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Recent questions tagged 2009
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Let A be a $2 \times 2$ matrix <br> Statement-1: adj (adj A) = A <br> Statement-2 : |adj A| = |A|
jeemain
math
past papers
2009
90
asked
Nov 29
by
pady_1
0
answers
Statement -1 : $\sim (p \leftrightarrow \sim q) $ is equivalent to $p \leftrightarrow q$ <br> Statement -2: $\sim (p \leftrightarrow \sim q) $ is a tautology.
jeemain
math
past papers
2009
89
asked
Nov 29
by
pady_1
0
answers
Statement -1: The variance of first n even natural numbers is $\frac{n^2-1}{4}$ <br> Statement -2 :The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$
jeemain
math
past papers
2009
88
asked
Nov 29
by
pady_1
0
answers
Let $f(x) = x|x| $ and $g(x) = \sin x$ <br> Statement -1 : gof is differentiable at $x=0$ and its derivative is continuous at the point. <br> Statement -2 : gof is twice differentiable at $x=0$
jeemain
math
past papers
2009
87
asked
Nov 29
by
pady_1
0
answers
Let $f(x) = (x+1)^2 - 1, x \geq -1$ <br> Statement -1 : The set $\{ x : f(x) = f^{-1} (x) \} = \{0, -1\}$ <br> Statement-2: f is a bijection.
jeemain
math
past papers
2009
86
asked
Nov 29
by
pady_1
0
answers
The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is
jeemain
math
past papers
2009
85
asked
Nov 29
by
pady_1
0
answers
Given $P(x) = x^4 + ax^3 + bx^2+cx+d$ such that $x=0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$, then in the interval $[-1, 1]$
jeemain
math
past papers
2009
84
asked
Nov 29
by
pady_1
0
answers
The area of the region bounded by the parabola $(y-2)^2 = x-1$, the tangent to the parabola at the point (2, 3) and the x-axis is
jeemain
math
past papers
2009
83
asked
Nov 29
by
pady_1
0
answers
Let $y$ be an implicit function of $x$ defined by $x^{2x} - 2x^{x} \cot y -1 =0$. Then $y'(1)$ equals
jeemain
math
past papers
2009
82
asked
Nov 29
by
pady_1
0
answers
One ticket is selected at random from 50 tickets numbered $00, 01, 02, .....49$. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
jeemain
math
past papers
2009
81
asked
Nov 29
by
pady_1
0
answers
The differential equation which represents the family of curves $y = c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is
jeemain
math
past papers
2009
80
asked
Nov 29
by
pady_1
0
answers
The sum of the infinity of the series $1 + \frac{2}{3} + \frac{6}{3^2} + \frac{10}{3^3}+\frac{14}{3^4} + . . . . $ is
jeemain
math
past papers
2009
79
asked
Nov 29
by
pady_1
0
answers
The ellipse $x^2+4y^2 = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is
jeemain
math
past papers
2009
78
asked
Nov 29
by
pady_1
0
answers
The remainder left out when $8^{2n} - (62)^{2n+1}$ is divided by 9 is
jeemain
math
past papers
2009
77
asked
Nov 29
by
pady_1
0
answers
Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) is equal to $\frac{1}{3}$. Then the circumcentre of the triangle ABC is at the point
jeemain
math
past papers
2009
76
asked
Nov 29
by
pady_1
0
answers
If $|z - \frac{4}{z}| = 2$, then the maximum value of $|z|$ is equal to
jeemain
math
past papers
2009
75
asked
Nov 29
by
pady_1
0
answers
The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction consines of the vector are
jeemain
math
past papers
2009
74
asked
Nov 29
by
pady_1
0
answers
If P and Q are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2 = 0$ then there is a circle passing through P, Q and (1, 1) for
jeemain
math
past papers
2009
73
asked
Nov 29
by
pady_1
0
answers
In a binomial distribution $B ( n, p = \frac{1}{4})$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then $n$ is greater than
jeemain
math
past papers
2009
72
asked
Nov 29
by
pady_1
0
answers
For real $x$, let $f(x) = x^3 + 5x + 1$, then
jeemain
math
past papers
2009
71
asked
Nov 29
by
pady_1
0
answers
$\begin{align*} \int_0^{\pi} [\cot x] dx, \;[.] \end{align*} $ denotes the greatest integer function, is equal to
jeemain
math
past papers
2009
70
asked
Nov 29
by
pady_1
0
answers
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is
jeemain
math
past papers
2009
69
asked
Nov 29
by
pady_1
0
answers
Let the line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x+3y -\alpha z + \beta = 0$. Then $(\alpha, \beta)$ equals
jeemain
math
past papers
2009
68
asked
Nov 29
by
pady_1
0
answers
If $\overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $[3\overrightarrow{u} \;\; p\overrightarrow{v} \;\; p\overrightarrow{w}] - [p \overrightarrow{v} \;\; \overrightarrow{w}\; \; q \overrightarrow{u}] - [2 \overrightarrow{w}\; \; q \overrightarrow{v}\;\;q \overrightarrow{u}] = 0$ holds for
jeemain
math
past papers
2009
67
asked
Nov 29
by
pady_1
0
answers
If A, B and C are three sets suct that $A \cap B = A \cap C$ and $A \cup B = A \cup C$, then
jeemain
math
past papers
2009
66
asked
Nov 29
by
pady_1
0
answers
The lines $p(p^2+1) x-y+q = 0$ and $(p^2 + 1)^2 x + (p^2+1)y + 2q = 0$ are perpendicular to a common line for
jeemain
math
past papers
2009
65
asked
Nov 29
by
pady_1
0
answers
Let A and B denote the statements <br> A : $\cos \alpha + \cos \beta + \cos \gamma = 0$ <br> $B: \sin \alpha + \sin \beta + \sin \gamma = 0$ <br> If $\cos (\beta-\gamma) + \cos(\gamma - \alpha) + \cos (\alpha - \beta) = -\frac{3}{2}$, then
jeemain
math
past papers
2009
64
asked
Nov 29
by
pady_1
0
answers
If the roots of the equation $bx^2 + cx + a = 0$ be imaginary, then for all real values of $x$, the expression $3b^2x^2 + 6bcx+2c^2$ is
jeemain
math
past papers
2009
63
asked
Nov 29
by
pady_1
0
answers
If the mean deviation of number $1, 1+d, 1 +2d, . . . ., 1 + 100d$ from their mean is 255, then the $d$ is equal to
jeemain
math
past papers
2009
62
asked
Nov 29
by
pady_1
0
answers
Let a, b, c be such that $b(a+c) \neq 0$. If $\begin{vmatrix} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \end{vmatrix}$ + $\begin{vmatrix} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ (-1)^{n+2}a & (-1)^{n+1}b & (-1)^n c \end{vmatrix} = 0$, then the value of 'n' is
jeemain
math
past papers
2009
61
asked
Nov 29
by
pady_1
0
answers
Buna-N synthetic rubber is a copolymer of :
jeemain
chemistry
past papers
2009
60
asked
Nov 29
by
pady_1
0
answers
Which of the following pairs represents linkage isomers ?
jeemain
chemistry
past papers
2009
59
asked
Nov 29
by
pady_1
0
answers
In Cannizzaro reaction given below <br> $2 Ph \; CHO \xrightarrow{\overset{(-)}{: OH}} Ph \; CH_2OH + PhC\overset{..}{O}_2^{(-)}$ the slowest step is :
jeemain
chemistry
past papers
2009
58
asked
Nov 29
by
pady_1
0
answers
The bond dissociation energy of $B-F$ in $BF_3$ is $646 \; kJ\; mol^{-1}$ whereas that of $C-F$ in $CF_4$ is $515 \; kJ\; mol^{-1}$. The correct reason for higher $B-F$ bond dissociation energy as compared to that of $C-F$ is :
jeemain
chemistry
past papers
2009
57
asked
Nov 29
by
pady_1
0
answers
The two functional groups present in a typical carbohydrate are:
jeemain
chemistry
past papers
2009
56
asked
Nov 29
by
pady_1
0
answers
The set representing the correct order of ionic radius is :
jeemain
chemistry
past papers
2009
55
asked
Nov 29
by
pady_1
0
answers
The IUPAC name of neopentane is
jeemain
chemistry
past papers
2009
54
asked
Nov 29
by
pady_1
0
answers
The number of stereoisomers possible for a compound of the molecular formula $CH_3 - CH = CH - CH(OH)-Me$ is :
jeemain
chemistry
past papers
2009
53
asked
Nov 29
by
pady_1
0
answers
A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?
jeemain
chemistry
past papers
2009
52
asked
Nov 29
by
pady_1
0
answers
Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^3 \; ms^{-1}$ (Mass of proton = $1.67 \times 10^{-27} kg$ and $h = 6.63 \times 10^{-34} Js$ ):
jeemain
chemistry
past papers
2009
51
asked
Nov 29
by
pady_1
0
answers
In context with the transition elements, which of the following statements is incorrect ?
jeemain
chemistry
past papers
2009
50
asked
Nov 29
by
pady_1
0
answers
Using MO theory predict which of the following species has the shortest bond length ?
jeemain
chemistry
past papers
2009
49
asked
Nov 29
by
pady_1
0
answers
Which one of the following reactions of Xenon compounds is not feasible ?
jeemain
chemistry
past papers
2009
48
asked
Nov 29
by
pady_1
0
answers
Solid $Ba(NO_3)_2$ is gradually dissolved in a $1.0 \times 10^{-4} M\; Na_2CO_3$ solution. At what concentration of $Ba^{2+}$ will a precipitate begin to form ? ($K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9} $ ).
jeemain
chemistry
past papers
2009
47
asked
Nov 29
by
pady_1
0
answers
Which of the following has as optical isomer ?
jeemain
chemistry
past papers
2009
46
asked
Nov 29
by
pady_1
0
answers
Copper crystallizes in fcc wih a unit cell length of 361 pm. What is the radius of copper atom ?
jeemain
chemistry
past papers
2009
45
asked
Nov 29
by
pady_1
0
answers
On the basis of the following thermochemical data : $(\Delta f G^{\circ} H^+_{(aq)} = 0 ) $ <br> $ H_2O (\ell) \to H^+ (aq) + OH^- (aq); \Delta H= 57.32 \; kJ$ <br> $H_2 (g) + \frac{1}{2} O_2 (g) \to H_2O (\ell); \Delta H = -286.20 \; kJ$ <br> The value of enthalpy of formation of $OH^-$ ion at $25^{\circ}C$ is :
jeemain
chemistry
past papers
2009
44
asked
Nov 29
by
pady_1
0
answers
Given : $E^o_{Fe^{3+}/Fe} = - 0.036V,$ $E^o_{Fe^{2+}/Fe} = -0.439\; V$. The value of standard electrode potential for the change, $Fe^{3+}_{(aq)} + e^- \to Fe^{2+} (aq)$ will be :
jeemain
chemistry
past papers
2009
43
asked
Nov 29
by
pady_1
0
answers
The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301) :
jeemain
chemistry
past papers
2009
42
asked
Nov 29
by
pady_1
0
answers
Two liquid X and Y form an ideal solution. At 300 K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mm Hg) of X and Y in their pure states will be, respectively :
jeemain
chemistry
past papers
2009
41
asked
Nov 29
by
pady_1
0
answers
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