JEE Main 2018 (Online) 15th April Morning Slot

n\(-\)digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

A box 'A' contains \(2\) white, \(3\) red and \(2\) black balls. Another box 'B' contains \(4\) white, \(2\) red and \(3\) black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns ou...

If tanA and tanB are the roots of the quadratic equation, 3x2 \(-\) 10x \(-\) 25 = 0, then the value of 3 sin2(A + B) \(-\) 10 sin(A + B).cos(A + B) \(-\) 25 cos2(A + B) is :

If \(\lambda\) \(\in\) R is such that the sum of the cubes of the roots of the equation,
x2 + (2 \(-\) \(\lambda\)) x + (10 \(-\) \(\lambda\)) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

If x1, x2, . . ., xn and \({1 \over {{h_1}}}\), \({1 \over {{h_2}}}\), . . . , \({1 \over {{h_n}}}\) are two A.P..s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals :

Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number \(\lambda\) and then each of them is decreased by 25, their mean remains the same. Then \(\lambda\) is equal to :

In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of \(\Delta\) ABC (in sq. units) is :

If \(\overrightarrow a ,\,\,\overrightarrow b ,\) and \(\overrightarrow C\) are unit vectors such that \(\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,\) then $$\left| {\overrightarrow a \times \over...

An ideal capacitor of capacitance \(0.2\,\mu F\) is charged to a potential difference of \(10\) \(V.\) The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance \(0.5\) \(mH.\) The cu...

The energy required to remove the electron from a singly ionized Helium atom is \(2.2\) times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :

A solution containing active cobalt \({^{60}_{27}}Co\) having activity of \(0.8\) \(\mu Ci\) and decay constant \(\lambda\) is injected in an animal's body. If \(1\,c{m^3}\) of blood is drawn from the animal's body after \(10\) hrs of inje...

The equivalent capacitance between \(A\) and \(B\) in the circuit given below, is :

The number of amplitude modulted broadcast stations that can be accomodated in a \(300\) \(kHz\) band width for the highest modulating frequency \(15\) \(kHz\) will be :

In the given circuit all resistances are of value \(R\) \(ohm\) each. The equivalent resistance between \(A\) and \(B\) is :

In a meter bridge, as shown in the figure, it is given that resistance \(Y = 12.5\,\,\Omega\) and that the balance is obtained at a distance \(39.5\) \(cm\) from end \(A\) (by Jockey J). After interchanging the resistances \(X\) and $$Y$...

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are \({\lambda _1}\) and \({\lambda _2},\) their de Broglie wavelength in the frame of reference attached to their cent...

A monochromatic beam of light has a frequency \(v = {3 \over {2\pi }} \times {10^{12}}Hz\) and is propagating along the direction \({{\widehat i + \widehat j} \over {\sqrt 2 }}.\)
It is polarized along the \(\widehat k\) direction. The acc...

In a common emitter configuration with suitable bias, it is given that \({R_L}\) is the load resistance and \({R_{BE}}\) is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respective...

A body of mass \(M\) and charge \(q\) is connected to spring of spring constant \(k.\) It is oscillating along \(x\)-direction about its equilibrium position, taken to be at \(x=0,\) with an amplitude \(A\). An electric field \(E\) is appl...

A charge \(Q\) is placed at a distance \(a/2\) above the center of the square surface of edge a as shown in the figure. The electric flux through the square surface is

A particle is oscillating on the \(X\)-axis with an amplitude \(2\) \(cm\) about the point \({x_0} = 10\,cm,\) with a frequency \(\omega\). A concave mirror of local length \(5\) \(cm\) is placed at the origin (see figure).
Identify the co...

A planoconvex lens becomes an optical system of \(28\) \(cm\) focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.
If the same lens is instead silvered on the curved surface and illuminated f...

Take the mean distance of the moon and the sun from the earth to be \(0.4 \times {10^6}\) km and \(150 \times {10^6}\) km respectively. Their masses are \(8 \times {10^{22}}\) kg and \(2 \times {10^{30}}\) kg respectively. The radius of the...

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \({R \over 2},\) and the other mass, in a circular orb...

A Carnot's engine works as a refrigerator between \(250\) K and \(300\) K. It receives \(500\) cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \({27^ \circ }C.\) The work done on the gas will be :

A given object takes n times more time to slide down a \({45^ \circ }\) rough inclined plane as it takes to slide down a perfectly smooth \({45^ \circ }\) incline. The coefficient of kinetic friction between the object and the incline is :

The \(B\)-\(H\) curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with \(1000\) turns/cm. The current that should be passed in the solended to demagnetise the ferromagnet completely is :

A Helmholtz coil has a pair of loops, each with \(N\) turns and radius \(R\). They are placed coaxially at distance \(R\) and the same current \({\rm I}\) flows through the loops in the same direction. \(P,\) midway between the centers $$A$...

An automobile, travelling at \(40\,\) km/h, can be stopped at a distance of \(40\,\) m by applying brakes. If the same automobile is travelling at \(80\,\) km/h, the minimum stopping distance, in metres, is (assume no skidding) :

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in \(15\) \(s\) and (ii) the time at which the car will catch up with the scooter are, res...

A thin uniform tube is bent into a circle of radius \(r\) in the vertical plane. Equal volumes of two immiscible liquids, whose densities are \({\rho _1}\) and \({\rho _2}\) \(\left( {{\rho _1} > {\rho _2}} \right),\) fill half the circle. ...

A uniform rod \(AB\) is suspended from a point \(X,\) at a variable distance \(x\) from \(A\), as shown, To make the rod horizontal, a mass \(m\) is suspended from its end \(A.\)A\(set of\)(m,x)$$ values is recorded. The appropriate varia...

A force of \(40\) \(N\) acts on a point \(B\) at the end of an \(L\)-shaped object, as shown in the figure. The angle \(\theta\) that will produce maximum moment of the force about point \(A\) is given by :

In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\) \(cm.\) There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main sc...

The relative error in the determination of the surface area of sphere is \(\alpha\). Then the relative error in the determination of its volume is :

Light of wavelength \(550\) \(nm\) falls normally on a slit of width \(22.0 \times {10^{ - 5}}\) \(cm.\) The angular position of the second minima from the central maximum will (in radians) :

A tuning fork vibrates with frequency \(256\) \(Hz\) and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is \(340\,m{s^{ - 1}}\))