From the given options, choose the correct one that will replace the question mark(?) in the following series.

$$2,0,3,2,4,6,5,12,6, ?, 7,30 $$

In a certain code language, 'RUBBER' is coded as '102' and 'JELLY' is coded as '76'. How will 'LABEL' be coded in the same language?

Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the letter-cluster that is different.

In a code language, 'SAUCE' is written as 'ASVEC'. How will 'MEANT' be written as in that language?

Select the number from among the given options that can replace the question mark (?) in the following series.

$$3,10,24, ? , 73, 108$$

What is the average income of the company over the years?

Which of the following pairs of years, shows the equal expenditure of the company?

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements

1. Few gentlemen are rich.

2. Few gentlemen are not fools.

3. Everyone is either a fool or rich.

Conclusions

I. No gentleman is rich.

II. Few gentlemen being fools is a possibility.

III. No one is both a fool and rich.

How is P related to R?

I. $$Q$$ is the son of $$R$$.

II. $$\mathrm{Q}$$ is the brother of $$\mathrm{P}$$.

Six persons A, B, C, D, E and F are sitting in a row. A and F are sitting at two extreme ends of the row. B is to the immediate right of A and D is 2nd left of F. What is the position of E with respect to A ?

I. $$\mathrm{E}$$ is to the right of $$\mathrm{A}$$.

II. $$\mathrm{E}$$ is to the left of $$\mathrm{C}$$.

In context of the lanthanoides, which of the following statements is not correct?

The number of peptide bonds in a linear tetrapeptide (made of different amino acids) are

The uncertainty in the momentum of an electron is $$2.0 \times 10^{-8} \mathrm{~kg} \mathrm{~ms}^{-1}$$. The uncertainty in its position will be

A metal has bcc structure and the edge length of its unit cell is $$8 \mathop A\limits^o$$. The volume of the unit cell ( in $$\mathrm{cm}^3$$) will be

$$\mathrm{MnO}_4^{-}$$ is good oxidising agent in different medium changing to

$$\mathrm{MnO}_4^{-} \rightarrow \mathrm{Mn}^{2+} \rightarrow \mathrm{MnO}_4^{2-} \rightarrow \mathrm{MnO}_2 \rightarrow \mathrm{Mn}_2 \mathrm{O}_3$$

Change in oxidation number respectively are :

In the reaction, $$\mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI}$$. In a 4L flask, 0.8 mole of each $$\mathrm{H}_2$$ and $$\mathrm{I}_2$$ are taken. All equilibrium, 1 mole of $$\mathrm{HI}$$ is formed. What will be the value of equilibrium constant $$K_C$$ ?

The ionic conductance of following cation in a given concentration are in the order.

$$\mathrm{H}$$-bonding is maximum in

The stability of dihalides of $$\mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}$$ and decreases gradually in the sequence.

The structure of $$\mathrm{XeOF}_4$$ is

$$\mathrm{PH}_3$$ has much lower boiling point than $$\mathrm{NH}_3$$ because :

Match the following Column I and Column II

ortho-silicate ion is

Which is correct about zero order reaction?

Which of the following compounds is used as the starting material for the preparation of potassium dichromate?

The total number of metal-metal bond present in $$\left[\mathrm{Co}_2(\mathrm{CO})_8\right]$$ is

Which of the following is an intensive property?

Plot of $$\log x / m$$ against $$\log p$$ is a straight line inclined at an angle of $$45^{\circ}$$. When the pressure is $$2 \mathrm{~atm}$$ and Freundlich parameter, $$k$$ is 10, the amount of solute adsorbed per gram of adsorbent.

The value of $$\Delta E$$ for combustion of $$32 \mathrm{~g}$$ of $$\mathrm{CH}_4$$ is $$-1770778 \mathrm{~J}$$ at $$298 \mathrm{~K}$$. The $$\Delta H$$ combustion for $$\mathrm{CH}_4$$ in $$\mathrm{J} \mathrm{~mol}^{-1}$$ at this temperature will be (Given that, $$R=8.314 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$$ )

The standard $$E_{\text {red }}^{\circ}$$ values of $$A, B$$ and $$C$$ are $$+0.52 \mathrm{~V},-23.6 \mathrm{~V},-0.44 \mathrm{~V}$$ respectively. The order of their reducing power is

Addition of water to butyne occurs in acidic medium and in the presence of $$\mathrm{Hg}^{2+}$$ ions as a catalyst. The compound obtained

The reaction,

is called

Which of the following products is formed in the given reaction?

The acidic strength of following compounds are in the order

Consider the following cell reaction.

$$\begin{aligned} & 2 \mathrm{Fe}(s)+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longrightarrow \\ & 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_2 \mathrm{O}(l), E^{\circ}=1.67 \mathrm{~V} \\ \end{aligned}$$

At $$[\mathrm{Fe}^{2+}]=10^{-5} \mathrm{M}, {\mathrm{P}}{ }_2=3 \mathrm{~atm}$$ and $$\mathrm{pH}=2.5$$, the cell potential at $$25^{\circ} \mathrm{C}$$ is

In a set of reactions acetophenone gave a product $$B$$. Identify the product $$B$$.

$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCH}_3 \xrightarrow{\mathrm{C}_6 \mathrm{H}_5 \mathrm{MgBr}} A \xrightarrow{\mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}} B$$

Glucose contains $$-\mathrm{CHO}$$ group and Which of the following solution or reagent can be used to distinguish these two compounds?

In the given reaction,

The product P is

Which one of the following concentration terms is/are independent of temperature?

In a set of reactions nitrobenzene gave a product $$C$$. Identify the product $$C$$.

$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NO}_2 \xrightarrow{\mathrm{Fe} / \mathrm{HCl}} A \xrightarrow[273 \mathrm{~K}]{\mathrm{NaNO}_2 / \mathrm{HCl}} B \xrightarrow[\Delta]{\mathrm{H}_2 \mathrm{O} / \mathrm{H}^{+}} C$$

Which one of the following compounds is formed in the laboratory from benzene by a substitution reaction?

Atomic number of $$\mathrm{Mn}, \mathrm{Fe}$$ and $$\mathrm{Co}$$ are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complex ions are diamagnetic?

I. $$\left[\mathrm{CO}\left(\mathrm{NH}_3\right)_6\right]^{3+}$$

II. $$\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$$

III. $$\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$$

IV. $$\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$$

Choose the correct option.

Arrhenius equation may not be represented as

Match the Column I with Column II.

Mark the correct option

Choose the wrong statements.

I. $$\mathrm{CO}_2$$ is responsible for greenhouse effect.

II. Acid rain contains mainly $$\mathrm{HNO}_3$$.

III. NO is more harmful than $$\mathrm{NO}_2$$.

IV. $$\mathrm{CO}_2$$ can absorb infrared.

Mark the correct option

Fill in the blank with most suitable word. I ............. for forty minutes to see the doctor before my name was announced.

Pick out the correct synonym of the word-'Prerogative'.

Select the antonym for the word 'Dishevelled'

What is '$$\mathrm{I}$$' in the above lines?

The rain calls itself the 'dotted silver threads' as

Let $$a_n$$ be a sequence of numbers which is defined by relation $$a_1=2, \frac{a_n}{a_{n+1}}=3^{-n}$$, then $$\log _2\left(a_{50}\right)$$ is equal to (take $$\log _2 3=1.6$$ )

The value of $$\frac{1}{2}\left(\frac{1}{5}\right)^2+\frac{2}{3}\left(\frac{1}{5}\right)^3+\frac{3}{4}\left(\frac{1}{5}\right)^4+\ldots . . \infty$$ is

Out of 9 consonants and 4 vowels, how many words of 4 consonants and 3 vowels can be formed?

Last three digits in $$(9)^{50}$$ be

The minium value of $$\left[2-\cos \theta+\sin ^2 \theta\right]$$ is

If $$z_1, z_2$$ and $$z_3$$ are the vertices $$A, B$$ and $$C$$ respectively of an isosceles right angled triangle with right angled at $$C$$, then $$\left(z_1-z_3^{\prime}\right)\left(z_2-z_3\right)$$ equals to

The line $$a x+b y+c=0$$ will be a tangent to the circle $$x^2+y^2=r^2$$, then

The image of the point $$(2,3,7)$$ in the plane $$2 x+5 y-3 z-19=0$$, is

The distance between the point $$(7,2,4)$$ and the plane determined by the points $$(2,5,-3),(-2,-3,5)$$ and $$(5,3,-3)$$ is

The value of $$\int_\lambda^{\lambda+\pi / 2}\left(\cos ^4 x+\sin ^4 x\right) d x$$ is

If matrix $$A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]$$ is given to be symmetric, then the value of $$a b$$ is

If the 4th term in the expansion of $$\left(p x+\frac{1}{x}\right)^n, n \in N$$ is $$\frac{5}{2}$$ and three normals to the parabola $$y^2=x$$ are drawn through a point $$(q, 0)$$, then

The area of the region containing the points $$(x, y)$$ satisfying $$4 \leq x^2+y^2 \leq 2|x|+|y|$$, is

If $$\alpha$$ is a non -real fifth root of unity, then the value of $$3^{\left|1+\alpha+\alpha^2+\alpha^{-2}-\alpha^{-1 \mid}\right|}$$, is

If $$\alpha, \beta$$ and $$\gamma$$ are the cube roots of $$P,(P<0)$$, then for any $$x, y$$ and $$z$$ which does not make denominator zero, the expression $$\frac{x \alpha+y \beta+z \gamma}{x \beta+y \gamma+z \alpha}$$ equals to

If $$x+\frac{1}{x}=1$$ and $$p=x^{4000}+\frac{1}{x^{4000}}$$ and $$q$$ is the digit at unit place in the number $$2^{2 n}+1$$, then the value of $$(p+q)$$ is equal to

Let $$z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots \ldots \ldots$$ 9, then $$\frac{1}{10}\left\{\left|1-z_1\right|\left|1-z_2\right| \ldots .\left|1-z_a\right|\right\}$$ equals to

If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2\right)^3}{\left(d^4 y / d x^4\right)^5}+\left(\frac{d^4 y}{d x^4}\right)=x^2+4$$, then $$m-n$$ is equal to

If $$\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2$$, then the range of $$a$$ is

The equation $$3 \cos ^{-1} x-\pi x-\pi / 2=0$$ has

The area enclosed by $$y=x^3+1$$ and $$y=x+2$$ in first quadrant, is

If $$R$$ is a relation from a finite set A having $$m$$ elements to finite set $$B$$ having $$n$$ elements, then the number of relation from $$A$$ to $$B$$ is

If $$\sin A, \sin B$$ and $$\cos A$$ are in GP, then the roots of $$x^2+2 x \cot B+1=0$$ are always

The determinant of the matrix $$\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]$$ is

Let $$A$$ and $$B$$ be two independent events such that the odds in favour of $$A$$ and $$B$$ are $$1: 1$$ and $$3: 2$$, respectively. Then, the probability that only one of the two occurs is

The plane is perpendicular to the planes $$x-y+2 z-4=0$$ and $$2 x-2 y+z=0$$ and passes through $$(1,-2,1)$$ is

If $$\theta_1, \theta_2$$ and $$\theta_3$$ are the angles made by a line with the positive direction of $$X, Y$$ and $$Z$$-axes, then $$\cos 2 \theta_1+\cos 2 \theta_2+\cos 2 \theta_3$$ is equal to

Suppose, $$A=\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$$ is an adjoint of the matrix $$\left[\begin{array}{rrr}1 & 3 & -3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$$. The value of $$\frac{a_1+b_2+c_3}{b_1 a_2}$$ is

The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x+7$$ occurs at the point

The solution of $$d y / d x=1+x+y+x y$$ is

A unit vector perpendicular to both the vectors $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathbf{k}}$$ is

If $$\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)$$, then the value of $$y$$ is

$$\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$$ equals to

If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to

The sum of all the numbers of four different digits that can be made using the digits 0, 1, 2 and 3 is

If $$x^n=a_0+a_1(1+x)+a_2(1+x)^2+\ldots \ldots \ldots+ a_n(1+x)^n=b_0+b_1(1-x)+b_2(1-x)^2+\ldots . .+ b_n(1-x)^n$$, then for $$n=201,\left(a_{101}, b_{101}\right)$$ is equal to

The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\left(y^2 / x^2\right)}\right)$$ is

For $$x \in R, f(x)=|\log 2-\sin x|$$ and $$g(x)=f(f(x))$$, then

$$\lim _\limits{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \ldots 3 n}{n^{2 n}}\right)^{1 / n}$$ is equal to

Let $$a, b$$ and $$c$$ be three unit vectors such that $$a \times(b \times c)=\frac{\sqrt{3}}{2}(b+c)$$. If $$b$$ is not parallel to $$c$$, then the angle between $$a$$ and $$b$$ is

The upper end of a wire of diameter $$24 \mathrm{~mm}$$ and length $$1 \mathrm{~m}$$ is damped and its other end is twisted through an angle is $$30^{\circ}$$. The angle of shear is

What is the voltage gain in a common emitter amplifier, where input resistance is $$6 \Omega$$ and load resistance $$48 \Omega, \beta=0.3$$ ?

When $${ }_{92} \mathrm{U}^{235}$$ undergoes fission, $$0.1 \%$$ of its original mass is changed into energy. How much energy is released if $$5 \mathrm{Kg}$$ of $${ }_{92} \mathrm{U}^{235}$$ undergoes fission?

A copper sphere cools from $$82^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 10 minutes and to $$42^{\circ} \mathrm{C}$$ in the next $$10 \mathrm{~min}$$. Calculate the temperature of the surrounding?

Two gases occupy two containers $$A$$ and $$B$$. The gas in $$A$$ of volume $$0.20 \mathrm{~m}^3$$, exerts a pressure of $$1.40 \mathrm{~MPa}$$ and that in $$B$$, of volume $$0.30 \mathrm{~m}^3$$ exerts a pressure of $$0.7 \mathrm{~MPa}$$. The two containers and united by a tube of negligible volume and the gases are allowed to exchange. Then, if the temperature remains constants. the final pressure in the container will be (in MPa).

Assuming the diodes to be of silicon with forward resistance zero, the current $$i$$ in the following circuit is

With increasing temperature, the angle of contact,

In a $$n$$-$$p$$-$$n$$ transistor $$10^{10}$$ electrons enter the emitter in $$10^{-6}$$ s. $$6 \%$$ of the other electrons are lost in the base. The current transfer ratio will be.

The position of a projectile launched from the origin at $$t=0$$ is given $$\mathbf{r}=(40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}) \mathrm{m}$$ at $$t=4 \mathrm{~s}$$. If the projectile was launded at an angle $$\theta$$ from the horizontal, then $$\theta$$ is (take, $$g=10 \mathrm{~m} / \mathrm{s}^2$$ )

Electric field in the region is given by $$\mathbf{E}=\left(M / x^4\right) \hat{\mathbf{i}}$$, then the correct expression for the potential in the region is (assume potential at infinity is zero)

The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$$. The change in the gravitational potential energy of a particle of mass $$1 \mathrm{~kg}$$ when it is taken from the origin to a point ($$5 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$) is

Two parallel conductors carry current in opposite directions as shown in the figure. One conductor carries a current of $$20 \mathrm{~A}$$. Point $$C$$ is a distance $$d / 2$$ to the right of a 20 A current. If $$d=18 \mathrm{~cm}$$ and $$i$$ is adjusted so that the magnetic field at $$C$$ is zero, the value of the current $$i$$ is

The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ counts per minute at $$t=6 \mathrm{~min}$$. The time (in minutes) at which the activity reduces to half its value is.

A ball is allowed to fall from a height of $$10 \mathrm{~m}$$. If there is $$30 \%$$ loss of energy due to impact, then after one impact ball will go up to.

The elastic limit of $$1 \mathrm{~kg}$$ mass is $$3.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$$. Find the maximum load that can be applied to a brass wire of a $$1 \mathrm{~mm}$$ diameter without exceeding the elastic unit.

The focal length of thin convex lens for red and blue rays are $$100 \mathrm{~cm}$$ and $$98.01 \mathrm{~cm}$$, respectively. There, the dispersive power of the material of the lens is

The ratio of the acceleration for a solid sphere (mass $$m$$ and radius $$R$$) rolling down an incline of angle '$$\theta$$' without slipping down the incline without rolling is.

The de-Broglie wavelength of a proton $$\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$$ acclerated through a potential difference of $$2 \mathrm{~kV}$$ is

The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immersed in water, the frequence becomes $$60 \mathrm{~Hz}$$ and on immersing the weights in a certain liquid, the frequency becomes $$40 \mathrm{~Hz}$$. The specific gravity of the liquid is

A particle of mass $m$ is projected with a velocity $$v$$ making an angle of $$45^{\circ}$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $$h$$ is.

A parallel plate capacitor with air between the plates has a capacitance of $$15 \mathrm{~pF}$$. the separation between the plates is $$d$$. The space between the plates is now filled with two dielectrics constant $$k_1=3$$ and thickness $$d / 3$$ while the other one has dielectric constant $$k_2=6$$ and thickness $$2 d / 3$$. Capacitance of the capacitor is now

A constant voltage is applied between the two ends of a uniform metallic wire, Some heat is developed in it. The heat developed is halved if

The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The wavelength of the $$k_\beta$$-line emitted by the same element will be

A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the faces at a point that is directly above the centre of the face at a height 3a/4 above the base. The minimum value of F for which the cube begins to topple an edge is (assume that cube does not slide)

Susceptibility of ferromagnetic substance is

A particle of mass $$10 \mathrm{~kg}$$ moving eastwards with a speed $$10 \mathrm{~m} / \mathrm{s}$$ collides with another particle of the same mass moving northward with the same speed $$10 \mathrm{~m} / \mathrm{s}$$. The two particles coalesce on collision. The new particle of mass $$20 \mathrm{~kg}$$ will move in the north-east direction with velocity.

A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is

A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $$10^{-2} \mathrm{~T}$$. If it is now turned through an angle of $$60^{\circ}$$ about on axis in its plane. Find the charge indicted in the coil. (Area of a coil $$=10^{-2} \mathrm{~m}^2$$ )

A geostationary satellite is orbiting the Earth at a height of $$4 R$$ above that surface of the Earth. $R$ being the radius of the earth. The, time period of another stellite in coins at a height of $$2 R$$ from the surface of the Earth is.

Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The magnetic field $$B$$ at a point $$P$$ lying on the perpendicular line joining the wires and at a distance $$x$$ from the mid-point is

0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cross-section $$A$$ closed by a massless piston. The cylinder is attached with a conducting rod of length L$$_1$$ cross-section area $$(1 / 9) \mathrm{m}^2$$ and thermal conductivity $$k_1$$ whose other end is maintained at $$0^{\circ} \mathrm{C}$$. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height $$L / 2$$ from the bottom of cylinder is (neglect any kind of heat loss from system)

In the formula $$X=3 Y Z^2, X$$ and $$Z$$ have dimensions of capacitance and magnetic induction respectively. The dimensions of $$Y$$ is MKS system are.

Three blocks of masses $$m_1, m_2$$ and $$m_3$$ are connected by massless strings, as shown, on a frictionless table. They are pulled with a force, $$T_3=40 \mathrm{~N}$$. If $$m_1=10 \mathrm{~kg}, m_2=8 \mathrm{~kg}$$ and $$m_3=2 \mathrm{~kg}$$, the tension $$T_2$$ will be

The susceptibility of a magnetism at $$300 \mathrm{~K}$$ is $$1.5 \times 10^{-5}$$. The temperature at which the susceptibility increases to $$4.5 \times 10^{-5}$$ is

A transmitting antenna is kept on the surface of the Earth. The minimum height of receiving antenna required to receive the signal in line of sight at $$4 \mathrm{~km}$$ distance from it is $$x \times 10^{-2} \mathrm{~m}$$. The value of $$x$$ is