Recent questions in JEEMAIN-2015

In the circuit shown, the current in the $1\Omega$ resistor is :

asked Nov 2, 2015 by meena.p

1 answer

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three are col linear and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}= \large\frac{1}{3} |\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}$ . If $\theta$ is the angle between vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ , then a value of $\sin \theta$ is :

asked Oct 30, 2015 by meena.p

1 answer

Let A and B be two sets containing four and two elements respectively . Then the number of subset of the set $A \times B$ , each having at least three elements is :

asked Oct 30, 2015 by meena.p

1 answer

If the angles of elevation of the top of a tower from three collinear points $A,B$ and $C$ on a line leading to the foot of the tower , are $30^{\circ},45^{\circ}$ and $60^{\circ}$ respectively , then the ratio , $AB:BC$ , is :

asked Oct 30, 2015 by meena.p

1 answer

$\lim \limits_{x \to 0} \large\frac{(1- \cos 2x)(3+ \cos x)}{x \tan 4x}$ is equal to :

asked Oct 30, 2015 by meena.p

1 answer

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,k \in R$ , is a :

asked Oct 30, 2015 by meena.p

1 answer

If the function $g(x) = \left\{ \begin{array} {1 1} k \sqrt{x+1} , & \quad 0 \leq x \leq 3 \\ mx+2,& \quad 3 < x \leq 5 \end{array} \right.$ is differentiable , then the value of $k+m$ is :

asked Oct 30, 2015 by meena.p

1 answer

The integral $\int \limits_2^4 \large\frac{\log x^2}{\log x^2+\log(36-12x+x^2)}$ $dx$ is equal to :

asked Oct 30, 2015 by meena.p

1 answer

The sum of coefficient on integral powers of x in the binomial expansion of $(1-2 \sqrt {x})^{50}$ is :

asked Oct 30, 2015 by meena.p

1 answer

If $12$ identical balls are to be placed in 3 identical boxes ,then the probability that one of the boxes contains exactly 3 balls is :

asked Oct 30, 2015 by meena.p

1 answer

The set of all values of $\lambda$ for which the system of linear of linear equations : $2x_1-2x_2+x_3 =\lambda x_1 \\ 2x_1-3x_2+2x_3 =\lambda x_2 \\ -x_1 + 2x_2 = \lambda x_3$ has a non- trivital solution,

asked Oct 30, 2015 by meena.p

1 answer

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ , is :

asked Oct 30, 2015 by meena.p

1 answer

The equation of the plane containing the line $2x-5y+z=3; x+y+4z=5$ and parallel to the plane , $x+3y+6z=1$ , is :

asked Oct 30, 2015 by meena.p

1 answer

The area (in sq.units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\large\frac{x^2}{9} + \frac{y^2}{5}$ $=1$ is :

asked Oct 30, 2015 by meena.p

1 answer

The mean of the data set comprising of 16 observations is $16$ . If one of the observation valued 16 is deleted and three new observations, valued 16 is deleted and three new observation valued $3,4$ and $5$ are added to the mean of the resultant data, is :

asked Oct 30, 2015 by meena.p

1 answer

Let O be the vertex and Q be any point on the parabola , $x^2=8y$ . If the point P divides the line segment OQ internally in the ratio $1:3$ , then the locus of P is :

asked Oct 30, 2015 by meena.p

1 answer

The area (in sq.units ) of the region described by : $\{(x,y):y^2 \leq 2x\;and\;y \geq 4x-1\}$ is :

asked Oct 30, 2015 by meena.p

1 answer

The distance of the point $(1,0,2)$ from the point of intersection of the line $\large\frac{x-2}{3} =\frac{y+1}{4} =\frac{z-2}{12}$ and the plane $x-y+z=16,$ is :

asked Oct 30, 2015 by meena.p

1 answer

Let $\tan^{-1}y = \tan ^{-1}x + \tan^{-1} \bigg(\large\frac{2x}{1-x^2}\bigg)$ , where $|x| < \frac{1}{\sqrt 3 }$ . Then a value of y is :

asked Oct 30, 2015 by meena.p

1 answer

Let $\alpha$ and $B$ be the roots of equation $x^2-6x-2=0$ .If $a_n= \alpha^n- \beta^n,$ for $n \geq 1$ then the value of $\large\frac{a_{10}-2_{a8}} {2a_{9}}$ is equal to :

asked Oct 30, 2015 by meena.p

1 answer

The number of points , having both co-ordinates as integers,that lie in the interior of the triangle of the triangle with vertices $(0,0),(0,41)$ and $(41,0)$ is :

asked Oct 30, 2015 by meena.p

1 answer

The number of integers greater than $6,000$ that can be formed , using the digits $3,5,6,7$ and $8$ , with out repetion, is :

asked Oct 30, 2015 by meena.p

1 answer

Let $y(x)$ be the solution of the differential equation $(x log x) \frac{dy}{dz}$ $+y=2x \log x , x (\geq 1)$ Then $y(e)$ i equal to :

asked Oct 29, 2015 by meena.p

1 answer

If m is the A.M of two distinct real number l and n (l,n >1) and $G_1,G_2$ and $G_3$ are three geometric means between l and n, then $G_1^4 +2 G_2^4+G_3^4$ equals

asked Oct 29, 2015 by meena.p

1 answer

The integral $\int \frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

asked Oct 29, 2015 by meena.p

1 answer

If $A=\begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T=9I$ , where I is $3 \times 3$ identity matrix , then the ordered pair $(a,b)$ is equal to :

asked Oct 29, 2015 by meena.p

1 answer

The negation of $s\approx V ( \approx s)$ is equivalent to :

asked Oct 29, 2015 by meena.p

1 answer

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$ If $\lim\limits_{x \to 0} \bigg[1+\large\frac{f(x)}{x^2}\bigg]$ $=3$ then $(2)$ is equal to :

asked Oct 29, 2015 by meena.p

1 answer

The sum of first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}$ +.....is :

asked Oct 29, 2015 by meena.p

1 answer

The normal to the curve , $x^2+2xy-3y^2=0$ at (1,1):

asked Oct 29, 2015 by meena.p

1 answer

A complex number z is said to be uni modular if $|z|=1$ . suppose $z_1$ and $z_2$ are complex numbers such that $\large\frac{z_1-2z_2}{2-z_1z_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

asked Oct 29, 2015 by meena.p

1 answer

On a hot summer night, the refractive index of air is smallest near the ground and increase with height from the ground . when a light beam is directed horizontally, the Huygen's principle leads us to conclude that as it travels, the light beam:

asked Oct 29, 2015 by meena.p

1 answer

Two long current carrying thin wires, both with current I, are held by insulting threads of length L and are in equilibrium as shown in the figure, with threads making an angle $\theta$ with the vertical. If wires have mass $\lambda$ per unit length then the value of I is : (g= gravitational acceleration )

asked Oct 29, 2015 by meena.p

1 answer

Assuming human pupil to have a radius of $0.25\;cm$ and a comfortable viewing distance of $25\;cm$ , the minimum separation between two objects that human eye can resolve at 500 nm wave length is :

asked Oct 29, 2015 by meena.p

1 answer

A solid body of constant heat capacity $1\;J/c^{\circ}$ is being heating by keeping it in contact with reservation in two ways : (i) sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat (ii) sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat . In both cases body is brought from initial temperature $100^{\circ}$ to final temperature $200 ^{\circ}C$ Entropy change of the body in the two cases respectively is :

asked Oct 29, 2015 by meena.p

1 answer

Two stones are thrown up simultaneously from the edge of a cliff $240\;m$ high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance , take $g= 10 m/s^2)$

asked Oct 29, 2015 by meena.p

1 answer

For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly ?

asked Oct 29, 2015 by meena.p

1 answer

When 5V potential difference is applied across a wire of length $0.1\;m$ , the drift speed of electrons is $2.5 \times 10^{-4}\;ms^{-1}$ . If the electron density in the wire is $8 \times 10^{28}\;m^{-3}$ , the resistivity of the material is close to :

asked Oct 29, 2015 by meena.p

1 answer

Match List - I (Fundamental experiment ) with List -II (its conclusion) and select the correct option from the choices given below the list :

asked Oct 29, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

asked Oct 28, 2015 by meena.p

1 answer

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$ , a ray , incident at an angle $\theta$ , on the face AB would get transmitted through the face AC of the prism provided :

asked Oct 28, 2015 by meena.p

1 answer

A particle of mass m moving in the x direction with speed $2v$ is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic , the percentage loss in the energy during the collision is close to :

asked Oct 28, 2015 by meena.p

1 answer

In the given circuit , charge $Q_2$ on the $2 \mu F$ capacitor changes as C is varied from 1 \mu F $to$ 3 \mu F $.$ Q_2$ as a function of 'C' is given properly by :

asked Oct 28, 2015 by meena.p

1 answer

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials $\large\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\frac{V_0}{4}$ has radius $R_1, R_2,R_3$ and $R_4$ respectively . Then ,

asked Oct 28, 2015 by meena.p

1 answer

In the circuit shown , the current in the $1\;\omega$ resistor is:

asked Oct 28, 2015 by meena.p

2 answers

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientation as shown in the figures below : If there is a uniform magnetic field of $0.3\;T$ in the positive z direction , in which orientations loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?

asked Oct 28, 2015 by meena.p

1 answer

Distance of the center of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is R and its height is h then $z_0$ is equal to :

asked Oct 28, 2015 by meena.p

1 answer

Given in the figure are two blocks A and B of weight $20\;N$ and $100\;N$ , respectively. These are being pressed against a wall by a force F as shown . If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15,$ the frictional force applied by the wall on block B is :

asked Oct 28, 2015 by meena.p

1 answer

A train is moving on a straight track with speed $20\;ms^{-1}$ . It is blowing its whistle at the frequency of $1000\;Hz$ . The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = $320\;ms^{-1})$ close to :

asked Oct 28, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R, a spherical portion of radius $\large\frac{R}{2}$ is removed , as shown in fig. Taking gravitational potential $V=0$ at $r= \infty$ , the potential at the center of tge cavity thus formed is :

asked Oct 28, 2015 by meena.p

1 answer

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