Recent questions tagged 2015

Which of the following is the energy of a possible excited state of hydrogen ?

asked Oct 13, 2015 by meena.p

1 answer

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of $ 4.29 \mathring{A}$. The radius of sodium atom is approximately :

asked Oct 13, 2015 by meena.p

1 answer

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (Mol.wt.206)What would be the maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin ?

asked Oct 13, 2015 by meena.p

1 answer

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to $Q_0$ and then connected to the L and R as shown below : If a student plots graphs of the square of maximum charge $(Q^2_{max})$ on the capacitor with time(t) for two different values $L_1$ and $L_2(L_1 > L_2)$ of L then which of the following represents this graph correctly ?

asked Oct 13, 2015 by meena.p

1 answer

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is /are :

asked Oct 13, 2015 by meena.p

1 answer

Match list -I (Fundamental experiment) with List - II (its conclusion ) and select the correct option from the choices given below the list :

asked Oct 13, 2015 by meena.p

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As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom / ion :

asked Oct 13, 2015 by meena.p

1 answer

Assuming human pupil to have a radius of $0.25\;cm$ and a comfortable viewing distance of $25\;cm$ , the minimum separation between two objects that human eye can resolve at 500 nm wavelength is :

asked Oct 13, 2015 by meena.p

1 answer

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally,the Huygen's principle leads us to conclude that as it travels , the light beam

asked Oct 12, 2015 by meena.p

1 answer

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $ \mu$, a ray, incident at an angle $\theta$ , on the face $AC$ of the prism provided:

asked Oct 12, 2015 by meena.p

1 answer

A red LED emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1m$ from the diode is

asked Oct 12, 2015 by meena.p

1 answer

An inductor $(L=0.03H)$ and a resistor $(R= 0.15\;k\Omega)$ are connected in series to battery of $15\;V\;EMF$ in a circuit shown below. The key $K_1$ has been kept closed below. . The key kept closed for a long time. Then at $ t=0$, $K_1$ is opened and the key $K_2$ is closed simultaneously . At $t= 1\;ms$ , the current in the circuit will be : $(e^5 \approx 150)$

asked Oct 12, 2015 by meena.p

1 answer

A rectangular loop of sides 10 cm and 5 cm carrying a current 1 of 12 A is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of $0.3 \;T$ in the positive Z direction , in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?

asked Oct 12, 2015 by meena.p

1 answer

Two long current thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the fig, with threads making an angle $\theta$ with the vertical . If wires have mass $\lambda$ per unit length then the value of I is :

asked Oct 12, 2015 by meena.p

1 answer

Two coaxial solenoids of different radii carry current I in the same direction. Let $\overrightarrow{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\overrightarrow{F_2}$ be the magnetic force on the outer solenoid due to the inner one . Then :

asked Oct 12, 2015 by meena.p

1 answer

In the circuit shown, the current ion the $1 \Omega$ resistor is :

asked Oct 12, 2015 by meena.p

1 answer

When $5V$ potential difference is applied across a wire of length $0.1\;m$, the drift speed of electrons density in the wire is $8 \times 10^{28}\;m^{-3}$, the resistivity of the material is close to :

asked Oct 12, 2015 by meena.p

1 answer

In the given circuit , charge $Q_2$ on the $2 \mu F$ capacitor changes as C is varied from $1 \mu F$ to $3 \mu F$ . $Q_2$ as function of 'C' is given properly by :

asked Oct 12, 2015 by meena.p

1 answer

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\large\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\large\frac{V_0}{4}$ have radius $R_1, R_2, R_3$ and $R_4$ respectively . Then

asked Oct 12, 2015 by meena.p

2 answers

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface $- \sigma$ in the lower half. The electric field lines around the cylinder will look figure given in :

asked Oct 12, 2015 by meena.p

1 answer

A train is moving on a straight track with speed $20ms^{-1}$. It is blowing its Whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound =$320\;ms^{-1})$ close to :

asked Oct 12, 2015 by meena.p

1 answer

For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly?

asked Oct 12, 2015 by meena.p

1 answer

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion , the average time of collision between molecules increases as $V^q$, where V is the volume of the gas. The value of q is : $\bigg[\gamma =\large\frac{C_p}{C_v}\bigg]$

asked Oct 12, 2015 by meena.p

1 answer

A solid body of constant heat capacity $1 L/^{\circ}C$ is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat . (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat . In both the cases body is brought from initial temperature $100^{\circ}$ to final temperaure $200 ^{\circ}$ Entropy change of the body in the two cases respectively is :

asked Oct 12, 2015 by meena.p

1 answer

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u= \large\frac{U}{V}$$ \infty T^4$ and pressure $p= \large\frac{1}{3}\bigg( \frac{U}{V}\bigg)$. If the shell now undergoes an adiabatic expansion the relation between T and R is :

asked Oct 8, 2015 by meena.p

1 answer

A pendulum made of a uniform wire of cross sectional area A has time period T.When an addition mass M is added to its bob, the time period change to $T_M$. If the young's modulus of material of the wire is Y then $\large\frac{1}{Y}$ is equal to:

asked Oct 8, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R, a spherical portion of radius $\large\frac{R}{2}$ is removed , as shown in fig. Taking gravitational potential $V=0$ at $ r= \infty$ , the potential at the center of the cavity thus formed is

asked Oct 8, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

asked Oct 8, 2015 by meena.p

1 answer

Distance of the center of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is R and its height is h then $ z_0$ is equal to :

asked Oct 8, 2015 by meena.p

1 answer

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic , the percentage loss in the energy during the collision is close to :

asked Oct 8, 2015 by meena.p

1 answer

Given in the figure are two blocks A and B of weight 20 N and 100 N , respectively . These are being pressed against a wall by a force as shown in fig. If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15$ , the frictional force applied by the wall on block B is

asked Oct 8, 2015 by meena.p

1 answer

The period of oscillation of a simple pendulum is $ T= 2 \pi \sqrt {\large\frac{L}{g}}$ Measured value of L is $20.0\;cm$ known to 1mm accuracy and time for 100 oscillation of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is :

asked Oct 8, 2015 by meena.p

1 answer

Two stones are thrown up simultaneously from the edge of a cliff $240\;m$ high with initial speed of $10 m/s$ and $40 m/s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance , take $g= 10 m/s^2$) (The figures are schematic and not drawn to scale )

asked Oct 8, 2015 by meena.p

1 answer

Consider the following statement : P: Suman is brilliant Q: Suman is rich R: Suman is honest . The negation of the statement , "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as :

asked Oct 8, 2015 by meena.p

1 answer

Let $10$ vertical poles standing at equal distance on a straight line, subtend the same angle of elevation $\alpha$ at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from O is 'a'; then the distance between two consecutive poles, is :

asked Oct 8, 2015 by meena.p

1 answer

If $\cos \alpha+ \cos \beta= \large\frac{3}{2}$ and $\sin \alpha +\sin \beta=\frac{1}{2}$ and $\theta$ is the airthmetic mean of $\alpha$ and $\beta$ then $\sin 2 \theta+ \cos 2 \theta$ is equal to :

asked Oct 8, 2015 by meena.p

1 answer

If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a values greater than or equal to one is :

asked Oct 8, 2015 by meena.p

1 answer

If the length of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum are given that it is an isosceles triangle , is :

asked Oct 8, 2015 by meena.p

1 answer

In a parallelogram $ABCD, |\overrightarrow{AB}|=a;|\overrightarrow{AD}|=b $ and $|\overrightarrow{AC}|=c$, then $\overrightarrow{DB}.\overrightarrow{AB}$ has the value :

asked Oct 8, 2015 by meena.p

1 answer

A plane containing the point $(3,2,0)$ and the line $ \large\frac{x-1}{1} =\frac{y-2}{5} =\frac{z-3}{4}$ also contains the point :

asked Oct 8, 2015 by meena.p

1 answer

The shortest distance between the z- axis and the line $x+y+2z-3=0=2x+3y+4z-4$ is

asked Oct 8, 2015 by meena.p

1 answer

Let $PQ$ be a double ordinate of the parabola, $y^2=-4x$ , Where $P$ lies in the second quadrant . If R divides PQ in the ratio $2:1$ then the locus of R is :

asked Oct 8, 2015 by meena.p

1 answer

If the distance between the foci of an ellipse is half the length of its latus recturn , then the eccentricity of the ellipse is :

asked Oct 8, 2015 by meena.p

1 answer

If a circle passing through the point $(-1,0)$ touches y-axis at $(0,2)$ then the length of the chord of the circle along the x- axis is :

asked Oct 8, 2015 by meena.p

1 answer

If the incentre of an equilateral triangle is $(1,1)$ and the equation of its one side is $3x+4y+3=0$, then the equation of the circumcircle of this triangle is :

asked Oct 8, 2015 by meena.p

1 answer

A straight line L through the point $(3,-1)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt 3 x+y=1$ . If L also intersects the x- axis then the equation of L is :

asked Oct 8, 2015 by meena.p

1 answer

The solution of the differential equation $ydx-(x+2y^2)dy=0$ is $x=f(0)$. If $f(-1)=1$ then $f(1)$ is equal to

asked Oct 7, 2015 by meena.p

1 answer

Let $f:(-1,1) \to R$ be a continuous function . If $\int\limits_0^{\sin x }f(t)dt =\large\frac{\sqrt 3}{2}$$x$ , then $f\bigg(\large\frac{\sqrt 3}{2} \bigg)$ is equal to

asked Oct 7, 2015 by meena.p

1 answer

Let $f: R \to R $ be a function such that $f(2-x)=f(2+x) $ and $f(4-x)=f(4+x) ,$ for all $x \in R$ and $\int \limits_0^2 f(x) dx =5$ Then the values of $\int \limits_{10}^{50} f(x) dx$ is

asked Oct 7, 2015 by meena.p

1 answer

If $\int \large\frac{\log(t+\sqrt{1+t^2})}{\sqrt {1+t^2}}$$dt= \large\frac{1}{2}$$(g(t))^2+C$, Where C is a constant , then $g(2)$ is equal to :

asked Oct 7, 2015 by meena.p

1 answer

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