:\overrightarrow v$ if $(a-b)\overrightarrow u+(b-c)\overrightarrow v+(c-a)(\overrightarrow u\times\overrightarrow v)=0$, then the $\Delta$ is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q41
asked
Nov 13, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j+\hat k\:\:\overrightarrow b=4\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow c=\hat i+\alpha\hat j+\beta\hat k$ are linear dependent vectors and $|\overrightarrow c|=\sqrt 3$ then $ (\alpha,\beta)=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q40
asked
Nov 12, 2013
1
answer
The value of $a$ for which the volume of the parallelopiped formed by vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k\:\:and\:\: a\hat i+\hat k$ becomes minimum is ?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q39
asked
Nov 12, 2013
1
answer
If $ \overrightarrow x=\large\frac{\overrightarrow b\times\overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:\overrightarrow y=\large\frac{\overrightarrow c\times\overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:and\:\:\overrightarrow z=\large\frac{\overrightarrow a\times\overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow x.(\overrightarrow a+\overrightarrow b)+\overrightarrow y.(\overrightarrow b+\overrightarrow c)+\overrightarrow z.(\overrightarrow c+\overrightarrow a)=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q38
asked
Nov 12, 2013
1
answer
For non zero vectors $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c,\:\:if\:\:|(\overrightarrow a\times\overrightarrow b).\overrightarrow c|=|\overrightarrow a||\overrightarrow b||\overrightarrow c|$ then ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q37
asked
Nov 11, 2013
1
answer
If $a,b,c$ are non negative and distinct numbers and vectors $a\hat i+a\hat j+c\hat k,\:\:\hat i+\hat k\:\:and\:\:c\hat i+c\hat j+b\hat k$ lie in a plane then c is ?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q36
asked
Nov 11, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow a.\overrightarrow b=1$ and $\overrightarrow a\times\overrightarrow b=\hat j-\hat k,$ then $\overrightarrow b=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q35
asked
Nov 10, 2013
1
answer
If $\overrightarrow a,\overrightarrow b\:\:and\:\:\overrightarrow c$ are non coplanar vectors, then for real $\lambda$, $[\lambda(\overrightarrow a+\overrightarrow b)\:\lambda^2\overrightarrow b\:\lambda\overrightarrow c]=[\overrightarrow a\:\overrightarrow b+\overrightarrow c\:\overrightarrow c]$, for:
jeemain
math
class12
ch10
vector-algebra
medium
scalar-product
q34
asked
Nov 10, 2013
1
answer
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