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The negation of $s\approx V ( \approx s)$ is equivalent to :

asked Oct 29, 2015 by meena.p

1 answer

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$ If $\lim\limits_{x \to 0} \bigg[1+\large\frac{f(x)}{x^2}\bigg]$ $=3$ then $(2)$ is equal to :

asked Oct 29, 2015 by meena.p

1 answer

The sum of first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}$ +.....is :

asked Oct 29, 2015 by meena.p

1 answer

The normal to the curve , $x^2+2xy-3y^2=0$ at (1,1):

asked Oct 29, 2015 by meena.p

1 answer

A complex number z is said to be uni modular if $|z|=1$ . suppose $z_1$ and $z_2$ are complex numbers such that $\large\frac{z_1-2z_2}{2-z_1z_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

asked Oct 29, 2015 by meena.p

1 answer

On a hot summer night, the refractive index of air is smallest near the ground and increase 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 29, 2015 by meena.p

1 answer

Two long current carrying thin wires, both with current I, are held by insulting threads of length L and are in equilibrium as shown in the figure, with threads making an angle $\theta$ with the vertical. If wires have mass $\lambda$ per unit length then the value of I is : (g= gravitational acceleration )

asked Oct 29, 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 wave length is :

asked Oct 29, 2015 by meena.p

1 answer

A solid body of constant heat capacity $1\;J/c^{\circ}$ is being heating by keeping it in contact with reservation 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 cases body is brought from initial temperature $100^{\circ}$ to final temperature $200 ^{\circ}C$ Entropy change of the body in the two cases respectively is :

asked Oct 29, 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 $g= 10 m/s^2)$

asked Oct 29, 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 29, 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 is $2.5 \times 10^{-4}\;ms^{-1}$ . If the electron density in the wire is $8 \times 10^{28}\;m^{-3}$ , the resistivity of the material is close to :

asked Oct 29, 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 29, 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 28, 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 AB would get transmitted through the face AC of the prism provided :

asked Oct 28, 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 28, 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 a function of 'C' is given properly by :

asked Oct 28, 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 $\frac{V_0}{4}$ has radius $R_1, R_2,R_3$ and $R_4$ respectively . Then ,

asked Oct 28, 2015 by meena.p

1 answer

In the circuit shown , the current in the $1\;\omega$ resistor is:

asked Oct 28, 2015 by meena.p

2 answers

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientation 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 loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?

asked Oct 28, 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 28, 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 F as shown . 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 28, 2015 by meena.p

1 answer

A train is moving on a straight track with speed $20\;ms^{-1}$ . 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 28, 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 tge cavity thus formed is :

asked Oct 28, 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 then which of the following represents this graph correctly ?

asked Oct 28, 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 values of q is : $\bigg(\gamma= \large\frac{C_P}{C_V} \bigg)$

asked Oct 28, 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 28, 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 dipole is :

asked Oct 28, 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 changes to $T_M$ . If the young's modulus of the material of the wire is Y then $\large\frac{1}{Y}$ is equal to : (g = gravitational acceleration)

asked Oct 28, 2015 by meena.p

1 answer

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

asked Oct 28, 2015 by meena.p

1 answer

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

asked Oct 28, 2015 by meena.p

1 answer

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

asked Oct 28, 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 a diabatic axpansion the relation between T and R is :

asked Oct 28, 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 cm known to 1 mm accuracy and time for 100 oscillations 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 28, 2015 by meena.p

1 answer

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

asked Oct 28, 2015 by meena.p

1 answer

Let $y(x)$ be the solution of the differential equation : $(x log x) \large\frac{dy}{dx}$ $4+y = 2x \log x, (x \geq).$ then $y(e)$ is equal to :

asked Oct 26, 2015 by meena.p

1 answer

The number of common tangent to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ , is :

asked Oct 26, 2015 by meena.p

1 answer

The normal to the curve $x^2+2xy-3y^2=0$ at $(1,1)$ :

asked Oct 26, 2015 by meena.p

1 answer

The set of all values of $\lambda$ for which the system of linear equations : $2x_1-2x_2+x_3 = \lambda x_1 \\2x_1 -3x_2+2x_3 = \lambda x_2 \\ -x_1 +2x_2 = \lambda x_3\\$ has a non- trivial solution ,

asked Oct 26, 2015 by meena.p

1 answer

If the function $g(x) = \left\{ \begin{array} {1 1} k \sqrt{x+1} , & \quad 0 \leq x \leq 3 \\ mx+2,& \quad 3 < x \leq 5 \end{array} \right.$ is differentiable , then the value of $k+m$ is :

asked Oct 26, 2015 by meena.p

1 answer

If $A=\begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & -2 \\a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $Aa^T= 9I$ Where $I$ is $3 \times 3$ identify matrix, then the ordered pair $(a,b)$ is equal to :

asked Oct 26, 2015 by meena.p

1 answer

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{a}$ be three non-zero vectors such that no two of them are col linear and $(\overrightarrow{a},\overrightarrow{b}) \times \overrightarrow{c}= \frac{1}{3}|\overrightarrow{b}||\overrightarrow{c}|,\overrightarrow{a}$ . If $\theta$ is the angle between vector $\overrightarrow{b}$ and $\overrightarrow{c}$ , then a value of $\sin \theta$ is :

asked Oct 26, 2015 by meena.p

1 answer

$lim _{x \to 0}$ $\large\frac{(1-\cos 2x)(3+ \cos x)}{x \tan 4x}$ is equal to :

asked Oct 26, 2015 by meena.p

1 answer

If the angles of elevation of the top of a tower from three collinear points A,B and C on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively , the the ratio , $AB:BC$ is

asked Oct 26, 2015 by meena.p

1 answer

The negation of $\approx s \vee (r \wedge s)$ is equivalent to :

asked Oct 26, 2015 by meena.p

1 answer

The integral $\int\limits_2^4 \frac{\log x^2}{\log x^2 +\log (36 -12x+x^2)}$ $dx$ is equal to :

asked Oct 26, 2015 by meena.p

1 answer

The integral $\int\limits_2^4 \frac{\log x^2}{\log x^2+\log(36-12x+x^2)}$ $dx$ is equal to :

asked Oct 26, 2015 by meena.p

0 answers

Let $\tan^{-1}y = \tan ^{-1} x +\tan ^{-1} \bigg( \large\frac{2x}{1-x^2}\bigg)$ , where $|x| < \frac{1}{\sqrt 3}$ . Then a value of y is :

asked Oct 26, 2015 by meena.p

1 answer

Let A and B be two sets containing four and two elements respectively . Then the number of subset of the set $A \times B$ , each having at least three elements is :

asked Oct 26, 2015 by meena.p

1 answer

The number of integers given than $6,000$ that can be formed, using the digit $3,5,6,7$ and $8$ without repetition , is :

asked Oct 26, 2015 by meena.p

1 answer

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