Recent questions in JEEMAIN-2014

Equation of the line of the shortest distance between the lines $\;\large\frac{x}{1}=\large\frac{y}{-1}=\large\frac{z}{1}\;$ ans $\;\large\frac{x-1}{0}=\large\frac{y+1}{-2}=\large\frac{z}{i}\;$ is :

asked May 24, 2014 by yamini.v

0 answers

The tangent at an extremely (in the first quadrant) of latus rectum of the hyperbola $\;\large\frac{x^{2}}{4}-\large\frac{y^{2}}{5}=0\;$ , meets x -axis and y -axis at A and B respectively .Then $\;(OA)^{2}-(OB)^{2}\;$ , where O is the origin , equals :

asked May 24, 2014 by yamini.v

0 answers

A chord is drawn through the focus of the parabola $\;y^{2}=6x\;$ such that its distance from the vertex of this parabola is $\;\large\frac{\sqrt{5}}{2}\;$ , then its slope can be :

asked May 24, 2014 by yamini.v

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The equation of the circle described on the chord $\;3x+y+5=0\;$ of the circle $\;x^{2}+y^{2}=16\;$ as diameter is :

asked May 24, 2014 by yamini.v

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If a line L is perpendicular to the line $\;5x-y=1\;$ , and the area of the triangle formed by the line L and the coordinate axes is 5 , then the distance of line L from the line $\;x+5y=0\;$ is :

asked May 24, 2014 by yamini.v

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The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $\;(a^{2}+1,a^{2}+1)\;$ and $\;(2a ,-2a)\;, a \neq 0\;$.Then for any a , the orthocentre of this triangle lies on the line :

asked May 24, 2014 by yamini.v

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If $\;\large\frac{dy}{dx} + y tan x=sin 2x\;$ and $\;y(0)=1\;$ , then $\;y(\pi)\;$ is equal to :

asked May 24, 2014 by yamini.v

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The area of the region above the x - axis bounded by the curve $\;y=tan x\;,0 \leq x \leq \large\frac{\pi}{2}\;$ and the tangent to the curve at $\;x= \large\frac{\pi}{4}\;$ is :

asked May 24, 2014 by yamini.v

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Let function F be defined as $\;F(x) =\int \limits_{1}^{x} \large\frac{e^{t}}{t} dt\;$ , x > 0 then the value of the integral $\;\int \limits_{1}^{x} \large\frac{e^{t}}{t+a} dt\;$ , where a > 0 , is :

asked May 24, 2014 by yamini.v

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If the volume of a spherical ball is increasing at the rate of $\;4 \pi \;cc/sec\;$ , then the rate of increase of its radius (in cm/sec) , when the volume is $\;288 \pi\;cc\;$ , is :

asked May 24, 2014 by yamini.v

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If non - zero real numbers b and c are such that min f(x) > max g(x) , where $\;f(x)=x^{2}+2bx+2c^{2}\;$ and $\;g(x)=-x^{2}-2cx+b^{2}\;(x \in R)\;$ ;then $\;|\large\frac{c}{b}|\;$ lies in the interval :

asked May 24, 2014 by yamini.v

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Let $\;f: R \to R\;$ be a function such that $\;|f(x)| \leq x^{2}\;$ , for all $\;x \in R\;$.Then , at x= 0 , f is :

asked May 24, 2014 by yamini.v

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Let $\;f(n)=[\large\frac{1}{3} + \large\frac{3n}{100}]n\;$ , where [n] denotes the greatest integer less than or equal to n .Then $\;\sum_{n=1}^{56} f(n)\;$ is equal to :

asked May 24, 2014 by yamini.v

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The number of terms in an A.P. is even ; the sum of the odd terms in it is 24 and that the even terms is 30 . If the last term exceeds the first term by $\;10 \large\frac{1}{2}\;$, then the number of terms in the A.P. is :

asked May 24, 2014 by yamini.v

1 answer

The coefficient of $\;x^{1012}\;$ in the expansion of $\;(1+x^{n}+x^{253})^{10}\;$,(where $\;n \leq 22\;$ is any positive integer),is :

asked May 24, 2014 by yamini.v

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Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants .If the number of games that the men played between them - selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval :

asked May 24, 2014 by yamini.v

1 answer

If $\;\bigtriangleup_{r}=\begin{vmatrix} r & 2r-1 & 3r-2 \\[0.3em] \large\frac{n}{2} & n-1 & a \\[0.3em] \large\frac{1}{2}n(n-\normalsize 1) & (n-\normalsize 1)^{2} & \large\frac{1}{2} (n-\normalsize 1)(\normalsize 3n-\normalsize 4)\end{vmatrix}\;$ , then the value of $\;\sum_{r=1}^{n-1} \bigtriangleup_{r}\;$ :

asked May 24, 2014 by yamini.v

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Let A and B be any $\;3 \times 3\;$ matrices . If A is symmetric and B is skewsymmetric , then the matrix AB - BA is :

asked May 24, 2014 by yamini.v

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The equation $\;\sqrt{3x^{2}+x5}=x-3\;$ , where x is real , has :

asked May 24, 2014 by yamini.v

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For all complex numbers z of the form $\;1+i \alpha\;, \alpha \in R\;$ , if $\;z^{2}=x+iy\;$ , then :

asked May 24, 2014 by yamini.v

1 answer

Let $\;f: R \to R \;$ be defined by $\;f(x) = \large\frac{|x|-1}{|x|+1}\;$ then f is :

asked May 24, 2014 by yamini.v

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Interference pattern is absorbed at ' P ' due to superimposition of two rays coming out from a source ' S ' as shown in the figure . The value of ' l ' for which maxima is obtained at ' P ' is : (R is perfect reflecting surface)

asked May 24, 2014 by yamini.v

0 answers

A lamp emits monochromatic green light uniformly in all directions . The lamp is $\;3 \%\;$ efficient in converting electrical power to electromangetic waves and consumes 100 W of power .The amplitude of the electric filed associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :

asked May 24, 2014 by yamini.v

0 answers

A sinusoidal voltage $\;V(t)=100\;sin (500 t)\;$ is applied across a pure inductance of $\;L=0.02 \;H\;$ . The current through the coil is :

asked May 24, 2014 by yamini.v

0 answers

Consider two thin identical conducting wires covered with very thin insulating material . One of the wires is bent into a loop and produces magnetic field $\;B_{1}\;$ , at its center when a current I passes through it .The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field $\;B_{2}\;$ at the center of the loops when current $\;\large\frac{I}{3}\;$ passes through it . The ratio $\;B_{1} : B_{2}\;$ is :

asked May 24, 2014 by yamini.v

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A positive charge ' q ' of mass ' m ' is moving along the $\;+ x\;$ axis .We wish to apply a uniform magnetic field B for time $\;\Delta t\;$ so that the charge reverses its direction crossing the y- axis at a distance d . Then :

asked May 24, 2014 by yamini.v

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The circuit as shown here has two batteries of 8.0 V and 16.0 V and three resistors $\;3 \Omega,9 \Omega\;$ and $\;9 \Omega\;$ and a capacitor $\;5.0\;\mu F\;$ . How much is the current I in the circuit in steady state ?

asked May 24, 2014 by yamini.v

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The space between the plates of a parallel plate capacitor is filled with a ' dielectric ' whose dielectric constant varies with distance as for the relation : $\;K(x)=K_{0}+\lambda x\;$ ($\lambda\;$)=a constant . The capacitance C , of this capacitor , would be related to its ' vacuum ' capacitance $\;C_{0}\;$ as for the relation :

asked May 24, 2014 by yamini.v

1 answer

A spherically symmetric charge distribution is characterised by a charge density having the following variation : \[\]$\;\rho(r)=\rho_{0}(1-\large\frac{r}{R})\;for\;r < \normalsize R\;$\[\]$\;\rho(r) =0 \;\; r \geq R\;$ \[\] where r is the distance from the center of the charge distribution and $\;\rho_{0}\;$ is a constant .The electric field at an internal point $(r < R)$ is :

asked May 23, 2014 by yamini.v

1 answer

A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v .The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz .The source A receives waves , reflected from ground , of frequency nearly : (Speed of sound =343 m/s)

asked May 23, 2014 by yamini.v

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Which of the following expressions corresponds to simple harmonic motion along a straight line , where x is the displacement and a,b,c are positive constants ?

asked May 23, 2014 by yamini.v

1 answer

At room temperature a diatomic gas is found to have an r.m.s. speed of $\;1930\;ms^{-1}\;$ .The gas is :

asked May 23, 2014 by yamini.v

1 answer

A car not engine absorbs 1000 J of heat energy from a reservoir at $\;127^{0}C\;$ and rejects 600 J of heat energy during each cycle .The efficiency of engine and temperature of sink will be :

asked May 23, 2014 by yamini.v

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Hot water cools from $\;60^{0}\;$ to $\;50^{0}\;$ in the first 10 minutes and to $\;42^{0}\;$ in the next 10 minutes .The temperature of the surroundings is :

asked May 23, 2014 by yamini.v

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Two soap bubbles coalesce to form a single bubble . If V is the subsequent change in volume of contained air and S the change in total surface area , T is the surface tension and P atmospheric pressure ,which of the following relation is correct ?

asked May 23, 2014 by yamini.v

1 answer

A cylindrical vessel of cross - section A contains water to a height h.There is a hole in the bottom of radius ' a ' .The time in which it will be emptied is :

asked May 23, 2014 by yamini.v

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Steel ruptures when a shear of $\;3.5 \times 10^{8}\;Nm^{-2}\;$ is applied .The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly :

asked May 23, 2014 by yamini.v

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Two hypothetical plates masses $\;m_{1}\;$ and $\;m_{2}\;$ are at rest when they are infinite distance apart .Because of the gravitational force they move towards each other along the line joining their centers .What is their speed when their separation is 'd ' ? (Speed of $\;m_{1}\;$ is $\;v_{1}\;$ and that of $\;m_{2}\;$ is $\;v_{2}\;$)

asked May 23, 2014 by yamini.v

1 answer

A particle is moving in a circular path of radius a , with a constant velocity v as shown in the figure . The center of circle is marked by 'C' .The angular momentum from the origin O can be written as :

asked May 23, 2014 by yamini.v

1 answer

A spring of unstretched length l has a mass m with one end fixed to a rigid support .Assuming spring to be made of a uniform wire , the kinetic energy possessed by it if its free end is pulled with uniform velocity v is :

asked May 23, 2014 by yamini.v

1 answer

A 4 g bullet is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table .If the coefficient of friction between the block and the table is 0.3 , how far will the block side approximately ?

asked May 23, 2014 by yamini.v

1 answer

Three masses m,2m and 3m are moving in x - y plane with speed 3u,2u and u respectively as shown in figure . The three masses collide at the same point at P and stick together .The velocity of resulting mass will be :

asked May 23, 2014 by yamini.v

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A person climbs up a stalled escalator in 60 s .If standing on the same but escalator running with constant velocity he takes 40 s.How much time is taken by the person to walk up the moving escalator ?

asked May 23, 2014 by yamini.v

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From the following combinations of physical constants (expressed through their usual symbols) the only combination , that would have the same value in different systems of units , is :

asked May 23, 2014 by yamini.v

1 answer

In the experiment of calibration of voltmeter , a standard cell of e.m.f.1.1 volt is balanced against 440 cm of potentiometer wire .The potential difference across the ends of resistance is found to balance against 220 cm of the wire . The corresponding reading of voltmeter is 0.5 volt .The error in the reading of voltmeter will be :

asked May 23, 2014 by yamini.v

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For sky wave propagation , the radio waves must have a frequency range in between :

asked May 23, 2014 by yamini.v

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For LED's to emit light in visible region of electromagnetic light , it should have energy band gap in the range of :

asked May 22, 2014 by yamini.v

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A piece of bone of an animal from a ruin is found to have $\;^{14}C\;$ activity of 12 disintegrations per minute per gm of its carbon content .The $\;^{14}C\;$ activity of a living animal is 16 disintegrations per minute per gm .How long ago nearly did the animal die ? (Given half life of $\;^{14}C\;$ is $\;t_{\large\frac{1}{2}}\;$=5760 years)

asked May 22, 2014 by yamini.v

1 answer

A beam of light has two wavelengths $\;4972A^{0}\;$ and $\;6216A^{0}\;$ with a total intensity of $\;3.6 \times 10^{-3} \;Wm^{-2}\;$ equally distributed among the two wavelengths . The beam falls normally on the area of $\;1\;cm^{2}\;$ of a clean metallic surface of work function 2.3 eV.Assume that there is no loss of weight by reflection and that each capable photon ejects one electron .The number of photo electrons liberated in 2s is approximately :

asked May 22, 2014 by yamini.v

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The major product obtained in the photo catalysed bromination of 2 - methylbutane is :

asked May 22, 2014 by yamini.v

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