Recent questions in JEEMAIN-2014

A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of $\;\Omega\;$. The battery terminals are connected to an external resistance ' R ' . The minimum value of ' R ' , so that a current passes through the battery to charge it is :

asked May 3, 2014 by yamini.v

0 answers

Three capacitance ,each of $\;3 \;mu F\;$ , are provided . These can not be combined to provide the resultant capacitance of :

asked May 3, 2014 by yamini.v

0 answers

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C , directed inward towards the centre of the earth .This gives the total net surface charge carried by the Earth to be : $\;[Given \;\in_{0} =8.85 \times 10^{-12} \;C^{2}/N-m^{2} , R_{E} = 6.37 \times 10^{6}\;m\;]$

asked May 3, 2014 by yamini.v

0 answers

A transverse wave is represented by : $\;y=\large\frac{10}{\pi} sin (\large\frac{2 \pi}{T} t - \large\frac{2 \pi}{\lambda} x)\;$ . For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

asked May 3, 2014 by yamini.v

1 answer

Modern vacuum pumps can evacuate a vessel down to pressure of $\;4.0 \times 10^{-15}\;atm\;$.at room temperature (300 K). Taking $\;R=8.3 JK^{-1}mole^{-1},1\;atm=10^{5}\;Pa\;$and $\;N_{Avogadro}=6 \times 10^{23}\;mole^{-1}\;$ the mean distance between molecules of gas in an evacuated vessel will be the order of :

asked May 3, 2014 by yamini.v

0 answers

The equation of state for a gas is given by $\;PV=nRT+ \alpha V\;$ ,where n is the number of moles and $\;\alpha\;$ is a positive constant . The initial temperature and pressure of one mole of the gas contained in a cylinder are $\;T_{0}\;$ and $\;P_{0}\;$ respectively . The work done by the gas when its temperature doubles isobarically will be :

asked May 3, 2014 by yamini.v

0 answers

Water of volume 2 L in a closed container is heated with a coil of 1kW .While water is heated , the container loses energy at a rate of 160 J/s . In how much time will the temperature of water rise from $\;27^{0}C\;$ to $\;77^{0}C\;$ ? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible) .

asked May 3, 2014 by yamini.v

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A capillary tube is immersed vertically in water and the height of the water column is x .When this arrangement is taken into a mine of depth d , the height of the water column is y .If R is the radius of the earth , the ratio $\;\large\frac{x}{y}\;$ is :

asked May 3, 2014 by yamini.v

0 answers

The amplitude of a simple pendulum , oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds .Assuming that Stokes law is valid , and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3 , the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will close to (ln 5=1.601, ln 2=0.693)

asked May 3, 2014 by yamini.v

0 answers

In materials like aluminium and copper , the correct order of magnitude of various elastic modulii is :

asked May 3, 2014 by yamini.v

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India's mangalyan was sent to the mars by launching it into a transfer orbit EOM around the sun .It leaves the earth at E and meets mars at M.If the semi - major axis of earth's orbit is $\;a_{e}=1.5 \times 10^{11} m\;$ , that of Mar's orbit $\;a_{m}=2.28 \times 10^{11} m\;$, taken Kepler's law give the estimate of time for mangalyan to reach Mars from Earth to be close to :

asked May 3, 2014 by yamini.v

1 answer

A cylinder of mass $\;M_{c}\;$ and sphere of mass $\;M_{s}\;$ are placed at points A and B of two inclines, respectively .(see figure) . If they role on the incline without slipping such that their accelerations are the same , then the ratio $\; \large\frac{sin \theta_{c}}{sin\theta_{s}}\;$ is :

asked May 3, 2014 by yamini.v

0 answers

Two bodies of masses 1 kg and 4 kg are connected to a vertical spring , as shown in the figure . The smaller mass executes simple harmonic motion of angular frequency 25 rad/s , and amplitude 1.6 cm while the bigger mass remains stationary on the ground . The maximum force exerted by the system on the floor is (take g=$\;10 ms^{-2}$) .

asked May 3, 2014 by yamini.v

1 answer

A block A of mass 4 kg is placed on another block B of mass 5 kg , and the block B rests on a smooth horizontal table . If the minimum force that can be applied on A so that both the blocks move together is 12 N , the maximum force that can be applied on B for the blocks to move together will be :

asked May 3, 2014 by yamini.v

1 answer

Water is flowing a speed of $\;1.5 ms^{-1} \;$ through a horizontal tube cross - sectional area $\;10^{-2}m^{2}\;$ and you are trying to stop the flow by your palm . Assuming that the water stops immediately after hitting the palm , the minimum force that you must exert should be (density of water =$\; 10^{3}\;kgm^{-3}\;$).

asked May 3, 2014 by yamini.v

1 answer

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

asked May 2, 2014 by yamini.v

0 answers

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L .In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds .The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm.The error in the determination of g would be :

asked May 2, 2014 by yamini.v

1 answer

If $\;\alpha ,\beta \neq o\;$ , and $\;f(n)=\alpha^{n} + \beta^{n}\;$ and $\;\begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4)\end{vmatrix} = K (1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2}\;$, then$\;K\;$is equal to :

asked May 2, 2014 by yamini.v

0 answers

The statement $\;\sim(p \leftrightarrow \sim q)\;$ is :

asked May 2, 2014 by yamini.v

0 answers

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is $\;45^{0}\;$. It flies off horizontally straight way from the point O . After one second ,the elevation of the bird from O is reduced to $\;30^{0}\;$. Then the speed in $(m/s)\;$ of the bird is :

asked May 2, 2014 by yamini.v

0 answers

Let $\;f_{k}(x)= \large\frac{1}{k}(sin^{k}x+cos^{k}x)\;$ where $\;x \in R\;$ and $\;k \geq 1\;$. Then $\;f_{4}(x) - f_{6}(x)$ equals :

asked May 2, 2014 by yamini.v

0 answers

The variance of first 50 even natural numbers is :

asked May 2, 2014 by yamini.v

1 answer

Let A and B be two events such that $\;P (\overline{A \cup B}) = \large\frac{1}{6}\;,P (\overline{A \cap B}) = \large\frac{1}{4} \;$ where $\;\overline{A}\;$ stands for the compliment of the event A .Then the events A and B are :

asked May 2, 2014 by yamini.v

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If $\;[\overrightarrow{a} \times \overrightarrow{b} \;\;\overrightarrow{b}\times \overrightarrow{c} \;\;\overrightarrow{c} \times \overrightarrow{a} ]= \lambda [\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}]^{2}\;$ then $\;\lambda\;$ is equal to :

asked May 2, 2014 by yamini.v

0 answers

The angle between the lines whose direction cosines satisfy the equations $\;l+m+n=0\;$ and $\;l^{2}=m^{2}+n^{2}\;$ is :

asked May 2, 2014 by yamini.v

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The image of the line $\;\large\frac{x-1}{3} =\large\frac{y-3}{1} =\large\frac{z-4}{-5}\;$ in the plane $\;2x-y+z+3=0\;$ is the plane :

asked May 2, 2014 by yamini.v

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The slope of the line touching both the parabolas $\;y^{2}=4x\;$ and $\;x^{2}=-32y\;$ is :

asked May 2, 2014 by yamini.v

0 answers

Let C be the circle with centre at (1,1) and radius=1 . If T is the circle centred at (0,y) ,passing through origin and touching the circle C externally ,then the radius of T is equal to :

asked May 2, 2014 by yamini.v

0 answers

The locus of the foot of perpendicular drawn from the centre of the ellipse $\;x^{2}+3y^{2}=6\;$ on any tangent to it is :

asked May 2, 2014 by yamini.v

1 answer

Let a,b,c and d be non-zero numbers .If the point of intersection of the lines $\;4ax+2ay+c=0\;$ and $\;5bx+2by+d=0\;$ lies in the fourth quadrant and is equidistant from the two axis then :

asked May 2, 2014 by yamini.v

0 answers

Let PS be the median of the triangle with vertices P(2,2) , Q(6,-1) and R(7,3) . The equation of the line passing through (1,-1) and parallel to PS is :

asked May 2, 2014 by yamini.v

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Let the population of rabbits surviving at a time t be governed by the differential equation $\; \large\frac{d p(t)}{dt} = \large\frac{1}{2} p(t) -200 \;$ . If$\;p(0) = 100\;$ , then $\;p(t)\;$ equals :

asked May 2, 2014 by yamini.v

1 answer

The area of the region described by $\;A=\{(x,y) : x^{2}+y^{2} \leq 1 \;and\; y^{2} \leq 1-x\}\;$ is :

asked May 2, 2014 by yamini.v

0 answers

The integral $\; \int_{0}^{\pi} \sqrt{1+4sin^{2} \large\frac{x}{2}-4 sin \large\frac{x}{2}} dx\;$ equals :

asked May 2, 2014 by yamini.v

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The integral $\;\int (1+x-\large\frac{1}{x})\;e^{x+\large\frac{1}{x}} dx\;$ is equal to :

asked May 2, 2014 by yamini.v

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If x=-1 and x=2 are extreme points of $\;f(x) =\alpha log|x|+ \beta x^{2}+x\;$ then :

asked May 2, 2014 by yamini.v

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If f and g are differentiable functions in [0 , 1] satisfying $\;f(0)=2=g(1)\;,g(0)=0\;$ and $\;f(1)=6\;$, then for some $\;c \in ]0 ,1[\;$ :

asked May 1, 2014 by yamini.v

0 answers

If g is the inverse of a function f and $\;f^{'}(x) =\large\frac{1}{1 + x^{5}}\;$ , then $\;g^{'}(x)\;$ is equal to :

asked May 1, 2014 by yamini.v

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$\; \lim_{x \to 0} \large\frac{sin (\pi cos^{2} x)}{x^{2}}\;$ is equal to :

asked May 1, 2014 by yamini.v

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Three positive numbers from an increasing G.P. if the middle term in this G.P. is doubled , the new numbers are in A.P. Then the common ratio of the G.P. is :

asked May 1, 2014 by yamini.v

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If $\;(10)^{9} + 2 (11)^{1} (10)^{8} + 3(11)^{2} (10)^{7}+....+10 (11)^{9} = k (11)^{9}\;$, then k is equal to :

asked May 1, 2014 by yamini.v

0 answers

If the coefficients of $\;x^{2}\;$ and $\;x^{3}\;$ in the expansion of $\;(1+ax+bx^{2}) (1-2x)^{18}\;$ in powers of x are both zero , then (a,b) is equal to :

asked May 1, 2014 by yamini.v

0 answers

If A is an $\;3 \times 3\;$ non - singular matrix such that $\;A^{'}A=AA^{'}\;$ and $\;B=A^{-1}A^{'}\;$ , then $\;BB^{'} =\;$ :

asked May 1, 2014 by yamini.v

0 answers

Let $\;\alpha\;$ and $\;\beta\;$ be the roots of equation $\;px^{2} +qx + r=0\;,p \neq 0\;$ .if p ,q ,r are in A.P. and $\;\large\frac{1}{\alpha} + \large\frac{1}{\beta}=4\;$ then the value of $\;|\alpha - \beta|\;$ is :

asked May 1, 2014 by yamini.v

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If $\; a \in R\;$ and the equation $\;-3(x-[x])^{2} + 2(x-[x]) + a^{2} =0\;$ (where [x] denotes the greatest integer $\; \leq x )\;$ has no integral solution , then all possible values of a lie in the interval :

asked May 1, 2014 by yamini.v

0 answers

If z is a complex number such that $\;|z| \geq 2\;$ , then the minimum value of $\;|z + \large\frac{1}{2}|\;$ :

asked May 1, 2014 by yamini.v

0 answers

If $\; (X =4^{n} -3n-1) : n \in N \;$ and $\;Y=9(n-1) : n \in N\;$ where N is the set of natural numbers then $\;X \cup Y\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

In the reaction , $\;CH_{3}OOH\; \underrightarrow{LiAlH_{4}}\; A \; \underrightarrow{PCl_{5}}\;B\;\underrightarrow{Alc.KOH}\;C \; $ , the product C is :

asked May 1, 2014 by yamini.v

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Which one of the following bases is not present in DNA ?

asked May 1, 2014 by yamini.v

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Which one is classified as a condensation polymer ?

asked May 1, 2014 by yamini.v

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