Recent questions in JEEMAIN and NEET

Let $f : (-1, 1) \to R$ be a differentiable function with $f(0) = -1$ and $f'(0)=1$ . Let $g(x) = [f(2f(x) + 2)]^2$ . Then $g'(0)=$

asked Dec 11, 2018 by pady_1

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Let $p(x)$ be a function defined on $R$ such that $p'(x) = p'(1-x)$ , for all $x \in [0,1], \; p(0)=1$ and $p(1) =41$ . Then $\begin{align} \int_0 ^1p(x) \; dx\end{align}$ equals

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be a positive increasing function with $\displaystyle\lim_{x \to \infty} \frac{f(3x)}{f(x)} = 1$ Then $\displaystyle\lim_{x \to \infty} \frac{f(2x)}{f(x)} =$

asked Dec 11, 2018 by pady_1

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A person is to count 4500 currency notes. Let $a_n$ denote the number of notes the counts in the $n^{th}$ minute. If $a_1 = a_2 = .......= a_{10} = 150$ and $a_{10}, a_{11}, ....$ are in A.P. with common difference $-2$ , then the time taken by him to count all notes is

asked Dec 11, 2018 by pady_1

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The line L given by $\frac{x}{5}+ \frac{y}{b} = 1$ passes through the poin (13, 32). The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$ . Then the distance between $L$ and $K$ is

asked Dec 11, 2018 by pady_1

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A line AB in three-dimensional space makes angle $45^{\circ}$ and $120^{\circ}$ with the positive $x-axis$ and the positive $y-axis$ respectively. If AB makes an acute $\theta$ with the positive $z-axis$ , then $\theta$ equals

asked Dec 11, 2018 by pady_1

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The number of complex number $z$ such that $|z-1| = | z+ 1| = |z-i|$ equals

asked Dec 11, 2018 by pady_1

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If $\alpha$ and $\beta$ are the roots of the equation $x^2 - x + 1 =0$ , then $\alpha^{2009} + \beta^{2009}$ =

asked Dec 11, 2018 by pady_1

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For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be a continuous function defined by $f(x) = \frac{1}{e^x + 2e^{-x}}$ . Statement-1 : $f(c) = \frac{1}{3}$ , for some $c \in R$ . Statement-2 : $0 < f(x) \leq \frac{1}{2 \sqrt{2}}$ , for all $x \in R$

asked Dec 11, 2018 by pady_1

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Let $A$ be a $2 \times 2$ matrix with non-zero entries and let $A^2 =I$ , where $I$ is $2 \times 2$ identity matrix. Define $Tr(A)$ = sum of diagonal elements of $A$ and $|A|$ = determinant of matrix A. Assertion : Statement -1: $Tr(A) = 0$ Reason : Statement-2 : $|A| =1$

asked Dec 11, 2018 by pady_1

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Let $S_1 = \displaystyle\sum_{j=1}^{10} j (j - 1)^{10} C_j, S_2 = \displaystyle\sum_{j=1}^{10} j \;^{10} C_j$ and $S_3 = \displaystyle\sum_{j=1}^{10} j^2 \;^{10} C_j$ Statement-1 : $S_3 = 55 \times 2^9$ Statement-2 : $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$ .

asked Dec 11, 2018 by pady_1

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Statement-1: The point $A(3, 1, 6)$ is the mirror image of the point $B (1, 3, 4)$ in the plane $x - y +z =5$ . Statement-2 : The plane $x-y +z=5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4)$

asked Dec 11, 2018 by pady_1

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Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$ . Statement-1 : The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$ . Statement-2 : If the four chosen numbers from an AP, then the set of all possible values of common difference is $\{ \pm1, \pm 2, \pm 3, \pm 4, \pm 5 \}$ .

asked Dec 11, 2018 by pady_1

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The number of $3 \times 3$ non-singular matrices, with four entries as 1 and all other entries as 0, is

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be defined by $f(x) = \begin{cases} k-2x, & \quad \text{if } \text{ x $\leq$ -1}\\ 2x + 3, & \quad \text{if } \text{ x > -1} \end{cases}$ . If $f$ has a local minimum at $x=-1$ , then a possible value of $k$ is

asked Dec 11, 2018 by pady_1

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Consider the following relations : $R = \{ (x, y) | x, \; y$ are real number and $x = wy$ for some rational number $w \}$ ; $S = \{ (\frac{m}{n}, \frac{p}{q} ) | m, \; n, \; p$ and $q$ are integers such that $n, \;q \neq 0$ and $qm = pn \}$ . Then

asked Dec 11, 2018 by pady_1

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If the vectors $\overrightarrow{a} = \hat{i} - \hat{j} + 2 \hat{k}, \; \overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ and $\overrightarrow{c} = \lambda \hat{i} + \hat{j} + \mu \hat{k}$ are mutually orthogonal, then $(\lambda, \mu)$ =

asked Dec 11, 2018 by pady_1

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If two tangets drawn from a point P to the parabola $y^2 = 4x$ are at right angles, then the locus of P is

asked Dec 11, 2018 by pady_1

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The area bounded by the curves $y = \cos x$ and $y = \sin x$ between the ordinates $x=0$ and $x =\frac{3 \pi}{2}$ is

asked Dec 11, 2018 by pady_1

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Solution of the differential equation $\cos x\; dy = y (\sin x - y) dx, \; 0 < x < \frac{\pi}{2}$ is

asked Dec 11, 2018 by pady_1

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The equation of the tangent to the curve $y = x + \frac{4}{x^2}$ , that is parallel to the $x-axis$ , is

asked Dec 11, 2018 by pady_1

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Let $\overrightarrow{a} = \hat{j} - \hat{k}$ and $\overrightarrow{c} = \hat{i} - \hat{j} - \hat{k}$ . Then vector $\overrightarrow{b}$ satisfying $\overrightarrow{a} \times \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$ and $\overrightarrow{a}.\overrightarrow{b} = 3$ is

asked Dec 11, 2018 by pady_1

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Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement P ?

asked Dec 11, 2018 by pady_1

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Let $\cos (\alpha + \beta) = \frac{4}{5}$ and let $\sin (\alpha - \beta) = \frac{5}{13}$ , where $0 \leq \alpha, \; \beta \leq \frac{\pi}{4}$ , then $\tan 2 \alpha =$

asked Dec 11, 2018 by pady_1

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The equation of a wave on a string of linear mass density $0.04\; kg\;m^{-1}$ is given by $y = 0.02 (m) \sin [ 2 \pi (\frac{t}{0.04 (s)} - \frac{x}{0.50(m)} ) ]$ . The tension in the string is

asked Dec 11, 2018 by pady_1

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A small particleof mass m is projected at an angle $\theta$ with the x-axis with a initial velocity $v_0$ in the x-yplane as shown in the figure. At a time $t < \frac{v_0 \sin \theta}{g}$ , the angular momentum of the particle is where $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along $x, \; y$ and $z-axis$ respectively.

asked Dec 11, 2018 by pady_1

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The speed of light in the medium is

asked Dec 11, 2018 by pady_1

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An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$ , where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. QUESTION : The initial shape of the wave front of the beam is

asked Dec 11, 2018 by pady_1

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An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$ , where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. Question : As the beam enters the medium, it will

asked Dec 11, 2018 by pady_1

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For a particle in uniform circular motion the acceleration $\overrightarrow{a}$ at a point $P (R, \theta)$ on the circle of radius R is (here $\theta$ is measured from the x-axis)

asked Dec 11, 2018 by pady_1

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Two fixed frictionless inclined plane making an angle $30^{\circ}$ and $60^{\circ}$ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ?

asked Dec 11, 2018 by pady_1

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A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $'P'$ is such that it sweeps out a length $s = t^3 +5$ , where $s$ is metres and $t$ is in seconds. The radius of the path is $20 \;m$ . The acceleration of $'P'$ when $t = 2\;s$ is nearly

asked Dec 11, 2018 by pady_1

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Two conductors have the same resistance at $0^{\circ}C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$ . The respective temperature coefficients of their series and parallel combinations are nearly

asked Dec 11, 2018 by pady_1

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Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8\;g\;cm^{-3}$ , the angle remains the same. If density of the material of the sphere is $16\;g\; cm^{-3}$ , the dielectric constant of the liquid is

asked Dec 11, 2018 by pady_1

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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U_{(x = \infty)} - U_{at\; equilibrium}], \; D$ is

asked Dec 11, 2018 by pady_1

1 answer

Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r) = \rho_{_0}(\frac{5}{4} - \frac{r}{R})$ upto $r = R$ and $\rho (r) = 0$ for $r > R$ , where $r$ is the distance from the origin. The electric field at a distance $r (r < R)$ from the origin is given by

asked Dec 11, 2018 by pady_1

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In a series LCR circuit $R = 200 \Omega$ and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ}$ . On taking out the inductor from the circuit leads the voltage by $30^{\circ}$ . The power dissipiated in the LCR circuit is

asked Dec 11, 2018 by pady_1

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The respective number of significant figures for the numbers $23.023, 0.0003$ and $2.1 \times 10^{–3}$ are

asked Dec 11, 2018 by pady_1

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If a source of power 4 kW produces $10^{20}$ photons/second, the radiation belong to a part of the spectrum called

asked Dec 11, 2018 by pady_1

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A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is

asked Dec 11, 2018 by pady_1

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The combination of gates shown below yields

asked Dec 11, 2018 by pady_1

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A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E at the centre O is

asked Dec 11, 2018 by pady_1

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A radioactive nucleus (initial mass number A and atomic number Z) emits 3 $\alpha$ particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

asked Dec 11, 2018 by pady_1

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The speed of daughter nuclei is

asked Dec 11, 2018 by pady_1

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The binding energy per nucleon for the parent nucleus is $E_1$ and that for the daughter nuclei is $E_2$ .Then

asked Dec 11, 2018 by pady_1

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The figure shows the position â€“ time (x â€“ t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

asked Dec 11, 2018 by pady_1

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In the circuit shown below, the key K is closed at t = 0. The current through the battery is

asked Dec 11, 2018 by pady_1

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Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX ' is given by

asked Dec 11, 2018 by pady_1

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A particle is moving with velocity $v = K(y \hat i + x \hat j)$ , where K is a constant. The general equation for its path is

asked Dec 11, 2018 by pady_1

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