What would be the EMF of the cell in which the following reaction occurs:

$$\begin{aligned} & \mathrm{Cd}(\mathrm{S})+2 \mathrm{H}^{+} \rightarrow \mathrm{Cd}^{2+}+\mathrm{H}_{2(\mathrm{~g})} \\ & {\left[\mathrm{H}^{+}\right]=0.02 \mathrm{M} \quad \mathrm{E}^0\left(\mathrm{Cd}^{2+} / \mathrm{Cd}\right)=-0.4 \mathrm{~V},\left[\mathrm{Cd}^{2+}\right]=0.01 \mathrm{M} \text { and partial pressure of } \mathrm{H}_2 \text { gas }=0.8 \mathrm{~atm} .} \end{aligned}$$

$$\text { Identify }[\mathrm{B}] \text { and }[\mathrm{C}] \text { formed in the reactions given below. }$$

Identify the 2 chemical tests which is not answered by Glucose having an open chain structure

[A] Reaction with Schiff's reagent and with Sodium bisulphite

[B] Reaction with $$\mathrm{HCN}$$ and with $$\mathrm{HI}$$

[C] Reaction with $$\mathrm{HNO}_3$$ and with Acetic anhydride

[D] Reaction with aqueous Bromine and with Hydroxylamine

A d - block metal $$\mathrm{X}(\mathrm{Z}=26)$$ forms a compound $$[\mathrm{X}(\mathrm{CN})_2(\mathrm{CO})_4]^{+}$$. Calculate its spin magnetic moment value.

Which one of the following compounds shows Geometrical isomerism?

A sweet smelling organic compound $$[\mathrm{A}]\left(\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}_2\right)$$ undergoes acid hydrolysis to form an acid [B].
Compound [B] further reacts with Ammonia followed by heating to yield [C].
Compound $$[\mathrm{C}]$$ when reacted with $$\mathrm{Br}_2$$ in caustic potash gave compound $$[\mathrm{D}]\left(\mathrm{C}_6 \mathrm{H} 7 \mathrm{~N}\right)$$ which gives a white precipitate with aqueous $$\mathrm{Br}_2$$.
Identify compounds $$[\mathrm{A}]$$ & $$[\mathrm{D}]$$

Arrange the following ions in the increasing order of their $$\Delta H_{(\text {hydration})}$$ values.

$$\mathrm{Cr}^{2+}, \mathrm{Co}^{2+}, \mathrm{Mn}^{2+}, \mathrm{Ni}^{2+}$$

What is the final product formed when Toluene undergoes the following series of reactions?

The time required for $$80 \%$$ of a first order reaction is "$$y$$" times the half-life period of the same reaction. What is the value of "$$y$$"?

The standard enthalpy of formation of $$\mathrm{CH}_4$$, the standard enthalpy of sublimation of Carbon and the bond dissociation enthalpy of Hydrogen gas are $$-74.8,+719.6$$ and $$436 \mathrm{~kJ} / \mathrm{mol}$$ respectively. What is the bond enthalpy of $$\mathrm{C}-\mathrm{H}$$ bond in Methane?

From the following compounds, identify the one which is most acidic.

An inorganic salt comprises of atoms of elements $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$. If the oxidation numbers of A, B and $$\mathrm{C}$$ are $$+3,+6$$ and $$-$$2 respectively, what is the possible formula of the compound?

The rate constant for the reaction $$\mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$$ at $$500 \mathrm{~K}$$ is given as $$0.004 \mathrm{~s}^{-1}$$. At what temperature will the rate constant become $$0.014 \mathrm{~s}^{-1}$$ ? $$\mathrm{E}_{\mathrm{a}}$$ for the reaction is $$18.231 \mathrm{~kJ}$$.

An organic compound $$[\mathrm{A}]\left(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}\right)$$, on reaction with conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ at $$443 \mathrm{~K}$$ gives $$[\mathrm{B}]$$ as one of the products. Compound [B] undergoes further reaction with $$\mathrm{O}_3$$ and $$\mathrm{Zn} / \mathrm{H}_2 \mathrm{O}$$ to give Propanone and Ethanal as products. Identify compound [A]

For the reaction $$\mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \rightarrow 2 \mathrm{NOCl}_{(\mathrm{g})}$$, the following data was obtained:

Identify the order of the reaction with respect to $$\mathrm{Cl}_2, \mathrm{NO}$$ and the value of Rate constant.

$$\mathrm{K}_{\mathrm{H}}$$ for $$\mathrm{O}_2$$ at $$293 \mathrm{~K}$$ is $$34.86 \mathrm{~kbar}$$. What should be the partial pressure of $$\mathrm{O}_2$$ gas so that it has a solubility of $$0.08 \mathrm{~g} / \mathrm{L}$$ in water at $$293 \mathrm{~K}$$ ? (Density of solution $$=1 \mathrm{~g} / \mathrm{ml}$$)

The permanganate ion in acid medium acts as an oxidant and gets converted to its lower oxidation state. What would be the spin only magnetic moment of such reduced manganese ion?

$$\mathrm{A}_3 \mathrm{~B}_4$$ is a sparingly soluble salt with a solubility of $$\mathrm{s} g / \mathrm{L}$$. If the Molar mass of $$\mathrm{A}_3 \mathrm{~B}_4$$ is $$\mathrm{Mg} / \mathrm{mol}$$, what is the expression for its $$\mathrm{K}_{\text {sp }}$$ ?

Given below are 4 graphs [A], [B], [C] and [D]

Identify the 2 graphs that represent a Zero order reaction?

A given mass of a hydrocarbon on complete combustion produced $$176 \mathrm{~g}$$ of $$\mathrm{CO}_2$$ and $$90 \mathrm{~g}$$ of $$\mathrm{H}_2 \mathrm{O}$$. What is the Molecular formula of the compound?

An unsaturated hydrocarbon $$[\mathrm{A}]$$ reacts with $$\mathrm{HBr}$$ in presence of Benzoyl peroxide to yield [B] Compound [A] when reacted with cold, dilute alkaline $$\mathrm{KMnO}_4$$ gave compound [C], 2-Methylbutane-2, 3-diol But when [A] is reacted with hot $$\mathrm{KMnO}_4$$, it yielded $$\mathrm{CH}_3 \mathrm{COOH}$$ and a compound [D] Identify compounds [A], [B] and [D]

Match the compounds given in Column I with their characteristic features listed in Column II

Choose the group of ions / molecules in which none of the species undergo Disproportionation reaction.

What is the amount of ice that separates out on cooling a solution containing $$60 \mathrm{~g}$$ of Ethylene glycol in $$250 \mathrm{~g}$$ of water to $$-9.3^{\circ} \mathrm{C}$$ ? $$\mathrm{K}_{\mathrm{f}}$$ of $$\mathrm{H}_2 \mathrm{O}=1.86 \mathrm{~K} / \mathrm{m} ;$$ MM of ethylene glycol= $$62 \mathrm{~amu}$$

$$\text { If a compound } \mathrm{X}_3 \mathrm{Y} \text { is } 60 \% \text { ionised in aqueous medium, what is its van't Hoff factor value? }$$

A Coordination compound is represented by the formula $$[\mathrm{CoBr}_3(e n) x]$$. This compound required one mole of $$\mathrm{AgNO}_3$$ to form a pale yellow precipitate of $$\mathrm{AgBr}$$. What is the value of $$\mathrm{x}$$ in the compound?

Propane in presence of $$\mathrm{O}_2$$ gas undergoes complete combustion to produce $$\mathrm{CO}_2$$ and $$\mathrm{H}_2 \mathrm{O}$$. The required $$\mathrm{O}_2$$ for this combustion reaction was produced by the electrolysis of water. For what duration of time had water been electrolysed by passing $$200 \mathrm{~A}$$ current so that Oxygen gas produced could completely burn $$44 \mathrm{~g}$$ of Propane?

Arrange the following compounds in the decreasing order of reactivity towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction.

Above figure represents Vapour pressure versus Temperature graphs of 2 pure volatile liquids and a solution formed by the 2 liquids.

(i) Which curve represents the solution?

(ii) Which curve represents the liquid with the strongest intermolecular forces of attraction?

Which one of the following statements is incorrect regarding acetal and ketal formation when Propanal and Propanone are separately reacted with Ethanol in presence of anhydrous $$\mathrm{HCl}$$ gas.

Choose the incorrect statement from the following.

$$0.1 \mathrm{M}$$ solution of $$\mathrm{AgNO}_3$$ is taken in a Conductivity cell and a potential difference of $$40 \mathrm{~V}$$ is applied across the ends of a column of this solution whose diameter is $$4.0 \mathrm{~cm}$$ and length of the column is $$12 \mathrm{~cm}$$. The current used is $$0.4 \mathrm{~A}$$. The Molar conductivity of the solution is _________.

A statement of Assertion followed by a statement of Reason is given. Choose the correct answer out of the following options.

Assertion : Energy of $$2 \mathrm{~s}$$ orbital of Hydrogen is less than the energy of the $$2 \mathrm{~s}$$ orbital of Lithium.

Reason : Energies of orbitals in the same subshell decrease with increase in atomic number.

$$300 \mathrm{ml}$$ of an aqueous solution of $$\mathrm{NaOH}$$ with $$\mathrm{pH}$$ value of 10 is mixed with $$200 \mathrm{ml}$$ of an aqueous solution of $$\mathrm{HCl}$$ with a $$\mathrm{pH}$$ value of 4. What will be the $$\mathrm{pH}$$ of the resultant solution at room temperature?

Aniline undergoes reactions with reagents given in the order shown

(i) Aqueous $$\mathrm{Br}_2$$

(ii) $$\mathrm{NaNO}_2 / \mathrm{HCl} / 0^0 \mathrm{C}$$

(iii) Hypophosphorous acid

What is the product formed at the end of these reactions?

Which one of the following shows the correct increasing order of basic nature of the given compounds?

A: Phenylmethanamine

B: N-Ethylethanamine

C:N, N-Dimethylaniline

D : N, N-Dimethylmethanamine

Given: $$\Delta \mathrm{G}^0{ }_{\mathrm{f}}$$ of $$\mathrm{C}_2 \mathrm{H}_2$$ is $$2.09 \times 10^5 \mathrm{~J} / \mathrm{mol}$$ and $$\Delta \mathrm{G}_{\mathrm{f}}^0$$ of $$\mathrm{C}_6 \mathrm{H}_6$$ is $$1.24 \times 10^5 \mathrm{~J} / \mathrm{mol}$$. Calculate the equilibrium constant for the cyclic polymerisation of Ethyne to Benzene at $$27^{\circ} \mathrm{C}$$. $$(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1})$$

A Carbonyl compound $$\mathrm{X}$$ when reacted with Methyl magnesium bromide followed by hydrolysis gave product $$\mathrm{Y}$$. When $$\mathrm{Y}$$ is heated with $$\mathrm{Cu}$$ at $$573 \mathrm{~K}$$, it gave $$\mathrm{Z}$$ (2- Methylbut-2-ene) as one of the products. Identify $$\mathrm{X}$$.

Identify the Reagents I and II to be used in the course of the given reactions.

Given below are 4 species with one odd electron on the Carbon atom.

$$\begin{array}{ll} \mathrm{A}=\left(\mathrm{CH}_3\right)_3 \stackrel{\bullet}{\mathrm{C}} & \mathrm{B}=\left(\mathrm{C}_6 \mathrm{H}_5\right)_3 \stackrel{\bullet}{\mathrm{C}} \\ \mathrm{C}=\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \stackrel{\bullet}{\mathrm{C}} \mathrm{H} & \mathrm{D}=\left(\mathrm{CH}_3\right)_2 \stackrel{\bullet}{\mathrm{C}} \mathrm{H} \end{array} $$

Choose the correct decreasing order of stability of the species.

Which one of the following compounds when reacted with $$\mathrm{NaOH}$$ (aq) undergoes Substitution Nucleophilic Bimolecular reaction with retention of configuration?

A statement of Assertion followed by a statement of Reason is given. Choose the correct answer out of the following options.

Assertion: The Eclipsed and the Staggered conformations of Ethane continuously flip from one form to the other.

Reason: The torsional barrier between the Conformers of Ethane has a high value of about $$50 \mathrm{~kJ} / \mathrm{mol}$$ and this restricts free rotation around $$\mathrm{C}-\mathrm{C}$$ bond.

Match the Hormones listed in Column I with their characteristics listed in Column II

Identify the product [D] formed when Reactant [A] $$(M M 78 \mathrm{~g} / \mathrm{mol})$$ undergoes the series of reactions shown

The boiling point of a $$4 \%$$ aqueous solution of a non-volatile solute $$\mathrm{P}$$ is equal to the boiling point of $$\mathrm{X} \%$$ solution of another non-volatile solute $$\mathrm{Q}$$. The relation between their Molar masses is $$\mathrm{M}_{\mathrm{Q}}=4 \mathrm{~Mp}$$. What is $$\mathrm{X}$$ ?

Given below are 4 statements about Insulin. Which of these statement/(s) is/are correct?

[A] Insulin is a globular protein consisting of 51 Amino acids.

[B] Insulin is constituted of 3 polypeptide chains linked together.

[C] Insulin is constituted of 2 polypeptide chains linked together by disulphide bonds.

[D] The 3 polypeptide chains in Insulin are linked together by Hydrogen bonding.

Given below are 4 subatomic particles travelling with the same velocity "v". Which of them will have the shortest wavelength?

$$[A]=\text { Proton }[B]=\text { Neutron. }[C]=\text { Alpha particle. }[D]=\text { Electron. }$$

The mass number of an element $$\mathrm{X}$$ is 175 with 104 neutrons in its nucleus. Into which one of the following orbitals will the last electron enter?

What is the number of mono-chloro derivatives of Ethyl cyclohexane possible?

Which one of the following is the correct IUPAC name of the given compound?

An aromatic hydrocarbon $$[\mathrm{A}]\left(\mathrm{Molecular}\right.$$ formula $$\left.\mathrm{C}_9 \mathrm{H}_{12}\right)$$, undergoes air oxidation followed by reaction with dil. $$\mathrm{HCl}$$ to give [B] as one of the products

Compound [B] forms a white precipitate on treatment with $$\mathrm{Br}_2(\mathrm{aq})$$

Sodium salt of [B] reacts with $$\mathrm{CO}_2$$ at $$400 \mathrm{~K}$$ under high pressure followed by acid hydrolysis to give [C]

Compound [C] reacts with acetic anhydride / conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ to form [D] Identify compound $$[\mathrm{D}]$$

A given chemical reaction is represented by the following stoichiometric equation.

$$3 X+2 Y+\frac{5}{2} Z \rightarrow P_1+P_2+P_3$$

The rate of reaction can be expressed as _________.

Match the chemical reactions taking place at the Anode of the cell with the correct cell in which the reaction occurs.

If the enthalpy of formation of a diatomic molecule $$\mathrm{AB}$$ is $$-400 \mathrm{~kJ} / \mathrm{mol}$$ and the bond dissociation energies of $$\mathrm{A}_2$$ and $$\mathrm{B}_2$$ and $$\mathrm{AB}$$ are in the ratio $$2: 1: 2$$, what is the bond dissociation enthalpy of $$\mathrm{B}_2$$ ?

Choose the incorrect statement from the following

Given below are 4 equations showing Molar conductivities at infinite dilution of various electrolytes. Which one of them represents the correct equation?

$$\begin{aligned} & \left(\Lambda_m^0\right)_{N a B r}-\left(\Lambda_m^0\right)_{N a C l}=\left(\Lambda_m^0\right)_{\mathrm{KCl}}-\left(\Lambda_m^0\right)_{\mathrm{KBr}} \\ & \left(\Lambda_m^0\right)_{\mathrm{HCl}}+\left(\Lambda_m^0\right)_{\mathrm{KOH}}-\left(\Lambda_m^0\right)_{\mathrm{KCl}}=\left(\Lambda_m^0\right)_{\mathrm{H}_2 \mathrm{O}} \\ & \left(\Lambda_m^0\right)_{\mathrm{KBr}}-\left(\Lambda_m^0\right)_{\mathrm{NaBr}}=\left(\Lambda_m^0\right)_{\mathrm{NaBr}}-\left(\Lambda_m^0\right)_{\mathrm{Nal}} \\ & \left(\Lambda_m^0\right)_{N H_4 \mathrm{Cl}}-\left(\Lambda_m^0\right)_{\mathrm{NH}_4 \mathrm{NO}_3}=\left(\Lambda_m^0\right)_{N H_4 \mathrm{Cl}}-\left(\Lambda_m^0\right)_{N H 4 B r} \end{aligned}$$

On the basis of VSEPR theory, match the molecules listed in Column I with their shapes given in Column II.

Match the compounds given in column I with the corresponding most stable Carbocations formed by each, as given in Column II, when they undergo acidic dehydration in presence of Conc. $$\mathrm{H}_2 \mathrm{SO}_4$$.

Identify the pair of molecules, both of which have positive values of Dipole moment.

Given below are 4 molecular species/ions. Identify the species/ion which exhibits diamagnetic nature.

$$[\mathrm{A}]=\mathrm{N}_2^{+} \quad[\mathrm{B}]=\mathrm{O}_2^{-} \quad[\mathrm{C}]=\mathrm{B}_2 \quad[\mathrm{D}]=\mathrm{C}_2$$

The side of an equilateral triangle expands at the rate of $$\sqrt{3} \mathrm{~cm} / \mathrm{sec}$$. When the side is $$12 \mathrm{~cm}$$, the rate of increase of its area is

$$ \text { If } P=\left[\begin{array}{lll} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}\right] \text { is the adjoint of a } 3 \times 3 \text { matrix } A \text { and }|A|=4 \text { then } \alpha \text { is equal to } $$

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \\ \lambda, & \text { if } x=\frac{\pi}{2} \end{array}\right. $$

Then $$f(x)$$ will be continues function at $$x=\frac{\pi}{2}$$, then $$\lambda=$$

$$\begin{aligned} &\begin{aligned} & \text { A, B, C are subsets of the Universal set U } \\ & \text { If } \mathrm{A}=\{x: x \text { is even number, } x \leq 20\} \\ & \mathrm{B}=\{x: x \text { is multiple of } 3, x \leq 15\} \\ & \mathrm{C}=\{x: x \text { is multiple of } 5, x \leq 20\} \\ & \mathrm{U}=\text { Set of whole numbers } \end{aligned}\\ &\text { then the Venn diagram representing } \mathrm{U}, \mathrm{A}, \mathrm{B} \text { and } \mathrm{C} \text { is } \end{aligned}$$

The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is

In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to

A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability that the two numbers are equal is

If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$

The probability that a randomly chosen number from one to twelve is a divisor of twelve is

Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)$$

If $$f(x)=f^{\prime}(x)$$ and $$f(1)=2$$, then $$f(3)$$ is

The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadratic equation $$2 x^2-3 x+1=0$$, is

If $$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$ then the inverse of $$(A I)^t$$ (where $$\mathrm{I}$$ is an identity matrix) is

$$ \text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{array}\right] \text { is } $$

If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$

If $$\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c$$ then the value of $$k$$ is

$$P$$ is a point on the line segment joining the points $$(3,2,-1)$$ and $$(6,2,-2)$$. If $$x$$ coordinate of $$\mathrm{P}$$ is 5, then its $$y$$ co-ordinate is

A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio of the G.P is

The particular solution of $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$, when $$x=0, y=\frac{1}{2}$$ is

If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ then the possible values of $x$ lies in the interval

The mean of the numbers $$a, b, 8,5,10$$ is 6 and the variance is 6.80 , then which of the following gives possible values of $$a$$ & $$b$$

If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, then $$\lambda$$ is equal to

$$\int \sqrt{x^2-4 x+2} d x=$$

$$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }$$

The minimum value of $$Z=150 x+200 y$$ for the given constraints

$$\begin{aligned} & 3 x+5 y \geq 30 \\ & x+y \geq 8 ; x \geq 0, y \geq 0 \text { is } \end{aligned}$$

The vector equation of two lines are

$$\begin{aligned} & \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\ & \vec{r}=(s+1) \hat{\imath}+(2 s-1) \hat{\jmath}-(2 s+1) \hat{k} \end{aligned}$$

Then the shortest distance between them is

$$ \text { If the matrix } A=\left(\begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array}\right) \text { then } A^{n+1}= $$

$$ \text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \cap(B \times A) \text { is equal to } $$

If $$ \left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]\left[\begin{array}{l} 1 \\ 2 \\ x \end{array}\right]=[0] $$ then x is equal to

$$ \int \frac{x}{x^4-16} d x= $$

Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection with the line $$x+y=4$$ may be at a distance of $$\sqrt{\frac{2}{3}}$$ from this point.

An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the third ball drawn is black is

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is

Given $$a, b, c$$ are three unequal numbers such that $$\mathrm{b}$$ is arithmetic mean of $$a$$ and $$c$$ and $$(b-a),(c-b), a$$ are in geometric progression. Then $$a: b: c$$ is

$$ \text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to } $$

The equation of a circle passing through the origin is $$x^2+y^2-6 x+2 y=0$$. The equation of one of its diameter is

The particular solution of the differential equation $$\cos x \frac{d y}{d x}+y=\sin x$$ at $$y(0)=1$$

A random variable X with probability distribution is given below

The mean of this distribution is

$$ \text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is } $$

$$ \text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is } $$

$$ \text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is } $$

The area (in sq units) of the minor segment bounded by the circle $$x^2+y^2=a^2$$ and the line $$x=\frac{a}{\sqrt{2}}$$ is

Let $$f: R \rightarrow R$$ be a function defined by $$f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}$$ then

$$ \lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals } $$

$$ \text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0 $$

The vector $$(\vec{r})$$ whose magnitude is $$3 \sqrt{2}$$ units which makes an angle of $$\frac{\pi}{4}$$ and $$\frac{\pi}{2}$$ with $$y$$ and $$z$$- axis respectively is

$$ \text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sin ^{-1} \frac{1}{\sqrt{2}}\right)\right] $$ is

For a given curve $$y=2 x-x^2$$, when $$x$$ increases at the rate of 3 units/sec, then how does the slope of the curve change?

The coefficient of the third term in the expansion of $$\left(x^2-\frac{1}{4}\right)^n$$, when expanded in the descending power of $$x$$ is 31, then $$n$$ is

$$ \text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|= $$

$$ \text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)= $$

$$ \int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is } $$

$$ \text { If } \frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6), x \in R \text { then } $$

$$ \text { The area (in sq units) enclosed by the parabola } y^2=8 x \text {, its latus-rectum and the } x \text {-axis is } $$

The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side three times as long as the other, is

Express the set $$A=\{1,7,17,31,49\}$$ in set builder form

$$ (32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to } $$

$$ \text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is } $$

Which of the following is not a homogenous function of $$x$$ and $$y$$

The resistance of the galvanometer and shunt of an ammeter are $$90 \mathrm{~ohm}$$ and $$10 \mathrm{~ohm}$$ respectively, then the fraction of the main current passing through the galvanometer and the shut respectively are:

A glass of hot water cools from $$90^{\circ} \mathrm{C}$$ to $$70^{\circ} \mathrm{C}$$ in 3 minutes when the temperature of surroundings is $$20^{\circ} \mathrm{C}$$. What is the time taken by the glass of hot water to cool from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$ if the surrounding temperature remains the same at $$20^{\circ} \mathrm{C}$$ ?

When two objects are moving along a straight line in the same direction, the distance between them increases by $$6 \mathrm{~m}$$ in one second. If the objects move with their constant speed towards each other the distance decreases by $$8 \mathrm{~m}$$ in one second, then the speed of the objects are :

In the Young's double slit experiment $$n^{\text {th }}$$ bright for red coincides with $$(n+1)^{\text {th }}$$ bright for violet. Then the value of '$$n$$' is: (given: wave length of red light $$=6300^{\circ} \mathrm{A}$$ and wave length of violet $$=4200^{\circ} \mathrm{A}$$).

A metal ball of $$20 \mathrm{~g}$$ is projected at an angle $$30^{\circ}$$ with the horizontal with an initial velocity $$10 \mathrm{~ms}^{-1}$$. If the mass and angle of projection are doubled keeping the initial velocity the same, the ratio of the maximum height attained in the former to the latter case is :

The threshold frequency for a metal surface is '$$n_0$$'. A photo electric current '$$I$$' is produced when it is exposed to a light of frequency $$\left(\frac{11}{6}\right) \mathrm{n}_{\mathrm{o}}$$ and intensity $$\mathrm{I}_{\mathrm{n}}$$. If both the frequency and intensity are halved, the new photoelectric current '$$\mathrm{I}^1$$' will become:

A $$500 \mathrm{~W}$$ heating unit is designed to operate on a $$400 \mathrm{~V}$$ line. If line voltage drops to $$160 \mathrm{~V}$$, the percentage drop in heat output will be:

Current flows through uniform, square frames as shown in the figure. In which case is the magnetic field at the centre of the frame not zero?

A transformer which steps down $$330 \mathrm{~V}$$ to $$33 \mathrm{~V}$$ is to operate a device having impedance $$110 \Omega$$. The current drawn by the primary coil of the transformer is :

A cell of emf E and internal resistance r is connected to two external resistances $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ and a perfect ammeter. The current in the circuit is measured in four different situations:

(a) without any external resistance in the circuit.

(b) with resistance $$\mathrm{R_1}$$ only

(c) with $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ in series combination.

(d) with $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ in parallel combination.

The currents measured in the four cases in ascending order are

Select the unit of the coefficient of mutual induction from the following.

Steel is preferred to soft iron for making permanent magnets because,

A particle executes a simple harmonic motion of amplitude $$\mathrm{A}$$. The distance from the mean position at which its kinetic energy is equal to its potential energy is

A body of mass $$5 \mathrm{~kg}$$ at rest is rotated for $$25 \mathrm{~s}$$ with a constant moment of force $$10 \mathrm{~Nm}$$. Find the work done if the moment of inertia of the body is $$5 \mathrm{~kg} \mathrm{~m}^2$$.

In the normal adjustment of an astronomical telescope, the objective and eyepiece are $$32 \mathrm{~cm}$$ apart. If the magnifying power of the telescope is 7, find the focal lengths of the objective and eyepiece.

In a given semiconductor, the ratio of the number density of electron to number density of hole is $$2: 1$$. If $$\frac{1}{7}$$th of the total current is due to the hole and the remaining is due to the electrons, the ratio of the drift velocity of holes to the drift velocity of electrons is :

If $$\mathrm{A}$$ is the areal velocity of a planet of mass $$\mathrm{M}$$, then its angular momentum is

When a particular wave length of light is used the focal length of a convex mirror is found to be $$10 \mathrm{~cm}$$. If the wave length of the incident light is doubled keeping the area of the mirror constant, the focal length of the mirror will be:

The mass of a particle $$\mathrm{A}$$ is double that of the particle $$\mathrm{B}$$ and the kinetic energy of $$\mathrm{B}$$ is $$\frac{1}{8}$$th that of A then the ratio of the de- Broglie wavelength of A to that of B is:

A coil of inductance $$1 \mathrm{H}$$ and resistance $$100 \Omega$$ is connected to an alternating current source of frequency $$\frac{50}{\pi} \mathrm{~Hz}$$. What will be the phase difference between the current and voltage?

The current through a conductor is '$$\mathrm{a}$$' when the temperature is $$0^{\circ} \mathrm{C}$$. It is '$$\mathrm{b}$$' when the temperature is $$100^{\circ} \mathrm{C}$$. The current through the conductor at $$220^{\circ} \mathrm{C}$$ is

Which of the following graph shows the variation of velocity with mass for the constant momentum?

For a $$30^{\circ}$$ prism when a ray of light is incident at an angle $$60^{\circ}$$ on one of its faces, the emergent ray passes normal to the other surface. Then the refractive index of the prism is:

A coil offers a resistance of $$20 \mathrm{~ohm}$$ for a direct current. If we send an alternating current through the same coil, the resistance offered by the coil to the alternating current will be :

A square shaped aluminium coin weighs $$0.75 \mathrm{~g}$$ and its diagonal measures $$14 \mathrm{~mm}$$. It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges $$(+Q$$ and $$-Q)$$ that are separated by a distance equal to the side of the coin, the dipole moment of the dipole is

If the earth has a mass nine times and radius four times that of planet X, the ratio of the maximum speed required by a rocket to pull out of the gravitational force of planet $$\mathrm{X}$$ to that of the earth is

Two similar coils $A$ and $B$ of radius '$$r$$' and number of turns '$$N$$' each are placed concentrically with their planes perpendicular to each other. If I and $$2 \mathrm{I}$$ are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be:

An ideal diode is connected in series with a capacitor. The free ends of the capacitor and the diode are connected across a $$220 \mathrm{~V}$$ ac source. Now the potential difference across the capacitor is :

Which of the following statement is true regarding the centre of mass of a system?

A ray of light travelling through a medium of refractive index $$\frac{5}{4}$$ is incident on a glass of refractive index $$\frac{3}{2}$$. Find the angle of refraction in the glass, if the angle of incidence at the given medium - glass interface is $$30^{\circ}$$.

The ratio of the radii of the nucleus of two element $$\mathrm{X}$$ and $$\mathrm{Y}$$ having the mass numbers 232 and 29 is:

When light wave passes from a medium of refractive index '$$\mu$$' to another medium of refractive index '$$2 \mu$$' the phase change occurs to the light is :

On increasing the temperature of a conductor, its resistance increases because

The difference in energy levels of an electron at two excited levels is $$13.75 \mathrm{~eV}$$. If it makes a transition from the higher energy level to the lower energy level then what will be the wave length of the emitted radiation? [given $$h=6.6 \times 10^{-34} \mathrm{~m}^2 \mathrm{~kg} \mathrm{~s}^{-1} ; c=3 \times 10^8 \mathrm{~ms}^{-1} ; 1 \mathrm{~eV}=1.6 \times 10^{-19} \mathrm{~J}$$]

A string of length $$25 \mathrm{~cm}$$ and mass $$10^{-3} \mathrm{~kg}$$ is clamped at its ends. The tension in the string is $$2.5 \mathrm{~N}$$. The identical wave pulses are generated at one end and at regular interval of time, $$\Delta \mathrm{t}$$. The minimum value of $$\Delta \mathrm{t}$$, so that a constructive interference takes place between successive pulses is

A cubical box of side $$1 \mathrm{~m}$$ contains Boron gas at a pressure of $$100 \mathrm{~Nm}^{-2}$$. During an observation time of 1 second, an atom travelling with the rms speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. The total mass of gas in the box in gram is

Around the central part of an air cored solenoid of length $$20 \mathrm{~cm}$$ and area of cross section $$1.4 \times 10^{-3} \mathrm{~m}^2$$ and 3000 turns, another coil of 250 turns is closely wound. A current $$2 \mathrm{~A}$$ in the solenoid is reversed in $$0.2 \mathrm{~s}$$, then the induced emf produced is

A circular coil of radius $$0.1 \mathrm{~m}$$ is placed in the $$\mathrm{X}-\mathrm{Y}$$ plane and a current $$2 \mathrm{~A}$$ is passed through the coil in the clockwise direction when looking from above. Find the magnetic dipole moment of the current loop

A body is moving along a circular path of radius '$$r$$' with a frequency of revolution numerically equal to the radius of the circular path. What is the acceleration of the body if radius of the path is $$\left(\frac{5}{\pi}\right) m$$ ?

Which of the given dimensional formula represents heat capacity

If potential (in volt) in a region is expressed as $$\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathrm{y}+2 \mathrm{yz}$$, the electric field (in $$N C^{-1}$$) at point $$(1,0,1)$$ is

The closest approach of an alpha particle when it make a head on collision with a gold nucleus is $$10 \times 10^{-14} \mathrm{~m}$$, then the kinetic energy of the alpha particle is :

A one $\mathrm{kg}$ block of ice at $$-1.5^{\circ} \mathrm{C}$$ falls from a height of $$1.5 \mathrm{~km}$$ and is found melting. The amount of ice melted due to fall, if $$60 \%$$ energy is converted into heat is (Specific heat capacity of ice is $$0.5 \mathrm{~cal} \mathrm{~g}^{-1} \mathrm{~C}^{-1}$$, Latent heat of fusion of ice $$=80 \mathrm{~cal~g}^{-1}$$ )

64 rain drops of the same radius are falling through air with a steady velocity of $$0.5 \mathrm{~cm} \mathrm{~s}^{-1}$$. If the drops coalesce, the terminal velocity would be

The capacitance of a parallel plate capacitor is $$400 \mathrm{~pF}$$. It is connected to an ac source of $$100 \mathrm{~V}$$ having an angular frequency $$100 \mathrm{~rad~s}^{-1}$$. If the rms value of the current is $$4 \mu \mathrm{A}$$, the displacement current is:

Though $$\mathrm{Sn}$$ and $$\mathrm{Si}$$ are $$4^{\text {th }}$$ group elements, $$\mathrm{Sn}$$ is a metal while $$\mathrm{Si}$$ is a semiconductor because

Five charges, '$$q$$' each are placed at the comers of a regular pentagon of side '$$a$$' as shown in figure. First, charge from '$$A$$' is removed with other charges intact, then charge at '$$A$$' is replaced with an equal opposite charge. The ratio of magnitudes of electric fields at $$\mathrm{O}$$, without charge at $$A$$ and that with equal and opposite charge at $$A$$ is

Two circular coils of radius '$$a$$' and '$$2 a$$' are placed coaxially at a distance ' $$x$$ and '$$2 x$$' respectively from the origin along the $$\mathrm{X}$$-axis. If their planes are parallel to each other and perpendicular to the $$\mathrm{X}$$ - axis and both carry the same current in the same direction, then the ratio of the magnetic field induction at the origin due to the smaller coil to that of the bigger one is:

A metallic rod of $$2 \mathrm{~m}$$ length is rotated with a frequency $$100 \mathrm{~Hz}$$ about an axis passing through the centre of the circular ring of radius $$2 \mathrm{~m}$$. A constant magnetic field $$2 \mathrm{~T}$$ is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :

The power of a gun which fires 120 bullet per minute with a velocity $$120 \mathrm{~ms}^{-1}$$ is : (given the mass of each bullet is $$100 \mathrm{~g}$$)

The width of the fringes obtained in the Young's double slit experiment is $$2.6 \mathrm{~mm}$$ when light of wave length $$6000^{\circ} \mathrm{A}$$ is used. If the whole apparatus is immersed in a liquid of refractive index 1.3 the new fringe width will be :

An electric bulb of volume $$300 \mathrm{~cm}^3$$ was sealed off during manufacture at a pressure of $$1 \mathrm{~mm}$$ of mercury at $$27{ }^{\circ} \mathrm{C}$$. The number of air molecules contained in the bulb is, $$(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$ and $$N_A=6.02 \times 10^{23})$$

Find the binding energy of the tritium nucleus: [Given: mass of $$1 \mathrm{H}^3=3.01605 \mathrm{~u} ; \mathrm{~m}_{\mathrm{p}}=1.00782 \mathrm{~u} ; \mathrm{~m}_{\mathrm{n}}=1.00866 \mathrm{~u}$$.]

In a single slit diffraction experiment, for slit width '$$\alpha$$' the width of the central maxima is '$$\beta$$'. If we double the slit width then the corresponding width of the central maxima will be:

Two charges '$$-q$$' each are fixed, separated by distance '$$2 d$$'. A third charge '$$q$$' of mass '$$m$$' placed at the mid-point is displaced slightly by '$$x$$' $$(x< < d)$$ perpendicular to the line joining the two fixed charges as shown in Fig. The time period of oscillation of '$$q$$' will be

Two metal spheres, one of radius $$\frac{R}{2}$$ and the other of radius $$2 \mathrm{R}$$ respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is

Find the value of '$$n$$' in the given equation $$P=\rho^n v^2$$ where '$$P$$' is the pressure, '$$\rho$$' density and '$$v$$' velocity.

A stone of mass $$2 \mathrm{~kg}$$ is hung from the ceiling of the room using two strings. If the strings make an angle $$60^{\circ}$$ and $$30^{\circ}$$ respectively with the horizontal surface of the roof then the tension on the longer string is : $$g=10 \mathrm{~ms}^{-2}$$

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as $$\epsilon=2 U$$. A similar capacitor with no dielectric is charged to $$U_0=78 \mathrm{~V}$$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are $$\mathrm{a}, \mathrm{b}$$ and $$\mathrm{c}$$ respectively, then the corresponding ratio of increase in their lengths would be