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Recent questions tagged 2006
Questions
If $0 < x < \pi$ and $\cos x + \sin x = \frac{1}{2}$, then $\tan x$ is:
jeemain
math
past papers
2006
150
asked
Nov 13, 2018
by
pady_1
0
answers
If $z^2 + z + 1 = 0$, where $z$ is complex number, then the value of $(z + \frac{1}{z})^2 + (z^2 + \frac{1}{z^2})^2 + (z^3 + \frac{1}{z^3})^2 + ...+ (z^6 + \frac{1}{z^6})^2$ is :
jeemain
math
past papers
2006
149
asked
Nov 13, 2018
by
pady_1
0
answers
If $a_1, a_2, ...., a_n$ are in HP, then the expression $a_1a_2 + a_2a_3 + .... + a_{n-1}a_n$ is equal to :
jeemain
math
past papers
2006
148
asked
Nov 13, 2018
by
pady_1
0
answers
Let C be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $ \frac{2\pi}{3}$ at its centre, is :
jeemain
math
past papers
2006
147
asked
Nov 13, 2018
by
pady_1
0
answers
The value of $\begin{align*} \int_1^a [x] \; f'(x) \;dx, \; a > 1 \end{align*}$, where $[x]$ denotes the greatest integer not exceeding $x$, is :
jeemain
math
past papers
2006
146
asked
Nov 13, 2018
by
pady_1
0
answers
The differential equation whose solution is $Ax^2 + By^2 = 1$, where $A$ and $B$ are arbitrary constant, is of :
jeemain
math
past papers
2006
145
asked
Nov 13, 2018
by
pady_1
0
answers
The image of the point $(-1, 3, 4)$ in the plane $x - 2y = 0$ is :
jeemain
math
past papers
2006
144
asked
Nov 13, 2018
by
pady_1
0
answers
If the lines $3x - 4y - 7=0$ and $2x- 3y-5=0$ are two diameters of a circle of area $49\; \pi\; square$ units, the equation of the circle is :
jeemain
math
past papers
2006
143
asked
Nov 13, 2018
by
pady_1
0
answers
If $x^m y^n = (x+y)^{m+n}$, then $\frac{dy}{dx}$ is :
jeemain
math
past papers
2006
142
asked
Nov 13, 2018
by
pady_1
0
answers
If $(a, a^2)$ falls inside the angle made by the lines $y=\frac{x}{2}, \;x > 0$ and $y = 3x,\; x > 0$, then $a$ belongs to :
jeemain
math
past papers
2006
141
asked
Nov 13, 2018
by
pady_1
1
answer
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $x$. The maximum area enclosed by the park is :
jeemain
math
past papers
2006
140
asked
Nov 13, 2018
by
pady_1
0
answers
If $x$ is real, the maximum value of $\frac{3x^2+9x+17}{3x^2+9x+7}$ is :
jeemain
math
past papers
2006
139
asked
Nov 13, 2018
by
pady_1
0
answers
Angle between the tangents to the curve $y=x^2-5x+6$ at the points $(2,0)$ and $(3,0)$ is :
jeemain
math
past papers
2006
138
asked
Nov 13, 2018
by
pady_1
0
answers
The function $f(x) = \frac{x}{2} +\frac{2}{x}$ has a local minimum at :
jeemain
math
past papers
2006
137
asked
Nov 13, 2018
by
pady_1
0
answers
Let $a_1, a_2, a_3, ....$ cannot be terms of an AP. If $\frac{a_1+a_2+....+a_p}{a_1 + a_2 + ....+ a_q} = \frac{p^2}{q^2}, \; p \neq q$, then $\frac{a_6}{a_{21}}$ equals :
jeemain
math
past papers
2006
136
asked
Nov 13, 2018
by
pady_1
0
answers
Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$, $a, \; b,\; \in N$. Then :
jeemain
math
past papers
2006
135
asked
Nov 13, 2018
by
pady_1
0
answers
The set of points, where $f(x) = \frac{x}{1 +|x|} $ is differentiable, is :
jeemain
math
past papers
2006
134
asked
Nov 13, 2018
by
pady_1
0
answers
A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 seconds prior to passing through P. If $g = 10\; m/s^2$, then the height above the point P from where the body began to fall is :
jeemain
math
past papers
2006
133
asked
Nov 13, 2018
by
pady_1
0
answers
At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call during a 10 minute time period, is :
jeemain
math
past papers
2006
132
asked
Nov 13, 2018
by
pady_1
0
answers
A particle has two velocities of equal magnitude inclined to each other at an angle $\theta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. The $\theta$ is :
jeemain
math
past papers
2006
131
asked
Nov 13, 2018
by
pady_1
0
answers
For natural numbers $m$, $n$ if $(1-y)^m (1+y)^n = 1 + a_{_1}y + a_{_2} y^2 + ...$ and $a_{_1} = a_{_2} = 10$, then $(m, n)$ is :
jeemain
math
past papers
2006
130
asked
Nov 13, 2018
by
pady_1
0
answers
If the expansion in power of $x$ of the function $\frac{1}{ (1-ax) (1-bx)}$ <br> $a_{_0} + a_1x + a_2x^2 + a_3x^3 + ....,$ then $a_n$ is :
jeemain
math
past papers
2006
129
asked
Nov 13, 2018
by
pady_1
0
answers
At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is :
jeemain
math
past papers
2006
128
asked
Nov 13, 2018
by
pady_1
0
answers
The two lines $x=ay + b, \; z = cy + d$ and $x = a' y + b', \; z = c'y + d'$ are perpendicular to each other, if :
jeemain
math
past papers
2006
127
asked
Nov 13, 2018
by
pady_1
0
answers
$\begin{align*} \int_0^{\pi} x f (\sin x ) dx \end{align*}$ is equal to :
jeemain
math
past papers
2006
126
asked
Nov 13, 2018
by
pady_1
0
answers
The value of $a$, for which the points A, B, C with position vectors $2 \hat{i} - \hat{j} + \hat{k}, \; \hat{i} - 3 \hat{j} - 5 \hat{k}$ and $a \hat {i} - 3 \hat {j} - \hat{k}$ respectively are the vertices of a right angled triangle with $C = \frac{\pi}{2}$ are :
jeemain
math
past papers
2006
125
asked
Nov 13, 2018
by
pady_1
0
answers
A straight line through the point $A (3, 4)$ is such that its intercept between the axes is bisected at $A$. Its equation is :
jeemain
math
past papers
2006
124
asked
Nov 13, 2018
by
pady_1
0
answers
The locus of the vertices of the family of parabolas $y = \frac{a^3 x^2}{3} + \frac{a^2x}{2} - 2a $ is :
jeemain
math
past papers
2006
123
asked
Nov 13, 2018
by
pady_1
0
answers
In an ellipse, the distances between its foci is 6 and minor axis is 8. Then its eccentricity is :
jeemain
math
past papers
2006
122
asked
Nov 13, 2018
by
pady_1
1
answer
$\begin{align*} \int^{-\pi/2}_{-3\pi/2} [(x+\pi)^3 + \cos^2 (x+3\pi)] dx \end{align*}$ is equal to :
jeemain
math
past papers
2006
121
asked
Nov 13, 2018
by
pady_1
0
answers
Suppose a population a has 100 observations 101, 102, ..., 200 and another population $B$ has 100 observations 151, 152, ...., 250. If $V_A$ and $V_B$ represent the variances of the two population respectively, then $\frac{V_A}{V_B}$ is :
jeemain
math
past papers
2006
120
asked
Nov 13, 2018
by
pady_1
0
answers
ABC is triangle, right angled at A. The resultant of the force acting along $\overrightarrow{AB}, \overrightarrow{AC}$ with magnitudes $\frac{1}{AB}$ and $\frac{1}{AC}$ respectively is the force along $\overrightarrow{AD}$, where $D$ is the foot of the perpendicular from $A$ onto $BC$. The magnitude of the resultant is :
jeemain
math
past papers
2006
119
asked
Nov 13, 2018
by
pady_1
0
answers
All the values of m for which both roots of the equation $x^2 - 2mx + m^2 -1 = 0$ are greater than $-2$ but less than 4 lie in the interval :
jeemain
math
past papers
2006
118
asked
Nov 13, 2018
by
pady_1
0
answers
Any three vectors such that $\overrightarrow{a}. \overrightarrow{b} \neq 0,\;\overrightarrow{b}. \overrightarrow{c} \neq 0$, then $\overrightarrow{a}$ and $\overrightarrow{c}$ are :
jeemain
math
past papers
2006
117
asked
Nov 13, 2018
by
pady_1
0
answers
The value of $ \displaystyle\sum_{k=1}^{10} (\sin \frac{2k \pi}{11} + i \cos \frac{2k \pi}{11})$ is :
jeemain
math
past papers
2006
116
asked
Nov 13, 2018
by
pady_1
0
answers
If A and B are square matrices of size $n \times n$ such that $A^2 - B^2 = (A-B) (A+B)$, then which of the following will be always true ?
jeemain
math
past papers
2006
115
asked
Nov 13, 2018
by
pady_1
0
answers
The number of values of $x$ in the interval $[0, 3 \pi]$ satisfying the equation $2 \sin^2x + 5 \sin x - 3 = 0 $ is :
jeemain
math
past papers
2006
114
asked
Nov 13, 2018
by
pady_1
0
answers
Let $W$ denote the words in the English dictionary. Define the relation R by : <br> $R = \{(x,y) \in W \times W| $ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is :
jeemain
math
past papers
2006
113
asked
Nov 13, 2018
by
pady_1
0
answers
The value of the integral $\begin{align*} \int_3^6 \frac{\sqrt{x}}{\sqrt{9 - x } + \sqrt{x}} dx \end{align*}$
jeemain
math
past papers
2006
112
asked
Nov 13, 2018
by
pady_1
0
answers
If the roots of the quadratic equation $x^2 + px + q = 0$ are tan $\tan 30^{\circ}$ and $\tan 15^{\circ}$ respectively, then the value of $2 + q - p$ is :
jeemain
math
past papers
2006
111
asked
Nov 13, 2018
by
pady_1
0
answers
$(\Delta H - \Delta U)$ for the formation of carbon monoxide (CO) from its elements at 298 K is : <br> $(R = 8.314 \; JK^{-1} mol^{-1})$
jeemain
chemistry
past papers
2006
110
asked
Nov 13, 2018
by
pady_1
0
answers
18 g of glucose $(C_6H_{12} O_6)$ is added to 178.2 g of water. The vapour pressure of water for this aqueous solution at $100^{\circ}C$ is :
jeemain
chemistry
past papers
2006
109
asked
Nov 13, 2018
by
pady_1
0
answers
<br> The electrophile involved in the above reaction is :
jeemain
chemistry
past papers
2006
108
asked
Nov 13, 2018
by
pady_1
0
answers
How many EDTA (ethylenediaminetetra acetic acid ) molecules are required to make an octahedral complex with a $Ca^{2+}$ ion ?
jeemain
chemistry
past papers
2006
107
asked
Nov 13, 2018
by
pady_1
0
answers
The enthalpy changes for the following processes are listed below : <br> $Cl_2 (g) = 2Cl (g), \; \; \; 242.3 \; kJ\; mol^{-1} $ <br> $I_2 (g) = 2I (g), \; \; \; 151.0 \; kJ\; mol^{-1} $ <br> $ICl (g) = I (g) + Cl(g), \; \; \; 211.3 \; kJ\; mol^{-1}$ <br> $I_2 (s) = I_2 (g), \; \; \; 62.76 \; kJ\; mol^{-1}$ <br> Given that the standard states for iodine and chlorine are $I_2 (s)$ and $Cl_2 (g)$, the standard enthalpy of formation of $ICl \; (g)$ is :
jeemain
chemistry
past papers
2006
106
asked
Nov 13, 2018
by
pady_1
0
answers
Density of a $2.05 \; M$ solution of acetic acid in water is $1.02\; g/mL$. The molality of the solution is :
jeemain
chemistry
past papers
2006
105
asked
Nov 13, 2018
by
pady_1
0
answers
The ionic mobility of alkali metal ions in aqueous solution is maximum for :
jeemain
chemistry
past papers
2006
104
asked
Nov 13, 2018
by
pady_1
0
answers
Resistance of a conductivity cell filled with a solution of an electrolyte of concentration $0.1\; M$ is $100\; \Omega$. The conductivity of this solution is $1.29\; S\; m^{-1}$. Resistance of the same cell when filled with $0.2\; M$ of the same solution is $520 \Omega$. The molar conductivity of $0.02 \; M$ solution of the electrolyte will be :
jeemain
chemistry
past papers
2006
103
asked
Nov 13, 2018
by
pady_1
0
answers
Lanthanide contraction is caused due to :
jeemain
chemistry
past papers
2006
102
asked
Nov 13, 2018
by
pady_1
0
answers
The following mechanism has been proposed for the reaction of $NO$ with $Br_2$ to form $NOBr$ : <br> $NO(g) + Br_2 (g) \rightleftharpoons NOBr_2 (g) $ <br> $NOBr_2 (g) + NO (g) \to 2NOBr (g) $ <br> If the second step is the rate determining step, the order of the reaction with respect to $NO (g)$ is :
jeemain
chemistry
past papers
2006
101
asked
Nov 13, 2018
by
pady_1
0
answers
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