Recent questions and answers in 2009

Two points P and Q are maintained at the potentials of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

answered Jun 6, 2021 by abinashkumarnath6

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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.

answered Feb 11, 2020 by bookinggo1

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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 $\frac{n(n+1)(2n+1)}{6}$

answered Feb 6, 2020 by laxmikntpanda25

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The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where g = the acceleration due to gravity on the surace of the earth) in terms of R, the radius of the earth is

answered Oct 14, 2019 by meena.clay6

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A particle has an initial velocity $3 \hat{i} + 4 \hat{j}$ and an acceleration of $0.4 \hat{i} + 0.3 \hat{j}$. Its speed after 10 s is

answered Jul 25, 2019 by meena.clay6

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Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be

answered Dec 20, 2018 by ravichandranashwin234

1 answer

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

asked Nov 29, 2018 by pady_1

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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.

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

asked Nov 29, 2018 by pady_1

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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 $[-1, 1]$

asked Nov 29, 2018 by pady_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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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

asked Nov 29, 2018 by pady_1

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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 :

asked Nov 29, 2018 by pady_1

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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 :

asked Nov 29, 2018 by pady_1

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The two functional groups present in a typical carbohydrate are:

asked Nov 29, 2018 by pady_1

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The set representing the correct order of ionic radius is :

asked Nov 29, 2018 by pady_1

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The IUPAC name of neopentane is

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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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 ?

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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

asked Nov 29, 2018 by pady_1

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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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