Recent questions in 2002

The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 - 2 =0$ :

asked Dec 11, 2018 by pady_1

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If $x^y = e^{x-y}$, then $\frac{dy}{dx}$ is :

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If $\sin y = x \sin (a + y) $, then $\frac{dy}{dx}$ is :

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The domain of definition of the function $f(x) = \sqrt{log_{10} (\frac{5x-x^2}{4})}$ is :

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The period of the function $f(x) = \sin^4 x + \cos^4 x$ is :

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$\begin{align} \int_{-\pi}^{\pi} \frac{2x ( 1+\sin x)} {1 + \cos^2 x} dx \end{align}$ is :

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$\begin{align}\int_0^2 [x^2] dx \end{align}$ is :

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$I_n = \begin{align} \int_0^{\pi/4} \tan^n x \; dx \end{align}$ then $\displaystyle\lim_{n \to \infty} n [I_n + I_{n+2} ]$ equals :

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$\begin{align} \int_0^{10 \pi} | \sin x |\; dx \end{align}$ is

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Fifth term of a GP is 2, then the product of its 9 terms is :

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The value of $2^{1/4}. 4^{1/8}. 8^{1/16}.....\infty$ is :

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The domain the $\sin^{-1} [\log_3 ( x/3)]$ is:

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$\displaystyle\lim_{x \to \infty}$ $\begin{pmatrix} \frac{x^2 + 5x + 3}{x^2 + x + 2} \end{pmatrix}^x$ is :

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The solution of the equation $\frac{d^2y}{dx^2} = e^{-2x}$ is

asked Dec 11, 2018 by pady_1

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A plane which passes through the point (3, 2, 0) and the line $\frac{x-4}{1} = \frac{y-7}{5} = \frac{z-4}{4} $ is :

asked Dec 11, 2018 by pady_1

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The order and degree of the differential equation $(1 + 3 \frac{dy}{dx})^{2/3} = 4 \frac{d^3y}{dx^3}$ are :

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$\cot^{-1} ( \cos \alpha ) - \tan^{-1} (\sqrt{\cos \alpha}) = x$ then $\sin x$ is equal to :

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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls ?

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A triangle with vertices (4, 0), (-1, -1), (3, 5) is :

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$\displaystyle\lim_{x \to 0} \frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}$ is :

asked Dec 11, 2018 by pady_1

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$l, \; m, n$ are the $p^{th}, q^{th}$ and $r^{th}$ term of an GP and all positive, then $\begin{vmatrix} \log l & p & 1 \\ \log m & q&1 \\ \log n & r & 1 \end{vmatrix}$ equals :

asked Dec 11, 2018 by pady_1

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The period of $\sin^2 \theta$ is:

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A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved, is :

asked Dec 11, 2018 by pady_1

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If 1, $\log_3 \sqrt{(3^{1-x} +2)}, \; \log_3 (4.3^x -1)$ are in AP, then $x$ equals :

asked Dec 11, 2018 by pady_1

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If $y = (x +\sqrt{1+x^2})^n $, then $(1+x^2) \frac{d^2y}{dx^2} + x \frac{dy}{dx}$ is :

asked Dec 11, 2018 by pady_1

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If $\alpha \neq \beta$ and $\alpha^2 = 5\alpha -3, \; \beta^2 = 5 \beta - 3$, then the equation having $\alpha/\beta$ and $\beta/\alpha$ as its roots, is :

asked Dec 11, 2018 by pady_1

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Picric acid is :

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Oxidation number of $Cl$ in $CaOCl_2$ (bleaching power) is :

asked Dec 11, 2018 by pady_1

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$SN^1$ reaction is feasible in :

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Maximum dehydration takes place that of :

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The metallic sodium dissolves in liquid ammonia to form a deep blue coloured solution. The deep blue colour is due to formation of :

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Select correct statement :

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A heat engine absorbs heat $q_1$ from a source at temperature $T_1$ and heat $q_2$ from a source at temperature $T_2$. Work done is found to be $J (q_1 +q_2)$. This is in accordance with :

asked Dec 11, 2018 by pady_1

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Conductivity (Seimen's S) is directly proportional to area of the vessel and the concentration of the soluion in it and is inversely proportional to the length of the vessel, then constant of proportionality is expressed in :

asked Dec 11, 2018 by pady_1

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Following types of compounds (as $I, II$) $(I) CH_3 CH = CH CH_3 $ (II) are studied in terms of isomerism in :

asked Dec 11, 2018 by pady_1

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$PCl_3$ and $PCl_5$ both exist; $NCl_3$ exists but $NCl_5$ does not exist. It is due to :

asked Dec 11, 2018 by pady_1

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In the followig benzyl/allyl system decreasing order of inductive effect is :

asked Dec 11, 2018 by pady_1

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On vigorous oxidation by permangnate solution $(CH_3)_2 C = CHCH_2CHO$ gives :

asked Dec 11, 2018 by pady_1

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Alum is widely used to purify water since :

asked Dec 11, 2018 by pady_1

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Rate constant $k$ of the first order reaction when initial concentration $C_0$ and concentration $C_t$ at time $t$ is given by equation $kt = \log C_0 - \log C_t$ Graph is a straight line if we plot :

asked Dec 11, 2018 by pady_1

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$H_2$ gas is absorbed on the metal surface like tungsten. This follows . . . . order reaction.

asked Dec 11, 2018 by pady_1

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pH of $0.005 \; M$ calcium acetate ($pK_a$ of $CH_3COOH = 4.74$) is :

asked Dec 11, 2018 by pady_1

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$Ce^{3+} , \; La^{3+}, \; Pm^{3+}$ and $Yb^{3+}$ have ionic radii in the increasing order as :

asked Dec 11, 2018 by pady_1

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Most common oxidation states of $Ce$ (Cerium) are :

asked Dec 11, 2018 by pady_1

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Increasing order of bond strength of $O_2, \; O_2^-, \; O_2^{2-}$ and $O_2^+$ is :

asked Dec 11, 2018 by pady_1

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Monomers are converted to polymer by :

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A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water then :

asked Dec 11, 2018 by pady_1

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Consider the following reactions at $1100^{\circ}C$ (I) $2C + O_2 \to 2CO, \; \; \; \; \Delta G^{\circ} = -460 \; k\;J\; mol^{-1}$ (II) $2Zn + O_2 \to 2ZnO, \; \; \; \; \Delta G^{\circ} = -360\; k\; J\; mol^{-1}$ Based on these, select correct alternate :

asked Dec 11, 2018 by pady_1

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Uncertainty in position of a particle of 25 g in space is $10^{-5}m$. Hence uncertainty in velocity $(ms^{-1})$ is (Planck's constant $h = 6.6 \times 10^{-34} Js$) :

asked Dec 11, 2018 by pady_1

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One of the following equilibria is not affected by change in volume of the flask :

asked Dec 11, 2018 by pady_1

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