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A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:

asked Mar 16, 2017 by meena.p

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Consider $f(x) = \tan ^{-1} \bigg( \sqrt{\Large\frac{1+ \sin x}{1- \sin x}}\bigg),$ $x \in \bigg(0, \large\frac{\pi}{2} \bigg)$ A normal to $y = f(x)$ at $x =\large\frac{\pi}{6}$ also passes through the point:

asked Mar 16, 2017 by meena.p

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For $x \in R ,f(x) = | \log 2 - \sin x |$ and $g(x) =f(f(x))$ , then

asked Mar 16, 2017 by meena.p

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Let $p = \lim \limits_{x \to 0+} (1+ \tan ^2 \sqrt x )^{1/2x}$ then long p is equal to

asked Mar 16, 2017 by meena.p

1 answer

If the sum of the first ten terms of the series $\bigg(1 \large\frac{3}{5}\bigg) \normalsize +\bigg(2 \large\frac{2}{5} \bigg)^2 \normalsize +\bigg(3 \large\frac{1}{5}\bigg)^2 \normalsize +4^2 +\bigg(4 \large\frac{4}{5} \bigg)^2 \normalsize +.....is\;\large\frac{16}{5}$ $\;m$ then m is equal to

asked Mar 16, 2017 by meena.p

1 answer

If the $2^{nd},5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

asked Mar 16, 2017 by meena.p

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If the number of terms in the expansion of $\bigg(1- \large\frac{2}{x}+\frac{4}{x^2}\bigg)^n,x \neq 0,$ is 28, then the sum of the coefficients of all the terms in this expansion, is

asked Mar 15, 2017 by meena.p

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If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

asked Mar 15, 2017 by meena.p

1 answer

The system of linear equations <br> $x + \lambda y - z = 0 \\\lambda x - y - z = 0 \\x + y - \lambda z = 0$ has a non-trivial solution for:

asked Mar 15, 2017 by meena.p

1 answer

If $A =\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \;adj A = AA^T$ , then $5a+b$ is equal to

asked Mar 15, 2017 by meena.p

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The sum of all real values of x satisfying the equation $(x^2-5x+5)^{x^2+4x-60}=1$ is :

asked Mar 15, 2017 by meena.p

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A value of $\theta$ for which $\large\frac{2+3 i \sin \theta}{1- 2 i \sin \theta}$ is purely imaginary , is

asked Mar 15, 2017 by meena.p

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If $f(x) +2y \bigg(\large\frac{1}{x}\bigg)$ $=3x,x \neq 0$ and $S=\{x \in R:f(x)=f(-x)\}$ then S:

asked Mar 15, 2017 by meena.p

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The hottest region of Bunsen flame shown in the figure below is :

asked Mar 14, 2017 by meena.p

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Which of the following is an anionic detergent ?

asked Mar 14, 2017 by meena.p

1 answer

Thiol group is present in :

asked Mar 14, 2017 by meena.p

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Which of the following statements about low density polythene is FALSE ?

asked Mar 14, 2017 by meena.p

1 answer

In the Hofmann bromamide degradation reaction, the number of moles of $NaOH$ and $Br_2$ used per mole of amine produced are :

asked Mar 14, 2017 by meena.p

1 answer

The reaction of propene with $HOCl(Cl_2 + H_2O)$ proceeds through the intermediate :

asked Mar 14, 2017 by meena.p

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2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields :

asked Mar 14, 2017 by meena.p

1 answer

The absolute configuration of

asked Mar 14, 2017 by meena.p

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The product of the reaction given below is :

asked Mar 14, 2017 by meena.p

1 answer

The distillation technique most suited for separating glycerol from spent - lye in the soap industry is :

asked Mar 14, 2017 by meena.p

1 answer

The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be $1000\;ppb, 40\;ppb, 100\; ppm$ and $0.2\;ppm$ , respectively. This water is unsuitable for drinking due to high concentration of :

asked Mar 14, 2017 by meena.p

1 answer

Which one of the following complexes shows optical isomerism ?

asked Mar 14, 2017 by meena.p

1 answer

The pair having the same magnetic moment is :[At. No : $Cr= 24, Mn=25, Fe=26,Co=27$ ]

asked Mar 14, 2017 by meena.p

1 answer

Which of the following compounds is metallic and ferromagnetic ?

asked Mar 13, 2017 by meena.p

1 answer

The pair in which phosphorous atoms have a formal oxidation state of $+ 3$ is :

asked Mar 13, 2017 by meena.p

1 answer

The reaction of zinc with dilute and concentrated nitric acid, respectively produces :

asked Mar 13, 2017 by meena.p

1 answer

The main oxides formed on combustion of $Li, Na$ and $K$ in excess of air are, respectively :

asked Mar 13, 2017 by meena.p

1 answer

Which one of the following statements about water is FALSE ?

asked Mar 13, 2017 by meena.p

1 answer

Which one of the following ores is best concentrated by froth floatation method ?

asked Mar 13, 2017 by meena.p

1 answer

Which of the following atoms has the highest first ionization energy ?

asked Mar 13, 2017 by meena.p

1 answer

For a linear plot of log (x/m) versus log p in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are constants)

asked Mar 13, 2017 by meena.p

1 answer

Decomposition of $H_2O_2$ follows a first order reaction. In fifty minutes the concentration of $H_2O_2$ decreases from $0.5$ to $0.125\;M$ in one such decomposition. When the concentration of $H_2O_2$ reaches $0.05\; M$ , the rate of formation of $O_2$ will be :

asked Mar 13, 2017 by meena.p

1 answer

Galvanization is applying a coating of :

asked Mar 13, 2017 by meena.p

1 answer

The equilibrium constant at $298\;K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$ . If the initial concentration of all the four species were $1\;M$ each, then equilibrium concentration of $D (in\; mol\; L^{-1})$ will be :

asked Mar 13, 2017 by meena.p

1 answer

$18\; g$ glucose $(C_6H_{12}O_6)$ is added to $178.2\; g$ water. The vapor pressure of water (in torr) for this aqueous solution is

asked Mar 9, 2017 by meena.p

1 answer

The heats of combustion of carbon and carbon monoxide are $-393.5$ and $-283.5\; kJ\; mol^{-1}$ , respectively. The heat of formation (in kJ) of carbon monoxide per mole is :

asked Mar 9, 2017 by meena.p

1 answer

The species in which the $N$ atom is in a state of $sp$ hybridization is :

asked Mar 9, 2017 by meena.p

1 answer

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference $V$ esu. If $e$ and $m$ are charge and mass of an electron, respectively, then the value of $\large\frac{h}{\lambda}$ (where $\lambda$ is wavelength associated with electron wave) is given by

asked Mar 9, 2017 by meena.p

1 answer

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$ . The final pressure $P_f$ is :

asked Mar 9, 2017 by meena.p

1 answer

At $300\;K$ and $1\;atm, 15\; mL$ of a gaseous hydrocarbon requires $375\; mL$ air containing $20\%$ $O_2$ by volume for complete combustion. After combustion the gases occupy $330\; mL$ . Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is

asked Mar 9, 2017 by meena.p

1 answer

For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings, the incorrect relationship between $\alpha$ and $\beta$ is :

asked Mar 8, 2017 by meena.p

1 answer

Identify the semiconductor devices whose characteristics are given below, in the order (a),(b),(c),(d) :

asked Mar 8, 2017 by meena.p

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In an experiment for determination of refractive index of glass of a prism by $i -\sigma$ , plot, it was found that a ray incident at angle $35 ^{\circ}$ , suffers a deviation of $40^{\circ}$ and that it emerges at angle $79^{\circ}$ .In that case which of the following is closest to the maximum possible value of the refractive index?

asked Mar 8, 2017 by meena.p

1 answer

A galvanometer having a coil resistance of $100 \Omega$ gives a full scale deflection, when a current of $1 \;mA$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10\; A$ is :

asked Mar 8, 2017 by meena.p

1 answer

A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

asked Mar 8, 2017 by meena.p

1 answer

A screw gauge with a pitch of $0.5\;mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge and brought in contact, the $45^{th}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5\;mm$ and the $25^th$ division coincides with the main scale line?

asked Mar 8, 2017 by meena.p

1 answer

Choose the correct statement :

asked Mar 7, 2017 by meena.p

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