Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine?

Product of the following reaction is

Acetophenone when reacted with a base, $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{ONa}$$, yields a stable compound which has the structure

Gabriel's synthesis is used frequency for the preparation of which of the following?

The product P in the reaction,

Pick out the incorrect statement(s) from the following.

1. Glucose exists in two different crystalline forms, $$\alpha$$-D-glucose and $$\beta$$-D-glucose.

2. $$\alpha$$-D-glucose and $$\beta$$-D-glucose are anomers.

3. $$\alpha$$-D-glucose and $$\beta$$-D-glucose are enantiomers.

4. Cellulose is a straight chain polysaccharide made of only $$\beta$$-D-glucose units.

5. Starch is a mixture of amylase and amylopectin, both contain unbranched chain of $$\alpha$$-D-glucose units.

Which of the following is incorrect?

Rank the following compounds in order of increasing basicity.

Ammoniacal silver nitrate forms a white precipitate easily with

Consider the following equilibrium,

$$\begin{aligned} & 2 \mathrm{No}(g) \rightleftharpoons \mathrm{N}_2+\mathrm{O}_2 ; \mathrm{K}_{\mathrm{G}}=2.4 \times 10^{20} \\ & \mathrm{No}(\mathrm{g})+\frac{1}{2} \mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons \mathrm{NoBr}(\mathrm{g}) ; \mathrm{K}_{\mathrm{C}_2}=1.4 \end{aligned}$$

Calculate $$K_C$$ for the reaction,

$$\frac{1}{2} \mathrm{~N}_2(g)+\frac{1}{2} \mathrm{O}_2(g)+\frac{1}{2} \mathrm{Br}_2(g) \rightleftharpoons \mathrm{NOBr}(g)$$

Which of the following is incorrect regarding Henry's law?

$$t$$-butyl chloride preferably undergo hydrolysis by

Which of these represents the correct order of decreasing bond order?

In a $$0.2 \mathrm{~M}$$ aqueous solution, lactic acid is $$6.9 \%$$ dissociated. The value of dissociation constant is

Pick up the correct statement.

Total number of $$\sigma$$ and $$\pi$$ bonds in ethene molecule is

A buffer solution has equal volumes of $$0.1 \mathrm{~M} \mathrm{~NH}_4 \mathrm{OH}$$ and $$0.01 \mathrm{~M} \mathrm{~NH}_4 \mathrm{Cl}$$. The $$\mathrm{pK}_b$$ of the base is 5. The $$\mathrm{pH}$$ is

Assuming no change in volume, the time required to obtain solution of $$\mathrm{pH}=4$$ by electrolysis of $$100 \mathrm{~mL}$$ of $$0.1 \mathrm{~M} \mathrm{~NaOH}$$ (using current $$0.5 \mathrm{~A}$$ ) will be

Which of the following compounds would not be expected to decarboxylate when heated?

Which of these molecules have non-bonding electron pairs on the cental atom?

$$\mathrm{I}: \mathrm{SF}_4 : \mathrm{II}: \mathrm{ICl}_3 : \mathrm{III}: \mathrm{SO}_2$$

For a cell reaction, $$A(s)+B^{2+}(a q) \longrightarrow A^{2+}(a q)+B(s)$$; the standard emf of the cell is $$0.295 \mathrm{~V}$$ at $$25^{\circ} \mathrm{C}$$. The equilibrium constant at $$25^{\circ} \mathrm{C}$$ will be

Which of the following shows negative deviation from Raoult's law?

$$5 \mathrm{~g}$$ of non-volatile water soluble compound $$X$$ is dissolved in $$100 \mathrm{~g}$$ of water. The elevation in boiling point is found to be 0.25. The molecular mass of compound $$X$$ is

The correct decreasing order of negative electron gain enthalpy for $$\mathrm{C}, \mathrm{Ca}, \mathrm{Al}, \mathrm{F}$$ and $$\mathrm{O}$$ is

I and II are

$$\mathrm{Ti}^{2+}$$ is purple while $$\mathrm{Ti}^{4+}$$ is colourless because

In Friedal-Crafts alkylation reaction of phenol with chloromethane, the product formed will be

Which among the following is diamagnetic?

Which one of the following is an important component of chlorophyll?

A volatile compound is formed by carbon monoxide and

The complex $$\left[\mathrm{PtCl}_2(\mathrm{en})_2\right]^{2+}$$ ion shows

$$15 \mathrm{~g}$$ of $$\mathrm{CaCO}_3$$ completely reacts with

Bohr's radius of 2 nd orbit of $$\mathrm{Be}^{3+}$$ is equal to that of

How much faster would a reaction proceed at $$25^{\circ} \mathrm{C}$$ than at $$0^{\circ} \mathrm{C}$$ if the activation energy is $$65 \mathrm{~kJ}$$?

The blue colouration obtained from the Lassaigne's test of nitrogen is due to the formation of

The ion that is isoelectronic with $$\mathrm{CO}$$ is

At $$300 \mathrm{~K}$$, the half-life period of a gaseous reaction at an initial pressure of $$40 \mathrm{~kPa}$$ is 350 s. When pressure is $$20 \mathrm{~kPa}$$, the half-life period is 175 s. What is the order of the reaction?

If 2 moles of $$\mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})$$ are completely burnt $$4100 \mathrm{~kJ}$$ of heat is liberated. If $$\Delta H^{\circ}$$ for $$\mathrm{CO}_2(\mathrm{~g})$$ and $$\mathrm{H}_2 \mathrm{O}(l)$$ are $$-410$$ and $$-285 \mathrm{~kJ}$$ per mole respectively then the heat of formation of $$\mathrm{C}_2 \mathrm{H}_6(g)$$ is

Abnormal colligative properties are observed only when the dissolved non-volatile solute in a given dilute solution

Aqueous $$\mathrm{CuSO}_4$$ changes its colour from sky blue to deep blue on addition of $$\mathrm{NH}_3$$ because

Identify A, B and C.

For a reaction, $$2 A+B \longrightarrow$$ products, If concentration of $$B$$ is kept constant and concentration of $$A$$ is doubled then rate of reaction is

For an adiabatic change in a system, the condition which is applicable is

In dilute alkaline solution $$\mathrm{MnO}_4^{-}$$ changes to

Which of the following complex show optical isomerism?

(i) $$c i s-\left[\mathrm{COCl}(\mathrm{en})_2\left(\mathrm{NH}_3\right)\right]^{2+}$$

(ii) $$cis-\left[\mathrm{CrCl}_2(\mathrm{ox})_2\right]^{3-}$$

(iii) $$cis-[ \left.\mathrm{CO}(\mathrm{en})_2 \mathrm{Cl}_2\right] \mathrm{Cl}$$

(iv) $$cis- \left[\mathrm{CO}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}$$

Mohr's salt has the formula

The value of $$a^{\log _b c}-c^{\log _b a}$$, where $$a, b, c>0$$ but $$a, b, c \neq 1$$, is

The slope of the tangent to the curve, $$y=x^2-x y$$ at $$\left(1, \frac{1}{2}\right)$$ is

The value of $$\lim _\limits{x \rightarrow 0} \frac{e^{a x}-e^{b x}}{2 x}$$ is equal to

The points of intersection of circles $$(x+1)^2+y^2=4$$ and $$(x-1)^2+y^2=9$$ are $$(a, \pm b)$$, then $$(a, b)$$ equals to

The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7 x^2+10$$

The circle $$x^2+y^2+3 x-y+2=0$$ cuts an intercept on $$X$$-axis of length

Let $$f(x)=a+(x-4)^{\frac{4}{9}}$$, then minima of $$f(x)$$ is

If $$f(x) = \left\{ {\matrix{ {2\sin x} & ; & { - \pi \le x \le {{ - \pi } \over 2}} \cr {a\sin x + b} & ; & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x} & ; & {{\pi \over 2} \le x \le \pi } \cr } } \right.$$ and it is continuous on $$[-\pi, \pi]$$, then

The value of $$\lim _\limits{x \rightarrow \infty}\left(\frac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}$$ is

$$S \equiv x^2+y^2-2 x-4 y-4=0$$ and $$S^{\prime} \equiv x^2+y^2-4 x-2 y-16=0$$ are two circles the point $$(-2,-1)$$ lies

A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a square $$\}$$, $$\mathrm{B}=\{n \in s: n$$ is a prime$$\}$$ and $$\mathrm{C}=\{n \in s: n$$ is a square$$\}$$. Then, correct order of their probabilities is

The feasible region for the inequations $$x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0$$ is

The maximum value of $$Z=10 x+16 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 12,2 x+y \leq 20$$ is

If $$A=\left[\begin{array}{ll}2 & 2 \\ 3 & 4\end{array}\right]$$, then $$A^{-1}$$ equals to

If $$A$$ is a matrix of order $$4 \operatorname{such}$$ that $$A(\operatorname{adj} A)=10 \mathrm{~I}$$, then $$|\operatorname{adj} A|$$ is equal to

If $$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$ is a singular matrix, then possible values of $$\mathrm{k}$$ are

The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$ is

If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$m$$ is

The maximum value of $$Z=12 x+13 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 5$$ and $$3 x+y \leq 9$$ is

$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is

The place $$x-2 y+z=0$$ is parallel to the line

$$\int \frac{x d x}{2(1+x)^{3 / 2}}$$ is equal to

$$\int \frac{4^x}{\sqrt{1-16^x}} d x$$ is equal to

$$\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x$$ is equal to

The lines $$\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}$$ and $$\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}$$ are perpendicular to each other, then $$a$$ equals to

If two lines $$L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$L_2: \frac{x-3}{1}=\frac{y-k}{2}=z$$ intersect at a point, then $$2 k$$ is equal to

A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1 and 5 are always together, is

If a number $n$ is chosen at random from the set $$\{11,12,13, \ldots \ldots, 30\}$$. Then, the probability that $$n$$ is neither divisible by 3 nor divisible by 5, is

Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form the vertices of an isosceles triangle, is

If $$A, B$$ and $$C$$ are mutually exclusive and exhaustive events of a random experiment such that $$P(B)=\frac{3}{2} P(A)$$ and $$P(C)=\frac{1}{2} P(B)$$, then $$P(A \cup C)$$ equals to

Using mathematical induction, the numbers $$a_n \delta$$ are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n, (n \geq 0)$$. Then, $$a_n$$ is equal to

If $$49^n+16^n+k$$ is divisible by 64 for $$n \in N$$, then the least negative integral value of $$k$$ is

$$2^{3 n}-7 n-1 \text { is divisible by }$$

The sum of $$n$$ terms of the series, $$\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$$ is

The value of $$\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}$$ is equal to

If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an $$\mathrm{AP}$$ is

The differential equation of all non-vertical lines in a plane is

The general solution of $$\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2$$ is

The solution of the differential equation $$\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)$$ is

$$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will be

If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ is equal to

The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as

The general solution of $$2 \cos 4 x+\sin ^2 2 x=0$$ is

If $$2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}$$, then $$f\left(x^8\right)$$ is equal to

If $$A=\{a, b, c\}, B=\{b, c, d\}$$ and $$C=\{a, d, c\}$$ then $$(A-B) \times(B \cap C)$$ is equal to

If $$n(A)=p$$ and $$n(B)=q$$, then the numbers of relations from the set $$A$$ to the set $$B$$ is

If $$z=\sqrt{3}+i$$, then the argument of $$z^2 e^{z-i}$$ is equal to

If $$i=\sqrt{-1}$$ and $$n$$ is a positive integer, then $$i^n+i^{n+1}+i^{n+2}+i^{n+3}$$ is equal to

If $$\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$$, where $$x$$ and $$y$$ are real, then the ordered pair $$(2 x, 2 y)$$ is

There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are

A polygon of n sides has 105 diagonals, then n is equal to

Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\right)=0$$. Then, the equation of the pair of the angle bisector of the line $$3 y^2-5 x y-2 x^2=0$$ is

The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is equal to

The slope of lines which makes an angle $$60^{\circ}$$ with the line $$y-3 x+18=0$$

3 and 5 are intercepts of a line $$L=0$$, then the distance of $$L=0$$ from $$(3,7)$$ is

The total number of terms in the expansion of $$(x+y)^{60}+(x-y)^{60}$$ is

The coefficient of $$x^{29}$$ in the expansion of $$\left(1-3 x+3 x^2-x^3\right)^{15}$$ is

In the expansion of $$\left(1+3 x+3 x^2+x^3\right)^{2 n}$$, the term which has greatest binomial coefficient, is

The mean energy per molecule for a diatomic gas is

The phase difference between displacement and velocity of a particle in simple harmonic motion is

The mass density of a nucleus varies with mass number $$A$$ as

A capacitor of capacity $$2 ~\mu \mathrm{F}$$ is charged upto a potential $$14 \mathrm{~V}$$ and then connected in parallel to an uncharged capacitor of capacity $$5 ~\mu \mathrm{F}$$. The final potential difference across each capacitor will be

The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in vacuum is

A particle is projected at an angle $$30^{\circ}$$ with horizontal having kinetic energy $$K$$. The kinetic energy of the particle at highest point is.

An air bubble in water $$\left(\mu=\frac{4}{3}\right)$$ is shown in figure. The apparent depth of the image of the bubble in plane mirror viewed by observer is.

A transistor is connected in CE configuration. The collector supply is $$10 \mathrm{~V}$$ and the voltage drop across a resistor of $$1000 \Omega$$ in the collector circuit is $$0.5 \mathrm{~V}$$. If the current gain factor is 0.96 , then the base current is

One end of the string of length $l$ is connected to a particle of mass $$m$$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $$v$$, the net force on the particle (directed towards centre) will be ( $$T$$ represents the tension in the string)

A thin circular ring of mass ,$$M$$ and radius $$R$$ rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity $$\omega$$. Four small spheres each of mass $$m$$ (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

Two wire of same material having radius in ratio 2 : 1 and lengths in ratio 1: 2. If same force is applied on them, then ratio of their change in length will be

In the figure, pendulum bob on left side is pulled a side to a height $$h$$ from its initial position. After it is released it collides with the right pendulum bob at rest, which is of same mass. After the collision, the two bobs stick together and rise to a height

A gas is taken through the cycle $$A \rightarrow B \rightarrow C \rightarrow A$$, as shown in figure. What is the net work done by the gas?

The gases carbon monoxide $$(\mathrm{CO})$$ and nitrogen at the same temperature have kinetic energies $$E_1$$ and $$E_2$$, respectively. Then,

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $$A$$ and the second wire has cross-sectional area $$3 A$$. If the length of the first wire is increased by $$\Delta l$$ on applying a force $$F$$, how much force is needed to stretch the second wire by the same amount?

Starting from the centre of the earth having radius $$R$$, the variation of $$g$$ (acceleration due to gravity) is shown by

A long spring, when stretched by a distance $$x$$, has potential energy $$U$$. On increasing the stretching to $$n x$$, the potential energy of the spring will be

With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency?

A dielectric of dielectric constant $$K$$ is introduced such that half of its area of a capacitor of capacitance $$C$$ is occupied by it. The new capacity is

Two very long straight parallel wires carry currents $$i$$ and $$2 i$$ in opposite directions. The distance between the wires is $$r$$. At a certain instant of time a point charge $$q$$ is at. a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity $$v$$ is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is

The magnetic flux linked with a coil satisfies the relation $$\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}$$, where $$t$$ is time in second. The emf induced in the coil at $$t=2 \mathrm{~s}$$ is

The instantaneous values of alternating current and voltages in a circuit given as

$$\begin{aligned} & i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \mathrm{amp} \\ & e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \text { volt } \end{aligned}$$

The average power (in watts) consumed in the circuit is

A car is moving towards a high cliff. The car driver sounds a horn of frequency $$f$$. The reflected sound heard by the driver has a frequency $$2 f$$. If $$v$$ be the velocity of sound, then the velocity of the car in the same velocity units, will be

If escape velocity on earth surface is $$11.1 \mathrm{~kmh}^{-1}$$, then find the escape velocity on moon surface. If mass of moon is $$\frac{1}{81}$$ times of mass of earth and radius of moon is $$\frac{1}{4}$$ times radius of earth.

An ideal gas goes from state $$A$$ to state $$B$$ via three different processes as indicated in the $$p$$-$$V$$ diagram. If $$Q_1, Q_2$$ and $$Q_3$$ indicate the heat absorbed by the three processes and $$\Delta U_1, \Delta U_2$$ and $$\Delta U_3$$ indicate the change in internal energy along the three processes respectively, then

In the series L-C-R circuit shown, the impedance is

In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio between bright and dark fringes is 3 . Then, the value of the ratio of the amplitudes of the wave that arrive there is

The wavelength of the first line of Lyman series for $$\mathrm{H}$$ - atom is equal to that of the second line of Balmer series for a $$\mathrm{H}$$-like ion. The atomic number $$\mathrm{Z}$$ of $$\mathrm{H}$$-like ion is

If $$150 \mathrm{~J}$$ of heat is added to a system and the work done by the system is $$110 \mathrm{~J}$$, then change in internal energy will be

In the figure below, the capacitance of each capacitor is $$3 \mu \mathrm{F}$$. The effective capacitance between $$A$$ and $$B$$ is

The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of

In Young's double slit experiment, the ratio of maximum and minimum intensities in the fringe system is $$9: 1$$. The ratio of amplitudes of coherent sources is

In the case of an inductor

The height vertically above the earth's surface at which the acceleration due to gravity becomes $$1 \%$$ of its value at the surface is

If $$C$$ be the capacitance and $$V$$ be the electric potential, then the dimensional formula of $$\mathrm{CV}^2$$ is

Which logic gate is represented by the following combination logic gates?

An LED is constructed from a $$p$$-$$n$$ junction diode using GaAsP. The energy gap is $$1.9 \mathrm{~eV}$$. The wavelength of the light emitted will be equal to

A body is projected vertically upwards. The times corresponding to height $$h$$ while ascending and while descending are $$t_1$$ and $$t_2$$, respectively. Then, the velocity of projection will be (take, $$g$$ as acceleration due to gravity)

When a certain metal surface is illuminated with light of frequency $$\nu$$, the stopping potential for photoelectric current is $$V_0$$. When the same surface is illuminated by light of frequency $$\frac{\nu}{2}$$, the stopping potential is $$\frac{V_0}{4}$$. The threshold frequency for photoelectric emission is

A fish in water (refractive index $$n$$ ) looks at a bird vertically above in the air. If $$y$$ is the height of the bird and $$x$$ is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

A car starts from rest and accelerates uniformly to a speed of $$180 \mathrm{~kmh}^{-1}$$ in $$10 \mathrm{~s}$$. The distance covered by the car in this time interval is

A plane electromagnetic wave of frequency $$20 \mathrm{~MHz}$$ travels through a space along $$x$$-direction. If the electric field vector at a certain point in space is $$6 \mathrm{~Vm}^{-1}$$, then what is the magnetic field vector at that point?

The sides of a parallelogram are represented by vectors $$\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ and $$\vec{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$. Then, the area of the parallelogram is

If $$\theta_1$$ and $$\theta_2$$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of $$\operatorname{dip} \theta$$ is given by

Let $$K_1$$ be the maximum kinetic energy of photoelectrons emitted by light of wavelength $$\lambda_1$$ and $$K_2$$ corresponding to wavelength $$\lambda_2$$. If $$\lambda_1=2 \lambda_2$$, then

A ball is projected horizontally with a velocity of $$5 \mathrm{~ms}^{-1}$$ from the top of a building $$19.6 \mathrm{~m}$$ high. How long will the ball take to hit the ground?

A galvanometer having a resistance of $$8 \Omega$$ is shunted by a wire of resistance $$2 \Omega$$. If the total current is $$1 \mathrm{~A}$$, the part of it passing through the shunt will be

In the diagram shown below, $$m_1$$ and $$m_2$$ are the masses of two particles and $$x_1$$ and $$x_2$$ are their respective distances from the origin $$O$$.

The centre of mass of the system is

A block of wood floats in water with $$(4 / 5)$$ th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in $$\mathrm{kgm}^{-3}$$)

A balloon with mass $m$ is descending down with an acceleration $$a$$ (where, $$a < g$$ ). How much mass should be removed from it so that it starts moving up with an acceleration $$a$$ ?

A straight wire of length $$2 \mathrm{~m}$$ carries a current of $$10 \mathrm{~A}$$. If this wire is placed in uniform magnetic field of $$0.15 \mathrm{~T}$$ making an angle of $$45^{\circ}$$ with the magnetic field, the applied force on the wire will be

Two slabs are of the thicknesses $$d_1$$ and $$d_2$$. Their thermal conductivities are $$K_1$$ and $$K_2$$, respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $$\theta_1$$ and $$\theta_2$$. Assume $$\theta_1 > \theta_2$$. The temperature $$\theta$$ of their common junction is

A square wire of each side l carries a current $$I$$. The magnetic field at the mid-point of the square

A cylinder of radius $$r$$ and of thermal conductivity $$K_1$$ is surrounded by a cylindrical shell of inner radius $$r$$ and outer radius $$2 r$$ made of a material of thermal conductivity $$K_2$$. The effective thermal conductivity of the system is

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $$v_1$$ and $$v_2$$, respectively. If $$A$$ is the cross-sectional area of the wing and $$\rho$$ is the density of air, then the upward lift is

Two cells with the same emf $$E$$ and different internal resistances $$r_1$$ and $$r_2$$ are connected in series to an external resistance $$R$$. If the potential difference across the first cell is zero then value of $$R$$.

A string vibrates with a frequency of $$200 \mathrm{~Hz}$$. When its length is doubled and tension is altered, it begins to vibrate with a frequency of $$300 \mathrm{~Hz}$$. The ratio of the new tension to the original tension is

When $$10^{19}$$ electrons are removed from a neutral metal plate, the electric charge on it is

In an electrical circuit $$R, L, C$$ and $$\mathrm{AC}$$ voltage source are all connected in series. When $$L$$ is removed from the circuit, the phase difference between the voltage and the current in the circuit is $$\pi / 3$$. If instead $$C$$ is removed from the circuit, the phase difference is again $$\pi / 3$$. The power factor of the circuit is