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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
Find the 10th term of the AP -3, -1, 1, 3, ....
jeemain
math
class11
sequences-and-series
ch9
arithmetic-progression
easy
asked
Nov 19, 2013
by
harini.tutor
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
For a $\Delta ABC$ it is given that : $\cos A+\cos B+\cos C=\large\frac{3}{2}$.What type of triangle is $ABC$?
jeemain
math
class11
ch3
trigonometric-functions
q40
trigonometric-identities
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Find the sum of the following series : $ 1^{2} + 2^{2} + 3^{2} + 4^{2} + .... + 20^{2}$
jeemain
math
class11
sequences-and-series
unit9
sum-of-n-terms-of-special-series
easy
asked
Nov 19, 2013
by
harini.tutor
1
answer
If $0\leq x\leq \large\frac{\pi}{2}$ and $81^{\large \sin^2x}+81^{\large\cos^2x}=30$ then $x$ is equal to
jeemain
math
class11
ch3
trigonometric-functions
q39
trigonometric-equations
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Total number of solutions of $\cos x.\cos 2x.\cos 3x=\large\frac{1}{4}$ in $[0,\pi]$ is equal to
jeemain
math
class11
ch3
trigonometric-functions
q38
trigonometric-equations
difficult
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
Solve :$\log _7\log _5(\sqrt{x+5}+\sqrt{x})=0$
jeemain
math
class11
ch3
trigonometric-functions
q35
trigonometric-equations
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
If $x>1,y>1,z>1$ are in G.P then $\large\frac{1}{1+ln\; x},\frac{1}{1+ln\; y},\frac{1}{1+ln \;z}$ are in
jeemain
math
class11
ch3
trigonometric-functions
q34
trignometric-equations
difficult
asked
Nov 19, 2013
by
sreemathi.v
1
answer
Let $ABCD$ be a quadrilateral with area 18 with side AB parallel to the side CD and AB=2CD.Let AD be $\perp$ to AB and CD.If a circle is drawn inside the quadrilateral ABCD touching all the sides then its radius is
jeemain
math
class11
ch3
trigonometric-functions
q33
angles
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
The radius of the circle passing through the centre of the inscribed circle of the $\Delta$le ABC and through the end point of the base BC is R then $\large\frac{a}{R}$$\sec \large\frac{A}{2}$ is equal to
jeemain
math
class11
ch3
trigonometric-functions
q32
angles
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
$ABC$ is a $\Delta$le.Its area is 12sqcm and base is 6cm.The difference of base angle is $60^{\large\circ}$.If $A$ be the angle opposite to the base,then the value of $8\sin A-6\cos A$ is
jeemain
math
class11
ch3
trigonometric-functions
q31
angles
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The number of all possible values of $\theta$ where $0 < \theta < \pi$ for which the system of equations $(y+z)\cos 3\theta=(xyz)\sin 3\theta$,$x\sin 3\theta=\large\frac{2\cos 3\theta}{y}+\frac{2\sin 3\theta}{z}$,$(xyz)\sin 3\theta=(y+2z)\cos 3\theta+y\sin 3\theta$ have a solution $(x_0,y_0,z_0)$ with $y_0,z_0\neq 0$ is
jeemain
math
class11
ch3
trigonometric-functions
q30
trignometric-equations
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The positive integer value of $n>3$ satisfying the equation $\large\frac{1}{\sin\big(\Large\frac{\pi}{n}\big)}=\frac{1}{\sin\big(\Large\frac{2\pi}{n}\big)}+\frac{1}{\sin\big(\Large\frac{3\pi}{n}\big)}$ is
jeemain
math
class11
ch3
trigonometric-functions
q29
trignometric-equations
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
If $\sin^{-1}\big(x-\large\frac{x^2}{2}+\frac{x^3}{4}-........)$$+\cos^{-1}(x^2-\large\frac{x^4}{2}+\frac{x^6}{4}.......)=\large\frac{\pi}{2}$.For $0<\mid x\mid<\sqrt 2$ then $x$ equals
jeemain
math
class12
inverse-trigonometric-functions
q28
inverse-trigonometric-properties
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Find all positive integral solutions of the equation $\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$
jeemain
math
class12
ch2
inverse-trigonometric-functions
q27
inverse-trignometric-properties
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Let $ABC$ be a triangle such that $\angle ACB=\large\frac{\pi}{6}$.Let $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively.The value of $x$ for which $a=x^2+x+1,b=x^2-1$ and $c=2x+1$ is
jeemain
math
class11
ch3
trigonometric-functions
q26
angles
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Two sides of a $\Delta$le are given by the roots of the equation $x^2-2\sqrt 3x+2=0$,The angle between the sides is $\large\frac{\pi}{3}$.The perimeter of the triangle is
jeemain
math
class11
ch3
trigonometric-functions
q25
trignometric-equations
difficult
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Find the maximum and minimum value of $\sin^6x+\cos^6x$
jeemain
math
class11
ch3
trigonometric-functions
q60
trigonometric-equations
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The value of $x$ where $d>0$ and $\tan[\sec^{-1}\big(\large\frac{1}{x}\big)]=$$\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
$ABC$ is a triangle with $\angle A=30^{\large\circ}$ $BC=10$cm.The area of the circumcircle of the $\Delta$le is?
jeemain
math
class11
ch3
trigonometric-functions
q57
angles
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The circumradius of the $\Delta$le whose sides are $13,12\; and\; 5 \;is$?
jeemain
math
class11
ch3
trigonometric-functions
q56
angles
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Two sides of $\Delta$le are $\sqrt 2-1$ and $\sqrt 2+1$ unit and their included angle is $60^{\large\circ}$.Then the third side of the $\Delta$le is
jeemain
math
class11
ch3
trigonometric-functions
q55
trignometric-identities
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The number of values of $x$ in $[0,2\pi]$ satisfying the equation $3\cos 2x-10\cos x+7=0$ is?
jeemain
math
class11
ch3
trigonometric-functions
q54
trignometric-equations
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The solution of the equation $4\sin^4x+\cos^4x=1$ is
jeemain
math
class11
ch3
trigonometric-functions
q53
trignometric-equations
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
The number of values of $x$ in the interval $[0,3\pi]$ .Satisfying the equation $2\sin^2x+5\sin x-3=0$ is
jeemain
math
class11
ch3
trigonometric-functions
q52
trignometric-equations
medium
asked
Nov 18, 2013
by
sreemathi.v
1
answer
Given $NaSO_4.10H_2O (s) \rightleftharpoons NaSO_4 (s) + 10H_2O (g) ; K_p =4.08 \times 10^{-25} $ and vapour pressure of water at $0^\circ$C = 4.58 Torr. At what relative humidity will $Na_2SO_4$ be deliquescent when exposed to the air at $0^\circ$C ?
jeemain
aipmt
chemistry
equilibrium
difficult
q29
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
For the equilibrium $2SO_2 + O_2 \rightleftharpoons 2SO_3$ we start with 2 moles of $SO_2$ and 1 mole of $O_2$ at 3 atm. When equilibrium is attained, pressure changes to 2.5 atm. Hence, $K_p$ is:
jeemain
aipmt
chemistry
equilibrium
difficult
q30
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
For a very small extent of dissociation of $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ is a gaseous phase reaction then degree of dissociation, x:
jeemain
aipmt
chemistry
equilibrium
medium
q28
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2 (g)$ In the dissociation of $PCl_5, x $ varies with $\frac{D}{d}$ according to:
jeemain
aipmt
chemistry
equilibrium
medium
q27
biology
asked
Nov 15, 2013
by
mosymeow_1
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
For the reversible reaction equilibrium is $ N_2(g) + O_2(g) \overset{\overset{k_r}{\rightleftharpoons}}{_{k_f}} 2NO(g), $ $C_0 = Ce^{-2.1 \times 10^{-3} t} $ for the forward reaction and $C'_0 = C'e^{-4.2 \times 10^{-4}} t$ for the backward reaction, hence, if both forward and backward reactions are first order reactions then $K_c$ for the above equilibrium is:
jeemain
aipmt
chemistry
equilibrium
medium
q26
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
$ Solute + H_2O \rightleftharpoons solution; \Delta H=\pm x $ For the given equation, Solubility(S) of a solute in the solvent (say $H_2O$) is given by $S = A e^{-\frac{\Delta H}{RT}}$ For a given solution, variation of log S with temperature is shown graphically. Hence, Solute is:
jeemain
aipmt
chemistry
equilibrium
medium
q25
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
$A + B \rightleftharpoons C + D$ One mole each of A and B and 3 moles each of C and D are placed in 1L flask, if equilibrium constant is 2.25. Equilibrium concentrations of A and C will be in the ratio:
jeemain
aipmt
chemistry
equilibrium
difficult
q24
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
Volume of the flask in which species are transferred is double of the earlier flask. In which of the following reversible reactions, equilibrium will be shifted in the forward direction?
jeemain
aipmt
chemistry
equilibrium
medium
q23
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
$ I_2 + I^- \rightleftharpoons I^-_3 $ This reaction is set-up in aqueous medium. Initially we have 1 mole of $I_2$ and 0.5 mole of $I^-$ in 1 L flask. After equilibrium is reached, excess of $AgNO_3$ gave 0.25 mole of yellow ppt. Equilibrium constant is
jeemain
aipmt
chemistry
equilibrium
medium
q22
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
We know that equilibrium constant, K changes with temperature. At 300K, equilibrium constant is 25 and at 400K it is 10. Hence, backward reaction will have energy of activation:
jeemain
aipmt
chemistry
equilibrium
difficult
q21
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
Given a reaction $ A + B \rightleftharpoons C + D $ taking place in a 1L vessel. If we start with 1 mole each of A and B, equilibrium concentration of [C] = [D] = 0.5 M. Percentage of A converted into C if we start with 2 moles of A and 1 mole of B, is
jeemain
aipmt
chemistry
equilibrium
difficult
q20
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
If $\beta_1, \beta_2$ and $\beta_3$ are stepwise formation constants of $MCl, MCl_2, MCl_3$ and K is the overall formation constants of $MCl_3$, then (charges ommitted) :
jeemain
aipmt
chemistry
equilibrium
medium
q19
biology
asked
Nov 15, 2013
by
mosymeow_1
1
answer
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