Recent questions in 2006

If $0 < x < \pi$ and $\cos x + \sin x = \frac{1}{2}$ , then $\tan x$ is:

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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The differential equation whose solution is $Ax^2 + By^2 = 1$ , where $A$ and $B$ are arbitrary constant, is of :

asked Nov 13, 2018 by pady_1

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The image of the point $(-1, 3, 4)$ in the plane $x - 2y = 0$ is :

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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If $x^m y^n = (x+y)^{m+n}$ , then $\frac{dy}{dx}$ is :

asked Nov 13, 2018 by pady_1

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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 :

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 :

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 :

asked Nov 13, 2018 by pady_1

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Angle between the tangents to the curve $y=x^2-5x+6$ at the points $(2,0)$ and $(3,0)$ is :

asked Nov 13, 2018 by pady_1

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The function $f(x) = \frac{x}{2} +\frac{2}{x}$ has a local minimum at :

asked Nov 13, 2018 by pady_1

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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 :

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 :

asked Nov 13, 2018 by pady_1

0 answers

The set of points, where $f(x) = \frac{x}{1 +|x|}$ is differentiable, is :

asked Nov 13, 2018 by pady_1

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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 :

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 :

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 :

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 :

asked Nov 13, 2018 by pady_1

0 answers

If the expansion in power of $x$ of the function $\frac{1}{ (1-ax) (1-bx)}$ $a_{_0} + a_1x + a_2x^2 + a_3x^3 + ....,$ then $a_n$ is :

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 :

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 :

asked Nov 13, 2018 by pady_1

0 answers

$\begin{align} \int_0^{\pi} x f (\sin x ) dx \end{align}$ is equal to :

asked Nov 13, 2018 by pady_1

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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 :

asked Nov 13, 2018 by pady_1

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A straight line through the point $A (3, 4)$ is such that its intercept between the axes is bisected at $A$ . Its equation is :

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 :

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 :

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 :

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 :

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 :

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 :

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 :

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 :

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 ?

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 :

asked Nov 13, 2018 by pady_1

0 answers

Let $W$ denote the words in the English dictionary. Define the relation R by : $R = \{(x,y) \in W \times W|$ the words $x$ and $y$ have at least one letter in common $\}$ . Then $R$ is :

asked Nov 13, 2018 by pady_1

0 answers

The value of the integral $\begin{align} \int_3^6 \frac{\sqrt{x}}{\sqrt{9 - x } + \sqrt{x}} dx \end{align}$

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 :

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 : $(R = 8.314 \; JK^{-1} mol^{-1})$

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 :

asked Nov 13, 2018 by pady_1

0 answers

The electrophile involved in the above reaction is :

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 ?

asked Nov 13, 2018 by pady_1

0 answers

The enthalpy changes for the following processes are listed below : $Cl_2 (g) = 2Cl (g), \; \; \; 242.3 \; kJ\; mol^{-1}$ $I_2 (g) = 2I (g), \; \; \; 151.0 \; kJ\; mol^{-1}$ $ICl (g) = I (g) + Cl(g), \; \; \; 211.3 \; kJ\; mol^{-1}$ $I_2 (s) = I_2 (g), \; \; \; 62.76 \; kJ\; mol^{-1}$ 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 :

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 :

asked Nov 13, 2018 by pady_1

0 answers

The ionic mobility of alkali metal ions in aqueous solution is maximum for :

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 :

asked Nov 13, 2018 by pady_1

0 answers

Lanthanide contraction is caused due to :

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 $NOBr$ : $NO(g) + Br_2 (g) \rightleftharpoons NOBr_2 (g)$ $NOBr_2 (g) + NO (g) \to 2NOBr (g)$ If the second step is the rate determining step, the order of the reaction with respect to $NO (g)$ is :

asked Nov 13, 2018 by pady_1

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