Recent questions in JEEMAIN-2016

The truth table given in fig. represents :

asked May 23, 2017 by meena.p

1 answer

A bottle has an opening of radius $a$ and length $b$. A cork of length $b$ and radius $(a + \Delta a)$ where is $(\Delta << a)$ is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is $B$ and frictional coefficient between the bottle and cork is $\mu$ then the force needed to push the cork into the bottle is :

asked May 23, 2017 by priyanka.c

1 answer

A hydrogen atom makes a transition from $n=2$ to $n=1$ and emits a photon. This photon strikes a doubly ionized lithium atom $(z=3)$ in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

asked May 22, 2017 by meena.p

1 answer

When photons of wavelength $\lambda_1$ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength $\lambda_2$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $\lambda_3$ is used then find the stopping potential for this case :

asked May 22, 2017 by meena.p

1 answer

An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth’s surface. The radius of the earth is $R$, while its mass is $M$. The gravitational pull $F_G$ on the astronaut is

asked May 22, 2017 by priyanka.c

1 answer

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $\frac{BC}{AB}$ is close to :

asked May 22, 2017 by priyanka.c

1 answer

In Young’s double slit experiment, the distance between slits and the screen is $1.0\; m$ and monochromatic light of $600\; nm$ is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance $d_0$ between the slits. If the angular resolution of the eye is $\large\frac{1^{\circ}}{60}$ the value of $d_0$ is close to

asked May 22, 2017 by meena.p

1 answer

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :

asked May 22, 2017 by meena.p

1 answer

Microwave oven acts on the principle of :

asked May 22, 2017 by meena.p

1 answer

A series $LR$ circuit is connected to a voltage source with $V(t)=V_0\; sin \omega t$. After very large time, current I(t) behaves as $\bigg( t_0 >> \large\frac{L}{R} \bigg)$:

asked May 22, 2017 by meena.p

1 answer

A $50 \Omega$ resistance is connected to a battery of $5 \;V$. A galvanometer of resistance $100\;Ω$ is to be used as an ammeter to measure current through the resistance, for this a resistance rs is connected to the galvanometer. Which of the following connections should be employed if the measured current is within $1 \%$ of the current without the ammeter in the circuit ?

asked May 22, 2017 by meena.p

1 answer

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

asked May 22, 2017 by priyanka.c

1 answer

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to : </br> (Take the radius of the drum to be 1.25 m and its axle to be horizontal) :

asked May 22, 2017 by priyanka.c

1 answer

A particle of mass $ M $is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^2 R t^2$ where $ n$ is a constant. The power delivered to the particle by the force acting on it, is:

asked May 22, 2017 by priyanka.c

1 answer

A, B, C and D are four different physical quantities having different dimensions. Now of them is dimensionless. But we know that the equation AD = C in (BD) holds true. Then which of the combination is not a meaningful quantity ?

asked May 22, 2017 by priyanka.c

1 answer

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of $75^{\circ}$. One of the fields has a magnitude of $15\; mT$. The dipole attains stable equilibrium at an angle of $30^{\circ}$ with this field. The magnitude of the other field (in mT ) is close to :

asked May 19, 2017 by meena.p

1 answer

In the circuit shown, the resistance r is a variable resistance. If for $r=f R$, the heat generation in r is maximum then the value of f is :

asked May 19, 2017 by meena.p

1 answer

Three capacitors each of $4 \mu F$ are to be connected in such a way that the effective capacitance is $6 \mu F$. This can be done by connecting them :

asked May 19, 2017 by meena.p

1 answer

The potential (in volts) of a charge distribution is given by $V(z) =30-5z^2$ for $|z| \leq 1\;m$$V(z) =35-10|z|$ for $|z| \geq 1\;m$ $V(z)$ does not depend on x and y .If this potential is generated by a constant charge per unit volume $\rho_0,$ (in units of $\in_0$) which is spread over certain region ,then choose the correct statement

asked May 18, 2017 by meena.p

1 answer

Two engines pass each other moving in opposite directions with uniform speed of $30\;m/s$. One of them is blowing a whistle of frequency $540\; Hz$. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is $330\; m/sec$

asked May 18, 2017 by meena.p

1 answer

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T$, respectively. At time $t=0$ one particle has displacement $A$ while the other one has displacement $\large\frac{−A}{2}$ and they are moving towards each other. If they cross each other at time t, then t is :

asked May 18, 2017 by meena.p

1 answer

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

asked May 18, 2017 by meena.p

1 answer

$200\; g$ water is heated from $40^{\circ}C$ to $60^{\circ}C$. Ignoring the slight expansion of water, the change in its internal energy is close to(Given specific heat of water$=4184\; J/kg/K)$ :

asked May 18, 2017 by meena.p

1 answer

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height h (see figure). Through a hole of radius $r (r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure.If the radius of the cross-section of water stream when it hits the ground is $x$. Then :

asked May 18, 2017 by meena.p

1 answer

Figure shows elliptical path abcd of a planet around the sun $S$ such that the area of triangle csa is $\large\frac{1}{4}$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If $t_1$ is the time taken for planet to go over path abc and $t_2$ for path taken over cda then :

asked May 18, 2017 by meena.p

1 answer

A cubical block of side $30\;cm$ is moving with velocity $2 \;ms^{−1}$ on a smooth horizontal surface. The surface has a bump at a point $O$ as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

asked May 18, 2017 by meena.p

1 answer

A car of weight $W$ is on an inclined road that rises by $100\; m$ over a distance of $1\; km$ and applies a constant frictional force $\large\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 ms^{−1},$ the car needs power $P$. If it needs power $\frac{P}{2}$ while moving downhill at speed $v$ then value of v is :

asked May 18, 2017 by meena.p

1 answer

A rocket is fired vertically from the earth with an acceleration of $2g,$ where $g$ is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$. With the horizontal , a point object of mass $m$ is kept. The minimum coefficient of friction $\mu_{min}$ between the mass and the inclined surface such that he mass does not move is :

asked May 18, 2017 by meena.p

1 answer

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force $F =−kv,$ where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

asked May 18, 2017 by meena.p

1 answer

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

asked May 18, 2017 by meena.p

1 answer

The Boolean Expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$\ is quivalent to :

asked Mar 22, 2017 by meena.p

1 answer

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ}$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ}$. Then the time taken (in minutes) by him, from B to reach the pillar, is :

asked Mar 22, 2017 by meena.p

1 answer

If $0 \leq x < 2 \pi$, then the number of real values of $x$, which satisfy the equation $\cos x + \cos 2x = \cos 3x + \cos 4x = 0,$ is :

asked Mar 22, 2017 by meena.p

1 answer

Let two fair six-faced dice A and B be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

asked Mar 21, 2017 by meena.p

1 answer

If the standard deviation of the numbers $2, 3, a$ and $11$ is $3.5,$ then which of the following is true?

asked Mar 21, 2017 by meena.p

1 answer

Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$be three unit vectors such that $\overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c}) = \large\frac{3}{2}(\overrightarrow{b}+\overrightarrow{c})$. If $\overrightarrow{b}$ If $\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$ , then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :

asked Mar 21, 2017 by meena.p

1 answer

If the line, $\large\frac{x-3}{2} =\frac{y+2}{-1}=\frac{z-4}{3}$ lies in the plane,$lx + my - z = 9,$ then $l^2+m^2$ is equal to :

asked Mar 21, 2017 by meena.p

1 answer

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half the distance between its foci, is:

asked Mar 21, 2017 by meena.p

1 answer

Let P be the point on the parabola, $y^2= 8x$ which is at a minimum distance from the centre $C$ of the circle, $x^2+(y + 6)^2= 1.$ Then the equation of the circle, passing through C and having its centre at P is:

asked Mar 21, 2017 by meena.p

1 answer

If one of the diameters of the circle, given by the equation, $x^2 + y^2-4x+6y -12 = 0,$ is a chord of a circle S, whose centre is at $(-3, 2),$ then the radius of S is:

asked Mar 21, 2017 by meena.p

1 answer

The centres of those circles which touch the circle, $x^2+y^2- 8x -8y-4 = 0,$ externally and also touch the x-axis, lie on:

asked Mar 21, 2017 by meena.p

1 answer

Two sides of a rhombus are along the lines, $x = y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

asked Mar 21, 2017 by meena.p

1 answer

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation,$y(1 + xy) dx = x dy,$ then $f\bigg(\large\frac{-1}{2}\bigg)$ is equal to :

asked Mar 20, 2017 by meena.p

1 answer

The area (in sq. units) of the region $\{(x,y):y^2 \leq 2x $ and $ x^2+y^2 \geq 4x, x \leq 0, y \geq 0 \} $ is

asked Mar 20, 2017 by meena.p

1 answer

$\lim_\limits{n \to \infty} \bigg( \large\frac{(n-1)(n+2)....3n}{n^{2n}}\bigg)^{1/n}$ is eaual to

asked Mar 20, 2017 by meena.p

1 answer

The integral $\int \large\frac{2x^{12} +5x^{9}}{(x^2+x^3+1)^3}$$dx$ is equal to

asked Mar 17, 2017 by meena.p

1 answer

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:

asked Mar 16, 2017 by meena.p

1 answer

Consider $f(x) = \tan ^{-1} \bigg( \sqrt{\Large\frac{1+ \sin x}{1- \sin x}}\bigg),$$x \in \bigg(0, \large\frac{\pi}{2} \bigg)$ A normal to $y = f(x)$ at $x =\large\frac{\pi}{6}$ also passes through the point:

asked Mar 16, 2017 by meena.p

1 answer

For $x \in R ,f(x) = | \log 2 - \sin x | $ and $g(x) =f(f(x))$, then

asked Mar 16, 2017 by meena.p

1 answer

Let $p = \lim \limits_{x \to 0+} (1+ \tan ^2 \sqrt x )^{1/2x}$ then long p is equal to

asked Mar 16, 2017 by meena.p

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