Recent questions in JEEMAIN PAST PAPERS

Let C be the circle with centre at $(1, 1)$ and $radius = 1$. If T is the circle centred at $(0, y)$, passing through origin and touching the circle C externally, then the radius of T is equal to

asked Dec 11, 2018 by pady_1

1 answer

Let the population of rabbits surviving at a time t be governed by the differential equation $\frac{dp(t)}{dt} = \frac{1}{2} p(t) - 200$ . If $p(0) = 100$, then $p(t)$ equals

asked Dec 11, 2018 by pady_1

1 answer

If f and g are differentiable functions in $[0, 1]$ satisfying $f(0) = 2 = g(1), g(0) = 0 $ and $f(1) = 6$, then for some $c \in ]0, 1[$

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

1 answer

Let $\alpha$ and $\beta$ be the roots of equation $px^2 + qx + r = 0,\; p \neq 0$. If $p, q, r$ are in A.P. and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$, then the value of $|\alpha - \beta|$ is

asked Dec 11, 2018 by pady_1

1 answer

Let $f_K(x) = \frac{1}{k} (\sin^k x + \cos^k x)$ where $x \in R$ and $k \geq 1$. Then $f_4(x) - f_6(x)$ equals

asked Dec 11, 2018 by pady_1

1 answer

If $\alpha, \beta \neq 0$, and $f(n) = \alpha^n + \beta^n$ and $ \begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) &1+f(4) \end{vmatrix} = K(1 - \alpha)^2 (1 - \beta)^2 (\alpha - \beta)^2$, then $K$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If $g$ is the inverse of a function $f$ and $f'(x) = \frac{1}{1+x^5}$ , then $g'(x)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If z is a complex number such that $|z| \geq 2$, then the minimum value of $| x + \frac{1}{2} |$

asked Dec 11, 2018 by pady_1

1 answer

The integral $\begin{align} \int \begin{pmatrix}1 + x - \frac{1}{x} \end{pmatrix} e^{x + \frac{1}{x}} dx \end{align}$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If A is an $3 \times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$, then $BB'$ equals

asked Dec 11, 2018 by pady_1

1 answer

The statement $\sim (p \leftrightarrow \sim q)$ is

asked Dec 11, 2018 by pady_1

1 answer

The integral $\begin{align} \int_0^{\pi} \sqrt{1 + 4 \sin^2 \frac{x}{2} - 4 \sin \frac{x}{2} \; dx} \end{align}$ equals

asked Dec 11, 2018 by pady_1

1 answer

A bird is sitting on the top of a vertical pole $20\; m$ high and its elevation from a point O on the ground is $45^{\circ}$. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to $30^{\circ}$. Then the speed (in m/s) of the bird is

asked Dec 11, 2018 by pady_1

1 answer

The variance of first 50 even natural numbers is

asked Dec 11, 2018 by pady_1

1 answer

If $[ \overrightarrow{a} \times \overrightarrow{b} \; \overrightarrow{ b} \times \overrightarrow{c } \; \overrightarrow{c} \times \overrightarrow{a} ] = \lambda [ \overrightarrow{a} \; \overrightarrow{b} \; \overrightarrow{c} ]^2$ , then $\lambda$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If $a \in R$ and the equation $-3(x - [x])^2 + 2 (x - [x]) + a^2 = 0$ (where $[x]$ denotes the greatest integer $\leq x$) has no integral solution, then all possible values of a lie in the interval

asked Dec 11, 2018 by pady_1

1 answer

If the coefficients of $x^3$ and $x^4$ in the expansion of $(1 + ax + bx^2 ) (1 - 2x)^{18}$ in powers of $x$ are both zero, then $(a, b)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The image of the line $\frac{x-1}{3} = \frac{y-3}{1} = \frac{z-4}{-5}$ in the plane $2x-y+z+3 = 0$ is the line

asked Dec 11, 2018 by pady_1

1 answer

Assume that an electric field $\overrightarrow{E} = 30 x^2 \hat{i}$ exists in space. Then the potential difference $V_A - V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x=2$ is :

asked Dec 11, 2018 by pady_1

0 answers

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively, then $I_A/I_B$ equals :

asked Dec 11, 2018 by pady_1

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On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R, and the surface tension of water is T, value of r just before bubbles detach is : (density of water is $\rho_w$)

asked Dec 11, 2018 by pady_1

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When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $F = ax + bx^2$ where a and b are constants. The work done in stretching the unstretched rubber band by L is :

asked Dec 11, 2018 by pady_1

0 answers

A block of mass m is placed on a surface with a vertical cross section given by $y = x^3 /6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :

asked Dec 11, 2018 by pady_1

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The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

asked Dec 11, 2018 by pady_1

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Hydrogen $(_1H^1 )$, Deuterium $(_1H^2 )$, singly ionised Helium $(_2He^4 )^+$ and doubly ionised lithium $(_3Li^6 )^{++}$ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of emitted radiation are $\lambda_1, \lambda_2, \lambda_3 \;and \;\lambda_4$ respectively then approximately which one of the following is correct?

asked Dec 11, 2018 by pady_1

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A green light is incident from the water to the air – water interface at the critical angle ($\theta$). Select the correct statement

asked Dec 11, 2018 by pady_1

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There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio $d_1/d_2$ is

asked Dec 11, 2018 by pady_1

0 answers

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

asked Dec 11, 2018 by pady_1

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Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross – section of each rod = $4\; cm^2$ . End of copper rod is maintained at $100^{\circ}C$ where as ends of brass and steel are kept at $0^{\circ}C$. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

asked Dec 11, 2018 by pady_1

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A thin convex lens made from crown glass $( \mu = \frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is :

asked Dec 11, 2018 by pady_1

0 answers

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

asked Dec 11, 2018 by pady_1

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One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

asked Dec 11, 2018 by pady_1

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A mass â€˜mâ€™ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

asked Dec 11, 2018 by pady_1

0 answers

In the circuit shown here, the point â€˜Câ€™ is kept connected to point â€˜Aâ€™ till the current flowing through the circuit becomes constant. Afterward, suddenly, point â€˜Câ€™ is disconnected from point â€˜Aâ€™ and connected to point â€˜Bâ€™ at time $t = 0$. Ratio of the voltage across resistance and the inductor at $t = L/R$ will be equal to :

asked Dec 11, 2018 by pady_1

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During the propagation of electromagnetic waves in a medium:

asked Dec 11, 2018 by pady_1

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The forward biased diode connection is:

asked Dec 11, 2018 by pady_1

0 answers

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^3 Am^{-1}$ . The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:

asked Dec 11, 2018 by pady_1

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A particle moves with simple harmonic motion in a straight line. In first $\tau$ s, after starting from rest it travels a distance a, and in next $\tau$ s it travels 2a, in same direction, then :

asked Dec 11, 2018 by pady_1

0 answers

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

asked Dec 11, 2018 by pady_1

0 answers

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

asked Dec 11, 2018 by pady_1

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A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

asked Dec 11, 2018 by pady_1

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A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 10^4 V/m$, the charge density of the positive plate will be close to :

asked Dec 11, 2018 by pady_1

0 answers

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct option from the choices given below the lists:

asked Dec 11, 2018 by pady_1

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An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)

asked Dec 11, 2018 by pady_1

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The current voltage relation of diode is given by $I = (e^{1000V/T}– 1) \;mA$, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring $\pm 0.01 \;V$ while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

asked Dec 11, 2018 by pady_1

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A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :

asked Dec 11, 2018 by pady_1

1 answer

A conductor lies along the z-axis at $-1.5 \leq z < 1.5$ and carries a fixed current of 10.0 A in $-\hat{a}_{_z}$ direction (see figure). For a field $\overrightarrow{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_{_y} \;T$, find the power required to move the conductor at constant speed to $x = 2.0\; m, \;y = 0 \;m$ in $5 \times 10^{-3} s$. Assume parallel motion along the x-axis

asked Dec 11, 2018 by pady_1

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The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by $100^{\circ}C$ is : (For steel Young’s modulus is $2 \times 10^{11} N m^{–2}$ and coefficient of thermal expansion is $1.1 \times 10^{–5} K^{–1}$ )

asked Dec 11, 2018 by pady_1

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Two short bar magnets of length 1 cm each have magnetic moments $1.20\; Am^2$ and $1.00\; Am^2 $ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to (Horizontal component of earth’s magnetic induction is $3.6 \times 10^{–5} Wb/m^2$)

asked Dec 11, 2018 by pady_1

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Ask Questions, Get Answers

Let C be the circle with centre at $(1, 1)$ and $radius = 1$. If T is the circle centred at $(0, y)$, passing through origin and touching the circle C externally, then the radius of T is equal to

Let the population of rabbits surviving at a time t be governed by the differential equation $\frac{dp(t)}{dt} = \frac{1}{2} p(t) - 200$ . If $p(0) = 100$, then $p(t)$ equals

If f and g are differentiable functions in $[0, 1]$ satisfying $f(0) = 2 = g(1), g(0) = 0 $ and $f(1) = 6$, then for some $c \in ]0, 1[$

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

Let $\alpha$ and $\beta$ be the roots of equation $px^2 + qx + r = 0,\; p \neq 0$. If $p, q, r$ are in A.P. and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$, then the value of $|\alpha - \beta|$ is

Let $f_K(x) = \frac{1}{k} (\sin^k x + \cos^k x)$ where $x \in R$ and $k \geq 1$. Then $f_4(x) - f_6(x)$ equals

If $\alpha, \beta \neq 0$, and $f(n) = \alpha^n + \beta^n$ and $ \begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) &1+f(4) \end{vmatrix} = K(1 - \alpha)^2 (1 - \beta)^2 (\alpha - \beta)^2$, then $K$ is equal to

If $g$ is the inverse of a function $f$ and $f'(x) = \frac{1}{1+x^5}$ , then $g'(x)$ is equal to

If z is a complex number such that $|z| \geq 2$, then the minimum value of $| x + \frac{1}{2} |$

The integral $\begin{align} \int \begin{pmatrix}1 + x - \frac{1}{x} \end{pmatrix} e^{x + \frac{1}{x}} dx \end{align}$ is equal to

If A is an $3 \times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$, then $BB'$ equals

The statement $\sim (p \leftrightarrow \sim q)$ is

The integral $\begin{align} \int_0^{\pi} \sqrt{1 + 4 \sin^2 \frac{x}{2} - 4 \sin \frac{x}{2} \; dx} \end{align}$ equals

The variance of first 50 even natural numbers is

If $[ \overrightarrow{a} \times \overrightarrow{b} \; \overrightarrow{ b} \times \overrightarrow{c } \; \overrightarrow{c} \times \overrightarrow{a} ] = \lambda [ \overrightarrow{a} \; \overrightarrow{b} \; \overrightarrow{c} ]^2$ , then $\lambda$ is equal to

If $a \in R$ and the equation $-3(x - [x])^2 + 2 (x - [x]) + a^2 = 0$ (where $[x]$ denotes the greatest integer $\leq x$) has no integral solution, then all possible values of a lie in the interval

If the coefficients of $x^3$ and $x^4$ in the expansion of $(1 + ax + bx^2 ) (1 - 2x)^{18}$ in powers of $x$ are both zero, then $(a, b)$ is equal to

The image of the line $\frac{x-1}{3} = \frac{y-3}{1} = \frac{z-4}{-5}$ in the plane $2x-y+z+3 = 0$ is the line

Assume that an electric field $\overrightarrow{E} = 30 x^2 \hat{i}$ exists in space. Then the potential difference $V_A - V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x=2$ is :

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $F = ax + bx^2$ where a and b are constants. The work done in stretching the unstretched rubber band by L is :

A block of mass m is placed on a surface with a vertical cross section given by $y = x^3 /6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :

A green light is incident from the water to the air – water interface at the critical angle ($\theta$). Select the correct statement

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio $d_1/d_2$ is <br>

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A thin convex lens made from crown glass $( \mu = \frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is :

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement: <br>

A mass â€˜mâ€™ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? <br>

During the propagation of electromagnetic waves in a medium:

The forward biased diode connection is:

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^3 Am^{-1}$ . The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:

A particle moves with simple harmonic motion in a straight line. In first $\tau$ s, after starting from rest it travels a distance a, and in next $\tau$ s it travels 2a, in same direction, then :

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 10^4 V/m$, the charge density of the positive plate will be close to :

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct option from the choices given below the lists: <br>

A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :