Recent questions in JEEMAIN and NEET

If $\overrightarrow{a} = \frac{1}{\sqrt{10}} (3 \hat{i} + \hat{k})$ and $\overrightarrow{b} =\frac{1}{7} (2 \hat{i} + 3 \hat{j} - 6\hat{k})$, then the value of $(2 \overrightarrow{a} - \overrightarrow{b} ) . [ (\overrightarrow{a} \times \overrightarrow{b} ) \times (\overrightarrow{a} + \overrightarrow{2b} ) ]$ is

asked Dec 11, 2018 by pady_1

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If the angle between the line $x= \frac{y-1}{2} = \frac{z-3}{\lambda}$ and the plane $x + 2y + 3z = 4$ is $\cos^{-1} (\sqrt{\frac{5}{14}})$, then $\lambda$ equals

asked Dec 11, 2018 by pady_1

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The domain of the function $f(x) = \frac{1}{\sqrt{|x|-x}}$ is

asked Dec 11, 2018 by pady_1

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A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

asked Dec 11, 2018 by pady_1

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Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then p lies in the interval

asked Dec 11, 2018 by pady_1

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Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^2 + \alpha z + \beta = 0$ has two distinct roots on the line $Rez=1$, then it is necessary that

asked Dec 11, 2018 by pady_1

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The value of $\begin{align} \int_0^1 \frac{8 \log (1+x)}{1+x^2} dx \end{align} $ is

asked Dec 11, 2018 by pady_1

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Let R be the set of real numbers Statement-1 : $A = \{ (x,y) \in R \times R : y - x$ is an integer $\}$ is an equivalence relation on R. Statement-2 : B = $\{ (x,y) \in R \times R : x = \alpha y$ for some rational number $\alpha \}$ is an equivalence relation on R.

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If $\frac{dy}{dx} = y + 3 > 0$ and $y(0) = 2$, then $y(In2)$ is equal to

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$\frac{d^2x}{dy^2}$ equals

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Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^9C_3$ Statement-2 : The number of ways of choosing any 3 places from 9 different places is $^9C_3$.

asked Dec 11, 2018 by pady_1

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$ \displaystyle{\lim_{x \to 2} ( \frac{\sqrt{1-\cos \{ 2 (x-2) \} }}{x-2} } )$

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The coefficient of $x^7$ in the expansion of $(1 - x - x^2 + x^3)^6$ is

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If $A = \sin^2 x + \cos^2 x $, then for all real $x$

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The lines $L_1 : y - x = 0$ an $L_2 : 2x + y =0$ intersect the line $L_3 : y + 2 = 0$ at P and Q respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersect $L_3$ at R. Statement-1 : The ratio PR : RQ equals $2\sqrt{2}:\sqrt{5}$. Statement -2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

asked Dec 11, 2018 by pady_1

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This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency $v > v_0$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $K_{max}$ and $V_0$ respectively. If the frequency incident on the surface doubled, both the $K_{max}$ and $V_0$ are also doubled. Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

asked Dec 11, 2018 by pady_1

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The half life of a radioactive substance is 20 minutes. The aproximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ and $\frac{1}{3}$ of it had decayed is :

asked Dec 11, 2018 by pady_1

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100 g of water is heated from $30^{\circ}C$ to $50^{\circ}C$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4148 J/Kg/K) :

asked Dec 11, 2018 by pady_1

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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is :

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The electrostatic potential inside a charged spherical ball is given by $\phi = \alpha \rho^2 + b$ where r is the distance from the centre, a, b are constants. Then the charge density inside ball is

asked Dec 11, 2018 by pady_1

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Energy required for the electron excitation in $Li^{++}$ from the first to the third Bohr orbit is :

asked Dec 11, 2018 by pady_1

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A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is :

asked Dec 11, 2018 by pady_1

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Direction : The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane - convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi$. Statement-2:The centre of the interference pattern is dark.

asked Dec 11, 2018 by pady_1

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If a wire is stretched to make it 0.1% longer, its resistance will :

asked Dec 11, 2018 by pady_1

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A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 $K$, its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are, respectively :

asked Dec 11, 2018 by pady_1

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A resistor 'R' and $2 \mu F$ capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. ($\log_{10} 2.5 = 0.4$)

asked Dec 11, 2018 by pady_1

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A pulley of radius 2 m is rotated about its axis by a force $F=(20t-5t^2)$ Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :

asked Dec 11, 2018 by pady_1

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Three perfect gases at absolute temperature $T_1, T_2, T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

asked Dec 11, 2018 by pady_1

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This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2: The state of ionosphere varies from hour to hour, day to day and season to season

asked Dec 11, 2018 by pady_1

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Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}$m. The water velocity as it leaves the tap is $0.4\; ms^{-1}$. The diameter of the water stream at a distance $2 \times 10^{-1}$ m below the lap is close to :

asked Dec 11, 2018 by pady_1

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A mass M, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude $A_2$. The ratio of $(\frac{A_1}{A_2})$ is :

asked Dec 11, 2018 by pady_1

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

asked Dec 11, 2018 by pady_1

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A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is

asked Dec 11, 2018 by pady_1

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Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z \geq 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z < 0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector $\overrightarrow{A} = 6\sqrt{3} \hat{i} + 8 \sqrt{3} \hat{j} - 10 \hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

asked Dec 11, 2018 by pady_1

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A fully charged capacitor C with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is :

asked Dec 11, 2018 by pady_1

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An object moving with a speed of 6.25 m/s, is decelerated at a rate given by : $\frac{dv}{dt} = -2.5 \sqrt{v}$ where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be :

asked Dec 11, 2018 by pady_1

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A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} NA^{-1}m^{-1}$ due north and horiontal. The boat carries a vertical aerial 2m long. If the speed of the boat is $1.50 \;ms^{-1}$, the magnitude of the induced emf in the wire of aerial is :

asked Dec 11, 2018 by pady_1

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Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d(d <<1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charge approach each other with a velocity v. Then as a function of distance x between them,

asked Dec 11, 2018 by pady_1

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Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is :

asked Dec 11, 2018 by pady_1

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Two particles are executing simple harmonic motion of the same amplitude A and frequency $\omega$ along the $x-axis$. Their mean position is separated by distance $X_0(X_0 > A)$. If the maximum separation between them is $(X_0+ A)$, the phase difference between their motion is :

asked Dec 11, 2018 by pady_1

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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.

asked Dec 11, 2018 by pady_1

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Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = $ 0.03 Nm^{-1}$) :

asked Dec 11, 2018 by pady_1

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A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

asked Dec 11, 2018 by pady_1

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A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is :

asked Dec 11, 2018 by pady_1

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The transverse displacement $y(x,t)$ of a wave on a string is given by $y (x,t) = e^{-(ax^2 + bx^2 + 2 \sqrt{ab}\; xt)}$. This represents a

asked Dec 11, 2018 by pady_1

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The circle $x^2+ y^2 = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two points if

asked Dec 11, 2018 by pady_1

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For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

asked Dec 11, 2018 by pady_1

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

asked Dec 11, 2018 by pady_1

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Consider the system of linear equations: $x_1 + 2x_2 + x_3 = 3$ $2x_1 + 3x_2 + x_3 = 3 $ $3x_1 +5 x_2 + 2x_3 = 1$ The system has

asked Dec 11, 2018 by pady_1

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There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out out at random and then transferred to the other. The number of ways in which this can be done is

asked Dec 11, 2018 by pady_1

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