At STP, a closed vessel contains I mole each of He and $\mathrm{CH}_4$. Through a small hole, 2 L of He and LL of $\mathrm{CH}_4 \mathrm{WHS}$ escaped from vessel in ' $t$ ' minutes. What are the mole fractions of He and $\mathrm{CH}_4$ respectively remaining in the vessel? ( Assume He and $\mathrm{CH}_4$ as ideal gases. At STP one mole of an ideal gas occupies 22.4 L of volume.)

What is the enthalpy change (in J ) for converting 98 of $\mathrm{H}_2 \mathrm{O}(t)+10^{\circ} \mathrm{C}$ to $\mathrm{H}_2 \mathrm{O}(l)$ at $+20^{\circ} \mathrm{C}$ ?

$$ \left(C_p\left(\mathrm{H}_2 \mathrm{O}(\eta)\right)=75 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}\right) $$

(density of $\mathrm{H}_2 \mathrm{O}(l)=1 \mathrm{gmL}^{-1}{ }^{})$

$A, B, C$ and $D$ are some compounds. The entnalpy of formation of $A(g), B(g), C(g)$ and $D(g)$ is $9.7,-110,81$ and $-393 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. What is $\Delta_r H$

(in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) for the given reaction ?

$$ A(g)+3 B(g) \longrightarrow C(g)+3 D(g) $$

At equilibrium of the reaction,

$$ A_2(g)+B_2(g) \rightleftharpoons 2 A B(g) $$

The concentrations of $A_2, B_2$ and $A B$ respectively are $15 \times 10^{-3} \mathrm{M}, 2.1 \times 10^{-3} \mathrm{M}$, and $1.4 \times 10^{-3} \mathrm{M}$ in a sealed vessel at 800 K . What will be $K_p$ for the decomposition of $A B$ at same temperature ?

Which of the following when added to 20 mL of a 0.01 M solution of HCl would decrease its pH ?

Which one of the following alkaline earth metals does not form hydride when it is heated with hydrogen directly?

$$ \text { In the given structure of diborane } \theta_1, \theta_2 \text { are respectively } $$

In which of the following sets allotropes of carbon are correctly matched with their uses?

i. Graphite - Crucibles

ii. Activated charcoal - Water filters

iii. Carbon black - Fuel

The correct answer is

Which of the following is/are estimated by tura polluted water with potassium dichromate solution in acidic medium?

$$ \begin{array}{c|c|c} \hline \text { COD } & \text { BOD } & \text { DO } \\ \hline \text { I } & \text { II } & \text { III } \\ \hline \end{array} $$

The number of isomers possible for a dibromo derivate (Molecular weight $=186 \mathrm{u}$ ) of an alkene is $(\mathrm{Br}=80 \mathrm{u}$ )

In Kolbe's electrolysis of sodium propanoate, products formed at anode and cathode are respectively

Benzoic acid undergoes dimerisation in benzene. $x \mathrm{~g}$ of benzoic acid (molar mass $122 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is dissolved in 49 g of benzene. The depression in freezing point is 1.12 K . If degree of association of acid is $88 \%$. What is the value of $x$ ? $\left(K_f\right.$ for benzene $\left.=4.9 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$

At $T(\mathrm{~K})$ two liquids $A$ and $B$ form an ideal solution. The vapour pressures of pure liquid $A$ and $B$ at that temperature are 400 and 600 mm Hg respectively, If the mole fraction of liquid $B$ is 0.3 in the mixture, the mole fractions of $A$ and $B$ in vapour phase respectively are

In which of the following Galvanic cells emf is maximum?

(Given, $E_{\mathrm{Mg}^{2+} \mid \mathrm{Mg}}^{\circ}=-2.36 \mathrm{~V}$

and $E_{\mathrm{Cl}_2 \mid 2 \mathrm{Cl}^{-}}^{\circ}=+136 \mathrm{~V}$ )

Isomerisation of gaseous cyclobutene to butadiene is first order reaction. At $T(\mathrm{~K})$. The rate constant of reaction is $33 \times 10^{-4} \mathrm{~s}^{-1}$. What is the time required (in min ) to complete $90 \%$ of this reaction at the temperature? $(\log 2=03)$

$$ \text { Match List-I with List-II } $$

In which of the following metals extraction, impurities are removed as slag?

i. Al

ii. Fe

iii. Cu

iv. Zn

The correct option is

The correct order of oxidising power of the given ions is

Match the complexes in List-I with their hybridisation in list-II.

$$ \text { Match the following. } $$

Which of the following molecules contain sulphur atom in their structures?

I. Morphine

II. Heroin

III, Penicillin

IV. Terpineol

V. Cimetidine

In Wurtz-Fittig reaction a compound $X$ reacts with alkyl halide. What is $X$ ?

$$ \text { The product }(C) \text { in the following reaction sequenceis } $$

Arrange the following in the correct order of their acidic strength.

$$ \text { What is } Y \text { in the given sequence? } $$

$$ \text { Identify } B \text { in the given reaction sequence. } $$

$$ 2+3+5+6+8+9+\ldots .2 n \text { terms }= $$

If the set of equations $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+a z=b$ has unique solution, then

If $P$ and $Q$ are two $3 \times 3$ matrices such that $|P Q|=1$ and $|P|=9$, then the determinant of adjoint of the matrix $P$. $\operatorname{adj} 3 Q$ is

If $A=\left[\begin{array}{lll}a & 1 & 2 \\ 1 & 2 & b \\ c & 1 & 3\end{array}\right]$ and $\operatorname{adj} A=\left[\begin{array}{ccc}7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5\end{array}\right]$, then $a^2+b^2+c^2=$

If $Z$ is a complex number such that $|Z| \leq 3$ and $\frac{-\pi}{2} \leq \operatorname{amp} Z \leq \frac{\pi}{2}$, then the area of the region formed by locus of $Z$ is

All the letters of the word 'TABLE' are permuted and the strings of letters (may or may not have meaning) thus formed are arranged in dictionary order. Then, the rank of the word 'TABLE' counted from the rank of the word 'BLATE' is

If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

$$ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}= $$

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :

In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is

In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ and $(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \mathbf{k})$are$\mathbf{}$ the position vectors of the vectices $P, Q$ and $R$ respectively then, the position vector fo the point ol intersection of the angle bisector of $P$ and $Q R$ is

If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ and $\sin \theta=\sqrt{\frac{24}{28}}$, then $7 a^2+24 a=$

Three numbers are chosen at random from 1 to 20 , then the probability that the sum of three numbers is divisible by 3 is

8 teachers and 4 students are sitting around a circular table at random, then the probability that no two students sit together is

A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability that exactly 5 of the balls in the bag are green is

In a binomial distribution the difference between the mean and standard deviation is 3 and the difference between their squares is 21 , then $P(x=1): P(x=2)=$

When an unfair dice is thrown the probability of getting a number $k$ on it is $P(X=k)=k^2 P$, where $k=1,2,3,4,5,6$ and $X$ is the random variable denoting a number on the dice, then the mean of X is

The transformed equation of $x^2-y^2+2 x+4 y=0$ when the origin is shifted to the point $(-1,2)$ is

If the slope of one of the pair of lines represented by $2 x^2+3 x y+K y^2=0$ is 2 , then the angle between the pair of lines is

$C_1$ is the circle with centre at $O(0,0)$ and radius $4, C_2$ is a variable circle with centre at $(\alpha, \beta)$ and radius 5 . If the common chord of $C_1$ and $C_2$ has slope $\frac{3}{4}$ and of maximum length, then one of the possible values of $\alpha+\beta$ is

If the pair of tangents drawn to the circle $x^2+y^2=a^2$ from the point $(10,4)$ are perpendicular. then $a=$

If $x-4=0$ is the radical axis of two orthogonal cirlces out of which one is $x^2+y^2=36$, then the centre of the other circle is

If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola, then the line $\frac{x}{2 e_1}+\frac{y}{2 e_2}=1$ touches the circle having centre at the origin, then its radius is

$$\mathop {\lim }\limits_{x \to o} \left[\frac{1}{x}-\frac{1}{e^x-1}\right]= $$

Let $f(x)=\left\{\begin{array}{cl}0, & x=0 \\ 2-x, & \text { for } 0 < x < 1 \\ 2, & \text { for } x=1 \\ \frac{1}{2}-x, & \text { for } 1 < x < 2 \\ \frac{-3}{2}, & \text { for } x \geq 2\end{array}\right.$

then which of the following is true

If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \infty}}}$, then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

$$ \int \frac{x^3 \tan ^{-1} x^4}{1+x^8} d x= $$

$$ \int \frac{1}{x^2\left(\sqrt{1+x^2}\right)} d x= $$

$$ \int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x= $$

$$ \int_0^{\pi / 4} \log (1+\tan x) d x= $$

$$\int\limits_\pi ^\pi {}\frac{x \sin x}{1+\cos ^2 x} d x= $$

The sum of the order and degree of differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{1 / 2}=\left(1+\frac{d y}{d x}\right)^{4 / 3}$

A body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3 H}{4}$ and $\frac{8 H}{9}$ from the ground is

The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y=3 x-0.8 x^2$. The time of flight of the projectile is (Acceleration due to gravity, $g=10 \mathrm{~ms}^{-2}$ )

A 100 kg cannon fires a ball of 1 kg horizontally from a cliff of height 500 m . It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A block of mass 5 kg is placed on a rough horizontal surface having coefficient of friction 0.5 . If a horizontal force of 60 N is acting on it, then the acceleration of the block is (Acceleration due ot gravity, $g=10 \mathrm{~ms}^{-2}$ )

A boy weighing 50 kg finished long jump at a distance of 8 m . Considering that he moved along a parabolic path and his angle of jump is $45^{\circ}$, his initial KE is

The moment of inetia of a rod about an axis passing through its centre and perpendicular to its length is $\frac{1}{12} M L^2$, where $M$ is the mass and $L$ is the length of the rod. The rod is bent in the middle, so that the two halves make an angle of $60^{\circ}$. The moment of inertia of the bent rod about the same axis would be

Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is

When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is

$$ \left(Y_{\text {Copper }}=10 \times 10^{10} \mathrm{Nm}^{-2} \text { and } g=10 \mathrm{~ms}^{-2}\right) $$

Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $10 \mathrm{~cm}^2$ and velocity $1 \mathrm{~ms}^{-1}$ is 2000 Pa , then the pressure of water at another point where the cross-sectional area $5 \mathrm{~cm}^2$ is

A metal ball of mass 100 g at $20^{\circ} \mathrm{C}$ is dropped in 200 g of water at $80^{\circ} \mathrm{C}$. If the resultant temperature is $70^{\circ} \mathrm{C}$, then the ratio of specific heat of the metal to that of water is

Initially the pressure of 1 mole of an ideal gas is $10^5 \mathrm{Nm}^{-2}$ and its volume is 16 L . When it is adiabatically compressed, its final volume is 2 L . Work-done on the gas is

An ideal gas is taken around $A B C A$ as shown in the $P^{\prime \prime}$ diagram. The work done during the cycle is

The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is

The vibrations of four air columns are shown below. The ratio of frequencies is

If a slit of width $x$ was illuminated by red light having wavelength $6500\mathop {\rm{A}}\limits^{\rm{^\circ }}$, the first minima was obtained at $\theta=30^{\circ}$. Then, the value of $x$ is

Eight capacitors each of capacity $2 \mu \mathrm{~F}$ are arranged as shown in figure. The effective capacitance between $A$ and $B$ is

If $E_1=4 \mathrm{~V}$ and $E_2=12 \mathrm{~V}$, the current in the circuit and potential difference between the points $P$ and $Q$ respectively are

Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. $I$ is current passing through each ring. The magnetic field value at the common centre is

One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased by 9 times the time period becomes

A coil of inductance $L$ is divided into 6 equal parts. All these are connected in parallel. The resultant inductance of this combination is

A 50 Hz AC circuit has a 10 mH inductor and a $2 \Omega$ resistor in series. The value of capacitance to be placed in series in the circuit to make the circuit power factor as unity is

The surface of a metal is first illuminated with a light of wavelength 300 nm and later illuminated by another light of wavelength 500 nm . It is observed that the ratio of maximum velocities of photoelectrons in two cases is 3 . The work function of metal value is close to

The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is

The half-life period of a radioactive element $A$ is 62 years. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in 1:15 ratio. The age of the sample is

The current gain of a transistor in common emitter configuration is 80 . The resistances in collector andbase sides of the circuit are $5 \mathrm{k} \Omega$ and $1 \mathrm{k} \Omega$ respectively. If the input voltage is 2 mV , the output voltage is

Four logic gates are connected as shown in the figure. If the inputs are $A=0, B=1$ and $C=1$, then the values of $Y_1$ and $Y_2$ respectively, are

The maximum distance between the transmitting and receiving antennas for satisfactory communication in line of sight mode is 57.6 km . If the height of the receiving antenna is 80 m , the height of the transmitting antenna is (radius of earth $=6.4 \times 10^6 \mathrm{~m}$ )