Recent questions tagged 2009

Let A be a $2 \times 2$ matrix Statement-1: adj (adj A) = A Statement-2 : |adj A| = |A|

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Statement -1 : $\sim (p \leftrightarrow \sim q) $ is equivalent to $p \leftrightarrow q$ Statement -2: $\sim (p \leftrightarrow \sim q) $ is a tautology.

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Statement -1: The variance of first n even natural numbers is $\frac{n^2-1}{4}$ 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 $\frac{n(n+1)(2n+1)}{6}$

asked Nov 29, 2018 by pady_1

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Let $f(x) = x|x| $ and $g(x) = \sin x$ Statement -1 : gof is differentiable at $x=0$ and its derivative is continuous at the point. Statement -2 : gof is twice differentiable at $x=0$

asked Nov 29, 2018 by pady_1

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Let $f(x) = (x+1)^2 - 1, x \geq -1$ Statement -1 : The set $\{ x : f(x) = f^{-1} (x) \} = \{0, -1\}$ Statement-2: f is a bijection.

asked Nov 29, 2018 by pady_1

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The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is

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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 $[-1, 1]$

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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

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Let $y$ be an implicit function of $x$ defined by $x^{2x} - 2x^{x} \cot y -1 =0$. Then $y'(1)$ equals

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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

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The differential equation which represents the family of curves $y = c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is

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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

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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

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The remainder left out when $8^{2n} - (62)^{2n+1}$ is divided by 9 is

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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

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If $|z - \frac{4}{z}| = 2$, then the maximum value of $|z|$ is equal to

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The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction consines of the vector are

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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

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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

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For real $x$, let $f(x) = x^3 + 5x + 1$, then

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$\begin{align} \int_0^{\pi} [\cot x] dx, \;[.] \end{align} $ denotes the greatest integer function, is equal to

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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

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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

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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

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If A, B and C are three sets suct that $A \cap B = A \cap C$ and $A \cup B = A \cup C$, then

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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

asked Nov 29, 2018 by pady_1

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Let A and B denote the statements A : $\cos \alpha + \cos \beta + \cos \gamma = 0$ $B: \sin \alpha + \sin \beta + \sin \gamma = 0$ If $\cos (\beta-\gamma) + \cos(\gamma - \alpha) + \cos (\alpha - \beta) = -\frac{3}{2}$, then

asked Nov 29, 2018 by pady_1

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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

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If the mean deviation of number $1, 1+d, 1 +2d, . . . ., 1 + 100d$ from their mean is 255, then the $d$ is equal to

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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Buna-N synthetic rubber is a copolymer of :

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Which of the following pairs represents linkage isomers ?

asked Nov 29, 2018 by pady_1

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In Cannizzaro reaction given below $2 Ph \; CHO \xrightarrow{\overset{(-)}{: OH}} Ph \; CH_2OH + PhC\overset{..}{O}_2^{(-)}$ the slowest step is :

asked Nov 29, 2018 by pady_1

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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 :

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The two functional groups present in a typical carbohydrate are:

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The set representing the correct order of ionic radius is :

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The IUPAC name of neopentane is

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The number of stereoisomers possible for a compound of the molecular formula $CH_3 - CH = CH - CH(OH)-Me$ is :

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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 ?

asked Nov 29, 2018 by pady_1

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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 $h = 6.63 \times 10^{-34} Js$ ):

asked Nov 29, 2018 by pady_1

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In context with the transition elements, which of the following statements is incorrect ?

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Using MO theory predict which of the following species has the shortest bond length ?

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Which one of the following reactions of Xenon compounds is not feasible ?

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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} $ ).

asked Nov 29, 2018 by pady_1

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Which of the following has as optical isomer ?

asked Nov 29, 2018 by pady_1

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Copper crystallizes in fcc wih a unit cell length of 361 pm. What is the radius of copper atom ?

asked Nov 29, 2018 by pady_1

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On the basis of the following thermochemical data : $(\Delta f G^{\circ} H^+_{(aq)} = 0 ) $ $ H_2O (\ell) \to H^+ (aq) + OH^- (aq); \Delta H= 57.32 \; kJ$ $H_2 (g) + \frac{1}{2} O_2 (g) \to H_2O (\ell); \Delta H = -286.20 \; kJ$ The value of enthalpy of formation of $OH^-$ ion at $25^{\circ}C$ is :

asked Nov 29, 2018 by pady_1

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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 :

asked Nov 29, 2018 by pady_1

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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) :

asked Nov 29, 2018 by pady_1

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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 :

asked Nov 29, 2018 by pady_1

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