Recent questions in JEEMAIN PAST PAPERS

An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears :

asked Dec 11, 2018 by pady_1

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Arrange the following electromagnetic radiations per quantum in the order of increasing energy : A : Blue light B : Yellow light C : X-ray D : Radiowave.

asked Dec 11, 2018 by pady_1

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An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

asked Dec 11, 2018 by pady_1

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Hysteresis loops for two magnetic materials A and B are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

asked Dec 11, 2018 by pady_1

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Two identical wires A and B, each of length $‘l’$ , carry the same current $I$ . Wire A is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $‘a’$ . If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is :

asked Dec 11, 2018 by pady_1

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The temperature dependence of resistances of Cu and undoped Si in the temperature range 300-400 K, is best described by :

asked Dec 11, 2018 by pady_1

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A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4\; \mu F$ and $9\; \mu F$ capacitors), at a point distant 30 m from it, would equal :

asked Dec 11, 2018 by pady_1

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The region between two concentric spheres of radii â€˜aâ€™ and â€˜bâ€™, respectively (see figure), has volume charge density $\rho = \frac{A}{r}$ , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :

asked Dec 11, 2018 by pady_1

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A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take $g = 10\; ms^{−2}$ )

asked Dec 11, 2018 by pady_1

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A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is :

asked Dec 11, 2018 by pady_1

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$'nâ€™$ moles of an ideal gas undergoes a process $A \to B$ as shown in the figure. The maximum temperature of the gas during the process will be :

asked Dec 11, 2018 by pady_1

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An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $PV^n$ =constant, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively) :

asked Dec 11, 2018 by pady_1

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A pendulum clock loses 12 s a day if the temperature is $40^oC$ and gains 4 s a day if the temperature is $20^oC$ . The temperature at which the clock will show correct time, and the co-efficient of linear expansion ( $\alpha$ ) of the metal of the pendulum shaft are respectively :

asked Dec 11, 2018 by pady_1

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A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R; $h << R$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)

asked Dec 11, 2018 by pady_1

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A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to :

asked Dec 11, 2018 by pady_1

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A person trying to lose weight by burning fat lifts a mass of $10\; kg$ upto a height of $1\; m \;1000\; times$ . Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies $3.8 \times 10^7 \;J$ of energy per kg which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g=9.8 \;ms^{−2}$ :

asked Dec 11, 2018 by pady_1

1 answer

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$ . The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction $\mu$ and the distance $x(=QR)$ , are, respectively close to :

asked Dec 11, 2018 by pady_1

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A particle of mass m is moving along the side of a square of side â€˜aâ€™, with a uniform speed $v$ in the x-y plane as shown in the figure : Which of the following statements is false for the angular momentum $\overrightarrow{L}$ about the origin ?

asked Dec 11, 2018 by pady_1

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A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

asked Dec 11, 2018 by pady_1

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The contrapositive of the statement "If it is raining, then I will not come", is :

asked Dec 11, 2018 by pady_1

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If $f(x)=2 \tan^{-1}x+\sin^{-1} (\frac{2x}{1+x^2}),\; x>1$ , then $f(5)$ is equal to:

asked Dec 11, 2018 by pady_1

1 answer

In a $\Delta ABC, \; \frac{a}{b} = 2 + \sqrt{3}$ and $\angle{C} = 60^{\circ}$ . Then the ordered pair $(\angle{A}, \angle{B})$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs 54 and per day mean wage of all the workers is Rs 60, then per day mean wage of the night shift workers (in Rs) is :

asked Dec 11, 2018 by pady_1

1 answer

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

asked Dec 11, 2018 by pady_1

1 answer

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a} +\overrightarrow{b} |= \sqrt{3}$ . If $\overrightarrow{c} = \overrightarrow{a} + 2\overrightarrow{b} + 3(\overrightarrow{a} \times \overrightarrow{b})^2$ , then $2|\overrightarrow{c}|$ is equal to:

asked Dec 11, 2018 by pady_1

1 answer

If the shortest distance between the lines $\frac{x-1}{\alpha} = \frac{y+1}{-1} = \frac{z}{1},\; (\alpha \neq -1)$ and $x+y+z+1=0=2x-y+z+3$ is $\frac{1}{\sqrt{3}}$ , then a value of $\alpha$ is :

asked Dec 11, 2018 by pady_1

1 answer

If the points $(1, 1, \lambda)$ and $(-3, 0, 1)$ are equidistant from the plane, $3x+4y+12z+13=0$ , then $\lambda$ satisfies the equation :

asked Dec 11, 2018 by pady_1

1 answer

An ellipse passes through the foci of the hyperbola, $9x^2 - 4y^2 = 36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2}$ , then which of the following points does not lie on the ellipse ?

asked Dec 11, 2018 by pady_1

1 answer

If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$ (for some fixed $k$ ) at a point $(\alpha, \beta)$ ; then $(\alpha, \beta)$ is:

asked Dec 11, 2018 by pady_1

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If $y+3x =0$ is the equation of a chord of the circle, $x^2+y^2-30x=0$ , then the equation of the circle with this chord as diameter is :

asked Dec 11, 2018 by pady_1

1 answer

Let $L$ be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at $P$ . If $L_1$ is the line perpendicular to $L$ and passing through the point $(-2, 1)$ , then the point of intersection of $L$ and $L_1$ is :

asked Dec 11, 2018 by pady_1

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The points $(0, \frac{8}{3})\; (1,3)$ and $(82, 30)$

asked Dec 11, 2018 by pady_1

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If $y(x)$ is the solution of the differential equation $(x+2) \frac{dy}{dx} = x^2+4x-9,\; x \neq -2$ and $y(0)=0$ , then $y(-4)$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The area (in square units) of the region bounded by the curves $y + 2x^2 =0$ and $y+3x^2 =1$ , is equal to :

asked Dec 11, 2018 by pady_1

1 answer

For $x>0$ , let $f(x) = \begin{align} \int_1^x \frac{\log t}{1+t} dt \end{align}$ . Then $f(x) + f(\frac{1}{x})$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The integral $\begin{align} \int \frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}\end{align}$ is equal to:

asked Dec 11, 2018 by pady_1

1 answer

Let the tangents drawn to the circle, $x^2+y^2 = 16$ from the point $P(0,h)$ meet the $x$ -axis at point A and B. If the area of $\Delta APB$ is minimum, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2+cx,\; x \in [-1, 1]$ , at the point $x= \frac{1}{2}$ , then $2b+c$ equals :

asked Dec 11, 2018 by pady_1

1 answer

The distance, from the origin of the normal to the curve, $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $t = \frac{\pi}{4}$ , is:

asked Dec 11, 2018 by pady_1

1 answer

$\displaystyle{\lim_{x \to 0} \frac{e^{x^2}-\cos x}{\sin^2x}}$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The value of $\displaystyle\sum_{r=16}^{30} (r+2)(r-3)$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$ , then the first of these terms in the expansion is :

asked Dec 11, 2018 by pady_1

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Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

asked Dec 11, 2018 by pady_1

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The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

asked Dec 11, 2018 by pady_1

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If $A = \begin{bmatrix} 0 & -1 \\ 1& 0 \end{bmatrix}$ , then which one of the following statement is not correct ?

asked Dec 11, 2018 by pady_1

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The least value of the product $xyz$ for which the determinant $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix}$ is non negative, is:

asked Dec 11, 2018 by pady_1

1 answer

If $2 + 3i$ is one of the roots of the equation $2x^3 - 9x^2 + kx - 13 = 0, \; k \in R$ , then the real root of this equation :

asked Dec 11, 2018 by pady_1

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The largest value of $r$ for which the region represented by the set $\{ \omega \in C | \omega - 4 - i | \leq r \}$ is contained in the region represented by the set $\{z \in C / |z-1| \leq |z+i| \}$ , is equal to :

asked Dec 11, 2018 by pady_1

1 answer

In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements : (a) 5% families own both a car and a phone. (b) 35% families own either a car or a phone. (c) 40,000 families live in the town. Then :

asked Dec 11, 2018 by pady_1

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The cation that will not be precipitated by $H_2S$ in the presence of $dil. HCl$ is :

asked Dec 11, 2018 by pady_1

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