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Questions asked by rvidyagovindarajan_1
Questions
870
questions
0
answers selected
Find the value of $\tan({\frac{1}{2}}\sin^{-1}{\frac{1}{4}})$
cbse
class12
ch2
q18
p37
exemplar
medium
sec-b
math
asked
Jan 28, 2014
1
answer
If $\ast$ is a binary operation on the set $(\{0, 1, 2, 3, 4, 5\})$ defined as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] then draw the composition table for the operation and find the identity element and inverse of $4$ if exists.
ch1
cbse
class12
sec-b
medium
additionalproblem
math
asked
Jan 27, 2014
1
answer
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
mock
asked
Jan 21, 2014
1
answer
$ \displaystyle\sum_ {i=o} ^{{m} ^{10}} C_i ^{20}C_{m-i}$ is maximum when $m=?$
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
asked
Jan 21, 2014
1
answer
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?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q99
asked
Jan 21, 2014
1
answer
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=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q122
asked
Jan 13, 2014
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 $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q121
asked
Jan 13, 2014
1
answer
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 ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q120
asked
Jan 13, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
easy
distance-between-two-points
q98
mock
asked
Jan 12, 2014
1
answer
Find the angle between any two diagonals of a cube.
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q97
asked
Jan 12, 2014
1
answer
The cosine of angle between the medians drawn from vertices of isosceles rt. angled triangle is?
jeemain
math
class12
ch12
3d-geometry
direction cosines
easy
q96
asked
Jan 12, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q95
asked
Jan 11, 2014
1
answer
If the vertices of a triangle are $A(1,4,2),\:B(-2,1,2)\:C(2,-3,4)$ then the angle $B$ = ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q94
asked
Jan 11, 2014
1
answer
The projection of a line segment on $x,y,z$ axes are $12,\:4,\:3$ respectively, then the length of the line segment is ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q93
asked
Jan 11, 2014
1
answer
The locus of a point $(x,y,z)$ for which $z=k$ is a ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q92
asked
Jan 11, 2014
1
answer
The points $(5,0,2),\:(2,-6,0),\:(4,-9,6)\:and\:(7,-3,8)$ represent vertices of a ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q91
asked
Jan 11, 2014
1
answer
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?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q90
asked
Jan 10, 2014
1
answer
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=?$
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q89
asked
Jan 10, 2014
1
answer
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?
jeemain
math
class11
ch12
3d-geometry
section formula
easy
q88
asked
Jan 10, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q87
asked
Jan 9, 2014
1
answer
The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q86
asked
Jan 9, 2014
1
answer
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$
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q85
asked
Jan 9, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q84
asked
Jan 8, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
difficult
q83
asked
Jan 8, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
direction cosines
easy
q82
asked
Jan 8, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q81
asked
Jan 7, 2014
1
answer
The equation of the plane which makes double the intercepts of the plane $3x+6y-z+12=0$ is ?
jeemain
math
class12
3d-geometry
easy
equations-of-planes
q80
ch11
asked
Jan 7, 2014
1
answer
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 $\overrightarrow r=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q119
asked
Jan 7, 2014
1
answer
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 $\overrightarrow x=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q118
asked
Jan 7, 2014
1
answer
In a rt. angled triangle $ABC$ if hypotenuse, $AB=p$, then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}$= ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q117
asked
Jan 7, 2014
1
answer
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
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q116
asked
Jan 7, 2014
1
answer
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 ?
jeemain
math
class12
ch10
vector-algebra
medium
multiplication-by-a-scalar
q115
asked
Jan 7, 2014
1
answer
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 $\overrightarrow b=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q114
asked
Jan 7, 2014
1
answer
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 $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q113
asked
Jan 7, 2014
1
answer
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 ?
jeemain
math
class12
vector-algebra
ch10
medium
vector-product
q112
asked
Jan 6, 2014
1
answer
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,
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q111
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q110
asked
Jan 6, 2014
1
answer
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 $\cot^2\theta=?$
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
medium
q79
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q78
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q77
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q76
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q75
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q74
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q73
asked
Jan 6, 2014
1
answer
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 ?
jeemain
math
class11
ch11
3d-geometry
coordinate-axes-and-planes
easy
q72
asked
Jan 6, 2014
1
answer
Distance of a point $P(\overrightarrow c)$ from the the line $\overrightarrow r=\overrightarrow a+\lambda \overrightarrow b$ is ?
jeemain
math
class11
ch11
3d-geometry
distance-between-two-points
easy
q71
asked
Jan 6, 2014
1
answer
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 $\lambda=?$
jeemain
math
class12
vector-algebra
ch10
medium
addition-of-vectors
q109
asked
Jan 6, 2014
1
answer
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?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q70
asked
Jan 5, 2014
1
answer
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q69
asked
Jan 5, 2014
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are the sides $BC,CA\:and \:AB$ respectively of the $\Delta \:ABC$, then
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q108
asked
Jan 5, 2014
1
answer
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