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Recent questions tagged class12
Questions
The system of equations $\lambda x+y+z=0$, $-x+\lambda y+z=0$, $-x-y+\lambda z=0$ will have a non-zero solutions if real values of $\lambda$ are given by
jeemain
class12
math
ch4
determinants
system-of-linear-equations
medium
asked
Nov 19, 2013
by
sreemathi.v
1
answer
If $\begin{bmatrix}1 &-\tan\theta\\\tan\theta&1\end{bmatrix}\begin{bmatrix}1 &\tan\theta\\-\tan\theta&1\end{bmatrix}^{-1}$ = $\begin{bmatrix}a &-b\\b&a\end{bmatrix}$ then find $a,b$
jeemain
math
class12
ch3
matrices
operations-on-matrices
medium
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Find the product of the matrices $\begin{bmatrix}2 &3&4\\-1&2&-5\end{bmatrix}$ and $\begin{bmatrix}1&2\\3&-4\\-5&6\end{bmatrix}$
jeemain
math
class12
ch3
matrices
operations-on-matrices
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Given matrices $A=\begin{bmatrix}5 &-2&0\\3&0&5\\-1&0&8\end{bmatrix}$, $B=\begin{bmatrix}0 &-2\\1 &0\\0&5\end{bmatrix}$, find $(A+B)$.
jeemain
math
ch3
matrices
operations-on-matrices
easy
class12
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Find the value of $\lambda$ for which the set of equations $x+y-2z=0$, $2x-3y+z=0$, $x-5y+4z=\lambda$ are consistent.
jeemain
math
class12
ch4
determinants
system-of-linear-equations
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
For what value of $k$ do the following homogeneous system of equations posses a non-trivial.$x+ky+3z=0,3x+ky-2z=0,2x+3y-4z=0$
jeemain
math
class12
ch4
determinants
system-of-linear-equations
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Evaluate :$\begin{vmatrix}y+z&z&y\\z&z+x&x\\y&x&x+y\end{vmatrix}$
jeemain
math
class12
ch4
determinants
evaluate-determinants
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Evaluate : $\begin{vmatrix}0 &a-b&b-c\\b-a&0&b-c\\c-a&c-b&0\end{vmatrix}$
jeemain
math
class12
ch4
determinants
evaluate-determinants
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Evaluate :$\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix}$
($\omega$: Cube root of unity)
jeemain
math
class12
ch4
determinants
evaluate-determinants
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Evaluate :$\begin{vmatrix}3 &2& 12\\0 &1&8\\2&9&7\end{vmatrix}$
jeemain
math
class12
ch4
determinants
evaluate-determinants
easy
asked
Nov 19, 2013
by
sreemathi.v
1
answer
If $\tan^{-1}(x-1)+\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ then $x$ is
jeemain
math
class12
ch2
inverse-trigonometric-functions
q37
inverse-trigonometric-properties
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
If $\cos^{-1}x-\cos^{-1}\large\frac{y}{2}$$=\alpha$ then $4x^2-4xy.\cos \alpha-y^2$ is equal to
jeemain
math
class12
ch2
inverse-trigonometric-functions
q36
inverse-trigonometric-properties
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q48
asked
Nov 18, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are three vectors such that $|\overrightarrow u|=1,\:|\overrightarrow v|=2,\:|\overrightarrow w|=3$ and if the projection of $\overrightarrow v$ along $\overrightarrow u$ is equal to that of $\overrightarrow w$ along $\overrightarrow u$ and also if $\overrightarrow u$ and $\overrightarrow v$ are $\perp$ to each other, then $ |\overrightarrow u-\overrightarrow v+\overrightarrow w|= ?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q47
asked
Nov 18, 2013
by
rvidyagovindarajan_1
1
answer
The value of $[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]$ where $|\overrightarrow a|=1,\:\:|\overrightarrow b|=5\:\:|\overrightarrow c|=3$ is ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q46
asked
Nov 18, 2013
by
rvidyagovindarajan_1
1
answer
The greatest value of $|\overrightarrow a+\overrightarrow b|+|\overrightarrow a-\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors is ?
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q45
asked
Nov 18, 2013
by
rvidyagovindarajan_1
1
answer
If $\sin^{-1}\big(x-\large\frac{x^2}{2}+\frac{x^3}{4}-........)$$+\cos^{-1}(x^2-\large\frac{x^4}{2}+\frac{x^6}{4}.......)=\large\frac{\pi}{2}$.For $0<\mid x\mid<\sqrt 2$ then $x$ equals
jeemain
math
class12
inverse-trigonometric-functions
q28
inverse-trigonometric-properties
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Find all positive integral solutions of the equation $\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$
jeemain
math
class12
ch2
inverse-trigonometric-functions
q27
inverse-trignometric-properties
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The value of $x$ where $d>0$ and $\tan[\sec^{-1}\big(\large\frac{1}{x}\big)]=$$\sin(\tan^{-1}2)$ is
jeemain
math
class12
ch2
inverse-trigonometric-functions
q59
inverse-trigonometric-properties
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$ then $\sin x$ is equal to
jeemain
math
class12
ch2
inverse-trigonometric-functions
q58
inverse-trigonometric-properties
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
If $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$, then the value of $\lambda$ for which $\overrightarrow c=\lambda\hat i+\hat j+(2\lambda+1)\hat k$ is parallel to the plane containing $\overrightarrow a\:\:and\:\:\overrightarrow b$ is
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q44
asked
Nov 15, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a,\overrightarrow b\:\overrightarrow c$ are three vectors of equal magnitude and angle between $\overrightarrow a\:and\:\overrightarrow b$ is $\alpha$, that between $\overrightarrow b\:\overrightarrow c$ is $\beta$, and that between $\overrightarrow a\:and\:\overrightarrow c$ is $\gamma$ then the minimum value of $cos\alpha+cos\beta+cos\gamma$ is ?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q43
asked
Nov 15, 2013
by
rvidyagovindarajan_1
1
answer
Solve for $x$: $\tan^{-1}x+2\cot^{-1}x=\large\frac{2\pi}{3}$.
jeemain
math
class12
ch2
inverse-trigonometric-functions
q95
inverse-trignometric-properties
easy
mock
asked
Nov 15, 2013
by
sreemathi.v
1
answer
If $-\large\frac{x}{2}$$<\sin^{-1}x<\large\frac{x}{2}$ then $\tan(\sin^{-1}x)$ is equal to
jeemain
math
class12
ch2
inverse-trigonometric-functions
q94
inverse-trignometric-properties
easy
asked
Nov 15, 2013
by
sreemathi.v
1
answer
If $\tan^{-1}\big(\large\frac{a}{x}\big)$$+\tan^{-1}\big(\large\frac{b}{x}\big)=\frac{\pi}{2}$ then $x$ is equal to
jeemain
math
class12
ch2
inverse-trigonometric-functions
q93
inverse-trignometric-properties
easy
asked
Nov 15, 2013
by
sreemathi.v
1
answer
If $\tan^{-1}\large\frac{1}{a-1}$$=\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ is
jeemain
math
class12
ch2
inverse-trigonometric-functions
q92
inverse-trignometric-properties
easy
asked
Nov 15, 2013
by
sreemathi.v
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
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
by
rvidyagovindarajan_1
1
answer
For any vector $\overrightarrow a$ the value of $(\overrightarrow a\times \hat i)^2+(\overrightarrow a\times \hat j)^2+(\overrightarrow a\times \hat i)^2=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q33
asked
Nov 10, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a=\hat i+2\hat j+\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k$ and $\overrightarrow c=\hat i+\hat j-\hat k$ and a vector $\overrightarrow d$ which is in the plane of $\overrightarrow a\:and\:\overrightarrow b$ and whose projection on $\overrightarrow c$ is $\large\frac{1}{\sqrt 3}, $ then $\overrightarrow d=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q32
asked
Nov 10, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a, \:\overrightarrow b,\: \overrightarrow c$ are position vectors of the points $A,B,C$ respectively, then under what condition the three points $A,B,C$ are collinear?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q31
asked
Nov 10, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c$ are non zero vectors that are pair wise non-collinear and if $\overrightarrow a+3\overrightarrow b$ is collinear with $ \overrightarrow c$ and $\overrightarrow b+2\overrightarrow c $ is collinear with $\overrightarrow a$, then $\overrightarrow a+3\overrightarrow b+6\overrightarrow c=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q30
asked
Nov 9, 2013
by
rvidyagovindarajan_1
1
answer
If $|\overrightarrow a+\overrightarrow b|=\sqrt {29}$ and $\overrightarrow a\times (2\hat i+3\hat j+4\hat k)=(2\hat i+3\hat j+4\hat k)\times \overrightarrow b,$ then $(\overrightarrow a+\overrightarrow b).(-7\hat i+2\hat j+3\hat k)=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q30
asked
Nov 9, 2013
by
rvidyagovindarajan_1
1
answer
If $|\overrightarrow a|=3,\:|\overrightarrow b|=\large\frac{\sqrt 2}{3}$, then $\overrightarrow a\times\overrightarrow b$ is a unit vector if the angle between $\overrightarrow a$ and $\overrightarrow b$ is ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q29
asked
Nov 8, 2013
by
rvidyagovindarajan_1
1
answer
The number of distinct real values of $\lambda$ for which the vectors $-\lambda^2\hat i+\hat j+\hat k,\:\hat i-\lambda^2\hat j+\hat k\:and\:\hat i+\hat k-\lambda^2 \hat k$ are coplanar is?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q28
asked
Nov 8, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow {OA}=\overrightarrow a,\:\overrightarrow {AB}=6\overrightarrow a+2\overrightarrow b\:and\:\overrightarrow {OC}=\overrightarrow b$, $p$ is area of quadrateral $OACB$ and $q$ is area of parallelogram with $OA$ and $OC$ as adjacent sides, and if $p=x.q$, then $x=?$
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q27
asked
Nov 8, 2013
by
rvidyagovindarajan_1
1
answer
The vector that makes equal angle with $\large\frac{1}{3}$$(\hat i-2\hat j+2\hat k), \:\large\frac{1}{5}$$(-4\hat i-3\hat k)$ and $\hat j$ is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q26
asked
Nov 7, 2013
by
rvidyagovindarajan_1
1
answer
The set of all possible values of $'c'$ for which $\overrightarrow a=c \log_3 x\hat i-6\hat j+3\hat k$ and $\overrightarrow b=\log_3x\hat i+2\hat j+2c\log_3x\hat k$ making acute angle for $\forall x\in (0,\infty)$ is ?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q25
asked
Nov 6, 2013
by
rvidyagovindarajan_1
1
answer
In a rt. angled $\Delta$ $ABC$, the hypotenuse $|\overrightarrow {AB}|=p$,then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
addition-of-vectors
q24
asked
Nov 6, 2013
by
rvidyagovindarajan_1
1
answer
Area of a parallelogram with adjacent sides $\overrightarrow a=\overrightarrow p+2\overrightarrow q,$ and $\overrightarrow b=2\overrightarrow p+\overrightarrow q$, where $\overrightarrow p,\overrightarrow q$ are unit vectors with angle $\large\frac{\pi}{6}$ between them is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q23
asked
Nov 6, 2013
by
rvidyagovindarajan_1
1
answer
$|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow a+\overrightarrow b|=5,$ then $|\overrightarrow a-\overrightarrow b|=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q22
asked
Nov 6, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a=\hat i-\hat j+2\hat k, \:\:\overrightarrow b=2\hat i+4\hat j+\hat k\:\:and\:\:\overrightarrow c=\lambda \hat i+\hat j+\mu k$ are mutually $\perp$ then $(\lambda,\mu)=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q21
asked
Nov 5, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a\;and\:\overrightarrow b$ are unit vectors and if vectors $\overrightarrow c=\overrightarrow a+2\overrightarrow b$ and $\overrightarrow d=5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\;and\:\overrightarrow b$ is ?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q19
asked
Nov 4, 2013
by
rvidyagovindarajan_1
1
answer
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