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Recent questions tagged 2010
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Questions from:
The circle $x^2+ y^2 = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two points if
jeemain
math
past papers
2010
90
asked
Dec 11
by
pady_1
0
answers
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
jeemain
math
past papers
2010
89
asked
Dec 11
by
pady_1
0
answers
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is
jeemain
math
past papers
2010
88
asked
Dec 11
by
pady_1
0
answers
Consider the system of linear equations: <br> $x_1 + 2x_2 + x_3 = 3$ <br> $2x_1 + 3x_2 + x_3 = 3 $ <br> $3x_1 +5 x_2 + 2x_3 = 1$ <br> The system has
jeemain
math
past papers
2010
87
asked
Dec 11
by
pady_1
0
answers
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out out at random and then transferred to the other. The number of ways in which this can be done is
jeemain
math
past papers
2010
86
asked
Dec 11
by
pady_1
0
answers
Let $f : (-1, 1) \to R$ be a differentiable function with $f(0) = -1$ and $f'(0)=1$. Let $g(x) = [f(2f(x) + 2)]^2$. Then $g'(0)=$
jeemain
math
past papers
2010
85
asked
Dec 11
by
pady_1
0
answers
Let $p(x)$ be a function defined on $R$ such that $p'(x) = p'(1-x)$, for all $x \in [0,1], \; p(0)=1$ and $p(1) =41$. Then $\begin{align*} \int_0 ^1p(x) \; dx\end{align*}$ equals
jeemain
math
past papers
2010
84
asked
Dec 11
by
pady_1
0
answers
Let $f : R \to R$ be a positive increasing function with $\displaystyle\lim_{x \to \infty} \frac{f(3x)}{f(x)} = 1$ Then $\displaystyle\lim_{x \to \infty} \frac{f(2x)}{f(x)} = $
jeemain
math
past papers
2010
83
asked
Dec 11
by
pady_1
0
answers
A person is to count 4500 currency notes. Let $a_n$ denote the number of notes the counts in the $n^{th} $ minute. If $a_1 = a_2 = .......= a_{10} = 150$ and $a_{10}, a_{11}, ....$ are in A.P. with common difference $-2$, then the time taken by him to count all notes is
jeemain
math
past papers
2010
82
asked
Dec 11
by
pady_1
0
answers
The line L given by $\frac{x}{5}+ \frac{y}{b} = 1$ passes through the poin (13, 32). The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is
jeemain
math
past papers
2010
81
asked
Dec 11
by
pady_1
0
answers
A line AB in three-dimensional space makes angle $45^{\circ}$ and $120^{\circ}$ with the positive $x-axis$ and the positive $y-axis$ respectively. If AB makes an acute $\theta$ with the positive $z-axis$, then $\theta$ equals
jeemain
math
past papers
2010
80
asked
Dec 11
by
pady_1
0
answers
The number of complex number $z$ such that $|z-1| = | z+ 1| = |z-i|$ equals
jeemain
math
past papers
2010
79
asked
Dec 11
by
pady_1
0
answers
If $\alpha$ and $\beta$ are the roots of the equation $x^2 - x + 1 =0$, then $\alpha^{2009} + \beta^{2009}$ =
jeemain
math
past papers
2010
78
asked
Dec 11
by
pady_1
0
answers
For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is
jeemain
math
past papers
2010
77
asked
Dec 11
by
pady_1
0
answers
Let $f : R \to R$ be a continuous function defined by $f(x) = \frac{1}{e^x + 2e^{-x}}$. <br> Statement-1 : $f(c) = \frac{1}{3}$, for some $c \in R$. <br> Statement-2 : $0 < f(x) \leq \frac{1}{2 \sqrt{2}}$, for all $x \in R$
jeemain
math
past papers
2010
76
asked
Dec 11
by
pady_1
0
answers
Let $A$ be a $ 2 \times 2$ matrix with non-zero entries and let $A^2 =I$, where $I$ is $2 \times 2$ identity matrix. Define $Tr(A)$ = sum of diagonal elements of $A$ and $|A|$ = determinant of matrix A. <br> Assertion : Statement -1: $Tr(A) = 0$ <br> Reason : Statement-2 : $|A| =1$
jeemain
math
past papers
2010
75
asked
Dec 11
by
pady_1
0
answers
Let $S_1 = \displaystyle\sum_{j=1}^{10} j (j - 1)^{10} C_j, S_2 = \displaystyle\sum_{j=1}^{10} j \;^{10} C_j $ and $S_3 = \displaystyle\sum_{j=1}^{10} j^2 \;^{10} C_j $ <br> Statement-1 : $S_3 = 55 \times 2^9$ <br> Statement-2 : $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$.
jeemain
math
past papers
2010
74
asked
Dec 11
by
pady_1
0
answers
Statement-1: The point $A(3, 1, 6)$ is the mirror image of the point $B (1, 3, 4)$ in the plane $x - y +z =5$. <br> Statement-2 : The plane $x-y +z=5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4)$
jeemain
math
past papers
2010
73
asked
Dec 11
by
pady_1
0
answers
Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$. Statement-1 : The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$. <br> Statement-2 : If the four chosen numbers from an AP, then the set of all possible values of common difference is $\{ \pm1, \pm 2, \pm 3, \pm 4, \pm 5 \}$.
jeemain
math
past papers
2010
72
asked
Dec 11
by
pady_1
0
answers
The number of $3 \times 3$ non-singular matrices, with four entries as 1 and all other entries as 0, is
jeemain
math
past papers
2010
71
asked
Dec 11
by
pady_1
0
answers
Let $f : R \to R$ be defined by $f(x) = \begin{cases} k-2x, & \quad \text{if } \text{ x $\leq$ -1}\\ 2x + 3, & \quad \text{if } \text{ x > -1} \end{cases} $. If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is
jeemain
math
past papers
2010
70
asked
Dec 11
by
pady_1
0
answers
Consider the following relations : <br> $R = \{ (x, y) | x, \; y$ are real number and $x = wy$ for some rational number $w \}$; <br> $S = \{ (\frac{m}{n}, \frac{p}{q} ) | m, \; n, \; p $ and $q$ are integers such that $n, \;q \neq 0$ and $qm = pn \}$. Then
jeemain
math
past papers
2010
69
asked
Dec 11
by
pady_1
0
answers
If the vectors $\overrightarrow{a} = \hat{i} - \hat{j} + 2 \hat{k}, \; \overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ and $\overrightarrow{c} = \lambda \hat{i} + \hat{j} + \mu \hat{k}$ are mutually orthogonal, then $(\lambda, \mu)$ =
jeemain
math
past papers
2010
68
asked
Dec 11
by
pady_1
0
answers
If two tangets drawn from a point P to the parabola $y^2 = 4x$ are at right angles, then the locus of P is
jeemain
math
past papers
2010
67
asked
Dec 11
by
pady_1
0
answers
The area bounded by the curves $y = \cos x$ and $ y = \sin x$ between the ordinates $x=0$ and $x =\frac{3 \pi}{2}$ is
jeemain
math
past papers
2010
66
asked
Dec 11
by
pady_1
0
answers
Solution of the differential equation $\cos x\; dy = y (\sin x - y) dx, \; 0 < x < \frac{\pi}{2}$ is
jeemain
math
past papers
2010
65
asked
Dec 11
by
pady_1
0
answers
The equation of the tangent to the curve $y = x + \frac{4}{x^2}$, that is parallel to the $x-axis$, is
jeemain
math
past papers
2010
64
asked
Dec 11
by
pady_1
0
answers
Let $\overrightarrow{a} = \hat{j} - \hat{k}$ and $\overrightarrow{c} = \hat{i} - \hat{j} - \hat{k}$. Then vector $\overrightarrow{b}$ satisfying $\overrightarrow{a} \times \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$ and $\overrightarrow{a}.\overrightarrow{b} = 3$ is
jeemain
math
past papers
2010
63
asked
Dec 11
by
pady_1
0
answers
Let S be a non-empty subset of R. Consider the following statement : <br> P : There is a rational number $x \in S$ such that $x > 0$. <br> Which of the following statements is the negation of the statement P ?
jeemain
math
past papers
2010
62
asked
Dec 11
by
pady_1
0
answers
Let $\cos (\alpha + \beta) = \frac{4}{5}$ and let $\sin (\alpha - \beta) = \frac{5}{13}$, where $0 \leq \alpha, \; \beta \leq \frac{\pi}{4}$, then $\tan 2 \alpha = $
jeemain
math
past papers
2010
61
asked
Dec 11
by
pady_1
0
answers
The equation of a wave on a string of linear mass density $0.04\; kg\;m^{-1}$ is given by$ y = 0.02 (m) \sin [ 2 \pi (\frac{t}{0.04 (s)} - \frac{x}{0.50(m)} ) ]$. The tension in the string is
jeemain
physics
past papers
2010
60
asked
Dec 11
by
pady_1
0
answers
A small particleof mass m is projected at an angle $\theta$ with the x-axis with a initial velocity $v_0$ in the x-yplane as shown in the figure. At a time $t < \frac{v_0 \sin \theta}{g}$, the angular momentum of the particle is <br> <img src="http://clay6.com/mpaimg/1179_a.jpg"/><br> where $\hat{i}, \hat{j} $ and $\hat{k}$ are unit vectors along $x, \; y$ and $z-axis$ respectively.
jeemain
physics
past papers
2010
59
asked
Dec 11
by
pady_1
0
answers
The speed of light in the medium is
jeemain
physics
past papers
2010
58
asked
Dec 11
by
pady_1
0
answers
An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$, where $\mu_0 $ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. <br><br> QUESTION : The initial shape of the wave front of the beam is
jeemain
physics
past papers
2010
57
asked
Dec 11
by
pady_1
0
answers
An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$, where $\mu_0 $ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. <br> <br> Question : As the beam enters the medium, it will
jeemain
physics
past papers
2010
56
asked
Dec 11
by
pady_1
0
answers
For a particle in uniform circular motion the acceleration $\overrightarrow{a}$ at a point $P (R, \theta)$ on the circle of radius R is (here $\theta$ is measured from the x-axis)
jeemain
physics
past papers
2010
55
asked
Dec 11
by
pady_1
0
answers
Two fixed frictionless inclined plane making an angle $30^{\circ}$ and $60^{\circ}$ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ? <br> <img src="http://clay6.com/mpaimg/1178_a.jpg"/>
jeemain
physics
past papers
2010
54
asked
Dec 11
by
pady_1
0
answers
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $'P'$ is such that it sweeps out a length $s = t^3 +5$, where $s$ is metres and $t$ is in seconds. The radius of the path is $20 \;m$. The acceleration of $'P'$ when $t = 2\;s$ is nearly <br> <img src="http://clay6.com/mpaimg/1177_a.jpg"/>
jeemain
physics
past papers
2010
53
asked
Dec 11
by
pady_1
0
answers
Two conductors have the same resistance at $0^{\circ}C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients of their series and parallel combinations are nearly
jeemain
physics
past papers
2010
52
asked
Dec 11
by
pady_1
0
answers
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8\;g\;cm^{-3}$, the angle remains the same. If density of the material of the sphere is $16\;g\; cm^{-3}$, the dielectric constant of the liquid is
jeemain
physics
past papers
2010
51
asked
Dec 11
by
pady_1
0
answers
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U_{(x = \infty)} - U_{at\; equilibrium}], \; D$ is
jeemain
physics
past papers
2010
50
asked
Dec 11
by
pady_1
0
answers
Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r) = \rho_{_0}(\frac{5}{4} - \frac{r}{R})$ upto $r = R$ and $\rho (r) = 0$ for $r > R$, where $r$ is the distance from the origin. The electric field at a distance $r (r < R) $ from the origin is given by
jeemain
physics
past papers
2010
49
asked
Dec 11
by
pady_1
0
answers
In a series LCR circuit $R = 200 \Omega$ and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ}$. On taking out the inductor from the circuit leads the voltage by $30^{\circ}$. The power dissipiated in the LCR circuit is
jeemain
physics
past papers
2010
48
asked
Dec 11
by
pady_1
0
answers
The respective number of significant figures for the numbers $23.023, 0.0003$ and $2.1 \times 10^{–3}$ are
jeemain
physics
past papers
2010
47
asked
Dec 11
by
pady_1
0
answers
If a source of power 4 kW produces $10^{20}$ photons/second, the radiation belong to a part of the spectrum called
jeemain
physics
past papers
2010
46
asked
Dec 11
by
pady_1
0
answers
A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is
jeemain
physics
past papers
2010
45
asked
Dec 11
by
pady_1
0
answers
The combination of gates shown below yields
jeemain
physics
past papers
2010
44
asked
Dec 11
by
pady_1
0
answers
A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E at the centre O is
jeemain
physics
past papers
2010
43
asked
Dec 11
by
pady_1
0
answers
A radioactive nucleus (initial mass number A and atomic number Z) emits 3 $\alpha$ particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
jeemain
physics
past papers
2010
42
asked
Dec 11
by
pady_1
0
answers
The speed of daughter nuclei is
jeemain
physics
past papers
2010
41
asked
Dec 11
by
pady_1
0
answers
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