\(20 \%\) of acetic acid is dissociated when its \(5\, g\) is added to \(500 \, mL\) of water The depression in freezing point of such water is ____ \(\times 10^{-3}{ }^{\circ} C\)Atomic mass of \(C , H\) and \(O\) are 12,1 and 16 amu respectively [Given : Molal depression constant and density of water are \(186 \,K \,kg\, mol ^{-1} and \ 1 \,g \,cm ^{-3}\)respectively
The molality of a 10% (v/v) solution of di-bromine solution in \(\text{CCl}_4\) (carbon tetrachloride) is \(x\). \(x = \, \_\_\_\_\ \times 10^{-2} \, \text{M}\). (Nearest integer)Given:Molar mass of \(\text{Br}_2 = 160 \, \text{g mol}^{-1}\)Atomic mass of \(\text{C} = 12 \, \text{g mol}^{-1}\)Atomic mass of \(\text{Cl} = 35.5 \, \text{g mol}^{-1}\)Density of dibromine = \(3.2 \, \text{g cm}^{-3}\)Density of \(\text{CCl}_4 = 1.6 \, \text{g cm}^{-3}\)
Among following compounds, the number of those present in copper matte is ___ .\(CuCO _3\)\(Cu _2 S\)\(Cu _2 O\)\(FeO\)
\(1 \times 10^{-5} M \,AgNO _3\)is added to \(1\, L\) of saturated solution of\(AgBr\) The conductivity of this solution at \(298 \,K\) is ___ [Given : \(K _{\text {SP }}( AgBr )=49 \times 10^{-13} at 298\, K\)\(\lambda_{ Ag ^{+}}^0=6 \times 10^{-3} S\, m ^2\, mol ^{-1}\) \(\lambda_{ Br ^{-}}^0=8 \times 10^{-3} S\, m ^2\, mol ^{-1}\) \(\lambda_{ NO _3^{-}}^0=7 \times 10^{-3} \,S\, m ^2 \,mol ^{-1}\) ]
A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 20 and \(25 \,\mathring{A}\) respectively The ratio of densities of lattices fcc to bcc for the metal M is ___(Nearest integer)
Testosterone, which is a steroidal hormone, has the following structure
The total number of asymmetric carbon atoms in testosterone is ___
The spin only magnetic moment of\(\left[ Mn \left( H _2 O \right)_6\right]^{2+}\) complexes is ____ BM (Nearest integer) (Given: Atomic no of $Mn$ is 25 )
A → B The above reaction is of zero order Half life of this reaction is 50 min The time taken for the concentration of A to reduce to one-fourth of its initial value is ____ min (Nearest integer)
The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is __
Number of integral solutions to the equation \(x+y+z=21\), where \(x \geq 1\), \(y \geq 3\), \(z \geq 4\), is equal to ___
Let the sixth term in the binomial expansion of \(({\sqrt{2}^{log_{2}}(10-3^{x})+\sqrt[5]{2^{(x-2)log_{2}{3}}}})^{m}\), in the increasing powers of \(2^{(x-2)log_{2}3}\), be 21 If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an AP, then the sum of the squares of all possible values of x is
If the term without \(x\) in the expansion of \(\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}\)is 7315 , then \(|\alpha|\) is equal to ___
The point of intersection \(C\) of the plane \(8 x+y+2 z=0\) and the line joining the points \(A (-3,-6,1)\) and \(B (2,4,-3)\)divides the line segment \(AB\) internally in the ratio\(k : 1 \ If a , b , c (| a |,| b |, | c |\)are coprime) are the direction ratios of the perpendicular from the point \(C\)on the line \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\), then \(| a + b + c |\)is equal to ___
The sum of the common terms of the following three arithmetic progressions\(3,7,11,15, \ldots , 399\), \(2,5,8,11, \ldots , 359\)and \(2,7,12,17, \ldots , 197,\) is equal to _____
If the x-intercept of a focal chord of the parabola \(y^2=8 x+4 y+4\) is 3 , then the length of this chord is equal to ___
Let \(\alpha x+\beta y+y z=1\) be the equation of a plane passing through the point\((3,-2,5)\)and perpendicular to the line joining the points \((1,2,3)\) and \((-2,3,5)\) Then the value of \(\alpha \beta y\)is equal to ____
The line \(x=8\) is the directrix of the ellipse \(E : \frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1\)with the corresponding focus \((2,0)\) If the tangent to \(E\)at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\)and intersects the\(x\)-axis at \(Q\), then \((3 PQ )^2\)is equal to ____
$0.3\, g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter The temperature of calorimeter system (including the water) is found to rise by $05^{\circ} C$ The heat evolved during combustion of ethane at constant pressure is ___$kJ \, mol ^{-1}$ (Nearest integer) [Given : The heat capacity of the calorimeter system is $20 \, kJ\, K ^{-1}, R =83 \, JK ^{-1}\, mol ^{-1}$ Assume ideal gas behaviour Atomic mass of $C$ and $H$ are 12 and $1\, g\, mol ^{-1}$ respectively]
In the figure given below, a block of mass $M=490 g$ placed on a frictionless table is connected with two springs having same spring constant $\left( K =2 N m ^{-1}\right)$ If the block is horizontally displaced through ' $X$ ' $m$ then the number of complete oscillations it will make in $14 \pi$ seconds will be
A solid sphere of mass $1 \,kg$ rolls without slipping on a plane surface Its kinetic energy is $7 \times 10^{-3} J$. The speed of the centre of mass of the sphere is ___$cm s ^{-1}$.
Expression for an electric field is given by $\overrightarrow{ E }=4000 x^2 i \frac{ V }{ m }$ The electric flux through the cube of side $20 cm$ when placed in electric field (as shown in the figure) is ___$V cm$
In a medium the speed of light wave decreases to $0.2$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $x: 1$ The value of $x$ is(Given speed of light in free space $=3 \times 10^8 m s ^{-1}$ and for the given medium \(\mu =1\))
Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ at the point $P$ Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$ If $\alpha$ is the area of triangle $P Q R$, then $\alpha^2$ is equal to
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to
