Recent questions in JEEMAIN PAST PAPERS

When $_3 Li^7$ nuclei are bombarded by protons, and the resultant nuclei are $_4Be^8$, the emitted particles will be :

asked Nov 13, 2018 by pady_1

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The time taken by a photoelectron to come out after the photon strikes is approximately :

asked Nov 13, 2018 by pady_1

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An alpha nucleus of energy $\frac{1}{2} mv^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to :

asked Nov 13, 2018 by pady_1

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The threshold frequeny for a metallic surface corresponds to an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in :

asked Nov 13, 2018 by pady_1

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A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple i kept hot and the other is kept cold, then, an electrix current will :

asked Nov 13, 2018 by pady_1

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In a common-base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor ($\beta$) will be:

asked Nov 13, 2018 by pady_1

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A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to :

asked Nov 13, 2018 by pady_1

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Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position ?

asked Nov 13, 2018 by pady_1

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A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is :

asked Nov 13, 2018 by pady_1

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A ball of mass 0.2 kg is thrown verticlly upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force, consider $g=10\; m/s^2$ :

asked Nov 13, 2018 by pady_1

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Which of the following units denotes the dimensions $[ML^2/Q^2]$, where $Q$ denotes the electric charge ?

asked Nov 13, 2018 by pady_1

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Assuming the Sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the Sun : where $r_0$ is the radius of the earth and $\sigma$ is Stefan's constant .

asked Nov 13, 2018 by pady_1

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Starting from the origin a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy ?

asked Nov 13, 2018 by pady_1

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The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is :

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A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is :

asked Nov 13, 2018 by pady_1

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A mass of M kg is suspened by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is :

asked Nov 13, 2018 by pady_1

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A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed $\nu \; ms^{-1}$. The velocity of sound in air is $300 \; ms^{-1}$. If the person can hear frequencies upto a maximum of 10,000 Hz, the maximum value of $\nu$ upto which he can hear the whistle is :

asked Nov 13, 2018 by pady_1

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A bomb of mass 16 kg at rest explodes into two pieces of masses $4\; kg$ and $12\; kg$. The velocity of the $12\; kg$ mass id $4\; m^{-1}$. The kinetic energy of the other mass is :

asked Nov 13, 2018 by pady_1

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A particle located at $x=0$ at time $t=0$, starts moving along the positive $x$-direction with a velocity $'v'$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle varies with time as :

asked Nov 13, 2018 by pady_1

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An electric dipole is placed at an angle of $30^{\circ}$ to a non-uniform electric field. The dipole will experience:

asked Nov 13, 2018 by pady_1

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In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a :

asked Nov 13, 2018 by pady_1

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A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to have the same resistance, the ratio $I_B/I_A$ of their respective lengths must be :

asked Nov 13, 2018 by pady_1

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Needles $N_1, \;N_2$ and $N_3$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will :

asked Nov 13, 2018 by pady_1

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The Kirchhoff's first law $(\sum i =0)$ and second law $(\sum i R = \sum E)$, where the symbols have their usual meanings, are respectively based on :

asked Nov 13, 2018 by pady_1

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If the pair of lines $ax^2 + 2(a+b) xy + by^2 = 0 $ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector, then :

asked Nov 5, 2018 by pady_1

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The plane $x + 2y - z = 4$ cuts the sphere $x^2 + y^2 + z^2 - x - 2 = 0 $ in a circle of radius :

asked Nov 5, 2018 by pady_1

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The value of $\begin{align} \int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx, a >0 \end{align}$, is :

asked Nov 5, 2018 by pady_1

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If the equation $a_n\; x^n + a_{n-1}\; x^{n-1} + ....+ a_1x = 0$, $a_1 \neq 0, n \geq 2$, has a positive root $x=\alpha$, then the equation $n a_n x^{n-1} + (n-1) a_{n-1}\; x^{n-2} + . . . + a_1 = 0$ has a positive root, which is :

asked Nov 5, 2018 by pady_1

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A real valued function $f(x)$ satisfies the functional equation $f(x-y) = f(x) f(y) - f(a-x) f(a+y)$ where $a$ is a given constant and $f(0) = 1, f(2a - x)$ is equal to :

asked Nov 5, 2018 by pady_1

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If $a_1, a_2, a_3, . . . .a_n,...$ are in GP, then the determinant $\Delta = \begin{vmatrix} \log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8} \end{vmatrix}$ is equal to :

asked Nov 5, 2018 by pady_1

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If both the roots of the quadratic equation $x^2-2kx + k^2+k - 5 = 0$ are less than 5, then $k$ lies in the interval :

asked Nov 5, 2018 by pady_1

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A particle is projected from a point $O$ with velocity $u$ at an angle of $60^{\circ}$ with the horizontal. When it is moving in a direction at right angle to its direction at O, then its velocity is given by :

asked Nov 5, 2018 by pady_1

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Let $x_1, x_2 , . . . . x_n$ be $n$ observation such that $ \Sigma x_i^2 = 400 $ and $ \Sigma x_i = 80$. Then a possible value of $n$ among the following is :

asked Nov 5, 2018 by pady_1

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The sum of the series $1 + \frac{1}{4.2!} + \frac{1}{16.4!} + \frac{1}{64.6!}. . . . \infty$ is :

asked Nov 5, 2018 by pady_1

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$A$ and $B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance :

asked Nov 5, 2018 by pady_1

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If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} $ are non-coplanar vectors and $\lambda$ is a real number, then $[\lambda(\overrightarrow{a} + \overrightarrow{b}) \;\lambda^2 \overrightarrow{b} \;\lambda \overrightarrow{c} ] = [\overrightarrow{a} \overrightarrow{b} + \overrightarrow{c} \overrightarrow{b} ] $ for :

asked Nov 5, 2018 by pady_1

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Let $a, b$ and $c$ be distinct non-negative numbers. If the vectors $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k}$ and $c \hat{i} + c \hat{j} + b \hat{k}$ lie in a plane, then $c$ is :

asked Nov 5, 2018 by pady_1

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Let $\overrightarrow{a} = \hat{i} - \hat{k}, \; \overrightarrow{b} = x \hat{i} + \hat{j} + (1-x) \hat{k}$ and $\overrightarrow{c} = y \hat{i} +x \hat{j} + (1+x -y) \hat{k}$. Then $[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}]$ depends on :

asked Nov 5, 2018 by pady_1

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The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is :

asked Nov 5, 2018 by pady_1

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A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of $2\; cm/s^2 $ and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. The the lizard will catch the insect after :

asked Nov 5, 2018 by pady_1

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Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f'$ respectively. If $A$ takes $m$ sec more than $B$ and describes $'n'$ unit more than $B$ in acquiring the same speed, then :

asked Nov 5, 2018 by pady_1

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A random variable $X$ has Poisson distribution with mean 2. Then $P(X > 1.5)$ equals :

asked Nov 5, 2018 by pady_1

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Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the apply for the same house, is :

asked Nov 5, 2018 by pady_1

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

asked Nov 5, 2018 by pady_1

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The angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is :

asked Nov 5, 2018 by pady_1

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If the angle $\theta$ between the line $\frac{x+1}{1} = \frac{y-1}{2} = \frac{z-2}{2}$ and the plane $ 2x - y + \sqrt{\lambda} z+4 = 0$ is such that $\sin \theta = \frac{1}{3}$. The value of $\lambda$ is :

asked Nov 5, 2018 by pady_1

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The locus of a point $P(\alpha, \beta)$ moving under the condition that the line $y = \alpha x+ \beta$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is :

asked Nov 5, 2018 by pady_1

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An ellipse has OB as semi minor axis, $F$ and $F'$ its foci and th angle $FBF'$ is a right angle. Then the eccentricity of the ellipse is :

asked Nov 5, 2018 by pady_1

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If a circcle passes through the point $(a, b)$ and cuts the circle $x^2 + y^2 = p^2$ orthogonally, then the equation of the locus of its centre is :

asked Nov 5, 2018 by pady_1

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A circle touches the $x-axis$ and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

asked Nov 5, 2018 by pady_1

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